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
Real symplectic formulation of local special geometry
Ferrara, Sergio; Ferrara, Sergio; Macia, Oscar
2006-01-01
We consider a formulation of local special geometry in terms of Darboux special coordinates $P^I=(p^i,q_i)$, $I=1,...,2n$. A general formula for the metric is obtained which is manifestly $\\mathbf{Sp}(2n,\\mathbb{R})$ covariant. Unlike the rigid case the metric is not given by the Hessian of the real function $S(P)$ which is the Legendre transform of the imaginary part of the holomorphic prepotential. Rather it is given by an expression that contains $S$, its Hessian and the conjugate momenta $S_I=\\frac{\\partial S}{\\partial P^I}$. Only in the one-dimensional case ($n=1$) is the real (two-dimensional) metric proportional to the Hessian with an appropriate conformal factor.
Geometry of the local equivalence of states
Energy Technology Data Exchange (ETDEWEB)
Sawicki, A; Kus, M, E-mail: assawi@cft.edu.pl, E-mail: marek.kus@cft.edu.pl [Center for Theoretical Physics, Polish Academy of Sciences, Al Lotnikow 32/46, 02-668 Warszawa (Poland)
2011-12-09
We present a description of locally equivalent states in terms of symplectic geometry. Using the moment map between local orbits in the space of states and coadjoint orbits of the local unitary group, we reduce the problem of local unitary equivalence to an easy part consisting of identifying the proper coadjoint orbit and a harder problem of the geometry of fibers of the moment map. We give a detailed analysis of the properties of orbits of 'equally entangled states'. In particular, we show connections between certain symplectic properties of orbits such as their isotropy and coisotropy with effective criteria of local unitary equivalence. (paper)
The local index formula in noncommutative geometry
International Nuclear Information System (INIS)
Higson, N.
2003-01-01
These notes present a partial account of the local index theorem in non-commutative geometry discovered by Alain Connes and Henri Moscovici. It includes Elliptic partial differential operators, cyclic homology theory, Chern characters, homotopy invariants and the index formulas
Index theory for locally compact noncommutative geometries
Carey, A L; Rennie, A; Sukochev, F A
2014-01-01
Spectral triples for nonunital algebras model locally compact spaces in noncommutative geometry. In the present text, the authors prove the local index formula for spectral triples over nonunital algebras, without the assumption of local units in our algebra. This formula has been successfully used to calculate index pairings in numerous noncommutative examples. The absence of any other effective method of investigating index problems in geometries that are genuinely noncommutative, particularly in the nonunital situation, was a primary motivation for this study and the authors illustrate this point with two examples in the text. In order to understand what is new in their approach in the commutative setting the authors prove an analogue of the Gromov-Lawson relative index formula (for Dirac type operators) for even dimensional manifolds with bounded geometry, without invoking compact supports. For odd dimensional manifolds their index formula appears to be completely new.
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.)
Thin shells joining local cosmic string geometries
International Nuclear Information System (INIS)
Eiroa, Ernesto F.; Rubin de Celis, Emilio; 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 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.)
Local coordination of polyvalent metal ions in molten halide mixtures
International Nuclear Information System (INIS)
Akdeniz, Z.; Tosi, M.P.
1989-07-01
Ample experimental evidence is available in the literature on the geometry and the stability of local coordination for polyvalent metal ions in molten mixtures of their halides with alkali halides. Recent schemes for classifying this evidence are discussed. Dissociation of tetrahedral halocomplexes in good ionic systems can be viewed as a classical Mott problem of bound-state stability in a conducting matrix. More generally, structural coordinates can be constructed from properties of the component elements, to separate out systems with long-lived fourfold or sixfold coordination and to distinguish between these. (author). 11 refs, 1 fig
Stabilizing embedology: Geometry-preserving delay-coordinate maps
Eftekhari, Armin; Yap, Han Lun; Wakin, Michael B.; Rozell, Christopher J.
2018-02-01
Delay-coordinate mapping is an effective and widely used technique for reconstructing and analyzing the dynamics of a nonlinear system based on time-series outputs. The efficacy of delay-coordinate mapping has long been supported by Takens' embedding theorem, which guarantees that delay-coordinate maps use the time-series output to provide a reconstruction of the hidden state space that is a one-to-one embedding of the system's attractor. While this topological guarantee ensures that distinct points in the reconstruction correspond to distinct points in the original state space, it does not characterize the quality of this embedding or illuminate how the specific parameters affect the reconstruction. In this paper, we extend Takens' result by establishing conditions under which delay-coordinate mapping is guaranteed to provide a stable embedding of a system's attractor. Beyond only preserving the attractor topology, a stable embedding preserves the attractor geometry by ensuring that distances between points in the state space are approximately preserved. In particular, we find that delay-coordinate mapping stably embeds an attractor of a dynamical system if the stable rank of the system is large enough to be proportional to the dimension of the attractor. The stable rank reflects the relation between the sampling interval and the number of delays in delay-coordinate mapping. Our theoretical findings give guidance to choosing system parameters, echoing the tradeoff between irrelevancy and redundancy that has been heuristically investigated in the literature. Our initial result is stated for attractors that are smooth submanifolds of Euclidean space, with extensions provided for the case of strange attractors.
Observations on the Darboux coordinates for rigid special geometry
Ferrara, Sergio; Ferrara, Sergio; Macia, Oscar
2006-01-01
We exploit some relations which exist when (rigid) special geometry is formulated in real symplectic special coordinates $P^I=(p^\\Lambda,q_\\Lambda), I=1,...,2n$. The central role of the real $2n\\times 2n$ matrix $M(\\Re \\mathcal{F},\\Im \\mathcal{F})$, where $\\mathcal{F} = \\partial_\\Lambda\\partial_\\Sigma F$ and $F$ is the holomorphic prepotential, is elucidated in the real formalism. The property $M\\Omega M=\\Omega$ with $\\Omega$ being the invariant symplectic form is used to prove several identities in the Darboux formulation. In this setting the matrix $M$ coincides with the (negative of the) Hessian matrix $H(S)=\\frac{\\partial^2 S}{\\partial P^I\\partial P^J}$ of a certain hamiltonian real function $S(P)$, which also provides the metric of the special K\\"ahler manifold. When $S(P)=S(U+\\bar U)$ is regarded as a "K\\"ahler potential'' of a complex manifold with coordinates $U^I=\\frac12(P^I+iZ^I)$, then it provides a K\\"ahler metric of an hyperk\\"ahler manifold which describes the hypermultiplet geometry obtained by...
Axisymmetric magnetohydrodynamic equilibria in local polar coordinates
International Nuclear Information System (INIS)
Clemente, R.A.
1982-01-01
The Grad--Shafranov equation for an ideal magnetohydrodynamic axisymmetric toroidal configuration is solved analytically in a local polar coordinate system using a novel method which produces solutions valid up to the second order in the inverse aspect ratio expansion
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.
Geometry optimization of molecules within an LCGTO local-density functional approach
International Nuclear Information System (INIS)
Mintmire, J.W.
1990-01-01
We describe our implementation of geometry optimization techniques within the linear combination of Gaussian-type orbitals (LCGTO) approach to local-density functional theory. The algorithm for geometry optimization is based on the evaluation of the gradient of the total energy with respect to internal coordinates within the local-density functional scheme. We present optimization results for a range of small molecules which serve as test cases for our approach
Indoor localization using unsupervised manifold alignment with geometry perturbation
Majeed, Khaqan
2014-04-01
The main limitation of deploying/updating Received Signal Strength (RSS) based indoor localization is the construction of fingerprinted radio map, which is quite a hectic and time-consuming process especially when the indoor area is enormous and/or dynamic. Different approaches have been undertaken to reduce such deployment/update efforts, but the performance degrades when the fingerprinting load is reduced below a certain level. In this paper, we propose an indoor localization scheme that requires as low as 1% fingerprinting load. This scheme employs unsupervised manifold alignment that takes crowd sourced RSS readings and localization requests as source data set and the environment\\'s plan coordinates as destination data set. The 1% fingerprinting load is only used to perturb the local geometries in the destination data set. Our proposed algorithm was shown to achieve less than 5 m mean localization error with 1% fingerprinting load and a limited number of crowd sourced readings, when other learning based localization schemes pass the 10 m mean error with the same information.
