Bis(O-ethyl dithio-carbonato-κS,S')bis-(pyridine-3-carbonitrile-κN)nickel(II).

Science.gov (United States)

Kapoor, Sanjay; Kour, Ramandeep; Sachar, Renu; Kant, Rajni; Gupta, Vivek K; Kapoor, Kamini

2012-01-01

The Ni(2+) ion in the title complex, [Ni(C(3)H(5)OS(2))(2)(C(6)H(4)N(2))(2)], is in a strongly distorted octa-hedral coordination environment formed by an N(2)S(4) donor set, with the Ni(2+) ion located on a centre of inversion. In the crystal, weak C-H⋯S and C-H⋯N inter-actions are observed.

Bis(O-ethyl dithio­carbonato-κ2 S,S′)bis­(pyridine-3-carbonitrile-κN 1)nickel(II)

Science.gov (United States)

Kapoor, Sanjay; Kour, Ramandeep; Sachar, Renu; Kant, Rajni; Gupta, Vivek K.; Kapoor, Kamini

2012-01-01

The Ni2+ ion in the title complex, [Ni(C3H5OS2)2(C6H4N2)2], is in a strongly distorted octa­hedral coordination environment formed by an N2S4 donor set, with the Ni2+ ion located on a centre of inversion. In the crystal, weak C—H⋯S and C—H⋯N inter­actions are observed. PMID:22259356

cis-Bis(O-methyl-dithio-carbonato-κ(2) S,S')bis-(tri-phenyl-phosphane-κP)ruthenium(II).

Science.gov (United States)

Valerio-Cárdenas, Cintya; Hernández-Ortega, Simón; Reyes-Martínez, Reyna; Morales-Morales, David

2013-01-01

In the title compound, [Ru(CH3OCS2)2(C18H15P)2], the Ru(II) atom is in a distorted octa-hedral coordination by two xanthate anions (CH3OCS2) and two tri-phenyl-phosphane (PPh3) ligands. Both bidentate xanthate ligands coordinate the Ru(II) atom with two slightly different Ru-S bond lengths but with virtually equal bite angles [71.57 (4) and 71.58 (3)°]. The packing of the complexes is assured by C-H⋯O and C-H⋯π inter-actions.

Trichlorido[(meth­yl{2-[meth­yl(2-pyridyl­meth­yl)amino]eth­yl}amino)acetonitrile]iron(III) methanol hemisolvate

Science.gov (United States)

Nielsen, Anne; McKenzie, Christine J.; Bond, Andrew D.

2009-01-01

The title compound, [FeCl3(C12H18N4)]·0.5CH3OH, contains an FeIII ion in a distorted octa­hedral coordination environment. The neutral N,N′,N′′-tridentate ligand adopts a fac coordination mode, and chloride ligands lie trans to each of the three coordinated N atoms. In the crystal, the complexes form columns extending parallel to the approximate local threefold axes of the FeN3Cl3 octa­hedra, and the columns are arranged so that the uncoordinated nitrile groups align in an anti­parallel manner and the pyridyl rings form offset face-to-face arrangements [inter­planar separations = 2.95 (1) and 3.11 (1) Å; centroid–centroid distances = 5.31 (1) and 4.92 (1) Å]. The methanol solvent mol­ecule is disordered about a twofold rotation axis. PMID:21578169

cis-Bis(O-methyl­dithio­carbonato-κ2 S,S′)bis­(tri­phenyl­phosphane-κP)ruthenium(II)

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Valerio-Cárdenas, Cintya; Hernández-Ortega, Simón; Reyes-Martínez, Reyna; Morales-Morales, David

2013-01-01

In the title compound, [Ru(CH3OCS2)2(C18H15P)2], the RuII atom is in a distorted octa­hedral coordination by two xanthate anions (CH3OCS2) and two tri­phenyl­phosphane (PPh3) ligands. Both bidentate xanthate ligands coordinate the RuII atom with two slightly different Ru—S bond lengths but with virtually equal bite angles [71.57 (4) and 71.58 (3)°]. The packing of the complexes is assured by C—H⋯O and C—H⋯π inter­actions. PMID:24046578

Pyridinium bis­(pyridine-κN)tetra­kis­(thio­cyanato-κN)ferrate(III)–pyrazine-2-carbo­nitrile–pyridine (1/4/1)

Science.gov (United States)

Shylin, Sergii I.; Gural’skiy, Il’ya A.; Haukka, Matti; Golenya, Irina A.

2013-01-01

In the title compound, (C5H6N)[Fe(NCS)4(C5H5N)2]·4C5H3N3·C5H5N, the FeIII ion is located on an inversion centre and is six-coordinated by four N atoms of the thio­cyanate ligands and two pyridine N atoms in a trans arrangement, forming a slightly distorted octa­hedral geometry. A half-occupied H atom attached to a pyridinium cation forms an N—H⋯N hydrogen bond with a centrosymmetrically-related pyridine unit. Four pyrazine-2-carbo­nitrile mol­ecules crystallize per complex anion. In the crystal, π–π stacking inter­actions are present [centroid–centroid distances = 3.6220 (9), 3.6930 (9), 3.5532 (9), 3.5803 (9) and 3.5458 (8) Å]. PMID:23723782

A second polymorph with composition Co3(PO4)2·H2O

Science.gov (United States)

Lee, Young Hoon; Clegg, Jack K.; Lindoy, Leonard F.; Lu, G. Q. Max; Park, Yu-Chul; Kim, Yang

2008-01-01

Single crystals of Co3(PO4)2·H2O, tricobalt(II) bis­[ortho­phosphate(V)] monohydrate, were obtained under hydro­thermal conditions. The compound is the second polymorph of this composition and is isotypic with its zinc analogue, Zn3(PO4)2·H2O. Three independent Co2+ cations are bridged by two independent orthophosphate anions. Two of the metal cations exhibit a distorted tetra­hedral coordination while the third exhibits a considerably distorted [5 + 1] octa­hedral coordination environment with one very long Co—O distance of 2.416 (3) Å. The former cations are bonded to four different phosphate anions, and the latter cation is bonded to four anions (one of which is bidentate) and one water mol­ecule, leading to a framework structure. Additional hydrogen bonds of the type O—H⋯O stabilize this arrangement. PMID:21200979

fac-Tris(pyridine-2-carboxyl­ato-κ2 N,O)cobalt(III)

Science.gov (United States)

Golenia, Irina A.; Boyko, Alexander N.; Kotova, Natalia V.; Haukka, Matti; Kalibabchuk, Valentina A.

2011-01-01

In the title compound, [Co(C6H4NO2)3], the CoIII ion lies on a threefold rotation axis and is in a distorted octa­hedral environment defined by three N and three O donor atoms from three fac-disposed pyridine-2-carboxyl­ate ligands. The ligands are coordinated in a chelate fashion, forming three five-membered rings. In the crystal, translationally related complex molecules are organized into columns along [001] via C—H⋯O hydrogen bonds. PMID:22219826

Sandwich-type mixed tetrapyrrole rare-earth triple-decker compounds. Effect of the coordination geometry on the single-molecule-magnet nature.

Science.gov (United States)

Kan, Jinglan; Wang, Hailong; Sun, Wei; Cao, Wei; Tao, Jun; Jiang, Jianzhuang

2013-08-05

Employment of the raise-by-one step method starting from M(TClPP)(acac) (acac = monoanion of acetylacetone) and [Pc(OPh)8]M'[Pc(OPh)8] led to the isolation and free modulation of the two rare-earth ions in the series of four mixed tetrapyrrole dysprosium sandwich complexes {(TClPP)M[Pc(OPh)8]M'[Pc(OPh)8]} [1-4; TClPP = dianion of meso-tetrakis(4-chlorophenyl)porphyrin; Pc(OPh)8 = dianion of 2,3,9,10,16,17,23,24-octa(phenoxyl)phthalocyanine; M-M' = Dy-Dy, Y-Dy, Dy-Y, and Y-Y]. Single-crystal X-ray diffraction analysis reveals different octacoordination geometries for the two metal ions in terms of the twist angle (defined as the rotation angle of one coordination square away from the eclipsed conformation with the other) between the two neighboring tetrapyrrole rings for the three dysprosium-containing isostructural triple-decker compounds, with the metal ion locating between an inner phthalocyanine ligand and an outer porphyrin ligand with a twist angle of 9.64-9.90° and the one between two phthalocyanine ligands of 25.12-25.30°. Systematic and comparative studies over the magnetic properties reveal magnetic-field-induced single-molecule magnet (SMM), SMM, and non-SMM nature for 1-3, respectively, indicating the dominant effect of the coordination geometry of the spin carrier, instead of the f-f interaction, on the magnetic properties. The present result will be helpful for the future design and synthesis of tetrapyrrole lanthanide SMMs with sandwich molecular structures.

Crystal structure of a looped-chain CoII coordination polymer: catena-poly[[bis-(nitrato-κO)cobalt(II)]bis-[μ-bis-(pyridin-3-ylmeth-yl)sulfane-κ2N:N'

Science.gov (United States)

Moon, Suk-Hee; Seo, Joobeom; Park, Ki-Min

2017-11-01

The asymmetric unit of the title compound, [Co(NO 3 ) 2 (C 12 H 12 N 2 S) 2 ] n , contains a bis-(pyridin-3-ylmeth-yl)sulfane ( L ) ligand, an NO 3 - anion and half a Co II cation, which lies on an inversion centre. The Co II cation is six-coordinated, being bound to four pyridine N atoms from four symmetry-related L ligands. The remaining coordination sites are occupied by two O atoms from two symmetry-related nitrate anions in a monodentate manner. Thus, the Co II centre adopts a distorted octa-hedral geometry. Two symmetry-related L ligands are connected by two symmetry-related Co II cations, forming a 20-membered cyclic dimer, in which the Co II atoms are separated by 10.2922 (7) Å. The cyclic dimers are connected to each other by sharing Co II atoms, giving rise to the formation of an infinite looped chain propagating along the [101] direction. Inter-molecular C-H⋯π (H⋯ring centroid = 2.89 Å) inter-actions between one pair of corresponding L ligands and C-H⋯O hydrogen bonds between the L ligands and the nitrate anions occur in the looped chain. In the crystal, adjacent looped chains are connected by inter-molecular π-π stacking inter-actions [centroid-to-centroid distance = 3.8859 (14) Å] and C-H⋯π hydrogen bonds (H⋯ring centroid = 2.65 Å), leading to the formation of layers parallel to (101). These layers are further connected through C-H⋯O hydrogen bonds between the layers, resulting in the formation of a three-dimensional supra-molecular architecture.

Lossless Geometry Compression Through Changing 3D Coordinates into 1D

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Yongkui Liu

2013-08-01

Full Text Available A method of lossless geometry compression on the coordinates of the vertexes for grid model is presented. First, the 3D coordinates are pre-processed to be transformed into a specific form. Then these 3D coordinates are changed into 1D data by making the three coordinates of a vertex represented by only a position number, which is made of a large integer. To minimize the integers, they are sorted and the differences between two adjacent vertexes are stored in a vertex table. In addition to the technique of geometry compression on coordinates, an improved method for storing the compressed topological data in a facet table is proposed to make the method more complete and efficient. The experimental results show that the proposed method has a better compression rate than the latest method of lossless geometry compression, the Isenburg-Lindstrom-Snoeyink method. The theoretical analysis and the experiment results also show that the important decompression time of the new method is short. Though the new method is explained in the case of a triangular grid, it can also be used in other forms of grid model.

μ-Peroxido-bis­[acetonitrile­bis­(ethyl­enediamine)­cobalt(III)] tetrakis(per­chlorate)

Science.gov (United States)

Regeta, Khrystyna O.; Odarich, Iryna; Pavlova, Svetlana V.; Kalibabchuk, Valentina A.; Haukka, Matti

2010-01-01

The title compound, [Co2(O2)(CH3CN)2(C2H8N2)4](ClO4)4, consists of centrosymmetric binuclear cations and perchlorate anions. Two CoIII atoms, which have a slightly distorted octa­hedral coordination, are connected through a peroxido bridge; the O—O distance is 1.476 (3) Å. Both acetonitrile ligands are situated in a trans position with respect to the O—O bridge. In the crystal, the complex cations are connected by N—H⋯O hydrogen bonds between ethyl­endiamine NH groups and O atoms from the perchlorate anions and peroxide O atoms. PMID:21589305

Crystal structure of tri­chlorido­(4'-ferrocenyl-2,2':6',2''-terpyridine-[kappa]3N,N',N'')iridium(III) aceto­nitrile disolvate

KAUST Repository

Davaasuren, Bambar

2015-02-25

In the title compound, [FeIr(C5H5)(C20H14N3)Cl3]·2CH3CN, the central IrIII atom is sixfold coordinated by three chloride ligands and three terpyridine N atoms in a slightly distorted octa­hedral fashion. The terpyridine ligand is functionalized at the 4\\'-position with a ferrocenyl group, the latter being in an eclipsed conformation. In the crystal, mol­ecules are stacked in rows parallel to [001], with the aceto­nitrile solvent mol­ecules situated between the rows. An extensive network of intra- and inter­molecular C-H...Cl inter­actions is present, stabilizing the three-dimensional structure.

Stabilizing embedology: Geometry-preserving delay-coordinate maps

Science.gov (United States)

Eftekhari, Armin; Yap, Han Lun; Wakin, Michael B.; Rozell, Christopher J.

2018-02-01

Delay-coordinate mapping is an effective and widely used technique for reconstructing and analyzing the dynamics of a nonlinear system based on time-series outputs. The efficacy of delay-coordinate mapping has long been supported by Takens' embedding theorem, which guarantees that delay-coordinate maps use the time-series output to provide a reconstruction of the hidden state space that is a one-to-one embedding of the system's attractor. While this topological guarantee ensures that distinct points in the reconstruction correspond to distinct points in the original state space, it does not characterize the quality of this embedding or illuminate how the specific parameters affect the reconstruction. In this paper, we extend Takens' result by establishing conditions under which delay-coordinate mapping is guaranteed to provide a stable embedding of a system's attractor. Beyond only preserving the attractor topology, a stable embedding preserves the attractor geometry by ensuring that distances between points in the state space are approximately preserved. In particular, we find that delay-coordinate mapping stably embeds an attractor of a dynamical system if the stable rank of the system is large enough to be proportional to the dimension of the attractor. The stable rank reflects the relation between the sampling interval and the number of delays in delay-coordinate mapping. Our theoretical findings give guidance to choosing system parameters, echoing the tradeoff between irrelevancy and redundancy that has been heuristically investigated in the literature. Our initial result is stated for attractors that are smooth submanifolds of Euclidean space, with extensions provided for the case of strange attractors.

(Carbonato-κO,O')bis-(di-2-pyridyl-amine-κN,N')cobalt(III) bromide.

Science.gov (United States)

Czapik, Agnieszka; Papadopoulos, Christos; Lalia-Kantouri, Maria; Gdaniec, Maria

2011-04-01

In the title compound, [Co(CO(3))(C(10)H(9)N(3))(2)]Br, a distorted octa-hedral coordination of the Co(III) atom is completed by four N atoms of the two chelating di-2-pyridyl-amine ligands and two O atoms of the chelating carbonate anion. The di-2-pyridyl-amine ligands are nonplanar and the dihedral angles between the 2-pyridyl groups are 29.11 (9) and 37.15 (12)°. The coordination cation, which has approximate C(2) symmetry, is connected to the bromide ion via an N-H⋯Br(-) hydrogen bond. The ionic pair thus formed is further assembled into a dimer via N-H⋯O inter-actions about an inversion centre. A set of weaker C-H⋯O and C-H⋯Br(-) inter-actions connect the dimers into a three-dimensional network.

Identification of different coordination geometries by XAFS in copper(II) complexes with trimesic acid

Science.gov (United States)

Gaur, A.; Klysubun, W.; Soni, Balram; Shrivastava, B. D.; Prasad, J.; Srivastava, K.

2016-10-01

X-ray absorption spectroscopy (XAS) is very useful in revealing the information about geometric and electronic structure of a transition-metal absorber and thus commonly used for determination of metal-ligand coordination. But XAFS analysis becomes difficult if differently coordinated metal centers are present in a system. In the present investigation, existence of distinct coordination geometries around metal centres have been studied by XAFS in a series of trimesic acid Cu(II) complexes. The complexes studied are: Cu3(tma)2(im)6 8H2O (1), Cu3(tma)2(mim)6 17H2O (2), Cu3(tma)2(tmen)3 8.5H2O (3), Cu3(tma) (pmd)3 6H2O (ClO4)3 (4) and Cu3(tma)2 3H2O (5). These complexes have not only Cu metal centres with different coordination but in complexes 1-3, there are multiple coordination geometries present around Cu centres. Using XANES spectra, different coordination geometries present in these complexes have been identified. The variation observed in the pre-edge features and edge features have been correlated with the distortion of the specific coordination environment around Cu centres in the complexes. XANES spectra have been calculated for the distinct metal centres present in the complexes by employing ab-initio calculations. These individual spectra have been used to resolve the spectral contribution of the Cu centres to the particular XANES features exhibited by the experimental spectra of the multinuclear complexes. Also, the variation in the 4p density of states have been calculated for the different Cu centres and then correlated with the features originated from corresponding coordination of Cu. Thus, these spectral features have been successfully utilized to detect the presence of the discrete metal centres in a system. The inferences about the coordination geometry have been supported by EXAFS analysis which has been used to determine the structural parameters for these complexes.

Observations on the Darboux coordinates for rigid special geometry

CERN Document Server

Ferrara, Sergio; Ferrara, Sergio; Macia, Oscar

2006-01-01

We exploit some relations which exist when (rigid) special geometry is formulated in real symplectic special coordinates $P^I=(p^\\Lambda,q_\\Lambda), I=1,...,2n$. The central role of the real $2n\\times 2n$ matrix $M(\\Re \\mathcal{F},\\Im \\mathcal{F})$, where $\\mathcal{F} = \\partial_\\Lambda\\partial_\\Sigma F$ and $F$ is the holomorphic prepotential, is elucidated in the real formalism. The property $M\\Omega M=\\Omega$ with $\\Omega$ being the invariant symplectic form is used to prove several identities in the Darboux formulation. In this setting the matrix $M$ coincides with the (negative of the) Hessian matrix $H(S)=\\frac{\\partial^2 S}{\\partial P^I\\partial P^J}$ of a certain hamiltonian real function $S(P)$, which also provides the metric of the special K\\"ahler manifold. When $S(P)=S(U+\\bar U)$ is regarded as a "K\\"ahler potential'' of a complex manifold with coordinates $U^I=\\frac12(P^I+iZ^I)$, then it provides a K\\"ahler metric of an hyperk\\"ahler manifold which describes the hypermultiplet geometry obtained by...

Potassium (2,2'-bipyridine-κN,N')bis-(carbonato-κO,O')cobaltate(III) dihydrate.

Science.gov (United States)

Wang, Jian-Fei; Lin, Jian-Li

2010-09-30

In the title compound, K[Co(CO(3))(2)(C(10)H(8)N(2))]·2H(2)O, the Co(III) atom is coordinated by two bipyridine N atoms and four O atoms from two bidentate chelating carbonate anions, and thus adopts a distorted octa-hedral N(2)O(4) environment. The [Co(bipy)(CO(3))(2)](-) (bipy is 2,2'-bipyridine) -units are stacked along [100] via π-π stacking inter-actions, with inter-planar distances between the bipyridine rings of 3.36 (4) and 3.44 (6) Å, forming chains. Classical O-H⋯O hydrogen-bonding inter-actions link the chains, forming channels along (100) in which the K(+) ions reside and leading to a three-dimensional supra-molecular architecture.

(Carbonato-κ2 O,O′)bis­(di-2-pyridyl­amine-κ2 N,N′)cobalt(III) bromide

Science.gov (United States)

Czapik, Agnieszka; Papadopoulos, Christos; Lalia-Kantouri, Maria; Gdaniec, Maria

2011-01-01

In the title compound, [Co(CO3)(C10H9N3)2]Br, a distorted octa­hedral coordination of the CoIII atom is completed by four N atoms of the two chelating di-2-pyridyl­amine ligands and two O atoms of the chelating carbonate anion. The di-2-pyridyl­amine ligands are nonplanar and the dihedral angles between the 2-pyridyl groups are 29.11 (9) and 37.15 (12)°. The coordination cation, which has approximate C 2 symmetry, is connected to the bromide ion via an N—H⋯Br− hydrogen bond. The ionic pair thus formed is further assembled into a dimer via N—H⋯O inter­actions about an inversion centre. A set of weaker C—H⋯O and C—H⋯Br− inter­actions connect the dimers into a three-dimensional network. PMID:21753946

Six-Coordinate Ln(III Complexes with Various Coordination Geometries Showing Distinct Magnetic Properties

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Mei Guo

2018-01-01

Full Text Available The syntheses, structural characterization, and magnetic properties of three lanthanide complexes with formulas [Ln(L13] (Ln = Dy (1Dy; Er (1Er; and [Dy(L22] (2Dy were reported. Complexes 1Dy and 1Er are isostructural with the metal ion in distorted trigonal-prismatic coordination geometry, but exhibit distinct magnetic properties due to the different shapes of electron density for DyIII (oblate and ErIII (prolate ions. Complex 1Dy shows obvious SMM behavior under a zero direct current (dc field with an effective energy barrier of 31.4 K, while complex 1Er only features SMM behavior under a 400 Oe external field with an effective energy barrier of 23.96 K. In stark contrast, complex 2Dy with the octahedral geometry only exhibits the frequency dependence of alternating current (ac susceptibility signals without χ″ peaks under a zero dc field.

Fabricating Bis(phthalocyaninato) Terbium SIM into Tetrakis(phthalocyaninato) Terbium SMM with Enhanced Performance through Sodium Coordination.

Science.gov (United States)

Chen, Yuxiang; Liu, Chao; Ma, Fang; Qi, Dongdong; Liu, Qingyun; Sun, Hao-Ling; Jiang, Jianzhuang

2018-04-23

The non-peripherally substituted 1,4,8,11,15,18,22,25-octa(butoxy)-phthalocyanine-involved unsymmetrical heteroleptic bis(phthalocyaninato) terbium double-decker, Tb(Pc){H[Pc(α-OC 4 H 9 ) 8 ]} (Pc=unsubstituted phthalocyanine) (1), was revealed to exhibit typical single ion magnet (SIM) behavior with effective energy barrier, 180 K (125 cm -1 ), and blocking temperature, 2 K, due to the severe deviation of the terbium coordination polyhedron from square-antiprismatic geometry. Fabrication of this double-decker compound into the novel tetrakis(phthalocyaninato) terbium pseudo-quadruple-decker Na 2 {Tb(Pc)[Pc(α-OC 4 H 9 ) 8 ]} 2 (2) single molecule magnet (SMM) not only optimizes the coordination polyhedron of terbium ion towards the square-antiprismatic geometry and intensifies the coordination field strength, but more importantly significantly enhances the molecular magnetic anisotropy in the unsymmetrical bis(phthalocyaninato) double-decker unit, along with the change of the counter cation from H + of 1 to Na + of 2, leading to an significantly enhanced magnetic behavior with spin-reversal energy barrier, 528 K (367 cm -1 ), and blocking temperature, 25 K. The present result is surely helpful towards developing novel tetrapyrrole lanthanide SMMs through rational design and self-assembly from bis(tetrapyrrole) lanthanide single ion magnet (SIM) building block. © 2018 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

Potassium (2,2′-bipyridine-κ2 N,N′)bis­(carbonato-κ2 O,O′)cobaltate(III) dihydrate

Science.gov (United States)

Wang, Jian-Fei; Lin, Jian-Li

2010-01-01

In the title compound, K[Co(CO3)2(C10H8N2)]·2H2O, the Co(III) atom is coordinated by two bipyridine N atoms and four O atoms from two bidentate chelating carbonate anions, and thus adopts a distorted octa­hedral N2O4 environment. The [Co(bipy)(CO3)2]− (bipy is 2,2′-bipyridine) ­units are stacked along [100] via π–π stacking inter­actions, with inter­planar distances between the bipyridine rings of 3.36 (4) and 3.44 (6) Å, forming chains. Classical O—H⋯O hydrogen-bonding inter­actions link the chains, forming channels along (100) in which the K+ ions reside and leading to a three-dimensional supra­molecular architecture. PMID:21587447

Poly[octa-μ-aqua-tetraaquabis(μ-5-sulfonatobenzene-1,3-dicarboxylatocobalt(IItetrasodium

Directory of Open Access Journals (Sweden)

Bing-Yu Zhang

2009-04-01

Full Text Available The title compound, [CoNa4(C8H3O7S2(H2O12]n, is a three-dimensional coordination polymer bridged by sulfoisophthalate trianions and water molecules. The CoII atom, located on an inversion centre, is coordinated by two carboxylate groups of the sulfoisophthalate trianions and by four water molecules in a distorted CoO6 octahedral geometry. Two independent NaI atoms also have a distorted octahedral coordination geometry formed by water, carboxylate O and sulfonate O atoms. An extensive O—H...O and C—H...O hydrogen-bonding network is present in the crystal structure, as well as weak π-π stacking [centroid–centroid distance = 3.9553 (11 Å].

The flux-coordinate independent approach applied to X-point geometries

International Nuclear Information System (INIS)

Hariri, F.; Hill, P.; Ottaviani, M.; Sarazin, Y.

2014-01-01

A Flux-Coordinate Independent (FCI) approach for anisotropic systems, not based on magnetic flux coordinates, has been introduced in Hariri and Ottaviani [Comput. Phys. Commun. 184, 2419 (2013)]. In this paper, we show that the approach can tackle magnetic configurations including X-points. Using the code FENICIA, an equilibrium with a magnetic island has been used to show the robustness of the FCI approach to cases in which a magnetic separatrix is present in the system, either by design or as a consequence of instabilities. Numerical results are in good agreement with the analytic solutions of the sound-wave propagation problem. Conservation properties are verified. Finally, the critical gain of the FCI approach in situations including the magnetic separatrix with an X-point is demonstrated by a fast convergence of the code with the numerical resolution in the direction of symmetry. The results highlighted in this paper show that the FCI approach can efficiently deal with X-point geometries

(Carbonato-κ(2)O,O')bis-(5,5'-dimethyl-2,2'-bipyridyl-κ(2)N,N')cobalt(III) bromide trihydrate.

Science.gov (United States)

Arun Kumar, Kannan; Meera, Parthsarathi; Amutha Selvi, Madhavan; Dayalan, Arunachalam

2012-04-01

In the title complex, [Co(CO(3))(C(12)H(12)N(2))(2)]Br·3H(2)O, the Co(III) cation has a distorted octa-hedral coordination environment. It is chelated by four N atoms of two different 5,5'-dimethyl-2,2'-bipyridyl (dmbpy) ligands in axial and equatorial positions, and by two O atoms of a carbonate anion completing the equatorial positions. Although the water mol-ecules are disordered and their H atoms were not located, there are typical O⋯O distances between 2.8 and 3.0 Å, indicating O-H⋯O hydrogen bonding. The crystal packing is consolidated by C-H⋯O and C-H⋯Br hydrogen bonds, as well as π-π stacking inter-actions between adjacent pyridine rings of the dmbpy ligands, with centroid-centroid distances of 3.694 (3) and 3.7053 (3) Å.

Relationship between mathematical abstraction in learning parallel coordinates concept and performance in learning analytic geometry of pre-service mathematics teachers: an investigation

Science.gov (United States)

Nurhasanah, F.; Kusumah, Y. S.; Sabandar, J.; Suryadi, D.

2018-05-01

As one of the non-conventional mathematics concepts, Parallel Coordinates is potential to be learned by pre-service mathematics teachers in order to give them experiences in constructing richer schemes and doing abstraction process. Unfortunately, the study related to this issue is still limited. This study wants to answer a research question “to what extent the abstraction process of pre-service mathematics teachers in learning concept of Parallel Coordinates could indicate their performance in learning Analytic Geometry”. This is a case study that part of a larger study in examining mathematical abstraction of pre-service mathematics teachers in learning non-conventional mathematics concept. Descriptive statistics method is used in this study to analyze the scores from three different tests: Cartesian Coordinate, Parallel Coordinates, and Analytic Geometry. The participants in this study consist of 45 pre-service mathematics teachers. The result shows that there is a linear association between the score on Cartesian Coordinate and Parallel Coordinates. There also found that the higher levels of the abstraction process in learning Parallel Coordinates are linearly associated with higher student achievement in Analytic Geometry. The result of this study shows that the concept of Parallel Coordinates has a significant role for pre-service mathematics teachers in learning Analytic Geometry.

XAFS study of copper(II) complexes with square planar and square pyramidal coordination geometries

Science.gov (United States)

Gaur, A.; Klysubun, W.; Nitin Nair, N.; Shrivastava, B. D.; Prasad, J.; Srivastava, K.

2016-08-01

X-ray absorption fine structure of six Cu(II) complexes, Cu2(Clna)4 2H2O (1), Cu2(ac)4 2H2O (2), Cu2(phac)4 (pyz) (3), Cu2(bpy)2(na)2 H2O (ClO4) (4), Cu2(teen)4(OH)2(ClO4)2 (5) and Cu2(tmen)4(OH)2(ClO4)2 (6) (where ac, phac, pyz, bpy, na, teen, tmen = acetate, phenyl acetate, pyrazole, bipyridine, nicotinic acid, tetraethyethylenediamine, tetramethylethylenediamine, respectively), which were supposed to have square pyramidal and square planar coordination geometries have been investigated. The differences observed in the X-ray absorption near edge structure (XANES) features of the standard compounds having four, five and six coordination geometry points towards presence of square planar and square pyramidal geometry around Cu centre in the studied complexes. The presence of intense pre-edge feature in the spectra of four complexes, 1-4, indicates square pyramidal coordination. Another important XANES feature, present in complexes 5 and 6, is prominent shoulder in the rising part of edge whose intensity decreases in the presence of axial ligands and thus indicates four coordination in these complexes. Ab initio calculations were carried out for square planar and square pyramidal Cu centres to observe the variation of 4p density of states in the presence and absence of axial ligands. To determine the number and distance of scattering atoms around Cu centre in the complexes, EXAFS analysis has been done using the paths obtained from Cu(II) oxide model and an axial Cu-O path from model of a square pyramidal complex. The results obtained from EXAFS analysis have been reported which confirmed the inference drawn from XANES features. Thus, it has been shown that these paths from model of a standard compound can be used to determine the structural parameters for complexes having unknown structure.

Poly[bis­[μ4-N-(2-hydroxy­imino­propion­yl)-N′-(2-oxidoimino­propion­yl)propane-1,3-diaminato]dimethano­lcalciumdicopper(II)

Science.gov (United States)

Kalibabchuk, Valentina A.; Usenko, Natalia I.; Golenya, Irina A.; Iskenderov, Turganbay S.; Haukka, Matti

2009-01-01

In the title compound, [CaCu2(C9H13N4O4)2(CH3OH)2]n, the CaII atom lies on an inversion center and is situated in a moderately distorted octa­hedral environment. The CuII atom is in a distorted square-pyramidal geometry, defined by four N atoms belonging to the amide and oxime groups of the triply deprotonated residue of N,N′-bis­(2-hydroxy­imino­propano­yl)propane-1,3-diamine (H4pap) and one oxime O atom from a neighboring Hpap ligand at the apical site, forming a dimeric [Cu2(Hpap)2]2− unit. Each dimeric unit connects four Ca atoms and each Ca atom links four [Cu2(Hpap)2]2− units through Ca—O(amide) bonds, leading to a three-dimensional framework. The crystal structure involves intra- and inter­molecular O—H⋯O hydrogen bonds. PMID:21577475

(Carbonato-κ2 O,O′)bis­(5,5′-dimethyl-2,2′-bipyridyl-κ2 N,N′)cobalt(III) bromide trihydrate

Science.gov (United States)

Arun Kumar, Kannan; Meera, Parthsarathi; Amutha Selvi, Madhavan; Dayalan, Arunachalam

2012-01-01

In the title complex, [Co(CO3)(C12H12N2)2]Br·3H2O, the CoIII cation has a distorted octa­hedral coordination environment. It is chelated by four N atoms of two different 5,5′-dimethyl-2,2′-bipyridyl (dmbpy) ligands in axial and equatorial positions, and by two O atoms of a carbonate anion completing the equatorial positions. Although the water mol­ecules are disordered and their H atoms were not located, there are typical O⋯O distances between 2.8 and 3.0 Å, indicating O—H⋯O hydrogen bonding. The crystal packing is consolidated by C—H⋯O and C—H⋯Br hydrogen bonds, as well as π–π stacking inter­actions between adjacent pyridine rings of the dmbpy ligands, with centroid–centroid distances of 3.694 (3) and 3.7053 (3) Å. PMID:22589773

Implementations of three OCT angiography (OCTA) methods with 1.7 MHz A-scan rate OCT system on imaging of human retinal and choroidal vasculature

Science.gov (United States)

Poddar, Raju; Werner, John S.

2018-06-01

We present noninvasive depth-resolved imaging of human retinal and choroidal microcirculation with an ultrahigh-speed (1.7 MHz A-scans/s), Fourier-domain mode locked (FDML) swept-source optical coherence tomography (SS-OCT) system having a central wavelength of 1065 nm. Three OCT angiography (OCTA) motion based contrast methods, namely phase variance (PV), amplitude decorrelation (AD) and Joint Spectral and Time domain OCT (STdOCT) were implemented. The OCTA imaging was performed with a field of view of 16° (5 mm × 5 mm) and 30° (9 mm × 9 mm), on the retina. A qualitative comparison of images obtained with all three OCTA methods is demonstrated using the same eye of a healthy volunteer. Different parameters, namely acquisition time, scanning area, and scanning density, are discussed. The phase-variance OCTA (PV-OCTA) method produced relatively better results than the other two. Different features regarding the retinal and choroidal vessels are described in different subjects.

Dielectric and conducting behaviour of polycrystalline holmium octa-molybdate

International Nuclear Information System (INIS)

Want, Basharat; Zahoor Ahmad, Bhat; Hamid Bhat, Bilal

2014-01-01

Polycrystalline holmium octa-molybdate spherulites have been obtained by using gel diffusion technique and characterized by different physio-chemical techniques. The surfaces of these spherulites are composed of nano-rod with an average diameter of about 80 nm. At room temperature the initial crystal structure is triclinic, space group P1. Thermal studies suggested a phase transition occurring in holmium octa-molybdate crystals at about 793 K. The electrical properties of the system have been studied as a function of frequency and temperature in the ranges of 20 Hz–3 MHz and 290–570 K, respectively. A giant dielectric constant and two loss peaks have been observed in the permittivity formalism. The conducting behaviour of the material is also discussed. The conductivity was found to be 1572 μ Ω −1 m −1 at room temperature and 3 MHz frequency. The conductivity of the polycrystalline material was attributed to the fact that it arises due to the migration of defects on the oxygen sub-lattice. Impedance studies were also performed in the frequency domain to infer the bulk and grain boundary contributions to the overall electric response of the material. The electrical responses have been attributed to the grain, grain-boundary, and interfacial effects. (paper)

A Lagrangian cylindrical coordinate system for characterizing dynamic surface geometry of tubular anatomic structures.

Science.gov (United States)

Lundh, Torbjörn; Suh, Ga-Young; DiGiacomo, Phillip; Cheng, Christopher

2018-03-03

Vascular morphology characterization is useful for disease diagnosis, risk stratification, treatment planning, and prediction of treatment durability. To quantify the dynamic surface geometry of tubular-shaped anatomic structures, we propose a simple, rigorous Lagrangian cylindrical coordinate system to monitor well-defined surface points. Specifically, the proposed system enables quantification of surface curvature and cross-sectional eccentricity. Using idealized software phantom examples, we validate the method's ability to accurately quantify longitudinal and circumferential surface curvature, as well as eccentricity and orientation of eccentricity. We then apply the method to several medical imaging data sets of human vascular structures to exemplify the utility of this coordinate system for analyzing morphology and dynamic geometric changes in blood vessels throughout the body. Graphical abstract Pointwise longitudinal curvature of a thoracic aortic endograft surface for systole and diastole, with their absolute difference.

Synthesis and characterization of a new composite based on copper (II) and octa (aminopropil)silsesquioxane; Sintese e caracterizacao de novos compositos a base de cobre (II) e octa(aminopropil)silsesquioxano

Energy Technology Data Exchange (ETDEWEB)

Magossi, M.S. de; Carmo, D.R. do, E-mail: marymagossi@gmail.com [Universidade Estadual Paulista Julio de Mesquita Filho (UNESP), Ilha Solteira, SP (Brazil). Faculdade de Engenharia

2014-07-01

In this work, a new compound based silsesquioxane and nitroprusside of copper was prepared starting from octa (aminopropyl)silsesquioxane following a new route of synthesis. The composite prepared as described ACCuN was preliminarily characterized by spectroscopic techniques, such as Infrared Spectroscopy in the Region of the Fourier transform (FTIR), Energy Dispersive X-ray (EDX), Scanning Electron Microscopy (SEM) and cyclic voltammetry (VC). The FTIR spectra showed absorption bands at 1106 cm{sup -1} due to stretching Si-O-Si{sub (νSi-O-Si)} characteristic of the structure of octa(aminopropylsilsesquioxane and absorption bands at 2063 cm{sup -1} ascribed to the stretching NO{sub (νN-O}) and 2192 cm{sup -1} attributed to the stretching C≡N{sub (ν≡}N{sub )}. SEM and EDX observed cluster of cubic particles with an average size of approximately 241 nm, containing Si, O, N, Cu and Fe. Cyclic voltammogram of the material (ACCuN) showed a redox couple with average potential Eθ '= 0.73 V. (author)

(O-Methyl di-thio-carbonato-κS)tri-phenyl-tin(IV).

Science.gov (United States)

Javed, Fatima; Ali, Saqib; Shah, Wajid; Tahir, M Nawaz; Ullah, Hameed

2013-06-01

In the title compound, [Sn(C6H5)3(C2H3OS2)], the Sn(IV) atom adopts a distorted SnC3S tetra-hedral coordination geometry. A short Sn⋯O contact [2.988 (4) Å] is also present. The phenyl rings are each disordered over two sets of sites with an occupancy ratio of 0.550 (8):0.450 (8). The crystal studied was found to be a racemic twin with a twin component ratio of 0.57 (18):0.43 (18).

Comparison of Nickel XANES Spectra and Elemental Maps from a Ureilite, a LL3.8 Ordinary Chondrite, Two Carbonaceous Chondrites and Two Large Cluster IDPs

Science.gov (United States)

Wirick, S.; Flynn, G. J.; Sutton, S.; Zolensky, M. E.

2014-01-01

Nickel in the extraterrestrial world is commonly found in both Fe-Ni sulfide and Fe-Ni met-al forms [1] and in the pure metal state in the interior of iron meteorites where it is not easily oxidized. Ni is also found in olivine, pyroxene and glasses and in some melts the partitioning of Ni between the olivines and glass is controlled by the amount of S in the melt [2]. Its most common valence state is Ni(2+) but Ni also occurs as Ni(0), Ni(+), and Ni(3+) and rarely as Ni(2-), Ni(1-) and Ni(4+) [3]. It's valence state in olivines is Ni(2+) in octa-hedral coordination on the M1 site and rarely on the M2 site.[4]. The chemical sensitivity of X-ray absorp-tion near-edge structure (XANES) spectroscopy is well established and can be used to determine not only va-lence states but also coordination sites [5]. We report here Ni XANES spectroscopy and elemental maps collected from 2 carbonaceous chondrites, 2 large clus-ter IDPs, 1 ureilite and 1 LL3 orginary chondrite.Using XANES it may be possible to find a common trait in the large cluster IDPs that will also be found in mete-orite samples.

A Note on the Dipole Coordinates

OpenAIRE

Kageyama, Akira; Sugiyama, Tooru; Watanabe, Kunihiko; Sato, Tetsuya

2004-01-01

A couple of orthogonal coordinates for dipole geometry are proposed for numerical simulations of plasma geophysics in the Earth's dipole magnetic field. These coordinates have proper metric profiles along field lines in contrast to the standard dipole coordinate system that is commonly used in analytical studies for dipole geometry.

A co-ordinate system for reactor physics calculations in hexagonal geometry

International Nuclear Information System (INIS)

Burte, D.P.

1990-01-01

A method for generating all the geometric information concerning typical reactor physics calculations for a basically hexagonal reactor core or its sector involving any of the possible symmetries is presented. The geometrically allowed symmetries for regular hexagons are discussed. The approach is based on the choice of a suitable co-ordinate system, viz. one using three coplanar (including one redundant) axes, each at 120 0 with its cyclically preceding one. A code named KEKULE' is developed for a 2-D, finite difference, one-group diffusion analysis of a hexagonal core using the approach. It can cater to a full hexagonal core as well as to any symmetric sectorial part of it. The main feature of the code is that the input concerning geometry is a bare minimum. It is hoped that the approach presented will be useful even for the calculations for hexagonal fuel assemblies. (author)

Amiloride-enhanced gene transfection of octa-arginine functionalized calcium phosphate nanoparticles.

Directory of Open Access Journals (Sweden)

Juan Ramón Vanegas Sáenz

Full Text Available Nanoparticles represent promising gene delivery systems in biomedicine to facilitate prolonged gene expression with low toxicity compared to viral vectors. Specifically, nanoparticles of calcium phosphate (nCaP, the main inorganic component of human bone, exhibit high biocompatibility and good biodegradability and have been reported to have high affinity for protein or DNA, having thus been used as gene transfer vectors. On the other hand, Octa-arginine (R8, which has a high permeability to cell membrane, has been reported to improve intracellular delivery systems. Here, we present an optimized method for nCaP-mediated gene delivery using an octa-arginine (R8-functionalized nCaP vector containing a marker or functional gene construct. nCaP particle size was between 220-580 nm in diameter and all R8-functionalized nCaPs carried a positive charge. R8 concentration significantly improved nCaP transfection efficiency with high cell compatibility in human mesenchymal stem cells (hMSC and human osteoblasts (hOB in particular, suggesting nCaPs as a good option for non-viral vector gene delivery. Furthermore, pre-treatment with different endocytosis inhibitors identified that the endocytic pathway differed among cell lines and functionalized nanoparticles, with amiloride increasing transfection efficiency of R8-functionalized nCaPs in hMSC and hOB.

Low temperature X-ray structure analyses combined with NBO studies of a new heteroleptic octa-coordinated Holmium(III) complex with N,N,N-tridentate hydrazono-phthalazine-type ligand

Science.gov (United States)

Soliman, Saied M.; El-Faham, Ayman

2018-04-01

The new heteroleptic [HoL(H2O)5]Br3 complex, L is hydrazono-phthalazine ligand, is synthesized and its molecular structure aspects were analyzed using single crystal X-ray structure (SCXRD), Hirshfeld (HF) analysis, quantum theory of atoms in molecules (QTAIM) and natural bond orbital (NBO) method. The SCXRD showed that the Ho is octa-coordinated with one N,N,N-tridentate ligand L and five water molecules. The HF analysis is used to analyze the molecular packing in the [HoL(H2O)5]Br3crystal structure. The complex cations are connected via strong Osbnd H⋯Br and Nsbnd H⋯Br H-bonding interactions which have greater importance than the Csbnd H⋯Br contacts. Also, all the Hosbnd N and Hosbnd O bonds have the characteristics of closed shell interactions using QTAIM. The natural orbitals included in these interactions were analyzed using NBO method. The alpha LP*(8)Ho and beta LP*(4)Ho which have mainly s-orbital characters are the most important anti-bonding natural orbitals included in all Ho-N and Hosbnd O bonds. The rest of the Ho anti-bonding orbitals which have either p or d-orbital characters shared partially in the Ho-ligands interactions. Natural charges analysis revealed the presence of significant amount of electron density (0.9225-0.9300 e) transferred from the ligands to Ho (2.0700-2.0775 e). Spherical spin density with ∼4.0 e is predicted over the Ho atom.

Spherical spacelike geometries in static spherically symmetric spacetimes: Generalized Painlevè–Gullstrand coordinates, foliation, and embedding

Energy Technology Data Exchange (ETDEWEB)

Akbar, M.M., E-mail: akbar@utdallas.edu

2017-06-10

It is well known that static spherically symmetric spacetimes can admit foliations by flat spacelike hypersurfaces, which are best described in terms of the Painlevè–Gullstrand coordinates. The uniqueness and existence of such foliations were addressed earlier. In this paper, we prove, purely geometrically, that any possible foliation of a static spherically symmetric spacetime by an arbitrary codimension-one spherical spacelike geometry, up to time translation and rotation, is unique, and we find the algebraic condition under which it exists. This leads us to what can be considered as the most natural generalization of the Painlevè–Gullstrand coordinate system for static spherically symmetric metrics, which, in turn, makes it easy to derive generic conclusions on foliation and to study specific cases as well as to easily reproduce previously obtained generalizations as special cases. In particular, we note that the existence of foliation by flat hypersurfaces guarantees the existence of foliation by hypersurfaces whose Ricci curvature tensor is everywhere non-positive (constant negative curvature is a special case). The study of uniqueness and the existence concurrently solves the question of embeddability of a spherical spacelike geometry in one-dimensional higher static spherically symmetric spacetimes, and this produces known and new results geometrically, without having to go through the momentum and Hamiltonian constraints.

μ-Hexa-thio-metadiphosphato-bis-[(1,4,7,10,13,16-hexa-oxa-cyclo-octa-decane-κ(6) O)rubidium] aceto-nitrile disolvate.

Science.gov (United States)

Gjikaj, Mimoza; Pook, Niels-Patrick; Qarri, Flora

2013-12-01

The asymmetric unit of the title compound, [Rb2(P2S6)(C12H24O6)2]·2CH3CN, contains one half of an [Rb(18-crown-6)2]2[P2S6] unit and one aceto-nitrile solvent mol-ecule. The [Rb(18-crown-6)]2[P2S6] unit is completed by inversion symmetry. Its Rb(+) ion is situated near the centre of the macrocyclic cavity, but is displaced by 0.8972 (1) Å from the O atoms of the crown in the direction of the [P2S6](2-) moiety. The overall coordination number of the cation is eight, defined by the six crown ether O atoms and by two terminal S atoms of the [P2S6](2-) anion. The hexa-thio-metadiphosphate anion is built up from two tetra-hedral PS4 units joined together by a common edge. The crystal structure is characterized by alternating layers of [Rb(18-crown-6)]2[P2S6] and aceto-nitrile solvent mol-ecules stacked along [010].

Synthesis and characterization of a new composite based on copper (II) and octa (aminopropil)silsesquioxane

International Nuclear Information System (INIS)

Magossi, M.S. de; Carmo, D.R. do

2014-01-01

In this work, a new compound based silsesquioxane and nitroprusside of copper was prepared starting from octa (aminopropyl)silsesquioxane following a new route of synthesis. The composite prepared as described ACCuN was preliminarily characterized by spectroscopic techniques, such as Infrared Spectroscopy in the Region of the Fourier transform (FTIR), Energy Dispersive X-ray (EDX), Scanning Electron Microscopy (SEM) and cyclic voltammetry (VC). The FTIR spectra showed absorption bands at 1106 cm"-"1 due to stretching Si-O-Si_(_ν_S_i_-_O_-_S_i_) characteristic of the structure of octa(aminopropylsilsesquioxane and absorption bands at 2063 cm"-"1 ascribed to the stretching NO_(_ν_N_-_O) and 2192 cm"-"1 attributed to the stretching C≡N_(_ν_≡N_). SEM and EDX observed cluster of cubic particles with an average size of approximately 241 nm, containing Si, O, N, Cu and Fe. Cyclic voltammogram of the material (ACCuN) showed a redox couple with average potential Eθ '= 0.73 V. (author)

[1,2-Bis(diisopropyl-phosphan-yl)ethane-κ(2) P,P'](carbonato-κ(2) O,O')nickel(II).

Science.gov (United States)

Morales-Becerril, Illan; Flores-Alamo, Marcos; Garcia, Juventino J

2013-04-01

In the crystal of the title compound, [Ni(CO3)(C14H32P2)], the metal center in each of three independent mol-ecules shows slight tetra-hedral distortion from ideal square-planar coordination geometry, with angles between the normals to the planes defined by the cis-P-Ni-P and cis-O-Ni-O fragments of 3.92 (17), 0.70 (16) and 2.17 (14)° in the three mol-ecules. In the crystal, there are inter-molecular C-H⋯O hydrogen bonds that show a laminar growth in the ab plane.

(O-Methyl di­thio­carbonato-κS)tri­phenyl­tin(IV)

Science.gov (United States)

Javed, Fatima; Ali, Saqib; Shah, Wajid; Tahir, M. Nawaz; Ullah, Hameed

2013-01-01

In the title compound, [Sn(C6H5)3(C2H3OS2)], the SnIV atom adopts a distorted SnC3S tetra­hedral coordination geometry. A short Sn⋯O contact [2.988 (4) Å] is also present. The phenyl rings are each disordered over two sets of sites with an occupancy ratio of 0.550 (8):0.450 (8). The crystal studied was found to be a racemic twin with a twin component ratio of 0.57 (18):0.43 (18). PMID:23794982

[4,6-Dimethyl­pyrimidine-2(1H)-thione-κS]iodidobis(triphenyl­phosphane-κP)copper(I)

Science.gov (United States)

Pakawatchai, Chaveng; Wattanakanjana, Yupa; Choto, Patcharanan; Nimthong, Ruthairat

2012-01-01

In the mononuclear title complex, [CuI(C6H8N2S)(C18H15P)2], the CuI ion is in a slightly distorted tetra­hedral coordination geometry formed by two P atoms from two triphenyl­phosphane ligands, one S atom from a 4,6-dimethyl­pyrimidine-2(1H)-thione ligand and one iodide ion. There is an intra­molecular N—H⋯I hydrogen bond. In the crystal, π–π stacking inter­actions [centroid–centroid distance = 3.594 (1) Å] are observed. PMID:22719327

Synergistic enhancement of supercapacitance upon integration of nickel (II) octa[(3,5-biscarboxylate)-phenoxy] phthalocyanine with SWCNT-phenylamine

CSIR Research Space (South Africa)

Agboola, BO

2010-06-01

Full Text Available Supercapacitive behaviour of a novel functional material, nickel (II) octa [(3,5-biscarboxylate)-phenoxy] phthalocyanine (NiOBCPPc) upon covalent integration with phenylamine functionalized single-walled carbon nanotubes (SWCNT...

Supervanadophile: Complexation, preconcentration and transport studies of vanadium by octa functionalized calix [4] resorcinarene - hydroxamic acid

International Nuclear Information System (INIS)

Jain, V. K.; Pillai, S. G.; Gupte, H. S.

2008-01-01

A new octa functionalized calix[4] resorcinarene bearing eight hydroxamic acid groups has been synthesized and its analytical properties have been investigated. To elucidate the structure of the compound, elemental analysis, fourier transform infrared and 1 H NMR spectral data have been used. The compound showed high affinity and selectivity for vanadium(V) in presence of large quantities of associated metal ions. The complexation of vanadium(V) with octa functionalized calix[4] resorcinarene bearing eight hydroxamic acid has a 4:1 metal: ligand stoichiometry as evaluated by Job's plot. A spectrophotometric method is proposed for the extractive determination of vanadium(V) in an acidic medium in the presence of diversified matrix, and verified by inductively coupled plasma-atomic emission spectrometry. Under the optimum condition of acidity, solvent, interfering ions and octa functionalized calix[4] resorcinarene bearing eight hydroxamic acid concentration, the molar absorptivity of the complex is 5630 1 mol -1 cm -1 at 495 nm. The system obeys Beer's law over the range 0.125-8.75 μg ml -1 of vanadium(V) with Sandell sensitivity 0.009 μg cm -2 . The preconcentration factor and overall stability constant evaluated at 25 d eg C were 142 and 14.18, respectively. The complexation is characterized by favorable enthalpy and entropy changes. Liquid membrane transport studies of vanadium(V) were carried out from source to the receiving phase under controlled conditions and a mechanism for transport is suggested. To check the validity of the proposed method, vanadium is determined in environmental, biological samples and some standard reference materials from NIST and BCS

Analytic geometry

CERN Document Server

Burdette, A C

1971-01-01

Analytic Geometry covers several fundamental aspects of analytic geometry needed for advanced subjects, including calculus.This book is composed of 12 chapters that review the principles, concepts, and analytic proofs of geometric theorems, families of lines, the normal equation of the line, and related matters. Other chapters highlight the application of graphing, foci, directrices, eccentricity, and conic-related topics. The remaining chapters deal with the concept polar and rectangular coordinates, surfaces and curves, and planes.This book will prove useful to undergraduate trigonometric st

Vector geometry

CERN Document Server

Robinson, Gilbert de B

2011-01-01

This brief undergraduate-level text by a prominent Cambridge-educated mathematician explores the relationship between algebra and geometry. An elementary course in plane geometry is the sole requirement for Gilbert de B. Robinson's text, which is the result of several years of teaching and learning the most effective methods from discussions with students. Topics include lines and planes, determinants and linear equations, matrices, groups and linear transformations, and vectors and vector spaces. Additional subjects range from conics and quadrics to homogeneous coordinates and projective geom

Pseudosymmetric fac-di-aqua-trichlorido[(di-methyl-phosphor-yl)methanaminium-κO]manganese(II).

Science.gov (United States)

Reiss, Guido J

2013-05-01

In the title compound, [Mn(C3H11NOP)Cl3(H2O)2], the Mn(II) metal center has a distorted o-cta-hedral geometry, coordinated by the three chloride ligands showing a facial arrangement. Two water mol-ecules and the O-coordinated dpmaH cation [dpmaH = (di-methyl-phosphor-yl)methanaminium] complete the coordination sphere. Each complex mol-ecule is connected to its neighbours by O-H⋯Cl and N-H⋯Cl hydrogen bonds. Two of the chloride ligands and the two water ligands form a hydrogen-bonded polymeric sheet in the ab plane. Furthermore, these planes are connected to adjacent planes by hydrogen bonds from the aminium function of cationic dpmaH ligand. A pseudo-mirror plane perpendicular to the b axis in the chiral space group P21 is observed together with inversion twinning [ratio = 0.864 (5):0.136 (5)].

[1,2-Bis(diisopropyl­phosphan­yl)ethane-κ2 P,P′](carbonato-κ2 O,O′)nickel(II)

Science.gov (United States)

Morales-Becerril, Illan; Flores-Alamo, Marcos; Garcia, Juventino J.

2013-01-01

In the crystal of the title compound, [Ni(CO3)(C14H32P2)], the metal center in each of three independent mol­ecules shows slight tetra­hedral distortion from ideal square-planar coordination geometry, with angles between the normals to the planes defined by the cis-P—Ni—P and cis-O—Ni—O fragments of 3.92 (17), 0.70 (16) and 2.17 (14)° in the three mol­ecules. In the crystal, there are inter­molecular C—H⋯O hydrogen bonds that show a laminar growth in the ab plane. PMID:23633999

Estudio teórico de la distribución catiónica en la capa octaédrica de silicatos laminares

Science.gov (United States)

Hernández-Laguna, A.

Los silicatos laminares son unos minerales de gran extensión en la corteza de nuestro y otros planetas, y se ha detectado su presencia en masas de partículas de polvo interplanatario. Están formados por láminas estructuradas en una capa tetraedros de sílice y una de octaédros de oxihidroxido de aluminio. Según el número de capas y la disposición aparecen distintos minerales. Además, también pueden aparecer distintos minerales como consecuencia de la substitución isomórfica de cationes en la capas, en particular, Al(III) por Si en la capa tetraédrica y Fe(III) y/o Mg(II) por Al(III) en la octaédrica. Cuando el catión substituyente presenta un estado de oxidación más bajo que al que substituye genera carga negativa que tiene que neutralizarse con cationes que se disponen en el espacio interlaminar. En este trabajo vamos a estudiar, mediante distintos métodos computacionales, las distribuciones de dichos cationes de substitución en la capa octaédrica de silicatos laminares 2:1 (dos capas tetraédricas y en medio una octaédrica), en particular, en los minerales esmectitas e ilitas. En primer lugar, estudiaremos la distribución de dichos cationes en la capa octaédrica en un modelo de gas reticular por el método de Monte Carlo, minimizando el número de pares de cationes Al, Fe y Mg de nuestro modelo con respecto a los procedentes de resultados espectroscópicos de muestras de minerales. Posteriormente, y mediante un modelo de potenciales empíricos, estudiamos la energética de las distribuciones binarias en dichos minerales, generando unos potenciales de interacción intercambio a dos y tres cationes (extrapolables a cualquier filosilicato) que son la base para una investigación Monte Carlo-"simulated-annealing" en la que se encuentran las transiciones de fase y las estructuras ordenadas, dependiendo dichas estructuras y la temperatura de cambio de fase de la de la naturaleza y concentración de los cationes de substitución. También se han

Developments in special geometry

International Nuclear Information System (INIS)

Mohaupt, Thomas; Vaughan, Owen

2012-01-01

We review the special geometry of N = 2 supersymmetric vector and hypermultiplets with emphasis on recent developments and applications. A new formulation of the local c-map based on the Hesse potential and special real coordinates is presented. Other recent developments include the Euclidean version of special geometry, and generalizations of special geometry to non-supersymmetric theories. As applications we discuss the proof that the local r-map and c-map preserve geodesic completeness, and the construction of four- and five-dimensional static solutions through dimensional reduction over time. The shared features of the real, complex and quaternionic version of special geometry are stressed throughout.

The Comparison of Regional RNFL and Fundus Vasculature by OCTA in Chinese Myopia Population.

Science.gov (United States)

Li, Yuanjun; Miara, Hamza; Ouyang, Pingbo; Jiang, Bing

2018-01-01

To determine the correlations between peripapillary vessel density, retinal nerve fibre layer (RNFL) thickness, and myopic indices at retina quadrants with optical coherence tomography angiography (OCTA) in Chinese. Fifty-six subjects with a mean spherical equivalent (MSE) of -3.63 ± 0.29 D were included. Peripapillary RNFL thickness and retinal vessel density in four sectors (superior, nasal, inferior, and temporal quadrants) were determined by OCTA, and correlations of the main outcomes were analyzed. Negative correlations were found between the peripapillary RNFL thickness and axial length (AL) at superior ( r = -0.335, P = 0.001) and inferior ( r = -0.551, P < 0.001) quadrants. There was a significant positive correlation with spherical equivalent (SE) at the corresponding quadrants as well as at the nasal quadrant ( r = 0.339, P = 0.001; r = 0.379, P < 0.001; and r = 0.209, P = 0.039, resp.). Peripapillary retinal vessel density was also negatively correlated with AL at the nasal quadrant ( r = -0.392, P < 0.001), and only at the nasal quadrant, there was a positive correlation between the peripapillary vessel density and SE ( r = 0.319, P = 0.001). The degree of myopia and elongation of AL were negatively correlated with peripapillary RNFL thickness at superior and inferior quadrants and with peripapillary retinal vessel density at the nasal quadrant.

Noncommutative geometry and twisted conformal symmetry

International Nuclear Information System (INIS)

Matlock, Peter

2005-01-01

The twist-deformed conformal algebra is constructed as a Hopf algebra with twisted coproduct. This allows for the definition of conformal symmetry in a noncommutative background geometry. The twisted coproduct is reviewed for the Poincare algebra and the construction is then extended to the full conformal algebra. The case of Moyal-type noncommutativity of the coordinates is considered. It is demonstrated that conformal invariance need not be viewed as incompatible with noncommutative geometry; the noncommutativity of the coordinates appears as a consequence of the twisting, as has been shown in the literature in the case of the twisted Poincare algebra

Pseudosymmetric fac-di­aqua­trichlorido[(di­methyl­phosphor­yl)methanaminium-κO]manganese(II)

Science.gov (United States)

Reiss, Guido J.

