Li, Yang; Lehmann, Teresa
2012-06-01
The solution structure of Fe(II)-peplomycin was determined from NMR data collected for this molecule. As found previously for Fe(II)- and Co(II)-bound bleomycin; the coordination sphere of the metal is composed of the primary and secondary amines in β-aminoalanine, the pyrimidine and imidazole rings in the pyrimidinylpropionamide, and β-hydroxyhistidine moieties, respectively, the amine nitrogen in β-hydroxyhistidine, and either the carbamoyl group in mannose or a solvent molecule. The two most discussed coordination geometries for the aforementioned ligands in metallo-bleomycins have been tested against the NMR data generated for Fe(II)-peplomycin. The interpretation of the experimental evidence obtained through molecular dynamics indicates that both geometries are equally likely in solution for this compound in the absence of DNA, but arguments are offered to explain why one of these geometries is preferred in the presence of DNA. Published by Elsevier Inc.
Directory of Open Access Journals (Sweden)
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.
Schwarzschild-de Sitter spacetimes, McVittie coordinates, and trumpet geometries
Dennison, Kenneth A.; Baumgarte, Thomas W.
2017-12-01
Trumpet geometries play an important role in numerical simulations of black hole spacetimes, which are usually performed under the assumption of asymptotic flatness. Our Universe is not asymptotically flat, however, which has motivated numerical studies of black holes in asymptotically de Sitter spacetimes. We derive analytical expressions for trumpet geometries in Schwarzschild-de Sitter spacetimes by first generalizing the static maximal trumpet slicing of the Schwarzschild spacetime to static constant mean curvature trumpet slicings of Schwarzschild-de Sitter spacetimes. We then switch to a comoving isotropic radial coordinate which results in a coordinate system analogous to McVittie coordinates. At large distances from the black hole the resulting metric asymptotes to a Friedmann-Lemaître-Robertson-Walker metric with an exponentially-expanding scale factor. While McVittie coordinates have another asymptotically de Sitter end as the radial coordinate goes to zero, so that they generalize the notion of a "wormhole" geometry, our new coordinates approach a horizon-penetrating trumpet geometry in the same limit. Our analytical expressions clarify the role of time-dependence, boundary conditions and coordinate conditions for trumpet slices in a cosmological context, and provide a useful test for black hole simulations in asymptotically de Sitter spacetimes.
Analyzing Group Coordination when Solving Geometry Problems with Dynamic Geometry Software
Oner, Diler
2013-01-01
In CSCL research, collaborative activity is conceptualized along various yet intertwined dimensions. When functioning within these multiple dimensions, participants make use of several resources, which can be social or content-related (and sometimes temporal) in nature. It is the effective coordination of these resources that appears to…
Energy Technology Data Exchange (ETDEWEB)
Singh, Nirupama; Niklas, Jens; Poluektov, Oleg; Van Heuvelen, Katherine M.; Mukherjee, Anusree
2017-01-01
The synthesis, characterization and density functional theory calculations of mononuclear Ni and Cu complexes supported by the N,N’-Dimethyl-N,N’-bis-(pyridine-2-ylmethyl)-1,2-diaminoethane ligand and its derivatives are reported. The complexes were characterized by X-ray crystallography as well as by UV-visible absorption spectroscopy and EPR spectroscopy. The solid state structure of these coordination complexes revealed that the geometry of the complex depended on the identity of the metal center. Solution phase characterization data are in accord with the solid phase structure, indicating minimal structural changes in solution. Optical spectroscopy revealed that all of the complexes exhibit color owing to d-d transition bands in the visible region. Magnetic parameters obtained from EPR spectroscopy with other structural data suggest that the Ni(II) complexes are in pseudo-octahedral geometry and Cu(II) complexes are in a distorted square pyramidal geometry. In order to understand in detail how ligand sterics and electronics affect complex topology detailed computational studies were performed. The series of complexes reported in this article will add significant value in the field of coordination chemistry as Ni(II) and Cu(II) complexes supported by tetradentate pyridyl based ligands are rather scarce.
Combariza, Marianny Y; Fermann, Justin T; Vachet, Richard W
2004-04-19
Five-coordinate metal complex ions of the type [ML](2+) [where M = Mn(II), Fe(II), Co(II), Ni(II), Cu(II), Zn(II) and L= 1,9-bis(2-pyridyl)-2,5,8-triazanonane (DIEN-(pyr)(2)) and 1,9-bis(2-imidazolyl)-2,5,8-triazanonane (DIEN-(imi)(2)] have been reacted with acetonitrile in the gas phase using a modified quadrupole ion trap mass spectrometer. The kinetics and thermodynamics of these reactions show that the reactivity of these complexes is affected by metal electronic structure and falls into three groups: Mn(II) and Ni(II) complexes are the most reactive, Fe(II) and Co(II) complexes exhibit intermediate reactivity, and Cu(II) and Zn(II) complexes are the least reactive. To help explain the experimental trends in reactivity, theoretical calculations have been used. Due to the relatively large size of the metal complexes involved, we have utilized a two-layered ONIOM method to perform geometry optimizations and single point energy calculations for the [ML](2+) and [ML + CH(3)CN](2+) systems. The calculations show that the reactant five-coordinate complexes ([ML](2+)) exhibit structures that are slightly distorted trigonal bipyramidal geometries, while the six-coordinate complexes ([ML + CH(3)CN](2+)) have geometries that are close to octahedral. The Delta G values obtained from the ONIOM calculations roughly agree with the experimental data, but the calculations fail to completely explain the trends for the different metal complexes. The failure to consider all possible isomers as well as adequately represent pi-d interactions for the metal complexes is the likely cause of this discrepancy. Using the angular overlap model (AOM) to obtain molecular orbital stabilization energies (MOSE) also fails to reproduce the experimental trends when only sigma interactions are considered but succeeds in explaining the trends when pi interactions are taken into account. These results indicate that the pi-donor character of the CH(3)CN plays a subtle, yet important, role in
Lalegani, Arash; Khalaj, Mehdi; Sedaghat, Sajjad; Łyczko, Krzysztof; Lipkowski, Janusz
2017-11-01
Two new coordination polymers, {[Co(bib)3](PF6)2}n (1) and [Cd (bib) Cl2]n (2), were prepared at room temperature by the reaction of appropriate salts of cobalt (II) and cadmium (II) with the flexible linker ligands 1,4-bis(imidazolyl) butane (bib). The compounds were characterized by elemental analyses, IR spectroscopy and single crystal X-ray diffraction. In the polymeric structure of 1, the Co(II) ion lies on an inversion centre and adopts the CoN6 octahedral geometry, while in the structure of 2, the Cd(II) ions adopt the CdN2Cl4 pseudo-octahedral geometry. In compound 1, six bib ligands are coordinated to one central cobalt (II) to form an open 3D 2-fold interpenetrating framework of the α-polonium (pcu) type topology, while in compound 2 two bib ligands are coordinated to one central cadmium (II) to form 2D network structure.
Energy Technology Data Exchange (ETDEWEB)
Chai, J.C.; Patankar, S.V. (Univ. of Minnesota, Minneapolis, MN (United States). Dept. of Mechanical Engineering); Lee, H.S. (NASA, Cleveland, OH (United States). Lewis Research Center)
1994-09-01
This article presents a blocked-off-region procedure to model radiative transfer in irregular geometries using a Cartesian coordinates finite-column method (FVM). Straight-edged, inclined and curved boundaries can be treated. It is capable of handling participating or transparent media enclosed by black or reflecting walls. With this procedure, irregular geometries can be specified through the problem specification portion of the program. Four test problems are used to show that the procedure is capable of reproducing available results for inclined and curved walls, transparent, nonscattering, and anisotropically scattering media.
XAFS study of copper(II) complexes with square planar and square pyramidal coordination geometries
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.
Simulation of Heat Transfer in Husk Furnace with Cone Geometry Based on Conical Coordinate System
Noor, Iman; Ahmad, Faozan; Irzaman; alatas, Husin
2017-07-01
Simulation of Heat Transfer in Husk Furnace with Cone Geometry Based on Conical Coordinates has been performed. This simulation aimed to study the heat distribution of temperature based on conduction and convection mechanism on conical coordinate system. Fluid dynamics inside the cone of husk furnace was obtained by solving the Navier - Stokes equations with laminar flow approach. The initial temperature in all parts of the cone is room temperature, except at the bottom of the cone is 700 °C. Through numerical calculation of heat conduction and convection equation by FDM method, we got that the velocity of fluid flow at the center cone is 13.69 m/s for 45 s, 11.90 m/s for 60 s, and 7.25 m/s for 120 s, with unfixed temperature condition in the cone.
Surprising Coordination Geometry Differences in Ce(IV)- and Pu(IV)-Maltol Complexes
Energy Technology Data Exchange (ETDEWEB)
Lawrence Berkeley National Laboratory; Raymond, Kenneth; Szigethy, Geza; Xu, Jide; Gorden, Anne E.V.; Teat, Simon J.; Shuh, David K.; Raymond, Kenneth N.
2008-02-12
As part of a study to characterize the detailed coordination behavior of Pu(IV), single crystal X-ray diffraction structures have been determined for Pu(IV) and Ce(IV) complexes with the naturally-occurring ligand maltol (3-hydroxy-2-methyl-pyran-4-one) and its derivative bromomaltol (5-bromo-3-hydroxy-2-methyl-pyran-4-one). Although Ce(IV) is generally accepted as a structural analog for Pu(IV), and the maltol complexes of these two metals are isostructural, the corresponding bromomaltol complexes are strikingly different with respect to ligand orientation about the metal ion: All complexes exhibit trigonal dodecahedral coordination geometry but the Ce(IV)-bromomaltol complex displays an uncommon ligand arrangement not mirrored in the Pu(IV) complex, although the two metal species are generally accepted to be structural analogs.
Berends, Hans-Martin; Manke, Anne-Marie; Näther, Christian; Tuczek, Felix; Kurz, Philipp
2012-05-28
In this work the synthesis of the novel manganese complex [Mn(2)(III,III)(tpdm)(2)(μ-O)(μ-OAc)(2)](2+) (1) is reported, containing two manganese centres ligated to the unusual, facially coordinating, all-pyridine ligand tpdm (tris(2-pyridyl)methane). The geometric and electronic properties of complex 1 were characterised by X-ray crystallography, vibrational (IR and Raman) and optical spectroscopy (UV/Vis and MCD). Cyclic voltammograms of 1 showed a quasi-reversible oxidation event at 950 mV and an irreversible reduction wave at -250 mV vs. Ag/Ag(+). The redox behaviour of the compound was investigated in detail by UV/Vis- and X-band EPR-spectroelectrochemistry. Both electrochemical (+1200 mV) and chemical (tBuOOH) oxidations transform 1 into the singly oxidized di-μ-oxido species [Mn(2)(III,IV)(tpdm)(2)(μ-O)(2)(μ-OAc)](2+). Further electrochemical oxidation at the same potential results in the removal of a second electron to obtain a Mn(2)(IV,IV)-species. The ability of compound 1 to evolve O(2) was studied using different reaction agents. While reactions with both hydrogen peroxide and peroxomonosulfate yield O(2), homogeneous water-oxidation using Ce(IV) was not observed. Nevertheless, the oxidation reactions of 1 are very interesting model processes for oxidation state (S-state) transitions of the natural manganese water-oxidation catalyst in photosynthesis. However, despite its favourable coordination geometry and multielectron redox chemistry, complex 1 fails to be a catalytically active model for natural water-oxidation.
Coordinate measurement in 2-D and 3-D geometries using frequency scanning interferometry
Gibson, S M; Howell, David Francis; Mitra, A; Nickerson, R B
2005-01-01
Frequency Scanning Interferometry (FSI) has been developed for robust precise distance measurements. We present the reconstruction of two and three dimensional geodetic grids, using simultaneous FSI measurements between grid nodes. The shape of the particle physics tracker inside the ATLAS experiment (currently under construction for the Large Hadron Collider at CERN) will be monitored using a geodetic grid of 842 remotely measured, fibre-coupled interferometers. The challenge is to make precise distance measurements in the hostile, high radiation environment and combine them to reconstruct node coordinates and hence the grid shape in quasi real time to a three dimensional precision of around 10mum. Two and three dimensional prototype grids with adjustable geometries have been measured, demonstrating shape reconstruction to a precision of around 1mum. Error propagation through these grids was studied with different reconstruction models. Grid redundancy allowed the agreement between software models and node c...
Smith, Jordan Neale; Hook, James M; Lucas, Nigel T
2017-12-18
Tertiary phosphines remain widely utilized in synthesis, most notably as supporting ligands in metal complexes. A series of triarylphosphines bearing one to three hexa-peri-hexabenzocoronene (HBC) substituents has been prepared by an efficient divergent route. These "superphenylphosphines", P{HBC(t-Bu)5}nPh3-n (n = 1-3), form the palladium complexes Pd2Cl2L2 and Pd2Cl4L2 where the isomer distribution in solution is dependent on the number of HBC substituents. The crystalline structures of five complexes all show intramolecular π-stacking between HBC-phosphines to form a supramolecular bidentate-like ligand that distorts the metal coordination geometry. When n = 2 or 3, the additional HBC substituents engage in intermolecular π-stacking to assemble the complexes into continuous ribbons or sheets. The phosphines adopt HBC's characteristics including strong optical absorption, green emission, and redox activity.
The flux-coordinate independent approach applied to X-point geometries
Hariri, F.; Hill, P.; Ottaviani, M.; Sarazin, Y.
2014-08-01
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.
The flux-coordinate independent approach applied to X-point geometries
Energy Technology Data Exchange (ETDEWEB)
Hariri, F., E-mail: Farah.Hariri@epfl.ch; Hill, P.; Ottaviani, M.; Sarazin, Y. [CEA, IRFM, F-13108 Saint-Paul-lez-Durance (France)
2014-08-15
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.
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
Indian Academy of Sciences (India)
of geometry he completely changed our way of thinking. Later geometers were to spend entire lifetimes trying ... dimensions up to and including three it is difficult to think of dimensions beyond except abstractly -in one's .... form I. gij ai aj is positive for any collection of numbers. (aI, ... , an). Moreover, the given form can easily ...
Tsai, Bor-sheng
1994-01-01
Describes the use of infometry, or informational geometry, to meet the challenges of information service businesses. Highlights include theoretical models for cognitive coordination and genetic programming; electronic information packaging; marketing electronic information products, including cost-benefit analyses; and recapitalization, including…
DEFF Research Database (Denmark)
Byg din egen boomerang, kast den, se den flyve, forstå hvorfor og hvordan den vender tilbage, og grib den. Det handler om opdriften på vingerne når du flyver, men det handler også og allermest om den mærkværdige gyroskop-effekt, du bruger til at holde balancen, når du kører på cykel. Vi vil bruge...... matematik, geometri, og fysik til at forstå, hvad det er, der foregår....
Peng, Yan; Mereacre, Valeriu; Anson, Christopher E; Zhang, Yiquan; Bodenstein, Tilmann; Fink, Karin; Powell, Annie K
2017-06-05
Three air-stable Co(II) mononuclear complexes with different aromatic substituents have been prepared and structurally characterized by single-crystal X-ray diffraction. The mononuclear complexes [Co(H2L1)2]·2THF (1), [Co(HL2)2] (2), and [Co(H2L3)2]·CH2Cl2 (3) (where H3L1, H2L2, and H3L3 represent 3-hydroxy-naphthalene-2-carboxylic acid (6-hydroxymethyl-pyridin-2-ylmethylene) hydrazide, nicotinic acid (6-hydroxymethyl-pyridin-2-ylmethylene) hydrazide, and 2-hydroxy-benzoic acid (6-hydroxymethyl-pyridin-2-ylmethylene) hydrazide, respectively) feature a distorted mer octahedral coordination geometry. Detailed magnetic studies of 1-3 have been conducted using direct and alternating current magnetic susceptibility data. Field-induced slow magnetic relaxation was observed for these three complexes. There are few examples of such behavior in (distorted) octahedral coordination geometry (OC) Co(II) mononuclear complexes with uniaxial anisotropy. Analysis of the six-coordinate Co(II) mononuclear single-ion magnets (SIMs) in the literature using the SHAPE program revealed that they all show what is best described as distorted trigonal prismatic (TRP) coordination geometry, and in general, these show negative D zero-field splitting (ZFS) values. On the other hand, all the Co(II) mononuclear complexes displaying what is best approximated as distorted octahedral (OC) coordination geometry show positive D values. In the new Co(II) mononuclear complexes we describe here, there is an ambiguity, since the rigid tridentate ligands confer what is best described for an octahedral complex as a mer coordination geometry, but the actual shape of the first coordination sphere is between octahedral and trigonal prismatic. The negative D values observed experimentally and supported by high-level electronic structure calculations are thus in line with a trigonal prismatic geometry. However, a consideration of the rhombicity as indicated by the E value of the ZFS in conjunction with the
Directory of Open Access Journals (Sweden)
Michael A. O'Donnell
2010-12-01
Full Text Available The reaction of 2-acetylpyridine with silver(I tetrafluoridoborate leads to the discrete title complex, [Ag(C7H7NO2]BF4, in the cation of which the Ag atom is coordinated by two 2-acetylpyridine ligands, each of which is N,O-bidentate, albeit with stronger bonding to the N atoms [Ag—N = 2.2018 (15 and 2.2088 (14 Å; Ag—O = 2.5380 (13 and 2.5454 (13 Å]. The four-coordinate Ag atom has a seesaw coordination geometry with a τ4 index of 0.51. The tetrafluoridoborate anion is disordered over two orientations with 0.568 (10:0.432 (10 occupancies.
Directory of Open Access Journals (Sweden)
Danuta Owczarek
2015-08-01
Full Text Available The paper presents a method for estimating the uncertainty of optical coordinate measurement based on the use of information about the geometry and the size of measured object as well as information about the measurement system, i.e. maximum permissible error (MPE of the machine, selection of a sensor, and also the required measurement accuracy, the number of operators, measurement strategy and external conditions contained in the developed uncertainty database. Estimation of uncertainty is done with the use of uncertainties of measurements of basic geometry elements determined by methods available in the Laboratory of Coordinate Metrology at Cracow University of Technology (LCM CUT (multi-position, comparative and developed in the LCM CUT method dedicated for non-contact measurements and then with the use of them to determine the uncertainty of a given measured object. Research presented in this paper are aimed at developing a complete database containing all information needed to estimate the measurement uncertainty of various objects, even of a very complex geometry based on previously performed measurements.
Tensors and Differential Geometry Applied to Analytic and Numerical Coordinate Generation
1981-01-01
and Tarapov [20], Stoker [21], Spivak [22], do Carmo [23], FlUgge [24], Howard [25], and Eiseman [26]. Part III of this monograph is the culmination...Mass. 02154 (1970). [23] do Carmo , M. P., Differential Geometry of Curves and Surfaces, Prentice-Hall, Inc. (1976). [24] Fligge, W., Tensor Analysis
Unusual coordination and metal-ligand geometry of a vanadyl porphyrin in aqueous solution
Energy Technology Data Exchange (ETDEWEB)
Shelnutt, J.A.; Dobry, M.M.
1983-08-04
Vanadyl uroporphyrin I in aqueous alkaline solution has considerably modified absorption and resonance Raman spectra when compared with vanadyl porphyrins in organic solvents or in the crystalline state. Under these latter conditions vanadyl porphyrins are known to contain 5-coordinate, out-of-plane vanadium(IV). The unusual spectra of vanadyl uroporphyrin in water can be converted to spectra typical of the 5-coordinate vanadyl prophyrins by formation of ..pi..-..pi.. complexes or by ..pi..-..pi.. dimerization. Because ..pi..-..pi.. complex formation and dimerization block addition of an axial sixth ligand a 6-coordinate, in-plane dihydroxide vanadium(IV) uroporphyrin complex is indicated. This hypothesis is consistent with an analysis of the frequencies of the core-size marker lines of metalloporphyrins indicating expansion of the metal core by 0.03 to 0.04 A in V(OH)/sub 2/UroP. 5 figures.
DEFF Research Database (Denmark)
Savio, Enrico; De Chiffre, Leonardo
2002-01-01
The paper describes some advances regarding establishment of traceability of freeform measurements on coordinate measuring machines using the “Uncalibrated Object” approach, which is currently being considered for development as a new ISO standard. The method deals with calibration of artefacts by...
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.
Directory of Open Access Journals (Sweden)
M.M. Akbar
2017-06-01
Full Text Available 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.
Suresh, Paladugu; Babu, Chatla Naga; Sampath, Natarajan; Prabusankar, Ganesan
2015-04-28
Despite the popularity and versatility of transition-metal–azolium carboxylate coordination polymers, there are very few examples of group 2 complexes supported by azolium carboxylate ligands in the literature, and there are none featuring luminescent calcium azolium carboxylates. New ionic calcium coordination networks, {[Ca2(L(1))2(H2O)4](Br)4·6H2O}∞ (1), {[(L(3))2Ca(H2O)2]2(Br)2}∞ (3), {[(L(4))2Ca(H2O)2]2(Br)2}∞ (4), and {[(L(5))2Ca3(Na)(H2O)9(Cl)](Br)6·2H2O}∞ (5) along with binuclear {[Ca2(L(2))2(H2O)9](Br)4·4H2O} (2), and trinuclear {[(L(6))2Ca3(H2O)9](Br)6} (6) were isolated from the reaction between the corresponding azolium carboxylates and calcium carbonate in aqueous solution. 1–6 were characterized by FT-IR, NMR, TGA, UV-vis, fluorescence and single crystal X-ray diffraction techniques. Interestingly, the first tetra-cationic binuclear calcium 2 was isolated using L(2)H2Br2 and hexa-cationic trinuclear calcium 6 was isolated using L(6)H3Br3. The 3D coordination polymers 1 and 4 were derived with the help of L(1)H2Br2 and L(4)H2Br2, respectively, through Br···H hydrogen bonding. The 3D MOF 3 with rhomboidal channels was constructed using L(3)H2Br2, where the channel size is about 4.8 × 2.9 nm. 5 was isolated as a rare 1D coordination polymer. The choice of azolium carboxylates in these solids not only changes the topology of the network but also affects the chemistry exhibited by the network. Calcium azolium carboxylate assemblies 1–4 and 6 exhibit interesting solid-state photoluminescence properties, driven by azolium carboxylate ligands. Variation of the bridging chromophore produced significant effects on the fluorescence properties. 1–4 and 6 represent the first examples of luminescent calcium azolium carboxylate complexes. As can be seen in the six metal–organic assemblies presented in this report, a combination of carboxylate groups and steric hindrance affects the topology and physical properties of the resultant solids.
Energy Technology Data Exchange (ETDEWEB)
Neu, Mary Patricia [Univ. of California, Berkeley, CA (United States)
1993-11-01
The coordination chemistry and solution behavior of the toxic ions lead(II) and plutonium(IV, V, VI) have been investigated. The ligand pK_{a}s and ligand-lead(II) stability constants of one hydroxamic acid and four thiohydroaxamic acids were determined. Solution thermodynamic results indicate that thiohydroxamic acids are more acidic and slightly better lead chelators than hydroxamates, e.g., N-methylthioaceto-hydroxamic acid, pK_{a} = 5.94, logβ_{120} = 10.92; acetohydroxamic acid, pK_{a} = 9.34, logβ_{120} = 9.52. The syntheses of lead complexes of two bulky hydroxamate ligands are presented. The X-ray crystal structures show the lead hydroxamates are di-bridged dimers with irregular five-coordinate geometry about the metal atom and a stereochemically active lone pair of electrons. Molecular orbital calculations of a lead hydroxamate and a highly symmetric pseudo octahedral lead complex were performed. The thermodynamic stability of plutonium(IV) complexes of the siderophore, desferrioxamine B (DFO), and two octadentate derivatives of DFO were investigated using competition spectrophotometric titrations. The stability constant measured for the plutonium(IV) complex of DFO-methylterephthalamide is logβ_{120} = 41.7. The solubility limited speciation of ^{242}Pu as a function of time in near neutral carbonate solution was measured. Individual solutions of plutonium in a single oxidation state were added to individual solutions at pH = 6.0, T = 30.0, 1.93 mM dissolved carbonate, and sampled over intervals up to 150 days. Plutonium solubility was measured, and speciation was investigated using laser photoacoustic spectroscopy and chemical methods.
Haut, T L; Hull, M L; Howell, S M
1998-06-01
This paper describes the design and performance evaluation of a three-dimensional (3-D) coordinate digitizing system (3-DCDS) for measuring both soft and hard biological tissue. The system incorporates a visible semiconducting laser beam and an X-Y positioning table to directly measure 3-D coordinates that define surface points. Experiments conducted to evaluate the performance of the system showed that it delivers an accuracy of 0.1 microm in the Z-direction and 1.4 microm in the X-Y plane, and an overall system root-mean-squared error (RMSE) of 8 microm on surfaces with slopes of less than 45 degrees . This error is lower than that of previously reported measurement techniques. The 3-DCDS measures 3-D coordinates of surface points uniformly separated by 500 microm in the X-Y plane. Because the 3-DCDS is automated, the coordinates are measured efficiently and the accuracy is independent of operator skill. These highly accurate coordinates can be easily incorporated into nodal values for 3-D finite element models (FEM) of diarthrodial joints. To show the use of the 3-DCDS, the 3-D surface coordinates of human menisci were measured from a cadaver specimen.
DEFF Research Database (Denmark)
Krauss, M; Olsen, Lars; Antony, J
2002-01-01
performed to analyze the experimentally determined chemical shifts at 212 and 116 ppm, respectively, for the CdCd enzyme. The calculated isotropic shieldings correlate with the coordination number of the metal ions, indicating that the CdCd enzyme has one more ligand at the high shift site than at the low...
Danielsen, E; Kroes, S J; Canters, G W; Bauer, R; Hemmingsen, L; Singh, K; Messerschmidt, A
1997-12-01
The structural details of the metal site in the [His121]azurin mutant from Alcaligenes denitrificans where the axial methionine has been replaced by a histidine have been studied after substitution with the divalent cadmium ion and the monovalent silver ion. The studies have been carried out in solution using the technique of perturbed angular correlations of gamma-rays (PAC) of the two isotopes, 111Ag and 111mCd. In the pH range 6-9, the PAC spectra for cadmium-substituted [His121]azurin reveals a pH-independent equilibrium between two different metal-coordination geometries. Interpretation of the PAC data shows agreement between the dominating coordination geometry and that derived from X-ray diffraction on the Cu(II)[His121] azurin at high pH (Messerschmidt, A., unpublished results). Thus, it appears likely that cadmium for this geometry is four coordinated to the ligands His46, His117, Cys112, and His121. The other geometry is best interpreted as a substitution of His121 by a solvent water ligand. These interpretations stem from predictions of the experimentally determined nuclear quadrupole interactions (NQI) via the simple angular overlap model (AOM). At low pH (3.8), the concentration of the former species is reduced to 50% of its high pH value suggesting a pK of about 4 for His121. Two different coordination geometries have also been observed for the Cu(II) protein and assigned a type 1.5 and a type 1 copper site [Kroes, S. J., Hoitink, C. W. G., Andrew, C. R., Ai, J., Sanders-Loehr, J., Messerschmidt, A., Hagen, W. R. & Canters, G. W. (1996a) Eur. J. Biochem. 240, 342-351]. For silver-substituted [His121]azurin, several notable changes occur relative to the cadmium-substituted protein. At least four different metal-coordination geometries exist for silver[His121]azurin in the pH range 4-8. Changes in the population of these coordination sites occurs between pH 4 and pH 5, and pH 5 and pH 6. Furthermore, in contrast to the cadmium-substituted protein, only
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
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
Chen, Zitao; Song, Enhai; Ye, Shi; Zhang, Qinyuan
2017-12-01
In contrast to generally single-band visible emission feature from Mn2+, simultaneous visible (VIS) and near-infrared (NIR) multiple emissions are demonstrated in Mn2+ concentrated sulfide (MnS) by only involving a single crystallographic site. Upon varying the Mn2+-site coordination and/or Mn-Mn pairs geometry in different structural MnS, the multiple emissions from divalent manganese can be easily tuned from 575 to 720 nm (VIS) or from 880 to 900 or 1380 nm (NIR), respectively. The excitation spectroscopy and the luminescent decay, together with crystal structural analyses, are employed to investigate the electronic transition and the excited state dynamics of these Mn2+ concentrated systems. It is found that the VIS and NIR emissions can be ascribed to the isolated Mn2+ ion and exchange coupled Mn-Mn pair center, respectively. The effect of crystal field and bridging geometry, as well as temperature on the exchange coupled Mn2+ pairs NIR emissive center, is also investigated in detail. This work not only provides keen insights into the de-excitation pathway of Mn2+-concentrated material, but also offers the possibilities of designing a novel NIR emitting source for various photonic applications.
Mondal, Amit Kumar; Goswami, Tamal; Misra, Anirban; Konar, Sanjit
2017-06-19
In this work, the effects of ligand field strength as well as the metal coordination geometry on magnetic anisotropy of pentacoordinated CoII complexes have been investigated using a combined experimental and theoretical approach. For that, a strategic design and synthesis of three pentacoordinate CoII complexes [Co(bbp)Cl2]·(MeOH) (1), [Co(bbp)Br2]·(MeOH) (2), and [Co(bbp)(NCS)2] (3) has been achieved by using the tridentate coordination environment of the ligand in conjunction with the accommodating terminal ligands (i.e., chloride, bromide, and thiocyanate). Detailed magnetic studies disclose the occurrence of slow magnetic relaxation behavior of CoII centers with an easy-plane magnetic anisotropy. A quantitative estimation of ZFS parameters has been successfully performed by density functional theory (DFT) calculations. Both the sign and magnitude of ZFS parameters are prophesied well by this DFT method. The theoretical results also reveal that the α → β (SOMO-SOMO) excitation contributes almost entirely to the total ZFS values for all complexes. It is worth noting that the excitation pertaining to the most positive contribution to the ZFS parameter is the dxy → dx2-y2 excitation for complexes 1 and 2, whereas for complex 3 it is the dz2 → dx2-y2 excitation.
Saleem, Zain Hamid
In this thesis we study a special class of black hole geometries called subtracted geometries. Subtracted geometry black holes are obtained when one omits certain terms from the warp factor of the metric of general charged rotating black holes. The omission of these terms allows one to write the wave equation of the black hole in a completely separable way and one can explicitly see that the wave equation of a massless scalar field in this slightly altered background of a general multi-charged rotating black hole acquires an SL(2, R) x SL(2, R) x SO(3) symmetry. The "subtracted limit" is considered an appropriate limit for studying the internal structure of the non-subtracted black holes because new 'subtracted' black holes have the same horizon area and periodicity of the angular and time coordinates in the near horizon regions as the original black hole geometry it was constructed from. The new geometry is asymptotically conical and is physically similar to that of a black hole in an asymptotically confining box. We use the different nice properties of these geometries to understand various classically and quantum mechanically important features of general charged rotating black holes.
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...
Proyeksi Geometri Fuzzy pada Ruang
Directory of Open Access Journals (Sweden)
Muhammad Izzat Ubaidillah
2012-11-01
Full Text Available Fuzzy geometry is an outgrowth of crisp geometry, which in crisp geometry elements are exist and not exist, but also while on fuzzy geometry elements are developed by thickness which is owned by each of these elements. Crisp projective geometries is the formation of a shadow of geometries element projected on the projectors element, with perpendicular properties which are represented by their respective elemental, the discussion focused on the results of the projection coordinates. While the fuzzy projective geometries have richer discussion, which includes about coordinates of projection results, the mutual relation of each element and the thickness of each element. This research was conducted to describe and analyzing procedure fuzzy projective geometries on the plane and explain the differences between crisp projective geometries and fuzzy projective geometries on plane.
Chu, Zhaolian; You, Wei; Huang, Wei
2009-02-01
Three dinuclear copper(II) macrocyclic complexes, formulated as [Cu 2L(N 3) 2(0.5H 2O) 2] n ( 1), [Cu 2L(ClO 4) 2(CH 3CH 2OH)] ( 2) and [Cu 2L(CH 3OH) 2](ClO 4) 2 ( 3) (LH 2 = [2+2] Schiff base macrocyclic ligand condensed from 4-chloro-2,6-diformylphenol and 1,3-diaminopropane), have been prepared and determined by X-ray single-crystal diffraction. Complex 1 shows two six-coordinate Cu(II) centers in which two monodentate N3- anions and two half-water molecules are bonded at the apical positions in the trans configuration. Furthermore, the dimeric half-water molecules serve as a μ2-bridge linking adjacent macrocyclic units together with the multiple O sbnd H…N hydrogen bonds with azide anions, forming a novel 1D chain-like coordination polymer. Complexes 2 and 3 are obtained from different solvents (ethanol and methanol) and they can be converted into each other. The molecular structures and packing mode of 2 and 3 are different where six-coordinate and five-coordinate copper(II) centers are present, respectively.
Directory of Open Access Journals (Sweden)
Emílio Borges
2007-04-01
Full Text Available A simple method to obtain molecular Cartesian coordinates as a function of vibrational normal modes is presented in this work. The method does not require the definition of special matrices, like the F and G of Wilson, neither of group theory. The Eckart's conditions together with the diagonalization of kinetic and potential energy are the only required expressions. This makes the present approach appropriate to be used as a preliminary study for more advanced concepts concerning vibrational analysis. Examples are given for diatomic and triatomic molecules.
Holme, Audun
1988-01-01
This volume presents selected papers resulting from the meeting at Sundance on enumerative algebraic geometry. The papers are original research articles and concentrate on the underlying geometry of the subject.
Coordination Chemistry of Microbial Iron Transport.
Raymond, Kenneth N; Allred, Benjamin E; Sia, Allyson K
2015-09-15
This Account focuses on the coordination chemistry of the microbial iron chelators called siderophores. The initial research (early 1970s) focused on simple analogs of siderophores, which included hydroxamate, catecholate, or hydroxycarboxylate ligands. The subsequent work increasingly focused on the transport of siderophores and their microbial iron transport. Since these are pseudo-octahedral complexes often composed of bidentate ligands, there is chirality at the metal center that in principle is independent of the ligand chirality. It has been shown in many cases that chiral recognition of the complex occurs. Many techniques have been used to elucidate the iron uptake processes in both Gram-positive (single membrane) and Gram-negative (double membrane) bacteria. These have included the use of radioactive labels (of ligand, metal, or both), kinetically inert metal complexes, and Mössbauer spectroscopy. In general, siderophore recognition and transport involves receptors that recognize the metal chelate portion of the iron-siderophore complex. A second, to date less commonly found, mechanism called the siderophore shuttle involves the receptor binding an apo-siderophore. Since one of the primary ways that microbes compete with each other for iron stores is the strength of their competing siderophore complexes, it became important early on to characterize the solution thermodynamics of these species. Since the acidity of siderophores varies significantly, just the stability constant does not give a direct measure of the relative competitive strength of binding. For this reason, the pM value is compared. The pM, like pH, is a measure of the negative log of the free metal ion concentration, typically calculated at pH 7.4, and standard total concentrations of metal and ligand. The characterization of the electronic structure of ferric siderophores has done much to help explain the high stability of these complexes. A new chapter in siderophore science has emerged
Directory of Open Access Journals (Sweden)
Wim P Burmeister
Full Text Available The vesivirus feline calicivirus (FCV is a positive strand RNA virus encapsidated by an icosahedral T=3 shell formed by the viral VP1 protein. Upon its expression in the insect cell - baculovirus system in the context of vaccine development, two types of virus-like particles (VLPs were formed, a majority built of 60 subunits (T=1 and a minority probably built of 180 subunits (T=3. The structure of the small particles was determined by x-ray crystallography at 0.8 nm resolution helped by cryo-electron microscopy in order to understand their formation. Cubic crystals belonged to space group P213. Their self-rotation function showed the presence of an octahedral pseudo-symmetry similar to the one described previously by Agerbandje and co-workers for human parvovirus VLPs. The crystal structure could be solved starting from the published VP1 structure in the context of the T=3 viral capsid. In contrast to viral capsids, where the capsomers are interlocked by the exchange of the N-terminal arm (NTA domain, this domain is disordered in the T=1 capsid of the VLPs. Furthermore it is prone to proteolytic cleavage. The relative orientation of P (protrusion and S (shell domains is alerted so as to fit VP1 to the smaller T=1 particle whereas the intermolecular contacts around 2-fold, 3-fold and 5-fold axes are conserved. By consequence the surface of the VLP is very similar compared to the viral capsid and suggests a similar antigenicity. The knowledge of the structure of the VLPs will help to improve their stability, in respect to a use for vaccination.