Indoor localization using unsupervised manifold alignment with geometry perturbation
Majeed, Khaqan; Sorour, Sameh; Al-Naffouri, Tareq Y.; Valaee, Shahrokh
2014-01-01
The main limitation of deploying/updating Received Signal Strength (RSS) based indoor localization is the construction of fingerprinted radio map, which is quite a hectic and time-consuming process especially when the indoor area is enormous and/or dynamic. Different approaches have been undertaken to reduce such deployment/update efforts, but the performance degrades when the fingerprinting load is reduced below a certain level. In this paper, we propose an indoor localization scheme that requires as low as 1% fingerprinting load. This scheme employs unsupervised manifold alignment that takes crowd sourced RSS readings and localization requests as source data set and the environment's plan coordinates as destination data set. The 1% fingerprinting load is only used to perturb the local geometries in the destination data set. Our proposed algorithm was shown to achieve less than 5 m mean localization error with 1% fingerprinting load and a limited number of crowd sourced readings, when other learning based localization schemes pass the 10 m mean error with the same information.
Distributed formation tracking using local coordinate systems
DEFF Research Database (Denmark)
Yang, Qingkai; Cao, Ming; Garcia de Marina, Hector
2018-01-01
This paper studies the formation tracking problem for multi-agent systems, for which a distributed estimator–controller scheme is designed relying only on the agents’ local coordinate systems such that the centroid of the controlled formation tracks a given trajectory. By introducing a gradient...... descent term into the estimator, the explicit knowledge of the bound of the agents’ speed is not necessary in contrast to existing works, and each agent is able to compute the centroid of the whole formation in finite time. Then, based on the centroid estimation, a distributed control algorithm...
Gaur, A.; Klysubun, W.; Soni, Balram; Shrivastava, B. D.; Prasad, J.; Srivastava, K.
2016-10-01
X-ray absorption spectroscopy (XAS) is very useful in revealing the information about geometric and electronic structure of a transition-metal absorber and thus commonly used for determination of metal-ligand coordination. But XAFS analysis becomes difficult if differently coordinated metal centers are present in a system. In the present investigation, existence of distinct coordination geometries around metal centres have been studied by XAFS in a series of trimesic acid Cu(II) complexes. The complexes studied are: Cu3(tma)2(im)6 8H2O (1), Cu3(tma)2(mim)6 17H2O (2), Cu3(tma)2(tmen)3 8.5H2O (3), Cu3(tma) (pmd)3 6H2O (ClO4)3 (4) and Cu3(tma)2 3H2O (5). These complexes have not only Cu metal centres with different coordination but in complexes 1-3, there are multiple coordination geometries present around Cu centres. Using XANES spectra, different coordination geometries present in these complexes have been identified. The variation observed in the pre-edge features and edge features have been correlated with the distortion of the specific coordination environment around Cu centres in the complexes. XANES spectra have been calculated for the distinct metal centres present in the complexes by employing ab-initio calculations. These individual spectra have been used to resolve the spectral contribution of the Cu centres to the particular XANES features exhibited by the experimental spectra of the multinuclear complexes. Also, the variation in the 4p density of states have been calculated for the different Cu centres and then correlated with the features originated from corresponding coordination of Cu. Thus, these spectral features have been successfully utilized to detect the presence of the discrete metal centres in a system. The inferences about the coordination geometry have been supported by EXAFS analysis which has been used to determine the structural parameters for these complexes.
The SUSY oscillator from local geometry: Dynamics and coherent states
International Nuclear Information System (INIS)
Thienel, H.P.
1994-01-01
The choice of a coordinate chart on an analytical R n (R a n ) provides a representation of the n-dimensional SUSY oscillator. The corresponding Hilbert space is Cartan's exterior algebra endowed with a suitable scalar product. The exterior derivative gives rise to the algebra of the n-dimensional SUSY oscillator. Its euclidean dynamics is an inherent consequence of the geometry imposed by the Lie derivative generating the dilations, i.e. evolution of the quantum system corresponds to parametrization of a sequence of charts by euclidean time. Coherent states emerge as a natural structure related to the Lie derivative generating the translations. (orig.)
Lossless Geometry Compression Through Changing 3D Coordinates into 1D
Directory of Open Access Journals (Sweden)
Yongkui Liu
2013-08-01
Full Text Available A method of lossless geometry compression on the coordinates of the vertexes for grid model is presented. First, the 3D coordinates are pre-processed to be transformed into a specific form. Then these 3D coordinates are changed into 1D data by making the three coordinates of a vertex represented by only a position number, which is made of a large integer. To minimize the integers, they are sorted and the differences between two adjacent vertexes are stored in a vertex table. In addition to the technique of geometry compression on coordinates, an improved method for storing the compressed topological data in a facet table is proposed to make the method more complete and efficient. The experimental results show that the proposed method has a better compression rate than the latest method of lossless geometry compression, the Isenburg-Lindstrom-Snoeyink method. The theoretical analysis and the experiment results also show that the important decompression time of the new method is short. Though the new method is explained in the case of a triangular grid, it can also be used in other forms of grid model.
Minimal local Lagrangians for higher-spin geometry
International Nuclear Information System (INIS)
Francia, Dario; Sagnotti, Augusto
2005-01-01
The Fronsdal Lagrangians for free totally symmetric rank-s tensors φ μ 1 ...μ s rest on suitable trace constraints for their gauge parameters and gauge fields. Only when these constraints are removed, however, the resulting equations reflect the expected free higher-spin geometry. We show that geometric equations, in both their local and non-local forms, can be simply recovered from local Lagrangians with only two additional fields, a rank-(s-3) compensator α μ 1 ...μ s-3 and a rank-(s-4) Lagrange multiplier β μ 1 ...μ s-4 . In a similar fashion, we show that geometric equations for unconstrained rank-n totally symmetric spinor-tensors ψ μ 1 ...μ n can be simply recovered from local Lagrangians with only two additional spinor-tensors, a rank-(n-2) compensator ξ μ 1 ...μ n-2 and a rank-(n-3) Lagrange multiplier λ μ 1 ...μ n-3
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.
Perez-Alday, Erick A; Thomas, Jason A; Kabir, Muammar; Sedaghat, Golriz; Rogovoy, Nichole; van Dam, Eelco; van Dam, Peter; Woodward, William; Fuss, Cristina; Ferencik, Maros; Tereshchenko, Larisa G
We conducted a prospective clinical study (n=14; 29% female) to assess the accuracy of a three-dimensional (3D) photography-based method of torso geometry reconstruction and body surface electrodes localization. The position of 74 body surface electrocardiographic (ECG) electrodes (diameter 5mm) was defined by two methods: 3D photography, and CT (marker diameter 2mm) or MRI (marker size 10×20mm) imaging. Bland-Altman analysis showed good agreement in X (bias -2.5 [95% limits of agreement (LoA) -19.5 to 14.3] mm), Y (bias -0.1 [95% LoA -14.1 to 13.9] mm), and Z coordinates (bias -0.8 [95% LoA -15.6 to 14.2] mm), as defined by the CT/MRI imaging, and 3D photography. The average Hausdorff distance between the two torso geometry reconstructions was 11.17±3.05mm. Thus, accurate torso geometry reconstruction using 3D photography is feasible. Body surface ECG electrodes coordinates as defined by the CT/MRI imaging, and 3D photography, are in good agreement. Copyright © 2017 Elsevier Inc. All rights reserved.
Majeed, Khaqan; Sorour, Sameh; Al-Naffouri, Tareq Y.; Valaee, Shahrokh
2015-01-01
The Received Signal Strength (RSS) based fingerprinting approaches for indoor localization pose a need for updating the fingerprint databases due to dynamic nature of the indoor environment. This process is hectic and time-consuming when the size of the indoor area is large. The semi-supervised approaches reduce this workload and achieve good accuracy around 15% of the fingerprinting load but the performance is severely degraded if it is reduced below this level. We propose an indoor localization framework that uses unsupervised manifold alignment. It requires only 1% of the fingerprinting load, some crowd sourced readings and plan coordinates of the indoor area. The 1% fingerprinting load is used only in perturbing the local geometries of the plan coordinates. The proposed framework achieves less than 5m mean localization error, which is considerably better than semi-supervised approaches at very small amount of fingerprinting load. In addition, the few location estimations together with few fingerprints help to estimate the complete radio map of the indoor environment. The estimation of radio map does not demand extra workload rather it employs the already available information from the proposed indoor localization framework. The testing results for radio map estimation show almost 50% performance improvement by using this information as compared to using only fingerprints.
Majeed, Khaqan
2015-12-22
The Received Signal Strength (RSS) based fingerprinting approaches for indoor localization pose a need for updating the fingerprint databases due to dynamic nature of the indoor environment. This process is hectic and time-consuming when the size of the indoor area is large. The semi-supervised approaches reduce this workload and achieve good accuracy around 15% of the fingerprinting load but the performance is severely degraded if it is reduced below this level. We propose an indoor localization framework that uses unsupervised manifold alignment. It requires only 1% of the fingerprinting load, some crowd sourced readings and plan coordinates of the indoor area. The 1% fingerprinting load is used only in perturbing the local geometries of the plan coordinates. The proposed framework achieves less than 5m mean localization error, which is considerably better than semi-supervised approaches at very small amount of fingerprinting load. In addition, the few location estimations together with few fingerprints help to estimate the complete radio map of the indoor environment. The estimation of radio map does not demand extra workload rather it employs the already available information from the proposed indoor localization framework. The testing results for radio map estimation show almost 50% performance improvement by using this information as compared to using only fingerprints.