2013-01-01

In the title compound, [Mn(C3H11NOP)Cl3(H2O)2], the MnII metal center has a distorted o­cta­hedral geometry, coordinated by the three chloride ligands showing a facial arrangement. Two water mol­ecules and the O-coordinated dpmaH cation [dpmaH = (di­methyl­phosphor­yl)methanaminium] complete the coordination sphere. Each complex mol­ecule is connected to its neighbours by O—H⋯Cl and N—H⋯Cl hydrogen bonds. Two of the chloride ligands and the two water ligands form a hydrogen-bonded polymeric sheet in the ab plane. Furthermore, these planes are connected to adjacent planes by hydrogen bonds from the aminium function of cationic dpmaH ligand. A pseudo-mirror plane perpendicular to the b axis in the chiral space group P21 is observed together with inversion twinning [ratio = 0.864 (5):0.136 (5)]. PMID:23723764

Optimization of strong and weak coordinates

NARCIS (Netherlands)

Swart, M.; Bickelhaupt, F.M.

2006-01-01

We present a new scheme for the geometry optimization of equilibrium and transition state structures that can be used for both strong and weak coordinates. We use a screening function that depends on atom-pair distances to differentiate strong coordinates from weak coordinates. This differentiation

A first course in geometry

CERN Document Server

Walsh, Edward T

2014-01-01

This introductory text is designed to help undergraduate students develop a solid foundation in geometry. Early chapters progress slowly, cultivating the necessary understanding and self-confidence for the more rapid development that follows. The extensive treatment can be easily adapted to accommodate shorter courses. Starting with the language of mathematics as expressed in the algebra of logic and sets, the text covers geometric sets of points, separation and angles, triangles, parallel lines, similarity, polygons and area, circles, space geometry, and coordinate geometry. Each chapter incl

The Comparison of Regional RNFL and Fundus Vasculature by OCTA in Chinese Myopia Population

Directory of Open Access Journals (Sweden)

Yuanjun Li

2018-01-01

Full Text Available Purpose. To determine the correlations between peripapillary vessel density, retinal nerve fibre layer (RNFL thickness, and myopic indices at retina quadrants with optical coherence tomography angiography (OCTA in Chinese. Methods. Fifty-six subjects with a mean spherical equivalent (MSE of −3.63 ± 0.29 D were included. Peripapillary RNFL thickness and retinal vessel density in four sectors (superior, nasal, inferior, and temporal quadrants were determined by OCTA, and correlations of the main outcomes were analyzed. Results. Negative correlations were found between the peripapillary RNFL thickness and axial length (AL at superior (r=−0.335, P=0.001 and inferior (r=−0.551, P<0.001 quadrants. There was a significant positive correlation with spherical equivalent (SE at the corresponding quadrants as well as at the nasal quadrant (r=0.339, P=0.001; r=0.379, P<0.001; and r=0.209, P=0.039, resp.. Peripapillary retinal vessel density was also negatively correlated with AL at the nasal quadrant (r=−0.392, P<0.001, and only at the nasal quadrant, there was a positive correlation between the peripapillary vessel density and SE (r=0.319, P=0.001. Conclusions. The degree of myopia and elongation of AL were negatively correlated with peripapillary RNFL thickness at superior and inferior quadrants and with peripapillary retinal vessel density at the nasal quadrant.

A vector space approach to geometry

CERN Document Server

Hausner, Melvin

2010-01-01

The effects of geometry and linear algebra on each other receive close attention in this examination of geometry's correlation with other branches of math and science. In-depth discussions include a review of systematic geometric motivations in vector space theory and matrix theory; the use of the center of mass in geometry, with an introduction to barycentric coordinates; axiomatic development of determinants in a chapter dealing with area and volume; and a careful consideration of the particle problem. 1965 edition.

Binding of cyclic carboxylates to octa-acid deep-cavity cavitand

Science.gov (United States)

Gibb, Corinne L. D.; Gibb, Bruce C.

2014-04-01

As part of the fourth statistical assessment of modeling of proteins and ligands (sampl.eyesopen.com) prediction challenge, the strength of association of nine guests ( 1- 9) binding to octa-acid host was determined by a combination of 1H NMR and isothermal titration calorimetry. Association constants in sodium tetraborate buffered (pH 9.2) aqueous solution ranged from 5.39 × 102 M-1 in the case of benzoate 1, up to 3.82 × 105 M-1 for trans-4-methylcyclohexanoate 7. Overall, the free energy difference between the free energies of complexation of these weakest and strongest binding guests was ΔΔG° = 3.88 kcal mol-1. Based on a multitude of previous studies, the anticipated order of strength of binding was close to that which was actually obtained. However, the binding of guest 3 (4-ethylbenzoate) was considerably stronger than initially estimated.

Geometry The Language of Space and Form (Revised Edition)

CERN Document Server

Tabak, John

2011-01-01

Geometry, Revised Edition describes geometry in antiquity. Beginning with a brief description of some of the geometry that preceded the geometry of the Greeks, it takes up the story of geometry during the European Renaissance as well as the significant mathematical progress in other areas of the world. It also discusses the analytic geometry of Ren Descartes and Pierre Fermat, the alternative coordinate systems invented by Isaac Newton, and the solid geometry of Leonhard Euler. Also included is an overview of the geometry of one of the most successful mathematicians of the 19th century, Bernha

Special geometry

International Nuclear Information System (INIS)

Strominger, A.

1990-01-01

A special manifold is an allowed target manifold for the vector multiplets of D=4, N=2 supergravity. These manifolds are of interest for string theory because the moduli spaces of Calabi-Yau threefolds and c=9, (2,2) conformal field theories are special. Previous work has given a local, coordinate-dependent characterization of special geometry. A global description of special geometries is given herein, and their properties are studied. A special manifold M of complex dimension n is characterized by the existence of a holomorphic Sp(2n+2,R)xGL(1,C) vector bundle over M with a nowhere-vanishing holomorphic section Ω. The Kaehler potential on M is the logarithm of the Sp(2n+2,R) invariant norm of Ω. (orig.)

Assessing the Underwater Acoustics of the World's Largest Vibration Hammer (OCTA-KONG) and Its Potential Effects on the Indo-Pacific Humpbacked Dolphin (Sousa chinensis)

Science.gov (United States)

Wang, Zhitao; Wu, Yuping; Duan, Guoqin; Cao, Hanjiang; Liu, Jianchang; Wang, Kexiong; Wang, Ding

2014-01-01

Anthropogenic noise in aquatic environments is a worldwide concern due to its potential adverse effects on the environment and aquatic life. The Hongkong-Zhuhai-Macao Bridge is currently under construction in the Pearl River Estuary, a hot spot for the Indo-Pacific humpbacked dolphin (Sousa chinensis) in China. The OCTA-KONG, the world's largest vibration hammer, is being used during this construction project to drive or extract steel shell piles 22 m in diameter. This activity poses a substantial threat to marine mammals, and an environmental assessment is critically needed. The underwater acoustic properties of the OCTA-KONG were analyzed, and the potential impacts of the underwater acoustic energy on Sousa, including auditory masking and physiological impacts, were assessed. The fundamental frequency of the OCTA-KONG vibration ranged from 15 Hz to 16 Hz, and the noise increments were below 20 kHz, with a dominant frequency and energy below 10 kHz. The resulting sounds are most likely detectable by Sousa over distances of up to 3.5 km from the source. Although Sousa clicks do not appear to be adversely affected, Sousa whistles are susceptible to auditory masking, which may negatively impact this species' social life. Therefore, a safety zone with a radius of 500 m is proposed. Although the zero-to-peak source level (SL) of the OCTA-KONG was lower than the physiological damage level, the maximum root-mean-square SL exceeded the cetacean safety exposure level on several occasions. Moreover, the majority of the unweighted cumulative source sound exposure levels (SSELs) and the cetacean auditory weighted cumulative SSELs exceeded the acoustic threshold levels for the onset of temporary threshold shift, a type of potentially recoverable auditory damage resulting from prolonged sound exposure. These findings may aid in the identification and design of appropriate mitigation methods, such as the use of air bubble curtains, “soft start” and “power down�

Assessing the underwater acoustics of the world's largest vibration hammer (OCTA-KONG and its potential effects on the Indo-Pacific humpbacked dolphin (Sousa chinensis.

Directory of Open Access Journals (Sweden)

Zhitao Wang

Full Text Available Anthropogenic noise in aquatic environments is a worldwide concern due to its potential adverse effects on the environment and aquatic life. The Hongkong-Zhuhai-Macao Bridge is currently under construction in the Pearl River Estuary, a hot spot for the Indo-Pacific humpbacked dolphin (Sousa chinensis in China. The OCTA-KONG, the world's largest vibration hammer, is being used during this construction project to drive or extract steel shell piles 22 m in diameter. This activity poses a substantial threat to marine mammals, and an environmental assessment is critically needed. The underwater acoustic properties of the OCTA-KONG were analyzed, and the potential impacts of the underwater acoustic energy on Sousa, including auditory masking and physiological impacts, were assessed. The fundamental frequency of the OCTA-KONG vibration ranged from 15 Hz to 16 Hz, and the noise increments were below 20 kHz, with a dominant frequency and energy below 10 kHz. The resulting sounds are most likely detectable by Sousa over distances of up to 3.5 km from the source. Although Sousa clicks do not appear to be adversely affected, Sousa whistles are susceptible to auditory masking, which may negatively impact this species' social life. Therefore, a safety zone with a radius of 500 m is proposed. Although the zero-to-peak source level (SL of the OCTA-KONG was lower than the physiological damage level, the maximum root-mean-square SL exceeded the cetacean safety exposure level on several occasions. Moreover, the majority of the unweighted cumulative source sound exposure levels (SSELs and the cetacean auditory weighted cumulative SSELs exceeded the acoustic threshold levels for the onset of temporary threshold shift, a type of potentially recoverable auditory damage resulting from prolonged sound exposure. These findings may aid in the identification and design of appropriate mitigation methods, such as the use of air bubble curtains, "soft start" and "power down

Geometry of the self-consistent collective-coordinate method for the large-amplitude collective motion

International Nuclear Information System (INIS)

Sakata, Fumihiko; Marumori, Toshio; Hashimoto, Yukio; Une, Tsutomu.

1983-05-01

The geometry of the self-consistent collective-coordinate (SCC) method formulated within the framework of the time-dependent Hartree-Fock (TDHF) theory is investigated by associating the variational parameters with a symplectic manifold (a TDHF manifold). With the use of a canonical-variables parametrization, it is shown that the TDHF equation is equivalent to the canonical equations of motion in classical mechanics in the TDHF manifold. This enables us to investigate geometrical structure of the SCC method in the language of the classical mechanics. The SCC method turns out to give a prescription how to dynamically extract a ''maximally-decoupled'' collective submanifold (hypersurface) out of the TDHF manifold, in such a way that a certain kind of trajectories corresponding to the large-amplitude collective motion under consideration can be reproduced on the hypersurface as precisely as possible. The stability of the hypersurface at each point on it is investigated, in order to see whether the hypersurface obtained by the SCC method is really an approximate integral surface in the TDHF manifold or not. (author)

Functional integration over geometries

International Nuclear Information System (INIS)

Mottola, E.

1995-01-01

The geometric construction of the functional integral over coset spaces M/G is reviewed. The inner product on the cotangent space of infinitesimal deformations of M defines an invariant distance and volume form, or functional integration measure on the full configuration space. Then, by a simple change of coordinates parameterizing the gauge fiber G, the functional measure on the coset space M/G is deduced. This change of integration variables leads to a Jacobian which is entirely equivalent to the Faddeev--Popov determinant of the more traditional gauge fixed approach in non-abelian gauge theory. If the general construction is applied to the case where G is the group of coordinate reparameterizations of spacetime, the continuum functional integral over geometries, i.e. metrics modulo coordinate reparameterizations may be defined. The invariant functional integration measure is used to derive the trace anomaly and effective action for the conformal part of the metric in two and four dimensional spacetime. In two dimensions this approach generates the Polyakov--Liouville action of closed bosonic non-critical string theory. In four dimensions the corresponding effective action leads to novel conclusions on the importance of quantum effects in gravity in the far infrared, and in particular, a dramatic modification of the classical Einstein theory at cosmological distance scales, signaled first by the quantum instability of classical de Sitter spacetime. Finite volume scaling relations for the functional integral of quantum gravity in two and four dimensions are derived, and comparison with the discretized dynamical triangulation approach to the integration over geometries are discussed. Outstanding unsolved problems in both the continuum definition and the simplicial approach to the functional integral over geometries are highlighted

Rietveld refinement of the mixed boracite Fe(1.59)Zn(1.41)B(7)O(13)Br.

Science.gov (United States)

Ulloa-Godínez, Sandra; Rosales, Ivonne; Bucio, Lauro; Farías, Mario H; Campa-Molina, Jorge

2009-10-31

The structural characterization of the new iron-zinc hepta-borate bromide with composition Fe(1.59)Zn(1.41)B(7)O(13)Br, prepared by chemical transport is reported. A rigid-body model with constrained generalized coordinates was defined in order to hold the positions of the B atoms at reasonable inter-atomic distances that typically would reach unacceptable values because of the weak scattering power of boron. There are three independent sites for the B atoms of which two are tetra-hedrally coordinated. The bond-valence sum around the third B atom, located on a threefold rotation axis, was calculated considering two cases of coordination of boron with oxygens: trigonal-planar and tetrahedral. The contribution of the fourth O atom to the bond-valence sum was found to be only 0.06 v.u., indicating the presence of a very weak bond in the right position to have a distorted tetra-hedral coordination in favour of the trigonal-planar coordination for the third B atom. X-ray fluorescence (XRF) was used to determinate the Fe/Zn ratio.

Nonlinear gyrokinetic Maxwell-Vlasov equations using magnetic coordinates

International Nuclear Information System (INIS)

Brizard, A.

1988-09-01

A gyrokinetic formalism using magnetic coordinates is used to derive self-consistent, nonlinear Maxwell-Vlasov equations that are suitable for particle simulation studies of finite-β tokamak microturbulence and its associated anomalous transport. The use of magnetic coordinates is an important feature of this work as it introduces the toroidal geometry naturally into our gyrokinetic formalism. The gyrokinetic formalism itself is based on the use of the Action-variational Lie perturbation method of Cary and Littlejohn, and preserves the Hamiltonian structure of the original Maxwell-Vlasov system. Previous nonlinear gyrokinetic sets of equations suitable for particle simulation analysis have considered either electrostatic and shear-Alfven perturbations in slab geometry, or electrostatic perturbations in toroidal geometry. In this present work, fully electromagnetic perturbations in toroidal geometry are considered. 26 refs

Simultaneous calibration phantom commission and geometry calibration in cone beam CT

Science.gov (United States)

Xu, Yuan; Yang, Shuai; Ma, Jianhui; Li, Bin; Wu, Shuyu; Qi, Hongliang; Zhou, Linghong

2017-09-01

Geometry calibration is a vital step for describing the geometry of a cone beam computed tomography (CBCT) system and is a prerequisite for CBCT reconstruction. In current methods, calibration phantom commission and geometry calibration are divided into two independent tasks. Small errors in ball-bearing (BB) positioning in the phantom-making step will severely degrade the quality of phantom calibration. To solve this problem, we propose an integrated method to simultaneously realize geometry phantom commission and geometry calibration. Instead of assuming the accuracy of the geometry phantom, the integrated method considers BB centers in the phantom as an optimized parameter in the workflow. Specifically, an evaluation phantom and the corresponding evaluation contrast index are used to evaluate geometry artifacts for optimizing the BB coordinates in the geometry phantom. After utilizing particle swarm optimization, the CBCT geometry and BB coordinates in the geometry phantom are calibrated accurately and are then directly used for the next geometry calibration task in other CBCT systems. To evaluate the proposed method, both qualitative and quantitative studies were performed on simulated and realistic CBCT data. The spatial resolution of reconstructed images using dental CBCT can reach up to 15 line pair cm-1. The proposed method is also superior to the Wiesent method in experiments. This paper shows that the proposed method is attractive for simultaneous and accurate geometry phantom commission and geometry calibration.

Geometry Euclid and beyond

CERN Document Server

Hartshorne, Robin

2000-01-01

In recent years, I have been teaching a junior-senior-level course on the classi­ cal geometries. This book has grown out of that teaching experience. I assume only high-school geometry and some abstract algebra. The course begins in Chapter 1 with a critical examination of Euclid's Elements. Students are expected to read concurrently Books I-IV of Euclid's text, which must be obtained sepa­ rately. The remainder of the book is an exploration of questions that arise natu­ rally from this reading, together with their modern answers. To shore up the foundations we use Hilbert's axioms. The Cartesian plane over a field provides an analytic model of the theory, and conversely, we see that one can introduce coordinates into an abstract geometry. The theory of area is analyzed by cutting figures into triangles. The algebra of field extensions provides a method for deciding which geometrical constructions are possible. The investigation of the parallel postulate leads to the various non-Euclidean geometries. And ...

Penta- and octa-bromodiphenyl ethers promote proinflammatory protein expression in human bronchial epithelial cells in vitro.

Science.gov (United States)

Koike, Eiko; Yanagisawa, Rie; Takigami, Hidetaka; Takano, Hirohisa

2014-03-01

Polybrominated diphenyl ethers (PBDEs) are widely used as flame retardants in consumer products. Humans can be exposed to PBDEs mainly through the inhalation of air or dust. Thus, PBDEs can affect respiratory and immune systems. In the present study, we investigated whether PBDEs stimulate bronchial epithelial cells. We examined commercial penta-BDE (DE-71), octa-BDE (DE-79), and deca-BDE (DE-83R). Human bronchial epithelial cells (BEAS-2B) were exposed to each PBDE for 24h. Subsequently, the expression of intercellular adhesion molecule-1 (ICAM-1) and proinflammatory cytokines were investigated. DE-71 and DE-79, but not DE-83R, significantly increased the expression of ICAM-1, interleukin-6 (IL-6), and IL-8 in BEAS-2B. Because these remarkable effects were observed with DE-71, we further investigated the underlying intracellular mechanisms. DE-71 promoted epidermal growth factor receptor (EGFR) phosphorylation. Inhibitors of EGFR-selective tyrosine kinase and p38 mitogen-activated protein kinase effectively blocked the increase of IL-6 and IL-8. Furthermore, antagonists of thyroid hormone receptor and aryl hydrocarbon receptor significantly suppressed the increase in IL-6 and/or IL-8 production. In conclusion, penta- and octa-BDE, but not deca-BDE, might promote the expression of proinflammatory proteins in bronchial epithelial cells possibly by activating protein kinases and/or stimulating nuclear receptors related to subsequent activation of transcriptional factors. Copyright © 2013 Elsevier Ltd. All rights reserved.

Aspects of non-geometry in string theory

International Nuclear Information System (INIS)

Patalong, Peter

2013-01-01

This thesis investigates various manifestations of non-geometry in string theory. It utilises different frameworks to study how non-geometry appears in the target space, how non-geometry and non-geometric fluxes are interconnected, how non-geometry can be captured in effective field theories and how a possible extension of the standard string worldsheet model can accommodate non-geometric setups. The first part provides an example that non-geometry can imply non-commutativity of the closed string coordinate fields. Three T-dual frames are investigated, the three-torus with constant H-flux, the twisted torus and the torus with non-geometric flux Q. Under the assumption of dilute flux, a mode expansion and the canonical quantisation are carried out in the second case up to linear order in the flux parameter. T-duality is then used to relate the commutators of the string expansion modes to the coordinate field commutator in the non-geometric third frame. Non-commutativity is found and related to the non-geometric flux Q and the string winding, it therefore appears as an intrinsically string theoretic feature. The second part investigates non-geometry in the context of ten-dimensional effective field theories, i.e. double field theory and supergravity. A field redefinition is implemented that takes the form of a T-duality transformation, it reveals an alternative set of field variables allowing to define non-geometric fluxes Q and R in higher dimensions. The perspective of double field theory provides a geometric interpretation of those by taking into account a new type of covariant winding derivative. The perspective of the ten-dimensional supergravity allows to investigate the interplay between non-geometric field configurations and non-geometric fluxes. For the three-torus example, a well-defined action can be found, and a simple dimensional reduction makes contact to the known four-dimensional potential. It thus proves the correct uplift of Q and R to higher

The influence of coordination geometry and valency on the K-edge absorption near edge spectra of selected chromium compounds

International Nuclear Information System (INIS)

Pantelouris, A.; Modrow, H.; Pantelouris, M.; Hormes, J.; Reinen, D.

2004-01-01

X-ray absorption spectra at the chromium K-edge are reported for a number of selected chromium compounds of known chemical structure. The spectra were obtained with use of synchrotron radiation available at the ELectron Stretcher Accelerator ELSA in Bonn. The compounds studied include the tetrahedrally coordinated compounds Ca 2 Ge 0.8 Cr 0.2 O 4 , Ba 2 Ge 0.1 Cr 0.9 O 4 , Sr 2 CrO 4 , Ca 2 (PO 4 ) x (CrO 4 ) 1-x Cl (x=0.25,0.5), Ca 5 (CrO 4 ) 3 Cl, CrO 3 , the octahedrally coordinated compounds Cr(II)-acetate, CrCl 3 , CrF 3 , Cr 2 O 3 , KCr(SO 4 ) 2 · 12H 2 O, CrO 2 and cubic coordinated metallic chromium. In these compounds chromium exhibits a wide range of formal oxidation states (0 to VI). The absorption features in the near edge region are shown to be characteristic of the spatial environment of the absorbing atom. The occurrence of a single pre-edge line easily allows one to distinguish between tetrahedral and octahedral coordination geometry, whereas the energy position of the absorption edge is found to be very sensitive to the valency of the excited chromium atom. Calculations of the ionisation potential of Cr in different oxidation states using the non-relativistic Hartree-Fock method (Froese-Fischer) confirm that the ionisation limit shifts to higher energy with increasing Cr valency. More detailed information on the electronic structure of the different compounds is gained by real-space full multiple scattering calculations using the FEFF8 code

The influence of coordination geometry and valency on the K-edge absorption near edge spectra of selected chromium compounds

Science.gov (United States)

Pantelouris, A.; Modrow, H.; Pantelouris, M.; Hormes, J.; Reinen, D.

2004-05-01

X-ray absorption spectra at the chromium K-edge are reported for a number of selected chromium compounds of known chemical structure. The spectra were obtained with use of synchrotron radiation available at the ELectron Stretcher Accelerator ELSA in Bonn. The compounds studied include the tetrahedrally coordinated compounds Ca 2Ge 0.8Cr 0.2O 4, Ba 2Ge 0.1Cr 0.9O 4, Sr 2CrO 4, Ca 2(PO 4) x(CrO 4) 1- xCl ( x=0.25,0.5), Ca 5(CrO 4) 3Cl, CrO 3, the octahedrally coordinated compounds Cr(II)-acetate, CrCl 3, CrF 3, Cr 2O 3, KCr(SO 4) 2 · 12H 2O, CrO 2 and cubic coordinated metallic chromium. In these compounds chromium exhibits a wide range of formal oxidation states (0 to VI). The absorption features in the near edge region are shown to be characteristic of the spatial environment of the absorbing atom. The occurrence of a single pre-edge line easily allows one to distinguish between tetrahedral and octahedral coordination geometry, whereas the energy position of the absorption edge is found to be very sensitive to the valency of the excited chromium atom. Calculations of the ionisation potential of Cr in different oxidation states using the non-relativistic Hartree-Fock method (Froese-Fischer) confirm that the ionisation limit shifts to higher energy with increasing Cr valency. More detailed information on the electronic structure of the different compounds is gained by real-space full multiple scattering calculations using the FEFF8 code.

μ-Hexa­thio­metadiphosphato-bis­[(1,4,7,10,13,16-hexa­oxa­cyclo­octa­decane-κ6 O)rubidium] aceto­nitrile disolvate

Science.gov (United States)

Gjikaj, Mimoza; Pook, Niels-Patrick; Qarri, Flora

2013-01-01

The asymmetric unit of the title compound, [Rb2(P2S6)(C12H24O6)2]·2CH3CN, contains one half of an [Rb(18-crown-6)2]2[P2S6] unit and one aceto­nitrile solvent mol­ecule. The [Rb(18-crown-6)]2[P2S6] unit is completed by inversion symmetry. Its Rb+ ion is situated near the centre of the macrocyclic cavity, but is displaced by 0.8972 (1) Å from the O atoms of the crown in the direction of the [P2S6]2− moiety. The overall coordination number of the cation is eight, defined by the six crown ether O atoms and by two terminal S atoms of the [P2S6]2− anion. The hexa­thio­metadiphosphate anion is built up from two tetra­hedral PS4 units joined together by a common edge. The crystal structure is characterized by alternating layers of [Rb(18-crown-6)]2[P2S6] and aceto­nitrile solvent mol­ecules stacked along [010]. PMID:24860286

Mathematical model of geometry and fibrous structure of the heart.

Science.gov (United States)

Nielsen, P M; Le Grice, I J; Smaill, B H; Hunter, P J

1991-04-01

We developed a mathematical representation of ventricular geometry and muscle fiber organization using three-dimensional finite elements referred to a prolate spheroid coordinate system. Within elements, fields are approximated using basis functions with associated parameters defined at the element nodes. Four parameters per node are used to describe ventricular geometry. The radial coordinate is interpolated using cubic Hermite basis functions that preserve slope continuity, while the angular coordinates are interpolated linearly. Two further nodal parameters describe the orientation of myocardial fibers. The orientation of fibers within coordinate planes bounded by epicardial and endocardial surfaces is interpolated linearly, with transmural variation given by cubic Hermite basis functions. Left and right ventricular geometry and myocardial fiber orientations were characterized for a canine heart arrested in diastole and fixed at zero transmural pressure. The geometry was represented by a 24-element ensemble with 41 nodes. Nodal parameters fitted using least squares provided a realistic description of ventricular epicardial [root mean square (RMS) error less than 0.9 mm] and endocardial (RMS error less than 2.6 mm) surfaces. Measured fiber fields were also fitted (RMS error less than 17 degrees) with a 60-element, 99-node mesh obtained by subdividing the 24-element mesh. These methods provide a compact and accurate anatomic description of the ventricles suitable for use in finite element stress analysis, simulation of cardiac electrical activation, and other cardiac field modeling problems.

Foundations of arithmetic differential geometry

CERN Document Server

Buium, Alexandru

2017-01-01

The aim of this book is to introduce and develop an arithmetic analogue of classical differential geometry. In this new geometry the ring of integers plays the role of a ring of functions on an infinite dimensional manifold. The role of coordinate functions on this manifold is played by the prime numbers. The role of partial derivatives of functions with respect to the coordinates is played by the Fermat quotients of integers with respect to the primes. The role of metrics is played by symmetric matrices with integer coefficients. The role of connections (respectively curvature) attached to metrics is played by certain adelic (respectively global) objects attached to the corresponding matrices. One of the main conclusions of the theory is that the spectrum of the integers is "intrinsically curved"; the study of this curvature is then the main task of the theory. The book follows, and builds upon, a series of recent research papers. A significant part of the material has never been published before.

In situ tetrazole templated chair-like decanuclear azido-cobalt(II) SMM containing both tetra- and octa-hedral Co(II) ions.

Science.gov (United States)

Zhang, Yuan-Zhu; Gao, Song; Sato, Osamu

2015-01-14

An azido-bridged chair-like decanuclear cluster: [Co(II)10(bzp)8(Metz)2(N3)18]·4MeOH·3H2O (1, bzp = 2-benzoylpyridine and HMetz = 5-methyl-1H-tetrazole) was prepared with in situ tetrazolate anions as templates in a sealed system. 1 containing both octahedral and tetrahedral Co(II) ions exhibited slow relaxation of magnetization with an effective barrier of 26 K under an applied dc field of 1 kOe.

Painleve-gullstrand-type Coordinates for the Five-dimensional Myers-Perry Black Hole

Science.gov (United States)

Finch, Tehani Kahi

2013-01-01

The Painleve-Gullstrand coordinates provide a convenient framework for presenting the Schwarzschild geometry because of their flat constant-time hypersurfaces, and the fact that they are free of coordinate singularities outside r=0. Generalizations of Painlev´e-Gullstrand coordinates suitable for the Kerr geometry have been presented by Doran and Nat´ario. These coordinate systems feature a time coordinate identical to the proper time of zero-angular-momentum observers that are dropped from infinity. Here, the methods of Doran and Nat´ario are extended to the five-dimensional rotating black hole found by Myers and Perry. The result is a new formulation of the Myers-Perry metric. The properties and physical significance of these new coordinates are discussed.

The influence of coordination geometry and valency on the K-edge absorption near edge spectra of selected chromium compounds

Energy Technology Data Exchange (ETDEWEB)

Pantelouris, A.; Modrow, H.; Pantelouris, M.; Hormes, J.; Reinen, D

2004-05-10

X-ray absorption spectra at the chromium K-edge are reported for a number of selected chromium compounds of known chemical structure. The spectra were obtained with use of synchrotron radiation available at the ELectron Stretcher Accelerator ELSA in Bonn. The compounds studied include the tetrahedrally coordinated compounds Ca{sub 2}Ge{sub 0.8}Cr{sub 0.2}O{sub 4}, Ba{sub 2}Ge{sub 0.1}Cr{sub 0.9}O{sub 4}, Sr{sub 2}CrO{sub 4}, Ca{sub 2}(PO{sub 4}){sub x}(CrO{sub 4}){sub 1-x}Cl (x=0.25,0.5), Ca{sub 5}(CrO{sub 4}){sub 3}Cl, CrO{sub 3}, the octahedrally coordinated compounds Cr(II)-acetate, CrCl{sub 3}, CrF{sub 3}, Cr{sub 2}O{sub 3}, KCr(SO{sub 4}){sub 2} {center_dot} 12H{sub 2}O, CrO{sub 2} and cubic coordinated metallic chromium. In these compounds chromium exhibits a wide range of formal oxidation states (0 to VI). The absorption features in the near edge region are shown to be characteristic of the spatial environment of the absorbing atom. The occurrence of a single pre-edge line easily allows one to distinguish between tetrahedral and octahedral coordination geometry, whereas the energy position of the absorption edge is found to be very sensitive to the valency of the excited chromium atom. Calculations of the ionisation potential of Cr in different oxidation states using the non-relativistic Hartree-Fock method (Froese-Fischer) confirm that the ionisation limit shifts to higher energy with increasing Cr valency. More detailed information on the electronic structure of the different compounds is gained by real-space full multiple scattering calculations using the FEFF8 code.

Modern differential geometry for physicists

CERN Document Server

Isham, C J

1989-01-01

These notes are the content of an introductory course on modern, coordinate-free differential geometry which is taken by the first-year theoretical physics PhD students, or by students attending the one-year MSc course "Fundamental Fields and Forces" at Imperial College. The book is concerned entirely with mathematics proper, although the emphasis and detailed topics have been chosen with an eye to the way in which differential geometry is applied these days to modern theoretical physics. This includes not only the traditional area of general relativity but also the theory of Yang-Mills fields

1,1′,2,2′,3,3′,4,4′-Octa­methyl­ferro­cenium 2,5-dibromo-4-hy­droxy-3,6-dioxocyclo­hexa-1,4-dien-1-olate

Science.gov (United States)

Mochida, Tomoyuki

2011-01-01

In the title salt, octa­methyl­ferrocenium bromanilate, [Fe(C9H13)2](C6HBr2O4), the Fe atom and the bromanilate anion lie on a mirror plane. The octa­methyl­ferrocenium cation adopts an eclipsed conformation. An intra­molecular O—H⋯O hydrogen bond is present in the bromanilate anion. In the crystal, the cations and anions are stacked alternately, forming a one-dimensional columnar structure along [010]. PMID:22090810

Riemannian geometry

CERN Document Server

Petersen, Peter

2016-01-01

Intended for a one year course, this text serves as a single source, introducing readers to the important techniques and theorems, while also containing enough background on advanced topics to appeal to those students wishing to specialize in Riemannian geometry. This is one of the few Works to combine both the geometric parts of Riemannian geometry and the analytic aspects of the theory. The book will appeal to a readership that have a basic knowledge of standard manifold theory, including tensors, forms, and Lie groups. Important revisions to the third edition include: a substantial addition of unique and enriching exercises scattered throughout the text; inclusion of an increased number of coordinate calculations of connection and curvature; addition of general formulas for curvature on Lie Groups and submersions; integration of variational calculus into the text allowing for an early treatment of the Sphere theorem using a proof by Berger; incorporation of several recent results about manifolds with posit...

Identification of the iron oxidation state and coordination geometry in iron oxide- and zeolite-based catalysts using pre-edge XAS analysis.

Science.gov (United States)

Boubnov, Alexey; Lichtenberg, Henning; Mangold, Stefan; Grunwaldt, Jan Dierk

2015-03-01

Analysis of the oxidation state and coordination geometry using pre-edge analysis is attractive for heterogeneous catalysis and materials science, especially for in situ and time-resolved studies or highly diluted systems. In the present study, focus is laid on iron-based catalysts. First a systematic investigation of the pre-edge region of the Fe K-edge using staurolite, FePO4, FeO and α-Fe2O3 as reference compounds for tetrahedral Fe(2+), tetrahedral Fe(3+), octahedral Fe(2+) and octahedral Fe(3+), respectively, is reported. In particular, high-resolution and conventional X-ray absorption spectra are compared, considering that in heterogeneous catalysis and material science a compromise between high-quality spectroscopic data acquisition and simultaneous analysis of functional properties is required. Results, which were obtained from reference spectra acquired with different resolution and quality, demonstrate that this analysis is also applicable to conventionally recorded pre-edge data. For this purpose, subtraction of the edge onset is preferentially carried out using an arctangent and a first-degree polynomial, independent of the resolution and quality of the data. For both standard and high-resolution data, multiplet analysis of pre-edge features has limitations due to weak transitions that cannot be identified. On the other hand, an arbitrary empirical peak fitting assists the analysis in that non-local transitions can be isolated. The analysis of the oxidation state and coordination geometry of the Fe sites using a variogram-based method is shown to be effective for standard-resolution data and leads to the same results as for high-resolution spectra. This method, validated by analysing spectra of reference compounds and their well defined mixtures, is finally applied to track structural changes in a 1% Fe/Al2O3 and a 0.5% Fe/BEA zeolite catalyst during reduction in 5% H2/He. The results, hardly accessible by other techniques, show that Fe(3+) is

coordination polymers derived from two different bis-pyridyl-bis-am

Indian Academy of Sciences (India)

Abstract. Three new Ni(II) coordination polymers exhibiting different 1D and 2D framework structures ... separation, magnetism, ion exchange and so on.5 8 ... of the coordination geometries of metal ions, which ... Cu(II)/Co(II)/Cd(II) coordination polymers containing ..... tion, the concentration of MB and RhB (C) versus reac-.

Tropical geometry of statistical models.

Science.gov (United States)

Pachter, Lior; Sturmfels, Bernd

2004-11-16

This article presents a unified mathematical framework for inference in graphical models, building on the observation that graphical models are algebraic varieties. From this geometric viewpoint, observations generated from a model are coordinates of a point in the variety, and the sum-product algorithm is an efficient tool for evaluating specific coordinates. Here, we address the question of how the solutions to various inference problems depend on the model parameters. The proposed answer is expressed in terms of tropical algebraic geometry. The Newton polytope of a statistical model plays a key role. Our results are applied to the hidden Markov model and the general Markov model on a binary tree.

Generalizing optical geometry

International Nuclear Information System (INIS)

Jonsson, Rickard; Westman, Hans

2006-01-01

We show that by employing the standard projected curvature as a measure of spatial curvature, we can make a certain generalization of optical geometry (Abramowicz M A and Lasota J-P 1997 Class. Quantum Grav. A 14 23-30). This generalization applies to any spacetime that admits a hypersurface orthogonal shearfree congruence of worldlines. This is a somewhat larger class of spacetimes than the conformally static spacetimes assumed in standard optical geometry. In the generalized optical geometry, which in the generic case is time dependent, photons move with unit speed along spatial geodesics and the sideways force experienced by a particle following a spatially straight line is independent of the velocity. Also gyroscopes moving along spatial geodesics do not precess (relative to the forward direction). Gyroscopes that follow a curved spatial trajectory precess according to a very simple law of three-rotation. We also present an inertial force formalism in coordinate representation for this generalization. Furthermore, we show that by employing a new sense of spatial curvature (Jonsson R 2006 Class. Quantum Grav. 23 1)) closely connected to Fermat's principle, we can make a more extensive generalization of optical geometry that applies to arbitrary spacetimes. In general this optical geometry will be time dependent, but still geodesic photons move with unit speed and follow lines that are spatially straight in the new sense. Also, the sideways experienced (comoving) force on a test particle following a line that is straight in the new sense will be independent of the velocity

Anion-Dependent Exocyclic Mercury(II) Coordination Polymers of Bis-dithiamacrocycle

Energy Technology Data Exchange (ETDEWEB)

Siewe, Arlette Deukam; Kim, Seul Gi; Choi, Kyu Seong [Kyungnam University, Changwon (Korea, Republic of); Lee, Shim Sung [Gyeongsang National University, Jinju (Korea, Republic of)

2014-09-15

Synthesis and structural characterization of mercury(II) halides and perchlorate complexes of bis-OS{sub 2}-Synthesis and structural characterization of mercury(II) halides and perchlorate complexes of bis-OS{sub 2}- macrocycle (L) are reported. L reacts with mercury(II) chloride and bromide to yield an isostructural 2D coordination polymers with type [Hg(L)X{sub 2}]n (1: X = Cl and 2: X = Br). In 1, each Hg atom which lies outside the cavity is six-coordinate with a distorted octahedral geometry, being bound to four adjacent ligands via monodentate Hg-S bonds and two remaining sites are occupied by two terminal chlorido ligands to form a fishnet-like 2D structure. When reacting with mercury(II) iodide, L afforded a 1D coordination polymer [Hg{sub 2}(L)I{sub 4}]·CHCl{sub 3}n in which each exocyclic Hg atom is four-coordinate, being bound to two sulfur donors from different ligands doubly bridging the ligand molecules in a head-to-tail mode. The coordination sphere in 3 is completed by two iodo terminal ligands, adopting a distorted tetrahedral geometry. On reacting with mercury(II) perchlorate, L forms solvent-coordinated 1D coordination polymer ([Hg{sub 2}(L)(DMF){sub 6}](ClO{sub 4}){sub 4}·2DMF)n instead of the anion-coordination. In 4, the Hg atom is five-coordinate, being bound to two sulfur donors from two different ligands doubly bridging the ligand molecules in a side-by-side mode to form a ribbon-like 1D structure.. The three remaining coordination sites in 4 are completed by three DMF molecules in a monodentate manner. Consequently, the different structures and connectivity patterns for the observed exocyclic coordination polymers depending on the anions used are influenced not only by the coordination ability of the anions but also by anion sizes macrocycle (L) are reported. L reacts with mercury(II) chloride and bromide to yield an isostructural 2D coordination polymers with type [Hg(L)X{sub 2}]n (1: X = Cl and 2: X = Br). In 1, each Hg atom which lies

Planetary Image Geometry Library

Science.gov (United States)

Deen, Robert C.; Pariser, Oleg

2010-01-01

The Planetary Image Geometry (PIG) library is a multi-mission library used for projecting images (EDRs, or Experiment Data Records) and managing their geometry for in-situ missions. A collection of models describes cameras and their articulation, allowing application programs such as mosaickers, terrain generators, and pointing correction tools to be written in a multi-mission manner, without any knowledge of parameters specific to the supported missions. Camera model objects allow transformation of image coordinates to and from view vectors in XYZ space. Pointing models, specific to each mission, describe how to orient the camera models based on telemetry or other information. Surface models describe the surface in general terms. Coordinate system objects manage the various coordinate systems involved in most missions. File objects manage access to metadata (labels, including telemetry information) in the input EDRs and RDRs (Reduced Data Records). Label models manage metadata information in output files. Site objects keep track of different locations where the spacecraft might be at a given time. Radiometry models allow correction of radiometry for an image. Mission objects contain basic mission parameters. Pointing adjustment ("nav") files allow pointing to be corrected. The object-oriented structure (C++) makes it easy to subclass just the pieces of the library that are truly mission-specific. Typically, this involves just the pointing model and coordinate systems, and parts of the file model. Once the library was developed (initially for Mars Polar Lander, MPL), adding new missions ranged from two days to a few months, resulting in significant cost savings as compared to rewriting all the application programs for each mission. Currently supported missions include Mars Pathfinder (MPF), MPL, Mars Exploration Rover (MER), Phoenix, and Mars Science Lab (MSL). Applications based on this library create the majority of operational image RDRs for those missions. A

Definition of treatment geometry in radiation therapy

International Nuclear Information System (INIS)

Aaltonen, P.

1996-01-01

When accurate systems for quality assurance and treatment optimization are employed, a precise system for fixation and dosimetric and portal verification are as important as a continued and standardized code of practice for dosimetry and patient follow-up, including registration of tumour responses and acute and late normal tissue reactions. To improve the accuracy of existing dose response relations in order to improve future therapy the treatment geometry and dose delivery concepts have to be accurately defined and uniformly employed. A Nordic working group was set up in 1991 (by Nordic Association of Clinica Physics) to standardize the concepts and quantities used during the whole radiotherapy process in the Nordic countries. Now the group is finalizing its report ''Specification of Dose Delivery in Radiation Therapy''. The report emphasizes that the treatment geometry shall be consistent with the geometry used during the diagnostic work up. The patient fixation is of importance early in the diagnostic phase to ensure that the same reference points and patients position will be used both during the diagnostic work up, simulation and treatment execution. Reference Coordinate System of the patient is a concept based on defined anatomic reference points. This Patient Reference System is a local system which has validity for the tissues, organs and volumes defined during radiotherapy. The reference points of the Patient Reference System should in turn be used for beam set-up. The treatment geometry is then defined by using different concepts describing tissues which are mobile in the Patient Reference System, and finally, volumes which are fixed in this coordinate system. A Set-up Margin has to be considered for movements of the volumes defined in the Reference Coordinate System of the Patient in relation to the radiation beam. The Set-up Margin is dependent on the treatment technique and it is needed in the treatment planning procedure to ensure that the prescribed

Definition of treatment geometry in radiation therapy

Energy Technology Data Exchange (ETDEWEB)

Aaltonen, P [Finnish Centre for Radiation and Nuclear Safety (STUK), Helsinki (Finland)

1996-08-01

When accurate systems for quality assurance and treatment optimization are employed, a precise system for fixation and dosimetric and portal verification are as important as a continued and standardized code of practice for dosimetry and patient follow-up, including registration of tumour responses and acute and late normal tissue reactions. To improve the accuracy of existing dose response relations in order to improve future therapy the treatment geometry and dose delivery concepts have to be accurately defined and uniformly employed. A Nordic working group was set up in 1991 to standardize the concepts and quantities used during the whole radiotherapy process in the Nordic countries. Now the group is finalizing its report ``Specification of Dose Delivery in Radiation Therapy``. The report emphasizes that the treatment geometry shall be consistent with the geometry used during the diagnostic work up. The patient fixation is of importance early in the diagnostic phase to ensure that the same reference points and patients position will be used both during the diagnostic work up, simulation and treatment execution. Reference Coordinate System of the patient is a concept based on defined anatomic reference points. This Patient Reference System is a local system which has validity for the tissues, organs and volumes defined during radiotherapy. The reference points of the Patient Reference System should in turn be used for beam set-up. The treatment geometry is then defined by using different concepts describing tissues which are mobile in the Patient Reference System, and finally, volumes which are fixed in this coordinate system. A Set-up Margin has to be considered for movements of the volumes defined in the Reference Coordinate System of the Patient in relation to the radiation beam. The Set-up Margin is dependent on the treatment technique and it is needed in the treatment planning procedure to ensure that the prescribed dose to the Target Volume is delivered.

Arbitrariness of geometry and the aether

International Nuclear Information System (INIS)

Browne, P.F.

1976-01-01

As emphasized by Milne, an observer ultimately depends on the transmission and reception of light signals for the measurement of natural lengths and periods remote from his world point. The laws of geometry which are obeyed when these lengths and periods are plotted on a space--time depend, inevitably, on assumptions concerning the dependence of light velocity on the spatial and temporal coordinates. A convention regarding light velocity fixes the geometry, and conversely. However, the convention of flat space--time implies nonintegrable ''radar distances'' unless the concept of coordinate-dependent units of measure is employed. Einstein's space--time has the advantage of admitting a special reference system R with respect to which the aether fluid is at rest and the total gravitational field vanishes. A holonomic transformation from R to another reference system R belonging to the same space--time introduces a nonpermanent gravitational field and holonomic aether motion. A nonholonomic transformation from R to a reference system R* which belongs to a different space--time introduces a permanent gravitational field and nonholonomic aether motion. The arbitrariness of geometry is expressed by extending covariance to include the latter transformation. By means of a nonholonomic (or units) transformation it is possible, with the aid of the principle of equivalence, to obtain the Schwarzschild and de Sitter metrics from the Newtonian fields that would arise in a flat space--time description. Some light is thrown on the interpretation of cosmological models

Towards the Rational Design of MRI Contrast Agents: Electron Spin Relaxation Is Largely Unaffected by the Coordination Geometry of Gadolinium(III)–DOTA-Type Complexes

Science.gov (United States)

Bean, Jonathan F.; Clarkson, Robert B.; Helm, Lothar; Moriggi, Loïck; Sherry, A. Dean

2009-01-01

Electron-spin relaxation is one of the determining factors in the efficacy of MRI contrast agents. Of all the parameters involved in determining relaxivity it remains the least well understood, particularly as it relates to the structure of the complex. One of the reasons for the poor understanding of electron-spin relaxation is that it is closely related to the ligand-field parameters of the Gd3+ ion that forms the basis of MRI contrast agents and these complexes generally exhibit a structural isomerism that inherently complicates the study of electron spin relaxation. We have recently shown that two DOTA-type ligands could be synthesised that, when coordinated to Gd3+, would adopt well defined coordination geometries and are not subject to the problems of intramolecular motion of other complexes. The EPR properties of these two chelates were studied and the results examined with theory to probe their electron-spin relaxation properties. PMID:18283704

ORGANIC/INORGANIC HYBRID EPOXY NANOCOMPOSITES BASED ON OCTA(AMINOPHENYL)SILSESQUIOXANE

Institute of Scientific and Technical Information of China (English)

Hai-bo Fan; Rong-jie Yang; Xiang-mei Li

2013-01-01

Octa(aminophenyl)silsesquioxane (OAPS) was used as the curing agent of diglycidyl ether of bisphenol-A (DGEBA) epoxy resin.A study on comparison of DGEBA/OAPS with DGEBA/4,4'-diaminodiphenyl sulfone (DDS) epoxy resins was achieved.Differential scanning calorimetry was used to investigate the curing reaction and its kinetics,and the glass transition of DGEBA/OAPS.Thermogravimetric analysis was used to investigate thermal decomposition of the two kinds of epoxy resins.The reactions between amino groups and epoxy groups were investigated using Fourier transform infrared spectroscopy.Scanning electron microscopy was used to observe morphology of the two epoxy resins.The results indicated that OAPS had very good compatibility with DGEBA in molecular level,and could form a transparent DGEBA/OAPS resin.The curing reaction of the DGEBA/OAPS prepolymer could occur under low temperatures compared with DGEBA/DDS.The DGEBA/OAPS resin didn't exhibit glass transition,but the DGEBA/DDS did,which meant that the large cage structure of OAPS limited the motion of chains between the cross-linking points.Measurements of the contact angle indicated that the DGEBA/OAPS showed larger angles with water than the DGEBA/DDS resin.Thermogravimetric analysis indicated that the incorporation of OAPS into epoxy system resulted in low mass loss rate and high char yield,but its initial decomposition temperature seemed to be lowered.

The Generation of Three-Dimensional Body-Fitted Coordinate Systems for Viscous Flow Problems.

Science.gov (United States)

1982-07-01

Geometries," NASA TM X-3206, 1975. iq p] Papers Written Under The Contract 1. "Basic Differential Models For Coordinate Generation ", Z . U. A. Warsi...8217 Ii (C) (4’) p Figure 1. Coordinate Surfaces fr. I • BASIC DIFFERENTIAL MODELS FOR COORDINATE GENERATION Z . U. A. WARSI* Department of Aerospace

Geometry optimization of molecules within an LCGTO local-density functional approach

International Nuclear Information System (INIS)

Mintmire, J.W.

1990-01-01

We describe our implementation of geometry optimization techniques within the linear combination of Gaussian-type orbitals (LCGTO) approach to local-density functional theory. The algorithm for geometry optimization is based on the evaluation of the gradient of the total energy with respect to internal coordinates within the local-density functional scheme. We present optimization results for a range of small molecules which serve as test cases for our approach

Spinning geometry = Twisted geometry

International Nuclear Information System (INIS)

Freidel, Laurent; Ziprick, Jonathan

2014-01-01

It is well known that the SU(2)-gauge invariant phase space of loop gravity can be represented in terms of twisted geometries. These are piecewise-linear-flat geometries obtained by gluing together polyhedra, but the resulting geometries are not continuous across the faces. Here we show that this phase space can also be represented by continuous, piecewise-flat three-geometries called spinning geometries. These are composed of metric-flat three-cells glued together consistently. The geometry of each cell and the manner in which they are glued is compatible with the choice of fluxes and holonomies. We first remark that the fluxes provide each edge with an angular momentum. By studying the piecewise-flat geometries which minimize edge lengths, we show that these angular momenta can be literally interpreted as the spin of the edges: the geometries of all edges are necessarily helices. We also show that the compatibility of the gluing maps with the holonomy data results in the same conclusion. This shows that a spinning geometry represents a way to glue together the three-cells of a twisted geometry to form a continuous geometry which represents a point in the loop gravity phase space. (paper)

Uranyl(VI)-acetylacetonate coordination compounds with various N-heterocyclic ligands

International Nuclear Information System (INIS)

Kawasaki, Takeshi; Nishimura, Tatsuru; Kitazawa, Takafumi

2010-01-01

Seven uranyl(VI) complexes, [UO 2 (acac) 2 (L)] [L=4-methylpyridine (1), 4-ethylpyridine (2), 2,4-dimethylpyridine (3), (-)-nicotine (4), and imidazole (5)], [{UO 2 (acac) 2 } 2 -(4,4'-bipyridine)] (6), and [(2,2'-bipyridine) 2 H][UO 2 (acac)(NO 3 ) 2 ] (7) have been synthesized and characterized crystallographically. The coordination geometry of U has a UNO 6 pentagonal-bipyramidal coordination in 1-6, and a UO 8 hexagonal-bipyramidal coordination in 7. (author)

The Schwarzschild metric: It's the coordinates, stupid!

Science.gov (United States)

Fromholz, Pierre; Poisson, Eric; Will, Clifford M.

2014-04-01

Every general relativity textbook emphasizes that coordinates have no physical meaning. Nevertheless, a coordinate choice must be made in order to carry out real calculations, and that choice can make the difference between a calculation that is simple and one that is a mess. We give a concrete illustration of the maxim that "coordinates matter" using the exact Schwarzschild solution for a vacuum, static spherical spacetime. We review the standard textbook derivation, Schwarzschild's original 1916 derivation, and a derivation using the Landau-Lifshitz formulation of the Einstein field equations. The last derivation is much more complicated, has one aspect for which we have been unable to find a solution, and gives an explicit illustration of the fact that the Schwarzschild geometry can be described in infinitely many coordinate systems.

Geometry of curves and surfaces with Maple

CERN Document Server

Rovenski, Vladimir

2000-01-01

This concise text on geometry with computer modeling presents some elementary methods for analytical modeling and visualization of curves and surfaces. The author systematically examines such powerful tools as 2-D and 3-D animation of geometric images, transformations, shadows, and colors, and then further studies more complex problems in differential geometry. Well-illustrated with more than 350 figures---reproducible using Maple programs in the book---the work is devoted to three main areas: curves, surfaces, and polyhedra. Pedagogical benefits can be found in the large number of Maple programs, some of which are analogous to C++ programs, including those for splines and fractals. To avoid tedious typing, readers will be able to download many of the programs from the Birkhauser web site. Aimed at a broad audience of students, instructors of mathematics, computer scientists, and engineers who have knowledge of analytical geometry, i.e., method of coordinates, this text will be an excellent classroom resource...

KENO-IV/CG, the combinatorial geometry version of the KENO Monte Carlo criticality safety program

International Nuclear Information System (INIS)

West, J.T.; Petrie, L.M.; Fraley, S.K.

1979-09-01

KENO-IV/CG was developed to merge the simple geometry input description utilized by combinatorial geometry with the repeating lattice feature of the original KENO geometry package. The result is a criticality code with the ability to model a complex system of repeating rectangular lattices inside a complicated three-dimensional geometry system. Furthermore, combinatorial geometry was modified to differentiate between combinatorial zones describing a particular KENO BOX to be repeated in a KENO array and those combinatorial zones describing geometry external to an array. This allows the user to maintain a simple coordinate system without any geometric conflict due to spatial overlap. Several difficult criticality design problems have been solved with the new geometry package in KENO-IV/CG, thus illustrating the power of the code to model difficult geometries with a minimum of effort

General Geometry and Geometry of Electromagnetism

OpenAIRE

Shahverdiyev, Shervgi S.

2002-01-01

It is shown that Electromagnetism creates geometry different from Riemannian geometry. General geometry including Riemannian geometry as a special case is constructed. It is proven that the most simplest special case of General Geometry is geometry underlying Electromagnetism. Action for electromagnetic field and Maxwell equations are derived from curvature function of geometry underlying Electromagnetism. And it is shown that equation of motion for a particle interacting with electromagnetic...

Novel 3D Compression Methods for Geometry, Connectivity and Texture

Science.gov (United States)

Siddeq, M. M.; Rodrigues, M. A.

2016-06-01

A large number of applications in medical visualization, games, engineering design, entertainment, heritage, e-commerce and so on require the transmission of 3D models over the Internet or over local networks. 3D data compression is an important requirement for fast data storage, access and transmission within bandwidth limitations. The Wavefront OBJ (object) file format is commonly used to share models due to its clear simple design. Normally each OBJ file contains a large amount of data (e.g. vertices and triangulated faces, normals, texture coordinates and other parameters) describing the mesh surface. In this paper we introduce a new method to compress geometry, connectivity and texture coordinates by a novel Geometry Minimization Algorithm (GM-Algorithm) in connection with arithmetic coding. First, each vertex ( x, y, z) coordinates are encoded to a single value by the GM-Algorithm. Second, triangle faces are encoded by computing the differences between two adjacent vertex locations, which are compressed by arithmetic coding together with texture coordinates. We demonstrate the method on large data sets achieving compression ratios between 87 and 99 % without reduction in the number of reconstructed vertices and triangle faces. The decompression step is based on a Parallel Fast Matching Search Algorithm (Parallel-FMS) to recover the structure of the 3D mesh. A comparative analysis of compression ratios is provided with a number of commonly used 3D file formats such as VRML, OpenCTM and STL highlighting the performance and effectiveness of the proposed method.

Luminescent lanthanide coordination polymers

Energy Technology Data Exchange (ETDEWEB)

Ma, L.; Evans, O.R.; Foxman, B.M.; Lin, W.

1999-12-13

One-dimensional lanthanide coordination polymers with the formula Ln(isonicotinate){sub 3}(H{sub 2}O){sub 2} (Ln = Ce, Pr, Nd, Sm, Eu, Tb; 1a-f) were synthesized by treating nitrate or perchlorate salts of Ln(III) with 4-pyridinecarboxaldehyde under hydro(solvo)thermal conditions. Single-crystal and powder X-ray diffraction studies indicate that these lanthanide coordination polymers adopt two different structures. While Ce(III), Pr(III), and Nd(III) complexes adopt a chain structure with alternating Ln-(carboxylate){sub 2}-Ln and Ln-(carboxylate){sub 4}-Ln linkages, Sm(III), Eu(III), and Tb(III) complexes have a doubly carboxylate-bridged infinite-chain structure with one chelating carboxylate group on each metal center. In both structures, the lanthanide centers also bind to two water molecules to yield an eight-coordinate, square antiprismatic geometry. The pyridine nitrogen atoms of the isonicotinate groups do not coordinate to the metal centers in these lanthanide(III) complexes; instead, they direct the formation of Ln(III) coordination polymers via hydrogen bonding with coordinated water molecules. Photoluminescence measurements show that Tb(isonicotinate){sub 3}(H{sub 2}O){sub 2} is highly emissive at room temperature with a quantum yield of {approximately}90%. These results indicate that highly luminescent lanthanide coordination polymers can be assembled using a combination of coordination and hydrogen bonds. Crystal data for 1a: monoclinic space group P2{sub 1}/c, a = 9.712(2) {angstrom}, b = 19.833(4) {angstrom}, c = 11.616(2) {angstrom}, {beta} = 111.89(3){degree}, Z = 4. Crystal data for 1f: monoclinic space group C2/c, a = 20.253(4) {angstrom}, b = 11.584(2) {angstrom}, c = 9.839(2) {angstrom}, {beta} = 115.64(3){degree}, Z = 8.

Crystal structure of an organic–inorganic supra­molecular salt based on a 4,4′-methyl­enebis(3,5-dimethyl-1H-pyrazol-2-ium) cation and a β-octa­molybdate anion

Science.gov (United States)

Amarante, Tatiana R.; Gonçalves, Isabel S.; Almeida Paz, Filipe A.

2016-01-01

The asymmetric unit of the title compound, bis­[4,4′-methyl­enebis(3,5-dimethyl-1H-pyrazol-2-ium)] β-octa­molybdate, (C11H18N4)2[Mo8O26] or (H4mbdpz)2[Mo8O26], is composed of an H4mbdpz2+ cation and half of the β-octa­molybdate anion which is completed by inversion symmetry. The organic mol­ecular units are engaged in a series of N—H⋯O hydrogen bonds with neighbouring anions, with N⋯O distances and N—H⋯O angles in the ranges 2.730 (2)–2.941 (2) Å and 122–166°, respectively. These inter­actions lead to the formation of a supra­molecular two-dimensional network parallel to the (010) plane. PMID:26958369

Spectral studies of coordination compounds of cobalt(II) with thiosemicarbazone of heterocyclic ketone

Science.gov (United States)

Chandra, Sulekh; Kumar, Umendra

2005-12-01

The paper presents the spectral analysis of cobalt(II) complexes with indoxyl thiosemicarbazone (ITSC) of general composition [CoL 2X 2] (where L = ITSC, X = Cl -, NO 3-, (1/2)SO 42-, NCS -). The geometry of the complexes have been characterized by elemental analysis, molar conductance, magnetic susceptibility measurements and spectral (electronic, IR, EPR, 1H NMR, mass) studies. The various physico-chemical techniques suggested a coordination number of six (octahedral) for chloro, nitrato and thiocyanato complexes. Whereas sulfato complex was found to have five coordinate trigonal-bipyramidal geometry. All the complexes are of high spin type showing magnetic moment corresponding to three unpaired electrons.

Local coordination of polyvalent metal ions in molten halide mixtures

International Nuclear Information System (INIS)

Akdeniz, Z.; Tosi, M.P.

1989-07-01

Ample experimental evidence is available in the literature on the geometry and the stability of local coordination for polyvalent metal ions in molten mixtures of their halides with alkali halides. Recent schemes for classifying this evidence are discussed. Dissociation of tetrahedral halocomplexes in good ionic systems can be viewed as a classical Mott problem of bound-state stability in a conducting matrix. More generally, structural coordinates can be constructed from properties of the component elements, to separate out systems with long-lived fourfold or sixfold coordination and to distinguish between these. (author). 11 refs, 1 fig

Integral Transport Theory in One-dimensional Geometries

Energy Technology Data Exchange (ETDEWEB)

Carlvik, I

1966-06-15

A method called DIT (Discrete Integral Transport) has been developed for the numerical solution of the transport equation in one-dimensional systems. The characteristic features of the method are Gaussian integration over the coordinate as described by Kobayashi and Nishihara, and a particular scheme for the calculation of matrix elements in annular and spherical geometry that has been used for collision probabilities in earlier Flurig programmes. The paper gives a general theory including such things as anisotropic scattering and multi-pole fluxes, and it gives a brief description of the Flurig scheme. Annular geometry is treated in some detail, and corresponding formulae are given for spherical and plane geometry. There are many similarities between DIT and the method of collision probabilities. DIT is in many cases faster, because for a certain accuracy in the fluxes DIT often needs fewer space points than the method of collision probabilities needs regions. Several computer codes using DIT, both one-group and multigroup, have been written. It is anticipated that experience gained in calculations with these codes will be reported in another paper.