Papatheodorou, G. N.; Chrissanthopoulos, A.
2007-04-01
Electronic absorption spectroscopy is used in the temperature range 850-1300 K, to study the vapor species over molten HoI 3-CsI (1:1), molten CsI and solid HoI 3. Quantitative absorbance measurements are used to calculate the following enthalpies of transition: Δ Hsubl(HoI 3) = 271 ± 3 kJ mol -1, Δ Hvap. (CsHoI 4) = 155 ± 2 kJ mol -1 and Δ Hvap. (CsI) = 151 ± 2 kJ mol -1. The ligand field components of the 5G 6 ← 5I 8 hypersensitive transition of Ho(III) for the three different, all iodide, coordination geometries of HoI 3(g), CsHoI 4(g) and HoI 63- (in molten CsI) have been examined in detail. The molar absorptivities ( ɛ) and oscillator strengths ( f) increase as the coordination decreases from the "octahedral" HoI 63- ( ɛ = 65 L mol -1 cm -1; f = 99 × 10 -6) to the distorted tetrahedral HoI 4- ( ɛ = 235 L mol -1 cm -1; f = 290 × 10 -6) to the trigonal HoI 3 ( ɛ = 390 L mol -1 cm -1; f = 500 × 10 -6). The main factors affecting the hypersensitive transition intensities are the coordination number and symmetry and the ligand polarizability as well as the Boltzmann population effects on the ground state levels which are responsible for the appearance of "hot" bands in the spectra. A C2v symmetry is anticipated for the CsHoI 4(g) with the HoI 4- "tetrahedra" distorted towards a square planar symmetry leading to a structure with a pseudo-like inversion center.
Guggenheimer, Heinrich W
1977-01-01
This is a text of local differential geometry considered as an application of advanced calculus and linear algebra. The discussion is designed for advanced undergraduate or beginning graduate study, and presumes of readers only a fair knowledge of matrix algebra and of advanced calculus of functions of several real variables. The author, who is a Professor of Mathematics at the Polytechnic Institute of New York, begins with a discussion of plane geometry and then treats the local theory of Lie groups and transformation groups, solid differential geometry, and Riemannian geometry, leading to a
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
Roberts, Fred S.
The author cites work on visual perception which indicates that in order to study perception it is necessary to replace such classical geometrical notions as betweeness, straightness, perpendicularity, and parallelism with more general concepts. The term tolerance geometry is used for any geometry when primitive notions are obtained from the…
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.
Faulkner, T Ewan
2006-01-01
This text explores the methods of the projective geometry of the plane. Some knowledge of the elements of metrical and analytical geometry is assumed; a rigorous first chapter serves to prepare readers. Following an introduction to the methods of the symbolic notation, the text advances to a consideration of the theory of one-to-one correspondence. It derives the projective properties of the conic and discusses the representation of these properties by the general equation of the second degree. A study of the relationship between Euclidean and projective geometry concludes the presentation. Nu
Graustein, William C
2006-01-01
This first course in differential geometry presents the fundamentals of the metric differential geometry of curves and surfaces in a Euclidean space of three dimensions. Written by an outstanding teacher and mathematician, it explains the material in the most effective way, using vector notation and technique. It also provides an introduction to the study of Riemannian geometry.Suitable for advanced undergraduates and graduate students, the text presupposes a knowledge of calculus. The first nine chapters focus on the theory, treating the basic properties of curves and surfaces, the mapping of
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
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...
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.
Pottmann, Helmut; Eigensatz, Michael; Vaxman, A.; Wallner, Johannes
2015-01-01
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
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 1; Issue 8. Geometry VI - Space-the Final Frontier. Kapil H Paranjape. Series Article Volume 1 Issue 8 August 1996 pp 28-33. Fulltext. Click here to view fulltext PDF. Permanent link: http://www.ias.ac.in/article/fulltext/reso/001/08/0028-0033 ...
Geometry -----------~--------------RESONANCE
Indian Academy of Sciences (India)
From a different perspective artists had all along pointed out that parallel lines do meet at the horizon (Figure 1). In fact all pairs of coplanar lines meet and parallel lines .... A more advanced treatment can be found in this book. D Hilbert and S Cohn-Vossen. Geometry and the Imagination. Chelsea, NY,. USA. 1952. A difficult ...
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
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 ...
Directory of Open Access Journals (Sweden)
Leonardo Paris
2012-06-01
Full Text Available Lo studio degli ingranaggi si basa sulle geometrie coniugate in cui due curve o due superfici si mantengono costantemente in contatto pur se in movimento reciproco. La teoria geometrica degli ingranaggi fino alla fine del XIX secolo era uno dei molteplici rami nelle applicazioni della Geometria Descrittiva. Lo studio si basa sulla conoscenza delle principali proprietà delle curve piane e gobbe e delle loro derivate. La specificità del tema è che queste geometrie nel momento in cui si devono relazionare con le loro coniugate, devono rispettare dei vincoli che altrimenti non avrebbero. Si vuole evidenziare attraverso casi concreti il ruolo della geometria descrittiva nel passaggio dal teorico al pratico riproponendo in chiave informatica, temi e procedure di indagine spesso passati in secondo piano se non addirittura dimenticati.
Ciarlet, Philippe G
2007-01-01
This book gives the basic notions of differential geometry, such as the metric tensor, the Riemann curvature tensor, the fundamental forms of a surface, covariant derivatives, and the fundamental theorem of surface theory in a selfcontained and accessible manner. Although the field is often considered a classical one, it has recently been rejuvenated, thanks to the manifold applications where it plays an essential role. The book presents some important applications to shells, such as the theory of linearly and nonlinearly elastic shells, the implementation of numerical methods for shells, and
Nicolaidis, A.; Kiosses, V.
2012-09-01
It has been proposed that quantum mechanics and string theory share a common inner syntax, the relational logic of C. S. Peirce. Along this line of thought we consider the relations represented by spinors. Spinor composition leads to the emergence of Minkowski space-time. Inversely, the Minkowski space-time is istantiated by the Weyl spinors, while the merger of two Weyl spinors gives rise to a Dirac spinor. Our analysis is applied also to the string geometry. The string constraints are represented by real spinors, which create a parametrization of the string worldsheet identical to the Enneper-Weierstass representation of minimal surfaces. Further, a spinorial study of the AdS3 space-time reveals a Hopf fibration AdS3 → AdS2. The conformal symmetry inherent in AdS3 is pointed out. Our work indicates the hidden ties between logic-quantum mechanics-string theory-geometry and vindicates the Wheeler's proposal of pregeometry as a large network of logical propositions.
Geometry The Language of Space and Form (Revised Edition)
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
A vector space approach to geometry
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.
Planetary Image Geometry Library
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
Pandey, Sharmila; Das, Partha Pratim; Singh, Akhilesh Kumar; Mukherjee, Rabindranath
2011-10-28
Using an acyclic hexadentate pyridine amide ligand, containing a -OCH(2)CH(2)O- spacer between two pyridine-2-carboxamide units (1,4-bis[o-(pyrydine-2-carboxamidophenyl)]-1,4-dioxabutane (H(2)L(9)), in its deprotonated form), four new complexes, [Co(II)(L(9))] (1) and its one-electron oxidized counterpart [Co(III)(L(9))][NO(3)]·2H(2)O (2), [Ni(II)(L(9))] (3) and [Cu(II)(L(9))] (4), have been synthesized. Structural analyses revealed that the Co(II) centre in 1 and the Ni(II) centre in 3 are six-coordinate, utilizing all the available donor sites and the Cu(II) centre in 4 is effectively five-coordinated (one of the ether O atoms does not participate in coordination). The structural parameters associated with the change in the metal coordination environment have been compared with corresponding complexes of thioether-containing hexadentate ligands. The μ(eff) values at 298 K of 1-4 correspond to S = 3/2, S = 0, S = 1 and S = 1/2, respectively. Absorption spectra for all the complexes have been investigated. EPR spectral properties of the copper(II) complex 4 have been investigated, simulated and analyzed. Cyclic voltammetric experiments in CH(2)Cl(2) reveal quasireversible Co(III)-Co(II), Ni(III)-Ni(II) and Cu(II)-Cu(I) redox processes. In going from ether O to thioether S coordination, the effect of the metal coordination environment on the redox potential values of Co(III)-Co(II) (here the effect of spin-state as well), Ni(III)-Ni(II) and Cu(II)-Cu(I) processes have been systematically analyzed.
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.
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.
Modeling of metal interaction geometries for protein-ligand docking.
Seebeck, Birte; Reulecke, Ingo; Kämper, Andreas; Rarey, Matthias
2008-05-15
The accurate modeling of metal coordination geometries plays an important role for structure-based drug design applied to metalloenzymes. For the development of a new metal interaction model, we perform a statistical analysis of metal interaction geometries that are relevant to protein-ligand complexes. A total of 43,061 metal sites of the Protein Data Bank (PDB), containing amongst others magnesium, calcium, zinc, iron, manganese, copper, cadmium, cobalt, and nickel, were evaluated according to their metal coordination geometry. Based on statistical analysis, we derived a model for the automatic calculation and definition of metal interaction geometries for the purpose of molecular docking analyses. It includes the identification of the metal-coordinating ligands, the calculation of the coordination geometry and the superposition of ideal polyhedra to identify the optimal positions for free coordination sites. The new interaction model was integrated in the docking software FlexX and evaluated on a data set of 103 metalloprotein-ligand complexes, which were extracted from the PDB. In a first step, the quality of the automatic calculation of the metal coordination geometry was analyzed. In 74% of the cases, the correct prediction of the coordination geometry could be determined on the basis of the protein structure alone. Secondly, the new metal interaction model was tested in terms of predicting protein-ligand complexes. In the majority of test cases, the new interaction model resulted in an improved docking accuracy of the top ranking placements. 2007 Wiley-Liss, Inc.
Notes on noncommutative geometry
Nikolaev, Igor
2015-01-01
The book covers basics of noncommutative geometry and its applications in topology, algebraic geometry and number theory. A brief survey of main parts of noncommutative geometry with historical remarks, bibliography and a list of exercises is attached. Our notes are intended for the graduate students and faculty with interests in noncommutative geometry; they can be read by non-experts in the field.
GEOMETRY AND COMPLEXITY IN ARCHITECTURE
Directory of Open Access Journals (Sweden)
RUSU Maria Ana
2015-06-01
Full Text Available As Constantin Brancuși (1876-1956 said „Simplicity is complexity itself“, simplicity and regularity through the use of basic geometric forms has always played a central role in architectural design, during the 20th century. A diachronic perspective, shows as the use of geometry and mathematics to describe built form provided a common basis for communication between the processes of design, fabrication and stability. Classic ways of representing geometry, based on descriptive methods, favor precise language of bidimensionality easy to represent in a rectangular coordinate system. In recent years, the importance of geometry has been re-emphasized by significant advances in the digital age, where computers are increasingly used in design, fabrication and construction to explore the art of the possible. Contemporary architecture transcend the limitations of Euclidean geometry and create new forms that are emerging through the convergence of complex systems, computational design and robotic fabrication devices, but which can also achieve higher levels of performance. Freeform architectural shapes and structures play an increasingly important role in 21st century architectural design. Through a series of examples, the paper relates to contemporary architectural explorations of complex, curvilinear surfaces in the digital age and discusses how it has required rethinking the mode in which we traditionally operate as architects. The analysis creates the possibility of comparisons between original and current design.
Mahé, Louis; Roy, Marie-Françoise
1992-01-01
Ten years after the first Rennes international meeting on real algebraic geometry, the second one looked at the developments in the subject during the intervening decade - see the 6 survey papers listed below. Further contributions from the participants on recent research covered real algebra and geometry, topology of real algebraic varieties and 16thHilbert problem, classical algebraic geometry, techniques in real algebraic geometry, algorithms in real algebraic geometry, semialgebraic geometry, real analytic geometry. CONTENTS: Survey papers: M. Knebusch: Semialgebraic topology in the last ten years.- R. Parimala: Algebraic and topological invariants of real algebraic varieties.- Polotovskii, G.M.: On the classification of decomposing plane algebraic curves.- Scheiderer, C.: Real algebra and its applications to geometry in the last ten years: some major developments and results.- Shustin, E.L.: Topology of real plane algebraic curves.- Silhol, R.: Moduli problems in real algebraic geometry. Further contribu...
The Geometry Of Preposition Meanings
Directory of Open Access Journals (Sweden)
Peter Gärdenfors
2015-12-01
Full Text Available This article presents a unified approach to the semantics of prepositions based on the theory of conceptual spaces. Following the themes of my recent book The Geometry of Meaning, I focus on the convexity of their meanings and on which semantic domains are expressed by prepositions. As regards convexity, using polar coordinates turns out to provide the most natural representation. In addition to the spatial domain, I argue that for many prepositions, the force domain is central. In contrast to many other analyses, I also defend the position that prepositions have a central meaning and that other meanings can be derived via a limited class of semantic transformations.
Kinematic dynamos in spheroidal geometries
Ivers, D. J.
2017-10-01
The kinematic dynamo problem is solved numerically for a spheroidal conducting fluid of possibly large aspect ratio with an insulating exterior. The solution method uses solenoidal representations of the magnetic field and the velocity by spheroidal toroidal and poloidal fields in a non-orthogonal coordinate system. Scaling of coordinates and fields to a spherical geometry leads to a modified form of the kinematic dynamo problem with a geometric anisotropic diffusion and an anisotropic current-free condition in the exterior, which is solved explicitly. The scaling allows the use of well-developed spherical harmonic techniques in angle. Dynamo solutions are found for three axisymmetric flows in oblate spheroids with semi-axis ratios 1≤a/c≤25. For larger aspect ratios strong magnetic fields may occur in any region of the spheroid, depending on the flow, but the external fields for all three flows are weak and concentrated near the axis or periphery of the spheroid.
Reshaping Mathematics for Understanding Motion Geometry.
Slovin, Hannah; Venenciano, Linda; Ishihara, Melanie; Beppu, Cynthia
This book introduces concepts of geometry that students use throughout middle-grade and higher-level mathematics courses. These concepts, presented through the study of transformations, provide a framework for other important topics such as number, measurement, proportional reasoning, and graphing on the coordinate plane. The book is designed for…
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...
Affine and Projective Geometry
Bennett, M K
1995-01-01
An important new perspective on AFFINE AND PROJECTIVE GEOMETRY. This innovative book treats math majors and math education students to a fresh look at affine and projective geometry from algebraic, synthetic, and lattice theoretic points of view. Affine and Projective Geometry comes complete with ninety illustrations, and numerous examples and exercises, covering material for two semesters of upper-level undergraduate mathematics. The first part of the book deals with the correlation between synthetic geometry and linear algebra. In the second part, geometry is used to introduce lattice theory
Introduction to projective geometry
Wylie, C R
2008-01-01
This lucid introductory text offers both an analytic and an axiomatic approach to plane projective geometry. The analytic treatment builds and expands upon students' familiarity with elementary plane analytic geometry and provides a well-motivated approach to projective geometry. Subsequent chapters explore Euclidean and non-Euclidean geometry as specializations of the projective plane, revealing the existence of an infinite number of geometries, each Euclidean in nature but characterized by a different set of distance- and angle-measurement formulas. Outstanding pedagogical features include w
Geometry essentials for dummies
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
Foundations of arithmetic differential geometry
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.
Moving KML geometry elements within Google Earth
Zhu, Liang-feng; Wang, Xi-feng; Pan, Xin
2014-11-01
During the process of modeling and visualizing geospatial information on the Google Earth virtual globe, there is an increasing demand to carry out such operations as moving geospatial objects defined by KML geometry elements horizontally or vertically. Due to the absence of the functionality and user interface for performing the moving transformation, it is either hard or impossible to interactively move multiple geospatial objects only using the existing Google Earth desktop application, especially when the data sets are in large volume. In this paper, we present a general framework and associated implementation methods for moving multiple KML geometry elements within Google Earth. In our proposed framework, we first load KML objects into the Google Earth plug-in, and then extract KML geometry elements from the imported KML objects. Subsequently, we interactively control the movement distance along a specified orientation by employing a custom user interface, calculate the transformed geographic location for each KML geometry element, and adjust geographic coordinates of the points in each KML objects. And finally, transformed KML geometry elements can be displayed in Google Earth for 3D visualization and spatial analysis. A key advantage of the proposed framework is that it provides a simple, uniform and efficient user interface for moving multiple KML geometry elements within Google Earth. More importantly, the proposed framework and associated implementations can be conveniently integrated into other customizable Google Earth applications to support interactively visualizing and analyzing geospatial objects defined by KML geometry elements.
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.
Smith, James T
2000-01-01
A practical, accessible introduction to advanced geometry Exceptionally well-written and filled with historical and bibliographic notes, Methods of Geometry presents a practical and proof-oriented approach. The author develops a wide range of subject areas at an intermediate level and explains how theories that underlie many fields of advanced mathematics ultimately lead to applications in science and engineering. Foundations, basic Euclidean geometry, and transformations are discussed in detail and applied to study advanced plane geometry, polyhedra, isometries, similarities, and symmetry. An
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
Euclidean geometry and transformations
Dodge, Clayton W
1972-01-01
This introduction to Euclidean geometry emphasizes transformations, particularly isometries and similarities. Suitable for undergraduate courses, it includes numerous examples, many with detailed answers. 1972 edition.
Fundamental concepts of geometry
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.
Geometry Professionalized for Teachers.
Christofferson, Halbert Carl
Written in 1933, this book grew out of the author's concern that college matehmatics sequences of the day, although appropriate in algebra preparation, did not adequately prepare teachers of geometry. This book describes a course intended to remedy this by providing for both a comprehensive study of geometry as an axiomatically defined structure…
Foundations of algebraic geometry
Weil, A
1946-01-01
This classic is one of the cornerstones of modern algebraic geometry. At the same time, it is entirely self-contained, assuming no knowledge whatsoever of algebraic geometry, and no knowledge of modern algebra beyond the simplest facts about abstract fields and their extensions, and the bare rudiments of the theory of ideals.
Lyublinskaya, Irina; Funsch, Dan
2012-01-01
Several interactive geometry software packages are available today to secondary school teachers. An example is The Geometer's Sketchpad[R] (GSP), also known as Dynamic Geometry[R] software, developed by Key Curriculum Press. This numeric based technology has been widely adopted in the last twenty years, and a vast amount of creativity has been…
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.
Supersymmetric Sigma Model Geometry
Directory of Open Access Journals (Sweden)
Ulf Lindström
2012-08-01
Full Text Available This is a review of how sigma models formulated in Superspace have become important tools for understanding geometry. Topics included are: The (hyperkähler reduction; projective superspace; the generalized Legendre construction; generalized Kähler geometry and constructions of hyperkähler metrics on Hermitian symmetric spaces.
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.
Spinors in Physics and Geometry
Trautman, A.; Furlan, G.
1988-11-01
The Table of Contents for the full book PDF is as follows: * Preface * Killing Spinors According to O. Hijazi and Applications * Self-Duality Conditions Satisfied by the Spin Connections on Spheres * Maslov Index and Half - Forms * Spin - 3/2 Fields on Black Hole Spacetimes * Indecomposable Conformal Spinors and Operator Product Expansions in a Massless QED Model * Nonlinear Spinor Representations * Nonlinear Wave Equations for Intrinsic Spinor Coordinates * Twistors - "Spinors" of SU(2,2), Their Generalizations and Achievements * Spinors, Reflections and Clifford Algebras: A Review * overline {SL}(n, R) Spinors for Particles, Gravity and Superstrings * Spinors on Compact Riemann Surfaces * Simple Spinors as Urfelder * Applications of Cartan Spinors to Differential Geometry in Higher Dimensions * Killing Spinors on Spheres and Projective Spaces * Spinor Structures on Homogeneous Riemannian Spaces * Classical Strings and Minimal Surfaces * Representing Spinors with Differential Forms * Inequalities for Spinors Norms in Clifford Algebras * The Importance of Spin * The Theory of World Spinors * Final List of Participants
A. Ball
Overview From a technical perspective, CMS has been in “beam operation” state since 6th November. The detector is fully closed with all components operational and the magnetic field is normally at the nominal 3.8T. The UXC cavern is normally closed with the radiation veto set. Access to UXC is now only possible during downtimes of LHC. Such accesses must be carefully planned, documented and carried out in agreement with CMS Technical Coordination, Experimental Area Management, LHC programme coordination and the CCC. Material flow in and out of UXC is now strictly controlled. Access to USC remains possible at any time, although, for safety reasons, it is necessary to register with the shift crew in the control room before going down.It is obligatory for all material leaving UXC to pass through the underground buffer zone for RP scanning, database entry and appropriate labeling for traceability. Technical coordination (notably Stephane Bally and Christoph Schaefer), the shift crew and run ...
Degrees of freedom in discrete geometry
Ariwahjoedi, Seramika; Rovelli, Carlo; Zen, Freddy P
2016-01-01
Following recent developments in discrete gravity, we study geometrical variables (angles and forms) of simplices in the discrete geometry point of view. Some of our relatively new results include: new ways of writing a set of simplices using vectorial (differential form) and coordinate-free pictures, and a consistent procedure to couple particles of space, together with a method to calculate the degrees of freedom of the system of 'quanta' of space in the classical framework.
Fuzzy Logic for Incidence Geometry
2016-01-01
The paper presents a mathematical framework for approximate geometric reasoning with extended objects in the context of Geography, in which all entities and their relationships are described by human language. These entities could be labelled by commonly used names of landmarks, water areas, and so forth. Unlike single points that are given in Cartesian coordinates, these geographic entities are extended in space and often loosely defined, but people easily perform spatial reasoning with extended geographic objects “as if they were points.” Unfortunately, up to date, geographic information systems (GIS) miss the capability of geometric reasoning with extended objects. The aim of the paper is to present a mathematical apparatus for approximate geometric reasoning with extended objects that is usable in GIS. In the paper we discuss the fuzzy logic (Aliev and Tserkovny, 2011) as a reasoning system for geometry of extended objects, as well as a basis for fuzzification of the axioms of incidence geometry. The same fuzzy logic was used for fuzzification of Euclid's first postulate. Fuzzy equivalence relation “extended lines sameness” is introduced. For its approximation we also utilize a fuzzy conditional inference, which is based on proposed fuzzy “degree of indiscernibility” and “discernibility measure” of extended points. PMID:27689133
Geometry of curves and surfaces with Maple
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...
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
Complex and symplectic geometry
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.
Equilibrium between Different Coordination Geometries in Oxidovanadium(IV) Complexes
Ugone, Valeria; Garribba, Eugenio; Micera, Giovanni; Sanna, Daniele
2015-01-01
In this laboratory activity, the equilibrium between square pyramidal and octahedral V(IV)O[superscript 2+] complexes is described. We propose a set of experiments to synthesize and characterize two types of V(IV)O[superscript 2+] complexes. The experiment allows great flexibility and may be effectively used at a variety of levels and the activity…
Geometry without topology as a new conception of geometry
Directory of Open Access Journals (Sweden)
Yuri A. Rylov
2002-01-01
geometry. In T-geometry, any space region is isometrically embeddable in the space, whereas in Riemannian geometry only convex region is isometrically embeddable. T-geometric conception appears to be more consistent logically, than the Riemannian one.
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.
Melzak, Z A
2008-01-01
Intended for students of many different backgrounds with only a modest knowledge of mathematics, this text features self-contained chapters that can be adapted to several types of geometry courses. 1983 edition.
Lectures on Symplectic Geometry
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...
Introduction to tropical geometry
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...
Geometry of differential equations
Khovanskiĭ, A; Vassiliev, V
1998-01-01
This volume contains articles written by V. I. Arnold's colleagues on the occasion of his 60th birthday. The articles are mostly devoted to various aspects of geometry of differential equations and relations to global analysis and Hamiltonian mechanics.
Bénichou, O; Chevalier, C; Klafter, J; Meyer, B; Voituriez, R
2010-06-01
It has long been appreciated that the transport properties of molecules can control reaction kinetics. This effect can be characterized by the time it takes a diffusing molecule to reach a target-the first-passage time (FPT). Determining the FPT distribution in realistic confined geometries has until now, however, seemed intractable. Here, we calculate this FPT distribution analytically and show that transport processes as varied as regular diffusion, anomalous diffusion, and diffusion in disordered media and fractals, fall into the same universality classes. Beyond the theoretical aspect, this result changes our views on standard reaction kinetics and we introduce the concept of 'geometry-controlled kinetics'. More precisely, we argue that geometry-and in particular the initial distance between reactants in 'compact' systems-can become a key parameter. These findings could help explain the crucial role that the spatial organization of genes has in transcription kinetics, and more generally the impact of geometry on diffusion-limited reactions.
Busemann, Herbert
2005-01-01
A comprehensive approach to qualitative problems in intrinsic differential geometry, this text examines Desarguesian spaces, perpendiculars and parallels, covering spaces, the influence of the sign of the curvature on geodesics, more. 1955 edition. Includes 66 figures.
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...
Elementary differential geometry
Pressley, Andrew
2001-01-01
Curves and surfaces are objects that everyone can see, and many of the questions that can be asked about them are natural and easily understood Differential geometry is concerned with the precise mathematical formulation of some of these questions, and with trying to answer them using calculus techniques It is a subject that contains some of the most beautiful and profound results in mathematics yet many of these are accessible to higher-level undergraduates Elementary Differential Geometry presents the main results in the differential geometry of curves and surfaces while keeping the prerequisites to an absolute minimum Nothing more than first courses in linear algebra and multivariate calculus are required, and the most direct and straightforward approach is used at all times Numerous diagrams illustrate both the ideas in the text and the examples of curves and surfaces discussed there The book will provide an invaluable resource to all those taking a first course in differential geometry, for their lecture...
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.
Intermediate algebra & analytic geometry
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
McAteer, R. T. J.
2013-06-01
When Mandelbrot, the father of modern fractal geometry, made this seemingly obvious statement he was trying to show that we should move out of our comfortable Euclidean space and adopt a fractal approach to geometry. The concepts and mathematical tools of fractal geometry provides insight into natural physical systems that Euclidean tools cannot do. The benet from applying fractal geometry to studies of Self-Organized Criticality (SOC) are even greater. SOC and fractal geometry share concepts of dynamic n-body interactions, apparent non-predictability, self-similarity, and an approach to global statistics in space and time that make these two areas into naturally paired research techniques. Further, the iterative generation techniques used in both SOC models and in fractals mean they share common features and common problems. This chapter explores the strong historical connections between fractal geometry and SOC from both a mathematical and conceptual understanding, explores modern day interactions between these two topics, and discusses how this is likely to evolve into an even stronger link in the near future.
A. Ball
2010-01-01
Operational Experience At the end of the first full-year running period of LHC, CMS is established as a reliable, robust and mature experiment. In particular common systems and infrastructure faults accounted for <0.6 % CMS downtime during LHC pp physics. Technical operation throughout the entire year was rather smooth, the main faults requiring UXC access being sub-detector power systems and rack-cooling turbines. All such problems were corrected during scheduled technical stops, in the shadow of tunnel access needed by the LHC, or in negotiated accesses or access extensions. Nevertheless, the number of necessary accesses to the UXC averaged more than one per week and the technical stops were inevitably packed with work packages, typically 30 being executed within a few days, placing a high load on the coordination and area management teams. It is an appropriate moment for CMS Technical Coordination to thank all those in many CERN departments and in the Collaboration, who were involved in CMS techni...
Marching Cubes in Cylindrical and Spherical Coordinates
Goldsmith, J.; Jacobson, A. S.
1996-01-01
Isosurface extraction is a common analysis and visualization technique for three-dimensional scalar data. Marching Cubes is the most commonly-used algorithm for finding polygonal representations of isosurfaces in such data. We extend Marching Cubes to produce geometry for data sets that lie in spherical and cylindrical coordinate systems as well as show the steps for derivation of transformations for other coordinate systems.
Sources of hyperbolic geometry
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...
Students Discovering Spherical Geometry Using Dynamic Geometry Software
Guven, Bulent; Karatas, Ilhan
2009-01-01
Dynamic geometry software (DGS) such as Cabri and Geometers' Sketchpad has been regularly used worldwide for teaching and learning Euclidean geometry for a long time. The DGS with its inductive nature allows students to learn Euclidean geometry via explorations. However, with respect to non-Euclidean geometries, do we need to introduce them to…
Cecil, Thomas E
2015-01-01
This exposition provides the state-of-the art on the differential geometry of hypersurfaces in real, complex, and quaternionic space forms. Special emphasis is placed on isoparametric and Dupin hypersurfaces in real space forms as well as Hopf hypersurfaces in complex space forms. The book is accessible to a reader who has completed a one-year graduate course in differential geometry. The text, including open problems and an extensive list of references, is an excellent resource for researchers in this area. Geometry of Hypersurfaces begins with the basic theory of submanifolds in real space forms. Topics include shape operators, principal curvatures and foliations, tubes and parallel hypersurfaces, curvature spheres and focal submanifolds. The focus then turns to the theory of isoparametric hypersurfaces in spheres. Important examples and classification results are given, including the construction of isoparametric hypersurfaces based on representations of Clifford algebras. An in-depth treatment of Dupin hy...
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...
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...
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.
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
Eisenhart, L P
1927-01-01
The use of the differential geometry of a Riemannian space in the mathematical formulation of physical theories led to important developments in the geometry of such spaces. The concept of parallelism of vectors, as introduced by Levi-Civita, gave rise to a theory of the affine properties of a Riemannian space. Covariant differentiation, as developed by Christoffel and Ricci, is a fundamental process in this theory. Various writers, notably Eddington, Einstein and Weyl, in their efforts to formulate a combined theory of gravitation and electromagnetism, proposed a simultaneous generalization o
Graumann, Günter; Blum, Werner
1989-01-01
My conception of "practice-oriented-mathematical-education", which must be seen as one point of view side-by-side with others, has the aim to qualify pupils to master life and is based on a method of working on problems which are true to life. Therefore I plead for geometry teaching, where the formation of sound geometric concepts and the relevance of applications of geometry in everyday life is important. After discussing this conception a schedule of activities of everyday life where geomet...
Bishop, Richard L
2001-01-01
First published in 1964, this book served as a text on differential geometry to several generations of graduate students all over the world. The first half of the book (Chapters 1-6) presents basics of the theory of manifolds, vector bundles, differential forms, and Lie groups, with a special emphasis on the theory of linear and affine connections. The second half of the book (Chapters 7-11) is devoted to Riemannian geometry. Following the definition and main properties of Riemannian manifolds, the authors discuss the theory of geodesics, complete Riemannian manifolds, and curvature. Next, the
New Tools for Computational Geometry and Rejuvenation of Screw Theory
Hestenes, David
Conformal Geometric Algebraic (CGA) provides ideal mathematical tools for construction, analysis, and integration of classical Euclidean, Inversive & Projective Geometries, with practical applications to computer science, engineering, and physics. This paper is a comprehensive introduction to a CGA tool kit. Synthetic statements in classical geometry translate directly to coordinate-free algebraic forms. Invariant and covariant methods are coordinated by conformal splits, which are readily related to the literature using methods of matrix algebra, biquaternions, and screw theory. Designs for a complete system of powerful tools for the mechanics of linked rigid bodies are presented.
C. Delaere
2013-01-01
Since the LHC ceased operations in February, a lot has been going on at Point 5, and Run Coordination continues to monitor closely the advance of maintenance and upgrade activities. In the last months, the Pixel detector was extracted and is now stored in the pixel lab in SX5; the beam pipe has been removed and ME1/1 removal has started. We regained access to the vactank and some work on the RBX of HB has started. Since mid-June, electricity and cooling are back in S1 and S2, allowing us to turn equipment back on, at least during the day. 24/7 shifts are not foreseen in the next weeks, and safety tours are mandatory to keep equipment on overnight, but re-commissioning activities are slowly being resumed. Given the (slight) delays accumulated in LS1, it was decided to merge the two global runs initially foreseen into a single exercise during the week of 4 November 2013. The aim of the global run is to check that we can run (parts of) CMS after several months switched off, with the new VME PCs installed, th...
Christophe Delaere
2013-01-01
The focus of Run Coordination during LS1 is to monitor closely the advance of maintenance and upgrade activities, to smooth interactions between subsystems and to ensure that all are ready in time to resume operations in 2015 with a fully calibrated and understood detector. After electricity and cooling were restored to all equipment, at about the time of the last CMS week, recommissioning activities were resumed for all subsystems. On 7 October, DCS shifts began 24/7 to allow subsystems to remain on to facilitate operations. That culminated with the Global Run in November (GriN), which took place as scheduled during the week of 4 November. The GriN has been the first centrally managed operation since the beginning of LS1, and involved all subdetectors but the Pixel Tracker presently in a lab upstairs. All nights were therefore dedicated to long stable runs with as many subdetectors as possible. Among the many achievements in that week, three items may be highlighted. First, the Strip...
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....
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 11; Issue 7. Foundations of Basic Geometry. Jasbir S Chahal. General Article Volume 11 Issue 7 July 2006 pp 30-41. Fulltext. Click here to view fulltext PDF. Permanent link: http://www.ias.ac.in/article/fulltext/reso/011/07/0030-0041. Keywords. Area ...
Coxeter, HSM
1965-01-01
This textbook introduces non-Euclidean geometry, and the third edition adds a new chapter, including a description of the two families of 'mid-lines' between two given lines and an elementary derivation of the basic formulae of spherical trigonometry and hyperbolic trigonometry, and other new material.
Diophantine geometry an introduction
Hindry, Marc
2000-01-01
This is an introduction to diophantine geometry at the advanced graduate level. The book contains a proof of the Mordell conjecture which will make it quite attractive to graduate students and professional mathematicians. In each part of the book, the reader will find numerous exercises.
Towards relativistic quantum geometry
Directory of Open Access Journals (Sweden)
Luis Santiago Ridao
2015-12-01
Full Text Available We obtain a gauge-invariant relativistic quantum geometry by using a Weylian-like manifold with a geometric scalar field which provides a gauge-invariant relativistic quantum theory in which the algebra of the Weylian-like field depends on observers. An example for a Reissner–Nordström black-hole is studied.
Indian Academy of Sciences (India)
IAS Admin
face area and perimeter of various shapes like sphere, cone, cylinder and circle. But an equally important geo- metric object `torus' { a shape like a scooter tube or a doughnut { is not discussed in school geometry. This is perhaps due to the non availability of this shape at the time when Archimedes (287 BC{212 BC) was ...
Boyer, Carl B
2012-01-01
Designed as an integrated survey of the development of analytic geometry, this study presents the concepts and contributions from before the Alexandrian Age through the eras of the great French mathematicians Fermat and Descartes, and on through Newton and Euler to the "Golden Age," from 1789 to 1850.
Atiyah, Michael; Dijkgraaf, Robbert; Hitchin, Nigel
2010-01-01
We review the remarkably fruitful interactions between mathematics and quantum physics in the past decades, pointing out some general trends and highlighting several examples, such as the counting of curves in algebraic geometry, invariants of knots and four-dimensional topology. PMID:20123740
Atiyah, M.; Dijkgraaf, R.; Hitchin, N.
2010-01-01
We review the remarkably fruitful interactions between mathematics and quantum physics in the past decades, pointing out some general trends and highlighting several examples, such as the counting of curves in algebraic geometry, invariants of knots and four-dimensional topology.
Indian Academy of Sciences (India)
revolutionised by the introduction of new con- cepts and techniques by Grothendieck and others; this progress has been instrumental in solving outstanding and famous problems not only in algebraic geometry but also in related fields like number theory. Mathematicians from India have made influ- ential and extensive ...