Sossinsky, A B
2012-01-01
The book is an innovative modern exposition of geometry, or rather, of geometries; it is the first textbook in which Felix Klein's Erlangen Program (the action of transformation groups) is systematically used as the basis for defining various geometries. The course of study presented is dedicated to the proposition that all geometries are created equal--although some, of course, remain more equal than others. The author concentrates on several of the more distinguished and beautiful ones, which include what he terms "toy geometries", the geometries of Platonic bodies, discrete geometries, and classical continuous geometries. The text is based on first-year semester course lectures delivered at the Independent University of Moscow in 2003 and 2006. It is by no means a formal algebraic or analytic treatment of geometric topics, but rather, a highly visual exposition containing upwards of 200 illustrations. The reader is expected to possess a familiarity with elementary Euclidean geometry, albeit those lacking t...
Lundh, Torbjörn; Suh, Ga-Young; DiGiacomo, Phillip; Cheng, Christopher
2018-03-03
Vascular morphology characterization is useful for disease diagnosis, risk stratification, treatment planning, and prediction of treatment durability. To quantify the dynamic surface geometry of tubular-shaped anatomic structures, we propose a simple, rigorous Lagrangian cylindrical coordinate system to monitor well-defined surface points. Specifically, the proposed system enables quantification of surface curvature and cross-sectional eccentricity. Using idealized software phantom examples, we validate the method's ability to accurately quantify longitudinal and circumferential surface curvature, as well as eccentricity and orientation of eccentricity. We then apply the method to several medical imaging data sets of human vascular structures to exemplify the utility of this coordinate system for analyzing morphology and dynamic geometric changes in blood vessels throughout the body. Graphical abstract Pointwise longitudinal curvature of a thoracic aortic endograft surface for systole and diastole, with their absolute difference.
Indian Academy of Sciences (India)
. In the previous article we looked at the origins of synthetic and analytic geometry. More practical minded people, the builders and navigators, were studying two other aspects of geometry- trigonometry and integral calculus. These are actually ...
Prasolov, V V
2015-01-01
This book provides a systematic introduction to various geometries, including Euclidean, affine, projective, spherical, and hyperbolic geometries. Also included is a chapter on infinite-dimensional generalizations of Euclidean and affine geometries. A uniform approach to different geometries, based on Klein's Erlangen Program is suggested, and similarities of various phenomena in all geometries are traced. An important notion of duality of geometric objects is highlighted throughout the book. The authors also include a detailed presentation of the theory of conics and quadrics, including the theory of conics for non-Euclidean geometries. The book contains many beautiful geometric facts and has plenty of problems, most of them with solutions, which nicely supplement the main text. With more than 150 figures illustrating the arguments, the book can be recommended as a textbook for undergraduate and graduate-level courses in geometry.
A co-ordinate system for reactor physics calculations in hexagonal geometry
International Nuclear Information System (INIS)
Burte, D.P.
1990-01-01
A method for generating all the geometric information concerning typical reactor physics calculations for a basically hexagonal reactor core or its sector involving any of the possible symmetries is presented. The geometrically allowed symmetries for regular hexagons are discussed. The approach is based on the choice of a suitable co-ordinate system, viz. one using three coplanar (including one redundant) axes, each at 120 0 with its cyclically preceding one. A code named KEKULE' is developed for a 2-D, finite difference, one-group diffusion analysis of a hexagonal core using the approach. It can cater to a full hexagonal core as well as to any symmetric sectorial part of it. The main feature of the code is that the input concerning geometry is a bare minimum. It is hoped that the approach presented will be useful even for the calculations for hexagonal fuel assemblies. (author)
The flux-coordinate independent approach applied to X-point geometries
International Nuclear Information System (INIS)
Hariri, F.; Hill, P.; Ottaviani, M.; Sarazin, Y.
2014-01-01
A Flux-Coordinate Independent (FCI) approach for anisotropic systems, not based on magnetic flux coordinates, has been introduced in Hariri and Ottaviani [Comput. Phys. Commun. 184, 2419 (2013)]. In this paper, we show that the approach can tackle magnetic configurations including X-points. Using the code FENICIA, an equilibrium with a magnetic island has been used to show the robustness of the FCI approach to cases in which a magnetic separatrix is present in the system, either by design or as a consequence of instabilities. Numerical results are in good agreement with the analytic solutions of the sound-wave propagation problem. Conservation properties are verified. Finally, the critical gain of the FCI approach in situations including the magnetic separatrix with an X-point is demonstrated by a fast convergence of the code with the numerical resolution in the direction of symmetry. The results highlighted in this paper show that the FCI approach can efficiently deal with X-point geometries
Local Gaussian approximation in the generator coordinate method
International Nuclear Information System (INIS)
Onishi, Naoki; Une, Tsutomu.
1975-01-01
A transformation from a non-orthogonal representation to an orthogonal representation of wave functions is studied in the generator coordinate method. A differential equation can be obtained by the transformation for a case that the eigenvalue equation of the overlap kernel is solvable. By assuming local Gaussian overlap, we derive a Schroedinger-type equation for the collective motion from the Hill-Wheeler integral equation. (auth.)
Local Gaussian approximation in the generator coordinate method
Energy Technology Data Exchange (ETDEWEB)
Onishi, N [Tokyo Univ. (Japan). Coll. of General Education; Une, Tsutomu
1975-02-01
A transformation from a non-orthogonal representation to an orthogonal representation of wave functions is studied in the generator coordinate method. A differential equation can be obtained by the transformation for a case that the eigenvalue equation of the overlap kernel is solvable. By assuming local Gaussian overlap, we derive a Schroedinger-type equation for the collective motion from the Hill-Wheeler integral equation.
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
Data Locality via Coordinated Caching for Distributed Processing
Fischer, M.; Kuehn, E.; Giffels, M.; Jung, C.
2016-10-01
To enable data locality, we have developed an approach of adding coordinated caches to existing compute clusters. Since the data stored locally is volatile and selected dynamically, only a fraction of local storage space is required. Our approach allows to freely select the degree at which data locality is provided. It may be used to work in conjunction with large network bandwidths, providing only highly used data to reduce peak loads. Alternatively, local storage may be scaled up to perform data analysis even with low network bandwidth. To prove the applicability of our approach, we have developed a prototype implementing all required functionality. It integrates seamlessly into batch systems, requiring practically no adjustments by users. We have now been actively using this prototype on a test cluster for HEP analyses. Specifically, it has been integral to our jet energy calibration analyses for CMS during run 2. The system has proven to be easily usable, while providing substantial performance improvements. Since confirming the applicability for our use case, we have investigated the design in a more general way. Simulations show that many infrastructure setups can benefit from our approach. For example, it may enable us to dynamically provide data locality in opportunistic cloud resources. The experience we have gained from our prototype enables us to realistically assess the feasibility for general production use.
The Weakly Nonlinear Magnetorotational Instability in a Local Geometry
Clark, S. E.; Oishi, Jeffrey S.
2017-05-01
The magnetorotational instability (MRI) is a fundamental process of accretion disk physics, but its saturation mechanism remains poorly understood despite considerable theoretical and computational effort. We present a multiple-scales analysis of the non-ideal MRI in the weakly nonlinear regime—that is, when the most unstable MRI mode has a growth rate asymptotically approaching zero from above. Here, we develop our theory in a local, Cartesian channel. Our results confirm the finding by Umurhan et al. that the perturbation amplitude follows a Ginzburg-Landau equation. We further find that the Ginzburg-Landau equation will arise for the local MRI system with shear-periodic boundary conditions, when the effects of ambipolar diffusion are considered. A detailed force balance for the saturated azimuthal velocity and vertical magnetic field demonstrates that, even when diffusive effects are important, the bulk flow saturates via the combined processes of reducing the background shear and rearranging and strengthening the background vertical magnetic field. We directly simulate the Ginzburg-Landau amplitude evolution for our system, and demonstrate the pattern formation our model predicts on long scales of length- and timescales. We compare the weakly nonlinear theory results to a direct numerical simulation of the MRI in a thin-gap Taylor Couette flow.