Determination of Copper in Different Ethanolic Matrices Using a Chloropropyl Silica Gel Modified with a Nanostructured Cubic Octa(3-aminopropyloctasilsesquioxane

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Devaney Ribeiro Do Carmo

2013-01-01

Full Text Available The chloropropyl silica gel was modified with octa(3-aminopropyloctasilsesquioxane and characterized by Fourier transform infrared (FTIR spectroscopy, nuclear magnetic resonance (NMR, spectroscopies, and surface and area porosity. The specific sorption capacity of metallic ions (Cu2+ and Ni2+ increases in the following solvent order: water < ethanol 42% < ethanol < ketone. The high values of the constant (K in the order of 103 L mol−1 suggested the high adsorbent capacity of the modified silica (SGAPC for Cu2+ and Ni2+. SGAPC was applied to a separation column and shows recoveries of around 100% of copper in samples of sugar cane spirit, vodka, ginger brandy, and ethanol fuel.

Torso geometry reconstruction and body surface electrode localization using three-dimensional photography.

Science.gov (United States)

Perez-Alday, Erick A; Thomas, Jason A; Kabir, Muammar; Sedaghat, Golriz; Rogovoy, Nichole; van Dam, Eelco; van Dam, Peter; Woodward, William; Fuss, Cristina; Ferencik, Maros; Tereshchenko, Larisa G

We conducted a prospective clinical study (n=14; 29% female) to assess the accuracy of a three-dimensional (3D) photography-based method of torso geometry reconstruction and body surface electrodes localization. The position of 74 body surface electrocardiographic (ECG) electrodes (diameter 5mm) was defined by two methods: 3D photography, and CT (marker diameter 2mm) or MRI (marker size 10×20mm) imaging. Bland-Altman analysis showed good agreement in X (bias -2.5 [95% limits of agreement (LoA) -19.5 to 14.3] mm), Y (bias -0.1 [95% LoA -14.1 to 13.9] mm), and Z coordinates (bias -0.8 [95% LoA -15.6 to 14.2] mm), as defined by the CT/MRI imaging, and 3D photography. The average Hausdorff distance between the two torso geometry reconstructions was 11.17±3.05mm. Thus, accurate torso geometry reconstruction using 3D photography is feasible. Body surface ECG electrodes coordinates as defined by the CT/MRI imaging, and 3D photography, are in good agreement. Copyright © 2017 Elsevier Inc. All rights reserved.

Geometric Transformations in Engineering Geometry

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I. F. Borovikov

2015-01-01

Full Text Available Recently, for business purposes, in view of current trends and world experience in training engineers, research and faculty staff there has been a need to transform traditional courses of descriptive geometry into the course of engineering geometry in which the geometrical transformations have to become its main section. On the basis of critical analysis the paper gives suggestions to improve a presentation technique of this section both in the classroom and in academic literature, extend an application scope of geometrical transformations to solve the position and metric tasks and simulation of surfaces, as well as to design complex engineering configurations, which meet a number of pre-specified conditions.The article offers to make a number of considerable amendments to the terms and definitions used in the existing courses of descriptive geometry. It draws some conclusions and makes the appropriate proposals on feasibility of coordination in teaching the movement transformation in the courses of analytical and descriptive geometry. This will provide interdisciplinary team teaching and allow students to be convinced that a combination of analytical and graphic ways to solve geometric tasks is useful and reasonable.The traditional sections of learning courses need to be added with a theory of projective and bi-rational transformations. In terms of application simplicity and convenience it is enough to consider the central transformations when solving the applied tasks. These transformations contain a beam of sub-invariant (low-invariant straight lines on which the invariant curve induces non-involution and involution projectivities. The expediency of nonlinear transformations application is shown in the article by a specific example of geometric modeling of the interfacing surface "spar-blade".Implementation of these suggestions will contribute to a real transformation of a traditional course of descriptive geometry to the engineering geometry

Geometry and Framework Interactions of Zeolite-Encapsulated Copper(II)-Histidine Complexes

NARCIS (Netherlands)

Weckhuysen, B.M.; Grommen, R.; Manikandan, P.; Gao, Y.; Shane, T.; Shane, J.J.; Schoonheydt, R.A.; Goldfarb, D.

2000-01-01

The coordination geometry of zeolite-encapsulated copper(II)-histidine (CuHis) complexes, prepared by ion exchange of the complexes from aqueous solutions into zeolite NaY, was determined by a combination of UV-vis-NIR diffuse reflectance spectroscopy (DRS), X-band EPR, electron-spin-echo envelope

Insulin fibrillation: The influence and coordination of Zn2+

DEFF Research Database (Denmark)

Frankær, Christian Grundahl; Sønderby, Pernille; Bang, Maria Blanner

2017-01-01

fibrils has been debated for some years. We have therefore investigated the influence and binding geometry of zinc in fibrillated insulin using extended X-ray absorption fine-structure and X-ray absorption near-edge structure spectroscopy. The results were validated with fibre diffraction, Transmission...... Electron Microscopy and Thioflavin T fluorescence measurements. It is well-known that Zn2+ ions coordinate and stabilize the hexameric forms of insulin. However, this study is the first to show that zinc indeed binds to the insulin fibrils. Furthermore, zinc influences the kinetics and the morphology...... of the fibrils. It also shows that zinc coordinates to histidine residues in an environment, which is similar to the coordination seen in the insulin R6 hexamers, where three histidine residues and a chloride ion is coordinating the zinc....

AN ENCODING METHOD FOR COMPRESSING GEOGRAPHICAL COORDINATES IN 3D SPACE

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C. Qian

2017-09-01

Full Text Available This paper proposed an encoding method for compressing geographical coordinates in 3D space. By the way of reducing the length of geographical coordinates, it helps to lessen the storage size of geometry information. In addition, the encoding algorithm subdivides the whole space according to octree rules, which enables progressive transmission and loading. Three main steps are included in this method: (1 subdividing the whole 3D geographic space based on octree structure, (2 resampling all the vertices in 3D models, (3 encoding the coordinates of vertices with a combination of Cube Index Code (CIC and Geometry Code. A series of geographical 3D models were applied to evaluate the encoding method. The results showed that this method reduced the storage size of most test data by 90 % or even more under the condition of a speed of encoding and decoding. In conclusion, this method achieved a remarkable compression rate in vertex bit size with a steerable precision loss. It shall be of positive meaning to the web 3d map storing and transmission.

Unusual Coordination Behavior of Cr3+ in Microporous Aluminophosphates

NARCIS (Netherlands)

Beale, AM; Grandjean, D; Kornatowski, J; Glatzel, P; de Groot, FMF; Weckhuysen, BM

2006-01-01

A CrAPO-5 molecular sieve has been investigated with X-ray absorption spectroscopy (EXAFS-XANES) as dehydrated material and after loading with water and ammonia to unravel the coordination geometries of Cr3+ in the framework of a microporous crystalline aluminophosphate, more particularly of the

Coordination chemistry of technetium as related to nuclear medicine

International Nuclear Information System (INIS)

Srivastava, S.C.; Richards, P.

1982-01-01

Significant advances have been made in the area of technetium coordination chemistry during the last five years. The main driving force behind this recent surge of interest in the field has been due to the practical application of technetium-99m in the rapidly growing speciality of nuclear medicine. Technetium-99 is one of the products of nuclear fission reactions, but it was the development of the molybdenum-99-technetium-99m generator about two decades ago that provided the basis for the development of radiopharmaceuticals routinely used in modern diagnostic applications. The chemistry of this element has proven to be quite rich owing to its multiple oxidation states and variable geometry. This can be attributed to its position in the middle of the periodic table. Diagnostic radiopharmaceuticals comprise predominantly III, IV and V oxidation states of Tc and involve a variety of coordination complexes. Even though the chemistry of Tc has been slow to evolve, recent synthetic advances have provided a more scientific basis for the study of a number of compounds with diverse coordination geometries and structures. Ligands with oxygen, nitrogen and sulfur donor atoms have been utilized to elucidate various aspects of the coordination chemistry of Tc. Single crystal X-ray structural analysis has been extensively used to characterize Tc complexes and thus construct a firm foundation for the study of synthetic and mechanistic aspects of the chemistry of this element. (author)

Clinical application of OCTA in observation of macular blood flow density in patients with diabetic retinopathy

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Xiang Xiang

2017-07-01

Full Text Available AIM: Using optical coherence tomography angiography(OCTAto observe the changes and clinical significance of macular blood flow density in patients with diabetic retinopathy(DR.METHODS: Totally 47 eyes(28 patientswith diabetic retinopathy(DRwere enrolled in the DR group. According to the international clinical grading criteria of diabetic retinopathy, 30 eyes(19 patientswith non-proliferative diabetic retinopathy were classified as the NPDR group, and 17 eyes(11 patientswith proliferative diabetic retinopathy were classified as PDR group. A total of 46(27 subjectshealthy eyes with matched age were enrolled in the control group. All the subjects underwent the 3mm×3mm scanning of macular retina by optical coherence tomography angiography(OCTA, obtaining 4 levels of macular blood flow density map. The macular blood flow density at 3 levels, including superficial retinal layer, deep retinal layer and choroidal capillaries layer, were measured. RESULTS: The macular blood flow density of superfical retinal layer, deep retinal layer and choroidal capillaries layer in DR group were 0.4963±0.0840, 0.4798±0.0801 and 0.5290±0.0528, respectively. Among them, the blood flow density of each layer were 0.5064±0.0843,0.4983±0.0766,0.5345±0.0529, respectively, for the NPDR group, and were 0.4786±0.0830, 0.4473±0.0778,0.5192±0.0526, respectively, for the PDR group. For the control group, the density of each layers were 0.5919±0.0704, 0.6301±0.0527, 0.5691±0.0169, respectively. The macular blood flow density was significantly different in the superficial retinal layer, deep retinal layer and choroidal capillary layer between the control group and the NPDR group, as well as the PDR group and the DR group(total PP=0.029, but not in the superficial retina layer and choroid capillary layer(P=0.236, 0.268. CONCLUSION: Compared with the control group, the macular blood flow density of superficial retinal layer, deep retinal layer and choroidal capillary

Crystal structure of poly[N,N-diethyl-2-hy-droxy-ethan-1-aminium [μ3-cyanido-κ(3) C:C:N-di-μ-cyanido-κ(4) C:N-dicuprate(I)

Science.gov (United States)

Corfield, Peter W R; Cleary, Emma; Michalski, Joseph F

2016-07-01

In the title compound, {(C6H16NO)[Cu2(CN)3]} n , the cyanide groups link the Cu(I) atoms into an open three-dimensional anionic network, with the mol-ecular formula Cu2(CN)3 (-). One Cu(I) atom is tetra-hedrally bound to four CN groups, and the other Cu(I) atom is bonded to three CN groups in an approximate trigonal-planar coordination. The tetra-hedrally coordinated Cu(I) atoms are linked into centrosymmetric dimers by the C atoms of two end-on bridging CN groups which bring the Cu(I) atoms into close contact at 2.5171 (7) Å. Two of the cyanide groups bonded to the Cu(I) atoms with trigonal-planar surrounding link the dimeric units into columns along the a axis, and the third links the columns together to form the network. The N,N-di-ethyl-ethano-lamine mol-ecules used in the synthesis have become protonated at the N atoms and are situated in cavities in the network, providing charge neutrality, with no covalent inter-actions between the cations and the anionic network.

Motivic amplitudes and cluster coordinates

International Nuclear Information System (INIS)

Golden, J.K.; Goncharov, A.B.; Spradlin, M.; Vergu, C.; Volovich, A.

2014-01-01

In this paper we study motivic amplitudes — objects which contain all of the essential mathematical content of scattering amplitudes in planar SYM theory in a completely canonical way, free from the ambiguities inherent in any attempt to choose particular functional representatives. We find that the cluster structure on the kinematic configuration space Conf n (ℙ 3 ) underlies the structure of motivic amplitudes. Specifically, we compute explicitly the coproduct of the two-loop seven-particle MHV motivic amplitude A 7,2 M and find that like the previously known six-particle amplitude, it depends only on certain preferred coordinates known in the mathematics literature as cluster X-coordinates on Conf n (ℙ 3 ). We also find intriguing relations between motivic amplitudes and the geometry of generalized associahedrons, to which cluster coordinates have a natural combinatoric connection. For example, the obstruction to A 7,2 M being expressible in terms of classical polylogarithms is most naturally represented by certain quadrilateral faces of the appropriate associahedron. We also find and prove the first known functional equation for the trilogarithm in which all 40 arguments are cluster X-coordinates of a single algebra. In this respect it is similar to Abel’s 5-term dilogarithm identity

Coordination of {Mo142} Ring to La3+ Provides Elliptical {Mo134La10} Ring with a Variety of Coordination Modes

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Eri Ishikawa

2009-12-01

Full Text Available A28-electron reduced C2h-Mo-blue 34Ǻ outer ring diameter circular ring, [Mo142O429H10(H2O49(CH3CO25(C2H5CO2]30- (≡{Mo142(CH3CO25(C2H5CO2} comprising eight carboxylate-coordinated (with disorder {Mo2} linkers and six defect pockets in two inner rings (four and three for each, respectively, reacts with La3+ in aqueous solutions at pH 3.5 to yield a 28-electron reduced elliptical Ci-Mo-blue ring of formula [Mo134O416H20(H2O46{La(H2O5}4{La(H2O7}4{LaCl2(H2O5}2]10- (≡{Mo134La10}, isolated as the Na10[Mo134O416H20(H2O46{La(H2O5}4{La(H2O7}4{LaCl2(H2O5}2]·144 H2O Na+ salt. The elliptical structure of {Mo134La10} showing 36 and 31 Å long and short axes for the outer ring diameters is attributed to four (A-D modes of LaO9/LaO7Cl2 tricapped-trigonal-prismatic coordination (TTP geometries. Two different LaO2(H2O7 and one LaO2(H2O2Cl2 TTP geometries (as A-C modes for each of two inner rings result from the coordination of all three defect pockets of the inner ring for {Mo142(CH3CO25(C2H5CO2}, and two LaO4(H2O5 TTP geometries (as D mode result from the displacement of two (acetate/propionate-coordinated binuclear {Mo2} linkers with La3+ in each inner ring. The isothermal titration calorimetry (ITC of the ring modification from circle to ellipsoid, showing the endothermic reaction of [La3+]/[{Mo142(CH3CO25(C2H5CO2}] = 6/1 with DH = 22 kJ×mol-1, DS = 172 J×K-1×mol-1, DG = −28 kJ×mol-1, and K = 9.9 ´ 104 M-1 at 293 K, leads to the conclusion that the coordination of the defect pockets to La3+ precedes the replacement of the {Mo2} linkers with La3+. 139La- NMR spectrometry of the coordination of {Mo142(CH3CO25(C2H5CO2} ring to La3+ is also discussed.

Coordinate transformations and matter waves cloaking

International Nuclear Information System (INIS)

Mohammadi, G.R.; Moghaddam, A.G.; Mohammadkhani, R.

2016-01-01

Transformation method provides an efficient tool to control wave propagation inside the materials. Using the coordinate transformation approach, we study invisibility cloaks with sphere, cylinder and ellipsoid structures for electronic waves propagation. The underlying physics behind this investigation is the fact that Schrödinger equation with position dependent mass tensor and potentials has a covariant form which follows the coordinate transformation. Using this technique we obtain the exact spatial form of the mass tensor and potentials for a variety of cloaks with different shapes. - Highlights: • Invisibility cloaks for matter waves with three different geometries. • Exact analytical form of the effective mass tensor and potential. • Analogy between cloaking for quantum mechanical waves with classical electromagnetic waves. • Possible experimental realization in engineered semiconducting structures.

Geometries

CERN Document Server

Sossinsky, A B

2012-01-01

The book is an innovative modern exposition of geometry, or rather, of geometries; it is the first textbook in which Felix Klein's Erlangen Program (the action of transformation groups) is systematically used as the basis for defining various geometries. The course of study presented is dedicated to the proposition that all geometries are created equal--although some, of course, remain more equal than others. The author concentrates on several of the more distinguished and beautiful ones, which include what he terms "toy geometries", the geometries of Platonic bodies, discrete geometries, and classical continuous geometries. The text is based on first-year semester course lectures delivered at the Independent University of Moscow in 2003 and 2006. It is by no means a formal algebraic or analytic treatment of geometric topics, but rather, a highly visual exposition containing upwards of 200 illustrations. The reader is expected to possess a familiarity with elementary Euclidean geometry, albeit those lacking t...

Crystal structure of bis-(3-bromo-pyridine-κN)bis-(O-ethyl di-thio-carbonato-κ(2) S,S')nickel(II).

Science.gov (United States)

Kant, Rajni; Kour, Gurvinder; Anthal, Sumati; Neerupama; Sachar, Renu

2015-01-01

In the title mol-ecular complex, [Ni(C3H5OS2)2(C5H4BrN)2], the Ni(2+) cation is located on a centre of inversion and has a distorted octa-hedral N2S4 environment defined by two chelating xanthate ligands and two monodentate pyridine ligands. The C-S bond lengths of the thio-carboxyl-ate group are indicative of a delocalized bond and the O-Csp (2) bond is considerably shorter than the O-Csp (3) bond, consistent with a significant contribution of one resonance form of the xanthate anion that features a formal C=O+ unit and a negative charge on each of the S atoms. The packing of the mol-ecules is stabilized by C-H⋯S and C-H⋯π inter-actions. In addition, π-π inter-actions between the pyridine rings [centroid-to-centroid distance = 3.797 (3) Å] are also present. In the crystal structure, mol-ecules are arranged in rows along [100], forming layers parallel to (010) and (001).

On the Lorentz invariance of bit-string geometry

International Nuclear Information System (INIS)

Noyes, H.P.

1995-09-01

We construct the class of integer-sided triangles and tetrahedra that respectively correspond to two or three discriminately independent bit-strings. In order to specify integer coordinates in this space, we take one vertex of a regular tetrahedron whose common edge length is an even integer as the origin of a line of integer length to the open-quotes pointclose quotes and three integer distances to this open-quotes pointclose quotes from the three remaining vertices of the reference tetrahedron. This - usually chiral - integer coordinate description of bit-string geometry is possible because three discriminately independent bit-strings generate four more; the Hamming measures of these seven strings always allow this geometrical interpretation. On another occasion we intend to prove the rotational invariance of this coordinate description. By identifying the corners of these figures with the positions of recording counters whose clocks are synchronized using the Einstein convention, we define velocities in this space. This suggests that it may be possible to define boosts and discrete Lorentz transformations in a space of integer coordinates. We relate this description to our previous work on measurement accuracy and the discrete ordered calculus of Etter and Kauffman (DOC)

Development of a discrete-ordinate approximation of the neutron transport equation for coupled xy-R-geometry

International Nuclear Information System (INIS)

Maertens, H.D.

1982-01-01

The inhomogenious structure of modern heavy water reactor fuel elements result in a strong spacial dependence of the neutron flux. The flux distribution can be calculated in detail by numerical methods, which describe exactly the geometrical heterogeniety and take into account the neutron flux anisotropy by higher transport theoretical approximations. Starting from the discrete ordinate method an approximation of the neutron transport equation has been developed, allowing for a cylindrical representation of the fuel-elements in a rectangular array of rods. The discretisation of the space variables, is based on the finite-difference approximation, defining a rectangular lattice in a two-dimensional cartesian coordinate system, which can be cut and replaced by circular mesh elements of a partially one-dimensional cylindrical coordinate system at arbitrary space points. To couple the two spacial regions the outer circle line of a cylindrical geometry is approximated in the cartesian system by a polygon with n >= 8. A cylindrical geometry is approximated in the cartesian system by a polygon with n>=8. A cylindrical geometry is thus enclosed by a system of two-dimensional rectangular, triangular and trapezoid mesh elements. The directional distribution of the neutron flux is conserved when switching from the xy-system to the cylindrical coordinate system. The angle discretisation by balanced sets of squares (EQsub(n)) allows a simple definition of transfer-coefficients for the redistribution of the neutron flux due to coordinate transformations. The procedure is verified and tested by selected problems. Possible applications and limits are discussed. (orig.) [de

Geometry

CERN Document Server

Prasolov, V V

2015-01-01

This book provides a systematic introduction to various geometries, including Euclidean, affine, projective, spherical, and hyperbolic geometries. Also included is a chapter on infinite-dimensional generalizations of Euclidean and affine geometries. A uniform approach to different geometries, based on Klein's Erlangen Program is suggested, and similarities of various phenomena in all geometries are traced. An important notion of duality of geometric objects is highlighted throughout the book. The authors also include a detailed presentation of the theory of conics and quadrics, including the theory of conics for non-Euclidean geometries. The book contains many beautiful geometric facts and has plenty of problems, most of them with solutions, which nicely supplement the main text. With more than 150 figures illustrating the arguments, the book can be recommended as a textbook for undergraduate and graduate-level courses in geometry.

Influence of probe geometry on pitot-probe displacement in supersonic turbulent flow

Science.gov (United States)

Allen, J. M.

1975-01-01

An experiment was conducted to determine the varying effects of six different probe-tip and support-shaft configurations on pitot tube displacement. The study was stimulated by discrepancies between supersonic wind-tunnel tests conducted by Wilson and Young (1949) and Allen (1972). Wilson (1973) had concluded that these discrepancies were caused by differences in probe geometry. It is shown that in fact, no major differences in profiles of streamwise velocity over streamwise velocity at boundary-layer edge vs normal coordinate over boundary-layer total thickness result from geometry. The true cause of the discrepancies, however, remains to be discovered.

Classical An-W-geometry

International Nuclear Information System (INIS)

Gervais, J.L.

1993-01-01

By analyzing the extrinsic geometry of two dimensional surfaces chirally embedded in C P n (the C P n W-surface), we give exact treatments in various aspects of the classical W-geometry in the conformal gauge: First, the basis of tangent and normal vectors are defined at regular points of the surface, such that their infinitesimal displacements are given by connections which coincide with the vector potentials of the (conformal) A n -Toda Lax pair. Since the latter is known to be intrinsically related with the W symmetries, this gives the geometrical meaning of the A n W-Algebra. Second, W-surfaces are put in one-to-one correspondence with solutions of the conformally-reduced WZNW model, which is such that the Toda fields give the Cartan part in the Gauss decomposition of its solutions. Third, the additional variables of the Toda hierarchy are used as coordinates of C P n . This allows us to show that W-transformations may be extended as particular diffeomorphisms of this target-space. Higher-dimensional generalizations of the WZNW equations are derived and related with the Zakharov-Shabat equations of the Toda hierarchy. Fourth, singular points are studied from a global viewpoint, using our earlier observation that W-surfaces may be regarded as instantons. The global indices of the W-geometry, which are written in terms of the Toda fields, are shown to be the instanton numbers for associated mappings of W-surfaces into the Grassmannians. The relation with the singularities of W-surface is derived by combining the Toda equations with the Gauss-Bonnet theorem. (orig.)

Optical profilometer using laser based conical triangulation for inspection of inner geometry of corroded pipes in cylindrical coordinates

Science.gov (United States)

Buschinelli, Pedro D. V.; Melo, João. Ricardo C.; Albertazzi, Armando; Santos, João. M. C.; Camerini, Claudio S.

2013-04-01

An axis-symmetrical optical laser triangulation system was developed by the authors to measure the inner geometry of long pipes used in the oil industry. It has a special optical configuration able to acquire shape information of the inner geometry of a section of a pipe from a single image frame. A collimated laser beam is pointed to the tip of a 45° conical mirror. The laser light is reflected in such a way that a radial light sheet is formed and intercepts the inner geometry and forms a bright laser line on a section of the inspected pipe. A camera acquires the image of the laser line through a wide angle lens. An odometer-based triggering system is used to shot the camera to acquire a set of equally spaced images at high speed while the device is moved along the pipe's axis. Image processing is done in real-time (between images acquisitions) thanks to the use of parallel computing technology. The measured geometry is analyzed to identify corrosion damages. The measured geometry and results are graphically presented using virtual reality techniques and devices as 3D glasses and head-mounted displays. The paper describes the measurement principles, calibration strategies, laboratory evaluation of the developed device, as well as, a practical example of a corroded pipe used in an industrial gas production plant.

Dibromidobis(N,N,N′,N′-tetra­methyl­thio­urea-κS)cadmium(II)

Science.gov (United States)

Nawaz, Sidra; Sadaf, Sana; Fettouhi, Mohammed; Fazal, Atif; Ahmad, Saeed

2010-01-01

In the title compound, [CdBr2(C5H12N2S)2], the CdII atom lies on a twofold rotation axis. It exhibits a distorted tetra­hedral coordination environment defined by two S atoms of two tetra­methyl­thio­urea (tmtu) ligands and two bromide ions. The crystal structure is consolidated by C—H⋯N and C—H⋯S hydrogen bonds. PMID:21588180

Complex geometry and quantum string theory

International Nuclear Information System (INIS)

Belavin, A.A.; Knizhnik, V.G.

1986-01-01

Summation over closed oriented surfaces of genus p ≥ 2 (p - loop vacuum amplitudes in boson string theory) in a critical dimensions D=26 is reduced to integration over M p space of complex structures of Riemann surfaces of genus p. The analytic properties of the integration measure as a function of the complex coordinates on M p are studied. It is shown that the measure multiplied by (det Im τ-circumflex) 13 (τ-circumflex is the surface period matrix) is the square of the modulus of a function which is holomorphic on M p and does not vanish anywhere. The function has a second order pole at infinity of compactified space of moduli M p . These properties define the measure uniquely up to a constant multiple and this permits one to set up explicitformulae for p=2,3 in terms of the theta-constants. Power and logarithmic divergences connected with renormalization of the tachyon wave function and of the slope respectively are involved in the theory. Quantum geometry of critical strings turns out to be a complex geometry

Geometry and dynamics of a tidally deformed black hole

International Nuclear Information System (INIS)

Poisson, Eric; Vlasov, Igor

2010-01-01

The metric of a nonrotating black hole deformed by a tidal interaction is calculated and expressed as an expansion in the strength of the tidal coupling. The expansion parameter is the inverse length scale R -1 , where R is the radius of curvature of the external spacetime in which the black hole moves. The expansion begins at order R -2 , and it is carried out through order R -4 . The metric is parametrized by a number of tidal multipole moments, which specify the black hole's tidal environment. The tidal moments are freely-specifiable functions of time that are related to the Weyl tensor of the external spacetime. At order R -2 the metric involves the tidal quadrupole moments E ab and B ab . At order R -3 it involves the time derivative of the quadrupole moments and the tidal octupole moments E abc and B abc . At order R -4 the metric involves the second time derivative of the quadrupole moments, the first time derivative of the octupole moments, the tidal hexadecapole moments E abcd and B abcd , and bilinear combinations of the quadrupole moments. The metric is presented in a light-cone coordinate system that possesses a clear geometrical meaning: The advanced-time coordinate v is constant on past light cones that converge toward the black hole; the angles θ and φ are constant on the null generators of each light cone; and the radial coordinate r is an affine parameter on each generator, which decreases as the light cones converge toward the black hole. The coordinates are well-behaved on the black-hole horizon, and they are adjusted so that the coordinate description of the horizon is the same as in the Schwarzschild geometry: r=2M+O(R -5 ). At the order of accuracy maintained in this work, the horizon is a stationary null hypersurface foliated by apparent horizons; it is an isolated horizon in the sense of Ashtekar and Krishnan. As an application of our results we examine the induced geometry and dynamics of the horizon, and calculate the rate at which the

Tensor calculus in polar coordinates using Jacobi polynomials

Science.gov (United States)

Vasil, Geoffrey M.; Burns, Keaton J.; Lecoanet, Daniel; Olver, Sheehan; Brown, Benjamin P.; Oishi, Jeffrey S.

2016-11-01

Spectral methods are an efficient way to solve partial differential equations on domains possessing certain symmetries. The utility of a method depends strongly on the choice of spectral basis. In this paper we describe a set of bases built out of Jacobi polynomials, and associated operators for solving scalar, vector, and tensor partial differential equations in polar coordinates on a unit disk. By construction, the bases satisfy regularity conditions at r = 0 for any tensorial field. The coordinate singularity in a disk is a prototypical case for many coordinate singularities. The work presented here extends to other geometries. The operators represent covariant derivatives, multiplication by azimuthally symmetric functions, and the tensorial relationship between fields. These arise naturally from relations between classical orthogonal polynomials, and form a Heisenberg algebra. Other past work uses more specific polynomial bases for solving equations in polar coordinates. The main innovation in this paper is to use a larger set of possible bases to achieve maximum bandedness of linear operations. We provide a series of applications of the methods, illustrating their ease-of-use and accuracy.

Intrinsic Losses Based on Information Geometry and Their Applications

Directory of Open Access Journals (Sweden)

Yao Rong

2017-08-01

Full Text Available One main interest of information geometry is to study the properties of statistical models that do not depend on the coordinate systems or model parametrization; thus, it may serve as an analytic tool for intrinsic inference in statistics. In this paper, under the framework of Riemannian geometry and dual geometry, we revisit two commonly-used intrinsic losses which are respectively given by the squared Rao distance and the symmetrized Kullback–Leibler divergence (or Jeffreys divergence. For an exponential family endowed with the Fisher metric and α -connections, the two loss functions are uniformly described as the energy difference along an α -geodesic path, for some α ∈ { − 1 , 0 , 1 } . Subsequently, the two intrinsic losses are utilized to develop Bayesian analyses of covariance matrix estimation and range-spread target detection. We provide an intrinsically unbiased covariance estimator, which is verified to be asymptotically efficient in terms of the intrinsic mean square error. The decision rules deduced by the intrinsic Bayesian criterion provide a geometrical justification for the constant false alarm rate detector based on generalized likelihood ratio principle.

Fuzzy Geometry of Commutative Spaces and Quantum Dynamics

International Nuclear Information System (INIS)

Mayburov, S.N.

2016-01-01

Fuzzy topology and geometry considered as the possible mathematical framework for novel quantum-mechanical formalism. In such formalism the states of massive particle m correspond to the elements of fuzzy manifold called fuzzy points. Due to the manifold weak topology, m space coordinate x acquires principal uncertainty σ_x and described by the positive, normalized density w(r-vector , t) in 3-dimensional case. It’s shown that the evolution of m state on such 3-dimensional manifold corresponds to Shroedinger dynamics of massive quantum particle

Protonated serotonin: Geometry, electronic structures and photophysical properties

Science.gov (United States)

Omidyan, Reza; Amanollahi, Zohreh; Azimi, Gholamhassan

2017-07-01

The geometry and electronic structures of protonated serotonin have been investigated by the aim of MP2 and CC2 methods. The relative stabilities, transition energies and geometry of sixteen different protonated isomers of serotonin have been presented. It has been predicted that protonation does not exhibit essential alteration on the S1 ← S0 electronic transition energy of serotonin. Instead, more complicated photophysical nature in respect to its neutral analogue is suggested for protonated system owing to radiative and non-radiative deactivation pathways. In addition to hydrogen detachment (HD), hydrogen/proton transfer (H/PT) processes from ammonium to indole ring along the NH+⋯ π hydrogen bond have been predicted as the most important photophysical consequences of SERH+ at S1 excited state. The PT processes is suggested to be responsible for fluorescence of SERH+ while the HD driving coordinate is proposed for elucidation of its nonradiative deactivation mechanism.

Decoupling limit and throat geometry of non-susy D3 brane

Energy Technology Data Exchange (ETDEWEB)

Nayek, Kuntal, E-mail: kuntal.nayek@saha.ac.in; Roy, Shibaji, E-mail: shibaji.roy@saha.ac.in

2017-03-10

Recently it has been shown by us that, like BPS Dp branes, bulk gravity gets decoupled from the brane even for the non-susy Dp branes of type II string theories indicating a possible extension of AdS/CFT correspondence for the non-supersymmetric case. In that work, the decoupling of gravity on the non-susy Dp branes has been shown numerically for the general case as well as analytically for some special case. Here we discuss the decoupling limit and the throat geometry of the non-susy D3 brane when the charge associated with the brane is very large. We show that in the decoupling limit the throat geometry of the non-susy D3 brane, under appropriate coordinate change, reduces to the Constable–Myers solution and thus confirming that this solution is indeed the holographic dual of a (non-gravitational) gauge theory discussed there. We also show that when one of the parameters of the solution takes a specific value, it reduces, under another coordinate change, to the five-dimensional solution obtained by Csaki and Reece, again confirming its gauge theory interpretation.

Crystal structure of a mononuclear Ru(II) complex with a back-to-back terpyridine ligand: [RuCl(bpy)(tpy-tpy)](.).

Science.gov (United States)

Rein, Francisca N; Chen, Weizhong; Scott, Brian L; Rocha, Reginaldo C

2015-09-01

We report the structural characterization of [6',6''-bis-(pyridin-2-yl)-2,2':4',4'':2'',2'''-quaterpyridine](2,2'-bi-pyridine)-chlorido-ruthenium(II) hexa-fluorido-phosphate, [RuCl(C10H8N2)(C30H20N6)]PF6, which contains the bidentate ligand 2,2'-bi-pyridine (bpy) and the tridendate ligand 6',6''-bis-(pyridin-2-yl)-2,2':4',4'':2'',2'''-quaterpyridine (tpy-tpy). The [RuCl(bpy)(tpy-tpy)](+) monocation has a distorted octa-hedral geometry at the central Ru(II) ion due to the restricted bite angle [159.32 (16)°] of the tridendate ligand. The Ru-bound tpy and bpy moieties are nearly planar and essentially perpendicular to each other with a dihedral angle of 89.78 (11)° between the least-squares planes. The lengths of the two Ru-N bonds for bpy are 2.028 (4) and 2.075 (4) Å, with the shorter bond being opposite to Ru-Cl. For tpy-tpy, the mean Ru-N distance involving the outer N atoms trans to each other is 2.053 (8) Å, whereas the length of the much shorter bond involving the central N atom is 1.936 (4) Å. The Ru-Cl distance is 2.3982 (16) Å. The free uncoordinated moiety of tpy-tpy adopts a trans,trans conformation about the inter-annular C-C bonds, with adjacent pyridyl rings being only approximately coplanar. The crystal packing shows significant π-π stacking inter-actions based on tpy-tpy. The crystal structure reported here is the first for a tpy-tpy complex of ruthenium.

Rare earth niobate coordination polymers

Science.gov (United States)

Muniz, Collin N.; Patel, Hiral; Fast, Dylan B.; Rohwer, Lauren E. S.; Reinheimer, Eric W.; Dolgos, Michelle; Graham, Matt W.; Nyman, May

2018-03-01

Rare-earth (RE) coordination polymers are infinitely tailorable to yield luminescent materials for various applications. Here we described the synthesis of a heterometallic rare-earth coordination compound ((CH3)2SO)3(RE)NbO(C2O4)3((CH3)2SO) = dimethylsulfoxide, DMSO, (C2O2= oxalate), (RE=La, Ce, Pr, Nd, Sm, Eu, Gd, Tb). The structure was obtained from single crystal X-ray diffraction of the La analogue. The Nb˭O and DMSO terminal-bonding character guides assembly of an open framework structure with noncentrosymmetric RE-coordination geometry, and large spacing between the RE centers. A second structure was observed by PXRD for the smaller rare earths (Dy, Ho, Er, Yb); this structure has not yet been determined. The materials were further characterized using FTIR, and photoluminescence measurements. Characteristic excitation and emission transitions were observed for RE = Nd, Sm, Eu, and Tb. Quantum yield (QY) measurements were performed by exciting Eu and Tb analoges at 394 nm (QY 66%) and 464 nm (QY 71%) for Eu; and 370 nm (QY=40%) for Tb. We attribute the high QY and bright luminescence to two main structure-function properties of the system; namely the absence of water in the structure, and absence of concentration quenching.

Metals in proteins: correlation between the metal-ion type, coordination number and the amino-acid residues involved in the coordination.

Science.gov (United States)

Dokmanić, Ivan; Sikić, Mile; Tomić, Sanja

2008-03-01

Metal ions are constituents of many metalloproteins, in which they have either catalytic (metalloenzymes) or structural functions. In this work, the characteristics of various metals were studied (Cu, Zn, Mg, Mn, Fe, Co, Ni, Cd and Ca in proteins with known crystal structure) as well as the specificity of their environments. The analysis was performed on two data sets: the set of protein structures in the Protein Data Bank (PDB) determined with resolution metal ion and its electron donors and the latter was used to assess the preferred coordination numbers and common combinations of amino-acid residues in the neighbourhood of each metal. Although the metal ions considered predominantly had a valence of two, their preferred coordination number and the type of amino-acid residues that participate in the coordination differed significantly from one metal ion to the next. This study concentrates on finding the specificities of a metal-ion environment, namely the distribution of coordination numbers and the amino-acid residue types that frequently take part in coordination. Furthermore, the correlation between the coordination number and the occurrence of certain amino-acid residues (quartets and triplets) in a metal-ion coordination sphere was analysed. The results obtained are of particular value for the identification and modelling of metal-binding sites in protein structures derived by homology modelling. Knowledge of the geometry and characteristics of the metal-binding sites in metalloproteins of known function can help to more closely determine the biological activity of proteins of unknown function and to aid in design of proteins with specific affinity for certain metals.

Optical geometry

International Nuclear Information System (INIS)

Robinson, I.; Trautman, A.

1988-01-01

The geometry of classical physics is Lorentzian; but weaker geometries are often more appropriate: null geodesics and electromagnetic fields, for example, are well known to be objects of conformal geometry. To deal with a single null congruence, or with the radiative electromagnetic fields associated with it, even less is needed: flag geometry for the first, optical geometry, with which this paper is chiefly concerned, for the second. The authors establish a natural one-to-one correspondence between optical geometries, considered locally, and three-dimensional Cauchy-Riemann structures. A number of Lorentzian geometries are shown to be equivalent from the optical point of view. For example the Goedel universe, the Taub-NUT metric and Hauser's twisting null solution have an optical geometry isomorphic to the one underlying the Robinson congruence in Minkowski space. The authors present general results on the problem of lifting a CR structure to a Lorentz manifold and, in particular, to Minkowski space; and exhibit the relevance of the deviation form to this problem

Differential geometry of curves and surfaces

CERN Document Server

Banchoff, Thomas F

2010-01-01

Students and professors of an undergraduate course in differential geometry will appreciate the clear exposition and comprehensive exercises in this book that focuses on the geometric properties of curves and surfaces, one- and two-dimensional objects in Euclidean space. The problems generally relate to questions of local properties (the properties observed at a point on the curve or surface) or global properties (the properties of the object as a whole). Some of the more interesting theorems explore relationships between local and global properties. A special feature is the availability of accompanying online interactive java applets coordinated with each section. The applets allow students to investigate and manipulate curves and surfaces to develop intuition and to help analyze geometric phenomena.

Introducing geometry concept based on history of Islamic geometry

Science.gov (United States)

Maarif, S.; Wahyudin; Raditya, A.; Perbowo, K. S.

2018-01-01

Geometry is one of the areas of mathematics interesting to discuss. Geometry also has a long history in mathematical developments. Therefore, it is important integrated historical development of geometry in the classroom to increase’ knowledge of how mathematicians earlier finding and constructing a geometric concept. Introduction geometrical concept can be started by introducing the Muslim mathematician who invented these concepts so that students can understand in detail how a concept of geometry can be found. However, the history of mathematics development, especially history of Islamic geometry today is less popular in the world of education in Indonesia. There are several concepts discovered by Muslim mathematicians that should be appreciated by the students in learning geometry. Great ideas of mathematicians Muslim can be used as study materials to supplement religious character values taught by Muslim mathematicians. Additionally, by integrating the history of geometry in teaching geometry are expected to improve motivation and geometrical understanding concept.

Dechlorination of the dietary nona-chlorinated toxaphene congeners 62 and 50 into the octa-chlorinated toxaphene congeners 44 and 40 in zebrafish (Danio rerio) and Atlantic salmon (Salmo salar)

Energy Technology Data Exchange (ETDEWEB)

Berntssen, M.H.G., E-mail: marc.berntssen@nifes.no [National Institute of Nutrition and Seafood Research (NIFES), Postbox 2029 Nordnes, 5817 Bergen (Norway); Lundebye, A.-K.; Hop-Johannessen, L.; Lock, E.-J. [National Institute of Nutrition and Seafood Research (NIFES), Postbox 2029 Nordnes, 5817 Bergen (Norway)

2012-05-15

Graphical abstract: - Abstract: The relative feed-to-fish accumulation and possible biotransformation of the nona-chlorinated toxaphene congeners currently included in EU-legislation (CHB-50 and -62) and the octa-chlorinated congeners recommended by the European Food Safety Authority to be included in future surveillance of fish samples (CHB-40, 41, and 44) were investigated in the present study. Model fish Danio rerio were fed either (a) diets spiked with a combination as well as the pure individual toxaphene congeners CHB-50 or 62 or (b) diets spiked with the combination of CHB N-Ary-Summation 50 + 62 and/or CHB N-Ary-Summation 40 + 41 + 44. In addition, seawater adapted Atlantic salmon smolts were fed technical toxaphene enriched feeds for 62 days. Zebrafish fed a diet containing CHB-50 and CHB-62 accumulated newly formed CHB-40 and 41 and CHB-44, respectively. The biomagnifications factors (BMF) of the toxaphene congeners in Atlantic salmon muscle from the feeds spiked with technical toxaphene were significantly correlated with their relative lipophilicity (expressed as log K{sub ow}). An exception was CHB-44 which had a higher BMF than could be expected from its specific log K{sub ow}, reflecting that CHB-44 is a metabolite formed under dietary exposure to CHB-62. This paper reports the in vivo dechlorination of nona-chlorinated toxaphene congeners into octa-chlorinated congeners in feeding trials with a model fish (zebrafish) and an oily food fish (Atlantic salmon).

Dechlorination of the dietary nona-chlorinated toxaphene congeners 62 and 50 into the octa-chlorinated toxaphene congeners 44 and 40 in zebrafish (Danio rerio) and Atlantic salmon (Salmo salar)

International Nuclear Information System (INIS)

Berntssen, M.H.G.; Lundebye, A.-K.; Hop-Johannessen, L.; Lock, E.-J.

2012-01-01

Graphical abstract: - Abstract: The relative feed-to-fish accumulation and possible biotransformation of the nona-chlorinated toxaphene congeners currently included in EU-legislation (CHB-50 and -62) and the octa-chlorinated congeners recommended by the European Food Safety Authority to be included in future surveillance of fish samples (CHB-40, 41, and 44) were investigated in the present study. Model fish Danio rerio were fed either (a) diets spiked with a combination as well as the pure individual toxaphene congeners CHB-50 or 62 or (b) diets spiked with the combination of CHB ∑50 + 62 and/or CHB ∑40 + 41 + 44. In addition, seawater adapted Atlantic salmon smolts were fed technical toxaphene enriched feeds for 62 days. Zebrafish fed a diet containing CHB-50 and CHB-62 accumulated newly formed CHB-40 and 41 and CHB-44, respectively. The biomagnifications factors (BMF) of the toxaphene congeners in Atlantic salmon muscle from the feeds spiked with technical toxaphene were significantly correlated with their relative lipophilicity (expressed as log K ow ). An exception was CHB-44 which had a higher BMF than could be expected from its specific log K ow , reflecting that CHB-44 is a metabolite formed under dietary exposure to CHB-62. This paper reports the in vivo dechlorination of nona-chlorinated toxaphene congeners into octa-chlorinated congeners in feeding trials with a model fish (zebrafish) and an oily food fish (Atlantic salmon).

Crystal structure of bis­(3-bromo­pyridine-κN)bis­(O-ethyl di­thio­carbonato-κ2 S,S′)nickel(II)

Science.gov (United States)

Kant, Rajni; Kour, Gurvinder; Anthal, Sumati; Neerupama; Sachar, Renu

2015-01-01

In the title mol­ecular complex, [Ni(C3H5OS2)2(C5H4BrN)2], the Ni2+ cation is located on a centre of inversion and has a distorted octa­hedral N2S4 environment defined by two chelating xanthate ligands and two monodentate pyridine ligands. The C—S bond lengths of the thio­carboxyl­ate group are indicative of a delocalized bond and the O—Csp 2 bond is considerably shorter than the O—Csp 3 bond, consistent with a significant contribution of one resonance form of the xanthate anion that features a formal C=O+ unit and a negative charge on each of the S atoms. The packing of the mol­ecules is stabilized by C—H⋯S and C—H⋯π inter­actions. In addition, π–π inter­actions between the pyridine rings [centroid-to-centroid distance = 3.797 (3) Å] are also present. In the crystal structure, mol­ecules are arranged in rows along [100], forming layers parallel to (010) and (001). PMID:25705471

catena-Poly[bis(1,3-benzo-thia-zol-3-ium) [[di-chlorido-anti-monate(III)]-di-μ-chlorido-μ-oxido-[chlorido-anti-monate(III)]-μ-chlorido

Science.gov (United States)

Chebout, Oussama; Boudraa, Mhamed; Bouacida, Sofiane; Merazig, Hocine; Boudaren, Chaouki

2016-02-01

The title compound, {(C7H6NS)2[Sb2Cl6O]} n , contains two benzo-thia-zolidium cations and one tri-μ-chlorido-tri-chlorido-μ-oxido-di-anti-monate(III) anion. The structure of the inorganic cation may be described as as being built up from two polyhedra, i.e. a square-pyramidal SbCl4O and a distorted octa-hedral SbOCl5 unit, sharing a common face (comprising the O atom and two Cl atoms). The two benzo-thia-zole cations are quasi-planar and subtend a dihedral angle of 19.93 (5)°. The crystal packing can be described by alternating (100) layers and [001] chains of the organic cations and inorganic anions connected through an extensive three-dimensional network of N-H⋯Cl, C-H⋯O and C-H⋯Cl hydrogen bonds. This is consolidated by slipped π-π stacking, with centroid-to-centroid distances between the benzo-thia-zole rings of 3.7111 (18)-3.8452 (16) Å. These inter-actions link the mol-ecules within the layers and also link the layers together and reinforce the cohesion of the ionic structure.

The generator coordinate method in nuclear physics

International Nuclear Information System (INIS)

Giraud, B.G.

1981-01-01

The generator coordinate method is introduced as a physical description of a N-body system in a subspace of a reduced number of degrees of freedom. Special attention is placed on the identification of these special, 'collective' degrees of freedom. It is shown in particular that the method has close links with the Born-Oppenheimer approximation and also that considerations of differential geometry are useful in the theory. A set of applications is discussed and in particular the case of nuclear collisions is considered. (Author) [pt

Geometry through history Euclidean, hyperbolic, and projective geometries

CERN Document Server

Dillon, Meighan I

2018-01-01

Presented as an engaging discourse, this textbook invites readers to delve into the historical origins and uses of geometry. The narrative traces the influence of Euclid’s system of geometry, as developed in his classic text The Elements, through the Arabic period, the modern era in the West, and up to twentieth century mathematics. Axioms and proof methods used by mathematicians from those periods are explored alongside the problems in Euclidean geometry that lead to their work. Students cultivate skills applicable to much of modern mathematics through sections that integrate concepts like projective and hyperbolic geometry with representative proof-based exercises. For its sophisticated account of ancient to modern geometries, this text assumes only a year of college mathematics as it builds towards its conclusion with algebraic curves and quaternions. Euclid’s work has affected geometry for thousands of years, so this text has something to offer to anyone who wants to broaden their appreciation for the...

One dimensional coordination polymers: Synthesis, crystal structures and spectroscopic properties

Science.gov (United States)

Karaağaç, Dursun; Kürkçüoğlu, Güneş Süheyla; Şenyel, Mustafa; Şahin, Onur

2016-11-01

Two new one dimensional (1D) cyanide complexes, namely [M(4-aepy)2(H2O)2][Pt(CN)4], (4-aepy = 4-(2-aminoethyl)pyridine M = Cu(II) (1) or Zn(II) (2)), have been synthesized and characterized by vibrational (FT-IR and Raman) spectroscopy, single crystal X-ray diffraction, thermal and elemental analyses techniques. The crystallographic analyses reveal that 1 and 2 are isomorphous and isostructural, and crystallize in the monoclinic system and C2 space group. The Pt(II) ions are coordinated by four cyanide-carbon atoms in the square-planar geometry and the [Pt(CN)4]2- ions act as a counter ion. The M(II) ions display an N4O2 coordination sphere with a distorted octahedral geometry, the nitrogen donors belonging to four molecules of the organic 4-aepy that act as unidentate ligands and two oxygen atoms from aqua ligands. The crystal structures of 1 and 2 are similar each other and linked via intermolecular hydrogen bonding, Pt⋯π interactions to form 3D supramolecular network. Vibration assignments of all the observed bands are given and the spectral features also supported to the crystal structures of the complexes.

Architectural geometry

KAUST Repository

Pottmann, Helmut

2014-11-26

Around 2005 it became apparent in the geometry processing community that freeform architecture contains many problems of a geometric nature to be solved, and many opportunities for optimization which however require geometric understanding. This area of research, which has been called architectural geometry, meanwhile contains a great wealth of individual contributions which are relevant in various fields. For mathematicians, the relation to discrete differential geometry is significant, in particular the integrable system viewpoint. Besides, new application contexts have become available for quite some old-established concepts. Regarding graphics and geometry processing, architectural geometry yields interesting new questions but also new objects, e.g. replacing meshes by other combinatorial arrangements. Numerical optimization plays a major role but in itself would be powerless without geometric understanding. Summing up, architectural geometry has become a rewarding field of study. We here survey the main directions which have been pursued, we show real projects where geometric considerations have played a role, and we outline open problems which we think are significant for the future development of both theory and practice of architectural geometry.

Architectural geometry

KAUST Repository

Pottmann, Helmut; Eigensatz, Michael; Vaxman, Amir; Wallner, Johannes

2014-01-01

Around 2005 it became apparent in the geometry processing community that freeform architecture contains many problems of a geometric nature to be solved, and many opportunities for optimization which however require geometric understanding. This area of research, which has been called architectural geometry, meanwhile contains a great wealth of individual contributions which are relevant in various fields. For mathematicians, the relation to discrete differential geometry is significant, in particular the integrable system viewpoint. Besides, new application contexts have become available for quite some old-established concepts. Regarding graphics and geometry processing, architectural geometry yields interesting new questions but also new objects, e.g. replacing meshes by other combinatorial arrangements. Numerical optimization plays a major role but in itself would be powerless without geometric understanding. Summing up, architectural geometry has become a rewarding field of study. We here survey the main directions which have been pursued, we show real projects where geometric considerations have played a role, and we outline open problems which we think are significant for the future development of both theory and practice of architectural geometry.

A Stable Coordination Complex of Rh(IV) in an N,O-Donor Environment

Energy Technology Data Exchange (ETDEWEB)

Sinha, Shashi B. [Department of Chemistry, Yale University, 225 Prospect; Shopov, Dimitar Y. [Department of Chemistry, Yale University, 225 Prospect; Sharninghausen, Liam S. [Department of Chemistry, Yale University, 225 Prospect; Vinyard, David J. [Department of Chemistry, Yale University, 225 Prospect; Mercado, Brandon Q. [Department of Chemistry, Yale University, 225 Prospect; Brudvig, Gary W. [Department of Chemistry, Yale University, 225 Prospect; Crabtree, Robert H. [Department of Chemistry, Yale University, 225 Prospect

2015-12-10

We describe facial and meridional isomers of [RhIII(pyalk)3], as well as meridional [RhIV(pyalk)3]+ {pyalk =2-(2-pyridyl)-2-propanoate}, the first coordination complex in an N,O-donor environment to show a clean, reversible RhIII/IV redox couple and to have a stable Rh(IV) form, which we characterize by EPR and UV–visible spectroscopy as well as X-ray crystallography. The unprecedented stability of the Rh(IV) species is ascribed to the exceptional donor strength of the ligands, their oxidation resistance, and the meridional coordination geometry.

Using satellite technology (global positioning system) to teach the spherical polar coordinate system

International Nuclear Information System (INIS)

O'Brien, William P Jr

2003-01-01

Students discover the equivalence between plausible geographic variables (co-latitude and longitude) of the Earth and less-familiar geometric variables (polar and azimuthal angles) of spherical polar coordinates by collecting and analysing positional data recorded during field exercises with a handheld global positioning system (GPS) receiver. This pedagogical approach to teaching spherical geometry, based on field experience rather than classroom theory, uses GPS technology to capture the curiosity of contemporary students, technical or otherwise, who might not normally find the topic of the spherical polar coordinate system comprehensible, relevant or interesting

Two lectures on D-geometry and noncommutative geometry

International Nuclear Information System (INIS)

Douglas, M.R.

1999-01-01

This is a write-up of lectures given at the 1998 Spring School at the Abdus Salam ICTP. We give a conceptual introduction to D-geometry, the study of geometry as seen by D-branes in string theory, and to noncommutative geometry as it has appeared in D-brane and Matrix theory physics. (author)

Twistor geometry

NARCIS (Netherlands)

van den Broek, P.M.

1984-01-01

The aim of this paper is to give a detailed exposition of the relation between the geometry of twistor space and the geometry of Minkowski space. The paper has a didactical purpose; no use has been made of differential geometry and cohomology.

A numerical calculation method for flow discretisation in complex geometry with body-fitted grids

International Nuclear Information System (INIS)

Jin, X.

2001-04-01

A numerical calculation method basing on body fitted grids is developed in this work for computational fluid dynamics in complex geometry. The method solves the conservation equations in a general nonorthogonal coordinate system which matches the curvilinear boundary. The nonorthogonal, patched grid is generated by a grid generator which solves algebraic equations. By means of an interface its geometrical data can be used by this method. The conservation equations are transformed from the Cartesian system to a general curvilinear system keeping the physical Cartesian velocity components as dependent variables. Using a staggered arrangement of variables, the three Cartesian velocity components are defined on every cell surface. Thus the coupling between pressure and velocity is ensured, and numerical oscillations are avoided. The contravariant velocity for calculating mass flux on one cell surface is resulting from dependent Cartesian velocity components. After the discretisation and linear interpolation, a three dimensional 19-point pressure equation is found. Using the explicit treatment for cross-derivative terms, it reduces to the usual 7-point equation. Under the same data and process structure, this method is compatible with the code FLUTAN using Cartesian coordinates. In order to verify this method, several laminar flows are simulated in orthogonal grids at tilted space directions and in nonorthogonal grids with variations of cell angles. The simulated flow types are considered like various duct flows, transient heat conduction, natural convection in a chimney and natural convection in cavities. Their results achieve very good agreement with analytical solutions or empirical data. Convergence for highly nonorthogonal grids is obtained. After the successful validation of this method, it is applied for a reactor safety case. A transient natural convection flow for an optional sump cooling concept SUCO is simulated. The numerical result is comparable with the

A numerical calculation method for flow discretisation in complex geometry with body-fitted grids; Rechenverfahren zur Diskretisierung von Stroemungen in komplexer Geometrie mittels koerperangepasster Gitter

Energy Technology Data Exchange (ETDEWEB)

Jin, X.

2001-04-01

A numerical calculation method basing on body fitted grids is developed in this work for computational fluid dynamics in complex geometry. The method solves the conservation equations in a general nonorthogonal coordinate system which matches the curvilinear boundary. The nonorthogonal, patched grid is generated by a grid generator which solves algebraic equations. By means of an interface its geometrical data can be used by this method. The conservation equations are transformed from the Cartesian system to a general curvilinear system keeping the physical Cartesian velocity components as dependent variables. Using a staggered arrangement of variables, the three Cartesian velocity components are defined on every cell surface. Thus the coupling between pressure and velocity is ensured, and numerical oscillations are avoided. The contravariant velocity for calculating mass flux on one cell surface is resulting from dependent Cartesian velocity components. After the discretisation and linear interpolation, a three dimensional 19-point pressure equation is found. Using the explicit treatment for cross-derivative terms, it reduces to the usual 7-point equation. Under the same data and process structure, this method is compatible with the code FLUTAN using Cartesian coordinates. In order to verify this method, several laminar flows are simulated in orthogonal grids at tilted space directions and in nonorthogonal grids with variations of cell angles. The simulated flow types are considered like various duct flows, transient heat conduction, natural convection in a chimney and natural convection in cavities. Their results achieve very good agreement with analytical solutions or empirical data. Convergence for highly nonorthogonal grids is obtained. After the successful validation of this method, it is applied for a reactor safety case. A transient natural convection flow for an optional sump cooling concept SUCO is simulated. The numerical result is comparable with the

Geometry

Indian Academy of Sciences (India)

. In the previous article we looked at the origins of synthetic and analytic geometry. More practical minded people, the builders and navigators, were studying two other aspects of geometry- trigonometry and integral calculus. These are actually ...

Hyperunified field theory and gravitational gauge-geometry duality

International Nuclear Information System (INIS)

Wu, Yue-Liang

2018-01-01

A hyperunified field theory is built in detail based on the postulates of gauge invariance and coordinate independence along with the conformal scaling symmetry. All elementary particles are merged into a single hyper-spinor field and all basic forces are unified into a fundamental interaction governed by the hyper-spin gauge symmetry SP(1, D h - 1). The dimension D h of hyper-spacetime is conjectured to have a physical origin in correlation with the hyper-spin charge of elementary particles. The hyper-gravifield fiber bundle structure of biframe hyper-spacetime appears naturally with the globally flat Minkowski hyper-spacetime as a base spacetime and the locally flat hyper-gravifield spacetime as a fiber that is viewed as a dynamically emerged hyper-spacetime characterized by a non-commutative geometry. The gravitational origin of gauge symmetry is revealed with the hyper-gravifield that plays an essential role as a Goldstone-like field. The gauge-gravity and gravity-geometry correspondences bring about the gravitational gauge-geometry duality. The basic properties of hyperunified field theory and the issue on the fundamental scale are analyzed within the framework of quantum field theory, which allows us to describe the laws of nature in deriving the gauge gravitational equation with the conserved current and the geometric gravitational equations of Einstein-like type and beyond. (orig.)

Hyperunified field theory and gravitational gauge-geometry duality

Energy Technology Data Exchange (ETDEWEB)

Wu, Yue-Liang [International Centre for Theoretical Physics Asia-Pacific (ICTP-AP), Beijing (China); Chinese Academy of Sciences, Institute of Theoretical Physics, Beijing (China); University of Chinese Academy of Sciences (UCAS), Beijing (China)

2018-01-15

A hyperunified field theory is built in detail based on the postulates of gauge invariance and coordinate independence along with the conformal scaling symmetry. All elementary particles are merged into a single hyper-spinor field and all basic forces are unified into a fundamental interaction governed by the hyper-spin gauge symmetry SP(1, D{sub h} - 1). The dimension D{sub h} of hyper-spacetime is conjectured to have a physical origin in correlation with the hyper-spin charge of elementary particles. The hyper-gravifield fiber bundle structure of biframe hyper-spacetime appears naturally with the globally flat Minkowski hyper-spacetime as a base spacetime and the locally flat hyper-gravifield spacetime as a fiber that is viewed as a dynamically emerged hyper-spacetime characterized by a non-commutative geometry. The gravitational origin of gauge symmetry is revealed with the hyper-gravifield that plays an essential role as a Goldstone-like field. The gauge-gravity and gravity-geometry correspondences bring about the gravitational gauge-geometry duality. The basic properties of hyperunified field theory and the issue on the fundamental scale are analyzed within the framework of quantum field theory, which allows us to describe the laws of nature in deriving the gauge gravitational equation with the conserved current and the geometric gravitational equations of Einstein-like type and beyond. (orig.)