Wares, Arsalan; Elstak, Iwan
2017-01-01
The purpose of this paper is to describe the mathematics that emanates from the construction of an origami box. We first construct a simple origami box from a rectangular sheet and then discuss some of the mathematical questions that arise in the context of geometry and algebra. The activity can be used as a context for illustrating how algebra…
Sliding vane geometry turbines
Sun, Harold Huimin; Zhang, Jizhong; Hu, Liangjun; Hanna, Dave R
2014-12-30
Various systems and methods are described for a variable geometry turbine. In one example, a turbine nozzle comprises a central axis and a nozzle vane. The nozzle vane includes a stationary vane and a sliding vane. The sliding vane is positioned to slide in a direction substantially tangent to an inner circumference of the turbine nozzle and in contact with the stationary vane.
Small N=2 Extremal Black Holes in Special Geometry
Ceresole, Anna; Marrani, Alessio
2010-01-01
We provide an intrinsic classification of the large and small orbits for N=2, 4D extremal black holes on symmetric spaces which does not depend on the duality frame used for the charges or on the special coordinates. A coordinate independent formula for the fake superpotential W, which (at infinity) represents the black hole ADM mass, is given explicitly in terms of invariants of the N=2 special geometry.
Small N=2 extremal black holes in special geometry
Ceresole, Anna; Ferrara, Sergio; Marrani, Alessio
2010-10-01
We provide an intrinsic classification of the large and small orbits for N=2, 4D extremal black holes on symmetric spaces which does not depend on the duality frame used for the charges or on the special coordinates. A coordinate independent formula for the fake superpotential W, which (at infinity) represents the black hole ADM mass, is given explicitly in terms of invariants of the N=2 special geometry.
N=1 Special Geometry, Mixed Hodge Variations and Toric Geometry
Lerche, Wolfgang; Warner, Nicholas P
2002-01-01
We study the superpotential of a certain class of N=1 supersymmetric type II compactifications with fluxes and D-branes. We show that it has an important two-dimensional meaning in terms of a chiral ring of the topologically twisted theory on the world-sheet. In the open-closed string B-model, this chiral ring is isomorphic to a certain relative cohomology group V, which is the appropriate mathematical concept to deal with both the open and closed string sectors. The family of mixed Hodge structures on V then implies for the superpotential to have a certain geometric structure. This structure represents a holomorphic, N=1 supersymmetric generalization of the well-known N=2 special geometry. It defines an integrable connection on the topological family of open-closed B-models, and a set of special coordinates on the space \\cal M of vev's in N=1 chiral multiplets. We show that it can be given a very concrete and simple realization for linear sigma models, which leads to a powerful and systematic method for comp...
(μ-Formato-κ2O:O′bis[dicarbonyl(η5-cyclopentadienyliron(II] tetrafluoridoborate
Directory of Open Access Journals (Sweden)
Cyprian M. M'thiruaine
2011-09-01
Full Text Available In the structure of the title compound [Fe2(C5H52(CHO2(CO4]BF4, each FeII atom is coordinated in a pseudo-octahedral three-legged piano-stool fashion. The cyclopentadienyl ligand occupies three fac coordination sites while the two carbonyl ligands and formate O atom occupy the remaining three sites.
Simultaneous calibration phantom commission and geometry calibration in cone beam CT
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.
Simultaneous calibration phantom commission and geometry calibration in cone beam CT.
Xu, Yuan; Yang, Shuai; Ma, Jianhui; Li, Bin; Wu, Shuyu; Qi, Hongliang; Zhou, Linghong
2017-08-09
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.
Transformational plane geometry
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...
Caravelli, Francesco
2011-01-01
Quantum Graphity is an approach to quantum gravity based on a background independent formulation of condensed matter systems on graphs. We summarize recent results obtained on the notion of emergent geometry from the point of view of a particle hopping on the graph. We discuss the role of connectivity in emergent Lorentzian perturbations in a curved background and the Bose--Hubbard (BH) model defined on graphs with particular symmetries.
Algebra, Arithmetic, and Geometry
Tschinkel, Yuri
2009-01-01
The two volumes of "Algebra, Arithmetic, and Geometry: In Honor of Y.I. Manin" are composed of invited expository articles and extensions detailing Manin's contributions to the subjects, and are in celebration of his 70th birthday. The well-respected and distinguished contributors include: Behrend, Berkovich, Bost, Bressler, Calaque, Carlson, Chambert-Loir, Colombo, Connes, Consani, Dabrowski, Deninger, Dolgachev, Donaldson, Ekedahl, Elsenhans, Enriques, Etingof, Fock, Friedlander, Geemen, Getzler, Goncharov, Harris, Iskovskikh, Jahnel, Kaledin, Kapranov, Katz, Kaufmann, Kollar, Kont
Emergent geometry, emergent forces
Selesnick, S. A.
2017-10-01
We give a brief account of some aspects of Finkelstein’s quantum relativity, namely an extension of it that derives elements of macroscopic geometry and the Lagrangians of the standard model including gravity from a presumed quantum version of spacetime. These emerge as collective effects in this quantal substrate. Our treatment, which is largely self-contained, differs mathematically from that originally given by Finkelstein. Dedicated to the memory of David Ritz Finkelstein
Integral geometry and valuations
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...
Emergent complex network geometry.
Wu, Zhihao; Menichetti, Giulia; Rahmede, Christoph; Bianconi, Ginestra
2015-05-18
Networks are mathematical structures that are universally used to describe a large variety of complex systems such as the brain or the Internet. Characterizing the geometrical properties of these networks has become increasingly relevant for routing problems, inference and data mining. In real growing networks, topological, structural and geometrical properties emerge spontaneously from their dynamical rules. Nevertheless we still miss a model in which networks develop an emergent complex geometry. Here we show that a single two parameter network model, the growing geometrical network, can generate complex network geometries with non-trivial distribution of curvatures, combining exponential growth and small-world properties with finite spectral dimensionality. In one limit, the non-equilibrium dynamical rules of these networks can generate scale-free networks with clustering and communities, in another limit planar random geometries with non-trivial modularity. Finally we find that these properties of the geometrical growing networks are present in a large set of real networks describing biological, social and technological systems.
Editors, LearningExpress
2010-01-01
Whether you're new to geometry or just looking for a refresher, this completely revised and updated third edition of 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 is an invaluable resource for both students and adults.
Graded geometry and Poisson reduction
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
Teaching of Geometry in Bulgaria
Bankov, Kiril
2013-01-01
Geometry plays an important role in the school mathematics curriculum all around the world. Teaching of geometry varies a lot (Hoyls, Foxman, & Kuchemann, 2001). Many countries revise the objectives, the content, and the approaches to the geometry in school. Studies of the processes show that there are not common trends of these changes…
REA, The Editors of
2012-01-01
REA's Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Geometry I includes methods of proof, points, lines, planes, angles, congruent angles and line segments, triangles, parallelism, quadrilaterals, geometric inequalities, and geometric
Kendig, Keith
2015-01-01
Designed to make learning introductory algebraic geometry as easy as possible, this text is intended for advanced undergraduates and graduate students who have taken a one-year course in algebra and are familiar with complex analysis. This newly updated second edition enhances the original treatment's extensive use of concrete examples and exercises with numerous figures that have been specially redrawn in Adobe Illustrator. An introductory chapter that focuses on examples of curves is followed by a more rigorous and careful look at plane curves. Subsequent chapters explore commutative ring th
Akopyan, A V
2007-01-01
The book is devoted to the properties of conics (plane curves of second degree) that can be formulated and proved using only elementary geometry. Starting with the well-known optical properties of conics, the authors move to less trivial results, both classical and contemporary. In particular, the chapter on projective properties of conics contains a detailed analysis of the polar correspondence, pencils of conics, and the Poncelet theorem. In the chapter on metric properties of conics the authors discuss, in particular, inscribed conics, normals to conics, and the Poncelet theorem for confoca
Flegg, H Graham
2001-01-01
This excellent introduction to topology eases first-year math students and general readers into the subject by surveying its concepts in a descriptive and intuitive way, attempting to build a bridge from the familiar concepts of geometry to the formalized study of topology. The first three chapters focus on congruence classes defined by transformations in real Euclidean space. As the number of permitted transformations increases, these classes become larger, and their common topological properties become intuitively clear. Chapters 4-12 give a largely intuitive presentation of selected topics.
Gruber, Peter M
1987-01-01
This volume contains a fairly complete picture of the geometry of numbers, including relations to other branches of mathematics such as analytic number theory, diophantine approximation, coding and numerical analysis. It deals with convex or non-convex bodies and lattices in euclidean space, etc.This second edition was prepared jointly by P.M. Gruber and the author of the first edition. The authors have retained the existing text (with minor corrections) while adding to each chapter supplementary sections on the more recent developments. While this method may have drawbacks, it has the definit
Dooner, David B
2012-01-01
Building on the first edition published in 1995 this new edition of Kinematic Geometry of Gearing has been extensively revised and updated with new and original material. This includes the methodology for general tooth forms, radius of torsure', cylinder of osculation, and cylindroid of torsure; the author has also completely reworked the '3 laws of gearing', the first law re-written to better parallel the existing 'Law of Gearing" as pioneered by Leonard Euler, expanded from Euler's original law to encompass non-circular gears and hypoid gears, the 2nd law of gearing describing a unique relat
Abhyankar, Shreeram Shankar
1964-01-01
This book provides, for use in a graduate course or for self-study by graduate students, a well-motivated treatment of several topics, especially the following: (1) algebraic treatment of several complex variables; (2) geometric approach to algebraic geometry via analytic sets; (3) survey of local algebra; (4) survey of sheaf theory. The book has been written in the spirit of Weierstrass. Power series play the dominant role. The treatment, being algebraic, is not restricted to complex numbers, but remains valid over any complete-valued field. This makes it applicable to situations arising from
2015-01-01
This stimulating volume offers a broad collection of the principles of geometry and trigonometry and contains colorful diagrams to bring mathematical principles to life. Subjects are enriched by references to famous mathematicians and their ideas, and the stories are presented in a very comprehensible way. Readers investigate the relationships of points, lines, surfaces, and solids. They study construction methods for drawing figures, a wealth of facts about these figures, and above all, methods to prove the facts. They learn about triangle measure for circular motion, sine and cosine, tangent
Haran, Shai
2015-01-01
We shall describe a simple generalization of commutative rings. The category GR of such "rings", contains the ordinary commutative rings (fully faithfully), but also the "integers" and "residue field" at a real or complex place of a field ; the "field with one element" (the initial object of GR ); the "arithmetical surface" ( the sum in the category GR of the integers with them self: Z(x)Z ) . We shall show that this geometry "see" the real and complex places of a number field (there is an Os...
Electrodynamics and spacetime geometry: Astrophysical applications
Cabral, Francisco; Lobo, Francisco S. N.
2017-07-01
After a brief review of the foundations of (pre-metric) electromagnetism, we explore some physical consequences of electrodynamics in curved spacetime. In general, new electromagnetic couplings and related phenomena are induced by the spacetime curvature. The applications of astrophysical interest considered here correspond essentially to the following geometries: the Schwarzschild spacetime and the spacetime around a rotating spherical mass in the weak field and slow rotation regime. In the latter, we use the Parameterised Post-Newtonian (PPN) formalism. We also explore the hypothesis that the electric and magnetic properties of vacuum reflect the spacetime isometries. Therefore, the permittivity and permeability tensors should not be considered homogeneous and isotropic a priori. For spherical geometries we consider the effect of relaxing the homogeneity assumption in the constitutive relations between the fields and excitations. This affects the generalized Gauss and Maxwell-Ampère laws, where the electric permittivity and magnetic permeability in vacuum depend on the radial coordinate in accordance with the local isometries of space. For the axially symmetric geometries we relax both the assumptions of homogeneity and isotropy. We explore simple solutions and discuss the physical implications related to different phenomena, such as the decay of electromagnetic fields in the presence of gravity, magnetic terms in Gauss law due to the gravitomagnetism of the spacetime around rotating objects, a frame-dragging effect on electric fields and the possibility of a spatial (radial) variability of the velocity of light in vacuum around spherical astrophysical objects for strong gravitational fields.
Bochnak, Jacek; Roy, Marie-Françoise
1998-01-01
This book is a systematic treatment of real algebraic geometry, a subject that has strong interrelation with other areas of mathematics: singularity theory, differential topology, quadratic forms, commutative algebra, model theory, complexity theory etc. The careful and clearly written account covers both basic concepts and up-to-date research topics. It may be used as text for a graduate course. The present edition is a substantially revised and expanded English version of the book "Géometrie algébrique réelle" originally published in French, in 1987, as Volume 12 of ERGEBNISSE. Since the publication of the French version the theory has made advances in several directions. Many of these are included in this English version. Thus the English book may be regarded as a completely new treatment of the subject.
DEFF Research Database (Denmark)
Tamke, Martin; Ramsgaard Thomsen, Mette; Riiber Nielsen, Jacob
2009-01-01
The versatility of wood constructions and traditional wood joints for the production of non standard elements was in focus of a design based research. Herein we established a seamless process from digital design to fabrication. A first research phase centered on the development of a robust parame...... parametric model and a generic design language a later explored the possibilities to construct complex shaped geometries with self registering joints on modern wood crafting machines. The research was carried out as collaboration with industrial partners.......The versatility of wood constructions and traditional wood joints for the production of non standard elements was in focus of a design based research. Herein we established a seamless process from digital design to fabrication. A first research phase centered on the development of a robust...
Representing Simple Geometry Types in NetCDF-CF
Blodgett, D. L.; Koziol, B. W.; Whiteaker, T. L.; Simons, R.
2016-12-01
The Climate and Forecast (CF) metadata convention is well-suited for representing gridded and point-based observational datasets. However, CF currently has no accepted mechanism for representing simple geometry types such as lines and polygons. Lack of support for simple geometries within CF has unintentionally excluded a broad set of geoscientific data types from NetCDF-CF data encodings. For example, hydrologic datasets often contain polygon watershed catchments and polyline stream reaches in addition to point sampling stations and water management infrastructure. The latter has an associated CF specification. In the interest of supporting all simple geometry types within CF, a working group was formed following an EarthCube workshop on Advancing NetCDF-CF [1] to draft a CF specification for simple geometries: points, lines, polygons, and their associated multi-geometry representations [2]. The draft also includes parametric geometry types such as circles and ellipses. This presentation will provide an overview of the scope and content of the proposed specification focusing on mechanisms for representing coordinate arrays using variable length or continuous ragged arrays, capturing multi-geometries, and accounting for type-specific geometry artifacts such as polygon holes/interiors, node ordering, etc. The concepts contained in the specification proposal will be described with a use case representing streamflow in rivers and evapotranspiration from HUC12 watersheds. We will also introduce Python and R reference implementations developed alongside the technical specification. These in-development, open source Python and R libraries convert between commonly used GIS software objects (i.e. GEOS-based primitives) and their associated simple geometry CF representation. [1] http://www.unidata.ucar.edu/events/2016CFWorkshop/[2] https://github.com/bekozi/netCDF-CF-simple-geometry
Octanuclear cubic coordination cages.
Tidmarsh, Ian S; Faust, Thomas B; Adams, Harry; Harding, Lindsay P; Russo, Luca; Clegg, William; Ward, Michael D
2008-11-12
Two new bis-bidentate bridging ligands have been prepared, L (naph) and L (anth), which contain two chelating pyrazolyl-pyridine units connected to an aromatic spacer (naphthalene-1,5-diyl and anthracene-9,10-diyl respectively) via methylene connectors. Each of these reacts with transition metal dications having a preference for octahedral coordination geometry to afford {M 8L 12} (16+) cages (for L (anth), M = Cu, Zn; for L (naph), M = Co, Ni, Cd) which have an approximately cubic arrangement of metal ions with a bridging ligand spanning each of the twelve edges, and a large central cavity containing a mixture of anions and/or solvent molecules. The cages based on L (anth) have two cyclic helical {M 4L 4} faces, of opposite chirality, connected by four additional L (anth) ligands as "pillars"; all metal centers have a meridional tris-chelate configuration. In contrast the cages based on L (naph) have (noncrystallographic) S 6 symmetry, with a diagonally opposite pair of corners having a facial tris-chelate configuration with the other six being meridional. An additional significant difference between the two types of structure is that the cubes containing L (anth) do not show significant interligand aromatic stacking interactions. However, in the cages based on L (naph), there are six five-membered stacks of aromatic ligand fragments around the periphery, each based on an alternating array of electron-rich (naphthyl) and electron-deficient (pyrazolyl-pyridine, coordinated to M (2+)) aromatic units. A consequence of this is that the cages {M 8(L (naph)) 12} (16+) retain their structural integrity in polar solvents, in contrast to the cages {M 8(L (anth)) 12} (16+) which dissociate in polar solvents. Consequently, the cages {M 8(L (naph)) 12} (16+) give NMR spectra in agreement with the symmetry observed in the solid state, and their fluorescence spectra (for M = Cd) display (in addition to the normal naphthalene-based pi-pi* fluorescence) a lower-energy exciplex
An introduction to incidence geometry
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...
Non covalent assembly of coordination superstructures
Khlobystov, A N
2002-01-01
The main topic of this work is the design of discrete and polymeric multi-component coordination structures using non-covalent interactions between organic and inorganic molecular components. All of the structures described herein are based on transition metal cations and N-donor heterocyclic bis-exodentate ligands with different geometries and various spacer functionalities. The predominant method used for the structural characterisation of the complexes was single crystal X-ray crystallography. X-ray powder diffraction, IR and NMR spectroscopies and TEM and AFM imaging were used to characterise the bulk products from the reactions. Chapter 1 is a comparative review of non-covalent interactions relevant to coordination superstructures and covers the latest developments in the area of crystal engineering and supramolecular chemistry. The nature, geometry and relative energy of the non-covalent interactions are considered in detail in order to reveal their influence on the structure and properties of complexes...
Thermodynamics of Asymptotically Conical Geometries.
Cvetič, Mirjam; Gibbons, Gary W; Saleem, Zain H
2015-06-12
We study the thermodynamical properties of a class of asymptotically conical geometries known as "subtracted geometries." We derive the mass and angular momentum from the regulated Komar integral and the Hawking-Horowitz prescription and show that they are equivalent. By deriving the asymptotic charges, we show that the Smarr formula and the first law of thermodynamics hold. We also propose an analog of Christodulou-Ruffini inequality. The analysis can be generalized to other asymptotically conical geometries.
Self-designing parametric geometries
Sobester, Andras
2015-01-01
The thesis of this paper is that script-based geometry modelling offers the possibility of building `self-designing' intelligence into parametric airframe geometries. We show how sophisticated heuristics (such as optimizers and complex decision structures) can be readily integrated into the parametric geometry model itself using a script-driven modelling architecture. The result is an opportunity for optimization with the scope of conceptual design and the fidelity of preliminary design. Addi...
Geometry aware Stationary Subspace Analysis
2016-11-22
JMLR: Workshop and Conference Proceedings 63:430–444, 2016 ACML 2016 Geometry -aware Stationary Subspace Analysis Inbal Horev inbal@ms.k.u-tokyo.ac.jp... geometry of the SPD matrix manifold and the invariance properties of its metrics. Most notably we show that these invariances alleviate the need to...Horev, F. Yger & M. Sugiyama. Geometry -aware SSA many theoretical and practical aspects have been addressed (see Sugiyama and Kawanabe (2012) for an in
Initiation to global Finslerian geometry
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
Guijosa, A
1999-01-01
This thesis explores some aspects of the recently uncovered connection between gauge theories and gravity, known as the AdS/CFT, or bulk-boundary, correspondence. This is a remarkable statement of equivalence between string or M-theory on certain backgrounds and field theories living on the boundaries of the corresponding spacetimes. Under the duality between four-dimensional N = 4 SU(N) superYang-Mills (SYM) and Type IIB string theory on AdS5 × S5, a baryon is mapped onto N fundamental strings terminating on a wrapped D5-brane. We examine the structure and energetics of this system from the vantage point of the fivebrane worldvolume action, making use of the Born-Infeld string approach. We construct supersymmetric fivebrane embeddings which correspond to gauge theory configurations with n external quarks, 0 ≤ n ≤ N. The extension of these solutions to the full asymptotically flat geometry of N D3-branes provides a detailed description of the creation of strings as the fivebrane is...
Directory of Open Access Journals (Sweden)
Šárka Nedomová
2013-01-01
Full Text Available Precise quantification of the profile of egg can provide a powerful tool for the analysis of egg shape for various biological problems. A new approach to the geometry of a Ostrich’s egg profile is presented here using an analysing the egg’s digital photo by edge detection techniques. The obtained points on the eggshell counter are fitted by the Fourier series. The obtained equations describing an egg profile have been used to calculate radii of curvature. The radii of the curvature at the important point of the egg profile (sharp end, blunt end and maximum thickness are independent on the egg shape index. The exact values of the egg surface and the egg volume have been obtained. These quantities are also independent on the egg shape index. These quantities can be successively estimated on the basis of simplified equations which are expressed in terms of the egg length, L¸ and its width, B. The surface area of the eggshells also exhibits good correlation with the egg long circumference length. Some limitations of the most used procedures have been also shown.
Speziale, Simone
2013-01-01
We define and investigate a quantisation of null hypersurfaces in the context of loop quantum gravity on a fixed graph. The main tool we use is the parametrisation of the theory in terms of twistors, which has already proved useful in discussing the interpretation of spin networks as the quantization of twisted geometries. The classical formalism can be extended in a natural way to null hypersurfaces, with the Euclidean polyhedra replaced by null polyhedra with space-like faces, and SU(2) by the little group ISO(2). The main difference is that the simplicity constraints present in the formalims are all first class, and the symplectic reduction selects only the helicity subgroup of the little group. As a consequence, information on the shapes of the polyhedra is lost, and the result is a much simpler, abelian geometric picture. It can be described by an Euclidean singular structure on the 2-dimensional space-like surface defined by a foliation of space-time by null hypersurfaces. This geometric structure is na...
Bhatia, Rajendra
2013-01-01
This book is an outcome of the Indo-French Workshop on Matrix Information Geometries (MIG): Applications in Sensor and Cognitive Systems Engineering, which was held in Ecole Polytechnique and Thales Research and Technology Center, Palaiseau, France, in February 23-25, 2011. The workshop was generously funded by the Indo-French Centre for the Promotion of Advanced Research (IFCPAR). During the event, 22 renowned invited french or indian speakers gave lectures on their areas of expertise within the field of matrix analysis or processing. From these talks, a total of 17 original contribution or state-of-the-art chapters have been assembled in this volume. All articles were thoroughly peer-reviewed and improved, according to the suggestions of the international referees. The 17 contributions presented are organized in three parts: (1) State-of-the-art surveys & original matrix theory work, (2) Advanced matrix theory for radar processing, and (3) Matrix-based signal processing applications.
Positive geometries and canonical forms
Arkani-Hamed, Nima; Bai, Yuntao; Lam, Thomas
2017-11-01
Recent years have seen a surprising connection between the physics of scattering amplitudes and a class of mathematical objects — the positive Grassmannian, positive loop Grassmannians, tree and loop Amplituhedra — which have been loosely referred to as "positive geometries". The connection between the geometry and physics is provided by a unique differential form canonically determined by the property of having logarithmic singularities (only) on all the boundaries of the space, with residues on each boundary given by the canonical form on that boundary. The structures seen in the physical setting of the Amplituhedron are both rigid and rich enough to motivate an investigation of the notions of "positive geometries" and their associated "canonical forms" as objects of study in their own right, in a more general mathematical setting. In this paper we take the first steps in this direction. We begin by giving a precise definition of positive geometries and canonical forms, and introduce two general methods for finding forms for more complicated positive geometries from simpler ones — via "triangulation" on the one hand, and "push-forward" maps between geometries on the other. We present numerous examples of positive geometries in projective spaces, Grassmannians, and toric, cluster and flag varieties, both for the simplest "simplex-like" geometries and the richer "polytope-like" ones. We also illustrate a number of strategies for computing canonical forms for large classes of positive geometries, ranging from a direct determination exploiting knowledge of zeros and poles, to the use of the general triangulation and push-forward methods, to the representation of the form as volume integrals over dual geometries and contour integrals over auxiliary spaces. These methods yield interesting representations for the canonical forms of wide classes of positive geometries, ranging from the simplest Amplituhedra to new expressions for the volume of arbitrary convex
Spatial geometry and special relativity
DEFF Research Database (Denmark)
Kneubil, Fabiana Botelho
2016-01-01
In this work, it is shown the interplay of relative and absolute entities, which are present in both spatial geometry and special relativity. In order to strengthen the understanding of special relativity, we discuss firstly an instance of geometry and the existence of both frame-dependent and fr...
Geometry of the quantum universe
Ambjørn, J.; Görlich, A.; Jurkiewicz, J.; Loll, R.
2010-01-01
A quantum universe with the global shape of a (Euclidean) de Sitter spacetime appears as dynamically generated background geometry in the causal dynamical triangulation (CDT) regularisation of quantum gravity. We investigate the micro- and macro-geometry of this universe, using geodesic shell
GPS: Geometry, Probability, and Statistics
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…
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....
Quantifying linguistic coordination
DEFF Research Database (Denmark)
Fusaroli, Riccardo; Tylén, Kristian
task (Bahrami et al 2010, Fusaroli et al. 2012) we extend to linguistic coordination dynamical measures of recurrence employed in the analysis of sensorimotor coordination (such as heart-rate (Konvalinka et al 2011), postural sway (Shockley 2005) and eye-movements (Dale, Richardson and Kirkham 2012...... of linguistic coordination and their effects at a fine-degree....
Nonlinear gyrokinetic Maxwell-Vlasov equations using magnetic coordinates
Energy Technology Data Exchange (ETDEWEB)
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-..beta.. 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.
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...
Ab initio coordination chemistry for nickel chelation motifs.
Sudan, R Jesu Jaya; Kumari, J Lesitha Jeeva; Sudandiradoss, C
2015-01-01
Chelation therapy is one of the most appreciated methods in the treatment of metal induced disease predisposition. Coordination chemistry provides a way to understand metal association in biological structures. In this work we have implemented coordination chemistry to study nickel coordination due to its high impact in industrial usage and thereby health consequences. This paper reports the analysis of nickel coordination from a large dataset of nickel bound structures and sequences. Coordination patterns predicted from the structures are reported in terms of donors, chelate length, coordination number, chelate geometry, structural fold and architecture. The analysis revealed histidine as the most favored residue in nickel coordination. The most common chelates identified were histidine based namely HHH, HDH, HEH and HH spaced at specific intervals. Though a maximum coordination number of 8 was observed, the presence of a single protein donor was noted to be mandatory in nickel coordination. The coordination pattern did not reveal any specific fold, nevertheless we report preferable residue spacing for specific structural architecture. In contrast, the analysis of nickel binding proteins from bacterial and archeal species revealed no common coordination patterns. Nickel binding sequence motifs were noted to be organism specific and protein class specific. As a result we identified about 13 signatures derived from 13 classes of nickel binding proteins. The specifications on nickel coordination presented in this paper will prove beneficial for developing better chelation strategies.
Ab initio coordination chemistry for nickel chelation motifs.
Directory of Open Access Journals (Sweden)
R Jesu Jaya Sudan
Full Text Available Chelation therapy is one of the most appreciated methods in the treatment of metal induced disease predisposition. Coordination chemistry provides a way to understand metal association in biological structures. In this work we have implemented coordination chemistry to study nickel coordination due to its high impact in industrial usage and thereby health consequences. This paper reports the analysis of nickel coordination from a large dataset of nickel bound structures and sequences. Coordination patterns predicted from the structures are reported in terms of donors, chelate length, coordination number, chelate geometry, structural fold and architecture. The analysis revealed histidine as the most favored residue in nickel coordination. The most common chelates identified were histidine based namely HHH, HDH, HEH and HH spaced at specific intervals. Though a maximum coordination number of 8 was observed, the presence of a single protein donor was noted to be mandatory in nickel coordination. The coordination pattern did not reveal any specific fold, nevertheless we report preferable residue spacing for specific structural architecture. In contrast, the analysis of nickel binding proteins from bacterial and archeal species revealed no common coordination patterns. Nickel binding sequence motifs were noted to be organism specific and protein class specific. As a result we identified about 13 signatures derived from 13 classes of nickel binding proteins. The specifications on nickel coordination presented in this paper will prove beneficial for developing better chelation strategies.
Movement coordination during conversation.
Directory of Open Access Journals (Sweden)
Nida Latif
Full Text Available Behavioral coordination and synchrony contribute to a common biological mechanism that maintains communication, cooperation and bonding within many social species, such as primates and birds. Similarly, human language and social systems may also be attuned to coordination to facilitate communication and the formation of relationships. Gross similarities in movement patterns and convergence in the acoustic properties of speech have already been demonstrated between interacting individuals. In the present studies, we investigated how coordinated movements contribute to observers' perception of affiliation (friends vs. strangers between two conversing individuals. We used novel computational methods to quantify motor coordination and demonstrated that individuals familiar with each other coordinated their movements more frequently. Observers used coordination to judge affiliation between conversing pairs but only when the perceptual stimuli were restricted to head and face regions. These results suggest that observed movement coordination in humans might contribute to perceptual decisions based on availability of information to perceivers.
Energy Technology Data Exchange (ETDEWEB)
Hogan, Craig
2013-03-24
Standard particle theory is based on quantized matter embedded in a classical geometry. Here, a complementary model is proposed, based on classical matter -- massive bodies, without quantum properties -- embedded in a quantum geometry. It does not describe elementary particles, but may be a better, fully consistent quantum description for position states in laboratory-scale systems. Gravitational theory suggests that the geometrical quantum system has an information density of about one qubit per Planck length squared. If so, the model here predicts that the quantum uncertainty of geometry creates a new form of noise in the position of massive bodies, detectable by interferometers.
Differential geometry curves, surfaces, manifolds
Kühnel, Wolfgang
2015-01-01
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. The second part studies the geometry of general manifolds, with particular emphasis on connections and curvature. The text is illustrated with many figures and examples. The prerequisites are undergraduate analysis and linear algebra. This new edition provides many advancements, including more figures and exercises, and-as a new feature-a good number of so
Differential geometry and symmetric spaces
Helgason, Sigurdur
2001-01-01
Sigurdur Helgason's Differential Geometry and Symmetric Spaces was quickly recognized as a remarkable and important book. For many years, it was the standard text both for Riemannian geometry and for the analysis and geometry of symmetric spaces. Several generations of mathematicians relied on it for its clarity and careful attention to detail. Although much has happened in the field since the publication of this book, as demonstrated by Helgason's own three-volume expansion of the original work, this single volume is still an excellent overview of the subjects. For instance, even though there
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
An improved combinatorial geometry model for arbitrary geometry in DSMC
Kargaran, H.; Minuchehr, A.; Zolfaghari, A.
2017-03-01
This paper focuses on a new direct simulation Monte Carlo (DSMC) code based on combinatorial geometry (CG) for simulation of any rarefied gas flow. The developed code, called DgSMC-A, has been supplied with an improved CG modeling able to significantly optimize the particle-tracking process, resulting in a highly reduced runtime compared to the conventional codes. The improved algorithm inserts a grid over the geometry and saves those grid elements containing some part of the geometry border. Since only a small part of a grid is engaged with the geometry border, significant time can be saved using the proposed algorithm. Embedding the modified algorithm in the DgSMC-A resulted in a fast, robust and self-governing code needless to any mesh generator. The code completely handles complex geometries created with first-and second-order surfaces. In addition, we developed a new surface area calculator in the CG methodology for complex geometries based on the Monte Carlo method with acceptable accuracy. Several well-known test cases are examined to indicate the code ability to deal with a wide range of realistic problems. Results are also found to be in good agreement with references and experimental data.
A spectral method is spherical coordinates with coordinate singularity at the origin
Energy Technology Data Exchange (ETDEWEB)
Kageyama, Akira; Kida, Shigeo
2000-04-01
A new spectral method in the spherical coordinate system with a coordinate singularity at the origin is proposed. An analytical condition of all spectral modes is satisfied exactly at the origin. Dependent functions are expanded in terms of Chebyshev polynomials of even order in radial direction. Unnecessarily increased resolution near the origin as well as the restriction of severe time step are avoided automatically. Numerical accuracy is confirmed by applying it to a free decay of magnetic field in spherical geometry. This method is applicable to quadratic nonlinear problems. (author)
Hyperbolic Metamaterials with Complex Geometry
DEFF Research Database (Denmark)
Lavrinenko, Andrei; Andryieuski, Andrei; Zhukovsky, Sergei
2016-01-01
We investigate new geometries of hyperbolic metamaterialssuch as highly corrugated structures, nanoparticle monolayer assemblies, super-structured or vertically arranged multilayersand nanopillars. All structures retain basic propertiesof hyperbolic metamaterials, but have functionality improved...
Advances in discrete differential geometry
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, ...
An introduction to differential geometry
Willmore, T J
2012-01-01
This text employs vector methods to explore the classical theory of curves and surfaces. Topics include basic theory of tensor algebra, tensor calculus, calculus of differential forms, and elements of Riemannian geometry. 1959 edition.
Higgs mass in noncommutative geometry
Energy Technology Data Exchange (ETDEWEB)
Devastato, A.; Martinetti, P. [Dipartimento di Fisica, Universita di Napoli Federico II, Via Cintia, 80126 Napoli (Italy); INFN, Sezione di Napoli, Via Cintia, 80126 Napoli (Italy); Lizzi, F. [Dipartimento di Fisica, Universita di Napoli Federico II, Via Cintia, 80126 Napoli (Italy); INFN, Sezione di Napoli, Via Cintia, 80126 Napoli (Italy); Departament de Estructura i Constituents de la Materia, Universitat de Barcelona, Marti y Franques, Barcelona, Catalonia (Spain)
2014-09-11
In the noncommutative geometry approach to the standard model, an extra scalar field σ - initially suggested by particle physicist to stabilize the electroweak vacuum - makes the computation of the Higgs mass compatible with the 126 GeV experimental value. We give a brief account on how to generate this field from the Majorana mass of the neutrino, following the principles of noncommutative geometry. (Copyright copyright 2014 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
The Common Geometry Module (CGM).
Energy Technology Data Exchange (ETDEWEB)
Tautges, Timothy James
2004-12-01
The Common Geometry Module (CGM) is a code library which provides geometry functionality used for mesh generation and other applications. This functionality includes that commonly found in solid modeling engines, like geometry creation, query and modification; CGM also includes capabilities not commonly found in solid modeling engines, like geometry decomposition tools and support for shared material interfaces. CGM is built upon the ACIS solid modeling engine, but also includes geometry capability developed beside and on top of ACIS. CGM can be used as-is to provide geometry functionality for codes needing this capability. However, CGM can also be extended using derived classes in C++, allowing the geometric model to serve as the basis for other applications, for example mesh generation. CGM is supported on Sun Solaris, SGI, HP, IBM, DEC, Linux and Windows NT platforms. CGM also includes support for loading ACIS models on parallel computers, using MPI-based communication. Future plans for CGM are to port it to different solid modeling engines, including Pro/Engineer or SolidWorks. CGM is being released into the public domain under an LGPL license; the ACIS-based engine is available to ACIS licensees on request.
Finite Geometries: a tool for better understanding of Euclidean Geometry
Directory of Open Access Journals (Sweden)
Antonio Maturo
2014-06-01
Full Text Available An effective tool to really understand Euclidean geometry is the study of alternative models and their applications. In fact, they allow you to understand the real extent of various axioms that, when viewed from the Euclidean geometry, seem obvious or even unnecessary. The work begins with a review of Hilbert's axiomatic, starting from more general point of view adopted by Albrecht Beutelspacher and Ute Rosenbaum in their book on the fundamentals of general projective geometry (1998, defined by a system of incidence axioms. Le Geometrie Finite: uno strumento per una migliore comprensione della Geometria Euclidea Uno strumento efficace per comprendere realmente la geometria euclidea è lo studio di modelli alternativi e delle loro applicazioni. Infatti essi permettono di capire la reale portata di vari assiomi che visti dall’interno della geometria euclidea sembrerebbero scontati o addirittura inutili. Il lavoro parte da una rivisitazione dell’assiomatica di Hilbert a partire dal punto di vista più generale adottato da Albrecht Beutelspacher e Ute Rosenbaum nel loro libro del 1998 sui fondamenti della geometria proiettiva generale, definita attraverso un sistema di assiomi di incidenza. Parole Chiave: Critica dei fondamenti; Geometrie finite; Assiomi di Hilbert; Applicazioni.