The Weakly Nonlinear Magnetorotational Instability in a Local Geometry
Energy Technology Data Exchange (ETDEWEB)
Clark, S. E. [Department of Astronomy, Columbia University, New York, NY 10027 (United States); Oishi, Jeffrey S., E-mail: seclark@astro.columbia.edu [Department of Physics and Astronomy, Bates College, Lewiston, ME 04240 (United States)
2017-05-20
The magnetorotational instability (MRI) is a fundamental process of accretion disk physics, but its saturation mechanism remains poorly understood despite considerable theoretical and computational effort. We present a multiple-scales analysis of the non-ideal MRI in the weakly nonlinear regime—that is, when the most unstable MRI mode has a growth rate asymptotically approaching zero from above. Here, we develop our theory in a local, Cartesian channel. Our results confirm the finding by Umurhan et al. that the perturbation amplitude follows a Ginzburg–Landau equation. We further find that the Ginzburg–Landau equation will arise for the local MRI system with shear-periodic boundary conditions, when the effects of ambipolar diffusion are considered. A detailed force balance for the saturated azimuthal velocity and vertical magnetic field demonstrates that, even when diffusive effects are important, the bulk flow saturates via the combined processes of reducing the background shear and rearranging and strengthening the background vertical magnetic field. We directly simulate the Ginzburg–Landau amplitude evolution for our system, and demonstrate the pattern formation our model predicts on long scales of length- and timescales. We compare the weakly nonlinear theory results to a direct numerical simulation of the MRI in a thin-gap Taylor Couette flow.
A fast direct solver for boundary value problems on locally perturbed geometries
Zhang, Yabin; Gillman, Adrianna
2018-03-01
Many applications including optimal design and adaptive discretization techniques involve solving several boundary value problems on geometries that are local perturbations of an original geometry. This manuscript presents a fast direct solver for boundary value problems that are recast as boundary integral equations. The idea is to write the discretized boundary integral equation on a new geometry as a low rank update to the discretized problem on the original geometry. Using the Sherman-Morrison formula, the inverse can be expressed in terms of the inverse of the original system applied to the low rank factors and the right hand side. Numerical results illustrate for problems where perturbation is localized the fast direct solver is three times faster than building a new solver from scratch.
Developments in special geometry
International Nuclear Information System (INIS)
Mohaupt, Thomas; Vaughan, Owen
2012-01-01
We review the special geometry of N = 2 supersymmetric vector and hypermultiplets with emphasis on recent developments and applications. A new formulation of the local c-map based on the Hesse potential and special real coordinates is presented. Other recent developments include the Euclidean version of special geometry, and generalizations of special geometry to non-supersymmetric theories. As applications we discuss the proof that the local r-map and c-map preserve geodesic completeness, and the construction of four- and five-dimensional static solutions through dimensional reduction over time. The shared features of the real, complex and quaternionic version of special geometry are stressed throughout.
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.
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.
Sanyal, Amit K.
2005-01-01
There are several attitude estimation algorithms in existence, all of which use local coordinate representations for the group of rigid body orientations. All local coordinate representations of the group of orientations have associated problems. While minimal coordinate representations exhibit kinematic singularities for large rotations, the quaternion representation requires satisfaction of an extra constraint. This paper treats the attitude estimation and filtering problem as an optimizati...
Robust 3D face landmark localization based on local coordinate coding.
Song, Mingli; Tao, Dacheng; Sun, Shengpeng; Chen, Chun; Maybank, Stephen J
2014-12-01
In the 3D facial animation and synthesis community, input faces are usually required to be labeled by a set of landmarks for parameterization. Because of the variations in pose, expression and resolution, automatic 3D face landmark localization remains a challenge. In this paper, a novel landmark localization approach is presented. The approach is based on local coordinate coding (LCC) and consists of two stages. In the first stage, we perform nose detection, relying on the fact that the nose shape is usually invariant under the variations in the pose, expression, and resolution. Then, we use the iterative closest points algorithm to find a 3D affine transformation that aligns the input face to a reference face. In the second stage, we perform resampling to build correspondences between the input 3D face and the training faces. Then, an LCC-based localization algorithm is proposed to obtain the positions of the landmarks in the input face. Experimental results show that the proposed method is comparable to state of the art methods in terms of its robustness, flexibility, and accuracy.
International Nuclear Information System (INIS)
Pantelouris, A.; Modrow, H.; Pantelouris, M.; Hormes, J.; Reinen, D.
2004-01-01
X-ray absorption spectra at the chromium K-edge are reported for a number of selected chromium compounds of known chemical structure. The spectra were obtained with use of synchrotron radiation available at the ELectron Stretcher Accelerator ELSA in Bonn. The compounds studied include the tetrahedrally coordinated compounds Ca 2 Ge 0.8 Cr 0.2 O 4 , Ba 2 Ge 0.1 Cr 0.9 O 4 , Sr 2 CrO 4 , Ca 2 (PO 4 ) x (CrO 4 ) 1-x Cl (x=0.25,0.5), Ca 5 (CrO 4 ) 3 Cl, CrO 3 , the octahedrally coordinated compounds Cr(II)-acetate, CrCl 3 , CrF 3 , Cr 2 O 3 , KCr(SO 4 ) 2 · 12H 2 O, CrO 2 and cubic coordinated metallic chromium. In these compounds chromium exhibits a wide range of formal oxidation states (0 to VI). The absorption features in the near edge region are shown to be characteristic of the spatial environment of the absorbing atom. The occurrence of a single pre-edge line easily allows one to distinguish between tetrahedral and octahedral coordination geometry, whereas the energy position of the absorption edge is found to be very sensitive to the valency of the excited chromium atom. Calculations of the ionisation potential of Cr in different oxidation states using the non-relativistic Hartree-Fock method (Froese-Fischer) confirm that the ionisation limit shifts to higher energy with increasing Cr valency. More detailed information on the electronic structure of the different compounds is gained by real-space full multiple scattering calculations using the FEFF8 code
Energy Technology Data Exchange (ETDEWEB)
Pantelouris, A.; Modrow, H.; Pantelouris, M.; Hormes, J.; Reinen, D
2004-05-10
X-ray absorption spectra at the chromium K-edge are reported for a number of selected chromium compounds of known chemical structure. The spectra were obtained with use of synchrotron radiation available at the ELectron Stretcher Accelerator ELSA in Bonn. The compounds studied include the tetrahedrally coordinated compounds Ca{sub 2}Ge{sub 0.8}Cr{sub 0.2}O{sub 4}, Ba{sub 2}Ge{sub 0.1}Cr{sub 0.9}O{sub 4}, Sr{sub 2}CrO{sub 4}, Ca{sub 2}(PO{sub 4}){sub x}(CrO{sub 4}){sub 1-x}Cl (x=0.25,0.5), Ca{sub 5}(CrO{sub 4}){sub 3}Cl, CrO{sub 3}, the octahedrally coordinated compounds Cr(II)-acetate, CrCl{sub 3}, CrF{sub 3}, Cr{sub 2}O{sub 3}, KCr(SO{sub 4}){sub 2} {center_dot} 12H{sub 2}O, CrO{sub 2} and cubic coordinated metallic chromium. In these compounds chromium exhibits a wide range of formal oxidation states (0 to VI). The absorption features in the near edge region are shown to be characteristic of the spatial environment of the absorbing atom. The occurrence of a single pre-edge line easily allows one to distinguish between tetrahedral and octahedral coordination geometry, whereas the energy position of the absorption edge is found to be very sensitive to the valency of the excited chromium atom. Calculations of the ionisation potential of Cr in different oxidation states using the non-relativistic Hartree-Fock method (Froese-Fischer) confirm that the ionisation limit shifts to higher energy with increasing Cr valency. More detailed information on the electronic structure of the different compounds is gained by real-space full multiple scattering calculations using the FEFF8 code.
Pantelouris, A.; Modrow, H.; Pantelouris, M.; Hormes, J.; Reinen, D.
2004-05-01
X-ray absorption spectra at the chromium K-edge are reported for a number of selected chromium compounds of known chemical structure. The spectra were obtained with use of synchrotron radiation available at the ELectron Stretcher Accelerator ELSA in Bonn. The compounds studied include the tetrahedrally coordinated compounds Ca 2Ge 0.8Cr 0.2O 4, Ba 2Ge 0.1Cr 0.9O 4, Sr 2CrO 4, Ca 2(PO 4) x(CrO 4) 1- xCl ( x=0.25,0.5), Ca 5(CrO 4) 3Cl, CrO 3, the octahedrally coordinated compounds Cr(II)-acetate, CrCl 3, CrF 3, Cr 2O 3, KCr(SO 4) 2 · 12H 2O, CrO 2 and cubic coordinated metallic chromium. In these compounds chromium exhibits a wide range of formal oxidation states (0 to VI). The absorption features in the near edge region are shown to be characteristic of the spatial environment of the absorbing atom. The occurrence of a single pre-edge line easily allows one to distinguish between tetrahedral and octahedral coordination geometry, whereas the energy position of the absorption edge is found to be very sensitive to the valency of the excited chromium atom. Calculations of the ionisation potential of Cr in different oxidation states using the non-relativistic Hartree-Fock method (Froese-Fischer) confirm that the ionisation limit shifts to higher energy with increasing Cr valency. More detailed information on the electronic structure of the different compounds is gained by real-space full multiple scattering calculations using the FEFF8 code.