Hyperunified field theory and gravitational gauge-geometry duality

Science.gov (United States)

Wu, Yue-Liang

2018-01-01

A hyperunified field theory is built in detail based on the postulates of gauge invariance and coordinate independence along with the conformal scaling symmetry. All elementary particles are merged into a single hyper-spinor field and all basic forces are unified into a fundamental interaction governed by the hyper-spin gauge symmetry SP(1, D_h-1). The dimension D_h of hyper-spacetime is conjectured to have a physical origin in correlation with the hyper-spin charge of elementary particles. The hyper-gravifield fiber bundle structure of biframe hyper-spacetime appears naturally with the globally flat Minkowski hyper-spacetime as a base spacetime and the locally flat hyper-gravifield spacetime as a fiber that is viewed as a dynamically emerged hyper-spacetime characterized by a non-commutative geometry. The gravitational origin of gauge symmetry is revealed with the hyper-gravifield that plays an essential role as a Goldstone-like field. The gauge-gravity and gravity-geometry correspondences bring about the gravitational gauge-geometry duality. The basic properties of hyperunified field theory and the issue on the fundamental scale are analyzed within the framework of quantum field theory, which allows us to describe the laws of nature in deriving the gauge gravitational equation with the conserved current and the geometric gravitational equations of Einstein-like type and beyond.

Automated calculation of point A coordinates for CT-based high-dose-rate brachytherapy of cervical cancer

Directory of Open Access Journals (Sweden)

Hyejoo Kang

2017-07-01

Full Text Available Purpose: The goal is to develop a stand-alone application, which automatically and consistently computes the coordinates of the dose calculation point recommended by the American Brachytherapy Society (i.e., point A based solely on the implanted applicator geometry for cervical cancer brachytherapy. Material and methods: The application calculates point A coordinates from the source dwell geometries in the computed tomography (CT scans, and outputs the 3D coordinates in the left and right directions. The algorithm was tested on 34 CT scans of 7 patients treated with high-dose-rate (HDR brachytherapy using tandem and ovoid applicators. A single experienced user retrospectively and manually inserted point A into each CT scan, whose coordinates were used as the “gold standard” for all comparisons. The gold standard was subtracted from the automatically calculated points, a second manual placement by the same experienced user, and the clinically used point coordinates inserted by multiple planners. Coordinate differences and corresponding variances were compared using nonparametric tests. Results: Automatically calculated, manually placed, and clinically used points agree with the gold standard to < 1 mm, 1 mm, 2 mm, respectively. When compared to the gold standard, the average and standard deviation of the 3D coordinate differences were 0.35 ± 0.14 mm from automatically calculated points, 0.38 ± 0.21 mm from the second manual placement, and 0.71 ± 0.44 mm from the clinically used point coordinates. Both the mean and standard deviations of the 3D coordinate differences were statistically significantly different from the gold standard, when point A was placed by multiple users (p < 0.05 but not when placed repeatedly by a single user or when calculated automatically. There were no statistical differences in doses, which agree to within 1-2% on average for all three groups. Conclusions: The study demonstrates that the automated algorithm

Geometry-invariant GRIN lens: finite ray tracing.

Science.gov (United States)

Bahrami, Mehdi; Goncharov, Alexander V

2014-11-17

The refractive index distribution of the geometry-invariant gradient refractive index lens (GIGL) model is derived as a function of Cartesian coordinates. The adjustable external geometry of the GIGL model aims to mimic the shape of the human and animal crystalline lens. The refractive index distribution is based on an adjustable power-law profile, which provides additional flexibility of the model. An analytical method for layer-by-layer finite ray tracing through the GIGL model is developed and used to calculate aberrations of the GIGL model. The result of the finite ray tracing aberrations of the GIGL model are compared to those obtained with paraxial ray tracing. The derived analytical expression for the refractive index distribution can be employed in the reconstruction processes of the eye using the conventional ray tracing methods. The layer-by-layer finite ray tracing approach would be an asset in ray tracing through a modified GIGL model, where the refractive index distribution cannot be described analytically. Using the layer-by-layer finite ray-tracing method, the potential of the GIGL model in representing continuous as well as shell-like layered structures is illustrated and the results for both cases are presented and analysed.

Molecular geometry

CERN Document Server

Rodger, Alison

1995-01-01

Molecular Geometry discusses topics relevant to the arrangement of atoms. The book is comprised of seven chapters that tackle several areas of molecular geometry. Chapter 1 reviews the definition and determination of molecular geometry, while Chapter 2 discusses the unified view of stereochemistry and stereochemical changes. Chapter 3 covers the geometry of molecules of second row atoms, and Chapter 4 deals with the main group elements beyond the second row. The book also talks about the complexes of transition metals and f-block elements, and then covers the organometallic compounds and trans

Hydrothermal synthesis and characterization of a binuclear complex and a coordination

Directory of Open Access Journals (Sweden)

Reza Mohamadinasab

2010-06-01

Full Text Available Two new copper complexes [(bipy(pydcCu(μ-OCO-pydcCu(bipy(H2O].3.5H¬2O (1 and {[(μ2-C2O4(2,2'-bipyCu].2H2O}n (2 (pydcH2 = pyridine-2,6-dicarboxylilic acid, bipy = 2,2'-bipyridine have been hydrothermally synthesized. Both complexes were characterized by IR spectroscopy, elemental analysis and single crystal X-ray diffraction studies. Complex 1 consists of two independent neutral molecules. In every moiety, metal ion center is in a distorted octahedral geometry. Coordination polymer (2 has been prepared from the reaction of bis-(cyclohexanone-oxal-dihydrazone,2,2'-bipyridine and Cu(NO32 in basic solution and under hydrothermal condition. The results showed that the bis-(cyclohexanone-oxal-dihydrazone was converted to oxalate ion under heating and basic pH. Each metal ion center in 2 is in a distorted octahedral geometry and is coordinated by four oxygen atoms of two bridged oxalate ions and two nitrogen atoms of 2,2'-bipyridine molecules. In the crystal structure of 2, some H-bonds and π-π interaction cause formation of a 3D network.

Influence of Surface Geometry of Grating Substrate on Director in Nematic Liquid Crystal Cell

International Nuclear Information System (INIS)

Ye Wenjiang; Xing Hongyu; Yang Guochen; Zhang Zhidong; Sun Yubao; Chen Guoying; Xuan Li

2011-01-01

The director in nematic liquid crystal cell with a weak anchoring grating substrate and a strong anchoring planar substrate is relative to the coordinates x and z. The influence of the surface geometry of the grating substrate in the cell on the director profile is numerically simulated using the two-dimensional finite-difference iterative method under the condition of one elastic constant approximation and zero driven voltage. The deepness of groove and the cell gap affect the distribution of director. For the relatively shallow groove and the relatively thick cell gap, the director is only dependent on the coordinate z. For the relatively deep groove and the relatively thin cell gap, the director must be dependent on the two coordinates x and z because of the increased elastic strain energy induced by the grating surface. (condensed matter: structural, mechanical, and thermal properties)

Synthesis, Structure and Properties of Two Novel 2D Zinc(II) Coordination Polymers based on Fluconazole and Benzene Carboxylic Acid

Energy Technology Data Exchange (ETDEWEB)

Pan, Ganghong; Tang, Jingniu; Xu, Wenjia; Liang, Peng; Huang, Zhongjing [Guangxi University for Nationalities, Nanning (China)

2013-12-15

The design and synthesis of coordination polymers have aroused great interest owing to their intriguing aesthetic structures and potential applications in nonlinear optics, gas storage, ion exchange, luminescence, magnetism and catalysis. Self-assembly of bridging organic ligands (connectors) and multi-connected metal ions can give rise to various types of interesting coordination polymers. Since metal ion Zn(II) with d{sup 10} electronic configuration permits a variety of coordination numbers and geometries which are not dependent on ligand field stabilization but on ligand size and charge, it is well suited for the construction of various coordination polymers. Its borderline hardness allows the coordination of N, O and S donor atoms.

Cisplatin coordination chemistry determination at hen egg white lysozyme His15 with ligand distances and angles, and their standard uncertainties, and also reporting a split occupancy effect

NARCIS (Netherlands)

Helliwell, John R.; Tanley, Simon W. M.; Schreurs, Antoine M. M.; Kroon - Batenburg, Louise

2016-01-01

Following the interest of L Messori and A Merlino 2016 Coordination Chemistry Reviews in the platinum ions coordination geometries in our PDB entries 4dd4 and 4dd6 we have extended our original analyses.

Coordination diversity of new mononucleating hydrazone in 3d metal complexes: Synthesis, characterization and structural studies

Directory of Open Access Journals (Sweden)

RAJESH S. BALIGAR

2006-12-01

Full Text Available The mononucleating hydrazone ligand LH3, a condensation product of salicyloylhydrazine and (2-formylphenoxyacetic acid, was synthesized and its coordination behavior with first row transition metal(II ions was investigated by isolating and elucidating the structure of the complexes using elemental analysis, conductivity and magnetic susceptibility measurements, as well as IR, 1H-NMR, electronic and EPR spectral techniques. The ligand forms mononuclear metal(II complexes of the type [CoLH(H2O2], [NiLH(H2O2, [CuLH] and [ZnLH]. The ligand field parameters, Dq, B and b values, in the case of the cobalt and nickel complexes support not only the octahedral geometry around the metal ion, but also imply the covalent nature of the bonding in the complexes. The EPR study revealed the presence of a spin exchange interaction in the solid copper complex and the covalent nature of the bonding. The 1H-NMR study of the zinc(II complex indicated the non-involvement of the COOH group in the coordination. The physico-chemical study supports for the presence of octahedral geometry around cobalt(II, nickel(II and tetrahedral geometry around copper(II and zinc(II ions.

Co(II) Coordination in Prokaryotic Zinc Finger Domains as Revealed by UV-Vis Spectroscopy

Science.gov (United States)

Sivo, Valeria; D'Abrosca, Gianluca; Russo, Luigi; Iacovino, Rosa; Pedone, Paolo Vincenzo; Fattorusso, Roberto

2017-01-01

Co(II) electronic configuration allows its use as a spectroscopic probe in UV-Vis experiments to characterize the metal coordination sphere that is an essential component of the functional structure of zinc-binding proteins and to evaluate the metal ion affinities of these proteins. Here, exploiting the capability of the prokaryotic zinc finger to use different combinations of residues to properly coordinate the structural metal ion, we provide the UV-Vis characterization of Co(II) addition to Ros87 and its mutant Ros87_C27D which bears an unusual CysAspHis2 coordination sphere. Zinc finger sites containing only one cysteine have been infrequently characterized. We show for the CysAspHis2 coordination an intense d-d transition band, blue-shifted with respect to the Cys2His2 sphere. These data complemented by NMR and CD data demonstrate that the tetrahedral geometry of the metal site is retained also in the case of a single-cysteine coordination sphere. PMID:29386985

Tetra- and octa-[4-(2-hydroxyethyl)phenoxy bearing novel metal-free and zinc(II) phthalocyanines: Synthesis, characterization and investigation of photophysicochemical properties

Energy Technology Data Exchange (ETDEWEB)

Köksoy, Baybars [Marmara University, Department of Chemistry, 34722 Kadıköy, Istanbul (Turkey); Durmuş, Mahmut [Gebze Technical University, Department of Chemistry, 41400 Gebze, Kocaeli (Turkey); Bulut, Mustafa, E-mail: mbulut@marmara.edu.tr [Marmara University, Department of Chemistry, 34722 Kadıköy, Istanbul (Turkey)

2015-05-15

In this study, four novel phthalonitriles (1–4) and their corresponding metal-free (5–8) and zinc(II) phthalocyanine derivatives (9–12) bearing 4-(hydroxyethyl)phenoxy groups were synthesized. These novel compounds were characterized by IR, elemental analyses, {sup 1}H-NMR, UV–vis, and MALDI-TOF spectral data. Furthermore, photophysical (fluorescence quantum yields and lifetimes) and photochemical properties (singlet oxygen generation and photodegradation quantum yields) of these phthalocyanines were investigated in dimethylsulfoxide. The studied zinc(II) phthalocyanines generated highly singlet oxygen which is very important for the photodynamic therapy (PDT) of cancer. The fluorescence quenching behaviour of the newly synthesized phthalocyanine compounds were also investigated using 1,4-benzoquinone. - Highlights: • Octa and tetra 4-(hydroxyethyl)phenoxy substituted metal-free and zinc(II) phthalocyanines. • Study of photophysicochemical properties of eight new phthalocyanines. • Highly singlet oxygen generation for novel zinc(II) phthalocyanine photosensitizers.

Hydrogen bonding strength of diblock copolymers affects the self-assembled structures with octa-functionalized phenol POSS nanoparticles.

Science.gov (United States)

Lu, Yi-Syuan; Yu, Chia-Yu; Lin, Yung-Chih; Kuo, Shiao-Wei

2016-02-28

In this study, the influence of the functional groups by the diblock copolymers of poly(styrene-b-4-vinylpyridine) (PS-b-P4VP), poly(styrene-b-2-vinylpyridine) (PS-b-P2VP), and poly(styrene-b-methyl methacrylate) (PS-b-PMMA) on their blends with octa-functionalized phenol polyhedral oligomeric silsesquioxane (OP-POSS) nanoparticles (NPs) was investigated. The relative hydrogen bonding strengths in these blends follow the order PS-b-P4VP/OP-POSS > PS-b-P2VP/OP-POSS > PS-b-PMMA/OP-POSS based on the Kwei equation from differential scanning calorimetry (DSC) and Fourier transform infrared spectroscopic analyses. Small-angle X-ray scattering and transmission electron microscopic analyses show that the morphologies of the self-assembly structures are strongly dependent on the hydrogen bonding strength at relatively higher OP-POSS content. The PS-b-P4VP/OP-POSS hybrid complex system with the strongest hydrogen bonds shows the order-order transition from lamellae to cylinders and finally to body-centered cubic spheres upon increasing OP-POSS content. However, PS-b-P2VP/OP-POSS and PS-b-PMMA/OP-POSS hybrid complex systems, having relatively weaker hydrogen bonds, transformed from lamellae to cylinder structures at lower OP-POSS content (50 wt%).

Symplectic and Poisson Geometry in Interaction with Analysis, Algebra and Topology & Symplectic Geometry, Noncommutative Geometry and Physics

CERN Document Server

Eliashberg, Yakov; Maeda, Yoshiaki; Symplectic, Poisson, and Noncommutative geometry

2014-01-01

Symplectic geometry originated in physics, but it has flourished as an independent subject in mathematics, together with its offspring, symplectic topology. Symplectic methods have even been applied back to mathematical physics. Noncommutative geometry has developed an alternative mathematical quantization scheme based on a geometric approach to operator algebras. Deformation quantization, a blend of symplectic methods and noncommutative geometry, approaches quantum mechanics from a more algebraic viewpoint, as it addresses quantization as a deformation of Poisson structures. This volume contains seven chapters based on lectures given by invited speakers at two May 2010 workshops held at the Mathematical Sciences Research Institute: Symplectic and Poisson Geometry in Interaction with Analysis, Algebra and Topology (honoring Alan Weinstein, one of the key figures in the field) and Symplectic Geometry, Noncommutative Geometry and Physics. The chapters include presentations of previously unpublished results and ...

Distance Adaptive Tensor Discriminative Geometry Preserving Projection for Face Recognition

Directory of Open Access Journals (Sweden)

Ziqiang Wang

2012-09-01

Full Text Available There is a growing interest in dimensionality reduction techniques for face recognition, however, the traditional dimensionality reduction algorithms often transform the input face image data into vectors before embedding. Such vectorization often ignores the underlying data structure and leads to higher computational complexity. To effectively cope with these problems, a novel dimensionality reduction algorithm termed distance adaptive tensor discriminative geometry preserving projection (DATDGPP is proposed in this paper. The key idea of DATDGPP is as follows: first, the face image data are directly encoded in high-order tensor structure so that the relationships among the face image data can be preserved; second, the data-adaptive tensor distance is adopted to model the correlation among different coordinates of tensor data; third, the transformation matrix which can preserve discrimination and local geometry information is obtained by an iteration algorithm. Experimental results on three face databases show that the proposed algorithm outperforms other representative dimensionality reduction algorithms.

Separation of attractors in 1-modulus quantum corrected special geometry

CERN Document Server

Bellucci, S; Marrani, A; Shcherbakov, A

2008-01-01

We study the solutions to the N=2, d=4 Attractor Equations in a dyonic, extremal, static, spherically symmetric and asymptotically flat black hole background, in the simplest case of perturbative quantum corrected cubic Special Kahler geometry consistent with continuous axion-shift symmetry, namely in the 1-modulus Special Kahler geometry described (in a suitable special symplectic coordinate) by the holomorphic Kahler gauge-invariant prepotential F=t^3+i*lambda, with lambda real. By performing computations in the ``magnetic'' charge configuration, we find evidence for interesting phenomena (absent in the classical limit of vanishing lambda). Namely, for a certain range of the quantum parameter lambda we find a ``splitting'' of attractors, i.e. the existence of multiple solutions to the Attractor Equations for fixed supporting charge configuration. This corresponds to the existence of ``area codes'' in the radial evolution of the scalar t, determined by the various disconnected regions of the moduli space, wh...

A boundary-fitted staggered difference method for incompressible flow using Riemann geometry

International Nuclear Information System (INIS)

Koshizuka, Seiichi; Kondo, Shunsuke; Oka, Yoshiaki.

1990-01-01

A boundary-fitted staggered difference method (BFSDM) is investigated for incompressible flow in nuclear plants. BFSDM employs control cells for scalars, staggered location of velocity components, and integrated formulation of div=0. Governing equations are written as coordinate-free forms using Riemann geometry. Flow velocity is represented with contravariant physical components in the present method. Connection terms emerge as source terms in the coordinate-free governing equations. These terms are studied from the viewpoints of physical meaning, numerical stability, and conservative property. Some flows on a round or slant boundary are solved using boundary-fitted curvilinear (BFC) grids and rectangular grids to compare the present method and the rectangular-type (R-type) staggered difference method (SDM). Supercomputing of the present method, including vector processing, is also discussed compared with the R-type method. (author)

A generic coordinate system and a set of generic variables for MFE database

International Nuclear Information System (INIS)

Miner, W.H. Jr.; Ross, D.W.; Solano, E.R.; Valanju, P.M.; Wiley, J.C.

1993-01-01

Over the last several years, profile data from nine different tokamaks have been stored in the magnetic fusion energy database (MFEDB). These data sets have come from a variety of sources and most are given in different coordinate systems. In order to attempt any intermachine analysis, it is convenient to transform these data sets into one generic coordinate system and to choose a uniform set of variable names. The authors describe the data sets from each tokamak indicating the source of the data and the coordinate system in which it is given. Next, they discuss the generic coordinate that has been adopted and show how it is implemented for each tokamak. Finally, the generic naming convention that has been adopted is discussed. It follows closely that which was used by Christiansen et al. for the ITER Global Energy Confinement H-Mode Database. For further clarification, they discuss the characteristics of the magnetic geometry given a Fourier representation of the magnetic equilibria

Arithmetic noncommutative geometry

CERN Document Server

Marcolli, Matilde

2005-01-01

Arithmetic noncommutative geometry denotes the use of ideas and tools from the field of noncommutative geometry, to address questions and reinterpret in a new perspective results and constructions from number theory and arithmetic algebraic geometry. This general philosophy is applied to the geometry and arithmetic of modular curves and to the fibers at archimedean places of arithmetic surfaces and varieties. The main reason why noncommutative geometry can be expected to say something about topics of arithmetic interest lies in the fact that it provides the right framework in which the tools of geometry continue to make sense on spaces that are very singular and apparently very far from the world of algebraic varieties. This provides a way of refining the boundary structure of certain classes of spaces that arise in the context of arithmetic geometry, such as moduli spaces (of which modular curves are the simplest case) or arithmetic varieties (completed by suitable "fibers at infinity"), by adding boundaries...

Real symplectic formulation of local special geometry

CERN Document Server

Ferrara, Sergio; Ferrara, Sergio; Macia, Oscar

2006-01-01

We consider a formulation of local special geometry in terms of Darboux special coordinates $P^I=(p^i,q_i)$, $I=1,...,2n$. A general formula for the metric is obtained which is manifestly $\\mathbf{Sp}(2n,\\mathbb{R})$ covariant. Unlike the rigid case the metric is not given by the Hessian of the real function $S(P)$ which is the Legendre transform of the imaginary part of the holomorphic prepotential. Rather it is given by an expression that contains $S$, its Hessian and the conjugate momenta $S_I=\\frac{\\partial S}{\\partial P^I}$. Only in the one-dimensional case ($n=1$) is the real (two-dimensional) metric proportional to the Hessian with an appropriate conformal factor.

Gauge symmetry, T-duality and doubled geometry

International Nuclear Information System (INIS)

Hull, C.M.

2007-11-01

String compactifications with T-duality twists are revisited and the gauge algebra of the dimensionally reduced theories calculated. These reductions can be viewed as string theory on T-fold backgrounds, and can be formulated in a 'doubled space' in which each circle is supplemented by a T-dual circle to construct a geometry which is a doubled torus bundle over a circle. We discuss a conjectured extension to include T-duality on the base circle, and propose the introduction of a dual base coordinate, to give a doubled space which is locally the group manifold of the gauge group. Special cases include those in which the doubled group is a Drinfel'd double. This gives a framework to discuss backgrounds that are not even locally geometric. (orig.)

Electron microscopy studies of octa-calcium phosphate thin films obtained by pulsed laser deposition

Energy Technology Data Exchange (ETDEWEB)

Iliescu, Monica; Nelea, V.; Werckmann, J.; Mihailescu, I.N.; Socol, G.; Bigi, Adriana; Bracci, Barbara

2004-04-01

Octa-calcium phosphate (OCP), Ca{sub 8}(HPO{sub 4}){sub 2}(PO{sub 4}){sub 4}{center_dot}5H{sub 2}O, is present as transient compound in the precipitation of hydroxyapatite (HA) and biological apatites. Because of these characteristics, OCP plays a crucial role in the in-vivo mineralization of human bones and teeth. The use of OCP in developing new generations of bone prosthesis stands therefore for an innovative challenge. This paper reports studies of OCP structures grown in the form of thin films by pulsed laser deposition (PLD) with emphasis on electron microscopy investigations. OCP films were grown on etched Ti substrates, using an UV KrF* excimer laser source ({lambda}=248 nm, {tau}{>=}20 ns). Films were deposited in low-pressure (50 Pa) water vapors environment on substrates heated at 20-180 deg. C. We performed annealing treatments in water vapors and ambient pressure at substrate temperatures identical to those used during deposition. Comprehensive structural and morphological investigations were carried out with different based-electron microscopy procedures. Grazing incidence X-ray diffraction (GIXRD) and white light confocal microscopy were also applied to characterize the films. Ca/P atomic ratio of films was determined by energy dispersive X-ray spectrometry, electron energy loss spectroscopy and X-ray photoelectron spectroscopy. The obtained films generally exhibit an amorphous structure, as evidenced by GIXRD. Nevertheless, cross-section transmission electron microscopy investigations provide supplementary information about the film characteristics and material crystallization in small domains. OCP nanoparticles coalesce and grow perpendicular to the substrate in a tree-like structure, comparable to a coral reef.

Higher geometry an introduction to advanced methods in analytic geometry

CERN Document Server

Woods, Frederick S

2005-01-01

For students of mathematics with a sound background in analytic geometry and some knowledge of determinants, this volume has long been among the best available expositions of advanced work on projective and algebraic geometry. Developed from Professor Woods' lectures at the Massachusetts Institute of Technology, it bridges the gap between intermediate studies in the field and highly specialized works.With exceptional thoroughness, it presents the most important general concepts and methods of advanced algebraic geometry (as distinguished from differential geometry). It offers a thorough study

Anion-Controlled Architecture and Photochromism of Naphthalene Diimide-Based Coordination Polymers

Directory of Open Access Journals (Sweden)

Jian-Jun Liu

2018-02-01

Full Text Available Three new cadmium coordination polymers, namely [Cd(NO32(DPNDI(CH3OH]·CH3OH (1, [Cd(SCN2(DPNDI] (2, and [Cd(DPNDI2(DMF2]·2ClO4 (3 (DPNDI = N,N-di(4-pyridyl-1,4,5,8-naphthalene diimide, DMF = N,N-dimethylformamide have been synthesized by reactions of DPNDI with Cd(NO32, Cd(SCN2, and Cd(ClO42, respectively. Compound 1 is a one-dimensional coordination polymer with strong lone pair-π interactions between the coordinated NO3− anions and the imide ring of DPNDI; while 2 is a two-dimensional network with a (4, 4 net topology. In the case of 3, due to the presence of uncoordinated perchlorate counter ions, it exhibits a non-interpenetrated square-grid coordination polymer containing one-dimensional rhomboid channels. The structural diversity in these compounds is attributed to different coordination abilities and geometries of counter anions. Due to the presence of electron-deficient NDI moiety, the photochromic behavior of these compounds was studied. Interestingly, only compounds 1 and 3 exhibit color changes under light irradiation. The influence of the anions on the photochromism process of the NDI-based materials has been discussed.

Non-Riemannian geometry

CERN Document Server

Eisenhart, Luther Pfahler

2005-01-01

This concise text by a prominent mathematician deals chiefly with manifolds dominated by the geometry of paths. Topics include asymmetric and symmetric connections, the projective geometry of paths, and the geometry of sub-spaces. 1927 edition.

Structures of plutonium coordination compounds: A review of past work, recent single crystal x-ray diffraction results, and what we're learning about plutonium coordination chemistry

Science.gov (United States)

Neu, M. P.; Matonic, J. H.; Smith, D. M.; Scott, B. L.

2000-07-01

The compounds we have isolated and characterized include plutonium(III) and plutonium(IV) bound by ligands with a range of donor types and denticity (halide, phosphine oxide, hydroxamate, amine, sulfide) in a variety of coordination geometries. For example, we have obtained the first X-ray structure of Pu(III) complexed by a soft donor ligand. Using a "one pot" synthesis beginning with Pu metal strips and iodine in acetonitrile and adding trithiacyclononane we isolated the complex, PuI3(9S3)(MeCN)2 (Figure 1). On the other end of the coordination chemistry spectrum, we have obtained the first single crystal structure of the Pu(IV) hexachloro anion (Figure 2). Although this species has been used in plutonium purification via anion exchange chromatography for decades, the bond distances and exact structure were not known. We have also characterized the first plutonium-biomolecule complex, Pu(IV) bound by the siderophore desferrioxamine E.In this presentation we will review the preparation, structures, and importance of previously known coordination compounds and of those we have recently isolated. We will show the coordination chemistry of plutonium is rich and varied, well worth additional exploration.

The Geometry Conference

CERN Document Server

Bárány, Imre; Vilcu, Costin

2016-01-01

This volume presents easy-to-understand yet surprising properties obtained using topological, geometric and graph theoretic tools in the areas covered by the Geometry Conference that took place in Mulhouse, France from September 7–11, 2014 in honour of Tudor Zamfirescu on the occasion of his 70th anniversary. The contributions address subjects in convexity and discrete geometry, in distance geometry or with geometrical flavor in combinatorics, graph theory or non-linear analysis. Written by top experts, these papers highlight the close connections between these fields, as well as ties to other domains of geometry and their reciprocal influence. They offer an overview on recent developments in geometry and its border with discrete mathematics, and provide answers to several open questions. The volume addresses a large audience in mathematics, including researchers and graduate students interested in geometry and geometrical problems.

Hyperbolic geometry

CERN Document Server

Iversen, Birger

1992-01-01

Although it arose from purely theoretical considerations of the underlying axioms of geometry, the work of Einstein and Dirac has demonstrated that hyperbolic geometry is a fundamental aspect of modern physics

Connes distance function on fuzzy sphere and the connection between geometry and statistics

International Nuclear Information System (INIS)

Devi, Yendrembam Chaoba; Chakraborty, Biswajit; Prajapat, Shivraj; Mukhopadhyay, Aritra K.; Scholtz, Frederik G.

2015-01-01

An algorithm to compute Connes spectral distance, adaptable to the Hilbert-Schmidt operatorial formulation of non-commutative quantum mechanics, was developed earlier by introducing the appropriate spectral triple and used to compute infinitesimal distances in the Moyal plane, revealing a deep connection between geometry and statistics. In this paper, using the same algorithm, the Connes spectral distance has been calculated in the Hilbert-Schmidt operatorial formulation for the fuzzy sphere whose spatial coordinates satisfy the su(2) algebra. This has been computed for both the discrete and the Perelemov’s SU(2) coherent state. Here also, we get a connection between geometry and statistics which is shown by computing the infinitesimal distance between mixed states on the quantum Hilbert space of a particular fuzzy sphere, indexed by n ∈ ℤ/2

Geometry of the q-exponential distribution with dependent competing risks and accelerated life testing

Science.gov (United States)

Zhang, Fode; Shi, Yimin; Wang, Ruibing

2017-02-01

In the information geometry suggested by Amari (1985) and Amari et al. (1987), a parametric statistical model can be regarded as a differentiable manifold with the parameter space as a coordinate system. Note that the q-exponential distribution plays an important role in Tsallis statistics (see Tsallis, 2009), this paper investigates the geometry of the q-exponential distribution with dependent competing risks and accelerated life testing (ALT). A copula function based on the q-exponential function, which can be considered as the generalized Gumbel copula, is discussed to illustrate the structure of the dependent random variable. Employing two iterative algorithms, simulation results are given to compare the performance of estimations and levels of association under different hybrid progressively censoring schemes (HPCSs).

Hallazgos cuantitativos y cualitativos en la OCTA en pacientes con y sin retinopatía diabética en el servicio de oftalmología del área este de Valladolid

OpenAIRE

Radoslaw Szewc, Marcin

2017-01-01

La retinopatía diabética (RD) es una de las complicaciones microvasculares más frecuentes de la diabetes mellitus (DM). La detección precoz de la RD permite evitar en numerosas ocasiones la aparición de complicaciones graves y ceguera. El diagnóstico es clínico y apoya en pruebas de imagen complementarías, entre ellas la angiofluoresceingrafía (AFG) y la tomografía de coherencia óptica (OCT) y un nuevo método de diagnóstico OCT Angiografía (OCTA) que permite visualizar las estr...

Geometry of the Universe

International Nuclear Information System (INIS)

Gurevich, L.Eh.; Gliner, Eh.B.

1978-01-01

Problems of investigating the Universe space-time geometry are described on a popular level. Immediate space-time geometries, corresponding to three cosmologic models are considered. Space-time geometry of a closed model is the spherical Riemann geonetry, of an open model - is the Lobachevskij geometry; and of a plane model - is the Euclidean geometry. The Universe real geometry in the contemporary epoch of development is based on the data testifying to the fact that the Universe is infinitely expanding

Special Geometry and Automorphic Forms

CERN Document Server

Berglund, P; Wyllard, N; Berglund, Per; Henningson, Mans; Wyllard, Niclas

1997-01-01

We consider special geometry of the vector multiplet moduli space in compactifications of the heterotic string on $K3 \\times T^2$ or the type IIA string on $K3$-fibered Calabi-Yau threefolds. In particular, we construct a modified dilaton that is invariant under $SO(2, n; Z)$ T-duality transformations at the non-perturbative level and regular everywhere on the moduli space. The invariant dilaton, together with a set of other coordinates that transform covariantly under $SO(2, n; Z)$, parameterize the moduli space. The construction involves a meromorphic automorphic function of $SO(2, n; Z)$, that also depends on the invariant dilaton. In the weak coupling limit, the divisor of this automorphic form is an integer linear combination of the rational quadratic divisors where the gauge symmetry is enhanced classically. We also show how the non-perturbative prepotential can be expressed in terms of meromorphic automorphic forms, by expanding a T-duality invariant quantity both in terms of the standard special coord...

Accuracy increase of the coordinate measurement based on the model production of geometrical parts specifications

Science.gov (United States)

Zlatkina, O. Yu

2018-04-01

There is a relationship between the service properties of component parts and their geometry; therefore, to predict and control the operational characteristics of parts and machines, it is necessary to measure their geometrical specifications. In modern production, a coordinate measuring machine is the advanced measuring instrument of the products geometrical specifications. The analysis of publications has shown that during the coordinate measurements the problems of choosing locating chart of parts and coordination have not been sufficiently studied. A special role in the coordination of the part is played by the coordinate axes informational content. Informational content is the sum of the degrees of freedom limited by the elementary item of a part. The coordinate planes of a rectangular coordinate system have different informational content (three, two, and one). The coordinate axes have informational content of four, two and zero. The higher the informational content of the coordinate plane or axis, the higher its priority for reading angular and linear coordinates is. The geometrical model production of the coordinate measurements object taking into account the information content of coordinate planes and coordinate axes allows us to clearly reveal the interrelationship of the coordinates of the deviations in location, sizes and deviations of their surfaces shape. The geometrical model helps to select the optimal locating chart of parts for bringing the machine coordinate system to the part coordinate system. The article presents an algorithm the model production of geometrical specifications using the example of the piston rod of a compressor.

Indium local geometry in In-Sb-Te thin films using XANES and DFT calculations

Science.gov (United States)

Bilovol, V.; Gil Rebaza, A. V.; Mudarra Navarro, A. M.; Errico, L.; Fontana, M.; Arcondo, B.

2017-12-01

In-Sb-Te when is a thin film presents a huge difference in its electrical resistivity when transform from the amorphous (insulating) to the crystalline (conducting) phase. This property made this system one of the main phase-change materials used in the data storage industry. The change in the electrical conductivity is probably associated to a change in the bonding geometry of some of its constituents. To explore this point, we present in this work an study of the bonding geometry of In atoms in In-Sb-Te films by means of In K-edge X-ray absorption near edge structure (XANES) spectroscopy using synchrotron radiation in both as deposited (amorphous) and crystalline thin films obtained as a result of resistance (R) vs temperature (T) measurements. Comparison of the XANES spectra obtained for ternary amorphous films and binary crystalline reference films suggests that in amorphous films the bonding geometry of In atoms is tetrahedral-like. After the thermal annealing has been carried out the differences in the XANES spectra of the as deposited and the annealed films indicate that the bonding geometry of In atoms changes. Based on X-ray diffraction results and ab initio calculations in the framework of the Density Functional Theory (DFT) we show that the new coordination geometry is associated with a tendency of In atoms towards octahedral-like.

The SUSY oscillator from local geometry: Dynamics and coherent states

International Nuclear Information System (INIS)

Thienel, H.P.

1994-01-01

The choice of a coordinate chart on an analytical R n (R a n ) provides a representation of the n-dimensional SUSY oscillator. The corresponding Hilbert space is Cartan's exterior algebra endowed with a suitable scalar product. The exterior derivative gives rise to the algebra of the n-dimensional SUSY oscillator. Its euclidean dynamics is an inherent consequence of the geometry imposed by the Lie derivative generating the dilations, i.e. evolution of the quantum system corresponds to parametrization of a sequence of charts by euclidean time. Coherent states emerge as a natural structure related to the Lie derivative generating the translations. (orig.)

Spectroscopic Studies of a Three-dimensional, Five-coordinated Copper(Ⅱ) Complex via Hydrogen Bonds: [Cu(PDA)(H2O)2](H2PDA=Pyridine-2,6-dicarboxylic Acid)

Institute of Scientific and Technical Information of China (English)

无

2003-01-01

A new copper(Ⅱ) complex [Cu(PDA)(H2O)2] was synthesized and its structure was determined. Cu(Ⅱ) is five-coordinated in a tetragonal pyramid geometry. The two coordinating water molecules are different and the two Cu-O bond lengths differ by nearly 0.02 nm. The whole crystal is linked to form a three-dimensional network by means of hydrogen bonds. The X-band ESR spectrum shows three different g tensors with a well-resolved hyperfine structure in the gz signal, giving the ESR parameters gx=2.05, gy=2.065 and gz=2.29. The covalency of the coordinate bonds and the deviation from tetragonal pyramid geometry for the complex are discussed based on the ESR spectra.

On organizing principles of discrete differential geometry. Geometry of spheres

International Nuclear Information System (INIS)

Bobenko, Alexander I; Suris, Yury B

2007-01-01

Discrete differential geometry aims to develop discrete equivalents of the geometric notions and methods of classical differential geometry. This survey contains a discussion of the following two fundamental discretization principles: the transformation group principle (smooth geometric objects and their discretizations are invariant with respect to the same transformation group) and the consistency principle (discretizations of smooth parametrized geometries can be extended to multidimensional consistent nets). The main concrete geometric problem treated here is discretization of curvature-line parametrized surfaces in Lie geometry. Systematic use of the discretization principles leads to a discretization of curvature-line parametrization which unifies circular and conical nets.

d-Cysteine Ligands Control Metal Geometries within De Novo Designed Three-Stranded Coiled Coils

DEFF Research Database (Denmark)

Ruckthong, Leela; Peacock, Anna F.A.; Pascoe, Cherilyn E.

2017-01-01

Although metal ion binding to naturally occurring l-amino acid proteins is well documented, understanding the impact of the opposite chirality (d-)amino acids on the structure and stereochemistry of metals is in its infancy. We examine the effect of a d-configuration cysteine within a designed l......-amino acid three-stranded coiled coil in order to enforce a precise coordination number on a metal center. The d chirality does not alter the native fold, but the side-chain re-orientation modifies the sterics of the metal binding pocket. l-Cys side chains within the coiled-coil structure have previously...... by comparison of the structure of ZnIICl(CSL16DC)3 2- to the published structure of ZnII(H2O)(GRAND-CSL12AL16LC)3 -. Moreover, spectroscopic analysis indicates that the CdII geometry observed by using l-Cys ligands (a mixture of three- and four-coordinate CdII) is altered to a single four-coordinate species...

Engineering the oxygen coordination in digital superlattices

Energy Technology Data Exchange (ETDEWEB)

Cook, Seyoung [Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA; Department of Materials Science, Northwestern University, Evanston, Illinois 60202, USA; Andersen, Tassie K. [Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA; Department of Materials Science, Northwestern University, Evanston, Illinois 60202, USA; Hong, Hawoong [X-Ray Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA; Rosenberg, Richard A. [X-Ray Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA; Marks, Laurence D. [Department of Materials Science, Northwestern University, Evanston, Illinois 60202, USA; Fong, Dillon D. [Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA

2017-12-01

The oxygen sublattice in the complex oxides is typically composed of corner-shared polyhedra, with transition metals at their centers. The electronic and chemical properties of the oxide depend on the type and geometric arrangement of these polyhedra, which can be controlled through epitaxial synthesis. Here, we use oxide molecular beam epitaxy to create SrCoOx:SrTiO3 superlattices with tunable oxygen coordination environments and sublattice geometries. Using soft X-ray spectroscopy, we find that the chemical state of Co can be varied with the polyhedral arrangement, demonstrating a new strategy for achieving unique electronic properties in the transition metal oxides.

Geometry and its applications

CERN Document Server

Meyer, Walter J

2006-01-01

Meyer''s Geometry and Its Applications, Second Edition, combines traditional geometry with current ideas to present a modern approach that is grounded in real-world applications. It balances the deductive approach with discovery learning, and introduces axiomatic, Euclidean geometry, non-Euclidean geometry, and transformational geometry. The text integrates applications and examples throughout and includes historical notes in many chapters. The Second Edition of Geometry and Its Applications is a significant text for any college or university that focuses on geometry''s usefulness in other disciplines. It is especially appropriate for engineering and science majors, as well as future mathematics teachers.* Realistic applications integrated throughout the text, including (but not limited to): - Symmetries of artistic patterns- Physics- Robotics- Computer vision- Computer graphics- Stability of architectural structures- Molecular biology- Medicine- Pattern recognition* Historical notes included in many chapters...

Gauge symmetry, T-duality and doubled geometry

Energy Technology Data Exchange (ETDEWEB)

Hull, C.M. [Imperial College London (United Kingdom). Inst. for Mathematical Sciences]|[Imperial College London (United Kingdom). Blackett Laboratory; Reid-Edwards, R.A. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik]|[Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)

2007-11-15

String compactifications with T-duality twists are revisited and the gauge algebra of the dimensionally reduced theories calculated. These reductions can be viewed as string theory on T-fold backgrounds, and can be formulated in a 'doubled space' in which each circle is supplemented by a T-dual circle to construct a geometry which is a doubled torus bundle over a circle. We discuss a conjectured extension to include T-duality on the base circle, and propose the introduction of a dual base coordinate, to give a doubled space which is locally the group manifold of the gauge group. Special cases include those in which the doubled group is a Drinfel'd double. This gives a framework to discuss backgrounds that are not even locally geometric. (orig.)

Beautiful geometry

CERN Document Server

Maor, Eli

2014-01-01

If you've ever thought that mathematics and art don't mix, this stunning visual history of geometry will change your mind. As much a work of art as a book about mathematics, Beautiful Geometry presents more than sixty exquisite color plates illustrating a wide range of geometric patterns and theorems, accompanied by brief accounts of the fascinating history and people behind each. With artwork by Swiss artist Eugen Jost and text by acclaimed math historian Eli Maor, this unique celebration of geometry covers numerous subjects, from straightedge-and-compass constructions to intriguing configur

Bound-Preserving Discontinuous Galerkin Methods for Conservative Phase Space Advection in Curvilinear Coordinates

Energy Technology Data Exchange (ETDEWEB)

Mezzacappa, Anthony [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Endeve, Eirik [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Hauck, Cory D. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Xing, Yulong [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

2015-02-01

We extend the positivity-preserving method of Zhang & Shu [49] to simulate the advection of neutral particles in phase space using curvilinear coordinates. The ability to utilize these coordinates is important for non-equilibrium transport problems in general relativity and also in science and engineering applications with specific geometries. The method achieves high-order accuracy using Discontinuous Galerkin (DG) discretization of phase space and strong stabilitypreserving, Runge-Kutta (SSP-RK) time integration. Special care in taken to ensure that the method preserves strict bounds for the phase space distribution function f; i.e., f ϵ [0, 1]. The combination of suitable CFL conditions and the use of the high-order limiter proposed in [49] is su cient to ensure positivity of the distribution function. However, to ensure that the distribution function satisfies the upper bound, the discretization must, in addition, preserve the divergencefree property of the phase space ow. Proofs that highlight the necessary conditions are presented for general curvilinear coordinates, and the details of these conditions are worked out for some commonly used coordinate systems (i.e., spherical polar spatial coordinates in spherical symmetry and cylindrical spatial coordinates in axial symmetry, both with spherical momentum coordinates). Results from numerical experiments - including one example in spherical symmetry adopting the Schwarzschild metric - demonstrate that the method achieves high-order accuracy and that the distribution function satisfies the maximum principle.

The use of the co-ordinate measuring machine for the study of three-dimensional biomechanics of the knee.

Science.gov (United States)

Veselko, M; Jenko, M; Lipuscek, I

1998-07-01

Original methodology for the study of three-dimensional biomechanics of the knee is presented in the paper. Defining the geometry of the rigid body in the body-fixed reference frame and the orientation of the body-fixed reference frame in the global co-ordinate system are the theoretic basis. The data in the form of co-ordinates of the Cartesian frame are gathered by the co-ordinate measuring machine and analysed by specially computer program. The theory and a practical example of the study of the three-dimensional biomechanics of the knee are presented. Various possibilities of the use of the methodology are discussed.

Sarcomere lattice geometry influences cooperative myosin binding in muscle.

Directory of Open Access Journals (Sweden)

Bertrand C W Tanner

2007-07-01

Full Text Available In muscle, force emerges from myosin binding with actin (forming a cross-bridge. This actomyosin binding depends upon myofilament geometry, kinetics of thin-filament Ca(2+ activation, and kinetics of cross-bridge cycling. Binding occurs within a compliant network of protein filaments where there is mechanical coupling between myosins along the thick-filament backbone and between actin monomers along the thin filament. Such mechanical coupling precludes using ordinary differential equation models when examining the effects of lattice geometry, kinetics, or compliance on force production. This study uses two stochastically driven, spatially explicit models to predict levels of cross-bridge binding, force, thin-filament Ca(2+ activation, and ATP utilization. One model incorporates the 2-to-1 ratio of thin to thick filaments of vertebrate striated muscle (multi-filament model, while the other comprises only one thick and one thin filament (two-filament model. Simulations comparing these models show that the multi-filament predictions of force, fractional cross-bridge binding, and cross-bridge turnover are more consistent with published experimental values. Furthermore, the values predicted by the multi-filament model are greater than those values predicted by the two-filament model. These increases are larger than the relative increase of potential inter-filament interactions in the multi-filament model versus the two-filament model. This amplification of coordinated cross-bridge binding and cycling indicates a mechanism of cooperativity that depends on sarcomere lattice geometry, specifically the ratio and arrangement of myofilaments.

Revolutions of Geometry

CERN Document Server

O'Leary, Michael

2010-01-01

Guides readers through the development of geometry and basic proof writing using a historical approach to the topic. In an effort to fully appreciate the logic and structure of geometric proofs, Revolutions of Geometry places proofs into the context of geometry's history, helping readers to understand that proof writing is crucial to the job of a mathematician. Written for students and educators of mathematics alike, the book guides readers through the rich history and influential works, from ancient times to the present, behind the development of geometry. As a result, readers are successfull

Analogy and Dynamic Geometry System Used to Introduce Three-Dimensional Geometry

Science.gov (United States)

Mammana, M. F.; Micale, B.; Pennisi, M.

2012-01-01

We present a sequence of classroom activities on Euclidean geometry, both plane and space geometry, used to make three dimensional geometry more catchy and simple. The activity consists of a guided research activity that leads the students to discover unexpected properties of two apparently distant geometrical entities, quadrilaterals and…

Information geometry

CERN Document Server

Ay, Nihat; Lê, Hông Vân; Schwachhöfer, Lorenz

2017-01-01

The book provides a comprehensive introduction and a novel mathematical foundation of the field of information geometry with complete proofs and detailed background material on measure theory, Riemannian geometry and Banach space theory. Parametrised measure models are defined as fundamental geometric objects, which can be both finite or infinite dimensional. Based on these models, canonical tensor fields are introduced and further studied, including the Fisher metric and the Amari-Chentsov tensor, and embeddings of statistical manifolds are investigated. This novel foundation then leads to application highlights, such as generalizations and extensions of the classical uniqueness result of Chentsov or the Cramér-Rao inequality. Additionally, several new application fields of information geometry are highlighted, for instance hierarchical and graphical models, complexity theory, population genetics, or Markov Chain Monte Carlo. The book will be of interest to mathematicians who are interested in geometry, inf...

Crystal structures of coordination polymers from CaI2 and proline

Directory of Open Access Journals (Sweden)

Kevin Lamberts

2015-06-01

Full Text Available Completing our reports concerning the reaction products from calcium halides and the amino acid proline, two different solids were found for the reaction of l- and dl-proline with CaI2. The enantiopure amino acid yields the one-dimensional coordination polymer catena-poly[[aqua-μ3-l-proline-tetra-μ2-l-proline-dicalcium] tetraiodide 1.7-hydrate], {[Ca2(C5H9NO25(H2O]I4·1.7H2O}n, (1, with two independent Ca2+ cations in characteristic seven- and eightfold coordination. Five symmetry-independent zwitterionic l-proline molecules bridge the metal sites into a cationic polymer. Racemic proline forms with Ca2+ cations heterochiral chains of the one-dimensional polymer catena-poly[[diaquadi-μ2-dl-proline-calcium] diiodide], {[Ca(C5H9NO22(H2O2]I2}n, (2. The centrosymmetric structure is built by one Ca2+ cation that is bridged towards its symmetry equivalents by two zwitterionic proline molecules. In both structures, the iodide ions remain non-coordinating and hydrogen bonds are formed between these counter-anions, the amino groups, coordinating and co-crystallized water molecules. While the overall composition of (1 and (2 is in line with other structures from calcium halides and amino acids, the diversity of the carboxylate coordination geometry is quite surprising.

A method for generating large datasets of organ geometries for radiotherapy treatment planning studies

International Nuclear Information System (INIS)

Hu, Nan; Cerviño, Laura; Segars, Paul; Lewis, John; Shan, Jinlu; Jiang, Steve; Zheng, Xiaolin; Wang, Ge

2014-01-01

With the rapidly increasing application of adaptive radiotherapy, large datasets of organ geometries based on the patient’s anatomy are desired to support clinical application or research work, such as image segmentation, re-planning, and organ deformation analysis. Sometimes only limited datasets are available in clinical practice. In this study, we propose a new method to generate large datasets of organ geometries to be utilized in adaptive radiotherapy. Given a training dataset of organ shapes derived from daily cone-beam CT, we align them into a common coordinate frame and select one of the training surfaces as reference surface. A statistical shape model of organs was constructed, based on the establishment of point correspondence between surfaces and non-uniform rational B-spline (NURBS) representation. A principal component analysis is performed on the sampled surface points to capture the major variation modes of each organ. A set of principal components and their respective coefficients, which represent organ surface deformation, were obtained, and a statistical analysis of the coefficients was performed. New sets of statistically equivalent coefficients can be constructed and assigned to the principal components, resulting in a larger geometry dataset for the patient’s organs. These generated organ geometries are realistic and statistically representative

Synthesis, structure and fluorescence properties of a novel 3D Sr(II) coordination polymer

Science.gov (United States)

Tan, Yu-Hui; Xu, Qing; Gu, Zhi-Feng; Gao, Ji-Xing; Wang, Bin; Liu, Yi; Yang, Chang-Shan; Tang, Yun-Zhi

2016-09-01

Solvothermal reaction of 2,2‧-bipyridine-5,5‧-dicarboxylic acid (H2bpdc) and SrCl2 affords a novel coordination polymer [Sr(Hbpdc)2]n1. X-ray structure determination shows that 1 exhibits a novel three-dimensional network. The unique Sr II cation sits on a two-fold axis and coordinated by four O-atom donors from four Hbptc- ligands and four N-atom donors from two Hbptc- ligands in distorted dodecahedral geometry. In 1 each Sr II cation connects to six different Hbptc- ligands and each Hbptc- ligand bridges three different Sr II cations which results in the formation of a three-dimensional polymeric structure. Corresponding to the free ligand, the fluorescent emission of complex 1 display remarkable "Einstain" shifts, which may be attributed to the coordination interaction of Sr atoms, thus reduce the rigidity of pyridyl rings.

PREFACE: Algebra, Geometry, and Mathematical Physics 2010

Science.gov (United States)

Stolin, A.; Abramov, V.; Fuchs, J.; Paal, E.; Shestopalov, Y.; Silvestrov, S.

2012-02-01

This proceedings volume presents results obtained by the participants of the 6th Baltic-Nordic workshop 'Algebra, Geometry, and Mathematical Physics (AGMP-6)' held at the Sven Lovén Centre for Marine Sciences in Tjärnö, Sweden on October 25-30, 2010. The Baltic-Nordic Network AGMP 'Algebra, Geometry, and Mathematical Physics' http://www.agmp.eu was created in 2005 on the initiative of two Estonian universities and two Swedish universities: Tallinn University of Technology represented by Eugen Paal (coordinator of the network), Tartu University represented by Viktor Abramov, Lund University represented by Sergei Silvestrov, and Chalmers University of Technology and the University of Gothenburg represented by Alexander Stolin. The goal was to promote international and interdisciplinary cooperation between scientists and research groups in the countries of the Baltic-Nordic region in mathematics and mathematical physics, with special emphasis on the important role played by algebra and geometry in modern physics, engineering and technologies. The main activities of the AGMP network consist of a series of regular annual international workshops, conferences and research schools. The AGMP network also constitutes an important educational forum for scientific exchange and dissimilation of research results for PhD students and Postdocs. The network has expanded since its creation, and nowadays its activities extend beyond countries in the Baltic-Nordic region to universities in other European countries and participants from elsewhere in the world. As one of the important research-dissimilation outcomes of its activities, the network has a tradition of producing high-quality research proceedings volumes after network events, publishing them with various international publishers. The PDF also contains the following: List of AGMP workshops and other AGMP activities Main topics discussed at AGMP-6 Review of AGMP-6 proceedings Acknowledgments List of Conference Participants

On the geometry of field lines in plasma flows

International Nuclear Information System (INIS)

Bagewadi, C.S.; Prasanna Kumar, K.N.

1988-01-01

Many research investigators have applied differential geometry to plasma. Intrinsic properties of fluid flows in streamline, vortex line geometries are we ll known under certain set of geometric conditions. Though this approach has yielded some interesting results but the most general properties of flows can be obtained, using eight geometric parameters ksub(s), tsub(s) θsub(ns), θsub(bs), phisub(s), Ωsub(s), div n, div b and the basic necessary conditions to be satisfied by the flow in general anholonomic co-ordinate system together with the conditions to be satisfied by the geometric parameters of triply orthogonal spatial curves of congruences. Adopting the above techniques for triply orthogonal spatial curves of congruences related to the lines of forces, Purushottam has studied the geometric properties of spatial hydromagnetic fluid flows. Again these results have been studied by him in general along the field lines. These results have been studied for plasma along field lines and the basic equations of plasma have been expressed in intrinsic decomposition forms. Furthe r complex lamellar magnetic field have been studied by introducing Lie surface. (a uthor)

Geometry essentials for dummies

CERN Document Server

Ryan, Mark

2011-01-01

Just the critical concepts you need to score high in geometry This practical, friendly guide focuses on critical concepts taught in a typical geometry course, from the properties of triangles, parallelograms, circles, and cylinders, to the skills and strategies you need to write geometry proofs. Geometry Essentials For Dummies is perfect for cramming or doing homework, or as a reference for parents helping kids study for exams. Get down to the basics - get a handle on the basics of geometry, from lines, segments, and angles, to vertices, altitudes, and diagonals Conque

Origin of hyperbolicity in brain-to-brain coordination networks

Science.gov (United States)

Tadić, Bosiljka; Andjelković, Miroslav; Šuvakov, Milovan

2018-02-01

Hyperbolicity or negative curvature of complex networks is the intrinsic geometric proximity of nodes in the graph metric space, which implies an improved network function. Here, we investigate hidden combinatorial geometries in brain-to-brain coordination networks arising through social communications. The networks originate from correlations among EEG signals previously recorded during spoken communications comprising of 14 individuals with 24 speaker-listener pairs. We find that the corresponding networks are delta-hyperbolic with delta_max=1 and the graph diameter D=3 in each brain. While the emergent hyperbolicity in the two-brain networks satisfies delta_max/D/2 neuronal correlation patterns ranging from weak coordination to super-brain structure. These topology features are in qualitative agreement with the listener’s self-reported ratings of own experience and quality of the speaker, suggesting that studies of the cross-brain connector networks can reveal new insight into the neural mechanisms underlying human social behavior.

Crystal Structures and Physical Properties of Ag(I) Coordination Polymers with Unsymmetrical Dipyridyl Ligand

International Nuclear Information System (INIS)

Lee, Eunji; Ryu, Hyunsoo; Park, Kimin

2013-01-01

Three Ag(I) coordination polymers with the formula [Ag(L)]·(X)·(DMSO) n (X = ClO 4 (1), BF 4 (2), and PF 6 (3), and L = dipyridyl ligand) were prepared and characterized fully their structures. All three compounds are isostructures and stable 2-D honeycomb type coordination polymers, in which 1-D zigzag chains with -(Ag-L)- motif are linked by the argentophilic interactions and the π···π stacking interactions between pyridine rings. The investigation on photophysical properties of all compounds shows that the nature of emission can be attributed to the metal-to-ligand charge transfer as well as the formation of the polymeric structures with restriction of the flexibility of the free ligand. Based on the present solid state results, further investigation on the development and characterization of new coordination polymers using flexible unsymmetrical ligand is in progress. During last two decades, silver coordination polymers based on dipyridyl type ligands have attracted particular interest because of the various intriguing architectures caused by a variety of coordination geometry of Ag(I) ion as well as their potential applications as functional materials

A novel nanostructured composite formed by interaction of copper octa(3-aminopropyl)octasilsesquioxane with azide ligands: Preparation, characterization and a voltammetric application

International Nuclear Information System (INIS)

Ribeiro do Carmo, Devaney; Paim, Leonardo Lataro; Metzker, Gustavo; Dias Filho, Newton Luiz; Stradiotto, Nelson Ramos

2010-01-01

This study presents the preparation, characterization and application of copper octa(3-aminopropyl)octasilsesquioxane following its subsequent reaction with azide ions (ASCA). The precursor (AC) and the novel compound (ASCA) were characterized by Fourier transform infrared spectra (FTIR), nuclear magnetic resonance (NMR), electron paramagnetic resonance (EPR), scanning electronic microscopy (SEM), X-ray diffraction (XRD), Thermogravimetric analyses and voltammetric technique. The cyclic voltammogram of the modified graphite paste electrode with ASCA (GPE-ASCA), showed one redox couple with formal potential (E 1/2 ox ) = 0.30 V and an irreversible process at 1.1 V (vs. Ag/AgCl; NaCl 1.0 M; v=20mVs -1 ). The material is very sensitive to nitrite concentrations. The modified graphite paste electrode (GPE-ASCA) gives a linear range from 1.0 x 10 -4 to 4.0 x 10 -3 mol L -1 for the determination of nitrite, with a detection limit of 2.1 x 10 -4 mol L -1 and the amperometric sensitivity of 8.04 mA/mol L -1 .

Complex analysis and geometry

CERN Document Server

Silva, Alessandro

1993-01-01

The papers in this wide-ranging collection report on the results of investigations from a number of linked disciplines, including complex algebraic geometry, complex analytic geometry of manifolds and spaces, and complex differential geometry.

Studies on new complexes of dioxo uranium(VI) and thorium(IV) with some schiff bases derived from trimethoprime salicyldehyde and o-vanillin (Paper No. AL-50)

International Nuclear Information System (INIS)

Pujar, M.A.; Pirgonde, B.R.

1990-02-01

Dioxouranium(VI) and thorium(IV) form 1:1(Metal:Ligands) complexes with some schiff bases. The complexes have been characterized through elemental analyses, electronic and IR spectral, conductance and magnetic susceptibility measurements. They are considered dimeric or polymeric hexa or octa-coordinated arrangement around metal ion moiety. Force constants and U-O bond lengths have been calculated. (author). 1 tab

Nodal integral method for the neutron diffusion equation in cylindrical geometry

International Nuclear Information System (INIS)

Azmy, Y.Y.

1987-01-01

The nodal methodology is based on retaining a higher a higher degree of analyticity in the process of deriving the discrete-variable equations compared to conventional numerical methods. As a result, extensive numerical testing of nodal methods developed for a wide variety of partial differential equations and comparison of the results to conventional methods have established the superior accuracy of nodal methods on coarse meshes. Moreover, these tests have shown that nodal methods are more computationally efficient than finite difference and finite-element methods in the sense that they require shorter CPU times to achieve comparable accuracy in the solutions. However, nodal formalisms and the final discrete-variable equations they produce are, in general, more complicated than their conventional counterparts. This, together with anticipated difficulties in applying the transverse-averaging procedure in curvilinear coordinates, has limited the applications of nodal methods, so far, to Cartesian geometry, and with additional approximations to hexagonal geometry. In this paper the authors report recent progress in deriving and numerically implementing a nodal integral method (NIM) for solving the neutron diffusion equation in cylindrical r-z geometry. Also, presented are comparisons of numerical solutions to two test problems with those obtained by the Exterminator-2 code, which indicate the superior accuracy of the nodal integral method solutions on much coarser meshes

A modular approach to neutral P,N-ligands: synthesis and coordination chemistry

Directory of Open Access Journals (Sweden)

Vladislav Vasilenko

2016-04-01

Full Text Available We report the modular synthesis of three different types of neutral κ2-P,N-ligands comprising an imine and a phosphine binding site. These ligands were reacted with rhodium, iridium and palladium metal precursors and the structures of the resulting complexes were elucidated by means of X-ray crystallography. We observed that subtle changes of the ligand backbone have a significant influence on the binding geometry und coordination properties of these bidentate P,N-donors.