Varadwaj, Pradeep R; Marques, Helder M
2010-03-07
Spin-unrestricted DFT-X3LYP/6-311++G(d,p) calculations have been performed on a series of complexes of the form [Co(H(2)O)(6-n)(NH(3))(n)](2+) (n = 0-6) to examine their equilibrium gas-phase structures, energetics, and electronic properties in their quartet electronic ground states. In all cases Co(2+) in the energy-minimised structures is in a pseudo-octahedral environment. The calculations overestimate the Co-O and Co-N bond lengths by 0.04 and 0.08 A, respectively, compared to the crystallographically observed mean values. There is a very small Jahn-Teller distortion in the structure of [Co(H(2)O)(6)](2+) which is in contrast to the very marked distortions observed in most (but not all) structures of this cation that have been observed experimentally. The successive replacement of ligated H(2)O by NH(3) leads to an increase in complex stability by 6 +/- 1 kcal mol(-1) per additional NH(3) ligand. Calculations using UB3LYP give stabilisation energies of the complexes about 5 kcal mol(-1) smaller and metal-ligand bond lengths about 0.005 A longer than the X3LYP values since the X3LYP level accounts for the London dispersion energy contribution to the overall stabilisation energy whilst it is largely missing at the B3LYP level. From a natural population analysis (NPA) it is shown that the formation of these complexes is accompanied by ligand-to-metal charge transfer the extent of which increases with the number of NH(3) ligands in the coordination sphere of Co(2+). From an examination of the topological properties of the electron charge density using Bader's quantum theory of atoms in molecules it is shown that the electron density rho(c) at the Co-O bond critical points is generally smaller than that at the Co-N bond critical points. Hence Co-O bonds are weaker than Co-N bonds in these complexes and the stability increases as NH(3) replaces H(2)O in the metal's coordination sphere. Several indicators, including the sign and magnitude of the Laplacian of the
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...
Coordination failure caused by sunspots
DEFF Research Database (Denmark)
Beugnot, Julie; Gürgüç, Zeynep; Øvlisen, Frederik Roose
2012-01-01
In a coordination game with Pareto-ranked equilibria, we study whether a sunspot can lead to either coordination on an inferior equilibrium (mis-coordination) or to out-of equilibrium behavior (dis-coordination). While much of the literature searches for mechanisms to attain coordination on the e......In a coordination game with Pareto-ranked equilibria, we study whether a sunspot can lead to either coordination on an inferior equilibrium (mis-coordination) or to out-of equilibrium behavior (dis-coordination). While much of the literature searches for mechanisms to attain coordination...
Ruthenium-based four-coordinate olefin metathesis catalysts
Energy Technology Data Exchange (ETDEWEB)
Sanford, M.S.; Henling, L.M.; Day, M.W.; Grubbs, R.H. [California Inst. of Tech., Pasadena (United States). Div. of Chemistry and Chemical Engineering
2000-10-02
A series of four-coordinate Ru{sup II} alkylidenes has been prepared as analogues of the proposed olefin metathesis intermediate [(PCy{sub 3})Cl{sub 2}Ru=CHPh]. These complexes exhibit unusual trigonal-pyramidal solid-state geometries, and are rendered highly active for ring-closing metathesis by the addition of HCl. (orig.)
Radiative heat transfer for irregular geometries with the collapsed dimension method
Energy Technology Data Exchange (ETDEWEB)
Talukdar, Prabal [Institute of Fluid Mechanics, University of Erlangen-Nuremberg, Cauerstrasse 4, 91058 Erlangen (Germany)
2006-02-15
A blocked-off region procedure is implemented with the collapsed dimension method (CDM) to deal with radiative transport problems in irregular geometries. Different test problems are validated for radiative and non-radiative equilibrium situations in participating or non-participating media. Results are found to be satisfactory for all straight edged, inclined and curved boundaries. The blocked-off region procedure based on Cartesian coordinate is found to be very convenient for a ray-tracing method like the CDM. The same ray tracing algorithm for a rectangular enclosure could be effectively used for any kind of 2-D geometries. This significantly reduces the effort of developing different ray-tracing algorithm for different geometries. In addition, it is an alternative than to write an algorithm in curvilinear coordinate for irregular geometries which found to be complicated for a ray-tracing method like the CDM. (author)
Quantum geometry and gravitational entropy
Energy Technology Data Exchange (ETDEWEB)
Simon, Joan; Balasubramanian, Vijay; Czech, Bart Iomiej; Larjo, Klaus; Marolf, Donald; Simon, Joan
2007-05-29
Most quantum states have wavefunctions that are widely spread over the accessible Hilbert space and hence do not have a good description in terms of a single classical geometry. In order to understand when geometric descriptions are possible, we exploit the AdS/CFT correspondence in the half-BPS sector of asymptotically AdS_5 x S5 universes. In this sector we devise a"coarse-grained metric operator" whose eigenstates are well described by a single spacetime topology and geometry. We show that such half-BPS universes have a non-vanishing entropy if and only if the metric is singular, and that the entropy arises from coarse-graining the geometry. Finally, we use our entropy formula to find the most entropic spacetimes with fixed asymptotic moments beyond the global charges.
Euclidean geometry and its subgeometries
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...
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...
Variable geometry Darrieus wind machine
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.
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
Geometry, topology, and string theory
Energy Technology Data Exchange (ETDEWEB)
Varadarajan, Uday [Univ. of California, Berkeley, CA (United States)
2003-01-01
A variety of scenarios are considered which shed light upon the uses and limitations of classical geometric and topological notions in string theory. The primary focus is on situations in which D-brane or string probes of a given classical space-time see the geometry quite differently than one might naively expect. In particular, situations in which extra dimensions, non-commutative geometries as well as other non-local structures emerge are explored in detail. Further, a preliminary exploration of such issues in Lorentzian space-times with non-trivial causal structures within string theory is initiated.
Stochastic geometry and its applications
Chiu, Sung Nok; Kendall, Wilfrid S; Mecke, Joseph
2013-01-01
An extensive update to a classic text Stochastic geometry and spatial statistics play a fundamental role in many modern branches of physics, materials sciences, engineering, biology and environmental sciences. They offer successful models for the description of random two- and three-dimensional micro and macro structures and statistical methods for their analysis. The previous edition of this book has served as the key reference in its field for over 18 years and is regarded as the best treatment of the subject of stochastic geometry, both as a subject with vital a
Algebraic geometry and theta functions
Coble, Arthur B
1929-01-01
This book is the result of extending and deepening all questions from algebraic geometry that are connected to the central problem of this book: the determination of the tritangent planes of a space curve of order six and genus four, which the author treated in his Colloquium Lecture in 1928 at Amherst. The first two chapters recall fundamental ideas of algebraic geometry and theta functions in such fashion as will be most helpful in later applications. In order to clearly present the state of the central problem, the author first presents the better-known cases of genus two (Chapter III) and
Introduction to topology and geometry
Stahl, Saul
2014-01-01
An easily accessible introduction to over three centuries of innovations in geometry Praise for the First Edition ". . . a welcome alternative to compartmentalized treatments bound to the old thinking. This clearly written, well-illustrated book supplies sufficient background to be self-contained." -CHOICE This fully revised new edition offers the most comprehensive coverage of modern geometry currently available at an introductory level. The book strikes a welcome balance between academic rigor and accessibility, providing a complete and cohesive picture of the science with an unparallele
Combinatorial geometry in the plane
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
Lectures on Algebraic Geometry I
Harder, Gunter
2012-01-01
This book and the following second volume is an introduction into modern algebraic geometry. In the first volume the methods of homological algebra, theory of sheaves, and sheaf cohomology are developed. These methods are indispensable for modern algebraic geometry, but they are also fundamental for other branches of mathematics and of great interest in their own. In the last chapter of volume I these concepts are applied to the theory of compact Riemann surfaces. In this chapter the author makes clear how influential the ideas of Abel, Riemann and Jacobi were and that many of the modern metho
Kremer-Aach, Andreas; Kläui, Wolfgang; Bell, Ralf; Strerath, Angela; Wunderlich, Hartmut; Mootz, Dietrich
1997-04-09
The reaction of cobalt(II) perchlorate with 1 equiv each of potassium hydroxide and potassium hydrotris(3-phenylpyrazolyl)borate (KTp(Ph)) leads to the formation of the blood-red bis(ligand) complex [Co(eta(3)-Tp(Ph))(eta(2)-Tp(Ph))]. This compound crystallizes in the monoclinic space group P2(1)/n, with a = 10.690(5) Å, b = 34.243(15) Å, c = 12.923(4) Å, beta = 96.17(3) degrees, Z = 4, V = 4703(3) Å(3), and R = 0.040. The molecular structure contains a square CoN(5) pyramid with an agostic BH.Co interaction of 2.17(2) Å. One Tp(Ph) ligand acts tridentate; the other, bidentate. The reaction of KTp(Ph) with zinc and cobalt halides yields a series of heteroleptic halogeno complexes [(Tp(Ph))MX]. The zinc species are all tetrahedral, while in the case of cobalt(II) the UV-vis spectra indicate an equilibrium of tetra- and pentacoordinated species depending on the anion size and the donor properties of the solvent. Metathesis reactions with carboxylates yield mononuclear complexes [(Tp(Ph))M(O(2)CR)]; M = Zn(II), Co(II); RCO(2)(-) = acetate, benzoate, 4-fluorobenzoate, and 4-nitrobenzoate. The infrared bands nu(as)(CO(2)) and nu(sym)(CO(2)) indicate monodentate carboxylate ligands in the zinc complexes in the solid state and in solution. The cobalt complexes [(Tp(Ph))Co(carboxylate)] are dark blue in dichloromethane and in the solid state when grown from dichloromethane solution. Tetrahydrofuran solutions and crystals grown from tetrahydrofuran are pink, purple, or reddish violet. The 2-aminobenzoate (anthranilate) complexes [(Th(Ph))M(anthranilate)], M = Zn(II), Co(II), have been prepared. [(eta(3)-Tp(Ph))Zn(anthranilate)] crystallizes in the monoclinic space group P2(1)/n, with a = 13.205(4) Å, b = 15.643(3) Å, c = 15.116(3) Å, beta = 98.86(2) degrees, Z = 4, V = 3085(1) Å(3), and R = 0.034. Anthranilate acts as a chelating oxygen ligand with Zn-O distances of 1.932(2) and 2.460(2) Å. The amino group is not involved in metal coordination. The reaction of the
Teaching Activity-Based Taxicab Geometry
Ada, Tuba
2013-01-01
This study aimed on the process of teaching taxicab geometry, a non-Euclidean geometry that is easy to understand and similar to Euclidean geometry with its axiomatic structure. In this regard, several teaching activities were designed such as measuring taxicab distance, defining a taxicab circle, finding a geometric locus in taxicab geometry, and…
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.
Wave-equation migration in generalized coordinate systems
Shragge, Jeffrey
Wave-equation migration using one-way wavefield extrapolation operators is commonly used in industry to generate images of complex geologic structure from 3D seismic data. By design, most conventional wave-equation approaches restrict propagation to downward continuation, where wavefields are recursively extrapolated to depth on Cartesian meshes. In practice, this approach is limited in high-angle accuracy and is restricted to down-going waves, which precludes the use of some steep dip and all turning wave components important for imaging targets in such areas as steep salt body flanks. This thesis discusses a strategy for improving wavefield extrapolation based on extending wavefield propagation to generalized coordinate system geometries that are more conformal to the wavefield propagation direction and permit imaging with turning waves. Wavefield propagation in non-Cartesian coordinates requires properly specifying the Laplacian operator in the governing Helmholtz equation. By employing differential geometry theory, I demonstrate how generalized a Riemannian wavefield extrapolation (RWE) procedure can be developed for any 3D non-orthogonal coordinate system, including those constructed by smoothing ray-based coordinate meshes formed from a suite of traced rays. I present 2D and 3D generalized RWE propagation examples illustrating the improved steep-dip propagation afforded by the coordinate transformation. One consequence of using non-Cartesian coordinates, though, is that the corresponding 3D extrapolation operators have up to 10 non-stationary coefficients, which can lead to imposing (and limiting) computer memory constraints for realistic 3D applications. To circumvent this difficulty, I apply the generalized RWE theory to analytic coordinate systems, rather than numerically generated meshes. Analytic coordinates offer the advantage of having straightforward analytic dispersion relationships and easy-to-implement extrapolation operators that add little
Microsphere Assemblies via Phosphonate Monoester Coordination Chemistry.
Bladek, Kamila J; Reid, Margaret E; Nishihara, Hirotomo; Akhtar, Farid; Gelfand, Benjamin S; Shimizu, George K H
2018-02-01
By complexing a bent phosphonate monoester ligand with cobalt(II), coupled with in situ ester hydrolysis, coordination microspheres (CALS=CALgary Sphere) are formed whereas the use of the phosphonic acid directly resulted in a sheet-like structure. Manipulation of the synthetic conditions gave spheres with different sizes, mechanical stabilities, and porosities. Time-dependent studies determined that the sphere formation likely occurred through the formation of a Co 2+ and ligand chain that propagates in three dimensions through different sets of interactions. The relative rates of these assembly processes versus annealing by ester hydrolysis and metal dehydration determine the growth of the microspheres. Hardness testing by nanoindentation is carried out on the spheres and sheets. Notably, no templates or capping agents are employed, the growth of the spheres is intrinsic to the ligand geometry and the coordination chemistry of cobalt(II) and the phosphonate monoester. © 2018 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.
Normal forms in Poisson geometry
Marcut, I.T.
2013-01-01
The structure of Poisson manifolds is highly nontrivial even locally. The first important result in this direction is Conn's linearization theorem around fixed points. One of the main results of this thesis (Theorem 2) is a normal form theorem in Poisson geometry, which is the Poisson-geometric
Math Sense: Algebra and Geometry.
Howett, Jerry
This book is designed to help students gain the range of math skills they need to succeed in life, work, and on standardized tests; overcome math anxiety; discover math as interesting and purposeful; and develop good number sense. Topics covered in this book include algebra and geometry. Lessons are organized around four strands: (1) skill lessons…
College geometry a unified development
Kay, David C
2011-01-01
""The book is a comprehensive textbook on basic geometry. … Key features of the book include numerous figures and many problems, more than half of which come with hints or even complete solutions. Frequent historical comments add to making the reading a pleasant one.""-Michael Joswig, Zentralblatt MATH 1273
Analogical Reasoning in Geometry Education
Magdas, Ioana
2015-01-01
The analogical reasoning isn't used only in mathematics but also in everyday life. In this article we approach the analogical reasoning in Geometry Education. The novelty of this article is a classification of geometrical analogies by reasoning type and their exemplification. Our classification includes: analogies for understanding and setting a…
Algebraic Methods in Plane Geometry
Indian Academy of Sciences (India)
Srimath
group, taxicab number, Carmi- chael number. Algebraic Methods in Plane Geometry. 2. Cubic Curves. Shailesh A Shirali. Shailesh Shirali heads a. Community Mathematics. Center at Rishi Valley. School (KFI). He has a ..... Ian Stewart and David Tall, Algebraic Number Theory and Fermat's Last. Theorem, A K Peters, 2002.
Fractal geometry and stochastics IV
Bandt, Christoph
2010-01-01
Over the years fractal geometry has established itself as a substantial mathematical theory in its own right. This book collects survey articles covering many of the developments, like Schramm-Loewner evolution, fractal scaling limits, exceptional sets for percolation, and heat kernels on fractals.
Learners engaging with transformation geometry
African Journals Online (AJOL)
able to move flexibly between the modes and who displayed a deep understanding of the concepts. ... However the strand remains in the curriculum for Grades R to 9, and will still provide rich learning opportunities ... There is limited available research on learners' understanding and learning of transformation geometry.
Optimization Problems in Elementary Geometry
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 13; Issue 6. Optimization Problems in Elementary Geometry. A K Mallik. General Article Volume 13 Issue 6 June 2008 pp 561-582 ... Author Affiliations. A K Mallik1. Department Of Mechanical Engineering, Indian Institute of Technology, Kanpur, India.
Multivariable calculus and differential geometry
Walschap, Gerard
2015-01-01
This text is a modern in-depth study of the subject that includes all the material needed from linear algebra. It then goes on to investigate topics in differential geometry, such as manifolds in Euclidean space, curvature, and the generalization of the fundamental theorem of calculus known as Stokes' theorem.
M. Deza; M. Laurent (Monique)
1997-01-01
htmlabstractCuts and metrics are well-known objects that arise - independently, but with many deep and fascinating connections - in diverse fields: in graph theory, combinatorial optimization, geometry of numbers, combinatorial matrix theory, statistical physics, VLSI design etc. This book offers a
Stochastic Modelling of River Geometry
DEFF Research Database (Denmark)
Sørensen, John Dalsgaard; Schaarup-Jensen, K.
1996-01-01
Numerical hydrodynamic river models are used in a large number of applications to estimate critical events for rivers. These estimates are subject to a number of uncertainties. In this paper, the problem to evaluate these estimates using probabilistic methods is considered. Stochastic models for ...... for river geometries are formulated and a coupling between hydraulic computational methods and numerical reliability methods is presented....
Axiomatic Differential Geometry Ⅱ-4
Nishimura, Hirokazu
2012-01-01
In our previous paper (Axiomatic Differential Geometry II-3) we havediscussed the general Jacobi identity, from which the Jacobi identity ofvector fields follows readily. In this paper we derive Jacobi-like identitiesof tangent-vector-valued forms from the general Jacobi identity.
Axiomatic Differential Geometry II-3
Nishimura, Hirokazu
2012-01-01
As the fourth paper of our series of papers concerned with axiomatic differential geometry, this paper is devoted to the general Jacobi identity supporting the Jacobi identity of vector fields. The general Jacobi identity can be regarded as one of the few fundamental results belonging properly to smootheology.
Axiomatic Differential Geometry II-4
Nishimura, Hirokazu
2012-01-01
In our previous paper (Axiomatic Differential Geometry II-3) we have discussed the general Jacobi identity, from which the Jacobi identity of vector fields follows readily. In this paper we derive Jacobi-like identities of tangent-vector-valued forms from the general Jacobi identity.
Improving Student Reasoning in Geometry
Wong, Bobson; Bukalov, Larisa
2013-01-01
In their years of teaching geometry, Wong and Bukalov realized that the greatest challenge has been getting students to improve their reasoning. Many students have difficulty writing formal proofs--a task that requires a good deal of reasoning. Wong and Bukalov reasoned that the solution was to divide the lessons into parallel tasks, allowing…
Fubini theorem in noncommutative geometry
Sukochev, Fedor; Zanin, Dmitriy
2016-01-01
We discuss the Fubini formula in Alain Connes' noncommutative geometry. We present a sufficient condition on spectral triples for which a Fubini formula holds true. The condition is natural and related to heat semigroup asymptotics. We provide examples of spectral triples for which the Fubini formula fails.
The curvature coordinate system
DEFF Research Database (Denmark)
Almegaard, Henrik
2007-01-01
The paper describes a concept for a curvature coordinate system on regular curved surfaces from which faceted surfaces with plane quadrangular facets can be designed. The lines of curvature are used as parametric lines for the curvature coordinate system on the surface. A new conjugate set of lines......, called middle curvature lines, is introduced. These lines define the curvature coordinate system. Using the curvature coordinate system, the surface can be conformally mapped on the plane. In this mapping, elliptic sections are mapped as circles, and hyperbolic sections are mapped as equilateral...... hyperbolas. This means that when a plane orthogonal system of curves for which the vertices in a mesh always lie on a circle is mapped on a surface with positive Gaussian curvature using inverse mapping, and the mapped vertices are connected by straight lines, this network will form a faceted surface...
Environmental Compliance Issue Coordination
An order to establish the Department of Energy (DOE) requirements for coordination of significant environmental compliance issues to ensure timely development and consistent application of Departmental environmental policy and guidance
Supercritical Airfoil Coordinates
National Aeronautics and Space Administration — Rectangular Supercritical Wing (Ricketts) - design and measured locations are provided in an Excel file RSW_airfoil_coordinates_ricketts.xls . One sheet is with Non...
Indian Academy of Sciences (India)
Limit: (of a sequence) A point such that the points of the sequence eventually approach it to within any previously specified distance. Some of the Greek mathematicians were quite confused! For example, let us take an empty cup and put it under a tap. Assume that it is half full in a minute. It is then 3/4-th full in another half.
Indian Academy of Sciences (India)
cartographer in the days before aerial travel) can determine the curvature. Hence the beauty of a surface is skin deep and yet is naturally associated with it! SERIES I ARTICLE cartographic surveys he was carrying out for the ruler of Germany) gave a new interpretation to Euler's theory. First consider the length of the vector t ...
Indian Academy of Sciences (India)
In order to utilise this Descartes devised the following scheme. By. fIXing a point, the origin, on a line it becomes possible to talk of a directed distance as a positive or negative number depending on whether the end point is to one or the other side of the origin. Similarly, he assigned a pair of numbers to every point of the.
Calcaterra, Craig; Boldt, Axel; Green, Michael; Bleecker, David
2002-01-01
Coordinate systems are defined on general metric spaces with the purpose of generalizing vector fields on a manifold. Conversion formulae are available between metric and Cartesian coordinates on a Hilbert space. Nagumo's Invariance Theorem is invoked to prove the analogue of the classical Cauchy-Lipschitz Theorem for vector fields on a locally compact coordinatized space. A metric space version of Nagumo's Theorem is one consequence. Examples are given throughout.
Painleve-gullstrand-type Coordinates for the Five-dimensional Myers-Perry Black Hole
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.
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.
Elizalde, J; Lorente, M
2006-01-01
The progressive incorporation of organ transplants as a therapeutic resource resulted in organisational adaptation and overall transplant management, leading to the emergence of the figure of the transplant coordinator in the mid-1980s. In Spain, the National Organisation of Transplants (Organización Nacional de Transplantes - ONT) was created, establishing a system - called the "Spanish model" - based on a network of coordinators at three levels: national, the autonomous community and the hospital. This organisational structure is a point of reference at the world level. The prevalence of the Intensive Medicine specialisation amongst hospital transplant coordinators is remarkable. The majority of organs proceed from brain-dead patients with beating hearts and this requires the infrastructure offered by intensive care units. The functions of the coordinator can be summarised in guaranteeing a synchrony of all the elements and teams that come together in an organisational chain that has come to be called the "process of donation". Schematically, the crucial points that the hospital coordinator develops are the following: - Detection of the potential donor. - Maintenance of the donor. - Diagnosis of brain death. - Family consent. - Preparation of the hospital logistics. - Helping the relatives. - Direct involvement in the Program of Guarantee of Quality. - Person of reference in any activity related to the transplant. It would be desirable to achieve the creation of transplant coordination teams, with univocal messages, professionalism and a permanent input of the so-called "human factor", which is so necessary and also so close to the transplant world.
Lee, Na Young; Mandal, Debasish; Bae, Seong Hee; Seo, Mi Sook; Lee, Yong-Min; Shaik, Sason
2017-01-01
The spin states (S = 1 and S = 2) of nonheme FeIVO intermediates are believed to play an important role in determining their chemical properties in enzymatic and biomimetic reactions. However, it is almost impossible to investigate the spin state effect of nonheme FeIVO species experimentally, since FeIVO models having the S = 1 and S = 2 spin states at the same time neither exist nor can be synthesized. However, recent synthesis of an FeIVO complex with an S = 1 spin state (triplet), [(Me3NTB)FeIVO]2+ (1), and a structurally similar FeIVO complex but with an S = 2 spin state (quintet), [(TQA)FeIVO]2+ (2), has allowed us to compare their reactivities at 233 K. In the present study, we show that structural variants control the spin-state selectivity and reactivity of nonheme FeIVO complexes. While 1 and 2 were proposed to be in an octahedral geometry based on DFT calculations and spectroscopic characterization done at 4 K, further DFT calculations show that these species may well assume a trigonal bipyramidal structure by losing one coordinated solvent ligand at 233 K. Thus, the present study demonstrates that the structure and spin state of nonheme FeIVO complexes can be different at different temperatures; therefore, the structural and/or spin state information obtained at 4 K should be carefully used at a higher temperature (e.g., 233 K). In addition to 1 and 2, [(TPA)FeIVO]2+ (3) with an S = 1 spin state, whose spin state was determined spectroscopically and theoretically at 233 K, is included in this study to compare the chemical properties of S = 1 and S = 2 FeIVO complexes. The present results add another dimension to the discussion of the reactivites of nonheme FeIVO species, in which the structural preference and spin state of nonheme FeIVO species can vary depending on temperature. PMID:28970926
Measuring Space-Time Geometry over the Ages
Energy Technology Data Exchange (ETDEWEB)
Stebbins, Albert; /Fermilab
2012-05-01
Theorists are often told to express things in the 'observational plane'. One can do this for space-time geometry, considering 'visual' observations of matter in our universe by a single observer over time, with no assumptions about isometries, initial conditions, nor any particular relation between matter and geometry, such as Einstein's equations. Using observables as coordinates naturally leads to a parametrization of space-time geometry in terms of other observables, which in turn prescribes an observational program to measure the geometry. Under the assumption of vorticity-free matter flow we describe this observational program, which includes measurements of gravitational lensing, proper motion, and redshift drift. Only 15% of the curvature information can be extracted without long time baseline observations, and this increases to 35% with observations that will take decades. The rest would likely require centuries of observations. The formalism developed is exact, non-perturbative, and more general than the usual cosmological analysis.
Separation of attractors in 1-modulus quantum corrected special geometry
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...
Protonated serotonin: Geometry, electronic structures and photophysical properties
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.
Geometry of shoot apical dome and distribution of growth rates
Directory of Open Access Journals (Sweden)
Jerzy Nakielski
2014-01-01
Full Text Available The distribution of the relative elementary rate of growth (RERG in apical domes of various shapes and patterns of displacement lines can be analytically examined. The geometry of these domes may be described by parabolas of n-th order, the variant of the distribution of linear growth rate should be established along any displacement line (e.g. along the axis and then the RERG can be studied as the function depending on the position coordinates and the parameter n. Such investigations of several aplical domes of various shapes have been performed. The results confirm the occurrence of the minimum of relative, elementary growth rate (in volume in the subapical region of the dome independently of the type of geometry (n parabola order.
Geometry-dependent atomic multipole models for the water molecule.
Loboda, O; Millot, C
2017-10-28
Models of atomic electric multipoles for the water molecule have been optimized in order to reproduce the electric potential around the molecule computed by ab initio calculations at the coupled cluster level of theory with up to noniterative triple excitations in an augmented triple-zeta quality basis set. Different models of increasing complexity, from atomic charges up to models containing atomic charges, dipoles, and quadrupoles, have been obtained. The geometry dependence of these atomic multipole models has been investigated by changing bond lengths and HOH angle to generate 125 molecular structures (reduced to 75 symmetry-unique ones). For several models, the atomic multipole components have been fitted as a function of the geometry by a Taylor series of fourth order in monomer coordinate displacements.
Grassmannian geometry of scattering amplitudes
Arkani-Hamed, Nima; Cachazo, Freddy; Goncharov, Alexander; Postnikov, Alexander; Trnka, Jaroslav
2016-01-01
Outlining a revolutionary reformulation of the foundations of perturbative quantum field theory, this book is a self-contained and authoritative analysis of the application of this new formulation to the case of planar, maximally supersymmetric Yang–Mills theory. The book begins by deriving connections between scattering amplitudes and Grassmannian geometry from first principles before introducing novel physical and mathematical ideas in a systematic manner accessible to both physicists and mathematicians. The principle players in this process are on-shell functions which are closely related to certain sub-strata of Grassmannian manifolds called positroids - in terms of which the classification of on-shell functions and their relations becomes combinatorially manifest. This is an essential introduction to the geometry and combinatorics of the positroid stratification of the Grassmannian and an ideal text for advanced students and researchers working in the areas of field theory, high energy physics, and the...
Euclidean distance geometry an introduction
Liberti, Leo
2017-01-01
This textbook, the first of its kind, presents the fundamentals of distance geometry: theory, useful methodologies for obtaining solutions, and real world applications. Concise proofs are given and step-by-step algorithms for solving fundamental problems efficiently and precisely are presented in Mathematica®, enabling the reader to experiment with concepts and methods as they are introduced. Descriptive graphics, examples, and problems, accompany the real gems of the text, namely the applications in visualization of graphs, localization of sensor networks, protein conformation from distance data, clock synchronization protocols, robotics, and control of unmanned underwater vehicles, to name several. Aimed at intermediate undergraduates, beginning graduate students, researchers, and practitioners, the reader with a basic knowledge of linear algebra will gain an understanding of the basic theories of distance geometry and why they work in real life.
Fractal geometry and computer graphics
Sakas, Georgios; Peitgen, Heinz-Otto; Englert, Gabriele
1992-01-01
Fractal geometry has become popular in the last 15 years, its applications can be found in technology, science, or even arts. Fractal methods and formalism are seen today as a general, abstract, but nevertheless practical instrument for the description of nature in a wide sense. But it was Computer Graphics which made possible the increasing popularity of fractals several years ago, and long after their mathematical formulation. The two disciplines are tightly linked. The book contains the scientificcontributions presented in an international workshop in the "Computer Graphics Center" in Darmstadt, Germany. The target of the workshop was to present the wide spectrum of interrelationships and interactions between Fractal Geometry and Computer Graphics. The topics vary from fundamentals and new theoretical results to various applications and systems development. All contributions are original, unpublished papers.The presentations have been discussed in two working groups; the discussion results, together with a...
Geometry of area without length
Ho, Pei-Ming; Inami, Takeo
2016-01-01
To define a free string by the Nambu-Goto action, all we need is the notion of area, and mathematically the area can be defined directly in the absence of a metric. Motivated by the possibility that string theory admits backgrounds where the notion of length is not well defined but a definition of area is given, we study space-time geometries based on the generalization of a metric to an area metric. In analogy with Riemannian geometry, we define the analogues of connections, curvatures, and Einstein tensor. We propose a formulation generalizing Einstein's theory that will be useful if at a certain stage or a certain scale the metric is ill defined and the space-time is better characterized by the notion of area. Static spherical solutions are found for the generalized Einstein equation in vacuum, including the Schwarzschild solution as a special case.
Foliation theory in algebraic geometry
McKernan, James; Pereira, Jorge
2016-01-01
Featuring a blend of original research papers and comprehensive surveys from an international team of leading researchers in the thriving fields of foliation theory, holomorphic foliations, and birational geometry, this book presents the proceedings of the conference "Foliation Theory in Algebraic Geometry," hosted by the Simons Foundation in New York City in September 2013. Topics covered include: Fano and del Pezzo foliations; the cone theorem and rank one foliations; the structure of symmetric differentials on a smooth complex surface and a local structure theorem for closed symmetric differentials of rank two; an overview of lifting symmetric differentials from varieties with canonical singularities and the applications to the classification of AT bundles on singular varieties; an overview of the powerful theory of the variety of minimal rational tangents introduced by Hwang and Mok; recent examples of varieties which are hyperbolic and yet the Green-Griffiths locus is the whole of X; and a classificati...
The geometry of celestial mechanics
Geiges, Hansjörg
2016-01-01
Celestial mechanics is the branch of mathematical astronomy devoted to studying the motions of celestial bodies subject to the Newtonian law of gravitation. This mathematical introductory textbook reveals that even the most basic question in celestial mechanics, the Kepler problem, leads to a cornucopia of geometric concepts: conformal and projective transformations, spherical and hyperbolic geometry, notions of curvature, and the topology of geodesic flows. For advanced undergraduate and beginning graduate students, this book explores the geometric concepts underlying celestial mechanics and is an ideal companion for introductory courses. The focus on the history of geometric ideas makes it perfect supplementary reading for students in elementary geometry and topology. Numerous exercises, historical notes and an extensive bibliography provide all the contextual information required to gain a solid grounding in celestial mechanics.
Differential geometry and mathematical physics
Rudolph, Gerd
Starting from an undergraduate level, this book systematically develops the basics of • Calculus on manifolds, vector bundles, vector fields and differential forms, • Lie groups and Lie group actions, • Linear symplectic algebra and symplectic geometry, • Hamiltonian systems, symmetries and reduction, integrable systems and Hamilton-Jacobi theory. The topics listed under the first item are relevant for virtually all areas of mathematical physics. The second and third items constitute the link between abstract calculus and the theory of Hamiltonian systems. The last item provides an introduction to various aspects of this theory, including Morse families, the Maslov class and caustics. The book guides the reader from elementary differential geometry to advanced topics in the theory of Hamiltonian systems with the aim of making current research literature accessible. The style is that of a mathematical textbook,with full proofs given in the text or as exercises. The material is illustrated by numerous d...
Hyperbolic geometry for colour metrics.
Farup, Ivar
2014-05-19
It is well established from both colour difference and colour order perpectives that the colour space cannot be Euclidean. In spite of this, most colour spaces still in use today are Euclidean, and the best Euclidean colour metrics are performing comparably to state-of-the-art non-Euclidean metrics. In this paper, it is shown that a transformation from Euclidean to hyperbolic geometry (i.e., constant negative curvature) for the chromatic plane can significantly improve the performance of Euclidean colour metrics to the point where they are statistically significantly better than state-of-the-art non-Euclidean metrics on standard data sets. The resulting hyperbolic geometry nicely models both qualitatively and quantitatively the hue super-importance phenomenon observed in colour order systems.
Groups and Geometries : Siena Conference
Kantor, William; Lunardon, Guglielmo; Pasini, Antonio; Tamburini, Maria
1998-01-01
On September 1-7, 1996 a conference on Groups and Geometries took place in lovely Siena, Italy. It brought together experts and interested mathematicians from numerous countries. The scientific program centered around invited exposi tory lectures; there also were shorter research announcements, including talks by younger researchers. The conference concerned a broad range of topics in group theory and geometry, with emphasis on recent results and open problems. Special attention was drawn to the interplay between group-theoretic methods and geometric and combinatorial ones. Expanded versions of many of the talks appear in these Proceedings. This volume is intended to provide a stimulating collection of themes for a broad range of algebraists and geometers. Among those themes, represented within the conference or these Proceedings, are aspects of the following: 1. the classification of finite simple groups, 2. the structure and properties of groups of Lie type over finite and algebraically closed fields of f...
Interaction geometry: an ecological perspective.
Rolfe A. Leary
1976-01-01
A new mathematical coordinate system results from a unique combination of two frameworks long used by ecologists: the phase plane and coaction cross-tabulation. The resulting construct combines the classifying power of the cross-tabulation and discriminating power of the phase plane. It may be used for analysis and synthesis.
Algebraic Methods in Plane Geometry
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 13; Issue 10. Algebraic Methods in ... General Article Volume 13 Issue 10 October 2008 pp 916-928 ... Keywords. Conics; family of curves; Pascal's theorem; homogeneous coordinates; Butterfly theorem; abelian group; associativity of addition; group law.
The geometry of continuum regularization
Energy Technology Data Exchange (ETDEWEB)
Halpern, M.B.
1987-03-01
This lecture is primarily an introduction to coordinate-invariant regularization, a recent advance in the continuum regularization program. In this context, the program is seen as fundamentally geometric, with all regularization contained in regularized DeWitt superstructures on field deformations.