Coordination Analysis Using Global Structural Constraints and Alignment-based Local Features
Hara, Kazuo; Shimbo, Masashi; Matsumoto, Yuji
We propose a hybrid approach to coordinate structure analysis that combines a simple grammar to ensure consistent global structure of coordinations in a sentence, and features based on sequence alignment to capture local symmetry of conjuncts. The weight of the alignment-based features, which in turn determines the score of coordinate structures, is optimized by perceptron training on a given corpus. A bottom-up chart parsing algorithm efficiently finds the best scoring structure, taking both nested or non-overlapping flat coordinations into account. We demonstrate that our approach outperforms existing parsers in coordination scope detection on the Genia corpus.
Nurhasanah, F.; Kusumah, Y. S.; Sabandar, J.; Suryadi, D.
2018-05-01
As one of the non-conventional mathematics concepts, Parallel Coordinates is potential to be learned by pre-service mathematics teachers in order to give them experiences in constructing richer schemes and doing abstraction process. Unfortunately, the study related to this issue is still limited. This study wants to answer a research question “to what extent the abstraction process of pre-service mathematics teachers in learning concept of Parallel Coordinates could indicate their performance in learning Analytic Geometry”. This is a case study that part of a larger study in examining mathematical abstraction of pre-service mathematics teachers in learning non-conventional mathematics concept. Descriptive statistics method is used in this study to analyze the scores from three different tests: Cartesian Coordinate, Parallel Coordinates, and Analytic Geometry. The participants in this study consist of 45 pre-service mathematics teachers. The result shows that there is a linear association between the score on Cartesian Coordinate and Parallel Coordinates. There also found that the higher levels of the abstraction process in learning Parallel Coordinates are linearly associated with higher student achievement in Analytic Geometry. The result of this study shows that the concept of Parallel Coordinates has a significant role for pre-service mathematics teachers in learning Analytic Geometry.
Localized excitations and the geometry of the 1nπ* excited states of pyrazine
International Nuclear Information System (INIS)
Kleier, D.A.; Martin, R.L.; Wadt, W.R.; Moomaw, W.R.
1982-01-01
Previous theoretical work has shown that the lowest excited singlet state of pyrazine, the π* 1 B 3 u state, is best described in terms of interacting excitations localized on each nitrogen. The present work refines the localized excitation model and considers its implications for the geometry of the 1 B 3 u state. Hartree-Fock calculations show that the best single configuration description of the nπ* state has broken ( 1 B 1 ) symmetry with the excitation strongly localized at one end of the molcule. If the symmetry-restricted hf result is used for reference, this localization describes an important correlation effect. The excited-state geometry was probed using configuration interaction wave functions based on the symmetry-restricted orbitals, as well as properly symmetrized ''valance-bond'' wave functions based on the broken symmetry solutions. Both descriptions lead to a very flat potential for a b/sub 1u/ vibrational mode. This mode reduces the molecular geometry from D/sub 2h/ to C/sub 2v/. We present spectroscopic evidence of our own and of other workers which is consistent with such a flat potential
Cortical basis of communication: local computation, coordination, attention.
Alexandre, Frederic
2009-03-01
Human communication emerges from cortical processing, known to be implemented on a regular repetitive neuronal substratum. The supposed genericity of cortical processing has elicited a series of modeling works in computational neuroscience that underline the information flows driven by the cortical circuitry. In the minimalist framework underlying the current theories for the embodiment of cognition, such a generic cortical processing is exploited for the coordination of poles of representation, as is reported in this paper for the case of visual attention. Interestingly, this case emphasizes how abstract internal referents are built to conform to memory requirements. This paper proposes that these referents are the basis for communication in humans, which is firstly a coordination and an attentional procedure with regard to their congeners.
Boubnov, Alexey; Lichtenberg, Henning; Mangold, Stefan; Grunwaldt, Jan Dierk
2015-03-01
Analysis of the oxidation state and coordination geometry using pre-edge analysis is attractive for heterogeneous catalysis and materials science, especially for in situ and time-resolved studies or highly diluted systems. In the present study, focus is laid on iron-based catalysts. First a systematic investigation of the pre-edge region of the Fe K-edge using staurolite, FePO4, FeO and α-Fe2O3 as reference compounds for tetrahedral Fe(2+), tetrahedral Fe(3+), octahedral Fe(2+) and octahedral Fe(3+), respectively, is reported. In particular, high-resolution and conventional X-ray absorption spectra are compared, considering that in heterogeneous catalysis and material science a compromise between high-quality spectroscopic data acquisition and simultaneous analysis of functional properties is required. Results, which were obtained from reference spectra acquired with different resolution and quality, demonstrate that this analysis is also applicable to conventionally recorded pre-edge data. For this purpose, subtraction of the edge onset is preferentially carried out using an arctangent and a first-degree polynomial, independent of the resolution and quality of the data. For both standard and high-resolution data, multiplet analysis of pre-edge features has limitations due to weak transitions that cannot be identified. On the other hand, an arbitrary empirical peak fitting assists the analysis in that non-local transitions can be isolated. The analysis of the oxidation state and coordination geometry of the Fe sites using a variogram-based method is shown to be effective for standard-resolution data and leads to the same results as for high-resolution spectra. This method, validated by analysing spectra of reference compounds and their well defined mixtures, is finally applied to track structural changes in a 1% Fe/Al2O3 and a 0.5% Fe/BEA zeolite catalyst during reduction in 5% H2/He. The results, hardly accessible by other techniques, show that Fe(3+) is
Geometry of convex polygons and locally minimal binary trees spanning these polygons
International Nuclear Information System (INIS)
Ivanov, A O; Tuzhilin, A A
1999-01-01
In previous works the authors have obtained an effective classification of planar locally minimal binary trees with convex boundaries. The main aim of the present paper is to find more subtle restrictions on the possible structure of such trees in terms of the geometry of the given boundary set. Special attention is given to the case of quasiregular boundaries (that is, boundaries that are sufficiently close to regular ones in a certain sense). In particular, a series of quasiregular boundaries that cannot be spanned by a locally minimal binary tree is constructed
International Nuclear Information System (INIS)
Strominger, A.
1990-01-01
A special manifold is an allowed target manifold for the vector multiplets of D=4, N=2 supergravity. These manifolds are of interest for string theory because the moduli spaces of Calabi-Yau threefolds and c=9, (2,2) conformal field theories are special. Previous work has given a local, coordinate-dependent characterization of special geometry. A global description of special geometries is given herein, and their properties are studied. A special manifold M of complex dimension n is characterized by the existence of a holomorphic Sp(2n+2,R)xGL(1,C) vector bundle over M with a nowhere-vanishing holomorphic section Ω. The Kaehler potential on M is the logarithm of the Sp(2n+2,R) invariant norm of Ω. (orig.)
A new approach for gravity localization in six-dimensional geometries
International Nuclear Information System (INIS)
Santos, Victor Pereira do Nascimento; Almeida, Carlos Alberto Santos de
2011-01-01
Full text: The idea that spacetime may have more than four dimensions is old, originally presented as an attempt to unify Maxwell's theory of Electromagnetism with the brand-new gravitation theory of Einstein. Such extra dimensions are in principle unobservable to the energy scales currently available. However, its effects can be seen in short distance gravity experiments and in observations in cosmology. Also, it is used as a mechanism to explain the difference between the energy scales of the weak force and gravity, which is called the hierarchy problem. The current framework for the extra dimension scenario is consider the four-dimensional known universe as embedded in a higher dimensional space called bulk. The form of this bulk determines how we perceive gravity in our universe; then, the behaviour of gravitational field depends on the geometry of the bulk. Metric solutions were already presented for string-like defect, with and without matter sources, where was shown that the gravity Newtonian potential grows with the inverse cube of distance. Such correction arises from a very particular mass spectrum for the gravitational field, which already contains the orbital angular momentum contributions. In this work we study the behaviour of gravitational field in a extra-dimensional braneworld scenario, using non-factorizable geometries (which preserves Poincare symmetry) and setting suitable matter distributions in order to verify its localization, for several geometries. For such geometries it is possible to find explicit solutions for the tensor fluctuations of the metric. (author)
Effect of conductor geometry on source localization: Implications for epilepsy studies
International Nuclear Information System (INIS)
Schlitt, H.; Heller, L.; Best, E.; Ranken, D.; Aaron, R.