Impact of geometry and viewing angle on classification accuracy of 2D based analysis of dysmorphic faces.

Science.gov (United States)

Vollmar, Tobias; Maus, Baerbel; Wurtz, Rolf P; Gillessen-Kaesbach, Gabriele; Horsthemke, Bernhard; Wieczorek, Dagmar; Boehringer, Stefan

2008-01-01

Digital image analysis of faces has been demonstrated to be effective in a small number of syndromes. In this paper we investigate several aspects that help bringing these methods closer to clinical application. First, we investigate the impact of increasing the number of syndromes from 10 to 14 as compared to an earlier study. Second, we include a side-view pose into the analysis and third, we scrutinize the effect of geometry information. Picture analysis uses a Gabor wavelet transform, standardization of landmark coordinates and subsequent statistical analysis. We can demonstrate that classification accuracy drops from 76% for 10 syndromes to 70% for 14 syndromes for frontal images. Including side-views achieves an accuracy of 76% again. Geometry performs excellently with 85% for combined poses. Combination of wavelets and geometry for both poses increases accuracy to 93%. In conclusion, a larger number of syndromes can be handled effectively by means of image analysis.

Classification of digital affine noncommutative geometries

Science.gov (United States)

Majid, Shahn; Pachoł, Anna

2018-03-01

It is known that connected translation invariant n-dimensional noncommutative differentials dxi on the algebra k[x1, …, xn] of polynomials in n-variables over a field k are classified by commutative algebras V on the vector space spanned by the coordinates. These data also apply to construct differentials on the Heisenberg algebra "spacetime" with relations [xμ, xν] = λΘμν, where Θ is an antisymmetric matrix, as well as to Lie algebras with pre-Lie algebra structures. We specialise the general theory to the field k =F2 of two elements, in which case translation invariant metrics (i.e., with constant coefficients) are equivalent to making V a Frobenius algebra. We classify all of these and their quantum Levi-Civita bimodule connections for n = 2, 3, with partial results for n = 4. For n = 2, we find 3 inequivalent differential structures admitting 1, 2, and 3 invariant metrics, respectively. For n = 3, we find 6 differential structures admitting 0, 1, 2, 3, 4, 7 invariant metrics, respectively. We give some examples for n = 4 and general n. Surprisingly, not all our geometries for n ≥ 2 have zero quantum Riemann curvature. Quantum gravity is normally seen as a weighted "sum" over all possible metrics but our results are a step towards a deeper approach in which we must also "sum" over differential structures. Over F2 we construct some of our algebras and associated structures by digital gates, opening up the possibility of "digital geometry."

Geometry

CERN Document Server

Pedoe, Dan

1988-01-01

""A lucid and masterly survey."" - Mathematics Gazette Professor Pedoe is widely known as a fine teacher and a fine geometer. His abilities in both areas are clearly evident in this self-contained, well-written, and lucid introduction to the scope and methods of elementary geometry. It covers the geometry usually included in undergraduate courses in mathematics, except for the theory of convex sets. Based on a course given by the author for several years at the University of Minnesota, the main purpose of the book is to increase geometrical, and therefore mathematical, understanding and to he

Connective Tissue Characteristics around Healing Abutments of Different Geometries: New Methodological Technique under Circularly Polarized Light.

Science.gov (United States)

Delgado-Ruiz, Rafael Arcesio; Calvo-Guirado, Jose Luis; Abboud, Marcus; Ramirez-Fernandez, Maria Piedad; Maté-Sánchez de Val, José Eduardo; Negri, Bruno; Gomez-Moreno, Gerardo; Markovic, Aleksa

2015-08-01

To describe contact, thickness, density, and orientation of connective tissue fibers around healing abutments of different geometries by means of a new method using coordinates. Following the bilateral extraction of mandibular premolars (P2, P3, and P4) from six fox hound dogs and a 2-month healing period, 36 titanium implants were inserted, onto which two groups of healing abutments of different geometry were screwed: Group A (concave abutments) and Group B (wider healing abutment). After 3 months the animals were sacrificed and samples extracted containing each implant and surrounding soft and hard tissues. Histological analysis was performed without decalcifying the samples by means of circularly polarized light under optical microscope and a system of vertical and horizontal coordinates across all the connective tissue in an area delimited by the implant/abutment, epithelium, and bone tissue. In no case had the connective tissue formed a connection to the healing abutment/implant in the internal zone; a space of 35 ± 10 μm separated the connective tissue fibers from the healing abutment surface. The total thickness of connective tissue in the horizontal direction was significantly greater in the medial zone in Group B than in Group A (p connective tissue thickness. © 2013 Wiley Periodicals, Inc.

Complex algebraic geometry

CERN Document Server

Kollár, János

1997-01-01

This volume contains the lectures presented at the third Regional Geometry Institute at Park City in 1993. The lectures provide an introduction to the subject, complex algebraic geometry, making the book suitable as a text for second- and third-year graduate students. The book deals with topics in algebraic geometry where one can reach the level of current research while starting with the basics. Topics covered include the theory of surfaces from the viewpoint of recent higher-dimensional developments, providing an excellent introduction to more advanced topics such as the minimal model program. Also included is an introduction to Hodge theory and intersection homology based on the simple topological ideas of Lefschetz and an overview of the recent interactions between algebraic geometry and theoretical physics, which involve mirror symmetry and string theory.

Gyrokinetic simulations in general geometry and applications to collisional damping of zonal flows

International Nuclear Information System (INIS)

Lin, Z.; Hahm, T.S.; Lee, W.W.; Tang, W.M.; White, R.B.

2000-01-01

A fully three-dimensional gyrokinetic particle code using magnetic coordinates for general geometry has been developed and applied to the investigation of zonal flows dynamics in toroidal ion-temperature-gradient turbulence. Full torus simulation results support the important conclusion that turbulence-driven zonal flows significantly reduce the turbulent transport. Linear collisionless simulations for damping of an initial poloidal flow perturbation exhibit an asymptotic residual flow. The collisional damping of this residual causes the dependence of ion thermal transport on the ion-ion collision frequency even in regimes where the instabilities are collisionless

Crystal structure of bis-[(acetato-κO)(imidazolidine-2-thione-κS)bis-(tri-phenyl-phosphane-κP)silver(I)] di-μ-imidazol-idine-2-thione-κ(4) S:S-bis-[(imidazol-id-ine-2-thione-κS)bis-(tri-phenyl-phosphane-κP)silver(I)] di-acetate aceto-nitrile disolvate tetra-hydrate.

Science.gov (United States)

Nimthong-Roldán, Arunpatcha; Ratthiwan, Janejira; Lakmas, Sawanya; Wattanakanjana, Yupa

2016-04-01

In the title compound, [Ag2(C3H6N2S)4(C18H15P)2](C2H3O2)2·[Ag(C2H3O2)(C3H6N2S)(C18H15P)2]2·2C2H3N·4H2O, the Ag(I) ion in the mononuclear neutral complex exhibits a distorted tetra-hedral environment with coordination by two P atoms from tri-phenyl-phosphane (PPh3) ligands, one S atom of an imidazolidine-2-thione (etu) ligand and one O atom of an acetate anion. The binuclear cationic complex comprises two inversion-related [Ag(C3H6N2S)2(C18H15P)] units with Ag(I) ions bridged by two S atoms from etu ligands forming a four-membered Ag-S-Ag-S ring. Each Ag(I) ion is coordinated by a P atom of a PPh3 ligand, two S atoms of bridging etu ligands and the terminal S atom of an etu ligand in a distorted tetra-hedral environment. In the crystal, the mononuclear complex is linked to lattice water mol-ecules through O-H⋯O and N-H⋯O hydrogen bonds, forming a chain along [100]. In addition, the binuclear complex mol-ecules are connected to acetate anions and lattice water mol-ecules via O-H⋯O, N-H⋯O and O-H⋯S hydrogen bonds, also along [100].

CMS geometry through 2020

International Nuclear Information System (INIS)

Osborne, I; Brownson, E; Eulisse, G; Jones, C D; Sexton-Kennedy, E; Lange, D J

2014-01-01

CMS faces real challenges with upgrade of the CMS detector through 2020 and beyond. One of the challenges, from the software point of view, is managing upgrade simulations with the same software release as the 2013 scenario. We present the CMS geometry description software model, its integration with the CMS event setup and core software. The CMS geometry configuration and selection is implemented in Python. The tools collect the Python configuration fragments into a script used in CMS workflow. This flexible and automated geometry configuration allows choosing either transient or persistent version of the same scenario and specific version of the same scenario. We describe how the geometries are integrated and validated, and how we define and handle different geometry scenarios in simulation and reconstruction. We discuss how to transparently manage multiple incompatible geometries in the same software release. Several examples are shown based on current implementation assuring consistent choice of scenario conditions. The consequences and implications for multiple/different code algorithms are discussed.

Seventeen-coordinate actinide helium complexes

Energy Technology Data Exchange (ETDEWEB)

Kaltsoyannis, Nikolas [School of Chemistry, The University of Manchester (United Kingdom)

2017-06-12

The geometries and electronic structures of molecular ions featuring He atoms complexed to actinide cations are explored computationally using density functional and coupled cluster theories. A new record coordination number is established, as AcHe{sub 17}{sup 3+}, ThHe{sub 17}{sup 4+}, and PaHe{sub 17}{sup 4+} are all found to be true geometric minima, with the He atoms clearly located in the first shell around the actinide. Analysis of AcHe{sub n}{sup 3+} (n=1-17) using the quantum theory of atoms in molecules (QTAIM) confirms these systems as having closed shell, charge-induced dipole bonding. Excellent correlations (R{sup 2}>0.95) are found between QTAIM metrics (bond critical point electron densities and delocalization indices) and the average Ac-He distances, and also with the incremental He binding energies. (copyright 2017 Wiley-VCH Verlag GmbH and Co. KGaA, Weinheim)

Engineering the oxygen coordination in digital superlattices

Science.gov (United States)

Cook, Seyoung; Andersen, Tassie K.; Hong, Hawoong; Rosenberg, Richard A.; Marks, Laurence D.; Fong, Dillon D.

2017-12-01

The oxygen sublattice in complex oxides is typically composed of corner-shared polyhedra, with transition metals at their centers. The electronic and chemical properties of the oxide depend on the type and geometric arrangement of these polyhedra, which can be controlled through epitaxial synthesis. Here, we use oxide molecular beam epitaxy to create SrCoOx:SrTiO3 superlattices with tunable oxygen coordination environments and sublattice geometries. Using synchrotron X-ray scattering in combination with soft X-ray spectroscopy, we find that the chemical state of Co can be varied with the polyhedral arrangement, with higher Co oxidation states increasing the valence band maximum. This work demonstrates a new strategy for engineering unique electronic structures in the transition metal oxides using short-period superlattices.

Analisis Keterampilan Geometri Siswa Dalam Memecahkan Masalah Geometri Berdasarkan Tingkat Berpikir Van Hiele

OpenAIRE

Muhassanah, Nuraini; Sujadi, Imam; Riyadi, Riyadi

2014-01-01

The objective of this research was to describe the VIII grade students geometry skills atSMP N 16 Surakarta in the level 0 (visualization), level 1 (analysis), and level 2 (informaldeduction) van Hiele level of thinking in solving the geometry problem. This research was aqualitative research in the form of case study analyzing deeply the students geometry skill insolving the geometry problem based on van Hiele level of thingking. The subject of this researchwas nine students of VIII grade at ...

Algorithms in Algebraic Geometry

CERN Document Server

Dickenstein, Alicia; Sommese, Andrew J

2008-01-01

In the last decade, there has been a burgeoning of activity in the design and implementation of algorithms for algebraic geometric computation. Some of these algorithms were originally designed for abstract algebraic geometry, but now are of interest for use in applications and some of these algorithms were originally designed for applications, but now are of interest for use in abstract algebraic geometry. The workshop on Algorithms in Algebraic Geometry that was held in the framework of the IMA Annual Program Year in Applications of Algebraic Geometry by the Institute for Mathematics and Its

Non-Euclidean geometry

CERN Document Server

Kulczycki, Stefan

2008-01-01

This accessible approach features two varieties of proofs: stereometric and planimetric, as well as elementary proofs that employ only the simplest properties of the plane. A short history of geometry precedes a systematic exposition of the principles of non-Euclidean geometry.Starting with fundamental assumptions, the author examines the theorems of Hjelmslev, mapping a plane into a circle, the angle of parallelism and area of a polygon, regular polygons, straight lines and planes in space, and the horosphere. Further development of the theory covers hyperbolic functions, the geometry of suff

[(Nitrato-κO,O')(nitrito-κO,O')(0.25/1.75)]bis-(1,10-phenanthroline-κN,N')cadmium(II).

Science.gov (United States)

Najafi, Ezzatollah; Amini, Mostafa M; Ng, Seik Weng

2011-01-22

The reaction of cadmium nitrate and sodium nitrite in the presence of 1,10-phenanthroline yields the mixed nitrate-nitrite title complex, [Cd(NO(2))(1.75)(NO(3))(0.25)(C(12)H(8)N(2))(2)]. The metal ion is bis-chelated by two N-heterocycles as well as by the nitrate/nitrite ions in a distorted dodeca-hedral CdN(4)O(4) coordination environment. One nitrite group is ordered; the other is disordered with respect to a nitrate group (ratio 0.75:0.25) concerning the O atom that is not involved in bonding to the metal ion.

Geometry on the space of geometries

International Nuclear Information System (INIS)

Christodoulakis, T.; Zanelli, J.

1988-06-01

We discuss the geometric structure of the configuration space of pure gravity. This is an infinite dimensional manifold, M, where each point represents one spatial geometry g ij (x). The metric on M is dictated by geometrodynamics, and from it, the Christoffel symbols and Riemann tensor can be found. A ''free geometry'' tracing a geodesic on the manifold describes the time evolution of space in the strong gravity limit. In a regularization previously introduced by the authors, it is found that M does not have the same dimensionality, D, everywhere, and that D is not a scalar, although it is covariantly constant. In this regularization, it is seen that the path integral measure can be absorbed in a renormalization of the cosmological constant. (author). 19 refs

A Lorentzian quantum geometry

Energy Technology Data Exchange (ETDEWEB)

Grotz, Andreas

2011-10-07

In this thesis, a formulation of a Lorentzian quantum geometry based on the framework of causal fermion systems is proposed. After giving the general definition of causal fermion systems, we deduce space-time as a topological space with an underlying causal structure. Restricting attention to systems of spin dimension two, we derive the objects of our quantum geometry: the spin space, the tangent space endowed with a Lorentzian metric, connection and curvature. In order to get the correspondence to classical differential geometry, we construct examples of causal fermion systems by regularizing Dirac sea configurations in Minkowski space and on a globally hyperbolic Lorentzian manifold. When removing the regularization, the objects of our quantum geometry reduce to the common objects of spin geometry on Lorentzian manifolds, up to higher order curvature corrections.

A Lorentzian quantum geometry

International Nuclear Information System (INIS)

Grotz, Andreas

2011-01-01

In this thesis, a formulation of a Lorentzian quantum geometry based on the framework of causal fermion systems is proposed. After giving the general definition of causal fermion systems, we deduce space-time as a topological space with an underlying causal structure. Restricting attention to systems of spin dimension two, we derive the objects of our quantum geometry: the spin space, the tangent space endowed with a Lorentzian metric, connection and curvature. In order to get the correspondence to classical differential geometry, we construct examples of causal fermion systems by regularizing Dirac sea configurations in Minkowski space and on a globally hyperbolic Lorentzian manifold. When removing the regularization, the objects of our quantum geometry reduce to the common objects of spin geometry on Lorentzian manifolds, up to higher order curvature corrections.

Research Article. Geodesic equations and their numerical solutions in geodetic and Cartesian coordinates on an oblate spheroid

Directory of Open Access Journals (Sweden)

Panou G.

2017-02-01

Full Text Available The direct geodesic problem on an oblate spheroid is described as an initial value problem and is solved numerically using both geodetic and Cartesian coordinates. The geodesic equations are formulated by means of the theory of differential geometry. The initial value problem under consideration is reduced to a system of first-order ordinary differential equations, which is solved using a numerical method. The solution provides the coordinates and the azimuths at any point along the geodesic. The Clairaut constant is not used for the solution but it is computed, allowing to check the precision of the method. An extensive data set of geodesics is used, in order to evaluate the performance of the method in each coordinate system. The results for the direct geodesic problem are validated by comparison to Karney’s method. We conclude that a complete, stable, precise, accurate and fast solution of the problem in Cartesian coordinates is accomplished.

μ(3)-Carbonato-κO:O':O''-tris-{(η-ben-zene)[(R)-1-(1-amino-ethyl)naphthyl-κC,N]ruthenium(II)} hexa-fluorido-phosphate dichloro-methane solvate.

Science.gov (United States)

Sortais, Jean-Baptiste; Brelot, Lydia; Pfeffer, Michel; Barloy, Laurent

2008-02-15

The title compound, [Ru(3)(C(12)H(12)N)(3)(CO(3))(C(6)H(6))(3)]PF(6)·CH(2)Cl(2), was obtained unintentionally as the product of an attempted deprotonation of the monomeric parent ruthenium complex [Ru(C(12)H(12)N)(C(6)H(6))(C(2)H(3)N)]PF(6). The carbonate ligand bridges three half-sandwich cyclo-ruthenated fragments, each of them exhibiting a pseudo-tetra-hedral geometry. The configuration of the Ru atoms is S. The naphthyl groups of the enanti-opure cyclo-ruthenated benzylic amine ligands point in the same direction, adopting a propeller shape.

Curvature of fluctuation geometry and its implications on Riemannian fluctuation theory

International Nuclear Information System (INIS)

Velazquez, L

2013-01-01

Fluctuation geometry was recently proposed as a counterpart approach of the Riemannian geometry of inference theory (widely known as information geometry). This theory describes the geometric features of the statistical manifold M of random events that are described by a family of continuous distributions dp(x|θ). A main goal of this work is to clarify the statistical relevance of the Levi-Civita curvature tensor R ijkl (x|θ) of the statistical manifold M. For this purpose, the notion of irreducible statistical correlations is introduced. Specifically, a distribution dp(x|θ) exhibits irreducible statistical correlations if every distribution dp(x-check|θ) obtained from dp(x|θ) by considering a coordinate change x-check = φ(x) cannot be factorized into independent distributions as dp(x-check|θ) = prod i dp (i) (x-check i |θ). It is shown that the curvature tensor R ijkl (x|θ) arises as a direct indicator about the existence of irreducible statistical correlations. Moreover, the curvature scalar R(x|θ) allows us to introduce a criterium for the applicability of the Gaussian approximation of a given distribution function. This type of asymptotic result is obtained in the framework of the second-order geometric expansion of the distribution family dp(x|θ), which appears as a counterpart development of the high-order asymptotic theory of statistical estimation. In physics, fluctuation geometry represents the mathematical apparatus of a Riemannian extension for Einstein’s fluctuation theory of statistical mechanics. Some exact results of fluctuation geometry are now employed to derive the invariant fluctuation theorems. Moreover, the curvature scalar allows us to express some asymptotic formulae that account for the system fluctuating behavior beyond the Gaussian approximation, e.g.: it appears as a second-order correction of the Legendre transformation between thermodynamic potentials, P(θ)=θ i x-bar i -s( x-bar |θ)+k 2 R(x|θ)/6. (paper)

Geometry and Combinatorics

DEFF Research Database (Denmark)

Kokkendorff, Simon Lyngby

2002-01-01

The subject of this Ph.D.-thesis is somewhere in between continuous and discrete geometry. Chapter 2 treats the geometry of finite point sets in semi-Riemannian hyperquadrics,using a matrix whose entries are a trigonometric function of relative distances in a given point set. The distance...... to the geometry of a simplex in a semi-Riemannian hyperquadric. In chapter 3 we study which finite metric spaces that are realizable in a hyperbolic space in the limit where curvature goes to -∞. We show that such spaces are the so called leaf spaces, the set of degree 1 vertices of weighted trees. We also...... establish results on the limiting geometry of such an isometrically realized leaf space simplex in hyperbolic space, when curvature goes to -∞. Chapter 4 discusses negative type of metric spaces. We give a measure theoretic treatment of this concept and related invariants. The theory developed...

Geometry and billiards

CERN Document Server

Tabachnikov, Serge

2005-01-01

Mathematical billiards describe the motion of a mass point in a domain with elastic reflections off the boundary or, equivalently, the behavior of rays of light in a domain with ideally reflecting boundary. From the point of view of differential geometry, the billiard flow is the geodesic flow on a manifold with boundary. This book is devoted to billiards in their relation with differential geometry, classical mechanics, and geometrical optics. The topics covered include variational principles of billiard motion, symplectic geometry of rays of light and integral geometry, existence and nonexistence of caustics, optical properties of conics and quadrics and completely integrable billiards, periodic billiard trajectories, polygonal billiards, mechanisms of chaos in billiard dynamics, and the lesser-known subject of dual (or outer) billiards. The book is based on an advanced undergraduate topics course (but contains more material than can be realistically taught in one semester). Although the minimum prerequisit...

Non-homogeneous updates for the iterative coordinate descent algorithm

Science.gov (United States)

Yu, Zhou; Thibault, Jean-Baptiste; Bouman, Charles A.; Sauer, Ken D.; Hsieh, Jiang

2007-02-01

Statistical reconstruction methods show great promise for improving resolution, and reducing noise and artifacts in helical X-ray CT. In fact, statistical reconstruction seems to be particularly valuable in maintaining reconstructed image quality when the dosage is low and the noise is therefore high. However, high computational cost and long reconstruction times remain as a barrier to the use of statistical reconstruction in practical applications. Among the various iterative methods that have been studied for statistical reconstruction, iterative coordinate descent (ICD) has been found to have relatively low overall computational requirements due to its fast convergence. This paper presents a novel method for further speeding the convergence of the ICD algorithm, and therefore reducing the overall reconstruction time for statistical reconstruction. The method, which we call nonhomogeneous iterative coordinate descent (NH-ICD) uses spatially non-homogeneous updates to speed convergence by focusing computation where it is most needed. Experimental results with real data indicate that the method speeds reconstruction by roughly a factor of two for typical 3D multi-slice geometries.

Drawing Dynamic Geometry Figures Online with Natural Language for Junior High School Geometry

Science.gov (United States)

Wong, Wing-Kwong; Yin, Sheng-Kai; Yang, Chang-Zhe

2012-01-01

This paper presents a tool for drawing dynamic geometric figures by understanding the texts of geometry problems. With the tool, teachers and students can construct dynamic geometric figures on a web page by inputting a geometry problem in natural language. First we need to build the knowledge base for understanding geometry problems. With the…

KEMAJUAN BELAJAR SISWA PADA GEOMETRI TRANSFORMASI MENGGUNAKAN AKTIVITAS REFLEKSI GEOMETRI

Directory of Open Access Journals (Sweden)

Irkham Ulil Albab

2014-10-01

Full Text Available Abstrak: Penelitian ini bertujuan untuk mendeskripsikan kemajuan belajar siswa pada materi geometri transformasi yang didukung dengan serangkaian aktivitas belajar berdasarkan Pendidikan Matematika Realistik Indonesia. Penelitian didesain melalui tiga tahap, yaitu tahapan perancangan desain awal, pengujian desain melalui pembelajaran awal dan pembelajaran eksperimental, dan tahap analisis retrospektif. Dalam penelitian ini, Hypothetical Learning Trajectory, HLT (HLT berperan penting sebagai desain pembelajaran sekaligus instrumen penelitian. HLT diujikan terhadap 26 siswa kelas VII. Data dikumpulkan dengan teknik wawancara, pengamatan, dan catatan lapangan. Hasil penelitian menunjukkan bahwa desain pembelajaran ini mampu menstimulasi siswa untuk memberikan karakteristik refleksi dan transformasi geometri lainnya secara informal, mengklasifikasikannya dalam transformasi isometri pada level kedua, dan menemukan garis bantuan refleksi pada level yang lebih formal. Selain itu, garis bantuan refleksi digunakan oleh siswa untuk menggambar bayangan refleksi dan pola pencerminan serta memahami bentuk rotasi dan translasi sebagai kombinasi refleksi adalah level tertinggi. Keyword: transformasi geometri, kombinasi refleksi, rotasi, translasi, design research, HLT STUDENTS’ LEARNING PROGRESS ON TRANSFORMATION GEOMETRY USING THE GEOMETRY REFLECTION ACTIVITIES Abstract: This study was aimed at describing the students’ learning progress on transformation geometry supported by a set of learning activities based on Indonesian Realistic Mathematics Education. The study was designed into three stages, that is, the preliminary design stage, the design testing through initial instruction and experiment, and the restrospective analysis stage. In this study, Hypothetical Learning Trajectory (HLT played an important role as an instructional design and a research instrument. HLT was tested to 26 seventh grade students. The data were collected through interviews

6j symbols for the modular double, quantum hyperbolic geometry, and supersymmetric gauge theories

Energy Technology Data Exchange (ETDEWEB)

Teschner, J.; Vartanov, G.S.

2012-02-15

We revisit the definition of the 6j-symbols from the modular double of U{sub q}(sl(2,R)), referred to as b-6j symbols. Our new results are (i) the identification of particularly natural normalization conditions, and (ii) new integral representations for this object. This is used to briefly discuss possible applications to quantum hyperbolic geometry, and to the study of certain supersymmetric gauge theories. We show, in particular, that the b-6j symbol has leading semiclassical asymptotics given by the volume of a non-ideal tetrahedron. We furthermore observe a close relation with the problem to quantize natural Darboux coordinates for moduli spaces of flat connections on Riemann surfaces related to the Fenchel-Nielsen coordinates. Our new integral representations finally indicate a possible interpretation of the b-6j symbols as partition functions of three-dimensional N=2 supersymmetric gauge theories. (orig.)

6j symbols for the modular double, quantum hyperbolic geometry, and supersymmetric gauge theories

International Nuclear Information System (INIS)

Teschner, J.; Vartanov, G.S.

2012-02-01

We revisit the definition of the 6j-symbols from the modular double of U q (sl(2,R)), referred to as b-6j symbols. Our new results are (i) the identification of particularly natural normalization conditions, and (ii) new integral representations for this object. This is used to briefly discuss possible applications to quantum hyperbolic geometry, and to the study of certain supersymmetric gauge theories. We show, in particular, that the b-6j symbol has leading semiclassical asymptotics given by the volume of a non-ideal tetrahedron. We furthermore observe a close relation with the problem to quantize natural Darboux coordinates for moduli spaces of flat connections on Riemann surfaces related to the Fenchel-Nielsen coordinates. Our new integral representations finally indicate a possible interpretation of the b-6j symbols as partition functions of three-dimensional N=2 supersymmetric gauge theories. (orig.)

Software Geometry in Simulations

Science.gov (United States)

Alion, Tyler; Viren, Brett; Junk, Tom

2015-04-01

The Long Baseline Neutrino Experiment (LBNE) involves many detectors. The experiment's near detector (ND) facility, may ultimately involve several detectors. The far detector (FD) will be significantly larger than any other Liquid Argon (LAr) detector yet constructed; many prototype detectors are being constructed and studied to motivate a plethora of proposed FD designs. Whether it be a constructed prototype or a proposed ND/FD design, every design must be simulated and analyzed. This presents a considerable challenge to LBNE software experts; each detector geometry must be described to the simulation software in an efficient way which allows for multiple authors to easily collaborate. Furthermore, different geometry versions must be tracked throughout their use. We present a framework called General Geometry Description (GGD), written and developed by LBNE software collaborators for managing software to generate geometries. Though GGD is flexible enough to be used by any experiment working with detectors, we present it's first use in generating Geometry Description Markup Language (GDML) files to interface with LArSoft, a framework of detector simulations, event reconstruction, and data analyses written for all LAr technology users at Fermilab. Brett is the other of the framework discussed here, the General Geometry Description (GGD).

Analysis of errors introduced by geographic coordinate systems on weather numeric prediction modeling

Directory of Open Access Journals (Sweden)

Y. Cao

2017-09-01

Full Text Available Most atmospheric models, including the Weather Research and Forecasting (WRF model, use a spherical geographic coordinate system to internally represent input data and perform computations. However, most geographic information system (GIS input data used by the models are based on a spheroid datum because it better represents the actual geometry of the earth. WRF and other atmospheric models use these GIS input layers as if they were in a spherical coordinate system without accounting for the difference in datum. When GIS layers are not properly reprojected, latitudinal errors of up to 21 km in the midlatitudes are introduced. Recent studies have suggested that for very high-resolution applications, the difference in datum in the GIS input data (e.g., terrain land use, orography should be taken into account. However, the magnitude of errors introduced by the difference in coordinate systems remains unclear. This research quantifies the effect of using a spherical vs. a spheroid datum for the input GIS layers used by WRF to study greenhouse gas transport and dispersion in northeast Pennsylvania.

Methods of information geometry

CERN Document Server

Amari, Shun-Ichi

2000-01-01

Information geometry provides the mathematical sciences with a new framework of analysis. It has emerged from the investigation of the natural differential geometric structure on manifolds of probability distributions, which consists of a Riemannian metric defined by the Fisher information and a one-parameter family of affine connections called the \\alpha-connections. The duality between the \\alpha-connection and the (-\\alpha)-connection together with the metric play an essential role in this geometry. This kind of duality, having emerged from manifolds of probability distributions, is ubiquitous, appearing in a variety of problems which might have no explicit relation to probability theory. Through the duality, it is possible to analyze various fundamental problems in a unified perspective. The first half of this book is devoted to a comprehensive introduction to the mathematical foundation of information geometry, including preliminaries from differential geometry, the geometry of manifolds or probability d...

Space–time and spatial geodesic orbits in Schwarzschild geometry

Science.gov (United States)

Resca, Lorenzo

2018-05-01

Geodesic orbit equations in the Schwarzschild geometry of general relativity reduce to ordinary conic sections of Newtonian mechanics and gravity for material particles in the non-relativistic limit. On the contrary, geodesic orbit equations for a proper spatial submanifold of Schwarzschild metric at any given coordinate-time correspond to an unphysical gravitational repulsion in the non-relativistic limit. This demonstrates at a basic level the centrality and critical role of relativistic time and its intimate pseudo-Riemannian connection with space. Correspondingly, a commonly popularised depiction of geodesic orbits of planets as resulting from the curvature of space produced by the Sun, represented as a rubber sheet dipped in the middle by the weighing of that massive body, is mistaken and misleading for the essence of relativity, even in the non-relativistic limit.

Attoclock reveals natural coordinates of the laser-induced tunnelling current flow in atoms

DEFF Research Database (Denmark)

Pfeiffer, Adrian N.; Cirelli, Claudio; Smolarski, Mathias

2012-01-01

the attoclock technique4 to obtain experimental information about the electron tunnelling geometry (the natural coordinates of the tunnelling current flow) and exit point. We confirm vanishing tunnelling delay time, show the importance of the inclusion of Stark shifts5, 6 and report on multi-electron effects......In the research area of strong-laser-field interactions and attosecond science1, tunnelling of an electron through the barrier formed by the electric field of the laser and the atomic potential is typically assumed to be the initial key process that triggers subsequent dynamics1, 2, 3. Here we use...... clearly identified by comparing results in argon and helium atoms. Our combined theory and experiment allows us to single out the geometry of the inherently one-dimensional tunnelling problem, through an asymptotic separation of the full three-dimensional problem. Our findings have implications for laser...

The design of geometry teaching: learning from the geometry textbooks of Godfrey and Siddons

OpenAIRE

Fujita, Taro; Jones, Keith

2002-01-01

Deciding how to teach geometry remains a demanding task with one of major arguments being about how to combine the intuitive and deductive aspects of geometry into an effective teaching design. In order to try to obtain an insight into tackling this issue, this paper reports an analysis of innovative geometry textbooks which were published in the early part of the 20th Century, a time when significant efforts were being made to improve the teaching and learning of geometry. The analysis sugge...

Towards canonical quantum gravity for 3+1 geometries admitting maximally symmetric two-dimensional surfaces

International Nuclear Information System (INIS)

Christodoulakis, T; Doulis, G; Terzis, Petros A; Melas, E; Grammenos, Th; Papadopoulos, G O; Spanou, A

2010-01-01

The canonical decomposition of all 3+1 geometries admitting two-dimensional space-like surfaces is exhibited as a generalization of a previous work. A proposal, consisting of a specific renormalization Assumption and an accompanying Requirement, which has been put forward in the 2+1 case is now generalized to 3+1 dimensions. This enables the canonical quantization of these geometries through a generalization of Kuchar's quantization scheme in the case of infinite degrees of freedom. The resulting Wheeler-DeWitt equation is based on a renormalized manifold parameterized by three smooth scalar functionals. The entire space of solutions to this equation is analytically given, a fact that is entirely new to the present case. This is made possible through the exploitation of the residual freedom in the choice of the third functional, which is left by the imposition of the Requirement, and is proven to correspond to a general coordinate transformation in the renormalized manifold.

Sources of hyperbolic geometry

CERN Document Server

Stillwell, John

1996-01-01

This book presents, for the first time in English, the papers of Beltrami, Klein, and Poincaré that brought hyperbolic geometry into the mainstream of mathematics. A recognition of Beltrami comparable to that given the pioneering works of Bolyai and Lobachevsky seems long overdue-not only because Beltrami rescued hyperbolic geometry from oblivion by proving it to be logically consistent, but because he gave it a concrete meaning (a model) that made hyperbolic geometry part of ordinary mathematics. The models subsequently discovered by Klein and Poincaré brought hyperbolic geometry even further down to earth and paved the way for the current explosion of activity in low-dimensional geometry and topology. By placing the works of these three mathematicians side by side and providing commentaries, this book gives the student, historian, or professional geometer a bird's-eye view of one of the great episodes in mathematics. The unified setting and historical context reveal the insights of Beltrami, Klein, and Po...

SPIRIT, Plot of Geometry and Results of 2-D Finite Elements Calculation

International Nuclear Information System (INIS)

Lambert, P.

1977-01-01

1 - Nature of the physical problem solved: SPIRIT plots the geometry and the results from a 2-D finite elements calculation. 2 - Method of solution: SPIRIT uses the Benson-Lehner graph plotter. The programme will draw each separate element of the mesh according to the description supplied and a complete picture of the mesh is therefore built up. The program can also construct an isothermal distribution using straight lines. Each line is constructed considering each element in isolation. 3 - Restrictions on the complexity of the problem: The program deals only with bodies entirely contained in the first quadrant and the x-coordinates should be less than 20.0

The geometry description markup language

International Nuclear Information System (INIS)

Chytracek, R.

2001-01-01

Currently, a lot of effort is being put on designing complex detectors. A number of simulation and reconstruction frameworks and applications have been developed with the aim to make this job easier. A very important role in this activity is played by the geometry description of the detector apparatus layout and its working environment. However, no real common approach to represent geometry data is available and such data can be found in various forms starting from custom semi-structured text files, source code (C/C++/FORTRAN), to XML and database solutions. The XML (Extensible Markup Language) has proven to provide an interesting approach for describing detector geometries, with several different but incompatible XML-based solutions existing. Therefore, interoperability and geometry data exchange among different frameworks is not possible at present. The author introduces a markup language for geometry descriptions. Its aim is to define a common approach for sharing and exchanging of geometry description data. Its requirements and design have been driven by experience and user feedback from existing projects which have their geometry description in XML

Complex analysis and CR geometry

CERN Document Server

Zampieri, Giuseppe

2008-01-01

Cauchy-Riemann (CR) geometry is the study of manifolds equipped with a system of CR-type equations. Compared to the early days when the purpose of CR geometry was to supply tools for the analysis of the existence and regularity of solutions to the \\bar\\partial-Neumann problem, it has rapidly acquired a life of its own and has became an important topic in differential geometry and the study of non-linear partial differential equations. A full understanding of modern CR geometry requires knowledge of various topics such as real/complex differential and symplectic geometry, foliation theory, the geometric theory of PDE's, and microlocal analysis. Nowadays, the subject of CR geometry is very rich in results, and the amount of material required to reach competence is daunting to graduate students who wish to learn it. However, the present book does not aim at introducing all the topics of current interest in CR geometry. Instead, an attempt is made to be friendly to the novice by moving, in a fairly relaxed way, f...

Polyethylene glycol and octa-arginine dual-functionalized nanographene oxide: an optimization for efficient nucleic acid delivery.

Science.gov (United States)

Imani, Rana; Prakash, Satya; Vali, Hojatollah; Faghihi, Shahab

2018-05-29

The successful application of nucleic acid-based therapy for the treatment of various cancers is largely dependent on a safe and efficient delivery system. A dual-functionalized graphene oxide (GO)-based nanocarrier with the conjugation of aminated-polyethylene glycol (PEG-diamine) and octa-arginine (R8) for the intracellular delivery of nucleic acids is proposed. The functionalized sites are covalently co-conjugated and the PEG : R8 molar ratio is optimized at 10 : 1 to achieve a hydrocolloidally stable size of 252 ± 2.0 nm with an effective charge of +40.97 ± 1.05 and an amine-rich content of 10.87 ± 0.4 μmol g-1. The uptake of the nanocarrier in breast cancer cell lines, MCF-7 and MDA-MB 231, is investigated. The siRNA and pDNA condensation ability in the presence and absence of enzymes and the endosomal buffering capacity, as well as the intracellular localization of the gene/nanocarrier complex are also evaluated. Furthermore, the delivery of functional genes associated with the nanocarrier is assessed using c-Myc protein knockdown and EGFP gene expression. The effective uptake of the nanocarrier by the cells shows superior cytocompatibility, and protects the siRNA and pDNA against enzyme degradation while inhibiting their migration with N : P ratios of 10 and 5, respectively. The co-conjugation of PEG-diamine and the cationic cell-penetrating peptide (CPP) into the GO nanocarrier also provides a superior internalization efficacy of 85% in comparison with a commercially available transfection reagent. The c-Myc protein knockdown and EGFP expression, which are induced by the nanocarrier, confirm that the optimized PEG-diamine/R8-functionalized GO could effectively deliver pDNA and siRNA into the cells and interfere with gene expression.

Global aspects of complex geometry

CERN Document Server

Catanese, Fabrizio; Huckleberry, Alan T

2006-01-01

Present an overview of developments in Complex Geometry. This book covers topics that range from curve and surface theory through special varieties in higher dimensions, moduli theory, Kahler geometry, and group actions to Hodge theory and characteristic p-geometry.

Physics- and engineering knowledge-based geometry repair system for robust parametric CAD geometries

OpenAIRE

Li, Dong

2012-01-01

In modern multi-objective design optimisation, an effective geometry engine is becoming an essential tool and its performance has a significant impact on the entire process. Building a parametric geometry requires difficult compromises between the conflicting goals of robustness and flexibility. The work presents a solution for improving the robustness of parametric geometry models by capturing and modelling relative engineering knowledge into a surrogate model, and deploying it automatically...

Analytical Model of Doppler Spectra of Light Backscattered from Rotating Convex Bodies of Revolution in the Global Cartesian Coordinate System

International Nuclear Information System (INIS)

Yan-Jun, Gong; Zhen-Sen, Wu; Jia-Ji, Wu

2009-01-01

We present an analytical model of Doppler spectra in backscattering from arbitrary rough convex bodies of revolution rotating around their axes in the global Cartesian coordinate system. This analytical model is applied to analyse Doppler spectra in backscatter from two cones and two cylinders, as well as two ellipsoids of revolution. We numerically analyse the influences of attitude and geometry size of objects on Doppler spectra. The analytical model can give contribution of the surface roughness, attitude and geometry size of convex bodies of revolution to Doppler spectra and may contribute to laser Doppler velocimetry as well as ladar applications

Tetra-, Penta- and Hexa-Coordinated Transition Metal Complexes Constructed from Coumarin-Containing N2O2 Ligand

Directory of Open Access Journals (Sweden)

Lei Gao

2018-02-01

Full Text Available Three newly designed complexes, [Cu(L]·CHCl3 (1, [Co(L(MeOH]·CHCl3 (2 and [{Ni(L(MeOH(PhCOO}2Ni] (3 a coumarin-containing Salamo-type chelating ligand (H2L have been synthesized and characterized by elemental analyses, IR and UV-VIS spectra, and X-ray crystallography. Complex 1 includes one Cu(II atom, one completely deprotonated (L2− unit and one crystalling chloroform molecule, the Cu(II atom shows a square-planar geometry. Complex 2 includes one Co(II atom, one completely deprotonated (L2− unit, one coordinated methanol molecule and one crystalling chloroform molecule. The Co(II atom is a distorted trigonal-bipyramidal geometry. While complex 3 includes three Ni(II atoms, two completely deprotonated (L2− units, two benzoates and two coordinated methanol molecules. The complexes 1 and 2 are both possess three-dimensional supra-molecular structures by abundant noncovalent interactions. But, complex 3 formed a two-dimensional supra-molecular structure by intra-molecular hydrogen bonds. In addition, the antimicrobial and fluorescence properties of H2L and its complexes 1, 2 and 3 were also investigated.

A Rapid Coordinate Transformation Method Applied in Industrial Robot Calibration Based on Characteristic Line Coincidence

Directory of Open Access Journals (Sweden)

Bailing Liu

2016-02-01

Full Text Available Coordinate transformation plays an indispensable role in industrial measurements, including photogrammetry, geodesy, laser 3-D measurement and robotics. The widely applied methods of coordinate transformation are generally based on solving the equations of point clouds. Despite the high accuracy, this might result in no solution due to the use of ill conditioned matrices. In this paper, a novel coordinate transformation method is proposed, not based on the equation solution but based on the geometric transformation. We construct characteristic lines to represent the coordinate systems. According to the space geometry relation, the characteristic line scan is made to coincide by a series of rotations and translations. The transformation matrix can be obtained using matrix transformation theory. Experiments are designed to compare the proposed method with other methods. The results show that the proposed method has the same high accuracy, but the operation is more convenient and flexible. A multi-sensor combined measurement system is also presented to improve the position accuracy of a robot with the calibration of the robot kinematic parameters. Experimental verification shows that the position accuracy of robot manipulator is improved by 45.8% with the proposed method and robot calibration.

A Rapid Coordinate Transformation Method Applied in Industrial Robot Calibration Based on Characteristic Line Coincidence

Science.gov (United States)

Liu, Bailing; Zhang, Fumin; Qu, Xinghua; Shi, Xiaojia

2016-01-01

Coordinate transformation plays an indispensable role in industrial measurements, including photogrammetry, geodesy, laser 3-D measurement and robotics. The widely applied methods of coordinate transformation are generally based on solving the equations of point clouds. Despite the high accuracy, this might result in no solution due to the use of ill conditioned matrices. In this paper, a novel coordinate transformation method is proposed, not based on the equation solution but based on the geometric transformation. We construct characteristic lines to represent the coordinate systems. According to the space geometry relation, the characteristic line scan is made to coincide by a series of rotations and translations. The transformation matrix can be obtained using matrix transformation theory. Experiments are designed to compare the proposed method with other methods. The results show that the proposed method has the same high accuracy, but the operation is more convenient and flexible. A multi-sensor combined measurement system is also presented to improve the position accuracy of a robot with the calibration of the robot kinematic parameters. Experimental verification shows that the position accuracy of robot manipulator is improved by 45.8% with the proposed method and robot calibration. PMID:26901203

Three-Dimensional Cadmium(II Cyanide Coordination Polymers with Ethoxy-, Butoxy- and Hexyloxy-ethanol

Directory of Open Access Journals (Sweden)

Takeshi Kawasaki

2016-08-01

Full Text Available The three novel cadmium(II cyanide coordination polymers with alkoxyethanols, [Cd(CN2(C2H5OCH2CH2OH]n (I, [{Cd(CN2(C4H9OCH2CH2OH}3{Cd(CN2}]n (II and [{Cd(CN2(H2O2}{Cd(CN2}3·2(C6H13OCH2CH2OH]n (III, were synthesized and charcterized by structural determination. Three complexes have three-dimensional Cd(CN2 frameworks; I has distorted tridymite-like structure, and, II and III have zeolite-like structures. The cavities of Cd(CN2 frameworks of the complexes are occupied by the alkoxyethanol molecules. In I and II, hydroxyl oxygen atoms of alkoxyethanol molecules coordinate to the Cd(II ions, and the Cd(II ions exhibit slightly distort trigonal-bipyramidal coordination geometry. In II, there is also tetrahedral Cd(II ion which is coordinated by only the four cyanides. The hydroxyl oxygen atoms of alkoxyethanol connects etheric oxygen atoms of the neighboring alkoxyethanol by hydrogen bond in I and II. In III, hexyloxyethanol molecules do not coordinate to the Cd(II ions, and two water molecules coordnate to the octahedral Cd(II ions. The framework in III contains octahedral Cd(II and tetrahedral Cd(II in a 1:3 ratio. The Cd(CN2 framework structures depended on the difference of alkyl chain for alkoxyethanol molecules.

Noncommutative geometry

CERN Document Server

Connes, Alain

1994-01-01

This English version of the path-breaking French book on this subject gives the definitive treatment of the revolutionary approach to measure theory, geometry, and mathematical physics developed by Alain Connes. Profusely illustrated and invitingly written, this book is ideal for anyone who wants to know what noncommutative geometry is, what it can do, or how it can be used in various areas of mathematics, quantization, and elementary particles and fields.Key Features* First full treatment of the subject and its applications* Written by the pioneer of this field* Broad applications in mathemat

Geometry Revealed

CERN Document Server

Berger, Marcel

2010-01-01

Both classical geometry and modern differential geometry have been active subjects of research throughout the 20th century and lie at the heart of many recent advances in mathematics and physics. The underlying motivating concept for the present book is that it offers readers the elements of a modern geometric culture by means of a whole series of visually appealing unsolved (or recently solved) problems that require the creation of concepts and tools of varying abstraction. Starting with such natural, classical objects as lines, planes, circles, spheres, polygons, polyhedra, curves, surfaces,

Discrete differential geometry. Consistency as integrability

OpenAIRE

Bobenko, Alexander I.; Suris, Yuri B.

2005-01-01

A new field of discrete differential geometry is presently emerging on the border between differential and discrete geometry. Whereas classical differential geometry investigates smooth geometric shapes (such as surfaces), and discrete geometry studies geometric shapes with finite number of elements (such as polyhedra), the discrete differential geometry aims at the development of discrete equivalents of notions and methods of smooth surface theory. Current interest in this field derives not ...

Spinorial Geometry and Branes

International Nuclear Information System (INIS)

Sloane, Peter

2007-01-01

We adapt the spinorial geometry method introduced in [J. Gillard, U. Gran and G. Papadopoulos, 'The spinorial geometry of supersymmetric backgrounds,' Class. Quant. Grav. 22 (2005) 1033 [ (arXiv:hep-th/0410155)

An introduction to incidence geometry

CERN Document Server

De Bruyn, Bart

2016-01-01

This book gives an introduction to the field of Incidence Geometry by discussing the basic families of point-line geometries and introducing some of the mathematical techniques that are essential for their study. The families of geometries covered in this book include among others the generalized polygons, near polygons, polar spaces, dual polar spaces and designs. Also the various relationships between these geometries are investigated. Ovals and ovoids of projective spaces are studied and some applications to particular geometries will be given. A separate chapter introduces the necessary mathematical tools and techniques from graph theory. This chapter itself can be regarded as a self-contained introduction to strongly regular and distance-regular graphs. This book is essentially self-contained, only assuming the knowledge of basic notions from (linear) algebra and projective and affine geometry. Almost all theorems are accompanied with proofs and a list of exercises with full solutions is given at the end...

Poisson Coordinates.

Science.gov (United States)

Li, Xian-Ying; Hu, Shi-Min

2013-02-01

Harmonic functions are the critical points of a Dirichlet energy functional, the linear projections of conformal maps. They play an important role in computer graphics, particularly for gradient-domain image processing and shape-preserving geometric computation. We propose Poisson coordinates, a novel transfinite interpolation scheme based on the Poisson integral formula, as a rapid way to estimate a harmonic function on a certain domain with desired boundary values. Poisson coordinates are an extension of the Mean Value coordinates (MVCs) which inherit their linear precision, smoothness, and kernel positivity. We give explicit formulas for Poisson coordinates in both continuous and 2D discrete forms. Superior to MVCs, Poisson coordinates are proved to be pseudoharmonic (i.e., they reproduce harmonic functions on n-dimensional balls). Our experimental results show that Poisson coordinates have lower Dirichlet energies than MVCs on a number of typical 2D domains (particularly convex domains). As well as presenting a formula, our approach provides useful insights for further studies on coordinates-based interpolation and fast estimation of harmonic functions.

Spinorial Geometry and Branes

Energy Technology Data Exchange (ETDEWEB)

Sloane, Peter [Department of Mathematics, King' s College, University of London, Strand, London WC2R 2LS (United Kingdom)

2007-09-15

We adapt the spinorial geometry method introduced in [J. Gillard, U. Gran and G. Papadopoulos, 'The spinorial geometry of supersymmetric backgrounds,' Class. Quant. Grav. 22 (2005) 1033 [ (arXiv:hep-th/0410155)

Introduction to non-Euclidean geometry

CERN Document Server

Wolfe, Harold E

2012-01-01

One of the first college-level texts for elementary courses in non-Euclidean geometry, this concise, readable volume is geared toward students familiar with calculus. A full treatment of the historical background explores the centuries-long efforts to prove Euclid's parallel postulate and their triumphant conclusion. Numerous original exercises form an integral part of the book.Topics include hyperbolic plane geometry and hyperbolic plane trigonometry, applications of calculus to the solutions of some problems in hyperbolic geometry, elliptic plane geometry and trigonometry, and the consistenc

Optical geometry across the horizon

International Nuclear Information System (INIS)

Jonsson, Rickard

2006-01-01

In a recent paper (Jonsson and Westman 2006 Class. Quantum Grav. 23 61), a generalization of optical geometry, assuming a non-shearing reference congruence, is discussed. Here we illustrate that this formalism can be applied to (a finite four-volume) of any spherically symmetric spacetime. In particular we apply the formalism, using a non-static reference congruence, to do optical geometry across the horizon of a static black hole. While the resulting geometry in principle is time dependent, we can choose the reference congruence in such a manner that an embedding of the geometry always looks the same. Relative to the embedded geometry the reference points are then moving. We discuss the motion of photons, inertial forces and gyroscope precession in this framework

Convection in Slab and Spheroidal Geometries

Science.gov (United States)

Porter, David H.; Woodward, Paul R.; Jacobs, Michael L.

2000-01-01

Three-dimensional numerical simulations of compressible turbulent thermally driven convection, in both slab and spheroidal geometries, are reviewed and analyzed in terms of velocity spectra and mixing-length theory. The same ideal gas model is used in both geometries, and resulting flows are compared. The piecewise-parabolic method (PPM), with either thermal conductivity or photospheric boundary conditions, is used to solve the fluid equations of motion. Fluid motions in both geometries exhibit a Kolmogorov-like k(sup -5/3) range in their velocity spectra. The longest wavelength modes are energetically dominant in both geometries, typically leading to one convection cell dominating the flow. In spheroidal geometry, a dipolar flow dominates the largest scale convective motions. Downflows are intensely turbulent and up drafts are relatively laminar in both geometries. In slab geometry, correlations between temperature and velocity fluctuations, which lead to the enthalpy flux, are fairly independent of depth. In spheroidal geometry this same correlation increases linearly with radius over the inner 70 percent by radius, in which the local pressure scale heights are a sizable fraction of the radius. The effects from the impenetrable boundary conditions in the slab geometry models are confused with the effects from non-local convection. In spheroidal geometry nonlocal effects, due to coherent plumes, are seen as far as several pressure scale heights from the lower boundary and are clearly distinguishable from boundary effects.

Complex and symplectic geometry

CERN Document Server

Medori, Costantino; Tomassini, Adriano

2017-01-01

This book arises from the INdAM Meeting "Complex and Symplectic Geometry", which was held in Cortona in June 2016. Several leading specialists, including young researchers, in the field of complex and symplectic geometry, present the state of the art of their research on topics such as the cohomology of complex manifolds; analytic techniques in Kähler and non-Kähler geometry; almost-complex and symplectic structures; special structures on complex manifolds; and deformations of complex objects. The work is intended for researchers in these areas.

Initiation to global Finslerian geometry

CERN Document Server

Akbar-Zadeh, Hassan

2006-01-01

After a brief description of the evolution of thinking on Finslerian geometry starting from Riemann, Finsler, Berwald and Elie Cartan, the book gives a clear and precise treatment of this geometry. The first three chapters develop the basic notions and methods, introduced by the author, to reach the global problems in Finslerian Geometry. The next five chapters are independent of each other, and deal with among others the geometry of generalized Einstein manifolds, the classification of Finslerian manifolds of constant sectional curvatures. They also give a treatment of isometric, affine, p

Precise measurement of cat patellofemoral joint surface geometry with multistation digital photogrammetry.

Science.gov (United States)

Ronsky, J L; Boyd, S K; Lichti, D D; Chapman, M A; Salkauskas, K

1999-04-01

Three-dimensional joint models are important tools for investigating mechanisms related to normal and pathological joints. Often these models necessitate accurate three-dimensional joint surface geometric data so that reliable model results can be obtained; however, in models based on small joints, this is often problematic due to limitations of the present techniques. These limitations include insufficient measurement precision the requirement of contact for the measurement process, and lack of entire joint description. This study presents a new non-contact method for precise determination of entire joint surfaces using multistation digital photogrammetry (MDPG) and is demonstrated by determining the cartilage and subchondral bone surfaces of the cat patellofemoral (PF) joint. The digital camera-lens setup was precisely calibrated using 16 photographs arranged to achieve highly convergent geometry to estimate interior and distortion parameters of the camera-lens setup. Subsequently, six photographs of each joint surface were then acquired for surface measurement. The digital images were directly imported to a computer and newly introduced semi-automatic computer algorithms were used to precisely determine the image coordinates. Finally, a rigorous mathematical procedure named the bundle adjustment was used to determine the three-dimensional coordinates of the joint surfaces and to estimate the precision of the coordinates. These estimations were validated by comparing the MDPG measurements of a cylinder and plane to an analytical model. The joint surfaces were successfully measured using the MDPG method with mean precision estimates in the least favorable coordinate direction being 10.3 microns for subchondral bone and 17.9 microns for cartilage. The difference in measurement precision for bone and cartilage primarily reflects differences in the translucent properties of the surfaces.

Algebraic geometry in India

Indian Academy of Sciences (India)

algebraic geometry but also in related fields like number theory. ... every vector bundle on the affine space is trivial. (equivalently ... les on a compact Riemann surface to unitary rep- ... tial geometry and topology and was generalised in.

Threedimensional system of coordinates used at CERN

International Nuclear Information System (INIS)

Gervaise, J.; Mayoud, M.; Menant, E.

1976-01-01

This report is a complete account of the transformations and corrections necessary for geodetic quantities, whether directly measured or derived, before they can be entered into calculations involving the basic reference system used at CERN. A special type of projection (orthographic projection) has been developed, with the aim that it be the best possible for the geodetic system employed for the Super Proton Synchrotron (SPS) whilst retaining the basic possibilities provided for the Proton Synchrotron (PS) and the Intersecting Storage Rings (ISR). The coordinate system in which the geometry of particle beams is defined is necessarily Cartesian. This feature, although mathematically simple, has a number of consequences for the treatment of measurements which are physically connected with the shape of the Earth. Details of the orthographic projection, the planimetry, and the altimetry are given. (Author) [fr

Theory for stationary nonlinear wave propagation in complex magnetic geometry

International Nuclear Information System (INIS)

Watanabe, T.; Hojo, H.; Nishikawa, Kyoji.

1977-08-01

We present our recent efforts to derive a systematic calculation scheme for nonlinear wave propagation in the self-consistent plasma profile in complex magnetic-field geometry. Basic assumptions and/or approximations are i) use of the collisionless two-fluid model with an equation of state; ii) restriction to a steady state propagation and iii) existence of modified magnetic surface, modification due to Coriolis' force. We discuss four situations: i) weak-field propagation without static flow, ii) arbitrary field strength with flow in axisymmetric system, iii) weak field limit of case ii) and iv) arbitrary field strength in nonaxisymmetric torus. Except for case iii), we derive a simple variation principle, similar to that of Seligar and Whitham, by introducing appropriate coordinates. In cases i) and iii), we derive explicit results for quasilinear profile modification. (auth.)

Introduction to combinatorial geometry

International Nuclear Information System (INIS)

Gabriel, T.A.; Emmett, M.B.

1985-01-01

The combinatorial geometry package as used in many three-dimensional multimedia Monte Carlo radiation transport codes, such as HETC, MORSE, and EGS, is becoming the preferred way to describe simple and complicated systems. Just about any system can be modeled using the package with relatively few input statements. This can be contrasted against the older style geometry packages in which the required input statements could be large even for relatively simple systems. However, with advancements come some difficulties. The users of combinatorial geometry must be able to visualize more, and, in some instances, all of the system at a time. Errors can be introduced into the modeling which, though slight, and at times hard to detect, can have devastating effects on the calculated results. As with all modeling packages, the best way to learn the combinatorial geometry is to use it, first on a simple system then on more complicated systems. The basic technique for the description of the geometry consists of defining the location and shape of the various zones in terms of the intersections and unions of geometric bodies. The geometric bodies which are generally included in most combinatorial geometry packages are: (1) box, (2) right parallelepiped, (3) sphere, (4) right circular cylinder, (5) right elliptic cylinder, (6) ellipsoid, (7) truncated right cone, (8) right angle wedge, and (9) arbitrary polyhedron. The data necessary to describe each of these bodies are given. As can be easily noted, there are some subsets included for simplicity

Application of the Fourier pseudospectral time-domain method in orthogonal curvilinear coordinates for near-rigid moderately curved surfaces.

Science.gov (United States)

Hornikx, Maarten; Dragna, Didier

2015-07-01

The Fourier pseudospectral time-domain method is an efficient wave-based method to model sound propagation in inhomogeneous media. One of the limitations of the method for atmospheric sound propagation purposes is its restriction to a Cartesian grid, confining it to staircase-like geometries. A transform from the physical coordinate system to the curvilinear coordinate system has been applied to solve more arbitrary geometries. For applicability of this method near the boundaries, the acoustic velocity variables are solved for their curvilinear components. The performance of the curvilinear Fourier pseudospectral method is investigated in free field and for outdoor sound propagation over an impedance strip for various types of shapes. Accuracy is shown to be related to the maximum grid stretching ratio and deformation of the boundary shape and computational efficiency is reduced relative to the smallest grid cell in the physical domain. The applicability of the curvilinear Fourier pseudospectral time-domain method is demonstrated by investigating the effect of sound propagation over a hill in a nocturnal boundary layer. With the proposed method, accurate and efficient results for sound propagation over smoothly varying ground surfaces with high impedances can be obtained.

Experimental approach for the uncertainty assessment of 3D complex geometry dimensional measurements using computed tomography at the mm and sub-mm scales

DEFF Research Database (Denmark)

Jiménez, Roberto; Torralba, Marta; Yagüe-Fabra, José A.

2017-01-01

The dimensional verification of miniaturized components with 3D complex geometries is particularly challenging. Computed Tomography (CT) can represent a suitable alternative solution to micro metrology tools based on optical and tactile techniques. However, the establishment of CT systems......’ traceability when measuring 3D complex geometries is still an open issue. In this work, an alternative method for the measurement uncertainty assessment of 3D complex geometries by using CT is presented. The method is based on the micro-CT system Maximum Permissible Error (MPE) estimation, determined...... experimentally by using several calibrated reference artefacts. The main advantage of the presented method is that a previous calibration of the component by a more accurate Coordinate Measuring System (CMS) is not needed. In fact, such CMS would still hold all the typical limitations of optical and tactile...