General Relativity by Kawaguchi geometry
Directory of Open Access Journals (Sweden)
Tanaka Erico
2013-09-01
Full Text Available We construct a parameterisation invariant Lagrange theory of fields up to second order by using multivector bundles and Kawaguchi geometry. In this setup, the spacetime is an dynamical object which is a submanifold of the greater manifold, and the actual spacetime is the solution of Euler-Lagrange equations. Such theory is a reasonable mathematical foundation to describe an extended theory of Einstein’s general relativity, and is capable of being a stage for unification with other physical fields.
Geometry Dependence of Stellarator Turbulence
Energy Technology Data Exchange (ETDEWEB)
H.E. Mynick, P. Xanthopoulos and A.H. Boozer
2009-08-10
Using the nonlinear gyrokinetic code package GENE/GIST, we study the turbulent transport in a broad family of stellarator designs, to understand the geometry-dependence of the microturbulence. By using a set of flux tubes on a given flux surface, we construct a picture of the 2D structure of the microturbulence over that surface, and relate this to relevant geometric quantities, such as the curvature, local shear, and effective potential in the Schrodinger-like equation governing linear drift modes.
Topics in modern differential geometry
Verstraelen, Leopold
2017-01-01
A variety of introductory articles is provided on a wide range of topics, including variational problems on curves and surfaces with anisotropic curvature. Experts in the fields of Riemannian, Lorentzian and contact geometry present state-of-the-art reviews of their topics. The contributions are written on a graduate level and contain extended bibliographies. The ten chapters are the result of various doctoral courses which were held in 2009 and 2010 at universities in Leuven, Serbia, Romania and Spain.
Brock, David S; Casalis de Pury, Jonathan J; Mercier, Hélène P A; Schrobilgen, Gary J; Silvi, Bernard
2010-07-19
The syntheses and structural characterizations of the [XOF(2)][AsF(6)] (X = Cl, Br) salts and the XeF(2) adduct-salts, [BrOF(2)][AsF(6)].nXeF(2) (n = 1, 2), are described. Although the [XOF(2)][AsF(6)] salts have been known for some time, their crystal structures had not been reported until the present study. The crystal structure of [BrOF(2)][AsF(6)] shows a positional disorder among the oxygen atom and the fluorine atoms. Both ClOF(2)(+) and BrOF(2)(+) have pseudo-octahedral coordination with a primary tripodal coordination sphere consisting of an oxygen atom and two fluorine atoms and a secondary coordination sphere consisting of three long contacts to fluorine atoms of different AsF(6)(-) anions. The low-temperature Raman spectra of [XOF(2)][AsF(6)] have been assigned on the basis of the crystal structures and with the aid of quantum-chemical calculations using [XOF(2)][AsF(6)](3)(2-) as a model for the crystallographic environment of XOF(2)(+). Several examples of XeF(2) coordinated through fluorine to transition metal centers are known, but no crystallographically characterized examples of XeF(2) coordinated to a nonmetal center other than xenon are known. The complex cation salts, [BrOF(2)][AsF(6)].nXeF(2) (n = 1, 2), were synthesized, and their Raman spectra have been assigned with the aid of quantum-chemical calculations. Although the structure of [BrOF(2)][AsF(6)].2XeF(2) is similar to that of the recently reported krypton analogue, notable differences occur. The contact distances between bromine and the fluorine atoms of NgF(2) (Ng = Kr, Xe) are shorter in [BrOF(2)][AsF(6)].2XeF(2) than in the KrF(2) analogue, which is attributed to the more polar natures of the Xe-F bonds. Unlike [BrOF(2)][AsF(6)].2KrF(2), which has been shown in the prior study to be stable in HF solution at room temperature, [BrOF(2)][AsF(6)].2XeF(2) enters into a dissociative equilibrium in which fluoride ion abstraction by BrOF(2)(+) occurs to give Xe(2)F(3)(+) and BrOF(3). The ELF
Riemannian geometry and geometric analysis
Jost, Jürgen
2017-01-01
This established reference work continues to provide its readers with a gateway to some of the most interesting developments in contemporary geometry. It offers insight into a wide range of topics, including fundamental concepts of Riemannian geometry, such as geodesics, connections and curvature; the basic models and tools of geometric analysis, such as harmonic functions, forms, mappings, eigenvalues, the Dirac operator and the heat flow method; as well as the most important variational principles of theoretical physics, such as Yang-Mills, Ginzburg-Landau or the nonlinear sigma model of quantum field theory. The present volume connects all these topics in a systematic geometric framework. At the same time, it equips the reader with the working tools of the field and enables her or him to delve into geometric research. The 7th edition has been systematically reorganized and updated. Almost no page has been left unchanged. It also includes new material, for instance on symplectic geometry, as well as the B...
Number theory III Diophantine geometry
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 ...
Introduction to geometry and relativity
2013-01-01
This book provides a lucid introduction to both modern differential geometry and relativity for advanced undergraduates and first-year graduate students of applied mathematics and physical sciences. This book meets an overwhelming need for a book on modern differential geometry and relativity that is student-friendly, and which is also suitable for self-study. The book presumes a minimal level of mathematical maturity so that any student who has completed the standard Calculus sequence should be able to read and understand the book. The key features of the book are: Detailed solutions are provided to the Exercises in each chapter; Many of the missing steps that are often omitted from standard mathematical derivations have been provided to make the book easier to read and understand; A detailed introduction to Electrodynamics is provided so that the book is accessible to students who have not had a formal course in this area; In its treatment of modern differential geometry, the book employs both a modern, c...
Aspects of differential geometry II
Gilkey, Peter
2015-01-01
Differential Geometry is a wide field. We have chosen to concentrate upon certain aspects that are appropriate for an introduction to the subject; we have not attempted an encyclopedic treatment. Book II deals with more advanced material than Book I and is aimed at the graduate level. Chapter 4 deals with additional topics in Riemannian geometry. Properties of real analytic curves given by a single ODE and of surfaces given by a pair of ODEs are studied, and the volume of geodesic balls is treated. An introduction to both holomorphic and Kähler geometry is given. In Chapter 5, the basic properties of de Rham cohomology are discussed, the Hodge Decomposition Theorem, Poincaré duality, and the Künneth formula are proved, and a brief introduction to the theory of characteristic classes is given. In Chapter 6, Lie groups and Lie algebras are dealt with. The exponential map, the classical groups, and geodesics in the context of a bi-invariant metric are discussed. The de Rham cohomology of compact Lie groups an...
Algebraic Geometry and Number Theory Summer School
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 success in 20 minutes a day
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
Coordinating Interactions: The Event Coordination Notation
DEFF Research Database (Denmark)
Kindler, Ekkart
The purpose of a domain model is to concisely capture the concepts of an application’s domain, and their relation among each other. Even though the main purpose of domain models is not on implementing the application, major parts of an application can be generated from the application’s domain...... on a much more technical level. The Event Coordination Notation (ECNO) allows modelling the behaviour of an application on a high level of abstraction that is closer to the application’s domain than to the software realizing it. Still, these models contain all necessary details for actually executing...... models fully automatically with today’s technologies. The focus of today’s code generation technologies, however, is mostly on the structural aspects of the domain; the domain’s behaviour is often not modelled at all, or implemented manually based on some informal models, or the behaviour is modelled...
Introduction to Coordination Chemistry
Lawrance, Geoffrey Alan
2010-01-01
Introduction to Coordination Chemistry examines and explains how metals and molecules that bind as ligands interact, and the consequences of this assembly process. This book describes the chemical and physical properties and behavior of the complex assemblies that form, and applications that may arise as a result of these properties. Coordination complexes are an important but often hidden part of our world?even part of us?and what they do is probed in this book. This book distills the essence of this topic for undergraduate students and for research scientists.
Polymeric coordination compounds
Indian Academy of Sciences (India)
Administrator
Metal coordination polymers with one- and two-dimensional structures are of current interest due to their possible relevance to material science 1. In continuation of our previous studies 2,3, several new polymeric compounds are reported here. Among the complexes of silver with aminomethyl pyridine (amp) ...
K.R. Apt (Krzysztof); M.M. Rahn (Mona); G. Schäfer (Guido); S.E. Simon (Sunil)
2014-01-01
htmlabstractWe introduce natural strategic games on graphs, which capture the idea of coordination in a local setting.We show that these games have an exact potential and have strong equilibria when the graph is a pseudoforest. We also exhibit some other classes of games for which a strong
Dimensions of Organizational Coordination
DEFF Research Database (Denmark)
Jensen, Andreas Schmidt; Aldewereld, Huib; Dignum, Virginia
2013-01-01
be supported to include organizational objectives and constraints into their reasoning processes by considering two alternatives: agent reasoning and middleware regulation. We show how agents can use an organizational specification to achieve organizational objectives by delegating and coordinating...... their activities with other agents in the society, using the GOAL agent programming language and the OperA organizational model....
Coordination Compounds in Biology
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 4; Issue 6. Coordination Compounds in Biology - The Chemistry of Vitamin B12 and Model Compounds. K Hussian Reddy. General Article Volume 4 Issue 6 June 1999 pp 67-77 ...
Recursive Advice for Coordination
DEFF Research Database (Denmark)
Terepeta, Michal Tomasz; Nielson, Hanne Riis; Nielson, Flemming
2012-01-01
Aspect-oriented programming is a programming paradigm that is often praised for the ability to create modular software and separate cross-cutting concerns. Recently aspects have been also considered in the context of coordination languages, offering similar advantages. However, introducing aspects...
Apt, K.R.; Rahn, M.; Schäfer, G.; Simon, S.; Liu, T.-Y.; Qi, Q.; Ye, Y.
2014-01-01
We introduce natural strategic games on graphs, which capture the idea of coordination in a local setting. We show that these games have an exact potential and have strong equilibria when the graph is a pseudoforest. We also exhibit some other classes of graphs for which a strong equilibrium exists.
Coordinating Supplemental Reading Instruction
Deeney, Theresa A.
2008-01-01
Although supplemental reading services are meant to improve reading achievement of struggling readers and students with reading disabilities, without concerted effort to ensure communication and coordination with in-school instruction, they may fall short of their desired mark. To promote learning, it is critical that any services provided outside…
Blow-Ups in Generalized Complex Geometry
van der Leer Duran, J.L.
2016-01-01
Generalized complex geometry is a theory that unifies complex geometry and symplectic geometry into one single framework. It was introduced by Hitchin and Gualtieri around 2002. In this thesis we address the following question: given a generalized complex manifold together with a submanifold, does
Geometry in the Early Years: A Commentary
Dindyal, Jaguthsing
2015-01-01
The primary goal of this paper is to provide a commentary on the teaching and learning of geometry in the early years of schooling with the set of papers in this issue as a guiding factor. It is structured around issues about geometry education of young learners, such as: what should we teach in geometry and why; representation of geometrical…
Global affine differential geometry of hypersurfaces
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.
Directory of Open Access Journals (Sweden)
Bruchholz U. E.
2009-10-01
Full Text Available The geometry of the space-time is deduced from gravitational and electromagnetic fields. We have to state that Rainich's "already unified field theory" is the ground work of the proposed theory. The latter is deduced independently on Rainich. Rainich's analogies are brilliantly validated. His formulae are verified this way. Further reaching results and insights demonstrate that Rainich's theory is viable. In final result, we can formulate an enhanced equivalence principle. It is the equivalence of Newton's force with the Lorentz force.
The geometry of musical chords.
Tymoczko, Dmitri
2006-07-07
A musical chord can be represented as a point in a geometrical space called an orbifold. Line segments represent mappings from the notes of one chord to those of another. Composers in a wide range of styles have exploited the non-Euclidean geometry of these spaces, typically by using short line segments between structurally similar chords. Such line segments exist only when chords are nearly symmetrical under translation, reflection, or permutation. Paradigmatically consonant and dissonant chords possess different near-symmetries and suggest different musical uses.
Porous media geometry and transports
Adler, Pierre
1992-01-01
The goal of ""Porous Media: Geometry and Transports"" is to provide the basis of a rational and modern approach to porous media. This book emphasizes several geometrical structures (spatially periodic, fractal, and random to reconstructed) and the three major single-phase transports (diffusion, convection, and Taylor dispersion).""Porous Media"" serves various purposes. For students it introduces basic information on structure and transports. Engineers will find this book useful as a readily accessible assemblage of al the major experimental results pertaining to single-phase tr
Integral geometry and representation theory
Gel'fand, I M; Vilenkin, N Ya
1966-01-01
Generalized Functions, Volume 5: Integral Geometry and Representation Theory is devoted to the theory of representations, focusing on the group of two-dimensional complex matrices of determinant one.This book emphasizes that the theory of representations is a good example of the use of algebraic and geometric methods in functional analysis, in which transformations are performed not on the points of a space, but on the functions defined on it. The topics discussed include Radon transform on a real affine space, integral transforms in the complex domain, and representations of the group of comp
Projective differential geometry of submanifolds
Akivis, M A
1993-01-01
In this book, the general theory of submanifolds in a multidimensional projective space is constructed. The topics dealt with include osculating spaces and fundamental forms of different orders, asymptotic and conjugate lines, submanifolds on the Grassmannians, different aspects of the normalization problems for submanifolds (with special emphasis given to a connection in the normal bundle) and the problem of algebraizability for different kinds of submanifolds, the geometry of hypersurfaces and hyperbands, etc. A series of special types of submanifolds with special projective structures are s
An invitation to noncommutative geometry
Marcolli, Matilde
2008-01-01
This is the first existing volume that collects lectures on this important and fast developing subject in mathematics. The lectures are given by leading experts in the field and the range of topics is kept as broad as possible by including both the algebraic and the differential aspects of noncommutative geometry as well as recent applications to theoretical physics and number theory. Sample Chapter(s). A Walk in the Noncommutative Garden (1,639 KB). Contents: A Walk in the Noncommutative Garden (A Connes & M Marcolli); Renormalization of Noncommutative Quantum Field Theory (H Grosse & R Wulke
Projective geometry and projective metrics
Busemann, Herbert
2005-01-01
The basic results and methods of projective and non-Euclidean geometry are indispensable for the geometer, and this book--different in content, methods, and point of view from traditional texts--attempts to emphasize that fact. Results of special theorems are discussed in detail only when they are needed to develop a feeling for the subject or when they illustrate a general method. On the other hand, an unusual amount of space is devoted to the discussion of the fundamental concepts of distance, motion, area, and perpendicularity.Topics include the projective plane, polarities and conic sectio
Number Theory, Analysis and Geometry
Goldfeld, Dorian; Jones, Peter
2012-01-01
Serge Lang was an iconic figure in mathematics, both for his own important work and for the indelible impact he left on the field of mathematics, on his students, and on his colleagues. Over the course of his career, Lang traversed a tremendous amount of mathematical ground. As he moved from subject to subject, he found analogies that led to important questions in such areas as number theory, arithmetic geometry, and the theory of negatively curved spaces. Lang's conjectures will keep many mathematicians occupied far into the future. In the spirit of Lang's vast contribution to mathematics, th
Clustering in Hilbert simplex geometry
Nielsen, Frank
2017-04-03
Clustering categorical distributions in the probability simplex is a fundamental primitive often met in applications dealing with histograms or mixtures of multinomials. Traditionally, the differential-geometric structure of the probability simplex has been used either by (i) setting the Riemannian metric tensor to the Fisher information matrix of the categorical distributions, or (ii) defining the information-geometric structure induced by a smooth dissimilarity measure, called a divergence. In this paper, we introduce a novel computationally-friendly non-Riemannian framework for modeling the probability simplex: Hilbert simplex geometry. We discuss the pros and cons of those three statistical modelings, and compare them experimentally for clustering tasks.
Exceptional geometry and Borcherds superalgebras
Energy Technology Data Exchange (ETDEWEB)
Palmkvist, Jakob [Mitchell Institute for Fundamental Physics and Astronomy, Texas A& M University,College Station, TX 77843 (United States)
2015-11-05
We study generalized diffeomorphisms in exceptional geometry with U-duality group E{sub n(n)} from an algebraic point of view. By extending the Lie algebra e{sub n} to an infinite-dimensional Borcherds superalgebra, involving also the extension to e{sub n+1}, the generalized Lie derivatives can be expressed in a simple way, and the expressions take the same form for any n≤7. The closure of the transformations then follows from the Jacobi identity and the grading of e{sub n+1} with respect to e{sub n}.
Exceptional geometry and Borcherds superalgebras
Palmkvist, Jakob
2015-11-01
We study generalized diffeomorphisms in exceptional geometry with U-duality group E n( n) from an algebraic point of view. By extending the Lie algebra {e}_n to an infinite-dimensional Borcherds superalgebra, involving also the extension to {e}_{n+1} , the generalized Lie derivatives can be expressed in a simple way, and the expressions take the same form for any n ≤ 7. The closure of the transformations then follows from the Jacobi identity and the grading of {e}_{n+1} with respect to {e}_n.
Stochastic geometry for image analysis
Descombes, Xavier
2013-01-01
This book develops the stochastic geometry framework for image analysis purpose. Two main frameworks are described: marked point process and random closed sets models. We derive the main issues for defining an appropriate model. The algorithms for sampling and optimizing the models as well as for estimating parameters are reviewed. Numerous applications, covering remote sensing images, biological and medical imaging, are detailed. This book provides all the necessary tools for developing an image analysis application based on modern stochastic modeling.
What is Coordinated in Bimanual Coordination?
Mechsner, Franz; Prinz, Wolfgang
In periodic bimanual movements there is a characteristic spontaneous tendency towards mirror-symmetry. This phenomenon has widely been interpreted as a tendency towards co-activation of homologous muscles, possibly originating in motoric neuronal structures. The experiments reported here provide evidence contrary to this common claim. The symmetry tendency in bimanual abductive/adductive finger oscillation as well as in bimanual multi-finger tapping is actually towards spatial, perceptual symmetry, without regard to the muscles and thus to the motor commands involved. It is hypothesized that, as a rule, spontaneous coordination phenomena of this kind are purely perceptual-cognitive in nature. Moreover, in the case of a bimanual circling paradigm, the reported findings reveal that highly complex, even 'impossible' movements can easily be performed if, rather than the bodily movements themselves, simple sensory consequences are controlled. It is suggested that voluntary movements are organized by representing and controlling their perceptual goals or anticipated effects, whereas the corresponding motor activity of sometimes high formal complexity is rather spontaneously and flexibly tuned in service of these effects.
Computational geometry algorithms and applications
de Berg, Mark; Overmars, Mark; Schwarzkopf, Otfried
1997-01-01
Computational geometry emerged from the field of algorithms design and anal ysis in the late 1970s. It has grown into a recognized discipline with its own journals, conferences, and a large community of active researchers. The suc cess of the field as a research discipline can on the one hand be explained from the beauty of the problems studied and the solutions obtained, and, on the other hand, by the many application domains--computer graphics, geographic in formation systems (GIS), robotics, and others-in which geometric algorithms play a fundamental role. For many geometric problems the early algorithmic solutions were either slow or difficult to understand and implement. In recent years a number of new algorithmic techniques have been developed that improved and simplified many of the previous approaches. In this textbook we have tried to make these modem algorithmic solutions accessible to a large audience. The book has been written as a textbook for a course in computational geometry, but it can ...
Entanglement classification with algebraic geometry
Sanz, M.; Braak, D.; Solano, E.; Egusquiza, I. L.
2017-05-01
We approach multipartite entanglement classification in the symmetric subspace in terms of algebraic geometry, its natural language. We show that the class of symmetric separable states has the structure of a Veronese variety and that its k-secant varieties are SLOCC invariants. Thus SLOCC classes gather naturally into families. This classification presents useful properties such as a linear growth of the number of families with the number of particles, and nesting, i.e. upward consistency of the classification. We attach physical meaning to this classification through the required interaction length of parent Hamiltonians. We show that the states W N and GHZ N are in the same secant family and that, effectively, the former can be obtained in a limit from the latter. This limit is understood in terms of tangents, leading to a refinement of the previous families. We compute explicitly the classification of symmetric states with N≤slant4 qubits in terms of both secant families and its refinement using tangents. This paves the way to further use of projective varieties in algebraic geometry to solve open problems in entanglement theory.
Coordinating Work with Groupware
DEFF Research Database (Denmark)
Pors, Jens Kaaber; Simonsen, Jesper
2003-01-01
One important goal of employing groupware is to make possible complex collaboration between geographically distributed groups. This requires a dual transformation of both technology and work practice. The challenge is to reduce the complexity of the coordination work by successfully inte......grating the protocol stipulating the collaboration and the artefact, in form of the groupware application, mediating the collaboration. This paper analyses a generic groupware application that was deployed in a large financial organisation in order to support working groups distributed throughout four countries....... Using the CSCW framework of coordination mechanisms, we have elicited six general factors influencing the integration of the groupware application in two situations....
Dai, Liang; Schmidt, Fabian
2015-01-01
Fermi Normal Coordinates (FNC) are a useful frame for isolating the locally observable, physical effects of a long-wavelength spacetime perturbation. Their cosmological application, however, is hampered by the fact that they are only valid on scales much smaller than the horizon. We introduce a generalization that we call Conformal Fermi Coordinates (CFC). CFC preserve all the advantages of FNC, but in addition are valid outside the horizon. They allow us to calculate the coupling of long- and short-wavelength modes on all scales larger than the sound horizon of the cosmological fluid, starting from the epoch of inflation until today, by removing the complications of the second order Einstein equations to a large extent, and eliminating all gauge ambiguities. As an application, we present a calculation of the effect of long-wavelength tensor modes on small scale density fluctuations. We recover previous results, but clarify the physical content of the individual contributions in terms of locally measurable ef...
Technical calculus with analytic geometry
Gersting, Judith L
2010-01-01
This well-thought-out text, filled with many special features, is designed for a two-semester course in calculus for technology students with a background in college algebra and trigonometry. The author has taken special care to make the book appealing to students by providing motivating examples, facilitating an intuitive understanding of the underlying concepts involved, and by providing much opportunity to gain proficiency in techniques and skills.Initial chapters cover functions and graphs, straight lines and conic sections, new coordinate systems, the derivative, using the derivative, in
Coordinating Shared Activities
Clement, Bradley
2004-01-01
Shared Activity Coordination (ShAC) is a computer program for planning and scheduling the activities of an autonomous team of interacting spacecraft and exploratory robots. ShAC could also be adapted to such terrestrial uses as helping multiple factory managers work toward competing goals while sharing such common resources as floor space, raw materials, and transports. ShAC iteratively invokes the Continuous Activity Scheduling Planning Execution and Replanning (CASPER) program to replan and propagate changes to other planning programs in an effort to resolve conflicts. A domain-expert specifies which activities and parameters thereof are shared and reports the expected conditions and effects of these activities on the environment. By specifying these conditions and effects differently for each planning program, the domain-expert subprogram defines roles that each spacecraft plays in a coordinated activity. The domain-expert subprogram also specifies which planning program has scheduling control over each shared activity. ShAC enables sharing of information, consensus over the scheduling of collaborative activities, and distributed conflict resolution. As the other planning programs incorporate new goals and alter their schedules in the changing environment, ShAC continually coordinates to respond to unexpected events.
Global coordination: weighted voting
Directory of Open Access Journals (Sweden)
Jan-Erik Lane
2014-03-01
Full Text Available In order to halt the depletion of global ecological capital, a number of different kinds of meetings between Governments of countries in the world has been scheduled. The need for global coordination of environmental policies has become ever more obvious, supported by more and more evidence of the running down of ecological capital. But there are no formal or binding arrangements in sight, as global environmental coordination suffers from high transaction costs (qualitative voting. The CO2 equivalent emissions, resulting in global warming, are driven by the unstoppable economic expansion in the global market economy, employing mainly fossil fuel generated energy, although at the same time lifting sharply the GDP per capita of several emerging countries. Only global environmental coordination on the successful model of the World Band and the IMF (quantitative voting can stem the rising emissions numbers and stop further environmental degradation. However, the system of weighted voting in the WB and the IMF must be reformed by reducing the excessive voting power disparities, for instance by reducing all member country votes by the cube root expression.
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.
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.
Some Progress in Conformal Geometry
Directory of Open Access Journals (Sweden)
Sun-Yung A. Chang
2007-12-01
Full Text Available This is a survey paper of our current research on the theory of partial differential equations in conformal geometry. Our intention is to describe some of our current works in a rather brief and expository fashion. We are not giving a comprehensive survey on the subject and references cited here are not intended to be complete. We introduce a bubble tree structure to study the degeneration of a class of Yamabe metrics on Bach flat manifolds satisfying some global conformal bounds on compact manifolds of dimension 4. As applications, we establish a gap theorem, a finiteness theorem for diffeomorphism type for this class, and diameter bound of the $sigma_2$-metrics in a class of conformal 4-manifolds. For conformally compact Einstein metrics we introduce an eigenfunction compactification. As a consequence we obtain some topological constraints in terms of renormalized volumes.
Applied geometry and discrete mathematics
Sturm; Gritzmann, Peter; Sturmfels, Bernd
1991-01-01
This volume, published jointly with the Association for Computing Machinery, comprises a collection of research articles celebrating the occasion of Victor Klee's sixty-fifth birthday in September 1990. During his long career, Klee has made contributions to a wide variety of areas, such as discrete and computational geometry, convexity, combinatorics, graph theory, functional analysis, mathematical programming and optimization, and theoretical computer science. In addition, Klee made important contributions to mathematics education, mathematical methods in economics and the decision sciences, applications of discrete mathematics in the biological and social sciences, and the transfer of knowledge from applied mathematics to industry. In honor of Klee's achievements, this volume presents more than forty papers on topics related to Klee's research. While the majority of the papers are research articles, a number of survey articles are also included. Mirroring the breadth of Klee's mathematical contributions, th...
Hue geometry and horizontal connections.
Ben-Shahar, Ohad; Zucker, Steven W
2004-01-01
Primate visual systems support an elaborate specialization for processing color information. Concentrating on the hue component, we observe that, contrary to Mondrian-like assumptions, hue varies in a smooth manner for ecologically important natural imagery. To represent these smooth variations, and to support those information processing tasks that utilize hue, a piecewise smooth hue field is postulated. The geometry of hue-patch interactions is developed analogously to orientation-patch interactions in texture. The result is a model for long-range (horizontal) interactions in the color domain, the power of which is demonstrated on a number of examples. Implications for computer image processing, computer vision, visual neurophysiology and psychophysics are discussed.
The geometry of dynamical triangulations
Ambjørn, Jan; Marzuoli, Annalisa
1997-01-01
We discuss the geometry of dynamical triangulations associated with 3-dimensional and 4-dimensional simplicial quantum gravity. We provide analytical expressions for the canonical partition function in both cases, and study its large volume behavior. In the space of the coupling constants of the theory, we characterize the infinite volume line and the associated critical points. The results of this analysis are found to be in excellent agreement with the MonteCarlo simulations of simplicial quantum gravity. In particular, we provide an analytical proof that simply-connected dynamically triangulated 4-manifolds undergo a higher order phase transition at a value of the inverse gravitational coupling given by 1.387, and that the nature of this transition can be concealed by a bystable behavior. A similar analysis in the 3-dimensional case characterizes a value of the critical coupling (3.845) at which hysteresis effects are present.
Conformal geometry and quasiregular mappings
Vuorinen, Matti
1988-01-01
This book is an introduction to the theory of spatial quasiregular mappings intended for the uninitiated reader. At the same time the book also addresses specialists in classical analysis and, in particular, geometric function theory. The text leads the reader to the frontier of current research and covers some most recent developments in the subject, previously scatterd through the literature. A major role in this monograph is played by certain conformal invariants which are solutions of extremal problems related to extremal lengths of curve families. These invariants are then applied to prove sharp distortion theorems for quasiregular mappings. One of these extremal problems of conformal geometry generalizes a classical two-dimensional problem of O. Teichmüller. The novel feature of the exposition is the way in which conformal invariants are applied and the sharp results obtained should be of considerable interest even in the two-dimensional particular case. This book combines the features of a textbook an...
Dialogues about geometry and light
Bermudez, David; Leonhardt, Ulf
2015-01-01
Throughout human history, people have used sight to learn about the world, but only in relatively recent times the science of light has been developed. Egyptians and Mesopotamians made the first known lenses out of quartz, giving birth to what was later known as optics. On the other hand, geometry is a branch of mathematics that was born from practical studies concerning lengths, areas and volumes in the early cultures, although it was not put into axiomatic form until the 3rd century BC. In this work, we will discuss the connection between these two timeless topics and show some new things in old things". There has been several works in this direction, but taking into account the didactic approach of the Enrico Fermi Summer School, we would like to address the subject and our audience in a new light.
Integrable systems, geometry, and topology
Terng, Chuu-Lian
2006-01-01
The articles in this volume are based on lectures from a program on integrable systems and differential geometry held at Taiwan's National Center for Theoretical Sciences. As is well-known, for many soliton equations, the solutions have interpretations as differential geometric objects, and thereby techniques of soliton equations have been successfully applied to the study of geometric problems. The article by Burstall gives a beautiful exposition on isothermic surfaces and their relations to integrable systems, and the two articles by Guest give an introduction to quantum cohomology, carry out explicit computations of the quantum cohomology of flag manifolds and Hirzebruch surfaces, and give a survey of Givental's quantum differential equations. The article by Heintze, Liu, and Olmos is on the theory of isoparametric submanifolds in an arbitrary Riemannian manifold, which is related to the n-wave equation when the ambient manifold is Euclidean. Mukai-Hidano and Ohnita present a survey on the moduli space of ...
Noncommutative geometry of multicore bions
Karczmarek, Joanna L.; Sibilia, Ariel
2013-01-01
We find new BPS solutions to the nonabelian theory on a world-volume of parallel D1-branes. Our solutions describe two parallel, separated bundles of N D1-branes expanding out to form a single orthogonal D3-brane. This configuration corresponds to two charge N magnetic monopoles in the world-volume of a single D3-brane, deforming the D3-brane into two parallel spikes. We obtain the emergent surface corresponding to our nonabelian D1-brane configuration and demonstrate, at finite N , a surprisingly accurate agreement with the shape of the D3-brane world-volume as obtained from the abelian Born-Infeld action. Our solution provides an explicit realization of topology change in noncommutative geometry at finite N.
Digital breast tomosynthesis geometry calibration
Wang, Xinying; Mainprize, James G.; Kempston, Michael P.; Mawdsley, Gordon E.; Yaffe, Martin J.
2007-03-01
Digital Breast Tomosynthesis (DBT) is a 3D x-ray technique for imaging the breast. The x-ray tube, mounted on a gantry, moves in an arc over a limited angular range around the breast while 7-15 images are acquired over a period of a few seconds. A reconstruction algorithm is used to create a 3D volume dataset from the projection images. This procedure reduces the effects of tissue superposition, often responsible for degrading the quality of projection mammograms. This may help improve sensitivity of cancer detection, while reducing the number of false positive results. For DBT, images are acquired at a set of gantry rotation angles. The image reconstruction process requires several geometrical factors associated with image acquisition to be known accurately, however, vibration, encoder inaccuracy, the effects of gravity on the gantry arm and manufacturing tolerances can produce deviations from the desired acquisition geometry. Unlike cone-beam CT, in which a complete dataset is acquired (500+ projections over 180°), tomosynthesis reconstruction is challenging in that the angular range is narrow (typically from 20°-45°) and there are fewer projection images (~7-15). With such a limited dataset, reconstruction is very sensitive to geometric alignment. Uncertainties in factors such as detector tilt, gantry angle, focal spot location, source-detector distance and source-pivot distance can produce several artifacts in the reconstructed volume. To accurately and efficiently calculate the location and angles of orientation of critical components of the system in DBT geometry, a suitable phantom is required. We have designed a calibration phantom for tomosynthesis and developed software for accurate measurement of the geometric parameters of a DBT system. These have been tested both by simulation and experiment. We will present estimates of the precision available with this technique for a prototype DBT system.
Symmetric two-coordinate photodiode
Directory of Open Access Journals (Sweden)
Dobrovolskiy Yu. G.
2008-12-01
Full Text Available The two-coordinate photodiode is developed and explored on the longitudinal photoeffect, which allows to get the coordinate descriptions symmetric on the steepness and longitudinal resistance great exactness. It was shown, that the best type of the coordinate description is observed in the case of scanning by the optical probe on the central part of the photosensitive element. The ways of improvement of steepness and linear of its coordinate description were analyzed.
Understanding Leadership A Coordination Theory
J. Foss, Nicolai
1999-01-01
Important aspects of leadership behavior can be rendered intelligible through a focus on coordination games. The concept of common knowledge is shown to be particularly important to understanding leadership. Thus, leaders may establish common knowledge conditions and assist the coordination of strategies in this way, or make decisions in situations where coordination problems persist in spite of common knowledge.
Zendejas, Silvino; Bui, Tung; Bui, Bach; Malhotra, Shantanu; Chen, Fannie; Kim, Rachel; Allen, Christopher; Luong, Ivy; Chang, George; Sadaqathulla, Syed
2009-01-01
The Work Coordination Engine (WCE) is a Java application integrated into the Service Management Database (SMDB), which coordinates the dispatching and monitoring of a work order system. WCE de-queues work orders from SMDB and orchestrates the dispatching of work to a registered set of software worker applications distributed over a set of local, or remote, heterogeneous computing systems. WCE monitors the execution of work orders once dispatched, and accepts the results of the work order by storing to the SMDB persistent store. The software leverages the use of a relational database, Java Messaging System (JMS), and Web Services using Simple Object Access Protocol (SOAP) technologies to implement an efficient work-order dispatching mechanism capable of coordinating the work of multiple computer servers on various platforms working concurrently on different, or similar, types of data or algorithmic processing. Existing (legacy) applications can be wrapped with a proxy object so that no changes to the application are needed to make them available for integration into the work order system as "workers." WCE automatically reschedules work orders that fail to be executed by one server to a different server if available. From initiation to completion, the system manages the execution state of work orders and workers via a well-defined set of events, states, and actions. It allows for configurable work-order execution timeouts by work-order type. This innovation eliminates a current processing bottleneck by providing a highly scalable, distributed work-order system used to quickly generate products needed by the Deep Space Network (DSN) to support space flight operations. WCE is driven by asynchronous messages delivered via JMS indicating the availability of new work or workers. It runs completely unattended in support of the lights-out operations concept in the DSN.
Automorphisms in Birational and Affine Geometry
Ciliberto, Ciro; Flenner, Hubert; McKernan, James; Prokhorov, Yuri; Zaidenberg, Mikhail
2014-01-01
The main focus of this volume is on the problem of describing the automorphism groups of affine and projective varieties, a classical subject in algebraic geometry where, in both cases, the automorphism group is often infinite dimensional. The collection covers a wide range of topics and is intended for researchers in the fields of classical algebraic geometry and birational geometry (Cremona groups) as well as affine geometry with an emphasis on algebraic group actions and automorphism groups. It presents original research and surveys and provides a valuable overview of the current state of the art in these topics. Bringing together specialists from projective, birational algebraic geometry and affine and complex algebraic geometry, including Mori theory and algebraic group actions, this book is the result of ensuing talks and discussions from the conference “Groups of Automorphisms in Birational and Affine Geometry” held in October 2012, at the CIRM, Levico Terme, Italy. The talks at the conference high...
Subsectors, Dynkin diagrams and new generalised geometries
Strickland-Constable, Charles
2017-08-01
We examine how generalised geometries can be associated with a labelled Dynkin diagram built around a gravity line. We present a series of new generalised geometries based on the groups Spin( d, d) × ℝ + for which the generalised tangent space transforms in a spinor representation of the group. In low dimensions these all appear in subsectors of maximal supergravity theories. The case d = 8 provides a geometry for eight-dimensional backgrounds of M theory with only seven-form flux, which have not been included in any previous geometric construction. This geometry is also one of a series of "half-exceptional" geometries, which "geometrise" a six-form gauge field. In the appendix, we consider exam-ples of other algebras appearing in gravitational theories and give a method to derive the Dynkin labels for the "section condition" in general. We argue that generalised geometry can describe restrictions and subsectors of many gravitational theories.
Connections between algebra, combinatorics, and geometry
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...