1994-01-01
We shall discuss the effects of conductor geometry on source localization for applications in epilepsy studies. The most popular conductor model for clinical MEG studies is a homogeneous sphere. However, several studies have indicated that a sphere is a poor model for the head when the sources are deep, as is the case for epileptic foci in the mesial temporal lobe. We believe that replacing the spherical model with a more realistic one in the inverse fitting procedure will improve the accuracy of localizing epileptic sources. In order to include a realistic head model in the inverse problem, we must first solve the forward problem for the realistic conductor geometry. We create a conductor geometry model from MR images, and then solve the forward problem via a boundary integral equation for the electric potential due to a specified primary source. One the electric potential is known, the magnetic field can be calculated directly. The most time-intensive part of the problem is generating the conductor model; fortunately, this needs to be done only once for each patient. It takes little time to change the primary current and calculate a new magnetic field for use in the inverse fitting procedure. We present the results of a series of computer simulations in which we investigate the localization accuracy due to replacing the spherical model with the realistic head model in the inverse fitting procedure. The data to be fit consist of a computer generated magnetic field due to a known current dipole in a realistic head model, with added noise. We compare the localization errors when this field is fit using a spherical model to the fit using a realistic head model. Using a spherical model is comparable to what is usually done when localizing epileptic sources in humans, where the conductor model used in the inverse fitting procedure does not correspond to the actual head
On the influence of microphone array geometry on HRTF-based Sound Source Localization
DEFF Research Database (Denmark)
Farmani, Mojtaba; Pedersen, Michael Syskind; Tan, Zheng-Hua
2015-01-01
The direction dependence of Head Related Transfer Functions (HRTFs) forms the basis for HRTF-based Sound Source Localization (SSL) algorithms. In this paper, we show how spectral similarities of the HRTFs of different directions in the horizontal plane influence performance of HRTF-based SSL...... algorithms; the more similar the HRTFs of different angles to the HRTF of the target angle, the worse the performance. However, we also show how the microphone array geometry can assist in differentiating between the HRTFs of the different angles, thereby improving performance of HRTF-based SSL algorithms....... Furthermore, to demonstrate the analysis results, we show the impact of HRTFs similarities and microphone array geometry on an exemplary HRTF-based SSL algorithm, called MLSSL. This algorithm is well-suited for this purpose as it allows to estimate the Direction-of-Arrival (DoA) of the target sound using any...
Local DER Driven Grid Support by Coordinated Operation of Devices
International Nuclear Information System (INIS)
Warmer, C.J.; Kamphuis, I.G.
2009-01-01
In the traditional operation of electricity networks the system operator has a number of ancillary services available for preservation of system balance. These services are called upon near real-time, after the planning phase. Ancillary services consist of regulating power, reserve capacity and emergency capacity, each with their own characteristics. Regulating power is deployed via load frequency control. Reserve capacity is used to release regulating power and can be called upon to maintain a balance or to counterbalance or resolve transmission restrictions. Both are traded at the Dutch energy market under an auction model with a single buyer (TenneT). Emergency capacity is rewarded on the basis of accessibility/availability within 15 minutes. In local electricity networks neither planning nor ancillary services exist. Planning is done by aggregation into large customer groups. For ancillary services one relies on the system operation as sketched above. In local electricity networks with a large share of distributed generation the costs of keeping the electricity system reliable and stable will increase further and technical problems may arise. The European SmartGrids initiative responds to these challenges in their strategic research agenda. One of the issues addressed in this agenda is the changing role of the distribution grid in which users get a more active role. One opportunity is the introduction of ancillary-type services at the distribution level, utilizing different types of producing and consuming devices in the local network, in order to make the total system more dependable. Distributed generation has a number of characteristics that are similar to characteristics of consumption. Part of it is intermittent / variable, although to a large extent predictable (PV, wind versus lighting, electronic devices). Another part is task-driven (micro-CHP versus electrical heating). Yet another part is controllable or shiftable in time. And storage can behave both
FORECAST, ORGANIZATION-COORDINATION AND MOTIVATION IN LOCAL PUBLIC ADMINISTRATION MANAGEMENT
Petronela SCUTARIU
2015-01-01
The proper functioning of local administrative system is not possible without the exercise of the functions of local public administration management. From such a direction, in this article we intend to analyze the contents of the functions of forecast, of organization-coordination and of motivation, in order to show how each of these contributes to good management of local public affairs. Defining the mission, the objectives of local government and the actions to be taken to achieve them, th...
Heed, Tobias; Möller, Johanna; Röder, Brigitte
2015-01-01
To localize touch, the brain integrates spatial information coded in anatomically based and external spatial reference frames. Sighted humans, by default, use both reference frames in tactile localization. In contrast, congenitally blind individuals have been reported to rely exclusively on anatomical coordinates, suggesting a crucial role of the visual system for tactile spatial processing. We tested whether the use of external spatial information in touch can, alternatively, be induced by a movement context. Sighted and congenitally blind humans performed a tactile temporal order judgment task that indexes the use of external coordinates for tactile localization, while they executed bimanual arm movements with uncrossed and crossed start and end postures. In the sighted, start posture and planned end posture of the arm movement modulated tactile localization for stimuli presented before and during movement, indicating automatic, external recoding of touch. Contrary to previous findings, tactile localization of congenitally blind participants, too, was affected by external coordinates, though only for stimuli presented before movement start. Furthermore, only the movement's start posture, but not the planned end posture affected blind individuals' tactile performance. Thus, integration of external coordinates in touch is established without vision, though more selectively than when vision has developed normally, and possibly restricted to movement contexts. The lack of modulation by the planned posture in congenitally blind participants suggests that external coordinates in this group are not mediated by motor efference copy. Instead the task-related frequent posture changes, that is, movement consequences rather than planning, appear to have induced their use of external coordinates.
Directory of Open Access Journals (Sweden)
Zielinski Stephanie M
2012-01-01
Full Text Available Abstract Background Surgeons in the Netherlands, Canada and the US participate in the FAITH trial (Fixation using Alternative Implants for the Treatment of Hip fractures. Dutch sites are managed and visited by a financed central trial coordinator, whereas most Canadian and US sites have local study coordinators and receive per patient payment. This study was aimed to assess how these different trial management strategies affected trial performance. Methods Details related to obtaining ethics approval, time to trial start-up, inclusion, and percentage completed follow-ups were collected for each trial site and compared. Pre-trial screening data were compared with actual inclusion rates. Results Median trial start-up ranged from 41 days (P25-P75 10-139 in the Netherlands to 232 days (P25-P75 98-423 in Canada (p = 0.027. The inclusion rate was highest in the Netherlands; median 1.03 patients (P25-P75 0.43-2.21 per site per month, representing 34.4% of the total eligible population. It was lowest in Canada; 0.14 inclusions (P25-P75 0.00-0.28, representing 3.9% of eligible patients (p Conclusions In this trial, a central financed trial coordinator to manage all trial related tasks in participating sites resulted in better trial progression and a similar follow-up. It is therefore a suitable alternative for appointing these tasks to local research assistants. The central coordinator approach can enable smaller regional hospitals to participate in multicenter randomized controlled trials. Circumstances such as available budget, sample size, and geographical area should however be taken into account when choosing a management strategy. Trial Registration ClinicalTrials.gov: NCT00761813
Energy Technology Data Exchange (ETDEWEB)
Sheikh-Jabbari, M.M. [Institute for Research in Fundamental Sciences (IPM), School of Physics, Tehran (Iran, Islamic Republic of); Yavartanoo, H. [Institute of Theoretical Physics, Chinese Academy of Sciences, State Key Laboratory of Theoretical Physics, Beijing (China)
2016-09-15
Expanding upon [arXiv:1404.4472, arXiv:1511.06079], we provide a further detailed analysis of Banados geometries, the most general solutions to the AdS{sub 3} Einstein gravity with Brown-Henneaux boundary conditions. We analyze in some detail the causal, horizon, and boundary structure, and the geodesic motion on these geometries, as well as the two classes of symplectic charges one can associate with these geometries: charges associated with the exact symmetries and the Virasoro charges. We elaborate on the one-to-one relation between the coadjoint orbits of two copies of the Virasoro group and Banados geometries. We discuss that the information as regards the Banados geometries falls into two categories: ''orbit invariant'' information and ''Virasoro hairs''. The former concerns geometric quantities, while the latter are specified by the non-local surface integrals. We elaborate on multi-BTZ geometries which have a number of disconnected pieces at the horizon bifurcation curve. We study multi-BTZ black hole thermodynamics and discuss that the thermodynamic quantities are orbit invariants. We also comment on the implications of our analysis for a 2d CFT dual which could possibly be dual to AdS{sub 3} Einstein gravity. (orig.)
International Nuclear Information System (INIS)
Sakata, Fumihiko; Marumori, Toshio; Hashimoto, Yukio; Une, Tsutomu.