Tetra­kis(aceto­nitrile)copper(I) hydrogen oxalate–oxalic acid–aceto­nitrile (1/0.5/0.5)

Science.gov (United States)

Royappa, A. Timothy; Stepherson, Jacob R.; Vu, Oliver D.; Royappa, Andrew D.; Stern, Charlotte L.; Müller, Peter

2013-01-01

In the title compound, [Cu(CH3CN)4](C2HO4)·0.5C2H2O4·0.5CH3CN, the CuI ion is coordinated by the N atoms of four aceto­nitrile ligands in a slightly distorted tetra­hedral environment. The oxalic acid mol­ecule lies across an inversion center. The aceto­nitrile solvent mol­ecule is disordered across an inversion center and was refined with half occupancy. In the crystal, the hydrogen oxalate anions and oxalic acid mol­ecules are linked via O—H⋯O hydrogen bonds, forming chains along [010]. PMID:24098175

[(Nitrato-κ2 O,O′)(nitrito-κ2 O,O′)(0.25/1.75)]bis­(1,10-phenanthroline-κ2 N,N′)cadmium(II)

Science.gov (United States)

Najafi, Ezzatollah; Amini, Mostafa M.; Ng, Seik Weng

2011-01-01

The reaction of cadmium nitrate and sodium nitrite in the presence of 1,10-phenanthroline yields the mixed nitrate–nitrite title complex, [Cd(NO2)1.75(NO3)0.25(C12H8N2)2]. The metal ion is bis-chelated by two N-heterocycles as well as by the nitrate/nitrite ions in a distorted dodeca­hedral CdN4O4 coordination environment. One nitrite group is ordered; the other is disordered with respect to a nitrate group (ratio 0.75:0.25) concerning the O atom that is not involved in bonding to the metal ion. PMID:21522904

Automatic astronomical coordinate determination using digital zenith cameras

Directory of Open Access Journals (Sweden)

S Farzaneh

2009-12-01

Full Text Available Celestial positioning has been used for navigation purposes for many years. Stars as the extra-terrestrial benchmarks provide unique opportunity in absolute point positioning. However, astronomical field data acquisition and data processing of the collected data is very time-consuming. The advent of the Global Positioning System (GPS nearly made the celestial positioning system obsolete. The new satellite-based positioning system has been very popular since it is very efficient and convenient for many daily life applications. Nevertheless, the celestial positioning method is never replaced by satellite-based positioning in absolute point positioning sense. The invention of electro-optical devices at the beginning of the 21st century was really a rebirth in geodetic astronomy. Today, the digital cameras with relatively high geometric and radiometric accuracy has opened a new insight in satellite attitude determination and the study of the Earth's surface geometry and physics of its interior, i.e., computation of astronomical coordinates and the vertical deflection components. This method or the so-called astrogeodetic vision-based method help us to determine astronomical coordinates with an accuracy better than 0.1 arc second. The theoretical background, an innovative transformation approach and the preliminary numerical results are addressed in this paper.

Comparison of anterior segment optical coherence tomography angiography and fluorescein angiography for iris vasculature analysis.

Science.gov (United States)

Zett, Claudio; Stina, Deborah M Rosa; Kato, Renata Tiemi; Novais, Eduardo Amorim; Allemann, Norma

2018-04-01

The aim of this study is to perform imaging of irises of different colors using spectral domain anterior segment optical coherence tomography angiography (AS-OCTA) and iris fluorescein angiography (IFA) and compare their effectiveness in examining iris vasculature. This is a cross-sectional observational clinical study. Patients with no vascular iris alterations and different pigmentation levels were recruited. Participants were imaged using OCTA adapted with an anterior segment lens and IFA with a confocal scanning laser ophthalmoscope (cSLO) adapted with an anterior segment lens. AS-OCTA and IFA images were then compared. Two blinded readers classified iris pigmentation and compared the percentage of visible vessels between OCTA and IFA images. Twenty eyes of 10 patients with different degrees of iris pigmentation were imaged using AS-OCTA and IFA. Significantly more visible iris vessels were observed using OCTA than using FA (W = 5.22; p Iris pigmentation was negatively correlated to the percentage of visible vessels in both imaging methods (OCTA, rho = - 0.73, p iris vasculature. In both AS-OCTA and IFA, iris pigmentation caused vasculature imaging blockage, but AS-OCTA provided more detailed iris vasculature images than IFA. Additional studies including different iris pathologies are needed to determine the most optimal scanning parameters in OCTA of the anterior segment.

Graded geometry and Poisson reduction

OpenAIRE

Cattaneo, A S; Zambon, M

2009-01-01

The main result of [2] extends the Marsden-Ratiu reduction theorem [4] in Poisson geometry, and is proven by means of graded geometry. In this note we provide the background material about graded geometry necessary for the proof in [2]. Further, we provide an alternative algebraic proof for the main result. ©2009 American Institute of Physics

Geometry of multihadron production

Energy Technology Data Exchange (ETDEWEB)

Bjorken, J.D.

1994-10-01

This summary talk only reviews a small sample of topics featured at this symposium: Introduction; The Geometry and Geography of Phase space; Space-Time Geometry and HBT; Multiplicities, Intermittency, Correlations; Disoriented Chiral Condensate; Deep Inelastic Scattering at HERA; and Other Contributions.

Geometry of multihadron production

International Nuclear Information System (INIS)

Bjorken, J.D.

1994-10-01

This summary talk only reviews a small sample of topics featured at this symposium: Introduction; The Geometry and Geography of Phase space; Space-Time Geometry and HBT; Multiplicities, Intermittency, Correlations; Disoriented Chiral Condensate; Deep Inelastic Scattering at HERA; and Other Contributions

μ3-Carbonato-κ3 O:O′:O′′-tris­{(η6-ben­zene)[(R)-1-(1-amino­ethyl)naphthyl-κ2 C 2,N]ruthenium(II)} hexa­fluorido­phosphate dichloro­methane solvate

Science.gov (United States)

Sortais, Jean-Baptiste; Brelot, Lydia; Pfeffer, Michel; Barloy, Laurent

2008-01-01

The title compound, [Ru3(C12H12N)3(CO3)(C6H6)3]PF6·CH2Cl2, was obtained unintentionally as the product of an attempted deprotonation of the monomeric parent ruthenium complex [Ru(C12H12N)(C6H6)(C2H3N)]PF6. The carbonate ligand bridges three half-sandwich cyclo­ruthenated fragments, each of them exhibiting a pseudo-tetra­hedral geometry. The configuration of the Ru atoms is S. The naphthyl groups of the enanti­opure cyclo­ruthenated benzylic amine ligands point in the same direction, adopting a propeller shape. PMID:21201869

Geometry of higher-dimensional black hole thermodynamics

International Nuclear Information System (INIS)

Aaman, Jan E.; Pidokrajt, Narit

2006-01-01

We investigate thermodynamic curvatures of the Kerr and Reissner-Nordstroem (RN) black holes in spacetime dimensions higher than four. These black holes possess thermodynamic geometries similar to those in four-dimensional spacetime. The thermodynamic geometries are the Ruppeiner geometry and the conformally related Weinhold geometry. The Ruppeiner geometry for a d=5 Kerr black hole is curved and divergent in the extremal limit. For a d≥6 Kerr black hole there is no extremality but the Ruppeiner curvature diverges where one suspects that the black hole becomes unstable. The Weinhold geometry of the Kerr black hole in arbitrary dimension is a flat geometry. For the RN black hole the Ruppeiner geometry is flat in all spacetime dimensions, whereas its Weinhold geometry is curved. In d≥5 the Kerr black hole can possess more than one angular momentum. Finally we discuss the Ruppeiner geometry for the Kerr black hole in d=5 with double angular momenta

On the integration of computer aided design and analysis using the finite element absolute nodal coordinate formulation

International Nuclear Information System (INIS)

Sanborn, Graham G.; Shabana, Ahmed A.

2009-01-01

For almost a decade, the finite element absolute nodal coordinate formulation (ANCF) has been used for both geometry and finite element representations. Because of the ANCF isoparametric property in the cases of beams, plates and shells, ANCF finite elements lend themselves easily to the geometric description of curves and surfaces, as demonstrated in the literature. The ANCF finite elements, therefore, are ideal for what is called isogeometric analysis that aims at the integration ofcomputer aided designandanalysis (ICADA), which involves the integration of what is now split into the separate fields of computer aided design (CAD) and computer aided analysis (CAA). The purpose of this investigation is to establish the relationship between the B-spline and NURBS, which are widely used in the geometric modeling, and the ANCF finite elements. It is shown in this study that by using the ANCF finite elements, one can in a straightforward manner obtain the control point representation required for the Bezier, B-spline and NURBS geometry. To this end, a coordinate transformation is used to write the ANCF gradient vectors in terms of control points. Unifying the CAD and CAA will require the use of such coordinate transformations and their inverses in order to transform control points to position vector gradients which are required for the formulation of the element transformations in the case of discontinuities as well as the formulation of the strain measures and the stress forces based on general continuum mechanics theory. In particular, fully parameterized ANCF finite elements can be very powerful in describing curve, surface, and volume geometry, and they can be effectively used to describe discontinuities while maintaining the many ANCF desirable features that include a constant mass matrix, zero Coriolis and centrifugal forces, no restriction on the amount of rotation or deformation within the finite element, ability for straightforward implementation of general

Development and application of the discrete ordinate method in orthogonal curvilinear coordinates; Developpement et application de la methode des ordonnees discretes en coordonnees curvilignes orthogonales

Energy Technology Data Exchange (ETDEWEB)

Vaillon, R; Lallemand, M; Lemonnier, D [Ecole Nationale Superieure de Mecanique et d` Aerotechnique (ENSMA), 86 - Poitiers (France)

1997-12-31

The method of discrete ordinates, which is more and more widely used in radiant heat transfer studies, is mainly developed in Cartesian, (r,z) and (r,{Theta}) cylindrical, and spherical coordinates. In this study, the approach of this method is performed in orthogonal curvilinear coordinates: determination of the radiant heat transfer equation, treatment of the angular redistribution terms, numerical procedure. Some examples of application are described in 2-D geometry defined in curvilinear coordinates along a curve and at the thermal equilibrium. A comparison is made with the discrete ordinates method in association with the finite-volumes method in non structured mesh. (J.S.) 27 refs.

Development and application of the discrete ordinate method in orthogonal curvilinear coordinates; Developpement et application de la methode des ordonnees discretes en coordonnees curvilignes orthogonales

Energy Technology Data Exchange (ETDEWEB)

Vaillon, R.; Lallemand, M.; Lemonnier, D. [Ecole Nationale Superieure de Mecanique et d`Aerotechnique (ENSMA), 86 - Poitiers (France)

1996-12-31

The method of discrete ordinates, which is more and more widely used in radiant heat transfer studies, is mainly developed in Cartesian, (r,z) and (r,{Theta}) cylindrical, and spherical coordinates. In this study, the approach of this method is performed in orthogonal curvilinear coordinates: determination of the radiant heat transfer equation, treatment of the angular redistribution terms, numerical procedure. Some examples of application are described in 2-D geometry defined in curvilinear coordinates along a curve and at the thermal equilibrium. A comparison is made with the discrete ordinates method in association with the finite-volumes method in non structured mesh. (J.S.) 27 refs.

Role of N-Donor Sterics on the Coordination Environment and Dimensionality of Uranyl Thiophenedicarboxylate Coordination Polymers

Energy Technology Data Exchange (ETDEWEB)

Thangavelu, Sonia G. [Department; Butcher, Ray J. [Department; Cahill, Christopher L. [Department

2015-06-09

Thiophene 2,5-dicarboxylic acid (TDC) was reacted with uranyl acetate dihydrate and one (or none) of six N-donor chelating ligands (2,2'-bipyridine (BPY), 4,4'-dimethyl-2,2'-bipyridine (4-MeBPY), 5,5'-dimethyl-2,2'-bipyridine (5-MeBPY), 6,6'-dimethyl-2,2'-bipyridine (6-MeBPY), 4,4',6,6'-tetramethyl-2,2'-bipyridine (4,6-MeBPY), and tetrakis(2-pyridyl)pyrazine (TPPZ) to result in the crystallization of seven uranyl coordination polymers, which were characterized by their crystal structures and luminescence properties. The seven coordination polymers, Na2[(UO2)2(C6H2O4S)3]·4H2O (1), [(UO2)4(C6H2O4S)5(C10H8N2)2]·C10H10N2·3H2O (2), [(UO2)(C6H2O4S)(C12H12N3)] (3), [(UO2)(C6H2O4S)(C12H12N3)]·H2O (4), [(UO2)2(C6H2O4S)3]·(C12H14N2)·5H2O (5), [(UO2)3(CH3CO2)(C6H2O4S)4](C14H17N2)3·(C14H16N2)·H2O (6), and [(UO2)2(C6H2O4S)3](C24H18N6) (7), consist of either uranyl hexagonal bipyramidal or pentagonal bipyramidal coordination geometries. In all structures, structural variations in the local and global structures of 1–7 are influenced by the positions (or number) of methyl groups or pyridyl rings on the N-donor species, thus resulting in a wide diversity of structures ranging from single chains, double chains, or 2-D sheets. Direct coordination of N-donor ligands to uranyl centers is observed in the chain structures of 2–4 using BPY, 4-MeBPY, and 5-MeBPY, whereas the N-donor species participate as guests (as either neutral or charge balancing species) in the chain and sheet structures of 5–7 using 6-MeBPY, 4,6-MeBPY, and TPPZ, respectively. Compound 1 is the only structure that does not contain any N-donor ligands and thus crystallizes as a 2-D interpenetrating sheet. The luminescent properties of 1–7 are influenced by the direct coordination or noncoordination of N-donor species to uranyl centers. Compounds 2–4 exhibit typical UO22+ emission upon direct coordination of N-donors, but its absence is observed in 1

Separation and characterization of metallosupramolecular libraries by ion mobility mass spectrometry.

Science.gov (United States)

Li, Xiaopeng; Chan, Yi-Tsu; Casiano-Maldonado, Madalis; Yu, Jing; Carri, Gustavo A; Newkome, George R; Wesdemiotis, Chrys

2011-09-01

The self-assembly of Zn(II) ions and bis(terpyridine) (tpy) ligands carrying 120° or 180° angles between their metal binding sites was utilized to prepare metallosupramolecular libraries with the connectivity. These combinatorial libraries were separated and characterized by ion mobility mass spectrometry (IM MS) and tandem mass spectrometry (MS(2)). The 180°-angle building blocks generate exclusively linear complexes, which were used as standards to determine the architectures of the assemblies resulting from the 120°-angle ligands. The latter ligand geometry promotes the formation of macrocyclic hexamers, but other n-mers with smaller (n = 5) or larger ring sizes (n = 7-9) were identified as minor products, indicating that the angles in the bis(terpyridine) ligand and within the coordinative tpy-Zn(II)-tpy bonds are not as rigid, as previously believed. Macrocyclic and linear isomers were detected in penta- and heptameric assemblies; in the larger octa- and nonameric assemblies, ring-opened conformers with compact and folded geometries were observed in addition to linear extended and cyclic architectures. IM MS(2) experiments provided strong evidence that the macrocycles present in the libraries were already formed in solution, during the self-assembly process, not by dissociation of larger complexes in the gas phase. The IM MS/MS(2) methods provide a means to analyze, based on size and shape (architecture), supramolecular libraries that are not amenable to liquid chromatography, LC-MS, NMR, and/or X-ray techniques.

A new one-dimensional NiII coordination polymer with a two-dimensional supramolecular architecture

Directory of Open Access Journals (Sweden)

Kai-Long Zhong

2017-02-01

Full Text Available A new one-dimensional NiII coordination polymer of 1,3,5-tris(imidazol-1-ylmethylbenzene, namely catena-poly[[aqua(sulfato-κOhemi(μ-ethane-1,2-diol-κ2O:O′[μ3-1,3,5-tris(1H-imidazol-1-ylmethylbenzene-κ3N3,N3′,N3′′]nickel(II] ethane-1,2-diol monosolvate monohydrate], {[Ni(SO4(C18H18N6(C2H6O20.5(H2O]·C2H6O2·H2O}n, was synthesized and characterized by elemental analysis, IR spectroscopy and single-crystal X-ray diffraction. The NiII cation is coordinated by three N atoms of three different 1,3,5-tris(imidazol-1-ylmethylbenzene ligands, one O atom of an ethane-1,2-diol molecule, by a sulfate anion and a water molecule, forming a distorted octahedral NiN3O3 coordination geometry. The tripodal 1,3,5-tris(imidazol-1-ylmethylbenzene ligands link the NiII cations, generating metal–organic chains running along the [100] direction. Adjacent chains are further connected by O—H...O hydrogen bonds, resulting in a two-dimensional supermolecular architecture running parallel to the (001 plane. Another water molecule and a second ethane-1,2-diol molecule are non-coordinating and are linked to the coordinating sulfate ions via O—H...O hydrogen bonds.

Lectures on Symplectic Geometry

CERN Document Server

Silva, Ana Cannas

2001-01-01

The goal of these notes is to provide a fast introduction to symplectic geometry for graduate students with some knowledge of differential geometry, de Rham theory and classical Lie groups. This text addresses symplectomorphisms, local forms, contact manifolds, compatible almost complex structures, Kaehler manifolds, hamiltonian mechanics, moment maps, symplectic reduction and symplectic toric manifolds. It contains guided problems, called homework, designed to complement the exposition or extend the reader's understanding. There are by now excellent references on symplectic geometry, a subset of which is in the bibliography of this book. However, the most efficient introduction to a subject is often a short elementary treatment, and these notes attempt to serve that purpose. This text provides a taste of areas of current research and will prepare the reader to explore recent papers and extensive books on symplectic geometry where the pace is much faster. For this reprint numerous corrections and cl...

Geometry of the 2+1 black hole

International Nuclear Information System (INIS)

Banados, M.; Henneaux, M.; Teitelboim, C.; Zanelli, J.

1993-01-01

The geometry of the spinning black holes of standard Einstein theory in 2+1 dimensions, with a negative cosmological constant, and without couplings to matter, is analyzed in detail. It is shown that the black hole arises from identifications of points of anti--de Sitter space by a discrete subgroup of SO(2,2). The generic black hole is a smooth manifold in the metric sense. The surface r=0 is not a curvature singularity but, rather, a singularity in the causal structure. Continuing past it would introduce closed timelike lines. However, simple examples show the regularity of the metric at r=0 to be unstable: couplings to matter bring in a curvature singularity there. Kruskal coordinates and Penrose diagrams are exhibited. Special attention is given to the limiting cases of (i) the spinless hole of zero mass, which differs from anti--de Sitter space and plays the role of the vacuum, and (ii) the spinning hole of maximal angular momentum. A thorough classification of the elements of the Lie algebra of SO(2,2) is given in an appendix

Complex differential geometry

CERN Document Server

Zheng, Fangyang

2002-01-01

The theory of complex manifolds overlaps with several branches of mathematics, including differential geometry, algebraic geometry, several complex variables, global analysis, topology, algebraic number theory, and mathematical physics. Complex manifolds provide a rich class of geometric objects, for example the (common) zero locus of any generic set of complex polynomials is always a complex manifold. Yet complex manifolds behave differently than generic smooth manifolds; they are more coherent and fragile. The rich yet restrictive character of complex manifolds makes them a special and interesting object of study. This book is a self-contained graduate textbook that discusses the differential geometric aspects of complex manifolds. The first part contains standard materials from general topology, differentiable manifolds, and basic Riemannian geometry. The second part discusses complex manifolds and analytic varieties, sheaves and holomorphic vector bundles, and gives a brief account of the surface classifi...

Computational synthetic geometry

CERN Document Server

Bokowski, Jürgen

1989-01-01

Computational synthetic geometry deals with methods for realizing abstract geometric objects in concrete vector spaces. This research monograph considers a large class of problems from convexity and discrete geometry including constructing convex polytopes from simplicial complexes, vector geometries from incidence structures and hyperplane arrangements from oriented matroids. It turns out that algorithms for these constructions exist if and only if arbitrary polynomial equations are decidable with respect to the underlying field. Besides such complexity theorems a variety of symbolic algorithms are discussed, and the methods are applied to obtain new mathematical results on convex polytopes, projective configurations and the combinatorics of Grassmann varieties. Finally algebraic varieties characterizing matroids and oriented matroids are introduced providing a new basis for applying computer algebra methods in this field. The necessary background knowledge is reviewed briefly. The text is accessible to stud...

Designs and finite geometries

CERN Document Server

1996-01-01

Designs and Finite Geometries brings together in one place important contributions and up-to-date research results in this important area of mathematics. Designs and Finite Geometries serves as an excellent reference, providing insight into some of the most important research issues in the field.

A two-dimensional Zn coordination polymer with a three-dimensional supramolecular architecture

Directory of Open Access Journals (Sweden)

Fuhong Liu

2017-10-01

Full Text Available The title compound, poly[bis{μ2-4,4′-bis[(1,2,4-triazol-1-ylmethyl]biphenyl-κ2N4:N4′}bis(nitrato-κOzinc(II], [Zn(NO32(C18H16N62]n, is a two-dimensional zinc coordination polymer constructed from 4,4′-bis[(1H-1,2,4-triazol-1-ylmethyl]-1,1′-biphenyl units. It was synthesized and characterized by elemental analysis and single-crystal X-ray diffraction. The ZnII cation is located on an inversion centre and is coordinated by two O atoms from two symmetry-related nitrate groups and four N atoms from four symmetry-related 4,4′-bis[(1H-1,2,4-triazol-1-ylmethyl]-1,1′-biphenyl ligands, forming a distorted octahedral {ZnN4O2} coordination geometry. The linear 4,4′-bis[(1H-1,2,4-triazol-1-ylmethyl]-1,1′-biphenyl ligand links two ZnII cations, generating two-dimensional layers parallel to the crystallographic (132 plane. The parallel layers are connected by C—H...O, C—H...N, C—H...π and π–π stacking interactions, resulting in a three-dimensional supramolecular architecture.

d-geometries revisited

CERN Document Server

Ceresole, Anna; Gnecchi, Alessandra; Marrani, Alessio

2013-01-01

We analyze some properties of the four dimensional supergravity theories which originate from five dimensions upon reduction. They generalize to N>2 extended supersymmetries the d-geometries with cubic prepotentials, familiar from N=2 special K\\"ahler geometry. We emphasize the role of a suitable parametrization of the scalar fields and the corresponding triangular symplectic basis. We also consider applications to the first order flow equations for non-BPS extremal black holes.

Changes in the geometries of C₂H₂ and C₂H₄ on coordination to CuCl revealed by broadband rotational spectroscopy and ab-initio calculations.

Science.gov (United States)

Stephens, Susanna L; Bittner, Dror M; Mikhailov, Victor A; Mizukami, Wataru; Tew, David P; Walker, Nicholas R; Legon, Anthony C

2014-10-06

The molecular geometries of isolated complexes in which a single molecule of C2H4 or C2H2 is bound to CuCl have been determined through pure rotational spectroscopy and ab-initio calculations. The C2H2···CuCl and C2H4···CuCl complexes are generated through laser vaporization of a copper rod in the presence of a gas sample undergoing supersonic expansion and containing C2H2 (or C2H4), CCl4, and Ar. Results are presented for five isotopologues of C2H2···CuCl and six isotopologues of C2H4···CuCl. Both of these complexes adopt C(2v), T-shaped geometries in which the hydrocarbon binds to the copper atom through its π electrons such that the metal is equidistant from all H atoms. The linear and planar geometries of free C2H2 and C2H4, respectively, are observed to distort significantly on attachment to the CuCl unit, and the various changes are quantified. The ∠(*-C-H) parameter in C2H2 (where * indicates the midpoint of the C≡C bond) is measured to be 192.4(7)° in the r0 geometry of the complex representing a significant change from the linear geometry of the free molecule. This distortion of the linear geometry of C2H2 involves the hydrogen atoms moving away from the copper atom within the complex. Ab-initio calculations at the CCSD(T)(F12*)/AVTZ level predict a dihedral ∠(HCCCu) angle of 96.05° in C2H4···CuCl, and the experimental results are consistent with such a distortion from planarity. The bonds connecting the carbon atoms within each of C2H2 and C2H4, respectively, extend by 0.027 and 0.029 Å relative to the bond lengths in the isolated molecules. Force constants, k(σ), and nuclear quadrupole coupling constants, χ(aa)(Cu), [χ(bb)(Cu) - χ(cc)(Cu)], χ(aa)(Cl), and [χ(bb)(Cl) - χ(cc)(Cl)], are independently determined for all isotopologues of C2H2···CuCl studied and for four isotopologues of C2H4···CuCl.

Geometry success in 20 minutes a day

CERN Document Server

LLC, LearningExpress

2014-01-01

Whether you're new to geometry or just looking for a refresher, Geometry Success in 20 Minutes a Day offers a 20-step lesson plan that provides quick and thorough instruction in practical, critical skills. Stripped of unnecessary math jargon but bursting with geometry essentials, Geometry Success in 20 Minutes a Day: Covers all vital geometry skills, from the basic building blocks of geometry to ratio, proportion, and similarity to trigonometry and beyond Provides hundreds of practice exercises in test format Applies geometr

Lectures on coarse geometry

CERN Document Server

Roe, John

2003-01-01

Coarse geometry is the study of spaces (particularly metric spaces) from a 'large scale' point of view, so that two spaces that look the same from a great distance are actually equivalent. This point of view is effective because it is often true that the relevant geometric properties of metric spaces are determined by their coarse geometry. Two examples of important uses of coarse geometry are Gromov's beautiful notion of a hyperbolic group and Mostow's proof of his famous rigidity theorem. The first few chapters of the book provide a general perspective on coarse structures. Even when only metric coarse structures are in view, the abstract framework brings the same simplification as does the passage from epsilons and deltas to open sets when speaking of continuity. The middle section reviews notions of negative curvature and rigidity. Modern interest in large scale geometry derives in large part from Mostow's rigidity theorem and from Gromov's subsequent 'large scale' rendition of the crucial properties of n...

Introduction to tropical geometry

CERN Document Server

Maclagan, Diane

2015-01-01

Tropical geometry is a combinatorial shadow of algebraic geometry, offering new polyhedral tools to compute invariants of algebraic varieties. It is based on tropical algebra, where the sum of two numbers is their minimum and the product is their sum. This turns polynomials into piecewise-linear functions, and their zero sets into polyhedral complexes. These tropical varieties retain a surprising amount of information about their classical counterparts. Tropical geometry is a young subject that has undergone a rapid development since the beginning of the 21st century. While establishing itself as an area in its own right, deep connections have been made to many branches of pure and applied mathematics. This book offers a self-contained introduction to tropical geometry, suitable as a course text for beginning graduate students. Proofs are provided for the main results, such as the Fundamental Theorem and the Structure Theorem. Numerous examples and explicit computations illustrate the main concepts. Each of t...

Integrability of geodesics in near-horizon extremal geometries: Case of Myers-Perry black holes in arbitrary dimensions

Science.gov (United States)

Demirchian, Hovhannes; Nersessian, Armen; Sadeghian, Saeedeh; Sheikh-Jabbari, M. M.

2018-05-01

We investigate dynamics of probe particles moving in the near-horizon limit of extremal Myers-Perry black holes in arbitrary dimensions. Employing ellipsoidal coordinates we show that this problem is integrable and separable, extending the results of the odd dimensional case discussed by Hakobyan et al. [Phys. Lett. B 772, 586 (2017)., 10.1016/j.physletb.2017.07.028]. We find the general solution of the Hamilton-Jacobi equations for these systems and present explicit expressions for the Liouville integrals and discuss Killing tensors and the associated constants of motion. We analyze special cases of the background near-horizon geometry were the system possesses more constants of motion and is hence superintegrable. Finally, we consider a near-horizon extremal vanishing horizon case which happens for Myers-Perry black holes in odd dimensions and show that geodesic equations on this geometry are also separable and work out its integrals of motion.

Low coordinated mononuclear erbium(iii) single-molecule magnets with C3v symmetry: a method for altering single-molecule magnet properties by incorporating hard and soft donors.

Science.gov (United States)

Zhang, Haitao; Nakanishi, Ryo; Katoh, Keiichi; Breedlove, Brian K; Kitagawa, Yasutaka; Yamashita, Masahiro

2018-01-02

Structures and magnetic characteristics of two three-coordinate erbium(iii) compounds with C 3v geometry, tris(2,6-di-tert-butyl-p-cresolate)erbium, Er(dbpc) 3 (1) and tris(bis(trimethylsilyl)methyl)erbium, Er(btmsm) 3 (2), were determined. Both underwent temperature-dependent slow magnetic relaxation processes in the absence of an external magnetic field. As a result of the differences in the coordination environment, they exhibit different energy barriers and quantum tunneling of magnetization (QTM) constants.

Basic algebraic geometry, v.2

CERN Document Server

Shafarevich, Igor Rostislavovich

1994-01-01

Shafarevich Basic Algebraic Geometry 2 The second edition of Shafarevich's introduction to algebraic geometry is in two volumes. The second volume covers schemes and complex manifolds, generalisations in two different directions of the affine and projective varieties that form the material of the first volume. Two notable additions in this second edition are the section on moduli spaces and representable functors, motivated by a discussion of the Hilbert scheme, and the section on Kähler geometry. The book ends with a historical sketch discussing the origins of algebraic geometry. From the Zentralblatt review of this volume: "... one can only respectfully repeat what has been said about the first part of the book (...): a great textbook, written by one of the leading algebraic geometers and teachers himself, has been reworked and updated. As a result the author's standard textbook on algebraic geometry has become even more important and valuable. Students, teachers, and active researchers using methods of al...

Canonical differential geometry of string backgrounds

International Nuclear Information System (INIS)

Schuller, Frederic P.; Wohlfarth, Mattias N.R.

2006-01-01

String backgrounds and D-branes do not possess the structure of Lorentzian manifolds, but that of manifolds with area metric. Area metric geometry is a true generalization of metric geometry, which in particular may accommodate a B-field. While an area metric does not determine a connection, we identify the appropriate differential geometric structure which is of relevance for the minimal surface equation in such a generalized geometry. In particular the notion of a derivative action of areas on areas emerges naturally. Area metric geometry provides new tools in differential geometry, which promise to play a role in the description of gravitational dynamics on D-branes

Coordination Chemistry of Linear Oligopyrrolic Fragments Inspired by Heme Metabolites

Science.gov (United States)

Gautam, Ritika

Linear oligopyrroles are degradation products of heme, which is converted in the presence of heme oxygenase to bile pigments, such as biliverdin and bilirubin. These tetrapyrrolic oligopyrroles are ubiquitously present in biological systems and find applications in the fields of catalysis and sensing. These linear tetrapyrrolic scaffolds are further degraded into linear tripyrrolic and dipyrrolic fragments. Although these lower oligopyrroles are abundantly present, their coordination chemistry requires further characterization. This dissertation focuses mainly on two classes of bioinspired linear oligopyrroles, propentdyopent and tripyrrindione, and their transition metal complexes, which present a rich ligand-based redox chemistry. Chapter 1 offers an overview of heme degradation to different classes of linear oligopyrroles and properties of their transition metal complexes. Chapter 2 is focused on the tripyrrin-1,14-dione scaffold of the urinary pigment uroerythrin, which coordinates divalent transition metals palladium and copper with square planar geometry. Specifically, the tripyrrin-1, 14-dione ligand binds Cu(II) and Pd(II) as a dianionic organic radical under ambient conditions. The electrochemical study confirms the presence of ligand based redox chemistry, and one electron oxidation or reduction reactions do not alter the planar geometry around the metal center. The X-Ray analysis and the electron paramagnetic resonance (EPR) studies of the complexes in the solid and solution phase reveals intermolecular interactions between the ligand based unpaired electrons and therefore formation of neutral pi-pi dimers. In Chapter 3, the antioxidant activity and the fluorescence sensor properties of the tripyrrin-1,14-dione ligand in the presence of superoxide are described. We found that the tripyrrindione ligand undergoes one-electron reduction in the presence of the superoxide radical anion (O2•- ) to form highly fluorescent H3TD1•- radical anion, which emits

Three-dimensional coordinate system used at CERN

International Nuclear Information System (INIS)

Gervaise, J.; Mayoud, M.; Menant, E.

1983-11-01

This report is a detailed account of the transformations and corrections that must be applied to any geodetic quantity - whether directly observed or derived - before it can be introduced into calculations relating to the reference system of coordinates used at CERN. In particular, a type of projection, called orthographic projection, has been developed to be as well adapted as possible to the geodetic network of the Subterranean Proton Synchrotron (SPS), while preserving the basic possibilities of the other installations - i.e., the Proton Synchrotron (PS) and the Intersecting Storage Rings (ISR). The system in which the particle beam geometry is defined is necessarily cartesian. This feature, though mathematically simple, nevertheless has numerous consequences for the treatment of measurements that are physically connected to the shape of the earth. The calculations of the orthographic projection, the planimetry and the altimetry are presented in detail. 12 figures

FENICIA: a generic plasma simulation code using a flux-independent field-aligned coordinate approach

International Nuclear Information System (INIS)

Hariri, Farah

2013-01-01

The primary thrust of this work is the development and implementation of a new approach to the problem of field-aligned coordinates in magnetized plasma turbulence simulations called the FCI approach (Flux-Coordinate Independent). The method exploits the elongated nature of micro-instability driven turbulence which typically has perpendicular scales on the order of a few ion gyro-radii, and parallel scales on the order of the machine size. Mathematically speaking, it relies on local transformations that align a suitable coordinate to the magnetic field to allow efficient computation of the parallel derivative. However, it does not rely on flux coordinates, which permits discretizing any given field on a regular grid in the natural coordinates such as (x, y, z) in the cylindrical limit. The new method has a number of advantages over methods constructed starting from flux coordinates, allowing for more flexible coding in a variety of situations including X-point configurations. In light of these findings, a plasma simulation code FENICIA has been developed based on the FCI approach with the ability to tackle a wide class of physical models. The code has been verified on several 3D test models. The accuracy of the approach is tested in particular with respect to the question of spurious radial transport. Tests on 3D models of the drift wave propagation and of the Ion Temperature Gradient (ITG) instability in cylindrical geometry in the linear regime demonstrate again the high quality of the numerical method. Finally, the FCI approach is shown to be able to deal with an X-point configuration such as one with a magnetic island with good convergence and conservation properties. (author) [fr

The Beauty of Geometry

Science.gov (United States)

Morris, Barbara H.

2004-01-01

This article describes a geometry project that used the beauty of stained-glass-window designs to teach middle school students about geometric figures and concepts. Three honors prealgebra teachers and a middle school mathematics gifted intervention specialist created a geometry project that covered the curriculum and also assessed students'…

A computational geometry framework for the optimisation of atom probe reconstructions

Energy Technology Data Exchange (ETDEWEB)

Felfer, Peter [Australian Centre for Microscopy and Microanalysis, The University of Sydney, NSW 2006 (Australia); Institute for General Materials Properties, Department of Materials Science, Friedrich-Alexander University Erlangen-Nürnberg, 91058 Erlangen (Germany); Cairney, Julie [Australian Centre for Microscopy and Microanalysis, The University of Sydney, NSW 2006 (Australia)

2016-10-15

In this paper, we present pathways for improving the reconstruction of atom probe data on a coarse (>10 nm) scale, based on computational geometry. We introduce a way to iteratively improve an atom probe reconstruction by adjusting it, so that certain known shape criteria are fulfilled. This is achieved by creating an implicit approximation of the reconstruction through a barycentric coordinate transform. We demonstrate the application of these techniques to the compensation of trajectory aberrations and the iterative improvement of the reconstruction of a dataset containing a grain boundary. We also present a method for obtaining a hull of the dataset in both detector and reconstruction space. This maximises data utilisation, and can be used to compensate for ion trajectory aberrations caused by residual fields in the ion flight path through a ‘master curve’ and correct for overall shape deviations in the data. - Highlights: • An atom probe reconstruction can be iteratively improved by using shape constraints. • An atom probe reconstruction can be inverted using barycentric coordinate transforms. • Hulls for atom probe datasets can be obtained from 2D detector outlines that are co-reconstructed with the data. • Ion trajectory compressions caused by instrument-specific residual fields in the drift tube can be corrected.

Teaching Spatial Geometry in a Virtual World

DEFF Research Database (Denmark)

Förster, Klaus-Tycho

2017-01-01

Spatial geometry is one of the fundamental mathematical building blocks of any engineering education. However, it is overshadowed by planar geometry in the curriculum between playful early primary education and later analytical geometry, leaving a multi-year gap where spatial geometry is absent...

Trends and developments in computational geometry

NARCIS (Netherlands)

Berg, de M.

1997-01-01

This paper discusses some trends and achievements in computational geometry during the past five years, with emphasis on problems related to computer graphics. Furthermore, a direction of research in computational geometry is discussed that could help in bringing the fields of computational geometry

Recommendations by NACP for accurate treatment geometry specification

International Nuclear Information System (INIS)

Aaltonen, P.

1995-01-01

An investigation among the Nordic radiotherapy centres in 1991 confirmed that inconsistent use of dose and volume concepts is jeopardizing the high standard of radiation therapy. A Nordic working group was set up by NACP to standardize the concepts and quantities used throughout the whole radiation process. Now the draft report 'Specification of Dose Delivery in Radiation Therapy' is discussed with the radiotherapy community. The recent ICRU 50 report is the first step towards a uniform terminology and procedure at all radiotherapy centres. The new NACP report will be an important and more detailed addition for level 2-3 radiotherapy clinics and it will be specially adopted to the situation at the Nordic centres as well as other well equipped centres. The aim has been to recommend the use of concepts based on recent scientific development in the field of radiation therapy which are needed for the development of daily clinical practice. The terms and concepts for treatment geometry have been chosen by separating the concepts of tissues and volumes inside a patient. The tissues can be fixed in the coordinate system of the patient by adding a margin around them. This margin accounts for the movements of the tissues of interest inside the patient. The outer boundary of this margin is then encompassing the Strict Target Volume or Organ at Risk Volume which are fixed in the patient coordinate system. The set-up uncertainties of the patient in relation to the beams are considered during treatment planning by adding set-up margins to the beams

Coordination geometries of Zn(II) and Cd(II) in phosphotriesterase: Influence of water molecules in the active site

DEFF Research Database (Denmark)

Krauss, M; Olsen, Lars; Antony, J

2002-01-01

Models of the metal ion binding sites of native ZnZn and of cadmium-substituted ZnCd and CdCd phosphotriesterase, including full amino acid side chains, were geometry optimized with quantum mechanical methods, with effective fragment potentials (EFP) representing the protein environment surroundi...... to the Od1 of the carboxylate of the first-shell aspartate designated M 1, but the energy difference between Cd1Zn2 and the lowest energy Zn1Cd2 structure is only about 2 kcal/mol and decreasing with the addition of water molecules. The Zn1Cd2 arrangement is found experimentally....

An approach for management of geometry data

Science.gov (United States)

Dube, R. P.; Herron, G. J.; Schweitzer, J. E.; Warkentine, E. R.

1980-01-01

The strategies for managing Integrated Programs for Aerospace Design (IPAD) computer-based geometry are described. The computer model of geometry is the basis for communication, manipulation, and analysis of shape information. IPAD's data base system makes this information available to all authorized departments in a company. A discussion of the data structures and algorithms required to support geometry in IPIP (IPAD's data base management system) is presented. Through the use of IPIP's data definition language, the structure of the geometry components is defined. The data manipulation language is the vehicle by which a user defines an instance of the geometry. The manipulation language also allows a user to edit, query, and manage the geometry. The selection of canonical forms is a very important part of the IPAD geometry. IPAD has a canonical form for each entity and provides transformations to alternate forms; in particular, IPAD will provide a transformation to the ANSI standard. The DBMS schemas required to support IPAD geometry are explained.

"WGL," a Web Laboratory for Geometry

Science.gov (United States)

Quaresma, Pedro; Santos, Vanda; Maric, Milena

2018-01-01

The role of information and communication technologies (ICT) in education is nowadays well recognised. The "Web Geometry Laboratory," is an e-learning, collaborative and adaptive, Web environment for geometry, integrating a well known dynamic geometry system. In a collaborative session, teachers and students, engaged in solving…

Analytische Geometrie

Science.gov (United States)

Kemnitz, Arnfried

Der Grundgedanke der Analytischen Geometrie besteht darin, dass geometrische Untersuchungen mit rechnerischen Mitteln geführt werden. Geometrische Objekte werden dabei durch Gleichungen beschrieben und mit algebraischen Methoden untersucht.

Connections between algebra, combinatorics, and geometry

CERN Document Server

Sather-Wagstaff, Sean

2014-01-01

Commutative algebra, combinatorics, and algebraic geometry are thriving areas of mathematical research with a rich history of interaction. Connections Between Algebra, Combinatorics, and Geometry contains lecture notes, along with exercises and solutions, from the Workshop on Connections Between Algebra and Geometry held at the University of Regina from May 29-June 1, 2012. It also contains research and survey papers from academics invited to participate in the companion Special Session on Interactions Between Algebraic Geometry and Commutative Algebra, which was part of the CMS Summer Meeting at the University of Regina held June 2–3, 2012, and the meeting Further Connections Between Algebra and Geometry, which was held at the North Dakota State University, February 23, 2013. This volume highlights three mini-courses in the areas of commutative algebra and algebraic geometry: differential graded commutative algebra, secant varieties, and fat points and symbolic powers. It will serve as a useful resou...

Binuclear new complexes of dioxouranium (VI) and thorium (IV) with some Schiff bases derived from 4,4'-diamino stilbene-2,2'-disulphonic acid-vanillin and O-vanillin

International Nuclear Information System (INIS)

Pujar, M.A.; Siddappa, K.

1992-01-01

Dioxouranium (VI) and thorium (IV) form 1:1 (metal:ligand) complexes with some Schiff bases. The complexes have been characterized through elemental analyses, conductance, UV-Visible, IR, NMR, TG data and magnetic susceptibility measurements. They are found to be dimeric with hexa or octa-coordinated arrangement around metal ion moiety. The Fsub(U-O) (mdyn A o ) and the length R UO (A o ) of U-O bond are calculated from the IR data. (author). 8 refs., 1 tab

Algebraic Geometry and Number Theory Summer School

CERN Document Server

Sarıoğlu, Celal; Soulé, Christophe; Zeytin, Ayberk

2017-01-01

This lecture notes volume presents significant contributions from the “Algebraic Geometry and Number Theory” Summer School, held at Galatasaray University, Istanbul, June 2-13, 2014. It addresses subjects ranging from Arakelov geometry and Iwasawa theory to classical projective geometry, birational geometry and equivariant cohomology. Its main aim is to introduce these contemporary research topics to graduate students who plan to specialize in the area of algebraic geometry and/or number theory. All contributions combine main concepts and techniques with motivating examples and illustrative problems for the covered subjects. Naturally, the book will also be of interest to researchers working in algebraic geometry, number theory and related fields.

Geometry of power flows and convex-relaxed power flows in distribution networks with high penetration of renewables

DEFF Research Database (Denmark)

Huang, Shaojun; Wu, Qiuwei; Zhao, Haoran

2016-01-01

Renewable energies are increasingly integrated in electric distribution networks and will cause severe overvoltage issues. Smart grid technologies make it possible to use coordinated control to mitigate the overvoltage issues and the optimal power flow (OPF) method is proven to be efficient...... in the applications such as curtailment management and reactive power control. Nonconvex nature of the OPF makes it difficult to solve and convex relaxation is a promising method to solve the OPF very efficiently. This paper investigates the geometry of the power flows and the convex-relaxed power flows when high...

Applications of Affine and Weyl geometry

CERN Document Server

García-Río, Eduardo; Nikcevic, Stana

2013-01-01

Pseudo-Riemannian geometry is, to a large extent, the study of the Levi-Civita connection, which is the unique torsion-free connection compatible with the metric structure. There are, however, other affine connections which arise in different contexts, such as conformal geometry, contact structures, Weyl structures, and almost Hermitian geometry. In this book, we reverse this point of view and instead associate an auxiliary pseudo-Riemannian structure of neutral signature to certain affine connections and use this correspondence to study both geometries. We examine Walker structures, Riemannia

The Idea of Order at Geometry Class.

Science.gov (United States)

Rishel, Thomas

The idea of order in geometry is explored using the experience of assignments given to undergraduates in a college geometry course "From Space to Geometry." Discussed are the definition of geometry, and earth measurement using architecture, art, and common experience. This discussion concludes with a consideration of the question of whether…

Jahn-Teller distortion in the phosphorescent excited state of three-coordinate Au(I) phosphine complexes.

Science.gov (United States)

Barakat, Khaldoon A; Cundari, Thomas R; Omary, Mohammad A

2003-11-26

DFT calculations were used to optimize the phosphorescent excited state of three-coordinate [Au(PR3)3]+ complexes. The results indicate that the complexes rearrange from their singlet ground-state trigonal planar geometry to a T-shape in the lowest triplet luminescent excited state. The optimized structure of the exciton contradicts the structure predicted based on the AuP bonding properties of the ground-state HOMO and LUMO. The rearrangement to T-shape is a Jahn-Teller distortion because an electron is taken from the degenerate e' (5dxy, 5dx2-y2) orbital upon photoexcitation of the ground-state D3h complex. The calculated UV absorption and visible emission energies are consistent with the experimental data and explain the large Stokes' shifts while such correlations are not possible in optimized models that constrained the exciton to the ground-state trigonal geometry.

Analytic evaluation of the weighting functions for remote sensing of blackbody planetary atmospheres : the case of limb viewing geometry

Science.gov (United States)

Ustinov, Eugene A.

2006-01-01

In a recent publication (Ustinov, 2002), we proposed an analytic approach to evaluation of radiative and geophysical weighting functions for remote sensing of a blackbody planetary atmosphere, based on general linearization approach applied to the case of nadir viewing geometry. In this presentation, the general linearization approach is applied to the limb viewing geometry. The expressions, similar to those obtained in (Ustinov, 2002), are obtained for weighting functions with respect to the distance along the line of sight. Further on, these expressions are converted to the expressions for weighting functions with respect to the vertical coordinate in the atmosphere. Finally, the numerical representation of weighting functions in the form of matrices of partial derivatives of grid limb radiances with respect to the grid values of atmospheric parameters is used for a convolution with the finite field of view of the instrument.

Finite element approach to global gyrokinetic particle-in-cell simulations using magnetic coordinate

International Nuclear Information System (INIS)

Fivaz, M.; Brunner, S.; Ridder, G. de; Sauter, O.; Tran, T.M.; Vaclavik, J.; Villard, L.; Appert, K.

1997-08-01

We present a fully-global linear gyrokinetic simulation code (GYGLES) aimed at describing the instable spectrum of the ion-temperature-gradient modes in toroidal geometry. We formulate the Particle-In-Cell method with finite elements defined in magnetic coordinates, which provides excellent numerical convergence properties. The poloidal mode structure corresponding to k // =0 is extracted without approximation from the equations, which reduces drastically the numerical resolution needed. The code can simulate routinely modes with both very long and very short toroidal wavelengths, can treat realistic (MHD) equilibria of any size and runs on a massively parallel computer. (author) 10 figs., 28 refs

Using Dynamic Geometry Software to Improve Eight Grade Students' Understanding of Transformation Geometry

Science.gov (United States)

Guven, Bulent

2012-01-01

This study examines the effect of dynamic geometry software (DGS) on students' learning of transformation geometry. A pre- and post-test quasi-experimental design was used. Participants in the study were 68 eighth grade students (36 in the experimental group and 32 in the control group). While the experimental group students were studying the…

Disformal transformation in Newton-Cartan geometry

Energy Technology Data Exchange (ETDEWEB)

Huang, Peng [Zhejiang Chinese Medical University, Department of Information, Hangzhou (China); Sun Yat-Sen University, School of Physics and Astronomy, Guangzhou (China); Yuan, Fang-Fang [Nankai University, School of Physics, Tianjin (China)

2016-08-15

Newton-Cartan geometry has played a central role in recent discussions of the non-relativistic holography and condensed matter systems. Although the conformal transformation in non-relativistic holography can easily be rephrased in terms of Newton-Cartan geometry, we show that it requires a nontrivial procedure to arrive at the consistent form of anisotropic disformal transformation in this geometry. Furthermore, as an application of the newly obtained transformation, we use it to induce a geometric structure which may be seen as a particular non-relativistic version of the Weyl integrable geometry. (orig.)

Geometry and symmetry

CERN Document Server

Yale, Paul B

2012-01-01

This book is an introduction to the geometry of Euclidean, affine, and projective spaces with special emphasis on the important groups of symmetries of these spaces. The two major objectives of the text are to introduce the main ideas of affine and projective spaces and to develop facility in handling transformations and groups of transformations. Since there are many good texts on affine and projective planes, the author has concentrated on the n-dimensional cases.Designed to be used in advanced undergraduate mathematics or physics courses, the book focuses on ""practical geometry,"" emphasi

Optimizing solar-cell grid geometry

Science.gov (United States)

Crossley, A. P.

1969-01-01

Trade-off analysis and mathematical expressions calculate optimum grid geometry in terms of various cell parameters. Determination of the grid geometry provides proper balance between grid resistance and cell output to optimize the energy conversion process.

Geometry and Cloaking Devices

Science.gov (United States)

Ochiai, T.; Nacher, J. C.

2011-09-01

Recently, the application of geometry and conformal mappings to artificial materials (metamaterials) has attracted the attention in various research communities. These materials, characterized by a unique man-made structure, have unusual optical properties, which materials found in nature do not exhibit. By applying the geometry and conformal mappings theory to metamaterial science, it may be possible to realize so-called "Harry Potter cloaking device". Although such a device is still in the science fiction realm, several works have shown that by using such metamaterials it may be possible to control the direction of the electromagnetic field at will. We could then make an object hidden inside of a cloaking device. Here, we will explain how to design invisibility device using differential geometry and conformal mappings.

Global affine differential geometry of hypersurfaces

CERN Document Server

Li, An-Min; Zhao, Guosong; Hu, Zejun

2015-01-01

This book draws a colorful and widespread picture of global affine hypersurface theory up to the most recent state. Moreover, the recent development revealed that affine differential geometry- as differential geometry in general- has an exciting intersection area with other fields of interest, like partial differential equations, global analysis, convex geometry and Riemann surfaces.

Syntheses, structures and properties of four 3D microporous lanthanide coordination polymers based on 3,5-pyrazoledicarboxylate and oxalate ligands

Science.gov (United States)

Song, Juan; Wang, Ji-Jiang; Hu, Huai-Ming; Wu, Qing-Ran; Xie, Juan; Dong, Fa-Xin; Yang, Meng-Lin; Xue, Gang-Lin

2014-04-01

Four three-dimensional lanthanide coordination polymers with reversible structural interconversions, [Ln2(Hpdc)2(C2O4)(H2O)4]n·2nH2O [Ln=Sm (1), Eu (2), Tb (3) and Dy (4)], have been synthesized by hydrothermal reactions of lanthanide nitrates with 3,5-pyrazoledicarboxylic (H3pdc) and oxalic acids. It is noteworthy that there is an in situ reaction in 1, in which H3pdc was decomposed into (ox)2- with Cu(II)-Sm(III) synergistic effect under hydrothermal conditions. These compounds are isostructural and crystallized in the monoclinic P21/c space group. The Ln(III) ions are eight-coordinated with dodecahedron coordination geometry. These polyhedra are linked by oxalate groups to form 1D zigzag chain, which are further connected by 3,5-pyrazoledicarboxylate to extend similar 3D frameworks with channels along c-axis in 1-4. These coordination polymers display the characteristic emission bands of the Ln(III) ions in the solid state and possess good thermal stabilities.

Evaluation of Corneal Neovascularization Using Optical Coherence Tomography Angiography in Patients With Limbal Stem Cell Deficiency.

Science.gov (United States)

Oie, Yoshinori; Nishida, Kohji

2017-11-01

Detection of the exact area of corneal neovascularization using slit-lamp photography is often difficult. Thus, we evaluated corneal neovascularization in patients with limbal stem cell deficiency using optical coherence tomography angiography (OCTA). Five patients with 5 eyes showing partial or total limbal stem cell deficiency were enrolled. Three eyes had severe corneal scarring. Five 6- × 6-mm images (frontal, upper, lower, nasal, and temporal) were obtained by OCTA. Slit-lamp photography was performed for all patients on the same day. OCTA has 2 advantages over slit-lamp photography for clear demonstration of corneal neovascularization. First, OCTA can show neovascularization in cases with severe corneal opacification. Second, OCTA can detect not only large vessels but also small vessels that cannot be seen by slit-lamp photography. OCTA is a powerful tool for objective evaluation of vascularization in the anterior and posterior segments of the eye. We have demonstrated that OCTA can visualize corneal neovascularization in patients with corneal diseases more clearly than slit-lamp photography.

Algebraic structure of Robinson–Trautman and Kundt geometries in arbitrary dimension

International Nuclear Information System (INIS)

Podolský, J; Švarc, R

2015-01-01

We investigate the Weyl tensor algebraic structure of a fully general family of D-dimensional geometries that admit a non-twisting and shear-free null vector field k. From the coordinate components of the curvature tensor we explicitly derive all Weyl scalars of various boost weights. This enables us to give a complete algebraic classification of the metrics in the case when the optically privileged null direction k is a (multiple) Weyl aligned null direction (WAND). No field equations are applied, so the results are valid not only in Einstein's gravity, including its extension to higher dimensions, but also in any metric gravitation theory that admits non-twisting and shear-free spacetimes. We prove that all such geometries are of type I(b), or more special, and we derive surprisingly simple necessary and sufficient conditions under which k is a double, triple or quadruple WAND. All possible algebraically special types, including the refinement to subtypes, are thus identified, namely II(a), II(b), II(c), II(d), III(a), III(b), N, O, II i , III i , D, D(a), D(b), D(c), D(d), and their combinations. Some conditions are identically satisfied in four dimensions. We discuss both important subclasses, namely the Kundt family of geometries with the vanishing expansion (Θ=0) and the Robinson–Trautman family (Θ ≠ 0, and in particular Θ=1/r). Finally, we apply Einstein's field equations and obtain a classification of all Robinson–Trautman vacuum spacetimes. This reveals fundamental algebraic differences in the D>4 and D=4 cases, namely that in higher dimensions there only exist such spacetimes of types D(a) ≡ D(abd), D(c) ≡ D(bcd) and O. (paper)

Spectral dimension of quantum geometries

International Nuclear Information System (INIS)

Calcagni, Gianluca; Oriti, Daniele; Thürigen, Johannes

2014-01-01

The spectral dimension is an indicator of geometry and topology of spacetime and a tool to compare the description of quantum geometry in various approaches to quantum gravity. This is possible because it can be defined not only on smooth geometries but also on discrete (e.g., simplicial) ones. In this paper, we consider the spectral dimension of quantum states of spatial geometry defined on combinatorial complexes endowed with additional algebraic data: the kinematical quantum states of loop quantum gravity (LQG). Preliminarily, the effects of topology and discreteness of classical discrete geometries are studied in a systematic manner. We look for states reproducing the spectral dimension of a classical space in the appropriate regime. We also test the hypothesis that in LQG, as in other approaches, there is a scale dependence of the spectral dimension, which runs from the topological dimension at large scales to a smaller one at short distances. While our results do not give any strong support to this hypothesis, we can however pinpoint when the topological dimension is reproduced by LQG quantum states. Overall, by exploring the interplay of combinatorial, topological and geometrical effects, and by considering various kinds of quantum states such as coherent states and their superpositions, we find that the spectral dimension of discrete quantum geometries is more sensitive to the underlying combinatorial structures than to the details of the additional data associated with them. (paper)

Algebraic geometry

CERN Document Server

Lefschetz, Solomon

2005-01-01

An introduction to algebraic geometry and a bridge between its analytical-topological and algebraical aspects, this text for advanced undergraduate students is particularly relevant to those more familiar with analysis than algebra. 1953 edition.

Geometry Design Optimization of Functionally Graded Scaffolds for Bone Tissue Engineering: A Mechanobiological Approach.

Directory of Open Access Journals (Sweden)

Antonio Boccaccio

Full Text Available Functionally Graded Scaffolds (FGSs are porous biomaterials where porosity changes in space with a specific gradient. In spite of their wide use in bone tissue engineering, possible models that relate the scaffold gradient to the mechanical and biological requirements for the regeneration of the bony tissue are currently missing. In this study we attempt to bridge the gap by developing a mechanobiology-based optimization algorithm aimed to determine the optimal graded porosity distribution in FGSs. The algorithm combines the parametric finite element model of a FGS, a computational mechano-regulation model and a numerical optimization routine. For assigned boundary and loading conditions, the algorithm builds iteratively different scaffold geometry configurations with different porosity distributions until the best microstructure geometry is reached, i.e. the geometry that allows the amount of bone formation to be maximized. We tested different porosity distribution laws, loading conditions and scaffold Young's modulus values. For each combination of these variables, the explicit equation of the porosity distribution law-i.e the law that describes the pore dimensions in function of the spatial coordinates-was determined that allows the highest amounts of bone to be generated. The results show that the loading conditions affect significantly the optimal porosity distribution. For a pure compression loading, it was found that the pore dimensions are almost constant throughout the entire scaffold and using a FGS allows the formation of amounts of bone slightly larger than those obtainable with a homogeneous porosity scaffold. For a pure shear loading, instead, FGSs allow to significantly increase the bone formation compared to a homogeneous porosity scaffolds. Although experimental data is still necessary to properly relate the mechanical/biological environment to the scaffold microstructure, this model represents an important step towards

Long ranging swept-source optical coherence tomography-based angiography outperforms its spectral-domain counterpart in imaging human skin microcirculations

Science.gov (United States)

Xu, Jingjiang; Song, Shaozhen; Men, Shaojie; Wang, Ruikang K.

2017-11-01

There is an increasing demand for imaging tools in clinical dermatology that can perform in vivo wide-field morphological and functional examination from surface to deep tissue regions at various skin sites of the human body. The conventional spectral-domain optical coherence tomography-based angiography (SD-OCTA) system is difficult to meet these requirements due to its fundamental limitations of the sensitivity roll-off, imaging range as well as imaging speed. To mitigate these issues, we demonstrate a swept-source OCTA (SS-OCTA) system by employing a swept source based on a vertical cavity surface-emitting laser. A series of comparisons between SS-OCTA and SD-OCTA are conducted. Benefiting from the high system sensitivity, long imaging range, and superior roll-off performance, the SS-OCTA system is demonstrated with better performance in imaging human skin than the SD-OCTA system. We show that the SS-OCTA permits remarkable deep visualization of both structure and vasculature (up to ˜2 mm penetration) with wide field of view capability (up to 18×18 mm2), enabling a more comprehensive assessment of the morphological features as well as functional blood vessel networks from the superficial epidermal to deep dermal layers. It is expected that the advantages of the SS-OCTA system will provide a ground for clinical translation, benefiting the existing dermatological practice.

A geometry calibration method for rotation translation trajectory

International Nuclear Information System (INIS)

Zhang Jun; Yan Bin; Li Lei; Lu Lizhong; Zhang Feng

2013-01-01

In cone-beam CT imaging system, it is difficult to directly measure the geometry parameters. In this paper, a geometry calibration method for rotation translation trajectory is proposed. Intrinsic parameters are solved from the relationship built on geometry parameter of the system and projection trajectory of calibration object. Parameters of rotation axis are extrapolated from the unified intrinsic parameter, and geometry parameters of the idle trajectory are acquired too. The calibration geometry can be analytically determined using explicit formulae, it can avoid getting into local optimum in iterative way. Simulation experiments are carried out on misaligned geometry, experiment results indicate that geometry artifacts due to misaligned geometry are effectively depressed by the proposed method, and the image quality is enhanced. (authors)

Differential geometry of groups in string theory

International Nuclear Information System (INIS)

Schmidke, W.B. Jr.