CHANGING GEOMETRY OF GLOBAL POLYCENTRICITY
Directory of Open Access Journals (Sweden)
Alexey Gromyko
2012-01-01
Full Text Available Abstract: Despite the changes, the configuration of global and regional power centers can still be represented as an hierarchy in which the first among equals, the equal, the peripheral and the marginal centers coexist with each other. BRICS’ as the means for increasing adaptivity to global realities and influencing global and regional process can potentially contribute to the shaping of multipolarity. The article suggests that BRICS is the most prospective project for coordinating of actions of various power centers of the world, as this format combines the political will, the economic foundation and the use of soft power tools. A Greater Europe continues to be the priority region for Russia in a political, economic, financial and cultural sense, and due to its geographical and civilizational particularity Russia can act as the link between other world major players both within BRICS and Russia-BRICS-EU triangle.
Markov stochasticity coordinates
Eliazar, Iddo
2017-01-01
Markov dynamics constitute one of the most fundamental models of random motion between the states of a system of interest. Markov dynamics have diverse applications in many fields of science and engineering, and are particularly applicable in the context of random motion in networks. In this paper we present a two-dimensional gauging method of the randomness of Markov dynamics. The method-termed Markov Stochasticity Coordinates-is established, discussed, and exemplified. Also, the method is tweaked to quantify the stochasticity of the first-passage-times of Markov dynamics, and the socioeconomic equality and mobility in human societies.
Engineering the oxygen coordination in digital superlattices
Directory of Open Access Journals (Sweden)
Seyoung Cook
2017-12-01
Full Text Available 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.
Engineering the oxygen coordination in digital superlattices
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.
Energy Technology Data Exchange (ETDEWEB)
Alonso, Rodrigo [Department of Physics, University of California at San Diego,La Jolla, CA 92093 (United States); Jenkins, Elizabeth E.; Manohar, Aneesh V. [Department of Physics, University of California at San Diego,La Jolla, CA 92093 (United States); CERN TH Division,CH-1211 Geneva 23 (Switzerland)
2016-08-17
The S-matrix of a quantum field theory is unchanged by field redefinitions, and so it only depends on geometric quantities such as the curvature of field space. Whether the Higgs multiplet transforms linearly or non-linearly under electroweak symmetry is a subtle question since one can make a coordinate change to convert a field that transforms linearly into one that transforms non-linearly. Renormalizability of the Standard Model (SM) does not depend on the choice of scalar fields or whether the scalar fields transform linearly or non-linearly under the gauge group, but only on the geometric requirement that the scalar field manifold M is flat. Standard Model Effective Field Theory (SMEFT) and Higgs Effective Field Theory (HEFT) have curved M, since they parametrize deviations from the flat SM case. We show that the HEFT Lagrangian can be written in SMEFT form if and only if M has a SU(2){sub L}×U(1){sub Y} invariant fixed point. Experimental observables in HEFT depend on local geometric invariants of M such as sectional curvatures, which are of order 1/Λ{sup 2}, where Λ is the EFT scale. We give explicit expressions for these quantities in terms of the structure constants for a general G→H symmetry breaking pattern. The one-loop radiative correction in HEFT is determined using a covariant expansion which preserves manifest invariance of M under coordinate redefinitions. The formula for the radiative correction is simple when written in terms of the curvature of M and the gauge curvature field strengths. We also extend the CCWZ formalism to non-compact groups, and generalize the HEFT curvature computation to the case of multiple singlet scalar fields.
Classical geometry Euclidean, transformational, inversive, and projective
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
Applications of Affine and Weyl geometry
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
Introduction to non-Euclidean geometry
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
Topics in Cubic Special Geometry
Bellucci, Stefano; Roychowdhury, Raju
2011-01-01
We reconsider the sub-leading quantum perturbative corrections to N=2 cubic special Kaehler geometries. Imposing the invariance under axion-shifts, all such corrections (but the imaginary constant one) can be introduced or removed through suitable, lower unitriangular symplectic transformations, dubbed Peccei-Quinn (PQ) transformations. Since PQ transformations do not belong to the d=4 U-duality group G4, in symmetric cases they generally have a non-trivial action on the unique quartic invariant polynomial I4 of the charge representation R of G4. This leads to interesting phenomena in relation to theory of extremal black hole attractors; namely, the possibility to make transitions between different charge orbits of R, with corresponding change of the supersymmetry properties of the supported attractor solutions. Furthermore, a suitable action of PQ transformations can also set I4 to zero, or vice versa it can generate a non-vanishing I4: this corresponds to transitions between "large" and "small" charge orbit...
Latent geometry of bipartite networks
Kitsak, Maksim; Papadopoulos, Fragkiskos; Krioukov, Dmitri
2017-03-01
Despite the abundance of bipartite networked systems, their organizing principles are less studied compared to unipartite networks. Bipartite networks are often analyzed after projecting them onto one of the two sets of nodes. As a result of the projection, nodes of the same set are linked together if they have at least one neighbor in common in the bipartite network. Even though these projections allow one to study bipartite networks using tools developed for unipartite networks, one-mode projections lead to significant loss of information and artificial inflation of the projected network with fully connected subgraphs. Here we pursue a different approach for analyzing bipartite systems that is based on the observation that such systems have a latent metric structure: network nodes are points in a latent metric space, while connections are more likely to form between nodes separated by shorter distances. This approach has been developed for unipartite networks, and relatively little is known about its applicability to bipartite systems. Here, we fully analyze a simple latent-geometric model of bipartite networks and show that this model explains the peculiar structural properties of many real bipartite systems, including the distributions of common neighbors and bipartite clustering. We also analyze the geometric information loss in one-mode projections in this model and propose an efficient method to infer the latent pairwise distances between nodes. Uncovering the latent geometry underlying real bipartite networks can find applications in diverse domains, ranging from constructing efficient recommender systems to understanding cell metabolism.
The geometry of population genetics
Akin, Ethan
1979-01-01
The differential equations which model the action of selection and recombination are nonlinear equations which are impossible to It is even difficult to describe in general the solve explicitly. Recently, Shahshahani began using qualitative behavior of solutions. differential geometry to study these equations [28]. with this mono graph I hope to show that his ideas illuminate many aspects of pop ulation genetics. Among these are his proof and clarification of Fisher's Fundamental Theorem of Natural Selection and Kimura's Maximum Principle and also the effect of recombination on entropy. We also discover the relationship between two classic measures of 2 genetic distance: the x measure and the arc-cosine measure. There are two large applications. The first is a precise definition of the biological concept of degree of epistasis which applies to general (i.e. frequency dependent) forms of selection. The second is the unexpected appearance of cycling. We show that cycles can occur in the two-locus-two-allele...
Linguistic geometry for technologies procurement
Stilman, Boris; Yakhnis, Vladimir; Umanskiy, Oleg; Boyd, Ron
2005-05-01
In the modern world of rapidly rising prices of new military hardware, the importance of Simulation Based Acquisition (SBA) is hard to overestimate. With SAB, DOD would be able to test, develop CONOPS for, debug, and evaluate new conceptual military equipment before actually building the expensive hardware. However, only recently powerful tools for real SBA have been developed. Linguistic Geometry (LG) permits full-scale modeling and evaluation of new military technologies, combinations of hardware systems and concepts of their application. Using LG tools, the analysts can create a gaming environment populated with the Blue forces armed with the new conceptual hardware as well as with appropriate existing weapons and equipment. This environment will also contain the intelligent enemy with appropriate weaponry and, if desired, with a conceptual counters to the new Blue weapons. Within such LG gaming environment, the analyst can run various what-ifs with the LG tools providing the simulated combatants with strategies and tactics solving their goals with minimal resources spent.
Fractal Geometry and Stochastics V
Falconer, Kenneth; Zähle, Martina
2015-01-01
This book brings together leading contributions from the fifth conference on Fractal Geometry and Stochastics held in Tabarz, Germany, in March 2014. The book is divided into five sections covering different facets of this fast developing area: geometric measure theory, self-similar fractals and recurrent structures, analysis and algebra on fractals, multifractal theory, and random constructions. There are state-of-the-art surveys as well as papers highlighting more specific recent advances. The authors are world-experts who present their topics comprehensibly and attractively. The book provides an accessible gateway to the subject for newcomers as well as a reference for recent developments for specialists. Authors include: Krzysztof Barański, Julien Barral, Kenneth Falconer, De-Jun Feng, Peter J. Grabner, Rostislav Grigorchuk, Michael Hinz, Stéphane Jaffard, Maarit Järvenpää, Antti Käenmäki, Marc Kesseböhmer, Michel Lapidus, Klaus Mecke, Mark Pollicott, Michał Rams, Pablo Shmerkin, and András Te...
Discrete transfer method with the concept of blocked-off region for irregular geometries
Energy Technology Data Exchange (ETDEWEB)
Talukdar, Prabal [Institute of Fluid Mechanics (LSTM), University of Erlangen-Nuremberg, Cauerstrasse 4, D-91058 Erlangen (Germany)]. E-mail: prabal_iitg@yahoo.com
2006-03-15
The discrete transfer method (DTM) is applied to irregular geometries with a concept of blocked-off region previously applied in the problems of computational fluid dynamics. This gives a new alternative to the DTM for its implementation to irregular structures. The Cartesian coordinate-based ray-tracing algorithm can be applied to the geometries with inclined or curved boundaries. Some test problems are considered and results are validated with the available results in the literature. Both radiative and non-radiative equilibrium situations are considered. The medium is assumed to be both participating and non-participating. Results are found to be accurate for all kinds of situations.
African Journals Online (AJOL)
sphere; not coordinating to the central 003' ion. Although some of the oxalate- ... The absorption bands in the range 3400—3000 cm" are attributed to the symmetric and antisymmetric N-H stretching [14]. ... 1A1a and 1T2“ <--~- 'Aw of cobaltﬂll) ion in the pseudo-octahedral symmetry [19]. It is evident that the amine ligands do ...
Teramoto, Hiroshi; Toda, Mikito; Takahashi, Masahiko; Kono, Hirohiko; Komatsuzaki, Tamiki
2015-08-28
We present a mechanism of global reaction coordinate switching, namely, a phenomenon in which the reaction coordinate dynamically switches to another coordinate as the total energy of the system increases. The mechanism is based on global changes in the underlying phase space geometry caused by a switching of dominant unstable modes from the original reactive mode to another nonreactive mode in systems with more than 2 degrees of freedom. We demonstrate an experimental observability to detect a reaction coordinate switching in an ionization reaction of a hydrogen atom in crossed electric and magnetic fields. For this reaction, the reaction coordinate is a coordinate along which electrons escape and its switching changes the escaping direction from the direction of the electric field to that of the magnetic field and, thus, the switching can be detected experimentally by measuring the angle-resolved momentum distribution of escaping electrons.
PREFACE: Water in confined geometries
Rovere, Mauro
2004-11-01
The study of water confined in complex systems in solid or gel phases and/or in contact with macromolecules is relevant to many important processes ranging from industrial applications such as catalysis and soil chemistry, to biological processes such as protein folding or ionic transport in membranes. Thermodynamics, phase behaviour and the molecular mobility of water have been observed to change upon confinement depending on the properties of the substrate. In particular, polar substrates perturb the hydrogen bond network of water, inducing large changes in the properties upon freezing. Understanding how the connected random hydrogen bond network of bulk water is modified when water is confined in small cavities inside a substrate material is very important for studies of stability and the enzymatic activity of proteins, oil recovery or heterogeneous catalysis, where water-substrate interactions play a fundamental role. The modifications of the short-range order in the liquid depend on the nature of the water-substrate interaction, hydrophilic or hydrophobic, as well as on its spatial range and on the geometry of the substrate. Despite extensive study, both experimentally and by computer simulation, there remain a number of open problems. In the many experimental studies of confined water, those performed on water in Vycor are of particular interest for computer simulation and theoretical studies since Vycor is a porous silica glass characterized by a quite sharp distribution of pore sizes and a strong capability to absorb water. It can be considered as a good candidate for studying the general behaviour of water in hydrophilic nanopores. But there there have been a number of studies of water confined in more complex substrates, where the interpretation of experiments and computer simulation is more difficult, such as in zeolites or in aerogels or in contact with membranes. Of the many problems to consider we can mention the study of supercooled water. It is
Alonso, Rodrigo; Manohar, Aneesh V.
2016-01-01
The $S$-matrix of a quantum field theory is unchanged by field redefinitions, and so only depends on geometric quantities such as the curvature of field space. Whether the Higgs multiplet transforms linearly or non-linearly under electroweak symmetry is a subtle question since one can make a coordinate change to convert a field that transforms linearly into one that transforms non-linearly. Renormalizability of the Standard Model (SM) does not depend on the choice of scalar fields or whether the scalar fields transform linearly or non-linearly under the gauge group, but only on the geometric requirement that the scalar field manifold ${\\mathcal M}$ is flat. We explicitly compute the one-loop correction to scalar scattering in the SM written in non-linear Callan-Coleman-Wess-Zumino (CCWZ) form, where it has an infinite series of higher dimensional operators, and show that the $S$-matrix is finite. Standard Model Effective Field Theory (SMEFT) and Higgs Effective Field Theory (HEFT) have curved ${\\mathcal M}$, ...
Noncommutative geometry and fluid dynamics
Energy Technology Data Exchange (ETDEWEB)
Das, Praloy; Ghosh, Subir [Indian Statistical Institute, Physics and Applied Mathematics Unit, Kolkata (India)
2016-11-15
In the present paper we have developed a Non-Commutative (NC) generalization of perfect fluid model from first principles, in a Hamiltonian framework. The noncommutativity is introduced at the Lagrangian (particle) coordinate space brackets and the induced NC fluid bracket algebra for the Eulerian (fluid) field variables is derived. Together with a Hamiltonian this NC algebra generates the generalized fluid dynamics that satisfies exact local conservation laws for mass and energy, thereby maintaining mass and energy conservation. However, nontrivial NC correction terms appear in the charge and energy fluxes. Other non-relativistic spacetime symmetries of the NC fluid are also discussed in detail. This constitutes the study of kinematics and dynamics of NC fluid. In the second part we construct an extension of the Friedmann-Robertson-Walker (FRW) cosmological model based on the NC fluid dynamics presented here. We outline the way in which NC effects generate cosmological perturbations bringing about anisotropy and inhomogeneity in the model. We also derive a NC extended Friedmann equation. (orig.)
Quantum groups: Geometry and applications
Energy Technology Data Exchange (ETDEWEB)
Chu, Chong -Sun [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Theoretical Physics Group; Univ. of California, Berkeley, CA (United States)
1996-05-13
The main theme of this thesis is a study of the geometry of quantum groups and quantum spaces, with the hope that they will be useful for the construction of quantum field theory with quantum group symmetry. The main tool used is the Faddeev-Reshetikhin-Takhtajan description of quantum groups. A few content-rich examples of quantum complex spaces with quantum group symmetry are treated in details. In chapter 1, the author reviews some of the basic concepts and notions for Hopf algebras and other background materials. In chapter 2, he studies the vector fields of quantum groups. A compact realization of these vector fields as pseudodifferential operators acting on the linear quantum spaces is given. In chapter 3, he describes the quantum sphere as a complex quantum manifold by means of a quantum stereographic projection. A covariant calculus is introduced. An interesting property of this calculus is the existence of a one-form realization of the exterior differential operator. The concept of a braided comodule is introduced and a braided algebra of quantum spheres is constructed. In chapter 4, the author considers the more general higher dimensional quantum complex projective spaces and the quantum Grassman manifolds. Differential calculus, integration and braiding can be introduced as in the one dimensional case. Finally, in chapter 5, he studies the framework of quantum principal bundle and construct the q-deformed Dirac monopole as a quantum principal bundle with a quantum sphere as the base and a U(1) with non-commutative calculus as the fiber. The first Chern class can be introduced and integrated to give the monopole charge.
Fingerprint pattern classification approach based on the coordinate geometry of singularities
CSIR Research Space (South Africa)
Msiza, IS
2009-10-01
Full Text Available The problem of Automatic Fingerprint Pattern Classification (AFPC) has been studied by many fingerprint biometric practitioners. It is an important concept because, in instances where a relatively large database is being queried for the purposes...
Algebra and Geometry of Hamilton's Quaternions
Indian Academy of Sciences (India)
IAS Admin
Inspired by the relation between the algebra of complex numbers and plane geometry, William. Rowan Hamilton sought an algebra of triples for application to three-dimensional geometry. Un- able to multiply and divide triples, he invented a non-commutative division algebra of quadru- ples, in what he considered his most ...
Cognitive Styles, Dynamic Geometry and Measurement Performance
Pitta-Pantazi, Demetra; Christou, Constantinos
2009-01-01
This paper reports the outcomes of an empirical study undertaken to investigate the effect of students' cognitive styles on achievement in measurement tasks in a dynamic geometry learning environment, and to explore the ability of dynamic geometry learning in accommodating different cognitive styles and enhancing students' learning. A total of 49…
Reasoning by Contradiction in Dynamic Geometry
Baccaglini-Frank, Anna; Antonini, Samuele; Leung, Allen; Mariotti, Maria Alessandra
2013-01-01
This paper addresses contributions that dynamic geometry systems (DGSs) may give in reasoning by contradiction in geometry. We present analyses of three excerpts of students' work and use the notion of pseudo object, elaborated from previous research, to show some specificities of DGS in constructing proof by contradiction. In particular, we…
Visual and Analytic Strategies in Geometry
Kospentaris, George; Vosniadou, Stella; Kazic, Smaragda; Thanou, Emilian
2016-01-01
We argue that there is an increasing reliance on analytic strategies compared to visuospatial strategies, which is related to geometry expertise and not on individual differences in cognitive style. A Visual/Analytic Strategy Test (VAST) was developed to investigate the use of visuo-spatial and analytic strategies in geometry in 30 mathematics…
Symposium on Differential Geometry and Differential Equations
Berger, Marcel; Bryant, Robert
1987-01-01
The DD6 Symposium was, like its predecessors DD1 to DD5 both a research symposium and a summer seminar and concentrated on differential geometry. This volume contains a selection of the invited papers and some additional contributions. They cover recent advances and principal trends in current research in differential geometry.
A Multivariate Model of Achievement in Geometry
Bailey, MarLynn; Taasoobshirazi, Gita; Carr, Martha
2014-01-01
Previous studies have shown that several key variables influence student achievement in geometry, but no research has been conducted to determine how these variables interact. A model of achievement in geometry was tested on a sample of 102 high school students. Structural equation modeling was used to test hypothesized relationships among…
Making Euclidean Geometry Compulsory: Are We Prepared?
Van Putten, Sonja; Howie, Sarah; Stols, Gerrit
2010-01-01
This study investigated the attitude towards, as well as the level of understanding of Euclidean geometry in pre-service mathematics education (PME) students. In order to do so, a case study was undertaken within which a one group pre-post-test procedure was conducted around a geometry module, and a representative group of students was interviewed…
Energy Technology Data Exchange (ETDEWEB)
1994-01-01
In December 1992, western governors and four federal agencies established a Federal Advisory Committee to Develop On-site Innovative Technologies for Environmental Restoration and Waste Management (the DOIT Committee). The purpose of the Committee is to advise the federal government on ways to improve waste cleanup technology development and the cleanup of federal sites in the West. The Committee directed in January 1993 that information be collected from a wide range of potential stakeholders and that innovative technology candidate projects be identified, organized, set in motion, and evaluated to test new partnerships, regulatory approaches, and technologies which will lead to improve site cleanup. Five working groups were organized, one to develop broad project selection and evaluation criteria and four to focus on specific contaminant problems. A Coordinating Group comprised of working group spokesmen and federal and state representatives, was set up to plan and organize the routine functioning of these working groups. The working groups were charged with defining particular contaminant problems; identifying shortcomings in technology development, stakeholder involvement, regulatory review, and commercialization which impede the resolution of these problems; and identifying candidate sites or technologies which could serve as regional innovative demonstration projects to test new approaches to overcome the shortcomings. This report from the Coordinating Group to the DOIT Committee highlights the key findings and opportunities uncovered by these fact-finding working groups. It provides a basis from which recommendations from the DOIT Committee to the federal government can be made. It also includes observations from two public roundtables, one on commercialization and another on regulatory and institutional barriers impeding technology development and cleanup.
Algorithm for the calculation of the horizontal coordinates of the Sun via spatial rotation matrices
Energy Technology Data Exchange (ETDEWEB)
Rapp-Arraras, Igor; Domingo-Santos, Juan M. [Escuela Politecnica Superior, Universidad de Huelva, Ctra. Palos de la Frontera-Huelva s/n, 21819 La Rabida (Huelva) (Spain)
2009-03-15
This paper presents a new algorithm for calculating azimuth and altitude of the Sun from its ecliptic coordinates. The equations of the new procedure are not based on spherical trigonometry, like the procedure currently used for computing the solar vector, but on analytic geometry enriched by matrix algebra. Our proposal allows the horizontal coordinates of the Sun to be determined with a significantly higher computational efficiency than the classic algorithm without any loss in accuracy. (author)
Cao, Y; G. Cervone; Z. Barkley; Lauvaux, T.; A. Deng; Taylor, A.
2017-01-01
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 withou...
Applications Of Nonclassical Geometry To String Theory
Zunger, Y
2003-01-01
String theory is built on a foundation of geometry. This thesis examines several applications of geometry beyond the classical Riemannian geometry of curved surfaces. The first part considers the use of extended spaces with internal dimensions to each point (“twistors”) to probe systems with a great deal of symmetry but complicated dynamics. These systems are of critical interest in understanding holographic phenomena in string theory and the origins of entropy. We develop a twistor formulation of coset spaces and use this to write simplified actions for particles and strings on anti-de Sitter space, which are easier to quantize than the ordinary (highly nonlinear) actions. In the second part, we consider two aspects of noncommutative geometry, a generalization of ordinary geometry where points are “fuzzed out” and functions of space become noncommuting operators. We first examine strings with one endpoint on a D-brane in a background magnetic field. (Strings with both ...
Special metrics and group actions in geometry
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.
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.
Energy Technology Data Exchange (ETDEWEB)
Lumetta, Gregg J.; Sinkov, Sergey I.; Krause, Jeanette A.; Sweet, Lucas E.
2016-01-27
The complexes formed during the extraction of neodymium(III) into hydrophobic solvents containing acidic organophosphorus extractants were probed by single-crystal X-ray diffractometry, visible spectrophotometry, and Fourier-transform infrared spectroscopy. The crystal structure of the compound Nd(DMP)3 (1, DMP = dimethyl phosphate) revealed a polymeric arrangement in which each Nd(III) center is surrounded by six DMP oxygen atoms in a pseudo-octahedral environment. Adjacent Nd(III) ions are bridged by (MeO)2POO– anions, forming the polymeric network. The diffuse reflectance visible spectrum of 1 is nearly identical to that of the solid that is formed when an n-dodecane solution of di-(2-ethylhexyl)phosphoric acid (HA) is saturated with Nd(III), indicating a similar coordination environment around the Nd center in the NdA3 solid. The visible spectrum of the HA solution fully loaded with Nd(III) is very similar to that of the NdA3 material, both displaying hypersensitive bands characteristic of an pseudo-octahedral coordination environment around Nd. These spectral characteristics persisted across a wide range of organic Nd concentrations, suggesting that the pseudo-octahedral coordination environment is maintained from dilute to saturated conditions.
McAndrew, Erica M.; Morris, Wendy L.; Fennell, Francis
2017-01-01
Use of mathematics-related literature can engage students' interest and increase their understanding of mathematical concepts. A quasi-experimental study of two second-grade classrooms assessed whether daily inclusion of geometry-related literature in the classroom improved attitudes toward geometry and achievement in geometry. Consistent with the…
Visuospatial Working Memory in Intuitive Geometry, and in Academic Achievement in Geometry
Giofre, David; Mammarella, Irene C.; Ronconi, Lucia; Cornoldi, Cesare
2013-01-01
A study was conducted on the involvement of visuospatial working memory (VSWM) in intuitive geometry and in school performance in geometry at secondary school. A total of 166 pupils were administered: (1) six VSWM tasks, comprising simple storage and complex span tasks; and (2) the intuitive geometry task devised by Dehaene, Izard, Pica, and…
Analogy and Dynamic Geometry System Used to Introduce Three-Dimensional Geometry
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…
Relativity explained by physical interpretation of coordinates of energy
Fernando, Viraj
2009-08-01
This paper is based on Einstein's key concept, 'Physical Interpretation of Co-ordinates' on which basis he developed his theory of relativity. However, in the present theory, space and time co-ordinates are abandoned and instead, internal components of energy are recognized as co-ordinates of Nature's geometry. This enables the development of the theory in full conformity to the principle of conservation of energy. Whereas, the co-ordinates that vary in the motions of matter particles are inertia and velocity of the applied momentum, in motion of photons, it is the inertia and frequency co-ordinates that vary, while velocity co-ordinate remains invariant at value c, making the result of Michelson's experiment self-explanatory. Thus, although this theory vindicates special theory of relativity in regard to the principle of the constancy of the velocity of light, it contradicts it by recognizing the possession of mass by a photon. By identifying that Newton has willfully omitted two important laws by the use of the Ockham's razor, since these have no significant effects on the motion of bodies at low velocities, and by re-instating these laws, classical mechanics is revised to apply to bodies moving at all velocities whatsoever, so that the revised theory becomes capable of accounting for gamma-factor, Lorentz transformation and other relativistic phenomena. The parallel between 'Lorentz transformation' of the displacement of a fast moving particle in a laboratory on earth, in terms of co-ordinate variation of inertia and velocity, and the relativistic Doppler effect of starlight incident on earth in terms of co-ordinate variation of inertia and frequency, is established.
Relativity free of coordinates
Wagner, Serge A
2016-01-01
The concept of an inertial reference frame, which actualizes Euclidean geometry, is not confined to the statics of solids but extendible to the phenomena where Newtonian mechanics is valid, defining its concept of time. The laws of propagation of electromagnetic waves modify Newtonian formalism for fast free motions within each spatial domain of its validity for slow motions and introduce the extended concept of time by uniting those of Newtonian which can exist in different spatial domains of their validity. A boost direction for a pair of frames is that spatial direction in one frame along which the other frame moves. Free motions of point particles make an instrumentation for identifying the boost direction as well as events on a straight line along that direction. The concept of a boost direction secures the physics-based formulation of the basic relativity effects, which eventually results in the relation between two arbitrary frames in terms of their position vectors and time moments for a given event. ...
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.)
Primes, Geometry and Condensed Matter
Directory of Open Access Journals (Sweden)
Al Rabeh R. H.
2009-07-01
Full Text Available Fascination with primes dates back to the Greeks and before. Primes are named by some "the elementary particles of arithmetic" as every nonprime integer is made of a unique set of primes. In this article we point to new connections between primes, geometry and physics which show that primes could be called "the elementary particles of physics" too. This study considers the problem of closely packing similar circles/spheres in 2D/3D space. This is in effect a discretization process of space and the allowable number in a pack is found to lead to some unexpected cases of prime configurations which is independent of the size of the constituents. We next suggest that a non-prime can be considered geometrically as a symmetric collection that is separable (factorable into similar parts- six is two threes or three twos for example. A collection that has no such symmetry is a prime. As a result, a physical prime aggregate is more difficult to split symmetrically resulting in an inherent stability. This "number/physical" stability idea applies to bigger collections made from smaller (prime units leading to larger stable prime structures in a limitless scaling up process. The distribution of primes among numbers can be understood better using the packing ideas described here and we further suggest that differing numbers (and values of distinct prime factors making a nonprime collection is an important factor in determining the probability and method of possible and subsequent disintegration. Disintegration is bound by energy conservation and is closely related to symmetry by Noether theorems. Thinking of condensed matter as the packing of identical elements, we examine plots of the masses of chemical elements of the periodic table, and also those of the elementary particles of physics, and show that prime packing rules seem to play a role in the make up of matter. The plots show convincingly that the growth of prime numbers and that of the masses of
Primes, Geometry and Condensed Matter
Directory of Open Access Journals (Sweden)
Al Rabeh R. H.
2009-07-01
Full Text Available Fascination with primes dates back to the Greeks and before. Primes are named by some “the elementary particles of arithmetic” as every nonprime integer is made of a unique set of primes. In this article we point to new connections between primes, geometry and physics which show that primes could be called “the elementary particles of physics” too. This study considers the problem of closely packing similar circles / spheres in 2D / 3D space. This is in effect a discretization process of space and the allowable num- ber in a pack is found to lead to some unexpected cases of prime configurations which is independent of the size of the constituents. We next suggest that a non-prime can be considered geometrically as a symmetric collection that is separable (factorable into similar parts- six is two threes or three twos for example. A collection that has no such symmetry is a prime. As a result, a physical prime aggregate is more difficult to split symmetrically resulting in an inherent stability. This “number / physical” stability idea applies to bigger collections made from smaller (prime units leading to larger sta- ble prime structures in a limitless scaling up process. The distribution of primes among numbers can be understood better using the packing ideas described here and we further suggest that differing numbers (and values of distinct prime factors making a nonprime collection is an important factor in determining the probability and method of possible and subsequent disintegration. Disintegration is bound by energy conservation and is closely related to symmetry by Noether theorems. Thinking of condensed matter as the packing of identical elements, we examine plots of the masses of chemical elements of the periodic table, and also those of the elementary particles of physics, and show that prime packing rules seem to play a role in the make up of matter. The plots show con- vincingly that the growth of prime numbers and that
basement reservoir geometry and properties
Walter, bastien; Geraud, yves; Diraison, marc
2017-04-01
Basement reservoirs are nowadays frequently investigated for deep-seated fluid resources (e.g. geothermal energy, groundwater, hydrocarbons). The term 'basement' generally refers to crystalline and metamorphic formations, where matrix porosity is negligible in fresh basement rocks. Geothermal production of such unconventional reservoirs is controlled by brittle structures and altered rock matrix, resulting of a combination of different tectonic, hydrothermal or weathering phenomena. This work aims to characterize the petro-structural and petrophysical properties of two basement surface analogue case studies in geological extensive setting (the Albert Lake rift in Uganda; the Ifni proximal margin of the South West Morocco Atlantic coast). Different datasets, using field structural study, geophysical acquisition and laboratory petrophysical measurements, were integrated to describe the multi-scale geometry of the porous network of such fractured and weathered basement formations. This study points out the multi-scale distribution of all the features constituting the reservoir, over ten orders of magnitude from the pluri-kilometric scale of the major tectonics structures to the infra-millimetric scale of the secondary micro-porosity of fractured and weathered basements units. Major fault zones, with relatively thick and impermeable fault core structures, control the 'compartmentalization' of the reservoir by dividing it into several structural blocks. The analysis of these fault zones highlights the necessity for the basement reservoirs to be characterized by a highly connected fault and fracture system, where structure intersections represent the main fluid drainage areas between and within the reservoir's structural blocks. The suitable fluid storage areas in these reservoirs correspond to the damage zone of all the fault structures developed during the tectonic evolution of the basement and the weathered units of the basement roof developed during pre
Unification of gravity and quantum field theory from extended noncommutative geometry
Yu, Hefu; Ma, Bo-Qiang
2017-02-01
We make biframe and quaternion extensions on the noncommutative geometry, and construct the biframe spacetime for the unification of gravity and quantum field theory (QFT). The extended geometry distinguishes between the ordinary spacetime based on the frame bundle and an extra non-coordinate spacetime based on the biframe bundle constructed by our extensions. The ordinary spacetime frame is globally flat and plays the role as the spacetime frame in which the fields of the Standard Model are defined. The non-coordinate frame is locally flat and is the gravity spacetime frame. The field defined in both frames of such “flat” biframe spacetime can be quantized and plays the role as the gravity field which couples with all the fields to connect the gravity effect with the Standard Model. Thus, we provide a geometric paradigm in which gravity and QFT can be unified.
Enterprise Coordination on the Internet
Charles Petrie
2011-01-01
Enterprises are now connected internally and externally to other Enterprises via the Internet in ways that are increasingly difficult to manage, especially as these interconnections become more dynamic. Current methods of coordinating the effects of change as they propagate through these networks of connections are not likely to scale. What is needed is a new paradigm for how the Internet supports such coordination. Indeed, the Internet should and could provide fundamental coordination functi...
Toroidal equilibria in spherical coordinates
Tsui, K. H.
2009-01-01
The standard Grad-Shafranov equation for axisymmetric toroidal plasma equilibrium is customary expressed in cylindrical coordinates with toroidal contours, and through which benchmark equilibria are solved. An alternative approach to cast the Grad-Shafranov equation in spherical coordinates is presented. This equation, in spherical coordinates, is examined for toroidal solutions to describe low $\\beta$ Solovev and high $\\beta$ plasma equilibria in terms of elementary functions.
Consideration in GIS insulation coordination
Energy Technology Data Exchange (ETDEWEB)
Bargigia, A.
1990-01-01
Analysis of electrical system failures reveals that many are caused by insulation breakdowns due to overvoltages. The problem of insulation co-ordination is then one of the most important aspects in the design of an electrical system. Insulation co-ordination of gas-insulated sub-stations (GIS) has recently received much attention especially due to a large diffusion of this insulation technique. In this review of GIS insulation co-ordination, attention is given to the impact on the insulation co-ordination strategy of the metal-clad disconnector performance during capacity current switching operations.
coordination polymer with a coordinated nitro group of 2-nitrobenzoate
Indian Academy of Sciences (India)
WINTEC
For correspondence. A one-dimensional barium(II) coordination polymer with a coordinated nitro group of 2-nitrobenzoate*. BIKSHANDARKOIL R SRINIVASAN. 1,#. , SANTOSH Y SHETGAONKAR. 1 and. PALLEPOGU RAGHAVAIAH. 1,2. 1. Department of Chemistry, Goa University, Goa 403 206. 2. School of Chemistry ...
Full-field drift Hamiltonian particle orbits in axisymmetric tokamak geometry
Cooper, W.A.; Cooper, G.A.; Graves, J P; Isaev, M. Yu
2011-01-01
A Hamiltonian/Lagrangian theory to describe guiding center orbit drift motion that is canonical in Boozer magnetic coordinates is developed to include full electrostatic and electromagnetic perturbed fields in axisymmetric tokamak geometry. Furthermore, the radial component of the equilibrium magnetic field in the covariant representation is retained and the background equilibrium state extends to anisotropic plasma pressure conditions. A gauge transformation on the perturbed vector potentia...
Discrete quantum geometries and their effective dimension
Energy Technology Data Exchange (ETDEWEB)
Thuerigen, Johannes
2015-07-02
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.
Geometry and symmetry in non-equilibrium thermodynamic systems
Sonnino, Giorgio
2017-06-01
The ultimate aim of this series of works is to establish the closure equations, valid for thermodynamic systems out from the Onsager region, and to describe the geometry and symmetry in thermodynamic systems far from equilibrium. Geometry of a non-equilibrium thermodynamic system is constructed by taking into account the second law of thermodynamics and by imposing the validity of the Glansdorff-Prigogine Universal Criterion of Evolution. These two constraints allow introducing the metrics and the affine connection of the Space of the Thermodynamic Forces, respectively. The Lie group associated to the nonlinear Thermodynamic Coordinate Transformations (TCT) leaving invariant both the entropy production σ and the Glansdorff-Prigogine dissipative quantity P, is also described. The invariance under TCT leads to the formulation of the Thermodynamic Covariance Principle (TCP): The nonlinear closure equations, i.e. the flux-force relations, must be covariant under TCT. In other terms, the fundamental laws of thermodynamics should be manifestly covariant under transformations between the admissible thermodynamic forces (i.e. under TCT). The symmetry properties of a physical system are intimately related to the conservation laws characterizing the thermodynamic system. Noether's theorem gives a precise description of this relation. The macroscopic theory for closure relations, based on this geometrical description and subject to the TCP, is referred to as the Thermodynamic Field Theory (TFT). This theory ensures the validity of the fundamental theorems for systems far from equilibrium.
Optimal walking speed following changes in limb geometry.