1983-05-01
The geometry of the self-consistent collective-coordinate (SCC) method formulated within the framework of the time-dependent Hartree-Fock (TDHF) theory is investigated by associating the variational parameters with a symplectic manifold (a TDHF manifold). With the use of a canonical-variables parametrization, it is shown that the TDHF equation is equivalent to the canonical equations of motion in classical mechanics in the TDHF manifold. This enables us to investigate geometrical structure of the SCC method in the language of the classical mechanics. The SCC method turns out to give a prescription how to dynamically extract a ''maximally-decoupled'' collective submanifold (hypersurface) out of the TDHF manifold, in such a way that a certain kind of trajectories corresponding to the large-amplitude collective motion under consideration can be reproduced on the hypersurface as precisely as possible. The stability of the hypersurface at each point on it is investigated, in order to see whether the hypersurface obtained by the SCC method is really an approximate integral surface in the TDHF manifold or not. (author)
International Nuclear Information System (INIS)
Yang, Xiao-Jun; Srivastava, H.M.; He, Ji-Huan; Baleanu, Dumitru
2013-01-01
In this Letter, we propose to use the Cantor-type cylindrical-coordinate method in order to investigate a family of local fractional differential operators on Cantor sets. Some testing examples are given to illustrate the capability of the proposed method for the heat-conduction equation on a Cantor set and the damped wave equation in fractal strings. It is seen to be a powerful tool to convert differential equations on Cantor sets from Cantorian-coordinate systems to Cantor-type cylindrical-coordinate systems.
Directory of Open Access Journals (Sweden)
Gao Guo-Ping
2016-01-01
Full Text Available In this article, we investigate the local fractional 3-D compressible Navier-Stokes equation via local fractional derivative. We use the Cantor-type cylindrical co-ordinate method to transfer 3-D compressible Navier-Stokes equation from the Cantorian co-ordinate system to the Cantor-type cylindrical co-ordinate system.
FORECAST, ORGANIZATION-COORDINATION AND MOTIVATION IN LOCAL PUBLIC ADMINISTRATION MANAGEMENT
Directory of Open Access Journals (Sweden)
Petronela\tSCUTARIU
2015-06-01
Full Text Available The proper functioning of local administrative system is not possible without the exercise of the functions of local public administration management. From such a direction, in this article we intend to analyze the contents of the functions of forecast, of organization-coordination and of motivation, in order to show how each of these contributes to good management of local public affairs. Defining the mission, the objectives of local government and the actions to be taken to achieve them, the design and harmonization of optimal local organizational structure components to achieve preset objectives, but also the human resources training from local public administration to use their skills and capacities towards achieving the objectives of the local public organization contribute to improving the local administrative process with effect on satisfying the interests of the local community
Local conformal symmetry in non-Riemannian geometry and the origin of physical scales
Energy Technology Data Exchange (ETDEWEB)
De Cesare, Marco [King' s College London, Theoretical Particle Physics and Cosmology Group, Department of Physics, London (United Kingdom); Moffat, John W. [Perimeter Institute for Theoretical Physics, Waterloo, ON (Canada); Sakellariadou, Mairi [King' s College London, Theoretical Particle Physics and Cosmology Group, Department of Physics, London (United Kingdom); Perimeter Institute for Theoretical Physics, Waterloo, ON (Canada)
2017-09-15
We introduce an extension of the Standard Model and General Relativity built upon the principle of local conformal invariance, which represents a generalization of a previous work by Bars, Steinhardt and Turok. This is naturally realized by adopting as a geometric framework a particular class of non-Riemannian geometries, first studied by Weyl. The gravitational sector is enriched by a scalar and a vector field. The latter has a geometric origin and represents the novel feature of our approach. We argue that physical scales could emerge from a theory with no dimensionful parameters, as a result of the spontaneous breakdown of conformal and electroweak symmetries. We study the dynamics of matter fields in this modified gravity theory and show that test particles follow geodesics of the Levi-Civita connection, thus resolving an old criticism raised by Einstein against Weyl's original proposal. (orig.)
Compounding local invariant features and global deformable geometry for medical image registration.
Directory of Open Access Journals (Sweden)
Jianhua Zhang
Full Text Available Using deformable models to register medical images can result in problems of initialization of deformable models and robustness and accuracy of matching of inter-subject anatomical variability. To tackle these problems, a novel model is proposed in this paper by compounding local invariant features and global deformable geometry. This model has four steps. First, a set of highly-repeatable and highly-robust local invariant features, called Key Features Model (KFM, are extracted by an effective matching strategy. Second, local features can be matched more accurately through the KFM for the purpose of initializing a global deformable model. Third, the positional relationship between the KFM and the global deformable model can be used to precisely pinpoint all landmarks after initialization. And fourth, the final pose of the global deformable model is determined by an iterative process with a lower time cost. Through the practical experiments, the paper finds three important conclusions. First, it proves that the KFM can detect the matching feature points well. Second, the precision of landmark locations adjusted by the modeled relationship between KFM and global deformable model is greatly improved. Third, regarding the fitting accuracy and efficiency, by observation from the practical experiments, it is found that the proposed method can improve 6~8% of the fitting accuracy and reduce around 50% of the computational time compared with state-of-the-art methods.
Relative-locality distant observers and the phenomenology of momentum-space geometry
International Nuclear Information System (INIS)
Amelino-Camelia, Giovanni; Rosati, Giacomo; Trevisan, Gabriele; Arzano, Michele; Kowalski-Glikman, Jerzy
2012-01-01
We study the translational invariance of the relative-locality framework proposed in Amelino-Camelia et al (2011 Phys. Rev. D 84 084010), which had been previously established only for the case of a single interaction. We provide an explicit example of boundary conditions at endpoints of worldlines, which indeed ensures the desired translational invariance for processes involving several interactions, even when some of the interactions are causally connected (particle exchange). We illustrate the properties of the associated relativistic description of distant observers within the example of a κ-Poincare-inspired momentum-space geometry, with de Sitter metric and parallel transport governed by a non-metric and torsionful connection. We find that in such a theory, simultaneously emitted massless particles do not reach simultaneously a distant detector, as expected in light of the findings of Freidel and Smolin (2011 arXiv:1103.5626) on the implications of non-metric connections. We also show that the theory admits a free-particle limit, where the relative-locality results of Amelino-Camelia et al (2011 Phys. Lett. B 700 150) are reproduced. We establish that the torsion of the κ-Poincare connection introduces a small (but observably large) dependence of the time of detection, for simultaneously emitted particles, on some properties of the interactions producing the particles at the source. (paper)
Relative-locality distant observers and the phenomenology of momentum-space geometry
Amelino-Camelia, Giovanni; Arzano, Michele; Kowalski-Glikman, Jerzy; Rosati, Giacomo; Trevisan, Gabriele
2012-04-01
We study the translational invariance of the relative-locality framework proposed in Amelino-Camelia et al (2011 Phys. Rev. D 84 084010), which had been previously established only for the case of a single interaction. We provide an explicit example of boundary conditions at endpoints of worldlines, which indeed ensures the desired translational invariance for processes involving several interactions, even when some of the interactions are causally connected (particle exchange). We illustrate the properties of the associated relativistic description of distant observers within the example of a κ-Poincaré-inspired momentum-space geometry, with de Sitter metric and parallel transport governed by a non-metric and torsionful connection. We find that in such a theory, simultaneously emitted massless particles do not reach simultaneously a distant detector, as expected in light of the findings of Freidel and Smolin (2011 arXiv:1103.5626) on the implications of non-metric connections. We also show that the theory admits a free-particle limit, where the relative-locality results of Amelino-Camelia et al (2011 Phys. Lett. B 700 150) are reproduced. We establish that the torsion of the κ-Poincaré connection introduces a small (but observably large) dependence of the time of detection, for simultaneously emitted particles, on some properties of the interactions producing the particles at the source.