1990-09-01

Techniques from differential geometry and group theory are applied to two topics from string theory. The first topic studied is quantum groups, with the example of GL (1|1). The quantum group GL q (1|1) is introduced, and an exponential description is derived. The algebra and coproduct are determined using the invariant differential calculus method introduced by Woronowicz and generalized by Wess and Zumino. An invariant calculus is also introduced on the quantum superplane, and a representation of the algebra of GL q (1|1) in terms of the super-plane coordinates is constructed. The second topic follows the approach to string theory introduced by Bowick and Rajeev. Here the ghost contribution to the anomaly of the energy-momentum tensor is calculated as the Ricci curvature of the Kaehler quotient space Diff(S 1 )/S 1 . We discuss general Kaehler quotient spaces and derive an expression for their Ricci curvatures. Application is made to the string and superstring diffeomorphism groups, considering all possible choices of subgroup. The formalism is extended to associated holomorphic vector bundles, where the Ricci curvature corresponds to the anomaly for different ghost sea levels. 26 refs

Geometry modeling for SAM-CE Monte Carlo calculations

International Nuclear Information System (INIS)

Steinberg, H.A.; Troubetzkoy, E.S.

1980-01-01

Three geometry packages have been developed and incorporated into SAM-CE, for representing in three dimensions the transport medium. These are combinatorial geometry - a general (non-lattice) system, complex combinatorial geometry - a very general system with lattice capability, and special reactor geometry - a special purpose system for light water reactor geometries. Their different attributes are described

Molecular motion in restricted geometries

Indian Academy of Sciences (India)

Molecular dynamics in restricted geometries is known to exhibit anomalous behaviour. Diffusion, translational or rotational, of molecules is altered significantly on confinement in restricted geometries. Quasielastic neutron scattering (QENS) offers a unique possibility of studying molecular motion in such systems. Both time ...

Numerical Calculation of Transport Based on the Drift Kinetic Equation for plasmas in General Toroidal Magnetic Geometry

International Nuclear Information System (INIS)

Reynolds, J. M.; Lopez-Bruna, D.

2009-01-01

This report is the first of a series dedicated to the numerical calculation of the evolution of fusion plasmas in general toroidal geometry, including TJ-II plasmas. A kinetic treatment has been chosen: the evolution equation of the distribution function of one or several plasma species is solved in guiding center coordinates. The distribution function is written as a Maxwellian one modulated by polynomial series in the kinetic coordinates with no other approximations than those of the guiding center itself and the computation capabilities. The code allows also for the inclusion of the three-dimensional electrostatic potential in a self-consistent manner, but the initial objective has been set to solving only the neoclassical transport. A high order conservative method (Spectral Difference Method) has been chosen in order to discretized the equation for its numerical solution. In this first report, in addition to justifying the work, the evolution equation and its approximations are described, as well as the baseline of the numerical procedures. (Author) 28 refs

Advances in discrete differential geometry

CERN Document Server

2016-01-01

This is one of the first books on a newly emerging field of discrete differential geometry and an excellent way to access this exciting area. It surveys the fascinating connections between discrete models in differential geometry and complex analysis, integrable systems and applications in computer graphics. The authors take a closer look at discrete models in differential geometry and dynamical systems. Their curves are polygonal, surfaces are made from triangles and quadrilaterals, and time is discrete. Nevertheless, the difference between the corresponding smooth curves, surfaces and classical dynamical systems with continuous time can hardly be seen. This is the paradigm of structure-preserving discretizations. Current advances in this field are stimulated to a large extent by its relevance for computer graphics and mathematical physics. This book is written by specialists working together on a common research project. It is about differential geometry and dynamical systems, smooth and discrete theories, ...

Data analytics and parallel-coordinate materials property charts

Science.gov (United States)

Rickman, Jeffrey M.

2018-01-01

It is often advantageous to display material properties relationships in the form of charts that highlight important correlations and thereby enhance our understanding of materials behavior and facilitate materials selection. Unfortunately, in many cases, these correlations are highly multidimensional in nature, and one typically employs low-dimensional cross-sections of the property space to convey some aspects of these relationships. To overcome some of these difficulties, in this work we employ methods of data analytics in conjunction with a visualization strategy, known as parallel coordinates, to represent better multidimensional materials data and to extract useful relationships among properties. We illustrate the utility of this approach by the construction and systematic analysis of multidimensional materials properties charts for metallic and ceramic systems. These charts simplify the description of high-dimensional geometry, enable dimensional reduction and the identification of significant property correlations and underline distinctions among different materials classes.

Coordinate measuring machines

DEFF Research Database (Denmark)

De Chiffre, Leonardo

This document is used in connection with three exercises of 2 hours duration as a part of the course GEOMETRICAL METROLOGY AND MACHINE TESTING. The exercises concern three aspects of coordinate measuring: 1) Measuring and verification of tolerances on coordinate measuring machines, 2) Traceabilit...... and uncertainty during coordinate measurements, 3) Digitalisation and Reverse Engineering. This document contains a short description of each step in the exercise and schemes with room for taking notes of the results.......This document is used in connection with three exercises of 2 hours duration as a part of the course GEOMETRICAL METROLOGY AND MACHINE TESTING. The exercises concern three aspects of coordinate measuring: 1) Measuring and verification of tolerances on coordinate measuring machines, 2) Traceability...

An Investigation into Conversion from Non-Uniform Rational B-Spline Boundary Representation Geometry to Constructive Solid Geometry

Science.gov (United States)

2015-12-01

ARL-SR-0347 ● DEC 2015 US Army Research Laboratory An Investigation into Conversion from Non-Uniform Rational B-Spline Boundary...US Army Research Laboratory An Investigation into Conversion from Non-Uniform Rational B-Spline Boundary Representation Geometry to...from Non-Uniform Rational B-Spline Boundary Representation Geometry to Constructive Solid Geometry 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c

W-geometry

International Nuclear Information System (INIS)

Hull, C.M.

1993-01-01

The geometric structure of theories with gauge fields of spins two and higher should involve a higher spin generalisation of Riemannian geometry. Such geometries are discussed and the case of W ∝ -gravity is analysed in detail. While the gauge group for gravity in d dimensions is the diffeomorphism group of the space-time, the gauge group for a certain W-gravity theory (which is W ∝ -gravity in the case d=2) is the group of symplectic diffeomorphisms of the cotangent bundle of the space-time. Gauge transformations for W-gravity gauge fields are given by requiring the invariance of a generalised line element. Densities exist and can be constructed from the line element (generalising √detg μν ) only if d=1 or d=2, so that only for d=1,2 can actions be constructed. These two cases and the corresponding W-gravity actions are considered in detail. In d=2, the gauge group is effectively only a subgroup of the symplectic diffeomorphisms group. Some of the constraints that arise for d=2 are similar to equations arising in the study of self-dual four-dimensional geometries and can be analysed using twistor methods, allowing contact to be made with other formulations of W-gravity. While the twistor transform for self-dual spaces with one Killing vector reduces to a Legendre transform, that for two Killing vectors gives a generalisation of the Legendre transform. (orig.)

Head First 2D Geometry

CERN Document Server

Fallow), Stray

2009-01-01

Having trouble with geometry? Do Pi, The Pythagorean Theorem, and angle calculations just make your head spin? Relax. With Head First 2D Geometry, you'll master everything from triangles, quads and polygons to the time-saving secrets of similar and congruent angles -- and it'll be quick, painless, and fun. Through entertaining stories and practical examples from the world around you, this book takes you beyond boring problems. You'll actually use what you learn to make real-life decisions, like using angles and parallel lines to crack a mysterious CSI case. Put geometry to work for you, and

Numerically robust geometry engine for compound solid geometries

International Nuclear Information System (INIS)

Vlachoudis, V.; Sinuela-Pastor, D.

2013-01-01

Monte Carlo programs heavily rely on a fast and numerically robust solid geometry engines. However the success of solid modeling, depends on facilities for specifying and editing parameterized models through a user-friendly graphical front-end. Such a user interface has to be fast enough in order to be interactive for 2D and/or 3D displays, but at the same time numerically robust in order to display possible modeling errors at real time that could be critical for the simulation. The graphical user interface Flair for FLUKA currently employs such an engine where special emphasis has been given on being fast and numerically robust. The numerically robustness is achieved by a novel method of estimating the floating precision of the operations, which dynamically adapts all the decision operations accordingly. Moreover a predictive caching mechanism is ensuring that logical errors in the geometry description are found online, without compromising the processing time by checking all regions. (authors)

Quantification of Porcine Vocal Fold Geometry.

Science.gov (United States)

Stevens, Kimberly A; Thomson, Scott L; Jetté, Marie E; Thibeault, Susan L

2016-07-01

The aim of this study was to quantify porcine vocal fold medial surface geometry and three-dimensional geometric distortion induced by freezing the larynx, especially in the region of the vocal folds. The medial surface geometries of five excised porcine larynges were quantified and reported. Five porcine larynges were imaged in a micro-CT scanner, frozen, and rescanned. Segmentations and three-dimensional reconstructions were used to quantify and characterize geometric features. Comparisons were made with geometry data previously obtained using canine and human vocal folds as well as geometries of selected synthetic vocal fold models. Freezing induced an overall expansion of approximately 5% in the transverse plane and comparable levels of nonuniform distortion in sagittal and coronal planes. The medial surface of the porcine vocal folds was found to compare reasonably well with other geometries, although the compared geometries exhibited a notable discrepancy with one set of published human female vocal fold geometry. Porcine vocal folds are qualitatively geometrically similar to data available for canine and human vocal folds, as well as commonly used models. Freezing of tissue in the larynx causes distortion of around 5%. The data can provide direction in estimating uncertainty due to bulk distortion of tissue caused by freezing, as well as quantitative geometric data that can be directly used in developing vocal fold models. Copyright © 2016 The Voice Foundation. Published by Elsevier Inc. All rights reserved.

Lanthanum(III) and Lutetium(III) in Nitrate-Based Ionic Liquids: A Theoretical Study of Their Coordination Shell.

Science.gov (United States)

Bodo, Enrico

2015-09-03

By using ab initio molecular dynamics, we investigate the solvent shell structure of La(3+) and Lu(3+) ions immersed in two ionic liquids, ethylammonium nitrate (EAN) and its hydroxy derivative (2-ethanolammonium nitrate, HOEAN). We provide the first study of the coordination properties of these heavy metal ions in such a highly charged nonacqueous environment. We find, as expected, that the coordination in the liquid is mainly due to nitrate anions and that, due to the bidentate nature of the ligand, the complexation shell of the central ion has a nontrivial geometry and a coordination number in terms of nitrate molecules that apparently violates the decrease of ionic radii along the lanthanides series, since the smaller Lu(3+) ion seems to coordinate six nitrate molecules and the La(3+) ion only five. A closer inspection of the structural features obtained from our calculations shows, instead, that the first shell of oxygen atoms is more compact for Lu(3+) than for La(3+) and that the former coordinates 8 oxygen atoms while the latter 10 in accord with the typical lanthanide's trend along the series and that their first solvation shells have a slight irregular and complex geometrical pattern. When moving to the HOEAN solutions, we have found that the solvation of the central ion is possibly also due to the cation itself through the oxygen atom on the side chain. Also, in this liquid, the coordination numbers in terms of oxygen atoms in both solvents is 10 for La(3+) and 8 for Lu(3+).

Lectures on discrete geometry

CERN Document Server

2002-01-01

Discrete geometry investigates combinatorial properties of configurations of geometric objects. To a working mathematician or computer scientist, it offers sophisticated results and techniques of great diversity and it is a foundation for fields such as computational geometry or combinatorial optimization. This book is primarily a textbook introduction to various areas of discrete geometry. In each area, it explains several key results and methods, in an accessible and concrete manner. It also contains more advanced material in separate sections and thus it can serve as a collection of surveys in several narrower subfields. The main topics include: basics on convex sets, convex polytopes, and hyperplane arrangements; combinatorial complexity of geometric configurations; intersection patterns and transversals of convex sets; geometric Ramsey-type results; polyhedral combinatorics and high-dimensional convexity; and lastly, embeddings of finite metric spaces into normed spaces. Jiri Matousek is Professor of Com...

Discrete and computational geometry

CERN Document Server

Devadoss, Satyan L

2011-01-01

Discrete geometry is a relatively new development in pure mathematics, while computational geometry is an emerging area in applications-driven computer science. Their intermingling has yielded exciting advances in recent years, yet what has been lacking until now is an undergraduate textbook that bridges the gap between the two. Discrete and Computational Geometry offers a comprehensive yet accessible introduction to this cutting-edge frontier of mathematics and computer science. This book covers traditional topics such as convex hulls, triangulations, and Voronoi diagrams, as well as more recent subjects like pseudotriangulations, curve reconstruction, and locked chains. It also touches on more advanced material, including Dehn invariants, associahedra, quasigeodesics, Morse theory, and the recent resolution of the Poincaré conjecture. Connections to real-world applications are made throughout, and algorithms are presented independently of any programming language. This richly illustrated textbook also fe...

A prediction for bubbling geometries

OpenAIRE

Okuda, Takuya

2007-01-01

We study the supersymmetric circular Wilson loops in N=4 Yang-Mills theory. Their vacuum expectation values are computed in the parameter region that admits smooth bubbling geometry duals. The results are a prediction for the supergravity action evaluated on the bubbling geometries for Wilson loops.

Geometry -----------~--------------RESONANCE

Indian Academy of Sciences (India)

Parallel: A pair of lines in a plane is said to be parallel if they do not meet. Mathematicians were at war ... Subsequently, Poincare, Klein, Beltrami and others refined non-. Euclidean geometry. ... plane divides the plane into two half planes and.

Anterior Segment Optical Coherence Tomography Angiography for Identification of Iris Vasculature and Staging of Iris Neovascularization: A Pilot Study.

Science.gov (United States)

Roberts, Philipp K; Goldstein, Debra A; Fawzi, Amani A

2017-08-01

Purpose/Aim of the study: To assess the ability of optical coherence tomographic angiography (OCTA) to visualize the normal iris vasculature as well as neovascularization of the iris (NVI). Study participants with healthy eyes, patients at risk of NVI development and patients with active or regressed NVI were consecutively included in this cross-sectional observational study. Imaging was performed using a commercially available OCTA system (RTVue- XR Avanti, Optovue Inc., Fremont, CA, USA). Abnormal iris vessels were graded on OCTA according to a modified clinical staging system and compared to slitlamp and gonioscopic findings. Fifty eyes of 26 study participants (16 healthy eyes, 19 eyes at risk, 15 eyes with different stages of NVI) were imaged using OCTA. In 11 out of 16 healthy eyes (69%) with light or moderately dark iris pigmentation, we observed physiological, radially aligned iris vasculature on OCTA imaging, which could not be visualized in five eyes (31%) with darkly pigmented irides. One eye in the "eyes at risk" group was diagnosed with NVI based on OCTA, which was not observed clinically. Fifteen eyes with clinically active or regressed NVI were imaged. Different stages of NVI could be differentiated by OCTA, corresponding well to an established clinical grading system. Four eyes showed regressed NVI by OCTA, not seen clinically, and were graded as a newly defined stage 4. This pilot clinical study showed that OCTA for imaging of the iris vasculature in health and disease is highly dependent on iris pigmentation. Fine, clinically invisible iris vessels can be visualized by OCTA in the very early stages as well as in the regressed stage of NVI.

Intermediate algebra & analytic geometry

CERN Document Server

Gondin, William R

1967-01-01

Intermediate Algebra & Analytic Geometry Made Simple focuses on the principles, processes, calculations, and methodologies involved in intermediate algebra and analytic geometry. The publication first offers information on linear equations in two unknowns and variables, functions, and graphs. Discussions focus on graphic interpretations, explicit and implicit functions, first quadrant graphs, variables and functions, determinate and indeterminate systems, independent and dependent equations, and defective and redundant systems. The text then examines quadratic equations in one variable, system

Four coordination polymers based on 5-tert-butyl isophthalic acid and rigid bis(imidazol-1yl)benzene linkers: Synthesis, luminescence detection of acetone and optical properties

International Nuclear Information System (INIS)

Arıcı, Mürsel; Zafer Yeşilel, Okan; Büyükgüngör, Orhan

2017-01-01

Four coordination polymers including, [Co(µ-Htbip) 2 (µ-dib)] n (1), [Co(µ-tbip)(µ-dmib) 0.5 ] n (2), [Zn 2 (µ-tbip)(µ 3 -tbip)(µ-dmib) 1.5 ] n (3) and [Cd(µ 3 -tbip)(µ-dib) 0.5 (H 2 O)] n (4) (tbip: 5-tert-butylisophthalate, dib: 1,4-bis(imidazol-1yl)benzene, dmib: 1,4-bis(imidazol-1yl)-2,5-dimethylbenzene), were hydrothermally synthesized and characterized by elemental analysis, IR spectra, single crystal and powder X-ray diffraction and thermal analysis (TG/DTA). The structural diversity is observed depending on ligands and coordination number of metal centers in the synthesized complexes. The tbip ligand displayed five different coordination modes in its complexes. In 1 and 2, complex 1 is 3D framework with the dia topology while complex 2 has 2D structure with the sql topology depending on coordination geometries of Co ions. Complex 3 is 3D framework with the fsh 4,6-conn topology and complex 4 has 2D 4-connected sql topology. Photoluminescent properties of complex 3 dispersed in various organic solvents were investigated and the results showed that 3 dispersed in methanol could be used as a fluorescent sensor for the detection of acetone. Moreover, thermal and optical properties of the complexes were also studied. - Graphical abstract: Four coordination polymers were hydrothermally synthesized and characterized by various techniques. The complexes showed the structural diversity depending on ligands and coordination number of metal centers. The tbip ligand displayed four different coordination modes in its complexes. In 1 and 2, complexes 1 and 2 are 3D and 2D structures with the dia and sql topologies depending on coordination geometries of Co ions, respectively. Complexes 3 and 4 are 3D and 2D structures with the fsh 4,6-conn and sql topology, respectively. Photoluminescent properties of complex 3 dispersed in various organic solvents were investigated and the results showed that 3 dispersed in methanol could be used as a fluorescent sensor for the

Coordinated School Health and the Contribution of a District Wellness Coordinator

Science.gov (United States)

Westrich, Lisa; Sanchez, Monika; Strobel, Karen

2015-01-01

Background: A San Francisco Bay Area school health initiative was established in fall 2010 to improve wellness programs in 4 local school districts using the Coordinated School Health (CSH) model. This study examines the role of district-wide wellness coordinators and the ways in which they contribute to intentional coordination of health and…

From geometry to algebra and vice versa: Realistic mathematics education principles for analyzing geometry tasks

Science.gov (United States)

Jupri, Al

2017-04-01

In this article we address how Realistic Mathematics Education (RME) principles, including the intertwinement and the reality principles, are used to analyze geometry tasks. To do so, we carried out three phases of a small-scale study. First we analyzed four geometry problems - considered as tasks inviting the use of problem solving and reasoning skills - theoretically in the light of the RME principles. Second, we tested two problems to 31 undergraduate students of mathematics education program and other two problems to 16 master students of primary mathematics education program. Finally, we analyzed student written work and compared these empirical to the theoretical results. We found that there are discrepancies between what we expected theoretically and what occurred empirically in terms of mathematization and of intertwinement of mathematical concepts from geometry to algebra and vice versa. We conclude that the RME principles provide a fruitful framework for analyzing geometry tasks that, for instance, are intended for assessing student problem solving and reasoning skills.

Coordination functionalization of graphene oxide with tetraazamacrocyclic complexes of nickel(II): Generation of paramagnetic centers

Energy Technology Data Exchange (ETDEWEB)

Basiuk, Vladimir A., E-mail: basiuk@nucleares.unam.mx [Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Circuito Exterior C.U., 04510 México D.F. (Mexico); Department of Chemistry,Tufts University, 62 Talbot Avenue, Medford, MA 02155 (United States); Alzate-Carvajal, Natalia [Centro de Ciencias Aplicadas y Desarrollo Tecnológico, Universidad Nacional Autónoma de México, Circuito Exterior C.U., 04510 México D.F. (Mexico); Henao-Holguín, Laura V. [Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Circuito Exterior C.U., 04510 México D.F. (Mexico); Rybak-Akimova, Elena V. [Department of Chemistry,Tufts University, 62 Talbot Avenue, Medford, MA 02155 (United States); Basiuk, Elena V., E-mail: elbg1111@gmail.com [Department of Chemistry,Tufts University, 62 Talbot Avenue, Medford, MA 02155 (United States); Centro de Ciencias Aplicadas y Desarrollo Tecnológico, Universidad Nacional Autónoma de México, Circuito Exterior C.U., 04510 México D.F. (Mexico)

2016-05-15

Highlights: • [Ni(cyclam)]{sup 2+} and [Ni(tet b)]{sup 2+} cations coordinate to carboxylic groups of GO. • The coordination takes place under basic conditions in aqueous-based medium. • The coordination results in the conversion from low-spin to high-spin Ni(II). • Functionalized GO samples were characterized by various instrumental techniques. - Abstract: We describe a novel approach to functionalization of graphene oxide (GO) which allows for a facile generation of paramagnetic centers from two diamagnetic components. Coordination attachment of [Ni(cyclam)]{sup 2+} or [Ni(tet b)]{sup 2+} tetraazamacrocyclic cations to carboxylic groups of GO takes place under basic conditions in aqueous-based reaction medium. The procedure is very straightforward and does not require high temperatures or other harsh conditions. Changing the coordination geometry of Ni(II) from square-planar tetracoordinated to pseudooctahedral hexacoordinated brings about the conversion from low-spin to high-spin state of the metal centers. Even though the content of tetraazamacrocyclic complexes in functionalized GO samples was found to be relatively low (nickel content of ca. 1 wt%, as determined by thermogravimetric analysis, elemental analysis and energy dispersive X-ray spectroscopy), room temperature magnetic susceptibility measurements easily detected the appearance of paramagnetic properties in GO + [Ni(cyclam)] and GO + [Ni(tet b)] nanohybrids, with effective magnetic moments of 1.95 BM and 2.2 BM for, respectively. According to density functional theory calculations, the main spin density is localized at the macrocyclic complexes, without considerable extension to graphene sheet, which suggests insignificant ferromagnetic coupling in the nanohybrids, in agreement with the results of magnetic susceptibility measurements. The coordination attachment of Ni(II) tetraazamacrocycles to GO results in considerable changes in Fourier-transform infrared and X-ray photoelectron spectra

Differential geometry curves, surfaces, manifolds

CERN Document Server

Kohnel, Wolfgang

2002-01-01

This carefully written book is an introduction to the beautiful ideas and results of differential geometry. The first half covers the geometry of curves and surfaces, which provide much of the motivation and intuition for the general theory. Special topics that are explored include Frenet frames, ruled surfaces, minimal surfaces and the Gauss-Bonnet theorem. The second part is an introduction to the geometry of general manifolds, with particular emphasis on connections and curvature. The final two chapters are insightful examinations of the special cases of spaces of constant curvature and Einstein manifolds. The text is illustrated with many figures and examples. The prerequisites are undergraduate analysis and linear algebra.

Projective Geometry

Indian Academy of Sciences (India)

mathematicians are trained to use very precise language, and so find it hard to simplify and state .... thing. If you take a plane on which there are two such triangles which enjoy the above ... within this geometry to simplify things if needed.

Second International workshop Geometry and Symbolic Computation

CERN Document Server

Walczak, Paweł; Geometry and its Applications

2014-01-01

This volume has been divided into two parts: Geometry and Applications. The geometry portion of the book relates primarily to geometric flows, laminations, integral formulae, geometry of vector fields on Lie groups, and osculation; the articles in the applications portion concern some particular problems of the theory of dynamical systems, including mathematical problems of liquid flows and a study of cycles for non-dynamical systems. This Work is based on the second international workshop entitled "Geometry and Symbolic Computations," held on May 15-18, 2013 at the University of Haifa and is dedicated to modeling (using symbolic calculations) in differential geometry and its applications in fields such as computer science, tomography, and mechanics. It is intended to create a forum for students and researchers in pure and applied geometry to promote discussion of modern state-of-the-art in geometric modeling using symbolic programs such as Maple™ and Mathematica®, as well as presentation of new results. ...

Network geometry with flavor: From complexity to quantum geometry

Science.gov (United States)

Bianconi, Ginestra; Rahmede, Christoph

2016-03-01

Network geometry is attracting increasing attention because it has a wide range of applications, ranging from data mining to routing protocols in the Internet. At the same time advances in the understanding of the geometrical properties of networks are essential for further progress in quantum gravity. In network geometry, simplicial complexes describing the interaction between two or more nodes play a special role. In fact these structures can be used to discretize a geometrical d -dimensional space, and for this reason they have already been widely used in quantum gravity. Here we introduce the network geometry with flavor s =-1 ,0 ,1 (NGF) describing simplicial complexes defined in arbitrary dimension d and evolving by a nonequilibrium dynamics. The NGF can generate discrete geometries of different natures, ranging from chains and higher-dimensional manifolds to scale-free networks with small-world properties, scale-free degree distribution, and nontrivial community structure. The NGF admits as limiting cases both the Bianconi-Barabási models for complex networks, the stochastic Apollonian network, and the recently introduced model for complex quantum network manifolds. The thermodynamic properties of NGF reveal that NGF obeys a generalized area law opening a new scenario for formulating its coarse-grained limit. The structure of NGF is strongly dependent on the dimensionality d . In d =1 NGFs grow complex networks for which the preferential attachment mechanism is necessary in order to obtain a scale-free degree distribution. Instead, for NGF with dimension d >1 it is not necessary to have an explicit preferential attachment rule to generate scale-free topologies. We also show that NGF admits a quantum mechanical description in terms of associated quantum network states. Quantum network states evolve by a Markovian dynamics and a quantum network state at time t encodes all possible NGF evolutions up to time t . Interestingly the NGF remains fully classical but

The Persistification of the ATLAS Geometry

CERN Document Server

AUTHOR|(INSPIRE)INSPIRE-00068562; The ATLAS collaboration; Bianchi, Riccardo-Maria

2016-01-01

The complex geometry of the whole detector of the ATLAS experiment at LHC is currently stored only in custom online databases, from which it is built on-the- y on request. Accessing the online geometry guarantees accessing the latest version of the detector description, but requires the setup of the full ATLAS so ware framework “Athena”, which provides the online services and the tools to retrieve the data from the database. is operation is cumbersome and slows down the applications that need to access the geometry. Moreover, all applications that need to access the detector geom- etry need to be built and run on the same platform as the ATLAS framework, preventing the usage of the actual detector geometry in stand-alone applications. Here we propose a new mechanism to persistify and serve the geometry of HEP experiments. e new mechanism is composed by a new le format and a REST API. e new le format allows to store the whole detector description locally in a at le, and it is especially optimized to descri...

Implosions and hypertoric geometry

DEFF Research Database (Denmark)

Dancer, A.; Kirwan, F.; Swann, A.

2013-01-01

The geometry of the universal hyperkahler implosion for SU (n) is explored. In particular, we show that the universal hyperkahler implosion naturally contains a hypertoric variety described in terms of quivers. Furthermore, we discuss a gauge theoretic approach to hyperkahler implosion.......The geometry of the universal hyperkahler implosion for SU (n) is explored. In particular, we show that the universal hyperkahler implosion naturally contains a hypertoric variety described in terms of quivers. Furthermore, we discuss a gauge theoretic approach to hyperkahler implosion....

Conformational differences in dioxouraniun(VI) coordination compounds. Crystal structure of the chloroform adduct of n,n'-bis-salicylidene-1,5-diamino-3-oxapentane-dioxouranium(VI)

Energy Technology Data Exchange (ETDEWEB)

Bombieri, G; Forsellini, E; Benetollo, F [Consiglio Nazionale delle Ricerche, Padua (Italy). Lab. di Chimica e Tecnologia dei Radioelementi; Fenton, D E

1979-01-01

The title compound (UO/sub 2/-saloden-CHCl/sub 3/) crystallizes in an orthorhombic system. Lattice parameters are given. The coordination geometry of the uranium atom is bipyramidal pentagonal with the ligand pentadentate in the equatorial plane of the uranyl ion. The chloroform molecule does not interact directly with the ligand. The IR spectral data are also discussed.

Potential applications of optical coherence tomography angiography in glaucoma.

Science.gov (United States)

Dastiridou, Anna; Chopra, Vikas

2018-05-01

Optical coherence tomography angiography (OCTA) is a novel, noninvasive imaging modality that allows assessment of the retinal and choroidal vasculature. The scope of this review is to summarize recent studies using OCTA in glaucoma and highlight potential applications of this new technology in the field of glaucoma. OCTA studies have shown that retinal vascular changes may not develop solely as a result of advanced glaucoma damage. OCTA-derived measurements have provided evidence for lower retinal vascular densities at the optic nerve head, peripapillary and macula in preperimetric-glaucoma and early-glaucoma, as well as, in more advanced glaucoma, in comparison to with normal eyes. OCTA is a novel imaging modality that has already started to expand our knowledge base regarding the role of ocular blood flow in glaucoma. Future studies will better elucidate the role of OCTA-derived measurements in clinical practice, research, and clinical trials in glaucoma.

Granular flows in constrained geometries

Science.gov (United States)

Murthy, Tejas; Viswanathan, Koushik

Confined geometries are widespread in granular processing applications. The deformation and flow fields in such a geometry, with non-trivial boundary conditions, determine the resultant mechanical properties of the material (local porosity, density, residual stresses etc.). We present experimental studies of deformation and plastic flow of a prototypical granular medium in different nontrivial geometries- flat-punch compression, Couette-shear flow and a rigid body sliding past a granular half-space. These geometries represent simplified scaled-down versions of common industrial configurations such as compaction and dredging. The corresponding granular flows show a rich variety of flow features, representing the entire gamut of material types, from elastic solids (beam buckling) to fluids (vortex-formation, boundary layers) and even plastically deforming metals (dead material zone, pile-up). The effect of changing particle-level properties (e.g., shape, size, density) on the observed flows is also explicitly demonstrated. Non-smooth contact dynamics particle simulations are shown to reproduce some of the observed flow features quantitatively. These results showcase some central challenges facing continuum-scale constitutive theories for dynamic granular flows.

Variationally optimal selection of slow coordinates and reaction coordinates in macromolecular systems

Science.gov (United States)

Noe, Frank

To efficiently simulate and generate understanding from simulations of complex macromolecular systems, the concept of slow collective coordinates or reaction coordinates is of fundamental importance. Here we will introduce variational approaches to approximate the slow coordinates and the reaction coordinates between selected end-states given MD simulations of the macromolecular system and a (possibly large) basis set of candidate coordinates. We will then discuss how to select physically intuitive order paremeters that are good surrogates of this variationally optimal result. These result can be used in order to construct Markov state models or other models of the stationary and kinetics properties, in order to parametrize low-dimensional / coarse-grained model of the dynamics. Deutsche Forschungsgemeinschaft, European Research Council.

Indoor Localization and Radio Map Estimation using Unsupervised Manifold Alignment with Geometry Perturbation

KAUST Repository

Majeed, Khaqan

2015-12-22

The Received Signal Strength (RSS) based fingerprinting approaches for indoor localization pose a need for updating the fingerprint databases due to dynamic nature of the indoor environment. This process is hectic and time-consuming when the size of the indoor area is large. The semi-supervised approaches reduce this workload and achieve good accuracy around 15% of the fingerprinting load but the performance is severely degraded if it is reduced below this level. We propose an indoor localization framework that uses unsupervised manifold alignment. It requires only 1% of the fingerprinting load, some crowd sourced readings and plan coordinates of the indoor area. The 1% fingerprinting load is used only in perturbing the local geometries of the plan coordinates. The proposed framework achieves less than 5m mean localization error, which is considerably better than semi-supervised approaches at very small amount of fingerprinting load. In addition, the few location estimations together with few fingerprints help to estimate the complete radio map of the indoor environment. The estimation of radio map does not demand extra workload rather it employs the already available information from the proposed indoor localization framework. The testing results for radio map estimation show almost 50% performance improvement by using this information as compared to using only fingerprints.

Indoor Localization and Radio Map Estimation using Unsupervised Manifold Alignment with Geometry Perturbation

KAUST Repository

Majeed, Khaqan; Sorour, Sameh; Al-Naffouri, Tareq Y.; Valaee, Shahrokh

2015-01-01

The Received Signal Strength (RSS) based fingerprinting approaches for indoor localization pose a need for updating the fingerprint databases due to dynamic nature of the indoor environment. This process is hectic and time-consuming when the size of the indoor area is large. The semi-supervised approaches reduce this workload and achieve good accuracy around 15% of the fingerprinting load but the performance is severely degraded if it is reduced below this level. We propose an indoor localization framework that uses unsupervised manifold alignment. It requires only 1% of the fingerprinting load, some crowd sourced readings and plan coordinates of the indoor area. The 1% fingerprinting load is used only in perturbing the local geometries of the plan coordinates. The proposed framework achieves less than 5m mean localization error, which is considerably better than semi-supervised approaches at very small amount of fingerprinting load. In addition, the few location estimations together with few fingerprints help to estimate the complete radio map of the indoor environment. The estimation of radio map does not demand extra workload rather it employs the already available information from the proposed indoor localization framework. The testing results for radio map estimation show almost 50% performance improvement by using this information as compared to using only fingerprints.

Integral geometry and valuations

CERN Document Server

Solanes, Gil

2014-01-01

Valuations are finitely additive functionals on the space of convex bodies. Their study has become a central subject in convexity theory, with fundamental applications to integral geometry. In the last years there has been significant progress in the theory of valuations, which in turn has led to important achievements in integral geometry. This book originated from two courses delivered by the authors at the CRM and provides a self-contained introduction to these topics, covering most of the recent advances. The first part, by Semyon Alesker, is devoted to the theory of convex valuations, with emphasis on the latest developments. A special focus is put on the new fundamental structures of the space of valuations discovered after Alesker's irreducibility theorem. Moreover, the author describes the newly developed theory of valuations on manifolds. In the second part, Joseph H. G. Fu gives a modern introduction to integral geometry in the sense of Blaschke and Santaló, based on the notions and tools presented...

CBM RICH geometry optimization

Energy Technology Data Exchange (ETDEWEB)

Mahmoud, Tariq; Hoehne, Claudia [II. Physikalisches Institut, Giessen Univ. (Germany); Collaboration: CBM-Collaboration

2016-07-01

The Compressed Baryonic Matter (CBM) experiment at the future FAIR complex will investigate the phase diagram of strongly interacting matter at high baryon density and moderate temperatures in A+A collisions from 2-11 AGeV (SIS100) beam energy. The main electron identification detector in the CBM experiment will be a RICH detector with a CO{sub 2} gaseous-radiator, focusing spherical glass mirrors, and MAPMT photo-detectors being placed on a PMT-plane. The RICH detector is located directly behind the CBM dipole magnet. As the final magnet geometry is now available, some changes in the RICH geometry become necessary. In order to guarantee a magnetic field of 1 mT at maximum in the PMT plane for effective operation of the MAPMTs, two measures have to be taken: The PMT plane is moved outwards of the stray field by tilting the mirrors by 10 degrees and shielding boxes have been designed. In this contribution the results of the geometry optimization procedure are presented.

Near-Horizon Geodesics for Astrophysical and Idealised Black Holes: Coordinate Velocity and Coordinate Acceleration

Directory of Open Access Journals (Sweden)

Petarpa Boonserm

2018-05-01

Full Text Available Geodesics (by definition have an intrinsic 4-acceleration zero. However, when expressed in terms of coordinates, the coordinate acceleration d 2 x i / d t 2 can very easily be non-zero, and the coordinate velocity d x i / d t can behave unexpectedly. The situation becomes extremely delicate in the near-horizon limit—for both astrophysical and idealised black holes—where an inappropriate choice of coordinates can quite easily lead to significant confusion. We shall carefully explore the relative merits of horizon-penetrating versus horizon-non-penetrating coordinates, arguing that in the near-horizon limit the coordinate acceleration d 2 x i / d t 2 is best interpreted in terms of horizon-penetrating coordinates.

Kaehler geometry and SUSY mechanics

International Nuclear Information System (INIS)

Bellucci, Stefano; Nersessian, Armen

2001-01-01

We present two examples of SUSY mechanics related with Kaehler geometry. The first system is the N = 4 supersymmetric one-dimensional sigma-model proposed in hep-th/0101065. Another system is the N = 2 SUSY mechanics whose phase space is the external algebra of an arbitrary Kaehler manifold. The relation of these models with antisymplectic geometry is discussed

GPS: Geometry, Probability, and Statistics

Science.gov (United States)

Field, Mike

2012-01-01

It might be said that for most occupations there is now less of a need for mathematics than there was say fifty years ago. But, the author argues, geometry, probability, and statistics constitute essential knowledge for everyone. Maybe not the geometry of Euclid, but certainly geometrical ways of thinking that might enable us to describe the world…

FINAL REPORT: GEOMETRY AND ELEMENTARY PARTICLE PHYSICS

Energy Technology Data Exchange (ETDEWEB)

Singer, Isadore M.

2008-03-04

The effect on mathematics of collaborations between high-energy theoretical physics and modern mathematics has been remarkable. Mirror symmetry has revolutionized enumerative geometry, and Seiberg-Witten invariants have greatly simplified the study of four manifolds. And because of their application to string theory, physicists now need to know cohomology theory, characteristic classes, index theory, K-theory, algebraic geometry, differential geometry, and non-commutative geometry. Much more is coming. We are experiencing a deeper contact between the two sciences, which will stimulate new mathematics essential to the physicists’ quest for the unification of quantum mechanics and relativity. Our grant, supported by the Department of Energy for twelve years, has been instrumental in promoting an effective interaction between geometry and string theory, by supporting the Mathematical Physics seminar, postdoc research, collaborations, graduate students and several research papers.

Final Report: Geometry And Elementary Particle Physics

International Nuclear Information System (INIS)

Singer, Isadore M.

2008-01-01

The effect on mathematics of collaborations between high-energy theoretical physics and modern mathematics has been remarkable. Mirror symmetry has revolutionized enumerative geometry, and Seiberg-Witten invariants have greatly simplified the study of four manifolds. And because of their application to string theory, physicists now need to know cohomology theory, characteristic classes, index theory, K-theory, algebraic geometry, differential geometry, and non-commutative geometry. Much more is coming. We are experiencing a deeper contact between the two sciences, which will stimulate new mathematics essential to the physicists quest for the unification of quantum mechanics and relativity. Our grant, supported by the Department of Energy for twelve years, has been instrumental in promoting an effective interaction between geometry and string theory, by supporting the Mathematical Physics seminar, postdoc research, collaborations, graduate students and several research papers.

Indoor localization using unsupervised manifold alignment with geometry perturbation

KAUST Repository

Majeed, Khaqan

2014-04-01

The main limitation of deploying/updating Received Signal Strength (RSS) based indoor localization is the construction of fingerprinted radio map, which is quite a hectic and time-consuming process especially when the indoor area is enormous and/or dynamic. Different approaches have been undertaken to reduce such deployment/update efforts, but the performance degrades when the fingerprinting load is reduced below a certain level. In this paper, we propose an indoor localization scheme that requires as low as 1% fingerprinting load. This scheme employs unsupervised manifold alignment that takes crowd sourced RSS readings and localization requests as source data set and the environment\\'s plan coordinates as destination data set. The 1% fingerprinting load is only used to perturb the local geometries in the destination data set. Our proposed algorithm was shown to achieve less than 5 m mean localization error with 1% fingerprinting load and a limited number of crowd sourced readings, when other learning based localization schemes pass the 10 m mean error with the same information.

Indoor localization using unsupervised manifold alignment with geometry perturbation

KAUST Repository

Majeed, Khaqan; Sorour, Sameh; Al-Naffouri, Tareq Y.; Valaee, Shahrokh

2014-01-01

The main limitation of deploying/updating Received Signal Strength (RSS) based indoor localization is the construction of fingerprinted radio map, which is quite a hectic and time-consuming process especially when the indoor area is enormous and/or dynamic. Different approaches have been undertaken to reduce such deployment/update efforts, but the performance degrades when the fingerprinting load is reduced below a certain level. In this paper, we propose an indoor localization scheme that requires as low as 1% fingerprinting load. This scheme employs unsupervised manifold alignment that takes crowd sourced RSS readings and localization requests as source data set and the environment's plan coordinates as destination data set. The 1% fingerprinting load is only used to perturb the local geometries in the destination data set. Our proposed algorithm was shown to achieve less than 5 m mean localization error with 1% fingerprinting load and a limited number of crowd sourced readings, when other learning based localization schemes pass the 10 m mean error with the same information.

Discrete quantum geometries and their effective dimension

International Nuclear Information System (INIS)

Thuerigen, Johannes

2015-01-01

In several approaches towards a quantum theory of gravity, such as group field theory and loop quantum gravity, quantum states and histories of the geometric degrees of freedom turn out to be based on discrete spacetime. The most pressing issue is then how the smooth geometries of general relativity, expressed in terms of suitable geometric observables, arise from such discrete quantum geometries in some semiclassical and continuum limit. In this thesis I tackle the question of suitable observables focusing on the effective dimension of discrete quantum geometries. For this purpose I give a purely combinatorial description of the discrete structures which these geometries have support on. As a side topic, this allows to present an extension of group field theory to cover the combinatorially larger kinematical state space of loop quantum gravity. Moreover, I introduce a discrete calculus for fields on such fundamentally discrete geometries with a particular focus on the Laplacian. This permits to define the effective-dimension observables for quantum geometries. Analysing various classes of quantum geometries, I find as a general result that the spectral dimension is more sensitive to the underlying combinatorial structure than to the details of the additional geometric data thereon. Semiclassical states in loop quantum gravity approximate the classical geometries they are peaking on rather well and there are no indications for stronger quantum effects. On the other hand, in the context of a more general model of states which are superposition over a large number of complexes, based on analytic solutions, there is a flow of the spectral dimension from the topological dimension d on low energy scales to a real number between 0 and d on high energy scales. In the particular case of 1 these results allow to understand the quantum geometry as effectively fractal.

Variable geometry truss manipulators: A new type of robot for site inspection and remediation

International Nuclear Information System (INIS)

Naccarato, F.

1996-01-01

A new type of robotic manipulator has been developed that offers many potential advantages over conventional robot arms for site inspection and remediation. This new robot is based on the variable geometry truss manipulator (VGTM) concept which combines the structural properties of a truss with the dexterous capabilities of a manipulator. By substituting linear actuators for some of the fixed-length members within a truss, the structure can be made to change its overall shape. By coordinating the motion of these actuators appropriately, a VGTM can perform tasks that are relevant to hazardous waste clean-up, including deployment through curved ducts, probing into crevices and obstacle avoidance. Trussarm trademark, a prototype VGTM with twelve degrees-of-freedom, has been constructed by Dynacon Enterprises Limited

Introduction into integral geometry and stereology

DEFF Research Database (Denmark)

Kiderlen, Markus

Statistics and Random Fields and is a self-containing introduction into integral geometry and its applications in stereology. The most important integral geometric tools for stereological applications are kinematic formulas and results of Blaschke-Petkantschin type. Therefore, Crofton's formula......This text is the extended version of two talks held at the Summer Academy Stochastic Geometry, Spatial Statistics and Random Fields in the Soellerhaus, Germany, in September 2009. It forms (with slight modifications) a chapter of the Springer lecture notes Lectures on Stochastic Geometry, Spatial...

Coordination, non-coordination and semi-coordination of perchlorates in the lanthanide adducts Ln (CLO4)3. 6dmba

International Nuclear Information System (INIS)

Tfouni, E.; Giesbrecht, E.

1983-01-01

The coordination or not of the perchlorate anions in the previously reported Ln(CLO 4 ) 3 .6 dmba is discussed. The analysis of the infrared spectral data and molar conductance data indicate that they may be formulated as [Ln(dmba) 6 (CLO 4 )n] (CLO 4 ) sub(3-n), n=0,1,2. The individual compounds may be a mixture of species with different n values and/or pure compounds with semi-coordinated and non-coordinated perchlorates. (Author) [pt

Magnetic Coordinate Systems

Science.gov (United States)

Laundal, K. M.; Richmond, A. D.

2017-03-01

Geospace phenomena such as the aurora, plasma motion, ionospheric currents and associated magnetic field disturbances are highly organized by Earth's main magnetic field. This is due to the fact that the charged particles that comprise space plasma can move almost freely along magnetic field lines, but not across them. For this reason it is sensible to present such phenomena relative to Earth's magnetic field. A large variety of magnetic coordinate systems exist, designed for different purposes and regions, ranging from the magnetopause to the ionosphere. In this paper we review the most common magnetic coordinate systems and describe how they are defined, where they are used, and how to convert between them. The definitions are presented based on the spherical harmonic expansion coefficients of the International Geomagnetic Reference Field (IGRF) and, in some of the coordinate systems, the position of the Sun which we show how to calculate from the time and date. The most detailed coordinate systems take the full IGRF into account and define magnetic latitude and longitude such that they are constant along field lines. These coordinate systems, which are useful at ionospheric altitudes, are non-orthogonal. We show how to handle vectors and vector calculus in such coordinates, and discuss how systematic errors may appear if this is not done correctly.

Quasilocal energy and surface geometry of Kerr spacetime

Science.gov (United States)

Yu, Chengjie; Liu, Jian-Liang

2017-04-01

We study the quasilocal energy (QLE) and the surface geometry for Kerr spacetime in the Boyer-Lindquist coordinates without taking the slow rotation approximation. We also consider in the region r ≤2 m , which is inside the ergosphere. For a certain region, r >rk(a ) , the Gaussian curvature of the surface with constant t , r is positive, and for r >√{3 }a the critical value of the QLE is positive. We found that the three curves: the outer horizon r =r+(a ), r =rk(a ) and r =√{3 }a intersect at the point a =√{3 }m /2 , which is the limit for the horizon to be isometrically embedded into R3. The numerical result indicates that the Kerr QLE is monotonically decreasing to the ADM m from the region inside the ergosphere to large r . Based on the second law of black hole dynamics, the QLE is increasing with respect to the irreducible mass Mir. From the results of Chen-Wang-Yau, we conclude that in a certain region, r >rh(a ), the critical value of the Kerr QLE is a global minimum.

Surrogate Modeling for Geometry Optimization

DEFF Research Database (Denmark)

Rojas Larrazabal, Marielba de la Caridad; Abraham, Yonas; Holzwarth, Natalie

2009-01-01

A new approach for optimizing the nuclear geometry of an atomic system is described. Instead of the original expensive objective function (energy functional), a small number of simpler surrogates is used.......A new approach for optimizing the nuclear geometry of an atomic system is described. Instead of the original expensive objective function (energy functional), a small number of simpler surrogates is used....

Geometric control theory and sub-Riemannian geometry

CERN Document Server

Boscain, Ugo; Gauthier, Jean-Paul; Sarychev, Andrey; Sigalotti, Mario

2014-01-01

This volume presents recent advances in the interaction between Geometric Control Theory and sub-Riemannian geometry. On the one hand, Geometric Control Theory used the differential geometric and Lie algebraic language for studying controllability, motion planning, stabilizability and optimality for control systems. The geometric approach turned out to be fruitful in applications to robotics, vision modeling, mathematical physics etc. On the other hand, Riemannian geometry and its generalizations, such as  sub-Riemannian, Finslerian  geometry etc., have been actively adopting methods developed in the scope of geometric control. Application of these methods  has led to important results regarding geometry of sub-Riemannian spaces, regularity of sub-Riemannian distances, properties of the group  of diffeomorphisms of sub-Riemannian manifolds, local geometry and equivalence of distributions and sub-Riemannian structures, regularity of the Hausdorff volume.

Special metrics and group actions in geometry

CERN Document Server

Fino, Anna; Musso, Emilio; Podestà, Fabio; Vezzoni, Luigi

2017-01-01

The volume is a follow-up to the INdAM meeting “Special metrics and quaternionic geometry” held in Rome in November 2015. It offers a panoramic view of a selection of cutting-edge topics in differential geometry, including 4-manifolds, quaternionic and octonionic geometry, twistor spaces, harmonic maps, spinors, complex and conformal geometry, homogeneous spaces and nilmanifolds, special geometries in dimensions 5–8, gauge theory, symplectic and toric manifolds, exceptional holonomy and integrable systems. The workshop was held in honor of Simon Salamon, a leading international scholar at the forefront of academic research who has made significant contributions to all these subjects. The articles published here represent a compelling testimony to Salamon’s profound and longstanding impact on the mathematical community. Target readership includes graduate students and researchers working in Riemannian and complex geometry, Lie theory and mathematical physics.

Motor coordination uses external spatial coordinates independent of developmental vision.

Science.gov (United States)

Heed, Tobias; Röder, Brigitte

2014-07-01

The constraints that guide bimanual movement coordination are informative about the processing principles underlying movement planning in humans. For example, symmetry relative to the body midline benefits finger and hand movements independent of hand posture. This symmetry constraint has been interpreted to indicate that movement coordination is guided by a perceptual code. Although it has been assumed implicitly that the perceptual system at the heart of this constraint is vision, this relationship has not been tested. Here, congenitally blind and sighted participants made symmetrical and non-symmetrical (that is, parallel) bimanual tapping and finger oscillation movements. For both groups, symmetrical movements were executed more correctly than parallel movements, independent of anatomical constraints like finger homology and hand posture. For the blind, the reliance on external spatial factors in movement coordination stands in stark contrast to their use of an anatomical reference frame in perceptual processing. Thus, the externally coded symmetry constraint evident in bimanual coordination can develop in the absence of the visual system, suggesting that the visual system is not critical for the establishment of an external-spatial reference frame in movement coordination. Copyright © 2014 Elsevier B.V. All rights reserved.

Guide to Computational Geometry Processing

DEFF Research Database (Denmark)

Bærentzen, Jakob Andreas; Gravesen, Jens; Anton, François

be processed before it is useful. This Guide to Computational Geometry Processing reviews the algorithms for processing geometric data, with a practical focus on important techniques not covered by traditional courses on computer vision and computer graphics. This is balanced with an introduction...... to the theoretical and mathematical underpinnings of each technique, enabling the reader to not only implement a given method, but also to understand the ideas behind it, its limitations and its advantages. Topics and features: Presents an overview of the underlying mathematical theory, covering vector spaces......, metric space, affine spaces, differential geometry, and finite difference methods for derivatives and differential equations Reviews geometry representations, including polygonal meshes, splines, and subdivision surfaces Examines techniques for computing curvature from polygonal meshes Describes...

A Whirlwind Tour of Computational Geometry.

Science.gov (United States)

Graham, Ron; Yao, Frances

1990-01-01

Described is computational geometry which used concepts and results from classical geometry, topology, combinatorics, as well as standard algorithmic techniques such as sorting and searching, graph manipulations, and linear programing. Also included are special techniques and paradigms. (KR)

Monte Carlo simulation of fully Markovian stochastic geometries

International Nuclear Information System (INIS)

Lepage, Thibaut; Delaby, Lucie; Malvagi, Fausto; Mazzolo, Alain

2010-01-01

The interest in resolving the equation of transport in stochastic media has continued to increase these last years. For binary stochastic media it is often assumed that the geometry is Markovian, which is never the case in usual environments. In the present paper, based on rigorous mathematical theorems, we construct fully two-dimensional Markovian stochastic geometries and we study their main properties. In particular, we determine a percolation threshold p c , equal to 0.586 ± 0.0015 for such geometries. Finally, Monte Carlo simulations are performed through these geometries and the results compared to homogeneous geometries. (author)

Tidal stresses and energy gaps in microstate geometries

Science.gov (United States)

Tyukov, Alexander; Walker, Robert; Warner, Nicholas P.

2018-02-01

We compute energy gaps and study infalling massive geodesic probes in the new families of scaling, microstate geometries that have been constructed recently and for which the holographic duals are known. We find that in the deepest geometries, which have the lowest energy gaps, the geodesic deviation shows that the stress reaches the Planck scale long before the probe reaches the cap of the geometry. Such probes must therefore undergo a stringy transition as they fall into microstate geometry. We discuss the scales associated with this transition and comment on the implications for scrambling in microstate geometries.

VIII International Meeting on Lorentzian Geometry

CERN Document Server

Flores, José; Palomo, Francisco; GeLoMa 2016; Lorentzian geometry and related topics

2017-01-01

This volume contains a collection of research papers and useful surveys by experts in the field which provide a representative picture of the current status of this fascinating area. Based on contributions from the VIII International Meeting on Lorentzian Geometry, held at the University of Málaga, Spain, this volume covers topics such as distinguished (maximal, trapped, null, spacelike, constant mean curvature, umbilical...) submanifolds, causal completion of spacetimes, stationary regions and horizons in spacetimes, solitons in semi-Riemannian manifolds, relation between Lorentzian and Finslerian geometries and the oscillator spacetime. In the last decades Lorentzian geometry has experienced a significant impulse, which has transformed it from just a mathematical tool for general relativity to a consolidated branch of differential geometry, interesting in and of itself. Nowadays, this field provides a framework where many different mathematical techniques arise with applications to multiple parts of mathem...

Transformational plane geometry

CERN Document Server

Umble, Ronald N

2014-01-01

Axioms of Euclidean Plane Geometry The Existence and Incidence Postulates The Distance and Ruler Postulates The Plane Separation Postulate The Protractor Postulate The Side-Angle-Side Postulate and the Euclidean Parallel Postulate Theorems of Euclidean Plane Geometry The Exterior Angle Theorem Triangle Congruence Theorems The Alternate Interior Angles Theorem and the Angle Sum Theorem Similar Triangles Introduction to Transformations, Isometries, and Similarities Transformations Isometries and SimilaritiesAppendix: Proof of Surjectivity Translations, Rotations, and Reflections Translations Rotations Reflections Appendix: Geometer's Sketchpad Commands Required by Exploratory Activities Compositions of Translations, Rotations, and Reflections The Three Points Theorem Rotations as Compositions of Two Reflections Translations as Compositions of Two Halfturns or Two Reflections The Angle Addition Theorem Glide Reflections Classification of Isometries The Fundamental Theorem and Congruence Classification of Isometr...

Multilevel geometry optimization

Science.gov (United States)

Rodgers, Jocelyn M.; Fast, Patton L.; Truhlar, Donald G.

2000-02-01

Geometry optimization has been carried out for three test molecules using six multilevel electronic structure methods, in particular Gaussian-2, Gaussian-3, multicoefficient G2, multicoefficient G3, and two multicoefficient correlation methods based on correlation-consistent basis sets. In the Gaussian-2 and Gaussian-3 methods, various levels are added and subtracted with unit coefficients, whereas the multicoefficient Gaussian-x methods involve noninteger parameters as coefficients. The multilevel optimizations drop the average error in the geometry (averaged over the 18 cases) by a factor of about two when compared to the single most expensive component of a given multilevel calculation, and in all 18 cases the accuracy of the atomization energy for the three test molecules improves; with an average improvement of 16.7 kcal/mol.

Fractal geometry mathematical foundations and applications

CERN Document Server

Falconer, Kenneth

2013-01-01

The seminal text on fractal geometry for students and researchers: extensively revised and updated with new material, notes and references that reflect recent directions. Interest in fractal geometry continues to grow rapidly, both as a subject that is fascinating in its own right and as a concept that is central to many areas of mathematics, science and scientific research. Since its initial publication in 1990 Fractal Geometry: Mathematical Foundations and Applications has become a seminal text on the mathematics of fractals.  The book introduces and develops the general theory and applica

Investigating the Constrained Action Hypothesis: A Movement Coordination and Coordination Variability Approach.

Science.gov (United States)

Vidal, Anthony; Wu, Will; Nakajima, Mimi; Becker, James

2017-09-19

The purpose of this study was to examine the effects of focus of attention cues on movement coordination and coordination variability in the lower extremity. Twenty participants performed the standing long jump under both internal and external focus of attention conditions. A modified vector coding technique was used to evaluate the influence of attentional focus cues on lower extremity coordination patterns and coordination variability during the jumps. Participants jumped significantly further under an external focus of attention condition compared with an internal focus of attention condition (p = .035, effect size = .29). Focus of attention also influenced coordination between the ankle and knee, F(6, 19) = 2.87, p = .012, effect size = .388, with participants primarily using their knees under the internal focus of attention, and using both their ankles and knees under the external focus of attention. Attentional focus cues did not influence ankle-knee, F(1, 19) = 0.02, p = .98, effect size = .02, or hip-knee, F(1, 19) = 5.00, p = .49, effect size = .16, coordination variability. Results suggest that while attentional focus may not directly influence movement coordination condition, there is still a change in movement strategy resulting in greater jump distances following an external focus of attention.

A numerical method for the solution of three-dimensional incompressible viscous flow using the boundary-fitted curvilinear coordinate transformation and domain decomposition technique

International Nuclear Information System (INIS)

Umegaki, Kikuo; Miki, Kazuyoshi

1990-01-01

A numerical method is developed to solve three-dimensional incompressible viscous flow in complicated geometry using curvilinear coordinate transformation and domain decomposition technique. In this approach, a complicated flow domain is decomposed into several subdomains, each of which has an overlapping region with neighboring subdomains. Curvilinear coordinates are numerically generated in each subdomain using the boundary-fitted coordinate transformation technique. The modified SMAC scheme is developed to solve Navier-Stokes equations in which the convective terms are discretized by the QUICK method. A fully vectorized computer program is developed on the basis of the proposed method. The program is applied to flow analysis in a semicircular curved, 90deg elbow and T-shape branched pipes. Computational time with the vector processor of the HITAC S-810/20 supercomputer system, is reduced to 1/10∼1/20 of that with a scalar processor. (author)

Planning for Evolution in a Production Environment: Migration from a Legacy Geometry Code to an Abstract Geometry Modeling Language in STAR

Science.gov (United States)

Webb, Jason C.; Lauret, Jerome; Perevoztchikov, Victor

2012-12-01

Increasingly detailed descriptions of complex detector geometries are required for the simulation and analysis of today's high-energy and nuclear physics experiments. As new tools for the representation of geometry models become available during the course of an experiment, a fundamental challenge arises: how best to migrate from legacy geometry codes developed over many runs to the new technologies, such as the ROOT/TGeo [1] framework, without losing touch with years of development, tuning and validation. One approach, which has been discussed within the community for a number of years, is to represent the geometry model in a higher-level language independent of the concrete implementation of the geometry. The STAR experiment has used this approach to successfully migrate its legacy GEANT 3-era geometry to an Abstract geometry Modelling Language (AgML), which allows us to create both native GEANT 3 and ROOT/TGeo implementations. The language is supported by parsers and a C++ class library which enables the automated conversion of the original source code to AgML, supports export back to the original AgSTAR[5] representation, and creates the concrete ROOT/TGeo geometry implementation used by our track reconstruction software. In this paper we present our approach, design and experience and will demonstrate physical consistency between the original AgSTAR and new AgML geometry representations.

MIFT: GIFT Combinatorial Geometry Input to VCS Code

Science.gov (United States)

1977-03-01

r-w w-^ H ^ß0318is CQ BRL °RCUMr REPORT NO. 1967 —-S: ... MIFT: GIFT COMBINATORIAL GEOMETRY INPUT TO VCS CODE Albert E...TITLE (and Subtitle) MIFT: GIFT Combinatorial Geometry Input to VCS Code S. TYPE OF REPORT & PERIOD COVERED FINAL 6. PERFORMING ORG. REPORT NUMBER...Vehicle Code System (VCS) called MORSE was modified to accept the GIFT combinatorial geometry package. GIFT , as opposed to the geometry package

Physical meaning of the optical reference geometry

International Nuclear Information System (INIS)

Abramowicz, M.A.