Leurs, Françoise; Ivanenko, Yuri P; Bengoetxea, Ana; Cebolla, Ana-Maria; Dan, Bernard; Lacquaniti, Francesco; Cheron, Guy A
2011-07-01
The principle of dynamic similarity states that the optimal walking speeds of geometrically similar animals are independent of size when speed is normalized to the dimensionless Froude number (Fr). Furthermore, various studies have shown similar dimensionless optimal speed (Fr ∼0.25) for animals with quite different limb geometries. Here, we wondered whether the optimal walking speed of humans depends solely on total limb length or whether limb segment proportions play an essential role. If optimal walking speed solely depends on the limb length then, when subjects walk on stilts, they should consume less metabolic energy at a faster optimal speed than when they walk without stilts. To test this prediction, we compared kinematics, electromyographic activity and oxygen consumption in adults walking on a treadmill at different speeds with and without articulated stilts that artificially elongated the shank segment by 40 cm. Walking on stilts involved a non-linear reorganization of kinematic and electromyography patterns. In particular, we found a significant increase in the alternating activity of proximal flexors-extensors during the swing phase, despite significantly shorter normalized stride lengths. The minimal metabolic cost per unit distance walked with stilts occurred at roughly the same absolute speed, corresponding to a lower Fr number (Fr ∼0.17) than in normal walking (Fr ∼0.25). These findings are consistent with an important role of limb geometry optimization and kinematic coordination strategies in minimizing the energy expenditure of human walking.
Geometric Stitching Method for Double Cameras with Weak Convergence Geometry
Zhou, N.; He, H.; Bao, Y.; Yue, C.; Xing, K.; Cao, S.
2017-05-01
In this paper, a new geometric stitching method is proposed which utilizes digital elevation model (DEM)-aided block adjustment to solve relative orientation parameters for dual-camera with weak convergence geometry. A rational function model (RFM) with affine transformation is chosen as the relative orientation model. To deal with the weak geometry, a reference DEM is used in this method as an additional constraint in the block adjustment, which only calculates the planimetry coordinates of tie points (TPs). After that we can use the obtained affine transform coefficients to generate virtual grid, and update rational polynomial coefficients (RPCs) to complete the geometric stitching. Our proposed method was tested on GaoFen-2(GF-2) dual-camera panchromatic (PAN) images. The test results show that the proposed method can achieve an accuracy of better than 0.5 pixel in planimetry and have a seamless visual effect. For regions with small relief, when global DEM with 1 km grid, SRTM with 90 m grid and ASTER GDEM V2 with 30 m grid replaced DEM with 1m grid as elevation constraint it is almost no loss of accuracy. The test results proved the effectiveness and feasibility of the stitching method.
On Coordinating Collaborative Objects
Directory of Open Access Journals (Sweden)
Abdessamad Imine
2010-07-01
Full Text Available A collaborative object represents a data type (such as a text document designed to be shared by a group of dispersed users. The Operational Transformation (OT is a coordination approach used for supporting optimistic replication for these objects. It allows the users to concurrently update the shared data and exchange their updates in any order since the convergence of all replicas, i.e. the fact that all users view the same data, is ensured in all cases. However, designing algorithms for achieving convergence with the OT approach is a critical and challenging issue. In this paper, we propose a formal compositional method for specifying complex collaborative objects. The most important feature of our method is that designing an OT algorithm for the composed collaborative object can be done by reusing the OT algorithms of component collaborative objects. By using our method, we can start from correct small collaborative objects which are relatively easy to handle and incrementally combine them to build more complex collaborative objects.
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.
On the physical geometry concept at the basis of space/time geostatistical hydrology
Christakos, G.; Hristopulos, D. T.; Bogaert, P.
The objective of this paper is to show that the structure of the spatiotemporal continuum has important implications in practical stochastic hydrology (e.g., geostatistical analysis of hydrologic sites) and is not merely an abstract mathematical concept. We propose that the concept of physical geometry as a spatiotemporal continuum with properties that are empirically defined is important in hydrologic analyses, and that the elements of the spatiotemporal geometry (e.g., coordinate system and space/time metric) should be selected based on the physical properties of the hydrologic processes. We investigate the concept of space/time distance (metric) in various physical spaces, and its implications for hydrologic modeling. More specifically, we demonstrate that physical geometry plays a crucial role in the determination of appropriate spatiotemporal covariance models, and it can affect the results of geostatistical operations involved in spatiotemporal hydrologic mapping.
An investigation of dynamic-analysis methods for variable-geometry structures
Austin, F.
1980-01-01
Selected space structure configurations were reviewed in order to define dynamic analysis problems associated with variable geometry. The dynamics of a beam being constructed from a flexible base and the relocation of the completed beam by rotating the remote manipulator system about the shoulder joint were selected. Equations of motion were formulated in physical coordinates for both of these problems, and FORTRAN programs were developed to generate solutions by numerically integrating the equations. These solutions served as a standard of comparison to gauge the accuracy of approximate solution techniques that were developed and studied. Good control was achieved in both problems. Unstable control system coupling with the system flexibility did not occur. An approximate method was developed for each problem to enable the analyst to investigate variable geometry effects during a short time span using standard fixed geometry programs such as NASTRAN. The average angle and average length techniques are discussed.
Wormhole inspired by non-commutative geometry
Energy Technology Data Exchange (ETDEWEB)
Rahaman, Farook, E-mail: rahaman@iucaa.ernet.in [Department of Mathematics, Jadavpur University, Kolkata 700032, West Bengal (India); Karmakar, Sreya, E-mail: sreya.karmakar@gmail.com [Department of Physics, Calcutta Institute of Engineering and Management, Kolkata 700040, West Bengal (India); Karar, Indrani, E-mail: indrani.karar08@gmail.com [Department of Mathematics, Saroj Mohan Institute of Technology, Guptipara, West Bengal (India); Ray, Saibal, E-mail: saibal@iucaa.ernet.in [Department of Physics, Government College of Engineering & Ceramic Technology, Kolkata 700010, West Bengal (India)
2015-06-30
In the present Letter we search for a new wormhole solution inspired by noncommutative geometry with the additional condition of allowing conformal Killing vectors (CKV). A special aspect of noncommutative geometry is that it replaces point-like structures of gravitational sources with smeared objects under Gaussian distribution. However, the purpose of this letter is to obtain wormhole solutions with noncommutative geometry as a background where we consider a point-like structure of gravitational object without smearing effect. It is found through this investigation that wormhole solutions exist in this Lorentzian distribution with viable physical properties.
Digital and discrete geometry theory and algorithms
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
Wormhole inspired by non-commutative geometry
Directory of Open Access Journals (Sweden)
Farook Rahaman
2015-06-01
Full Text Available In the present Letter we search for a new wormhole solution inspired by noncommutative geometry with the additional condition of allowing conformal Killing vectors (CKV. A special aspect of noncommutative geometry is that it replaces point-like structures of gravitational sources with smeared objects under Gaussian distribution. However, the purpose of this letter is to obtain wormhole solutions with noncommutative geometry as a background where we consider a point-like structure of gravitational object without smearing effect. It is found through this investigation that wormhole solutions exist in this Lorentzian distribution with viable physical properties.
Information geometry near randomness and near independence
Arwini, Khadiga A
2008-01-01
This volume will be useful to practising scientists and students working in the application of statistical models to real materials or to processes with perturbations of a Poisson process, a uniform process, or a state of independence for a bivariate process. We use information geometry to provide a common differential geometric framework for a wide range of illustrative applications including amino acid sequence spacings in protein chains, cryptology studies, clustering of communications and galaxies, cosmological voids, coupled spatial statistics in stochastic fibre networks and stochastic porous media, quantum chaology. Introduction sections are provided to mathematical statistics, differential geometry and the information geometry of spaces of probability density functions.
Fractal geometry mathematical foundations and applications
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
Differential geometry and topology of curves
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.
Introduction into integral geometry and stereology
DEFF Research Database (Denmark)
Kiderlen, Markus
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...... 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...
Coordination of Conditional Poisson Samples
Directory of Open Access Journals (Sweden)
Grafström Anton
2015-12-01
Full Text Available Sample coordination seeks to maximize or to minimize the overlap of two or more samples. The former is known as positive coordination, and the latter as negative coordination. Positive coordination is mainly used for estimation purposes and to reduce data collection costs. Negative coordination is mainly performed to diminish the response burden of the sampled units. Poisson sampling design with permanent random numbers provides an optimum coordination degree of two or more samples. The size of a Poisson sample is, however, random. Conditional Poisson (CP sampling is a modification of the classical Poisson sampling that produces a fixed-size πps sample. We introduce two methods to coordinate Conditional Poisson samples over time or simultaneously. The first one uses permanent random numbers and the list-sequential implementation of CP sampling. The second method uses a CP sample in the first selection and provides an approximate one in the second selection because the prescribed inclusion probabilities are not respected exactly. The methods are evaluated using the size of the expected sample overlap, and are compared with their competitors using Monte Carlo simulation. The new methods provide a good coordination degree of two samples, close to the performance of Poisson sampling with permanent random numbers.
75 FR 55947 - Coordinated Communications
2010-09-15
... for Final Rules on General Public Political Communications Coordinated with Candidates and Party... Coalition, the Commission defined a new term, ``coordinated general public political communication'' (``GPPC... communications directed or made by persons who previously served as an employee of a candidate or a political...
Introduction to coordinated linear systems
Kempker, P.L.
2014-01-01
This chapter serves as an introduction to the concepts of coordinated linear systems, in formal as well as intuitive terms. The concept of a coordinated linear system is introduced and formulated, and some basic properties are derived, providing both a motivaton and a formal basis for the following
A new twist on the geometry of gravitational plane waves
Shore, Graham M.
2017-09-01
The geometry of twisted null geodesic congruences in gravitational plane wave spacetimes is explored, with special focus on homogeneous plane waves. The rôle of twist in the relation of the Rosen coordinates adapted to a null congruence with the fundamental Brinkmann coordinates is explained and a generalised form of the Rosen metric describing a gravitational plane wave is derived. The Killing vectors and isometry algebra of homogeneous plane waves (HPWs) are described in both Brinkmann and twisted Rosen form and used to demonstrate the coset space structure of HPWs. The van Vleck-Morette determinant for twisted congruences is evaluated in both Brinkmann and Rosen descriptions. The twisted null congruences of the Ozsváth-Schücking, `anti-Mach' plane wave are investigated in detail. These developments provide the necessary geometric toolkit for future investigations of the rôle of twist in loop effects in quantum field theory in curved spacetime, where gravitational plane waves arise generically as Penrose limits; in string theory, where they are important as string backgrounds; and potentially in the detection of gravitational waves in astronomy.
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
Bimanual coordination in dyslexic adults.
Moore, L H; Brown, W S; Markee, T E; Theberge, D C; Zvi, J C
1995-06-01
Various types of dyslexia have been associated with tactile-motor coordination deficits and inefficient transfer of information between the two cerebral hemispheres. Twenty-one dyslexic adults were compared to 21 controls on the Bimanual Coordination Task, a test of tactile-motor coordination and interhemispheric collaboration. When compared to control subjects, dyslexics showed a consistent pattern of deficits in bimanual motor coordination, both with and without visual feedback. In particular, dyslexics had greater difficulty relative to normals when the left hand had to move faster than the right, and when the hands had to make opposite (mirror-image) movements, suggesting problems with interhemispheric modulation of visuomotor control. In addition, accuracy on this bimanual coordination task was significantly correlated with the Block Design subtest of the WAIS--R, but not with a rhyme fluency task, suggesting some contribution of right hemisphere controlled visuospatial skill to performance.
Structure analysis for plane geometry figures
Feng, Tianxiao; Lu, Xiaoqing; Liu, Lu; Li, Keqiang; Tang, Zhi
2013-12-01
As there are increasing numbers of digital documents for education purpose, we realize that there is not a retrieval application for mathematic plane geometry images. In this paper, we propose a method for retrieving plane geometry figures (PGFs), which often appear in geometry books and digital documents. First, detecting algorithms are applied to detect common basic geometry shapes from a PGF image. Based on all basic shapes, we analyze the structural relationships between two basic shapes and combine some of them to a compound shape to build the PGF descriptor. Afterwards, we apply matching function to retrieve candidate PGF images with ranking. The great contribution of the paper is that we propose a structure analysis method to better describe the spatial relationships in such image composed of many overlapped shapes. Experimental results demonstrate that our analysis method and shape descriptor can obtain good retrieval results with relatively high effectiveness and efficiency.
Gravity, Cartan geometry, and idealized waywisers
Westman, H F
2012-01-01
The primary aim of this paper is to provide a simple and concrete interpretation of Cartan geometry by pointing out that it is nothing but the mathematics of idealized waywisers. Waywisers, also called hodometers, are instruments traditionally used to measure distances. The mathematical representation of an idealized waywiser consists of a choice of symmetric space called a {\\em model space} and represents the `wheel' of the idealized waywiser. The geometry of a manifold is then completely characterized by a pair of variables $\\{V^A(x),A^{AB}(x)\\}$, each of which admit simple interpretations: $V^A$ is the point of contact between the waywiser's idealized wheel and the manifold whose geometry one wishes to characterize, and $A^{AB}=A_\\mu^{\\ AB}dx^\\mu$ is a connection one-form dictating how much the idealized wheel of the waywiser has rotated when rolled along the manifold. The familiar objects from differential geometry (e.g. metric $g_{\\mu\
Geometry, structure and randomness in combinatorics
Nešetřil, Jaroslav; Pellegrini, Marco
2014-01-01
This book collects some surveys on current trends in discrete mathematics and discrete geometry. The areas covered include: graph representations, structural graphs theory, extremal graph theory, Ramsey theory and constrained satisfaction problems.
Homological mirror symmetry and tropical geometry
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...
Track Geometry Measurement System Software Manual
1978-04-01
The Track Geometry Measurement System (TGMS) was developed through the United States Department of Transportation's, Urban Mass Transportation Administration by the Transportation Systems Center in Cambridge, Massachusetts under its Test and Evaluati...
10th China-Japan Geometry Conference
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 Soap-Bubble-Geometry Contest.
Morgan, Frank; Melnick, Edward R.; Nicholson, Ramona
1997-01-01
Presents an activity on soap-bubble geometry using a guessing contest, explanations, and demonstrations that allow students to mesh observation and mathematical reasoning to discover that mathematics is much more than just number crunching. (ASK)
ARC Code TI: Geometry Manipulation Protocol (GMP)
National Aeronautics and Space Administration — The Geometry Manipulation Protocol (GMP) is a library which serializes datatypes between XML and ANSI C data structures to support CFD applications. This library...
Quasi-crystalline geometry for architectural structures
DEFF Research Database (Denmark)
Weizierl, Barbara; Wester, Ture
2001-01-01
. The purpose of the paper is to investigate some possibilities for the application of Quasi-Crystal geometry for structures in architecture. The basis for the investigations is A: to use the Golden Cubes (the two different hexahedra consisting of rhombic facets where the length of the diagonals has the Golden......Artikel på CD-Rom 8 sider. The quasi-crystal (QC) type of material was discovered in 1983 by Dan Schechtman from Technion, Haifa. This new crystalline structure of material broke totally with the traditional conception of crystals and geometry introducing non-periodic close packing of cells...... ratio) as basic elements for aperiodic 3D geometries and B: to raise aperiodic Penrose tilings and its binary substitutions from their 2D basis into 3D QC geometries and describe the structural behaviour for these spatial configurations....
Extracting Entanglement Geometry from Quantum States
Hyatt, Katharine; Garrison, James R.; Bauer, Bela
2017-10-01
Tensor networks impose a notion of geometry on the entanglement of a quantum system. In some cases, this geometry is found to reproduce key properties of holographic dualities, and subsequently much work has focused on using tensor networks as tractable models for holographic dualities. Conventionally, the structure of the network—and hence the geometry—is largely fixed a priori by the choice of the tensor network ansatz. Here, we evade this restriction and describe an unbiased approach that allows us to extract the appropriate geometry from a given quantum state. We develop an algorithm that iteratively finds a unitary circuit that transforms a given quantum state into an unentangled product state. We then analyze the structure of the resulting unitary circuits. In the case of noninteracting, critical systems in one dimension, we recover signatures of scale invariance in the unitary network, and we show that appropriately defined geodesic paths between physical degrees of freedom exhibit known properties of a hyperbolic geometry.
Algebra, Geometry and Mathematical Physics Conference
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...
Robot Geometry and the High School Curriculum.
Meyer, Walter
1988-01-01
Description of the field of robotics and its possible use in high school computational geometry classes emphasizes motion planning exercises and computer graphics displays. Eleven geometrical problems based on robotics are presented along with the correct solutions and explanations. (LRW)
Energy Technology Data Exchange (ETDEWEB)
Bejarano, Cecilia; Guzman, Maria Jose [Instituto de Astronomia y Fisica del Espacio (IAFE, CONICET-UBA), Buenos Aires (Argentina); Ferraro, Rafael [Instituto de Astronomia y Fisica del Espacio (IAFE, CONICET-UBA), Buenos Aires (Argentina); Universidad de Buenos Aires, Departamento de Fisica, Facultad de Ciencias Exactas y Naturales, Buenos Aires (Argentina)
2015-02-01
Null tetrads are shown to be a valuable tool in teleparallel theories of modified gravity. We use them to prove that Kerr geometry remains a solution for a wide family of f(T) theories of gravity. (orig.)
The geometry of René Descartes
Descartes, René
1954-01-01
The great work that founded analytical geometry. Includes the original French text, Descartes' own diagrams, and the definitive Smith-Latham translation. "The greatest single step ever made in the progress of the exact sciences." - John Stuart Mill.
The elements of non-Euclidean geometry
Sommerville, D MY
2012-01-01
Renowned for its lucid yet meticulous exposition, this classic allows students to follow the development of non-Euclidean geometry from a fundamental analysis of the concept of parallelism to more advanced topics. 1914 edition. Includes 133 figures.
Tame geometry with application in smooth analysis
Yomdin, Yosef
2004-01-01
The Morse-Sard theorem is a rather subtle result and the interplay between the high-order analytic structure of the mappings involved and their geometry rarely becomes apparent. The main reason is that the classical Morse-Sard theorem is basically qualitative. This volume gives a proof and also an "explanation" of the quantitative Morse-Sard theorem and related results, beginning with the study of polynomial (or tame) mappings. The quantitative questions, answered by a combination of the methods of real semialgebraic and tame geometry and integral geometry, turn out to be nontrivial and highly productive. The important advantage of this approach is that it allows the separation of the role of high differentiability and that of algebraic geometry in a smooth setting: all the geometrically relevant phenomena appear already for polynomial mappings. The geometric properties obtained are "stable with respect to approximation", and can be imposed on smooth functions via polynomial approximation.
Variational principle and phase space measure in non-canonical coordinates
Directory of Open Access Journals (Sweden)
Sergi, A
2005-11-01
Full Text Available Non-canonical equations of motion are derived from a variational principle written in symplectic form. The invariant measure of phase space and the covariant expression for the entropy are derived from non-canonical transformations of coordinates. This shows that the geometry of non-canonical phase space is non trivial even if dynamics has no compressibility.
Magnetic anisotropy of a Co-II single ion magnet with distorted trigonal prismatic coordination
DEFF Research Database (Denmark)
Peng, Yan; Bodenstein, Tilmann; Fink, Karin
2016-01-01
The single ion magnetic properties of Co(II) are affected by the details of the coordination geometry of the ion. Here we show that a geometry close to trigonal prismatic which arises when the ligand 6,6'-((1Z)-((piperazine-1,4-diylbis(propane-3,1-diyl)) bis(azanylylidene)) bis(methanylylidene)) ......The single ion magnetic properties of Co(II) are affected by the details of the coordination geometry of the ion. Here we show that a geometry close to trigonal prismatic which arises when the ligand 6,6'-((1Z)-((piperazine-1,4-diylbis(propane-3,1-diyl)) bis(azanylylidene)) bis......(methanylylidene)) bis(2-methoxyphenol) coordinates to Co(II) does indeed lead to enhanced single-ion behaviour as has previously been predicted. Synthesis of the compound, structural information, and static as well as dynamic magnetic data are presented along with an analysis using quantum chemical ab initio...... calculations. Though the complex shows a slight deviation from an ideal trigonal prismatic coordination, the zero-field splitting as well as the g-tensor are strongly axial with D = -41 cm(-1) and E
Energy integral method for gravity field determination from satellite orbit coordinates
Visser, P.N.A.M.; Sneeuw, N.; Gerlach, C.
2003-01-01
A fast iterative method for gravity field determination from low Earth satellite orbit coordinates has been developed and implemented successfully. The method is based on energy conservation and avoids problems related to orbit dynamics and initial state. In addition, the particular geometry of a
DEFF Research Database (Denmark)
Häyrynen, Teppo; Østerkryger, Andreas Dyhl; de Lasson, Jakob Rosenkrantz
2017-01-01
. A33, 1298 (2016)]. Here, we generalize the approach to three-dimensional (3D)Cartesian coordinates allowing for the modeling of rectangular geometries inopen space. The open boundary condition is a consequence of having an infinitecomputational domain described using basis functions that expand...
Geometry and quantization of moduli spaces
Andersen, Jørgen; Riera, Ignasi
2016-01-01
This volume is based on four advanced courses held at the Centre de Recerca Matemàtica (CRM), Barcelona. It presents both background information and recent developments on selected topics that are experiencing extraordinary growth within the broad research area of geometry and quantization of moduli spaces. The lectures focus on the geometry of moduli spaces which are mostly associated to compact Riemann surfaces, and are presented from both classical and quantum perspectives.
Non-relativistic geometry of holographic screens
Moosa, Mudassir
2017-06-01
We propose that the intrinsic geometry of holographic screens should be described by the Newton-Cartan geometry. As a test of this proposal, we show that the evolution equations of the screen can be written in a covariant form in terms of a stress tensor, an energy current, and a momentum one-form. We derive the expressions for the stress tensor, energy density, and momentum one-form using Brown-York action formalism.
Perspectives in Analysis, Geometry, and Topology
Itenberg, I V; Passare, Mikael
2012-01-01
The articles in this volume are invited papers from the Marcus Wallenberg symposium and focus on research topics that bridge the gap between analysis, geometry, and topology. The encounters between these three fields are widespread and often provide impetus for major breakthroughs in applications. Topics include new developments in low dimensional topology related to invariants of links and three and four manifolds; Perelman's spectacular proof of the Poincare conjecture; and the recent advances made in algebraic, complex, symplectic, and tropical geometry.
Geometry of quantum computation with qutrits.
Li, Bin; Yu, Zu-Huan; Fei, Shao-Ming
2013-01-01
Determining the quantum circuit complexity of a unitary operation is an important problem in quantum computation. By using the mathematical techniques of Riemannian geometry, we investigate the efficient quantum circuits in quantum computation with n qutrits. We show that the optimal quantum circuits are essentially equivalent to the shortest path between two points in a certain curved geometry of SU(3(n)). As an example, three-qutrit systems are investigated in detail.
Keep Meaning in Conversational Coordination
Directory of Open Access Journals (Sweden)
Elena Clare Cuffari
2014-12-01
Full Text Available Coordination is a widely employed term across recent quantitative and qualitative approaches to intersubjectivity, particularly approaches that give embodiment and enaction central explanatory roles. With a focus on linguistic and bodily coordination in conversational contexts, I review the operational meaning of coordination in recent empirical research and related theorizing of embodied intersubjectivity. This discussion articulates what must be involved in treating linguistic meaning as dynamic processes of coordination. The coordination approach presents languaging as a set of dynamic self-organizing processes and actions on multiple timescales and across multiple modalities that come about and work in certain domains (those jointly constructed in social, interactive, high-order sense-making. These processes go beyond meaning at the level that is available to first-person experience. I take one crucial consequence of this to be the ubiquitously moral nature of languaging with others. Languaging coordinates experience, among other levels of behavior and event. Ethical effort is called for by the automatic autonomy-influencing forces of languaging as coordination.
Keep meaning in conversational coordination.
Cuffari, Elena C
2014-01-01
Coordination is a widely employed term across recent quantitative and qualitative approaches to intersubjectivity, particularly approaches that give embodiment and enaction central explanatory roles. With a focus on linguistic and bodily coordination in conversational contexts, I review the operational meaning of coordination in recent empirical research and related theorizing of embodied intersubjectivity. This discussion articulates what must be involved in treating linguistic meaning as dynamic processes of coordination. The coordination approach presents languaging as a set of dynamic self-organizing processes and actions on multiple timescales and across multiple modalities that come about and work in certain domains (those jointly constructed in social, interactive, high-order sense-making). These processes go beyond meaning at the level that is available to first-person experience. I take one crucial consequence of this to be the ubiquitously moral nature of languaging with others. Languaging coordinates experience, among other levels of behavior and event. Ethical effort is called for by the automatic autonomy-influencing forces of languaging as coordination.
Kossoy, Elizaveta; Weissman, Haim; Rybtchinski, Boris
2015-01-02
In the current work, we demonstrate how coordination chemistry can be employed to direct self-assembly based on strong hydrophobic interactions. To investigate the influence of coordination sphere geometry on aqueous self-assembly, we synthesized complexes of the amphiphilic perylene diimide terpyridine ligand with the first-row transition-metal centers (zinc, cobalt, and nickel). In aqueous medium, aggregation of these complexes is induced by hydrophobic interactions between the ligands. However, the final shapes of the resulting assemblies depend on the preferred geometry of the coordination spheres typical for the particular metal center. The self-assembly process was characterized by UV/Vis spectroscopy, zeta potential measurements, and cryogenic transmission electron microscopy (cryo-TEM). Coordination of zinc(II) and cobalt(II) leads to the formation of unique nanospiral assemblies, whereas complexation of nickel(II) leads to the formation of straight nanofibers. Notably, coordination bonds are utilized not as connectors between elementary building blocks, but as directing interactions, enabling control over supramolecular geometry. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Coordinating distributed work : Exploring situated coordination with gaming-simulation
van Laere, J.
2003-01-01
Organizational work has become more and more distributed nowadays. Information and communication technologies (ICT) provide opportunities to improve coordination of distributed work, but in practice many organizations struggle with integrating new organizational structures, new work practices and
Chandra, Sulekh; Sharma, Amit Kumar
2009-09-01
The coordination compounds of Cr III, Mn II and Co II metal ions derived from quinquedentate 2,6-diacetylpyridine derivative have been synthesized and characterized by using the various physicochemical studies like stoichiometric, molar conductivity and magnetic, and spectral techniques like IR, NMR, mass, UV and EPR. The general stoichiometries of the complexes are found to be [Cr(H 2L)X] and [M(HL)X], where M = Mn(II) and Co(II); H 2L = dideprotonated ligand, HL = monodeprotonated ligand and X = NO 3-, Cl - and OAc -. The studies reveal that the complexes possess monomeric compositions with six coordinated octahedral geometry (Cr III and Mn II complexes) and six coordinated tetragonal geometry (Co II complexes).
Geometry-induced protein pattern formation.
Thalmeier, Dominik; Halatek, Jacob; Frey, Erwin
2016-01-19
Protein patterns are known to adapt to cell shape and serve as spatial templates that choreograph downstream processes like cell polarity or cell division. However, how can pattern-forming proteins sense and respond to the geometry of a cell, and what mechanistic principles underlie pattern formation? Current models invoke mechanisms based on dynamic instabilities arising from nonlinear interactions between proteins but neglect the influence of the spatial geometry itself. Here, we show that patterns can emerge as a direct result of adaptation to cell geometry, in the absence of dynamical instability. We present a generic reaction module that allows protein densities robustly to adapt to the symmetry of the spatial geometry. The key component is an NTPase protein that cycles between nucleotide-dependent membrane-bound and cytosolic states. For elongated cells, we find that the protein dynamics generically leads to a bipolar pattern, which vanishes as the geometry becomes spherically symmetrical. We show that such a reaction module facilitates universal adaptation to cell geometry by sensing the local ratio of membrane area to cytosolic volume. This sensing mechanism is controlled by the membrane affinities of the different states. We apply the theory to explain AtMinD bipolar patterns in [Formula: see text] EcMinDE Escherichia coli. Due to its generic nature, the mechanism could also serve as a hitherto-unrecognized spatial template in many other bacterial systems. Moreover, the robustness of the mechanism enables self-organized optimization of protein patterns by evolutionary processes. Finally, the proposed module can be used to establish geometry-sensitive protein gradients in synthetic biological systems.
Synthesis of Oxovanadium(IV Complexes with Tetraaza Coordinating Ligands
Directory of Open Access Journals (Sweden)
Sanjay Singh
2013-01-01
Full Text Available Oxovanadium(IV complexes of the type [VO(mac]SO4 (where mac = tetraaza macrocyclic ligands derived by condensation of thenil with 1,4-diaminobenzene or 3,4-diaminopyridine and their reaction with β-diketones have been prepared using vanadyl ion as kinetic template. The prepared macrocyclic complexes were characterized by elemental analyses, molar conductance, magnetic moments, and infrared, electronic, and electron spin resonance data. From the spectroscopic studies, five-coordinate square-pyramidal geometry for the VO2+ complexes have been proposed wherein derived ligands act as tetradentate chelating agents.
Operator-based homogeneous coordinates: application in camera document scanning
Juarez-Salazar, Rigoberto; Diaz-Ramirez, Victor H.
2017-07-01
An operator-based approach for the study of homogeneous coordinates and projective geometry is proposed. First, some basic geometrical concepts and properties of the operators are investigated in the one- and two-dimensional cases. Then, the pinhole camera model is derived, and a simple method for homography estimation and camera calibration is explained. The usefulness of the analyzed theoretical framework is exemplified by addressing the perspective correction problem for a camera document scanning application. Several experimental results are provided for illustrative purposes. The proposed approach is expected to provide practical insights for inexperienced students on camera calibration, computer vision, and optical metrology among others.
Directory of Open Access Journals (Sweden)
Kakoma Luneta
2015-06-01
Full Text Available The role geometry plays in real life makes it a core component of mathematics that students must understand and master. Conceptual knowledge of geometric concepts goes beyond the development of skills required to manipulate geometric shapes. This study is focused on errors students made when solving coordinate geometry problems in the final Grade 12 examination in South Africa. An analysis of 1000 scripts from the 2008 Mathematics examination was conducted. This entailed a detailed analysis of one Grade 12 geometry examination question. Van Hiele levels of geometrical thought were used as a lens to understand students’ knowledge of geometry. Studies show that Van Hiele levels are a good descriptor of current and future performance in geometry. This study revealed that whilst students in Grade 12 are expected to operate at level 3 and level 4, the majority were operating at level 2 of Van Hiele’s hierarchy. The majority of students did not understand most of the basic concepts in Euclidian transformation. Most of the errors were conceptual and suggested that students did not understand the questions and did not know what to do as a result. It is also noted that when students lack conceptual knowledge the consequences are so severe that they hardly respond to the questions in the examination.
Indium local geometry in In-Sb-Te thin films using XANES and DFT calculations
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.
Global Materials Structure Search with Chemically Motivated Coordinates.
Panosetti, Chiara; Krautgasser, Konstantin; Palagin, Dennis; Reuter, Karsten; Maurer, Reinhard J
2015-12-09
Identification of relevant reaction pathways in ever more complex composite materials and nanostructures poses a central challenge to computational materials discovery. Efficient global structure search, tailored to identify chemically relevant intermediates, could provide the necessary first-principles atomistic insight to enable a rational process design. In this work we modify a common feature of global geometry optimization schemes by employing automatically generated collective curvilinear coordinates. The similarity of these coordinates to molecular vibrations enhances the generation of chemically meaningful trial structures for covalently bound systems. In the application to hydrogenated Si clusters, we concomitantly observe a significantly increased efficiency in identifying low-energy structures and exploit it for an extensive sampling of potential products of silicon-cluster soft landing on Si(001) surfaces.
Coordinated action in multiteam systems.
Davison, Robert B; Hollenbeck, John R; Barnes, Christopher M; Sleesman, Dustin J; Ilgen, Daniel R
2012-07-01
This study investigated coordinated action in multiteam systems employing 233 correspondent systems, comprising 3 highly specialized 6-person teams, that were engaged in an exercise that was simultaneously "laboratory-like" and "field-like." It enriches multiteam system theory through the combination of theoretical perspectives from the team and the large organization literatures, underscores the differential impact of large size and modular organization by specialization, and demonstrates that conventional wisdom regarding effective coordination in traditional teams and large organizations does not always transfer to multiteam systems. We empirically show that coordination enacted across team boundaries at the component team level can be detrimental to performance and that coordinated actions enacted by component team boundary spanners and system leadership positively impact system performance only when these actions are centered around the component team most critical to addressing the demands of the task environment. (PsycINFO Database Record (c) 2012 APA, all rights reserved).
Coordination Games on Dynamical Networks
Directory of Open Access Journals (Sweden)
Enea Pestelacci
2010-07-01
Full Text Available We propose a model in which agents of a population interacting according to a network of contacts play games of coordination with each other and can also dynamically break and redirect links to neighbors if they are unsatisfied. As a result, there is co-evolution of strategies in the population and of the graph that represents the network of contacts. We apply the model to the class of pure and general coordination games. For pure coordination games, the networks co-evolve towards the polarization of different strategies. In the case of general coordination games our results show that the possibility of refusing neighbors and choosing different partners increases the success rate of the Pareto-dominant equilibrium.
The Persistification of the ATLAS Geometry
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...
Extracting Entanglement Geometry from Quantum States.
Hyatt, Katharine; Garrison, James R; Bauer, Bela
2017-10-06
Tensor networks impose a notion of geometry on the entanglement of a quantum system. In some cases, this geometry is found to reproduce key properties of holographic dualities, and subsequently much work has focused on using tensor networks as tractable models for holographic dualities. Conventionally, the structure of the network-and hence the geometry-is largely fixed a priori by the choice of the tensor network ansatz. Here, we evade this restriction and describe an unbiased approach that allows us to extract the appropriate geometry from a given quantum state. We develop an algorithm that iteratively finds a unitary circuit that transforms a given quantum state into an unentangled product state. We then analyze the structure of the resulting unitary circuits. In the case of noninteracting, critical systems in one dimension, we recover signatures of scale invariance in the unitary network, and we show that appropriately defined geodesic paths between physical degrees of freedom exhibit known properties of a hyperbolic geometry.
Coordination theory and collaboration technology
Olson, Gary M; Smith, John B
2001-01-01
The National Science Foundation funded the first Coordination Theory and Collaboration Technology initiative to look at systems that support collaborations in business and elsewhere. This book explores the global revolution in human interconnectedness. It will discuss the various collaborative workgroups and their use in technology. The initiative focuses on processes of coordination and cooperation among autonomous units in human systems, in computer and communication systems, and in hybrid organizations of both systems. This initiative is motivated by three scientific issues which have been
Muscle coordination: the discussion continues
Prilutsky
2000-01-01
In this response, the major criticisms of the target article are addressed. Terminology from the target article that may have caused some confusion is clarified. In particular, the tasks that have the basic features of muscle coordination, as identified in the target article, have been limited in scope. A new metabolic optimization criterion suggested by Alexander (2000) is examined for its ability to predict muscle coordination in walking. Issues concerning the validation of muscle force predictions, the rules of muscle coordination, and the role of directional constraints in coordination of two-joint muscles are discussed. It is shown in particular that even in one-joint systems, the forces predicted by the criterion of Crowninshield and Brand (1981) depend upon the muscle moment arms and the physiological cross-sectional areas in much more complex ways than either previously assumed in the target article, or incorrectly derived by Herzog and Ait-Haddou (2000). It is concluded that the criterion of Crowninshield and Brand qualitatively predicts the basic coordination features of the major one- and two-joint muscles in a number of highly skilled, repetitive motor tasks performed by humans under predictable conditions and little demands on stability and accuracy. A possible functional significance of such muscle coordination may be the minimization of perceived effort, muscle fatigue, and/or energy expenditure.
Lobachevsky geometry in TTW and PW systems
Hakobyan, T.; Nersessian, A.; Shmavonyan, H.