1990-09-01

I show that contrary to a popular misconception the optical reference geometry, introduced a few years ago as a formally possible metric of a 3-space corresponding to a static spacetime, is quite satisfactory also from the physical point of view. The optical reference geometry has a clear physical meaning, as it may be constructed experimentally by measuring light round travel time between static observers. Distances and directions in the optical reference geometry are more strongly connected to experiment than distances and directions in the widely used directly projected metric (discussed e.g. in Landau and Lifshitz textbook. In addition, the optical reference geometry is more natural and convenient than the directly projected one in application to dynamics. In the optical geometry dynamical behaviour of matter is described by concepts and formulae identical to those well known in Newtonian dynamics on a given two dimensional (curved) surface. (author). 22 refs

Synthesis, Structural Characterization, and Antitumor Activity of a Ca(II Coordination Polymer Based on 1,6-Naphthalenedisulfonate and 4,4′-Bipyridyl

Directory of Open Access Journals (Sweden)

Xishi Tai

2013-08-01

Full Text Available A novel Ca(II coordination polymer, [CaL(4,4′-bipyridyl(H2O4]n (L = 1,6-naphthalenedisulfonate, was synthesized by reaction of calcium perchlorate with 1,6-naphthalenedisulfonic acid disodium salt and 4,4′-bipyridyl in CH3CH2OH/H2O. It was characterized by elemental analysis, IR, molar conductivity and thermogravimetric analysis. X-ray crystallography reveals that the Ca(II coordination polymer belongs to the orthorhombic system, with space group P212121. The geometry of the Ca(II ion is a distorted CaNO6 pengonal bipyramid, arising from its coordination by four water molecules, one nitrogen atom of 4,4′-bipyridyl molecule, and two oxygen atoms from two L ligands. The complex molecules form a helical chain by self-assembly. The antitumor activity of 1,6-naphthalenedisulfonic acid disodium salt and the Ca(II coordination polymer against human hepatoma smmc-7721 cell line and human lung adenocarcinoma A549 cell line reveals that the Ca(II coordination polymer inhibits cell growth of human lung adenocarcinoma A549 cell line with IC50 value of 27 μg/mL, and is more resistive to human lung adenocarcinoma A549 cell line as compared to 1,6-naphthalenedisulfonic acid disodium salt.

Transformasi Geometri Rotasi Berbantuan Software Geogebra

Directory of Open Access Journals (Sweden)

Muhamad Hanafi

2018-02-01

Full Text Available Penelitian  ini bertujuan untuk membantu visualisasi dan menemukan konsep pada Transformasi geometri Rotasi di titik Pusat  dengan menggunakan software GeoGebra. Penelitian ini mengulas tentang Koordinat Kartesius dan Polar, dan selanjutntya Transformasi geometri Rotasi di titik Pusat .

Algebra, Geometry and Mathematical Physics Conference

CERN Document Server

Paal, Eugen; Silvestrov, Sergei; Stolin, Alexander

2014-01-01

This book collects the proceedings of the Algebra, Geometry and Mathematical Physics Conference, held at the University of Haute Alsace, France, October 2011. Organized in the four areas of algebra, geometry, dynamical symmetries and conservation laws and mathematical physics and applications, the book covers deformation theory and quantization; Hom-algebras and n-ary algebraic structures; Hopf algebra, integrable systems and related math structures; jet theory and Weil bundles; Lie theory and applications; non-commutative and Lie algebra and more. The papers explore the interplay between research in contemporary mathematics and physics concerned with generalizations of the main structures of Lie theory aimed at quantization, and discrete and non-commutative extensions of differential calculus and geometry, non-associative structures, actions of groups and semi-groups, non-commutative dynamics, non-commutative geometry and applications in physics and beyond. The book benefits a broad audience of researchers a...

Homological mirror symmetry and tropical geometry

CERN Document Server

Catanese, Fabrizio; Kontsevich, Maxim; Pantev, Tony; Soibelman, Yan; Zharkov, Ilia

2014-01-01

The relationship between Tropical Geometry and Mirror Symmetry goes back to the work of Kontsevich and Y. Soibelman (2000), who applied methods of non-archimedean geometry (in particular, tropical curves) to Homological Mirror Symmetry. In combination with the subsequent work of Mikhalkin on the “tropical” approach to Gromov-Witten theory, and the work of Gross and Siebert, Tropical Geometry has now become a powerful tool. Homological Mirror Symmetry is the area of mathematics concentrated around several categorical equivalences connecting symplectic and holomorphic (or algebraic) geometry. The central ideas first appeared in the work of Maxim Kontsevich (1993). Roughly speaking, the subject can be approached in two ways: either one uses Lagrangian torus fibrations of Calabi-Yau manifolds (the so-called Strominger-Yau-Zaslow picture, further developed by Kontsevich and Soibelman) or one uses Lefschetz fibrations of symplectic manifolds (suggested by Kontsevich and further developed by Seidel). Tropical Ge...

Use of information technologies in teaching course "Analytical geometry" in higher schools on example of software "ANALYTICAL GEOMETRY"

OpenAIRE

V. B. Grigorieva

2009-01-01

In article are considered the methodical questions of using of computer technologies, for example, the software "Analytical geometry", in process of teaching course of analytical geometry in the higher school.

Variable geometry Darrieus wind machine

Science.gov (United States)

Pytlinski, J. T.; Serrano, D.

1983-08-01

A variable geometry Darrieus wind machine is proposed. The lower attachment of the blades to the rotor can move freely up and down the axle allowing the blades of change shape during rotation. Experimental data for a 17 m. diameter Darrieus rotor and a theoretical model for multiple streamtube performance prediction were used to develop a computer simulation program for studying parameters that affect the machine's performance. This new variable geometry concept is described and interrelated with multiple streamtube theory through aerodynamic parameters. The computer simulation study shows that governor behavior of a Darrieus turbine can not be attained by a standard turbine operating within normally occurring rotational velocity limits. A second generation variable geometry Darrieus wind turbine which uses a telescopic blade is proposed as a potential improvement on the studied concept.

Flux compactifications and generalized geometries

International Nuclear Information System (INIS)

Grana, Mariana

2006-01-01

Following the lectures given at CERN Winter School 2006, we present a pedagogical overview of flux compactifications and generalized geometries, concentrating on closed string fluxes in type II theories. We start by reviewing the supersymmetric flux configurations with maximally symmetric four-dimensional spaces. We then discuss the no-go theorems (and their evasion) for compactifications with fluxes. We analyse the resulting four-dimensional effective theories for Calabi-Yau and Calabi-Yau orientifold compactifications, concentrating on the flux-induced superpotentials. We discuss the generic mechanism of moduli stabilization and illustrate with two examples: the conifold in IIB and a T 6 /(Z 3 x Z 3 ) torus in IIA. We finish by studying the effective action and flux vacua for generalized geometries in the context of generalized complex geometry

Flux compactifications and generalized geometries

Energy Technology Data Exchange (ETDEWEB)

Grana, Mariana [Service de Physique Theorique, CEA/Saclay, 91191 Gif-sur-Yvette Cedex (France)

2006-11-07

Following the lectures given at CERN Winter School 2006, we present a pedagogical overview of flux compactifications and generalized geometries, concentrating on closed string fluxes in type II theories. We start by reviewing the supersymmetric flux configurations with maximally symmetric four-dimensional spaces. We then discuss the no-go theorems (and their evasion) for compactifications with fluxes. We analyse the resulting four-dimensional effective theories for Calabi-Yau and Calabi-Yau orientifold compactifications, concentrating on the flux-induced superpotentials. We discuss the generic mechanism of moduli stabilization and illustrate with two examples: the conifold in IIB and a T{sup 6} /(Z{sub 3} x Z{sub 3}) torus in IIA. We finish by studying the effective action and flux vacua for generalized geometries in the context of generalized complex geometry.

An arbitrary curvilinear-coordinate method for particle-in-cell modeling

International Nuclear Information System (INIS)

Fichtl, C A; Finn, J M; Cartwright, K L

2012-01-01

A new approach to kinetic simulation of plasmas in complex geometries, based on the particle-in-cell (PIC) simulation method, is explored. In the two-dimensional (2D) electrostatic version of our method, called the arbitrary curvilinear-coordinate PIC method, all essential PIC operations are carried out in 2D on a uniform grid on the unit square logical domain, and mapped to a nonuniform boundary-fitted grid on the physical domain. As the resulting logical grid equations of motion are not separable, we have developed an extension of the semi-implicit modified leapfrog integration technique to preserve the symplectic nature of the logical grid particle mover. A generalized, curvilinear-coordinate formulation of Poisson's equations to solve for the electrostatic fields on the uniform logical grid is also developed. By our formulation, we compute the plasma charge density on the logical grid based on the particles' positions on the logical domain. That is, the plasma particles are weighted to the uniform logical grid and the self-consistent mean electrostatic fields obtained from the solution of the logical grid Poisson equation are interpolated to the particle positions on the logical grid. This process eliminates the complexity associated with the weighting and interpolation processes on the nonuniform physical grid and allows us to run the PIC method on arbitrary boundary-fitted meshes. (paper)

Evaluation of vertical coordinate and vertical mixing algorithms in the HYbrid-Coordinate Ocean Model (HYCOM)

Science.gov (United States)

Halliwell, George R.

Vertical coordinate and vertical mixing algorithms included in the HYbrid Coordinate Ocean Model (HYCOM) are evaluated in low-resolution climatological simulations of the Atlantic Ocean. The hybrid vertical coordinates are isopycnic in the deep ocean interior, but smoothly transition to level (pressure) coordinates near the ocean surface, to sigma coordinates in shallow water regions, and back again to level coordinates in very shallow water. By comparing simulations to climatology, the best model performance is realized using hybrid coordinates in conjunction with one of the three available differential vertical mixing models: the nonlocal K-Profile Parameterization, the NASA GISS level 2 turbulence closure, and the Mellor-Yamada level 2.5 turbulence closure. Good performance is also achieved using the quasi-slab Price-Weller-Pinkel dynamical instability model. Differences among these simulations are too small relative to other errors and biases to identify the "best" vertical mixing model for low-resolution climate simulations. Model performance deteriorates slightly when the Kraus-Turner slab mixed layer model is used with hybrid coordinates. This deterioration is smallest when solar radiation penetrates beneath the mixed layer and when shear instability mixing is included. A simulation performed using isopycnic coordinates to emulate the Miami Isopycnic Coordinate Ocean Model (MICOM), which uses Kraus-Turner mixing without penetrating shortwave radiation and shear instability mixing, demonstrates that the advantages of switching from isopycnic to hybrid coordinates and including more sophisticated turbulence closures outweigh the negative numerical effects of maintaining hybrid vertical coordinates.

Four coordination polymers based on 5-tert-butyl isophthalic acid and rigid bis(imidazol-1yl)benzene linkers: Synthesis, luminescence detection of acetone and optical properties

Energy Technology Data Exchange (ETDEWEB)

Arıcı, Mürsel, E-mail: marici@ogu.edu.tr [Department of Chemistry, Faculty of Arts and Sciences, Eskişehir Osmangazi University, 26480 Eskişehir (Turkey); Zafer Yeşilel, Okan [Department of Chemistry, Faculty of Arts and Sciences, Eskişehir Osmangazi University, 26480 Eskişehir (Turkey); Büyükgüngör, Orhan [Department of Physics, Faculty of Arts and Sciences, Ondokuz Mayıs University, 55139 Samsun (Turkey)

2017-05-15

Four coordination polymers including, [Co(µ-Htbip){sub 2}(µ-dib)]{sub n} (1), [Co(µ-tbip)(µ-dmib){sub 0.5}]{sub n} (2), [Zn{sub 2}(µ-tbip)(µ{sub 3}-tbip)(µ-dmib){sub 1.5}]{sub n} (3) and [Cd(µ{sub 3}-tbip)(µ-dib){sub 0.5} (H{sub 2}O)]{sub n} (4) (tbip: 5-tert-butylisophthalate, dib: 1,4-bis(imidazol-1yl)benzene, dmib: 1,4-bis(imidazol-1yl)-2,5-dimethylbenzene), were hydrothermally synthesized and characterized by elemental analysis, IR spectra, single crystal and powder X-ray diffraction and thermal analysis (TG/DTA). The structural diversity is observed depending on ligands and coordination number of metal centers in the synthesized complexes. The tbip ligand displayed five different coordination modes in its complexes. In 1 and 2, complex 1 is 3D framework with the dia topology while complex 2 has 2D structure with the sql topology depending on coordination geometries of Co ions. Complex 3 is 3D framework with the fsh 4,6-conn topology and complex 4 has 2D 4-connected sql topology. Photoluminescent properties of complex 3 dispersed in various organic solvents were investigated and the results showed that 3 dispersed in methanol could be used as a fluorescent sensor for the detection of acetone. Moreover, thermal and optical properties of the complexes were also studied. - Graphical abstract: Four coordination polymers were hydrothermally synthesized and characterized by various techniques. The complexes showed the structural diversity depending on ligands and coordination number of metal centers. The tbip ligand displayed four different coordination modes in its complexes. In 1 and 2, complexes 1 and 2 are 3D and 2D structures with the dia and sql topologies depending on coordination geometries of Co ions, respectively. Complexes 3 and 4 are 3D and 2D structures with the fsh 4,6-conn and sql topology, respectively. Photoluminescent properties of complex 3 dispersed in various organic solvents were investigated and the results showed that 3 dispersed in

Curvature tensor copies in affine geometry

International Nuclear Information System (INIS)

Srivastava, P.P.

1981-01-01

The sets of space-time and spin-connections which give rise to the same curvature tensor are constructed. The corresponding geometries are compared. Results are illustrated by an explicit calculation and comment on the copies in Einstein-Cartan and Weyl-Cartan geometries. (Author) [pt

Poisson geometry from a Dirac perspective

Science.gov (United States)

Meinrenken, Eckhard

2018-03-01

We present proofs of classical results in Poisson geometry using techniques from Dirac geometry. This article is based on mini-courses at the Poisson summer school in Geneva, June 2016, and at the workshop Quantum Groups and Gravity at the University of Waterloo, April 2016.

Development of the geometry database for the CBM experiment

Science.gov (United States)

Akishina, E. P.; Alexandrov, E. I.; Alexandrov, I. N.; Filozova, I. A.; Friese, V.; Ivanov, V. V.

2018-01-01

The paper describes the current state of the Geometry Database (Geometry DB) for the CBM experiment. The main purpose of this database is to provide convenient tools for: (1) managing the geometry modules; (2) assembling various versions of the CBM setup as a combination of geometry modules and additional files. The CBM users of the Geometry DB may use both GUI (Graphical User Interface) and API (Application Programming Interface) tools for working with it.

SABRINA, Geometry Plot Program for MCNP

International Nuclear Information System (INIS)

SEIDL, Marcus

2003-01-01

1 - Description of program or function: SABRINA is an interactive, three-dimensional, geometry-modeling code system, primarily for use with CCC-200/MCNP. SABRINA's capabilities include creation, visualization, and verification of three-dimensional geometries specified by either surface- or body-base combinatorial geometry; display of particle tracks are calculated by MCNP; and volume fraction generation. 2 - Method of solution: Rendering is performed by ray tracing or an edge and intersection algorithm. Volume fraction calculations are made by ray tracing. 3 - Restrictions on the complexity of the problem: A graphics display with X Window capability is required

Differential geometry and topology of curves

CERN Document Server

Animov, Yu

2001-01-01

Differential geometry is an actively developing area of modern mathematics. This volume presents a classical approach to the general topics of the geometry of curves, including the theory of curves in n-dimensional Euclidean space. The author investigates problems for special classes of curves and gives the working method used to obtain the conditions for closed polygonal curves. The proof of the Bakel-Werner theorem in conditions of boundedness for curves with periodic curvature and torsion is also presented. This volume also highlights the contributions made by great geometers. past and present, to differential geometry and the topology of curves.

Geometry of surfaces a practical guide for mechanical engineers

CERN Document Server

Radzevich, Stephen P

2012-01-01

Presents an in-depth analysis of geometry of part surfaces and provides the tools for solving complex engineering problems Geometry of Surfaces: A Practical Guide for Mechanical Engineers is a comprehensive guide to applied geometry of surfaces with focus on practical applications in various areas of mechanical engineering. The book is divided into three parts on Part Surfaces, Geometry of Contact of Part Surfaces and Mapping of the Contacting Part Surfaces. Geometry of Surfaces: A Practical Guide for Mechanical Engineers combines differential geometry and gearing theory and presents new developments in the elementary theory of enveloping surfaces. Written by a leading expert of the field, this book also provides the reader with the tools for solving complex engineering problems in the field of mechanical engineering. Presents an in-depth analysis of geometry of part surfaces Provides tools for solving complex engineering problems in the field of mechanical engineering Combines differential geometry an...

Multilevel geometry optimization

Energy Technology Data Exchange (ETDEWEB)

Rodgers, Jocelyn M. [Department of Chemistry and Supercomputer Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431 (United States); Fast, Patton L. [Department of Chemistry and Supercomputer Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431 (United States); Truhlar, Donald G. [Department of Chemistry and Supercomputer Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431 (United States)

2000-02-15

Geometry optimization has been carried out for three test molecules using six multilevel electronic structure methods, in particular Gaussian-2, Gaussian-3, multicoefficient G2, multicoefficient G3, and two multicoefficient correlation methods based on correlation-consistent basis sets. In the Gaussian-2 and Gaussian-3 methods, various levels are added and subtracted with unit coefficients, whereas the multicoefficient Gaussian-x methods involve noninteger parameters as coefficients. The multilevel optimizations drop the average error in the geometry (averaged over the 18 cases) by a factor of about two when compared to the single most expensive component of a given multilevel calculation, and in all 18 cases the accuracy of the atomization energy for the three test molecules improves; with an average improvement of 16.7 kcal/mol. (c) 2000 American Institute of Physics.

Machine learning spatial geometry from entanglement features

Science.gov (United States)

You, Yi-Zhuang; Yang, Zhao; Qi, Xiao-Liang

2018-02-01

Motivated by the close relations of the renormalization group with both the holography duality and the deep learning, we propose that the holographic geometry can emerge from deep learning the entanglement feature of a quantum many-body state. We develop a concrete algorithm, call the entanglement feature learning (EFL), based on the random tensor network (RTN) model for the tensor network holography. We show that each RTN can be mapped to a Boltzmann machine, trained by the entanglement entropies over all subregions of a given quantum many-body state. The goal is to construct the optimal RTN that best reproduce the entanglement feature. The RTN geometry can then be interpreted as the emergent holographic geometry. We demonstrate the EFL algorithm on a 1D free fermion system and observe the emergence of the hyperbolic geometry (AdS3 spatial geometry) as we tune the fermion system towards the gapless critical point (CFT2 point).

GEOMETRY – AN IMPORTANT MEANS OF EDUCATION IN THE CIVILISATION SCOPE

OpenAIRE

Liliana TOCARIU, PhD

2017-01-01

Geometry (from the Greek: γεωμετρία; geo = earth, metria = measure) is a genuine science, rooted in mathematics, which studies the plane and spatial forms of bodies from the objective or conceptual reality and the nature of the relationship that exists between them. Due to its complexity, geometry is divided into: Euclidian geometry, analytical geometry, descriptive geometry, projective geometry, kinematic geometry, surface and curve differential geometry, axiomatic geometry,...

Analytical geometry of three dimensions

CERN Document Server

McCrea, William Hunter

1947-01-01

Brief but rigorous, this text is geared toward advanced undergraduates and graduate students. It covers the coordinate system, planes and lines, spheres, homogeneous coordinates, general equations of the second degree, quadric in Cartesian coordinates, and intersection of quadrics.Mathematician, physicist, and astronomer, William H. McCrea conducted research in many areas and is best known for his work on relativity and cosmology. McCrea studied and taught at universities around the world, and this book is based on a series of his lectures.

Random geometry and Yang-Mills theory

International Nuclear Information System (INIS)

Froehlich, J.

1981-01-01

The author states various problems and discusses a very few preliminary rigorous results in a branch of mathematics and mathematical physics which one might call random (or stochastic) geometry. Furthermore, he points out why random geometry is important in the quantization of Yang-Mills theory. (Auth.)

Quantification of variability in bedform geometry

NARCIS (Netherlands)

van der Mark, C.F.; Blom, Astrid; Hulscher, Suzanne J.M.H.

2008-01-01

We analyze the variability in bedform geometry in laboratory and field studies. Even under controlled steady flow conditions in laboratory flumes, bedforms are irregular in size, shape, and spacing, also in case of well-sorted sediment. Our purpose is to quantify the variability in bedform geometry.

Explicitly computing geodetic coordinates from Cartesian coordinates

Science.gov (United States)

Zeng, Huaien

2013-04-01

This paper presents a new form of quartic equation based on Lagrange's extremum law and a Groebner basis under the constraint that the geodetic height is the shortest distance between a given point and the reference ellipsoid. A very explicit and concise formulae of the quartic equation by Ferrari's line is found, which avoids the need of a good starting guess for iterative methods. A new explicit algorithm is then proposed to compute geodetic coordinates from Cartesian coordinates. The convergence region of the algorithm is investigated and the corresponding correct solution is given. Lastly, the algorithm is validated with numerical experiments.

10th China-Japan Geometry Conference

CERN Document Server

Miyaoka, Reiko; Tang, Zizhou; Zhang, Weiping

2016-01-01

Since the year 2000, we have witnessed several outstanding results in geometry that have solved long-standing problems such as the Poincaré conjecture, the Yau–Tian–Donaldson conjecture, and the Willmore conjecture. There are still many important and challenging unsolved problems including, among others, the Strominger–Yau–Zaslow conjecture on mirror symmetry, the relative Yau–Tian–Donaldson conjecture in Kähler geometry, the Hopf conjecture, and the Yau conjecture on the first eigenvalue of an embedded minimal hypersurface of the sphere. For the younger generation to approach such problems and obtain the required techniques, it is of the utmost importance to provide them with up-to-date information from leading specialists. The geometry conference for the friendship of China and Japan has achieved this purpose during the past 10 years. Their talks deal with problems at the highest level, often accompanied with solutions and ideas, which extend across various fields in Riemannian geometry, sympl...

The application of optical coherence tomography angiography in retinal diseases.

Science.gov (United States)

Sambhav, Kumar; Grover, Sandeep; Chalam, Kakarla V

Optical coherence tomography angiography (OCTA) is a new, noninvasive imaging technique that generates real-time volumetric data on chorioretinal vasculature and its flow pattern. With the advent of high-speed optical coherence tomography, established enface chorioretinal segmentation, and efficient algorithms, OCTA generates images that resemble an angiogram. The principle of OCTA involves determining the change in backscattering between consecutive B-scans and then attributing the differences to the flow of erythrocytes through retinal blood vessels. OCTA has shown promise in the evaluation of common ophthalmologic diseases such as diabetic retinopathy, age-related macular degeneration, and retinal vascular occlusions. It quantifies vascular compromise reflecting the severity of diabetic retinopathy. OCTA detects the presence of choroidal neovascularization in exudative age-related macular degeneration and maps loss of choriocapillaris in nonexudative age-related macular degeneration. We describe principles of OCTA and findings in common and some uncommon retinal pathologies. Finally, we summarize its potential future applications. Its current limitations include a relatively small field of view, inability to show leakage, and a tendency for image artifacts. Further larger studies will define OCTAs utility in clinical settings and establish if the technology may offer its utility in decreasing morbidity through early detection and guide therapeutic interventions in retinal diseases. Copyright © 2017 Elsevier Inc. All rights reserved.

Coordination failure caused by sunspots

DEFF Research Database (Denmark)

Beugnot, Julie; Gürgüç, Zeynep; Øvlisen, Frederik Roose

2012-01-01

on the efficient equilibrium, we consider sunspots as a potential reason for coordination failure. We conduct an experiment with a three player 2x2x2 game in which coordination on the efficient equilibrium is easy and should normally occur. In the control session, we find almost perfect coordination on the payoff......-dominant equilibrium, but in the sunspot treatment, dis-coordination is frequent. Sunspots lead to significant inefficiency, and we conclude that sunspots can indeed cause coordination failure....

DOGBONE GEOMETRY FOR RECIRCULATING ACCELERATORS

International Nuclear Information System (INIS)

BERG, J.S.; JOHNSTONE, C.; SUMMERS, D.

2001-01-01

Most scenarios for accelerating muons require recirculating acceleration. A racetrack shape for the accelerator requires particles with lower energy in early passes to traverse almost the same length of arc as particles with the highest energy. This extra arc length may lead to excess decays and excess cost. Changing the geometry to a dogbone shape, where there is a single linac and the beam turns completely around at the end of the linac, returning to the same end of the linac from which it exited, addresses this problem. In this design, the arc lengths can be proportional to the particle's momentum. This paper proposes an approximate cost model for a recirculating accelerator, attempts to make cost-optimized designs for both racetrack and dogbone geometries, and demonstrates that the dogbone geometry does appear to be more cost effective

A one-dimensional ladder-like coordination polymer: poly[[hexa-aqua-bis(μ-5-nitro-benzene-1,3-dicarboxyl-ato-κO,O',O'')(μ-oxalato-κO,O':O'',O''')diyttrium(III)] trihydrate].

Science.gov (United States)

Fu, Zhong; Lin, Ying; Zhou, Yun-You; Zhang, Hong-Tao

2007-12-06

In the crystal structure of the title one-dimensional coordination polymer, [Y(2)(C(8)H(3)NO(6))(2)(C(2)O(4))(H(2)O)(6)]·3H(2)O, each Y(III) ion is bridged to its neighbours by two 5-nitro-benzene-1,3-dicarboxyl-ate (nbdc) dianions and one oxalate dianion (located on an inversion centre) to form a ladder-like polymeric structure. The two carboxylate groups of nbdc assume different modes of coordination, one is chelating whereas the other is monodentate. Three water mol-ecules coordinate to the Y(III) ion to complete an eight-coordinate distorted dodecahedral geometry. The ladder-like polymers are assembled together by hydrogen bonding and π-π stacking [centrio-centriod distance = 3.819 (9) Å] in the crystal structure.

Increasing insightful thinking in analytic geometry

NARCIS (Netherlands)

Timmer, Mark; Verhoef, Neeltje Cornelia

Elsewhere in this issue Ferdinand Verhulst described the discussion of the interaction of analysis and geometry in the 19th century. In modern times such discussions come up again and again. As of 2014, synthetic geometry will not be part of the Dutch 'vwo - mathematics B' programme anymore.

Development and application of CATIA-GDML geometry builder

International Nuclear Information System (INIS)

Belogurov, S; Chernogorov, A; Ovcharenko, E; Schetinin, V; Berchun, Yu; Malzacher, P

2014-01-01

Due to conceptual difference between geometry descriptions in Computer-Aided Design (CAD) systems and particle transport Monte Carlo (MC) codes direct conversion of detector geometry in either direction is not feasible. The paper presents an update on functionality and application practice of the CATIA-GDML geometry builder first introduced at CHEP2010. This set of CATIAv5 tools has been developed for building a MC optimized GEANT4/ROOT compatible geometry based on the existing CAD model. The model can be exported via Geometry Description Markup Language (GDML). The builder allows also import and visualization of GEANT4/ROOT geometries in CATIA. The structure of a GDML file, including replicated volumes, volume assemblies and variables, is mapped into a part specification tree. A dedicated file template, a wide range of primitives, tools for measurement and implicit calculation of parameters, different types of multiple volume instantiation, mirroring, positioning and quality check have been implemented. Several use cases are discussed.

Numerical analysis of residual stresses in preforms of stress applying part for PANDA-type polarization maintaining optical fibers in view of technological imperfections of the doped zone geometry

Science.gov (United States)

Trufanov, Aleksandr N.; Trufanov, Nikolay A.; Semenov, Nikita V.

2016-09-01

The experimental data analysis of the stress applying rod section geometry for the PANDA-type polarization maintaining optical fiber has been performed. The dependencies of the change in the radial dimensions of the preform and the doping boundary on the angular coordinate have been obtained. The original algorithm of experimental data statistic analysis, which enables determination of the specimens' characteristic form of section, has been described. The influence of actual doped zone geometry on the residual stress fields formed during the stress rod preform fabrication has been investigated. It has been established that the deviation of the boundary between pure silica and the doped zone from the circular shape results in dissymmetry and local concentrations of the residual stress fields along the section, which can cause preforms destruction at high degrees of doping. The observed geometry deviations of up to 10% lead to the increase of the maximum stress intensity value by over 20%.

Self-propagating high temperature synthesis, structural morphology and magnetic interactions in rare earth Ho{sup 3+} doped CoFe{sub 2}O{sub 4} nanoparticles

Energy Technology Data Exchange (ETDEWEB)

Lohar, K.S. [Materials Research Laboratory, Srikrishna Mahavidyalaya Gunjoti, Omerga, Osmanabad 413 613, MS (India); Pachpinde, A.M.; Langade, M.M. [Department of Chemistry, Jawahar Art Science and Commerce College Andur, Osmanabad, MS (India); Kadam, R.H. [Materials Research Laboratory, Srikrishna Mahavidyalaya Gunjoti, Omerga, Osmanabad 413 613, MS (India); Shirsath, Sagar E., E-mail: shirsathsagar@hotmail.com [Spin Device Technology Center, Department of Information Engineering, Shinshu University, Nagano 380-8553 (Japan)

2014-08-01

Highlights: • Rare earth Ho{sup 3+} substituted CoFe{sub 2}O{sub 4.} • XRD and IR spectra reveal the spinel structure. • Magnetization and coercivity increased with Ho{sup 3+} substitution. - Abstract: Substitution effect of rare earth trivalent Ho{sup 3+} ions on the composition, Ho{sub x}CoFe{sub 2−x}O{sub 4}, with x varying from 0.0 to 0.1 in steps of 0.025 using sol–gel auto combustion route has been investigated. Examination of X-ray diffraction (XRD) patterns shows that all the samples consisted of ferrite phases of typical spinel cubic structure, and when Ho{sup 3+} ion content was x ⩾ 0.075, orthoferrite–HoFeO{sub 3} phase was detected. The micro and nanostructure of the synthesized Ho doped CoFe{sub 2}O{sub 4} ferrites were investigated by scanning and transmission electron microscopy respectively. With increasing doping content of Ho{sup 3+} ions, the lattice constant, particle size and bulk density increased, and after an increase to its maximum value, the sample particle size and density dropped down. Cation distribution estimated from XRD patter revealed that the Co{sup 2+} and Ho{sup 3+} ions prefer to occupy octahedral B-site whereas Fe{sup 3+} ions are distributed over tetra- and octa-hedral site. Oxygen positional parameter shows larger values than its ideal value. The analysis of magnetic properties revealed that the saturation magnetization and coercivity of CoFe{sub 2}O{sub 4} increased with the rare earth Ho{sup 3+} substitution.

Remarks on Hamiltonian structures in G2-geometry

International Nuclear Information System (INIS)

Cho, Hyunjoo; Salur, Sema; Todd, A. J.

2013-01-01

In this article, we treat G 2 -geometry as a special case of multisymplectic geometry and make a number of remarks regarding Hamiltonian multivector fields and Hamiltonian differential forms on manifolds with an integrable G 2 -structure; in particular, we discuss existence and make a number of identifications of the spaces of Hamiltonian structures associated to the two multisymplectic structures associated to an integrable G 2 -structure. Along the way, we prove some results in multisymplectic geometry that are generalizations of results from symplectic geometry

Coordination Behavior of Ni2+, Cu2+, and Zn2+ in Tetrahedral 1-Methylimidazole Complexes: A DFT/CSD Study

OpenAIRE

Tetteh, Samuel

2018-01-01

The interaction between nickel (Ni2+), copper (Cu2+), and zinc (Zn2+) ions and 1-methylimidazole has been studied by exploring the geometries of eleven crystal structures in the Cambridge Structural Database (CSD). The coordination behavior of the respective ions was further investigated by means of density functional theory (DFT) methods. The gas-phase complexes were fully optimized using B3LYP/GENECP functionals with 6-31G∗ and LANL2DZ basis sets. The Ni2+ and Cu2+ complexes show distorted ...

Classical geometry Euclidean, transformational, inversive, and projective

CERN Document Server

Leonard, I E; Liu, A C F; Tokarsky, G W

2014-01-01

Features the classical themes of geometry with plentiful applications in mathematics, education, engineering, and science Accessible and reader-friendly, Classical Geometry: Euclidean, Transformational, Inversive, and Projective introduces readers to a valuable discipline that is crucial to understanding bothspatial relationships and logical reasoning. Focusing on the development of geometric intuitionwhile avoiding the axiomatic method, a problem solving approach is encouraged throughout. The book is strategically divided into three sections: Part One focuses on Euclidean geometry, which p

MOCUM: A two-dimensional method of characteristics code based on constructive solid geometry and unstructured meshing for general geometries

International Nuclear Information System (INIS)

Yang Xue; Satvat, Nader

2012-01-01

Highlight: ► A two-dimensional numerical code based on the method of characteristics is developed. ► The complex arbitrary geometries are represented by constructive solid geometry and decomposed by unstructured meshing. ► Excellent agreement between Monte Carlo and the developed code is observed. ► High efficiency is achieved by parallel computing. - Abstract: A transport theory code MOCUM based on the method of characteristics as the flux solver with an advanced general geometry processor has been developed for two-dimensional rectangular and hexagonal lattice and full core neutronics modeling. In the code, the core structure is represented by the constructive solid geometry that uses regularized Boolean operations to build complex geometries from simple polygons. Arbitrary-precision arithmetic is also used in the process of building geometry objects to eliminate the round-off error from the commonly used double precision numbers. Then, the constructed core frame will be decomposed and refined into a Conforming Delaunay Triangulation to ensure the quality of the meshes. The code is fully parallelized using OpenMP and is verified and validated by various benchmarks representing rectangular, hexagonal, plate type and CANDU reactor geometries. Compared with Monte Carlo and deterministic reference solution, MOCUM results are highly accurate. The mentioned characteristics of the MOCUM make it a perfect tool for high fidelity full core calculation for current and GenIV reactor core designs. The detailed representation of reactor physics parameters can enhance the safety margins with acceptable confidence levels, which lead to more economically optimized designs.

Structural influence in the interaction of cysteine with five coordinated copper complexes: Theoretical and experimental studies

Science.gov (United States)

Huerta-Aguilar, Carlos Alberto; Thangarasu, Pandiyan; Mora, Jesús Gracia

2018-04-01

Copper complexes of N,N,N‧,N‧-tetrakis(pyridyl-2-ylmethyl)-1,2-diaminoethane (L1) and N,N,N‧,N‧-tetrakis(pyridyl-2-ylmethyl)-1,3-diaminopropane (L2) prepared were characterized completely by different analytical methods. The X-structure of the complexes shows that Cu(II) presents in trigonal bi-pyramidal (TBP) geometry, consisting with the electronic spectra where two visible bands corresponding to five coordinated structure were observed. Thus TD-DFT was used to analyze the orbital contribution to the electronic transitions for the visible bands. Furthermore, the interaction of cysteine with the complexes was spectrally studied, and the results were explained through DFT analysis, observing that the geometrical parameters and oxidation state of metal ions play a vital role in the binding of cysteine with copper ion. It appears that the TBP structure is being changed into octahedral geometry during the addition of cysteine to the complexes as two bands (from complex) is turned to a broad band in visible region, signifying the occupation of cysteine molecule at sixth position of octahedral geometry. In the molecular orbital analysis, the existence of a strong overlapping of HOMOs (from cysteine) with LUMOs of Cu ion was observed. The total energy of the systems calculated by DFT shows that cysteine binds favorably with copper (I) than that with Cu(II).

Electrodynamics and Spacetime Geometry: Foundations

Science.gov (United States)

Cabral, Francisco; Lobo, Francisco S. N.

2017-02-01

We explore the intimate connection between spacetime geometry and electrodynamics. This link is already implicit in the constitutive relations between the field strengths and excitations, which are an essential part of the axiomatic structure of electromagnetism, clearly formulated via integration theory and differential forms. We review the foundations of classical electromagnetism based on charge and magnetic flux conservation, the Lorentz force and the constitutive relations. These relations introduce the conformal part of the metric and allow the study of electrodynamics for specific spacetime geometries. At the foundational level, we discuss the possibility of generalizing the vacuum constitutive relations, by relaxing the fixed conditions of homogeneity and isotropy, and by assuming that the symmetry properties of the electro-vacuum follow the spacetime isometries. The implications of this extension are briefly discussed in the context of the intimate connection between electromagnetism and the geometry (and causal structure) of spacetime.

Dayside merging and cusp geometry

International Nuclear Information System (INIS)

Crooker, N.U.

1979-01-01

Geometrical considerations are presented to show that dayside magnetic merging when constrained to act only where the fields are antiparallel results in lines of merging that converge at the polar cusps. An important consequence of this geometry is that no accelerated flows are predicted across the dayside magnetopause. Acceleration owing to merging acts in opposition to the magnetosheath flow at the merging point and produces the variably directed, slower-than-magnetosheath flows observed in the entry layer. Another consequence of the merging geometry is that much of the time closed field lines constitute the subsolar region of the magnetopause. The manner in which the polar cap convection patterns predicted by the proposed geometry change as the interplanetary field is rotated through 360 0 provides a unifying description of how the observed single circular vortex and the crescent-shaped double vortex patterns mutually evolve under the influence of a single operating principle

Digital and discrete geometry theory and algorithms

CERN Document Server

Chen, Li

2014-01-01

This book provides comprehensive coverage of the modern methods for geometric problems in the computing sciences. It also covers concurrent topics in data sciences including geometric processing, manifold learning, Google search, cloud data, and R-tree for wireless networks and BigData.The author investigates digital geometry and its related constructive methods in discrete geometry, offering detailed methods and algorithms. The book is divided into five sections: basic geometry; digital curves, surfaces and manifolds; discretely represented objects; geometric computation and processing; and a

Attitudes of High School Students towards Geometry

Directory of Open Access Journals (Sweden)

Esat Avcı

2014-12-01

Full Text Available In this research, attitudes of high school students towards geometry were investigated in terms of gender, grade, types of the field and school. Population of research includes students who were studying at high school in five distincs of Mersin in 2013-2014 academical year. Sample of research includes 935 students from twelve high schools. Attitude scale which was developed by Su-Özenir (2008 was used for data collection. For data analysis, mean, standart deviation, t test and ANOVA were used. A meaningful difference between students’ attitudes towards geometry and variance of gender and grade level wasn’t observed, on the other hand a meaningful difference according to field and school type is observed.Key Words:    Attitudes towards geometry, high school geometry lesson, attitude scale

Commutative and Non-commutative Parallelogram Geometry: an Experimental Approach

OpenAIRE

Bertram, Wolfgang

2013-01-01

By "parallelogram geometry" we mean the elementary, "commutative", geometry corresponding to vector addition, and by "trapezoid geometry" a certain "non-commutative deformation" of the former. This text presents an elementary approach via exercises using dynamical software (such as geogebra), hopefully accessible to a wide mathematical audience, from undergraduate students and high school teachers to researchers, proceeding in three steps: (1) experimental geometry, (2) algebra (linear algebr...

Volatile constituents of Trichothecium roseum.

Science.gov (United States)

Vanhaelen, M; Vanhaelen-Fastre, R; Geeraerts, J

1978-06-01

In the course of investigation of Trichothecium roseum (Fungi Imperfecti) for its attractancy against Tyrophagus putrescentiae (cheese mite), the twenty following volatile compounds produced at a very low concentration by the microfungus were identified by gc, gc/ms, gc/c.i.ms and tlc: 3-methyl-1-butanol, 3-octanone, 1-octen-3-one, 3-octanol, octa-1,5-dien-3 one, 1-octen-3-ol, 6-methyl-5-hepten-2-ol, octa-1,5-dien-3 ol, furfural, linalool, linalyl acetate, terpineol (alpha and beta) citronellyl acetate, nerol, citronellol, phenylacetaldehyde, benzyl alcohol geranyl acetate, 1-phenyl ethanol and nerolidol. Octa-1,5-dien-3-ol and octa-1,5-dien-3-one have not been previously isolated from fungi; octa-1,5-dien-3-ol is the most potent attractant amount the volatile compounds detected by gc.

A Study of Geometry Content Knowledge of Elementary Preservice Teachers

Directory of Open Access Journals (Sweden)

Fatma ASLAN-TUTAK

2015-06-01

Full Text Available The purpose of this research is to examine preservice elementary school teachers’ geometry learning as investigated by both qualitative and quantitative methods. For the qualitative investigation, narrative analysis and thematic analysis methods were used. The findings of narrative analysis indicated two main kinds of stories: as a learner and as a beginning teacher. The thematic analysis findings yield to three themes: history of learning geometry, perceptions about geometry, effective geometry instructional practices. The findings informed the quantitative investigation on geometry content knowledge for the case of quadrilaterals. During the second phase of the study, 102 participants who enrolled in the methods course completed pre and post test of teachers’ geometry content knowledge. Treatment group participants (n=54 received series of activities (geometry activities and student work analysis focusing on quadrilaterals, and control group participants (n=48 received traditional instruction. Repeated measures ANOVA results showed a significant change in treatment group participants’ geometry content knowledge. The mixed ANOVA results indicated a significant main effect of knowledge but no significant interaction between geometry content knowledge and grouping. Even though treatment group participants’ geometry content knowledge growth was significant, the difference between treatment group and control group participants’ growth in geometry content knowledge was not significant. This study informs mathematics teacher education in three important areas; limited knowledge of preservice teachers’ geometry content knowledge, integrating mathematics content and the context of teaching into methods course, and use of student work with preservice teachers.

A study of geometry content knowledge of elementary preservice teachers

Directory of Open Access Journals (Sweden)

Fatma Aslan Tutak

2015-06-01

Full Text Available The purpose of this research is to examine preservice elementary school teachers’ geometry learning as investigated by both qualitative and quantitative methods. For the qualitative investigation, narrative analysis and thematic analysis methods were used. The findings of narrative analysis indicated two main kinds of stories: as a learner and as a beginning teacher. The thematic analysis findings yield to three themes: history of learning geometry, perceptions about geometry, effective geometry instructional practices. The findings informed the quantitative investigation on geometry content knowledge for the case of quadrilaterals. During the second phase of the study, 102 participants who enrolled in the methods course completed pre and post test of teachers’ geometry content knowledge. Treatment group participants (n=54 received series of activities (geometry activities and student work analysis focusing on quadrilaterals, and control group participants (n=48 received traditional instruction. Repeated measures ANOVA results showed a significant change in treatment group participants’ geometry content knowledge. The mixed ANOVA results indicated a significant main effect of knowledge but no significant interaction between geometry content knowledge and grouping. Even though treatment group participants’ geometry content knowledge growth was significant, the difference between treatment group and control group participants’ growth in geometry content knowledge was not significant. This study informs mathematics teacher education in three important areas; limited knowledge of preservice teachers’ geometry content knowledge, integrating mathematics content and the context of teaching into methods course, and use of student work with preservice teachers.

Combinatorial geometry in the plane

CERN Document Server

Hadwiger, Hugo; Klee, Victor

2014-01-01

Geared toward advanced undergraduates familiar with analysis and college geometry, this concise book discusses theorems on topics restricted to the plane such as convexity, coverings, and graphs. In addition to helping students cultivate rigorous thought, the text encourages the development of mathematical intuition and clarifies the nature of mathematical research.The two-part treatment begins with specific topics including integral distances, covering problems, point set geometry and convexity, simple paradoxes involving point sets, and pure combinatorics, among other subjects. The second pa

Topology and geometry for physicists

CERN Document Server

Nash, Charles

1983-01-01

Differential geometry and topology are essential tools for many theoretical physicists, particularly in the study of condensed matter physics, gravity, and particle physics. Written by physicists for physics students, this text introduces geometrical and topological methods in theoretical physics and applied mathematics. It assumes no detailed background in topology or geometry, and it emphasizes physical motivations, enabling students to apply the techniques to their physics formulas and research. ""Thoroughly recommended"" by The Physics Bulletin, this volume's physics applications range fr

Three-dimensional tracking of cardiac catheters using an inverse geometry x-ray fluoroscopy system

International Nuclear Information System (INIS)

Speidel, Michael A.; Tomkowiak, Michael T.; Raval, Amish N.; Van Lysel, Michael S.

2010-01-01

Purpose: Scanning beam digital x-ray (SBDX) is an inverse geometry fluoroscopic system with high dose efficiency and the ability to perform continuous real-time tomosynthesis at multiple planes. This study describes a tomosynthesis-based method for 3D tracking of high-contrast objects and present the first experimental investigation of cardiac catheter tracking using a prototype SBDX system. Methods: The 3D tracking algorithm utilizes the stack of regularly spaced tomosynthetic planes that are generated by SBDX after each frame period (15 frames/s). Gradient-filtered versions of the image planes are generated, the filtered images are segmented into object regions, and then a 3D coordinate is calculated for each object region. Two phantom studies of tracking performance were conducted. In the first study, an ablation catheter in a chest phantom was imaged as it was pulled along a 3D trajectory defined by a catheter sheath (10, 25, and 50 mm/s pullback speeds). SBDX tip tracking coordinates were compared to the 3D trajectory of the sheath as determined from a CT scan of the phantom after the registration of the SBDX and CT coordinate systems. In the second study, frame-to-frame tracking precision was measured for six different catheter configurations as a function of image noise level (662-7625 photons/mm 2 mean detected x-ray fluence at isocenter). Results: During catheter pullbacks, the 3D distance between the tracked catheter tip and the sheath centerline was 1.0±0.8 mm (mean ±one standard deviation). The electrode to centerline distances were comparable to the diameter of the catheter tip (2.3 mm), the confining sheath (4 mm outside diameter), and the estimated SBDX-to-CT registration error (±0.7 mm). The tip position was localized for all 332 image frames analyzed and 83% of tracked positions were inside the 3D sheath volume derived from CT. The pullback speeds derived from the catheter trajectories were within 5% of the programed pullback speeds. The

Fundamental concepts of geometry

CERN Document Server

Meserve, Bruce E

1983-01-01

Demonstrates relationships between different types of geometry. Provides excellent overview of the foundations and historical evolution of geometrical concepts. Exercises (no solutions). Includes 98 illustrations.

PREFACE: Nonlinearity and Geometry: connections with integrability Nonlinearity and Geometry: connections with integrability

Science.gov (United States)

Cieslinski, Jan L.; Ferapontov, Eugene V.; Kitaev, Alexander V.; Nimmo, Jonathan J. C.

2009-10-01

role in soliton theory unifying continuous, discrete and quantum integrable systems. Triply orthogonal coordinates proved to be of prime importance for the modern theory of Hamiltonian systems of hydrodynamic type and differential-geometric Poisson brackets, culminating in the construction of the rich and beautiful theory of Frobenius manifolds. The idea for this special issue developed out of the Second Workshop on Nonlinearity and Geometry, a successful conference held in the Mathematical Research and Conference Center at Będlewo, Poland, 13-19 April 2008 (http://wmii.uwm.edu.pl/˜doliwa/WNG-DD.html). However, there was an open call for papers for this issue and all contributions were peer reviewed according to the standards of the journal and taking into account their relevance to the subject of the planned issue. Among the 30 listed authors, 16 attended the conference and the remaining 14 submitted their papers in answer to this open call. The First School on Nolinearity and Geometry (`Bianchi Days') was organized by Antoni Sym and his students in 1995 at the Physics Faculty of Warsaw University, Poland. The proceedings of the workshop, edited by Daniel Wójcik and Jan Cieśliński, were published by Polish Scientific Publishers PWN (Warsaw, 1998). The Second Workshop (`Darboux Days') was organized in 2008 by Adam Doliwa and his coworkers, under the Honorary Chair of Antoni Sym, as a Banach Center Conference. Both workshops gathered around 50 participants. The purpose of these meetings was to bring together researchers with diverse backgrounds (e.g., mathematical physics and differential geometry), and to review the state of the art at the border between the two subjects: geometric inspirations in soliton theory and applications of soliton techniques in geometry. The format was designed to allow substantial time for interaction and research. The invited lectures were longer, intended to present the current trends and open problems in the fields, and to be

Kinetic Control of Intralayer Cobalt Coordination in Layered Hydroxides: CoxoctCoxtet(OH)2(Cl)x(H2O)n

International Nuclear Information System (INIS)

Neilson, James R.; Schwenzer, Birgit; Seshadri, Ram; Morse, Daniel E.

2009-01-01

We report the synthesis and characterization of new structural variants of the isotypic compound with the generic chemical formula, Co 1-0.5x oct Co x tet (OH) 2 (Cl) x (H 2 O) n , all modifications of an α-Co(OH) 2 lattice. We show that the occupancy of tetrahedrally coordinated cobalt sites and associated chloride ligands, x, is modulated by the rate of formation of the respective layered hydroxide salts from kinetically controlled aqueous hydrolysis at an air-water interface. This new level of structural control is uniquely enabled by the slow diffusion of a hydrolytic catalyst, a simple technique. Independent structural characterizations of the compounds separately describe various attributes of the materials on different length scales, revealing details hidden by the disordered average structures. The precise control over the population of distinct octahedrally and tetrahedrally coordinated cobalt ions in the lattice provides a gentle, generic method for modulating the coordination geometry of cobalt in the material without disturbing the lattice or using additional reagents. A mechanism is proposed to reconcile the observation of the kinetic control of the structure with competing interactions during the initial stages of hydrolysis and condensation.

Non-commutative geometry inspired charged black holes

International Nuclear Information System (INIS)

Ansoldi, Stefano; Nicolini, Piero; Smailagic, Anais; Spallucci, Euro

2007-01-01

We find a new, non-commutative geometry inspired, solution of the coupled Einstein-Maxwell field equations describing a variety of charged, self-gravitating objects, including extremal and non-extremal black holes. The metric smoothly interpolates between de Sitter geometry, at short distance, and Reissner-Nordstrom geometry far away from the origin. Contrary to the ordinary Reissner-Nordstrom spacetime there is no curvature singularity in the origin neither 'naked' nor shielded by horizons. We investigate both Hawking process and pair creation in this new scenario

ZONE, Finite Elements Method Quadrilateral and Triangular Mesh Generator for 2-D Axisymmetric Geometry

International Nuclear Information System (INIS)

Burger, M. J.

1981-01-01

1 - Description of problem or function: The ZONE program is a finite element mesh generator which produces the nodes and element description of any two-dimensional geometry. The geometry is divided into a mesh of quadrilateral and triangular zones defined by node points taken in a counter-clockwise sequence. The zones are arranged sequentially in an ordered march through the geometry. The order can be chosen so that the minimum bandwidth is obtained. The mesh that is generated can be used as input to any two-dimensional as well as any axisymmetrical structure program. 2 - Method of solution: The basic concept used is the definition of a two-dimensional structure by the intersection of two sets of lines which describe the geometric and material boundaries. A set of lines called meridians define the geometric and material boundaries and generally run in the same direction. Another set of linear line segments called rays which intersect the meridians are also defined at the material and geometric boundaries. The section of the structure between successive rays is called a region. The ray segment between any two consecutive ray-meridian intersections or void area in the structure is called a layer and is described as passing through, or bounding a material. The boundaries can be directly defined as a sequence of straight line segments or can be computed in terms of elliptic segments or circular arcs. A meridian or ray can also be made to follow a previously-defined meridian or ray at a fixed distance by invoking an offset option. 3 - Restrictions on the complexity of the problem: The following are limited only by a DIMENSION statement. The code currently has a maxima of: 100 coordinate points defining a meridian or ray, 40 meridians, 40 layers. There are no limits on the number of zones or nodes for any problems

Kinetic treatment of magnetosonic wave reflection by minority gyroresonant ballistic waves in tokamak geometry

International Nuclear Information System (INIS)

Kaufman, A.N.; Brizard, A.J.; Cook, D.R.

1993-01-01

The analysis of the minority-ion gyroresonant heating process by a magnetosonic wave in a general magnetic field geometry with one ignorable spatial coordinate can be divided into several steps, each defined in terms of a precise mathematical problem to be solved. In this work, the authors focus their attention on the magnetosonic wave reflection problem in axisymmetric tokamak geometry; the conversion and absorption of the minority-ion gyroresonant ballistic waves are treated elsewhere. In contrast to their previous work, they employ a kinetic model based on the perturbation generating function S for the gyroresonant minority-ions. The bulk plasma response is represented by the perturbation magnetic vector potential A, corresponding to a shielded magnetosonic wave. The set of coupled equations for S and A can be derived from an action principle, which can also be used to derive explicit wave-action conservation laws in ray phase space. The reflection problem is solved in ray phase space by considering three separate steps. In the first step, the incident magnetosonic ray propagates towards the first linear mode conversion region, where action is transferred to the minority-ion gyroresonant ballistic waves. In the second step, the continuum of excited gyroresonant ballistic rays propagate towards the second linear mode conversion region. In the third step, the reflected magnetosonic wave field is excited by linear mode conversion from the minority gyroresonant ballistic rays

Preparation and characterization of a new hybrid material formed by reaction of cobalt (II) nitroprusside and octa(aminopropyl)silsesquioxane

International Nuclear Information System (INIS)

Magossi, Mariana de Souza; Carmo, Devaney Ribeiro do

2016-01-01

Full text: The term silsesquioxane etymologically refers to the nanostructured compounds that has structures that feature the empirical formula (RSiO 1,5 ) n , where R is a hydrogen atom or an organic group. Each silicon atom is connected on an average of 1.5 oxygen atoms and a group R (hydrocarbon, or an organic group) [1]. In this work, a new hybrid material (ACCoN) based on octa(aminopropyl)silsesquioxane (AC) and cobalt (II) nitroprusside have been prepared following a new synthesis route. Within this context, the objective of this work was to prepare and characterize this new material for electro analytical purposes. The ACCoN was characterized by several techniques such as: spectroscopy in the region of infrared (FTIR), Energy-Dispersive X-ray spectroscopy (EDS), Scanning Electron microscopy (SEM) and X-Ray Diffraction (XRD). The FTIR spectra showed absorption bands in 1106 cm -1 refer to the stretching vibration ν s (Si-O-Si) characteristics of the structure of silsesquioxane. An important vibration can be observed which is related to the stretching vibrations of the type νN-O which occurs near 1945 cm -1 , characteristic of the sodium nitroprusside, where in the ACCoN the νN-O is shifted for more high frequency (about 117 cm -1 ) relative to sodium nitroprusside. Additionally a drastic reduction of stretching vibrations intensity νC≡N was observed in the ACCoN. This fact is an indicative of the formation of the intervalence complex, where the CN- and metal centers are bound. Through SEM and EDS spectroscopies was observed clusters of cubic particles with an average size of 325 nm. The ACCoN presents the elements Si, O, N, Co and Fe in its structure. Therefore through the aforementioned spectroscopic analysis, we conclude that the preparation of ACCoN was successfully conducted. [1] Cordes, D. B.; Lickiss, P. D.; Rataboul, F. Chemical Reviews, vol. 110, p. 2081-2173 (2010). (author)

Preparation and characterization of a new hybrid material formed by reaction of cobalt (II) nitroprusside and octa(aminopropyl)silsesquioxane

Energy Technology Data Exchange (ETDEWEB)

Magossi, Mariana de Souza; Carmo, Devaney Ribeiro do, E-mail: marymagossi@gmail.com [Universidade Estadual Paulista Julio de Mesquita Filho (UNESP), Ilha Solteira, SP (Brazil). Faculdade de Engenharia

2016-07-01

Full text: The term silsesquioxane etymologically refers to the nanostructured compounds that has structures that feature the empirical formula (RSiO{sub 1,5}){sub n}, where R is a hydrogen atom or an organic group. Each silicon atom is connected on an average of 1.5 oxygen atoms and a group R (hydrocarbon, or an organic group) [1]. In this work, a new hybrid material (ACCoN) based on octa(aminopropyl)silsesquioxane (AC) and cobalt (II) nitroprusside have been prepared following a new synthesis route. Within this context, the objective of this work was to prepare and characterize this new material for electro analytical purposes. The ACCoN was characterized by several techniques such as: spectroscopy in the region of infrared (FTIR), Energy-Dispersive X-ray spectroscopy (EDS), Scanning Electron microscopy (SEM) and X-Ray Diffraction (XRD). The FTIR spectra showed absorption bands in 1106 cm{sup -1} refer to the stretching vibration ν{sub s}(Si-O-Si) characteristics of the structure of silsesquioxane. An important vibration can be observed which is related to the stretching vibrations of the type νN-O which occurs near 1945 cm{sup -1}, characteristic of the sodium nitroprusside, where in the ACCoN the νN-O is shifted for more high frequency (about 117 cm{sup -1}) relative to sodium nitroprusside. Additionally a drastic reduction of stretching vibrations intensity νC≡N was observed in the ACCoN. This fact is an indicative of the formation of the intervalence complex, where the CN- and metal centers are bound. Through SEM and EDS spectroscopies was observed clusters of cubic particles with an average size of 325 nm. The ACCoN presents the elements Si, O, N, Co and Fe in its structure. Therefore through the aforementioned spectroscopic analysis, we conclude that the preparation of ACCoN was successfully conducted. [1] Cordes, D. B.; Lickiss, P. D.; Rataboul, F. Chemical Reviews, vol. 110, p. 2081-2173 (2010). (author)

A one-dimensional ladder-like coordination polymer: poly[[hexaaquabis(μ-5-nitrobenzene-1,3-dicarboxylato-κ3O,O′,O′′(μ-oxalato-κ4O,O′:O′′,O′′′diyttrium(III] trihydrate

Directory of Open Access Journals (Sweden)

Zhong Fu

2008-01-01

Full Text Available In the crystal structure of the title one-dimensional coordination polymer, [Y2(C8H3NO62(C2O4(H2O6]·3H2O, each YIII ion is bridged to its neighbours by two 5-nitrobenzene-1,3-dicarboxylate (nbdc dianions and one oxalate dianion (located on an inversion centre to form a ladder-like polymeric structure. The two carboxylate groups of nbdc assume different modes of coordination, one is chelating whereas the other is monodentate. Three water molecules coordinate to the YIII ion to complete an eight-coordinate distorted dodecahedral geometry. The ladder-like polymers are assembled together by hydrogen bonding and π–π stacking [centrio–centriod distance = 3.819 (9 Å] in the crystal structure.

Euclidean geometry and its subgeometries

CERN Document Server

Specht, Edward John; Calkins, Keith G; Rhoads, Donald H

2015-01-01

In this monograph, the authors present a modern development of Euclidean geometry from independent axioms, using up-to-date language and providing detailed proofs. The axioms for incidence, betweenness, and plane separation are close to those of Hilbert. This is the only axiomatic treatment of Euclidean geometry that uses axioms not involving metric notions and that explores congruence and isometries by means of reflection mappings. The authors present thirteen axioms in sequence, proving as many theorems as possible at each stage and, in the process, building up subgeometries, most notably the Pasch and neutral geometries. Standard topics such as the congruence theorems for triangles, embedding the real numbers in a line, and coordinatization of the plane are included, as well as theorems of Pythagoras, Desargues, Pappas, Menelaus, and Ceva. The final chapter covers consistency and independence of axioms, as well as independence of definition properties. There are over 300 exercises; solutions to many of the...

Number theory III Diophantine geometry

CERN Document Server

1991-01-01

From the reviews of the first printing of this book, published as Volume 60 of the Encyclopaedia of Mathematical Sciences: "Between number theory and geometry there have been several stimulating influences, and this book records of these enterprises. This author, who has been at the centre of such research for many years, is one of the best guides a reader can hope for. The book is full of beautiful results, open questions, stimulating conjectures and suggestions where to look for future developments. This volume bears witness of the broad scope of knowledge of the author, and the influence of several people who have commented on the manuscript before publication ... Although in the series of number theory, this volume is on diophantine geometry, and the reader will notice that algebraic geometry is present in every chapter. ... The style of the book is clear. Ideas are well explained, and the author helps the reader to pass by several technicalities. Reading and rereading this book I noticed that the topics ...