2017-05-01
We review the classical properties of Tremblay-Turbiner-Winternitz and Post-Wintenitz systems and their relation with N-dimensional rational Calogero model with oscillator and Coulomb potentials, paying special attention to their hidden symmetries. Then we show that combining the radial coordinate and momentum in a single complex coordinate in a proper way, we get an elegant description for the hidden and dynamical symmetries in these systems related with action-angle variables.
The geometry of soil crack networks
Chertkov, V Y
2014-01-01
The subject of this work is the modification and specification of an approach to detail the estimation of soil crack network characteristics. The modification aims at accounting for the corrected soil crack volume based on the corrected shrinkage geometry factor compared to known estimates of crack volume and shrinkage geometry factor. The mode of the correction relies on recent results of the soil reference shrinkage curve. The main exposition follows the preliminary brief review of available approaches to dealing with the geometry of soil crack networks and gives a preliminary brief summary of the approach to be modified and specified. To validate and illustrate the modified approach the latter is used in the analysis of available data on soil cracking in a lysimeter.
Conference on Strings, Duality, and Geometry
Phong, Duong; Yau, Shing-Tung; Mirror Symmetry IV
2002-01-01
This book presents contributions of participants of a workshop held at the Centre de Recherches Mathématiques (CRM), University of Montréal. It can be viewed as a sequel to Mirror Symmetry I (1998), Mirror Symmetry II (1996), and Mirror Symmetry III (1999), copublished by the AMS and International Press. The volume presents a broad survey of many of the noteworthy developments that have taken place in string theory, geometry, and duality since the mid 1990s. Some of the topics emphasized include the following: Integrable models and supersymmetric gauge theories; theory of M- and D-branes and noncommutative geometry; duality between strings and gauge theories; and elliptic genera and automorphic forms. Several introductory articles present an overview of the geometric and physical aspects of mirror symmetry and of corresponding developments in symplectic geometry. The book provides an efficient way for a very broad audience of mathematicians and physicists to explore the frontiers of research into this rapi...
Geometry and Physics of Null Infinity
Ashtekar, Abhay
2014-01-01
In asymptotically Minkowski space-times, one finds a surprisingly rich interplay between geometry and physics in both the classical and quantum regimes. On the mathematical side it involves null geometry, infinite dimensional groups, symplectic geometry on the space of gravitational connections and geometric quantization via K\\"ahler structures. On the physical side, null infinity provides a natural home to study gravitational radiation and its structure leads to several interesting effects such as an infinite dimensional enlargement of the Poincar\\'e group, geometrical expressions of energy and momentum carried by gravitational waves, emergence of non-trivial `vacuum configurations' and an unforeseen interplay between infrared properties of the quantum gravitational field and the enlargement of the asymptotic symmetry group. The goal of this article is to present a succinct summary of this subtle and beautiful interplay.
Geometric Monte Carlo and black Janus geometries
Energy Technology Data Exchange (ETDEWEB)
Bak, Dongsu, E-mail: dsbak@uos.ac.kr [Physics Department, University of Seoul, Seoul 02504 (Korea, Republic of); B.W. Lee Center for Fields, Gravity & Strings, Institute for Basic Sciences, Daejeon 34047 (Korea, Republic of); Kim, Chanju, E-mail: cjkim@ewha.ac.kr [Department of Physics, Ewha Womans University, Seoul 03760 (Korea, Republic of); Kim, Kyung Kiu, E-mail: kimkyungkiu@gmail.com [Department of Physics, Sejong University, Seoul 05006 (Korea, Republic of); Department of Physics, College of Science, Yonsei University, Seoul 03722 (Korea, Republic of); Min, Hyunsoo, E-mail: hsmin@uos.ac.kr [Physics Department, University of Seoul, Seoul 02504 (Korea, Republic of); Song, Jeong-Pil, E-mail: jeong_pil_song@brown.edu [Department of Chemistry, Brown University, Providence, RI 02912 (United States)
2017-04-10
We describe an application of the Monte Carlo method to the Janus deformation of the black brane background. We present numerical results for three and five dimensional black Janus geometries with planar and spherical interfaces. In particular, we argue that the 5D geometry with a spherical interface has an application in understanding the finite temperature bag-like QCD model via the AdS/CFT correspondence. The accuracy and convergence of the algorithm are evaluated with respect to the grid spacing. The systematic errors of the method are determined using an exact solution of 3D black Janus. This numerical approach for solving linear problems is unaffected initial guess of a trial solution and can handle an arbitrary geometry under various boundary conditions in the presence of source fields.
Lectures on formal and rigid geometry
Bosch, Siegfried
2014-01-01
A first version of this work appeared in 2005 as a Preprint of the Collaborative Research Center "Geometrical Structures in Mathematics" at the University of Münster. Its aim was to offer a concise and self-contained 'lecture-style' introduction to the theory of classical rigid geometry established by John Tate, together with the formal algebraic geometry approach launched by Michel Raynaud. These Lectures are now viewed commonly as an ideal means of learning advanced rigid geometry, regardless of the reader's level of background. Despite its parsimonious style, the presentation illustrates a number of key facts even more extensively than any other previous work. This Lecture Notes Volume is a revised and slightly expanded version of the original preprint and has been published at the suggestion of several experts in the field.
Geometry and dynamics of integrable systems
Matveev, Vladimir
2016-01-01
Based on lectures given at an advanced course on integrable systems at the Centre de Recerca Matemàtica in Barcelona, these lecture notes address three major aspects of integrable systems: obstructions to integrability from differential Galois theory; the description of singularities of integrable systems on the basis of their relation to bi-Hamiltonian systems; and the generalization of integrable systems to the non-Hamiltonian settings. All three sections were written by top experts in their respective fields. Native to actual problem-solving challenges in mechanics, the topic of integrable systems is currently at the crossroads of several disciplines in pure and applied mathematics, and also has important interactions with physics. The study of integrable systems also actively employs methods from differential geometry. Moreover, it is extremely important in symplectic geometry and Hamiltonian dynamics, and has strong correlations with mathematical physics, Lie theory and algebraic geometry (including mir...
From groups to geometry and back
Climenhaga, Vaughn
2017-01-01
Groups arise naturally as symmetries of geometric objects, and so groups can be used to understand geometry and topology. Conversely, one can study abstract groups by using geometric techniques and ultimately by treating groups themselves as geometric objects. This book explores these connections between group theory and geometry, introducing some of the main ideas of transformation groups, algebraic topology, and geometric group theory. The first half of the book introduces basic notions of group theory and studies symmetry groups in various geometries, including Euclidean, projective, and hyperbolic. The classification of Euclidean isometries leads to results on regular polyhedra and polytopes; the study of symmetry groups using matrices leads to Lie groups and Lie algebras. The second half of the book explores ideas from algebraic topology and geometric group theory. The fundamental group appears as yet another group associated to a geometric object and turns out to be a symmetry group using covering space...
Nozzle geometry variations on the discharge coefficient
Directory of Open Access Journals (Sweden)
M.M.A. Alam
2016-03-01
Full Text Available Numerical works have been conducted to investigate the effect of nozzle geometries on the discharge coefficient. Several contoured converging nozzles with finite radius of curvatures, conically converging nozzles and conical divergent orifices have been employed in this investigation. Each nozzle and orifice has a nominal exit diameter of 12.7×10−3 m. A 3rd order MUSCL finite volume method of ANSYS Fluent 13.0 was used to solve the Reynolds-averaged Navier–Stokes equations in simulating turbulent flows through various nozzle inlet geometries. The numerical model was validated through comparison between the numerical results and experimental data. The results obtained show that the nozzle geometry has pronounced effect on the sonic lines and discharge coefficients. The coefficient of discharge was found differ from unity due to the non-uniformity of flow parameters at the nozzle exit and the presence of boundary layer as well.
Early Geometry: A Visual, Intuitive Introduction to Plane Geometry for Elementary School Children.
Navarro, C. F.
Geometry is a fundamental part of the mathematics foundation provided by elementary education. Children have an intuitive understanding of geometry that they draw on when dealing with geometric concepts in activities like drawing, playing hopscotch, defending their "half of the room," and playing sports. This book offers no instruction…
Anderson, Karen L.; Casey, M. Beth; Thompson, William L.; Burrage, Marie S.; Pezaris, Elizabeth; Kosslyn, Stephen M.
2008-01-01
This study investigated the relationship between 3 ability-based cognitive styles (verbal deductive, spatial imagery, and object imagery) and performance on geometry problems that provided different types of clues. The purpose was to determine whether students with a specific cognitive style outperformed other students, when the geometry problems…
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…
Metallogels from Coordination Complexes, Organometallic, and Coordination Polymers.
Dastidar, Parthasarathi; Ganguly, Sumi; Sarkar, Koushik
2016-09-20
A supramolecular gel results from the immobilization of solvent molecules on a 3D network of gelator molecules stabilized by various supramolecular interactions that include hydrogen bonding, π-π stacking, van der Waals interactions, and halogen bonding. In a metallogel, a metal is a part of the gel network as a coordinated metal ion (in a discrete coordination complex), as a cross-linking metal node with a multitopic ligand (in coordination polymer), and as metal nanoparticles adhered to the gel network. Although the field is relatively new, research into metallogels has experienced a considerable upsurge owing to its fundamental importance in supramolecular chemistry and various potential applications. This focus review aims to provide an insight into the development of designing metallogelators. Because of the limited scope, discussions are confined to examples pertaining to metallogelators derived from discrete coordination complexes, organometallic gelators, and coordination polymers. This review is expected to enlighten readers on the current development of designing metallogelators of the abovementioned class of molecules. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
The organization of room geometry and object layout geometry in human memory.
Sluzenski, Julia; McNamara, Timothy P
2011-08-01
Research with humans and with nonhuman species has suggested a special role of room geometry in spatial memory functioning. In two experiments, participants learned the configuration of a room with four corners, along with the configuration of four objects within the room, while standing in a fixed position at the room's periphery. The configurations were either rectangular (Experiment 1) or irregular (Experiment 2). Room geometry was not recalled better than object layout geometry, and memories for both configurations were orientation dependent. These results suggest that room geometry and object layout geometry are represented similarly in human memory, at least in situations that promote long-term learning of object locations. There were also some differences between corners and objects in orientation dependence, suggesting that the two sources of information are represented in similar but separate spatial reference systems. [corrected
Recent topics in differential and analytic geometry
Ochiai, T
1990-01-01
Advanced Studies in Pure Mathematics, Volume 18-I: Recent Topics in Differential and Analytic Geometry presents the developments in the field of analytical and differential geometry. This book provides some generalities about bounded symmetric domains.Organized into two parts encompassing 12 chapters, this volume begins with an overview of harmonic mappings and holomorphic foliations. This text then discusses the global structures of a compact Kähler manifold that is locally decomposable as an isometric product of Ricci-positive, Ricci-negative, and Ricci-flat parts. Other chapters con
Solc filters in a reflective geometry
Messaadi, Abdelghafour; Vargas, Asticio; Sánchez-López, María M.; García-Martínez, Pascuala; Kula, Przemysław; Bennis, Noureddine; Moreno, Ignacio
2017-04-01
We present the realization of a bulk optics birefringent Solc filter in a reflective geometry. This geometry reduces by half the number of required retarders, ensures the same spectral retardance function in pairs of retarders, and helps to make more compact filters. The key element is a quarter-wave Fresnel rhomb located in between the set of retarders and a mirror. Two cases are considered: the first Solc filter uses multiple-order quartz retarders, and the second one uses two liquid-crystal retarders. The latter has the advantage of being tunable via an applied voltage. Experimental results show how to filter the spectral content of a supercontinuum laser.
Density and geometry of single component plasmas
Speck, A; Larochelle, P; Le Sage, D; Levitt, B; Kolthammer, W S; McConnell, R; Wrubel, J; Grzonka, D; Oelert, W; Sefzick, T; Zhang, Z; Comeau, D; George, M C; Hessels, E A; Storry, C H; Weel, M; Walz, J
2007-01-01
The density and geometry of p¯ and e+ plasmas in realistic trapping potentials are required to understand and optimize antihydrogen (H¯) formation. An aperture method and a quadrupole oscillation frequency method for characterizing such plasmas are compared for the first time, using electrons in a cylindrical Penning trap. Both methods are used in a way that makes it unnecessary to assume that the plasmas are spheroidal, and it is shown that they are not. Good agreement between the two methods illustrates the possibility to accurately determine plasma densities and geometries within non-idealized, realistic trapping potentials.
The VSEPR model of molecular geometry
Gillespie, Ronald J
2012-01-01
Valence Shell Electron Pair Repulsion (VSEPR) theory is a simple technique for predicting the geometry of atomic centers in small molecules and molecular ions. This authoritative reference was written by Istvan Hartiggai and the developer of VSEPR theory, Ronald J. Gillespie. In addition to its value as a text for courses in molecular geometry and chemistry, it constitutes a classic reference for professionals.Starting with coverage of the broader aspects of VSEPR, this volume narrows its focus to a succinct survey of the methods of structural determination. Additional topics include the appli
Topological gauge theory, Cartan geometry, and gravity
Wise, Derek Keith
2007-12-01
We investigate the geometry of general relativity, and of related topological gauge theories, using Cartan geometry. Cartan geometry---an 'infinitesimal' version of Klein's Erlanger Programm---allows us to view physical spacetime as tangentially approximated by a homogeneous 'model spacetime', such as de Sitter or anti de Sitter spacetime. This idea leads to a common geometric foundation for 3d Chern-Simons gravity, as studied by Witten, and 4d MacDowell-Mansouri gravity. We describe certain topological gauge theories, including BF theory---a natural generalization of 3d gravity to higher dimensions---as 'Cartan gauge theories' in which the gauge field is replaced by a 'Cartan connection' modeled on some Klein geometry G/H. Cartan-type BF theory has solutions that say spacetime is locally isometric to G/H itself; in this case Cartan geometry reduces to the theory of 'geometric structures'. This leads to generalizations of 3d gravity based on other 3d Klein geometries, including those in Thurston's classification of 3d Riemannian model geometries. In 4d gravity, we generalize MacDowell-Mansouri gravity to other Cartan geometries. For BF theory in n-dimensional spacetime, we also describe codimension-2 'branes' as topological defects. These branes---particles in 3d spacetime, strings in 4d, and so on---are shown to be classified by conjugacy classes in the gauge group G of the theory. They also obey 'exotic statistics' which are neither Bose-Einstein nor Fermi-Dirac, but are governed by representations of generalizations of the braid group known as 'motion groups'. These representations come from a natural action of the motion group on the moduli space of flat G-bundles on space. We study this in particular detail in the case of strings in 4d BF theory, where Lin has called the motion group the 'loop braid group', LBn. This makes 4d BF theory with strings into a 'loop braided quantum field theory'. We also use ideas from 'higher gauge theory' to study particles as
Geometry and conformations of benzenecarboxylic acids
Directory of Open Access Journals (Sweden)
IVAN GUTMAN
2004-11-01
Full Text Available The geometry, conformations and energy of mono-, di-, and tri-carboxylic derivatives of benzene were studied by means of the AM1 molecular-orbital method. Whereas the species having no carboxylic groups in the ortho-position (benzoic, isophthalic, terephthalic, and trimesic acids are planar in all their (stable conformations, those possessing carboxylic groups in the ortho-position (phthalic, 1,2,3-benzenetricarboxylic, and 1,2,4-benzenetricarboxylic acids assume a non-planar geometry, with one carboxyl group almost orthogonal to the plane of the benzene ring. Various rotamers of each of the studied benzenecarboxylic acids have nearly the same energy.
PODANÁ, Klára
2017-01-01
This bachelor thesis, Geometry in Art, is mainly focused on geometry in architecture during Gothic period. Its aim is to create an overview of this period and show what geometric parts were mostly used. The thesis is also introducing a few basic construction parts of a Gothic style. For the construction of the gothic windows we can use for example a homothety to which one of the chapters was also dedicated. In the connection with homothety we need to mention the Problem of Apollonius and for ...
Kinetics of Phase Separation in Confined Geometries
Puri, Sanjay
We review analytical and numerical results for the kinetics of phase separation in confined geometries. It is often the case that a confining surface has a preferential attraction for one of the components of a segregating mixture. The equilibrium surface morphology is either partially wet or completely wet, depending on the strength of the surface potential. The dynamical interplay of wetting and phase separation is referred to as surface-directed spinodal decomposition (SDSD), and is of considerable technological importance. We discuss the modeling of SDSD at both the microscopic and coarse-grained levels. We also present results for SDSD in both semi-infinite and confined geometries.
Heat diffusion in fractal geometry cooling surface
Directory of Open Access Journals (Sweden)
Ramšak Matjaz
2012-01-01
Full Text Available In the paper the numerical simulation of heat diffusion in the fractal geometry of Koch snowflake is presented using multidomain mixed Boundary Element Method. The idea and motivation of work is to improve the cooling of small electronic devices using fractal geometry of surface similar to cooling ribs. The heat diffusion is assumed as the only principle of heat transfer. The results are compared to the heat flux of a flat surface. The limiting case of infinite small fractal element is computed using Richardson extrapolation.
Thin shells joining local cosmic string geometries
Energy Technology Data Exchange (ETDEWEB)
Eiroa, Ernesto F. [Universidad de Buenos Aires, Ciudad Universitaria Pabellon I, Departamento de Fisica, Facultad de Ciencias Exactas y Naturales, Buenos Aires (Argentina); Instituto de Astronomia y Fisica del Espacio (IAFE, CONICET-UBA), Buenos Aires (Argentina); Rubin de Celis, Emilio; Simeone, Claudio [Universidad de Buenos Aires, Ciudad Universitaria Pabellon I, Departamento de Fisica, Facultad de Ciencias Exactas y Naturales, Buenos Aires (Argentina); Ciudad Universitaria Pabellon I, IFIBA-CONICET, Buenos Aires (Argentina)
2016-10-15
In this article we present a theoretical construction of spacetimes with a thin shell that joins two different local cosmic string geometries. We study two types of global manifolds, one representing spacetimes with a thin shell surrounding a cosmic string or an empty region with Minkowski metric, and the other corresponding to wormholes which are not symmetric across the throat located at the shell. We analyze the stability of the static configurations under perturbations preserving the cylindrical symmetry. For both types of geometries we find that the static configurations can be stable for suitable values of the parameters. (orig.)
Noncommutative Geometry, Quantum Fields and Motives
Connes, Alain
2007-01-01
The unifying theme of this book is the interplay among noncommutative geometry, physics, and number theory. The two main objects of investigation are spaces where both the noncommutative and the motivic aspects come to play a role: space-time, where the guiding principle is the problem of developing a quantum theory of gravity, and the space of primes, where one can regard the Riemann Hypothesis as a long-standing problem motivating the development of new geometric tools. The book stresses the relevance of noncommutative geometry in dealing with these two spaces. The first part of the book dea
Thin shells joining local cosmic string geometries
Eiroa, Ernesto F; Simeone, Claudio
2016-01-01
In this article we present a theoretical construction of spacetimes with a thin shell that joins two different local cosmic string geometries. We study two types of global manifolds, one representing spacetimes with a standard thin shell and the other corresponding to wormholes which are not symmetric across the throat located at the shell. We analyze the stability of the static configurations under perturbations preserving the cylindrical symmetry. For both types of geometries we find that the static configurations can be stable for suitable values of the parameters.
Thermal geometry from CFT at finite temperature
Energy Technology Data Exchange (ETDEWEB)
Gan, Wen-Cong, E-mail: ganwencong@gmail.com [Department of Physics, Nanchang University, Nanchang 330031 (China); Center for Relativistic Astrophysics and High Energy Physics, Nanchang University, Nanchang 330031 (China); Shu, Fu-Wen, E-mail: shufuwen@ncu.edu.cn [Department of Physics, Nanchang University, Nanchang 330031 (China); Center for Relativistic Astrophysics and High Energy Physics, Nanchang University, Nanchang 330031 (China); Wu, Meng-He, E-mail: menghewu.physik@gmail.com [Department of Physics, Nanchang University, Nanchang 330031 (China); Center for Relativistic Astrophysics and High Energy Physics, Nanchang University, Nanchang 330031 (China)
2016-09-10
We present how the thermal geometry emerges from CFT at finite temperature by using the truncated entanglement renormalization network, the cMERA. For the case of 2d CFT, the reduced geometry is the BTZ black hole or the thermal AdS as expectation. In order to determine which spacetimes prefer to form, we propose a cMERA description of the Hawking–Page phase transition. Our proposal is in agreement with the picture of the recent proposed surface/state correspondence.
Thermal geometry from CFT at finite temperature
Directory of Open Access Journals (Sweden)
Wen-Cong Gan
2016-09-01
Full Text Available We present how the thermal geometry emerges from CFT at finite temperature by using the truncated entanglement renormalization network, the cMERA. For the case of 2d CFT, the reduced geometry is the BTZ black hole or the thermal AdS as expectation. In order to determine which spacetimes prefer to form, we propose a cMERA description of the Hawking–Page phase transition. Our proposal is in agreement with the picture of the recent proposed surface/state correspondence.
Architectural Geometry and Fabrication-Aware Design
Pottmann, Helmut
2013-04-27
Freeform shapes and structures with a high geometric complexity play an increasingly important role in contemporary architecture. While digital models are easily created, the actual fabrication and construction remains a challenge. This is the source of numerous research problems many of which fall into the area of Geometric Computing and form part of a recently emerging research area, called "Architectural Geometry". The present paper provides a short survey of research in Architectural Geometry and shows how this field moves towards a new direction in Geometric Modeling which aims at combining shape design with important aspects of function and fabrication. © 2013 Kim Williams Books, Turin.
Method for Determining Optimum Injector Inlet Geometry
Trinh, Huu P. (Inventor); Myers, W. Neill (Inventor)
2015-01-01
A method for determining the optimum inlet geometry of a liquid rocket engine swirl injector includes obtaining a throttleable level phase value, volume flow rate, chamber pressure, liquid propellant density, inlet injector pressure, desired target spray angle and desired target optimum delta pressure value between an inlet and a chamber for a plurality of engine stages. The method calculates the tangential inlet area for each throttleable stage. The method also uses correlation between the tangential inlet areas and delta pressure values to calculate the spring displacement and variable inlet geometry of a liquid rocket engine swirl injector.
Riemannian geometry in an orthogonal frame
Cartan, Elie Joseph
2001-01-01
Foreword by S S Chern. In 1926-27, Cartan gave a series of lectures in which he introduced exterior forms at the very beginning and used extensively orthogonal frames throughout to investigate the geometry of Riemannian manifolds. In this course he solved a series of problems in Euclidean and non-Euclidean spaces, as well as a series of variational problems on geodesics. In 1960, Sergei P Finikov translated from French into Russian his notes of these Cartan's lectures and published them as a book entitled Riemannian Geometry in an Orthogonal Frame. This book has many innovations, such as the n
Effect of geometry on hydrodynamic film thickness
Brewe, D. E.; Hamrock, B. J.; Taylor, C. M.
1978-01-01
The influence of geometry on the isothermal hydrodynamic film separating two rigid solids was investigated. Pressure-viscosity effects were not considered. The minimum film thickness is derived for fully flooded conjunctions by using the Reynolds boundary conditions. It was found that the minimum film thickness had the same speed, viscosity, and load dependence as Kapitza's classical solution. However, the incorporation of Reynolds boundary conditions resulted in an additional geometry effect. Solutions using the parabolic film approximation are compared with those using the exact expression for the film in the analysis. Contour plots are shown that indicate in detail the pressure developed between the solids.
Project-Based Learning to Explore Taxicab Geometry
Ada, Tuba; Kurtulus, Aytac
2012-01-01
In Turkey, the content of the geometry course in the Primary School Mathematics Education, which is developed by The Council of Higher Education (YOK), comprises Euclidean and non-Euclidean types of geometry. In this study, primary mathematics teacher candidates compared these two geometries by focusing on Taxicab geometry among non-Euclidean…
Predicting the Geometry Knowledge of Pre-Service Elementary Teachers
Duatepe Aksu, Asuman
2013-01-01
In this study, the aim was to examine the factors that predict the geometry knowledge of pre-service elementary teachers. Data was collected on 387 pre-service elementary teachers from four universities by using a geometry knowledge test, the van Hiele geometric thinking level test, a geometry self efficacy scale and a geometry attitude scale.…
Werner coordination chemistry and neurodegeneration.
Telpoukhovskaia, Maria A; Orvig, Chris
2013-02-21
Neurodegenerative diseases are capturing the world's attention as being the next set of diseases we must tackle collectively. Not only are the patients experiencing gradual cognitive and physical decline in most cases, but these diseases are fatal with no prevention currently available. As these diseases are progressive, providing care and symptom treatment for the ageing population is becoming both a medical and a financial challenge. This review discusses how Werner coordination chemistry plays a role in three diseases - those of Alzheimer's, Parkinson's, and prions. Metal ions are considered to be involved in these diseases in part via their propensity to cause toxic aggregation of proteins. First, the coordination of metal ions, with emphasis on copper(II), to metalloproteins that are hallmarks of these diseases - amyloid β, α-synuclein, and prion, respectively - will be discussed. We will present the current understanding of the metal coordination environments created by the amino acids of these proteins, as well as metal binding affinity. Second, a diverse set of examples of rationally designed metal chelators to outcompete this deleterious binding will be examined based on coordination mode and affinity toward bio-relevant metal ions. Overall, this review will give a general overview of protein and metal chelator coordination environments in neurodegenerative diseases.
Application of Analytical Geometry to the
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 18; Issue 9. Application of Analytical Geometry to the Form of Gear Teeth. V G A Goss. General Article Volume 18 Issue 9 September 2013 pp 817-831. Fulltext. Click here to view fulltext PDF. Permanent link:
On Ancient Babylonian Algebra and Geometry
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 8; Issue 8. On Ancient Babylonian Algebra and Geometry. Rahul Roy. General Article Volume 8 Issue 8 August 2003 pp 27-42. Fulltext. Click here to view fulltext PDF. Permanent link: http://www.ias.ac.in/article/fulltext/reso/008/08/0027-0042. Keywords.
Causal random geometry from stochastic quantization
DEFF Research Database (Denmark)
Ambjørn, Jan; Loll, R.; Westra, W.
2010-01-01
in this short note we review a recently found formulation of two-dimensional causal quantum gravity defined through Causal Dynamical Triangulations and stochastic quantization. This procedure enables one to extract the nonperturbative quantum Hamiltonian of the random surface model including...... the sum over topologies. Interestingly, the generally fictitious stochastic time corresponds to proper time on the geometries...
Generalized geometry and non-symmetric gravity
Jurco, Branislav; Khoo, Fech Scen; Schupp, Peter; Vysoky, Jan
2015-01-01
Generalized geometry provides the framework for a systematic approach to non-symmetric metric gravity theory and naturally leads to an Einstein-Kalb-Ramond gravity theory with totally anti-symmetric contortion. The approach is related to the study of the low-energy effective closed string gravity actions.
D-instantons and asymptotic geometries
Bergshoeff, E.; Behrndt, K.
1998-01-01
The large-N limit of D-3-branes is expected to correspond to a superconformal field theory living on the boundary of the anti-de Sitter space appearing in the near-horizon geometry. Dualizing the D-3-brane to a D-instanton, we show that this limit is equivalent to a type IIB S-duality. In both cases
The Geometry of the Universe: Part 1
Francis, Stephanie
2009-01-01
This article describes how the author carries out an investigation into the geometry of the three possible curvatures of the universe. The author begins the investigation by looking on the web and in books. She found that the general consensus was that there were three different possible curvatures of the universe, namely: (1) flat; (2) positive;…
Mathematics: Algebra and Geometry. GED Scoreboost.
Hoyt, Cathy
GED "Scoreboost" materials target exactly the skills one needs to pass the General Educational Development (GED) tests. This book focuses on the GED Mathematics test. To prepare for the test, the test taker needs to learn skills in number and operation sense, data and statistics, geometry and measurement, and algebra. To pass the test,…
Quantum geometry of bosonic strings - revisited
Energy Technology Data Exchange (ETDEWEB)
Botelho, Luiz C.L.; Botelho, Raimundo C.L. [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil); Universidade Federal Rural do Rio de Janeiro, RJ (Brazil). Dept. de Fisica
1999-07-01
We review the original paper by A.M. Polyakov (Quantum Geometry of Bosonic Strings) with corrections and improvements the concepts exposed there and following as closely as possible to the original A.M. Polyakov's paper. (author)
Foliations and the geometry of 3-manifolds
Calegari, Danny
2014-01-01
This unique reference, aimed at research topologists, gives an exposition of the 'pseudo-Anosov' theory of foliations of 3-manifolds. This theory generalizes Thurston's theory of surface automorphisms and reveals an intimate connection between dynamics, geometry and topology in 3 dimensions.
Fast rendering of scanned room geometries
DEFF Research Database (Denmark)
Olesen, Søren Krarup; Markovic, Milos; Hammershøi, Dorte
2014-01-01
.g. the range detection sensors used in the kinect device. This device provides a high rate of range data, which can be combined to give a very detailed map of the surrounding geometry. Such data was captured and has been presented in an earlier paper, incl. a demonstration of the principle of voxel...
Geometry and the Design of Product Packaging
Cherico, Cindy M.
2011-01-01
The most common question the author's students ask is, "When will I ever use this in real life?" To address this question in her geometry classes, the author sought to create a project that would incorporate a real-world business situation with their lesson series on the surface area and volume of three-dimensional objects--specifically, prisms,…
Size and geometry of hepatic radiofrequency lesions.
Mulier, S; Ni, Y; Miao, Y; Rosière, A; Khoury, A; Marchal, G; Michel, L
2003-12-01
To report and compare the size and geometry of hepatic radiofrequency (RF) lesions using the currently available commercial devices. A literature search was carried out for the period from January 1st 1990 to June 15th 2003. The commercial suppliers were asked to provide all available data. For each electrode and protocol, size and geometry of single-cycle thermal lesions were registered. No information at all on size and geometry of the inducible lesions was available for 17 of the 28 current commercial electrodes. Many descriptions of RF lesions are limited to the mean transverse diameter. With normal blood flow, diameter of lesions is often smaller than suggested by the length of the electrode tip or the diameter of the deployed prongs. Lesions are rarely perfect spheres but either ellipses or flattened spheres. Distortion of the RF lesion by nearby blood vessels is very common. Fusion of thermal zones between prongs of expandable electrodes can be incomplete. Blood flow interruption using a Pringle maneuver yields larger lesions that are less distorted and more complete. There is insufficient experimental data for many electrodes that are currently used in patients. RF companies should provide these data before releasing electrodes for use. For those electrodes for which data exist, coagulation lesions are often smaller, less spherical, less complete and less regular than generally presumed. Accurate knowledge of size and geometry of RF lesions is crucial to prevent local recurrence.
Geometry task sheets : grades pk-2
Rosenberg, Mary
2009-01-01
For grades PK-2, our Common Core State Standards-based resource meets the geometry concepts addressed by the NCTM standards and encourages the students to learn and review the concepts in unique ways. Each task sheet is organized around a central problem taken from real-life experiences of the students.
Geometry task sheets : grades 3-5
Rosenberg, Mary
2009-01-01
For grades 3-5, our Common Core State Standards-based resource meets the geometry concepts addressed by the NCTM standards and encourages the students to learn and review the concepts in unique ways. Each task sheet is organized around a central problem taken from real-life experiences of the students.
Strontium clusters: electronic and geometry shell effects
DEFF Research Database (Denmark)
Lyalin, Andrey G.; Solov'yov, Ilia; Solov'yov, Andrey V.
2008-01-01
The optimized structure and electronic properties of neutral, singly and doubly charged strontium clusters have been investigated using it ab initio theoretical methods based on density-functional theory. We have systematically calculated the optimized geometries of neutral, singly and doubly...
User Interface Design for Dynamic Geometry Software
Kortenkamp, Ulrich; Dohrmann, Christian
2010-01-01
In this article we describe long-standing user interface issues with Dynamic Geometry Software and common approaches to address them. We describe first prototypes of multi-touch-capable DGS. We also give some hints on the educational benefits of proper user interface design.
Relating arithmetical techniques of proportion to geometry
DEFF Research Database (Denmark)
Wijayanti, Dyana
2015-01-01
The purpose of this study is to investigate how textbooks introduce and treat the theme of proportion in geometry (similarity) and arithmetic (ratio and proportion), and how these themes are linked to each other in the books. To pursue this aim, we use the anthropological theory of the didactic...
Fermoral Intercondylar Notch Geometry Of Nigerians | Didia ...
African Journals Online (AJOL)
The notch geometry had been implicated in anterior cruciate ligament (ACL) injuries and from this study we presume that the difference in incidence of ACL injuries between males and females is as a result of differences in intercondylar notch width index and the diameter of distal end of femur in both sexes. KEY WORDS: ...
Applications of Differential Geometry to Cartography
Benitez, Julio; Thome, Nestor
2004-01-01
This work introduces an application of differential geometry to cartography. The mathematical aspects of some geographical projections of Earth surface are revealed together with some of its more important properties. An important problem since the discovery of the 'spherical' form of the Earth is how to compose a reliable map of the surface of…
Parametric Study Of Window Frame Geometry
DEFF Research Database (Denmark)
Zajas, Jan Jakub; Heiselberg, Per
2013-01-01
This paper describes a parametric study on window frame geometry with the goal of designing frames with very good thermal properties. Three different parametric frame models are introduced, deseribed by a number of variables. In the first part of the study, a process of sensitivity analysis...
Quasi-crystalline geometry for architectural structures
DEFF Research Database (Denmark)
Wester, Ture; Weinzieri, Barbara
The quasi-crystal (QC) type of material was discovered in 1983 by Dan Schechtman from Technion, Haifa. This new crystalline structure of material broke totally with the traditional conception of crystals and geometry introducing non-periodic close packing of cells with fivefold symmetry in 3D space...
Toric Geometry of the Regular Convex Polyhedra
Directory of Open Access Journals (Sweden)
Fiammetta Battaglia
2017-01-01
Full Text Available We describe symplectic and complex toric spaces associated with the five regular convex polyhedra. The regular tetrahedron and the cube are rational and simple, the regular octahedron is not simple, the regular dodecahedron is not rational, and the regular icosahedron is neither simple nor rational. We remark that the last two cases cannot be treated via standard toric geometry.
Methods of algebraic geometry in control theory
Falb, Peter
1999-01-01
"Control theory represents an attempt to codify, in mathematical terms, the principles and techniques used in the analysis and design of control systems. Algebraic geometry may, in an elementary way, be viewed as the study of the structure and properties of the solutions of systems of algebraic equations. The aim of this book is to provide access to the methods of algebraic geometry for engineers and applied scientists through the motivated context of control theory" .* The development which culminated with this volume began over twenty-five years ago with a series of lectures at the control group of the Lund Institute of Technology in Sweden. I have sought throughout to strive for clarity, often using constructive methods and giving several proofs of a particular result as well as many examples. The first volume dealt with the simplest control systems (i.e., single input, single output linear time-invariant systems) and with the simplest algebraic geometry (i.e., affine algebraic geometry). While this is qui...
Geometry optimization and vibrational frequencies of tetracene ...
African Journals Online (AJOL)
Tetracene is an organic semiconductor with chemical formula C18H12 used in organic field effecttransistor (OFET) and organic light emitting diode (OLED). In this work, the molecular geometry (optimized bond lengths and bond angles), vibrational frequencies and intensities, HOMO-LUMO Energy gap and Atomic charge ...
Special Relativity as a Simple Geometry Problem
de Abreu, Rodrigo; Guerra, Vasco
2009-01-01
The null result of the Michelson-Morley experiment and the constancy of the one-way speed of light in the "rest system" are used to formulate a simple problem, to be solved by elementary geometry techniques using a pair of compasses and non-graduated rulers. The solution consists of a drawing allowing a direct visualization of all the fundamental…
Algebraic Geometry Solves an Old Matrix Problem
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 4; Issue 12. Algebraic Geometry Solves an Old Matrix Problem. R Bhatia. Research News Volume 4 Issue 12 ... Author Affiliations. R Bhatia1. Statistics and Mathematics Unit, Indian Statistical Institute, 7, SJS Sansanwal Marg, New Delhi 110 016, India.