Amin, Hayder; Maccione, Alessandro; Nieus, Thierry
2017-01-01
Developing neuronal systems intrinsically generate coordinated spontaneous activity that propagates by involving a large number of synchronously firing neurons. In vivo, waves of spikes transiently characterize the activity of developing brain circuits and are fundamental for activity-dependent circuit formation. In vitro, coordinated spontaneous spiking activity, or network bursts (NBs), interleaved within periods of asynchronous spikes emerge during the development of 2D and 3D neuronal cultures. Several studies have investigated this type of activity and its dynamics, but how a neuronal system generates these coordinated events remains unclear. Here, we investigate at a cellular level the generation of network bursts in spontaneously active neuronal cultures by exploiting high-resolution multielectrode array recordings and computational network modelling. Our analysis reveals that NBs are generated in specialized regions of the network (functional neuronal communities) that feature neuronal links with high cross-correlation peak values, sub-millisecond lags and that share very similar structural connectivity motifs providing recurrent interactions. We show that the particular properties of these local structures enable locally amplifying spontaneous asynchronous spikes and that this mechanism can lead to the initiation of NBs. Through the analysis of simulated and experimental data, we also show that AMPA currents drive the coordinated activity, while NMDA and GABA currents are only involved in shaping the dynamics of NBs. Overall, our results suggest that the presence of functional neuronal communities with recurrent local connections allows a neuronal system to generate spontaneous coordinated spiking activity events. As suggested by the rules used for implementing our computational model, such functional communities might naturally emerge during network development by following simple constraints on distance-based connectivity. PMID:28749937
Directory of Open Access Journals (Sweden)
Davide Lonardoni
2017-07-01
Full Text Available Developing neuronal systems intrinsically generate coordinated spontaneous activity that propagates by involving a large number of synchronously firing neurons. In vivo, waves of spikes transiently characterize the activity of developing brain circuits and are fundamental for activity-dependent circuit formation. In vitro, coordinated spontaneous spiking activity, or network bursts (NBs, interleaved within periods of asynchronous spikes emerge during the development of 2D and 3D neuronal cultures. Several studies have investigated this type of activity and its dynamics, but how a neuronal system generates these coordinated events remains unclear. Here, we investigate at a cellular level the generation of network bursts in spontaneously active neuronal cultures by exploiting high-resolution multielectrode array recordings and computational network modelling. Our analysis reveals that NBs are generated in specialized regions of the network (functional neuronal communities that feature neuronal links with high cross-correlation peak values, sub-millisecond lags and that share very similar structural connectivity motifs providing recurrent interactions. We show that the particular properties of these local structures enable locally amplifying spontaneous asynchronous spikes and that this mechanism can lead to the initiation of NBs. Through the analysis of simulated and experimental data, we also show that AMPA currents drive the coordinated activity, while NMDA and GABA currents are only involved in shaping the dynamics of NBs. Overall, our results suggest that the presence of functional neuronal communities with recurrent local connections allows a neuronal system to generate spontaneous coordinated spiking activity events. As suggested by the rules used for implementing our computational model, such functional communities might naturally emerge during network development by following simple constraints on distance-based connectivity.
Anatomical localization of electrophysiological recording sites by co-ordinate transformation.
Sinex, D G
1997-07-18
A method for estimating the anatomical locations of the units recorded in electrophysiological mapping experiments is described. A total of three locations must be marked by dye injections or electrolytic lesions and identified in tissue sections. From those locations, equations are derived to translate, scale, and rotate the three-dimensional co-ordinates of the recording sites, so that they are correct for a second, three-dimensional co-ordinate system based on the anatomy of the mapped structure. There is no limit to the number of recording sites that can be localized. This differs from methods that require a dye injection or lesion to be made at the exact location at which a particular unit was recorded. The accuracy of the transformed co-ordinates is limited by the accuracy with which the co-ordinates can be measured: in test measurements and in the experiments for which this algorithm was developed, the computed co-ordinates were typically accurate to within 100 microns or less.
Local Instruction Theory (LIT) on spherical geometry for enhancement students’ strategic competence
Nuraida, I.; Kusumah, Y. S.; Kartasasmita, B. G.
2018-03-01
This research focused on the analysis of the materials spherical geometry of the wake in an attempt to enhancemet the strategic competence of students and to produce learning trajectory. That is because the materials that are used less catchy concept gives students. Learning materials with Local Instructional Theory (LIT) can enhancemet the strategic competence of the students. This research aims to study the difference of achievement and improving the strategic competence of the students who got the Realistics Mathematics Education (RME) and (LIT) with conventional learning. This research is the Design Research with two cycles. This research has three phases i.e. 1) preparing for the experiment/preliminary; 2) teaching eksperiment; 3) retrospective analysis. The population of the research was the whole IX group junior high school 1 Rajapolah with samples of IXg and IXj group. Results of the analysis of the data shows that students based on Mathematical Prior Knowledge (MPK) acquire learning achievement have RME and LIT and enhancement strategic competence of the mathematical that are higher than those of students who obtain the conventional learning.
International Nuclear Information System (INIS)
Zhang, Dingkang; Rahnema, Farzad; Ougouag, Abderrfi M.
2011-01-01
A response-based local transport method has been developed in 2-D (r, θ) geometry for coupling to any coarse-mesh (nodal) diffusion method/code. Monte Carlo method is first used to generate a (pre-computed) the response function library for each unique coarse mesh in the transport domain (e.g., the outer reflector region of the Pebble Bed Reactor). The scalar flux and net current at the diffusion/transport interface provided by the diffusion method are used as an incoming surface source to the transport domain. A deterministic iterative sweeping method together with the response function library is utilized to compute the local transport solution within all transport coarse meshes. After the partial angular currents crossing the coarse mesh surfaces are converged, albedo coefficients are computed as boundary conditions for the diffusion methods. The iteration on the albedo boundary condition (for the diffusion method via transport) and the incoming angular flux boundary condition (for the transport via diffusion) is continued until convergence is achieved. The method was tested for in a simplified 2-D (r, θ) pebble bed reactor problem consisting of an inner reflector, an annular fuel region and a controlled outer reflector. The comparisons have shown that the results of the response-function-based transport method agree very well with a direct MCNP whole core solution. The agreement in coarse mesh averaged flux was found to be excellent: relative difference of about 0.18% and a maximum difference of about 0.55%. Note that the MCNP uncertainty was less than 0.1%. (author)
Buschinelli, Pedro D. V.; Melo, João. Ricardo C.; Albertazzi, Armando; Santos, João. M. C.; Camerini, Claudio S.
2013-04-01
An axis-symmetrical optical laser triangulation system was developed by the authors to measure the inner geometry of long pipes used in the oil industry. It has a special optical configuration able to acquire shape information of the inner geometry of a section of a pipe from a single image frame. A collimated laser beam is pointed to the tip of a 45° conical mirror. The laser light is reflected in such a way that a radial light sheet is formed and intercepts the inner geometry and forms a bright laser line on a section of the inspected pipe. A camera acquires the image of the laser line through a wide angle lens. An odometer-based triggering system is used to shot the camera to acquire a set of equally spaced images at high speed while the device is moved along the pipe's axis. Image processing is done in real-time (between images acquisitions) thanks to the use of parallel computing technology. The measured geometry is analyzed to identify corrosion damages. The measured geometry and results are graphically presented using virtual reality techniques and devices as 3D glasses and head-mounted displays. The paper describes the measurement principles, calibration strategies, laboratory evaluation of the developed device, as well as, a practical example of a corroded pipe used in an industrial gas production plant.
DEFF Research Database (Denmark)
Jalaal, M.; Soleimani, Soheil; Domairry, G.
2011-01-01
In this paper the meshless Local Multi Quadrics-based Differential Quadrature (MQ-DQ) method is applied to obtain the electric field distribution for different applicable irregular geometries. This method is the combination of Differential Quadrature approximation of derivatives and function...
Bean, Jonathan F.; Clarkson, Robert B.; Helm, Lothar; Moriggi, Loïck; Sherry, A. Dean
2009-01-01
Electron-spin relaxation is one of the determining factors in the efficacy of MRI contrast agents. Of all the parameters involved in determining relaxivity it remains the least well understood, particularly as it relates to the structure of the complex. One of the reasons for the poor understanding of electron-spin relaxation is that it is closely related to the ligand-field parameters of the Gd3+ ion that forms the basis of MRI contrast agents and these complexes generally exhibit a structural isomerism that inherently complicates the study of electron spin relaxation. We have recently shown that two DOTA-type ligands could be synthesised that, when coordinated to Gd3+, would adopt well defined coordination geometries and are not subject to the problems of intramolecular motion of other complexes. The EPR properties of these two chelates were studied and the results examined with theory to probe their electron-spin relaxation properties. PMID:18283704
International Nuclear Information System (INIS)
Lapillonne, X.
2010-04-01
In magnetically confined fusion devices, the energy and particle transport is significantly larger than expected from purely collisional processes. This degraded confinement mostly results from small-scale turbulence and prevents from reaching self-sustained burning plasma conditions in present day experiments. A better understanding of these nonlinear phenomena is therefore of key importance on the way towards controlled fusion. The small-scale microinstabilities and associated turbulence are investigated for Tokamak plasmas by means of numerical simulations in the frame of the gyrokinetic theory. This model describes the evolution of the particle distribution functions in phase space together with self-consistent electromagnetic fields, while neglecting the fast motion associated with the Larmor orbit of particles around the magnetic field lines. In the course of this thesis work, substantial modifications to the existing Eulerian gyrokinetic code GENE have been carried out in collaboration with the Max-Planck- Institute f¨ur Plasmaphysik in Garching, Germany. The code has been extended from a local approximation, which only considers a reduced volume of a fusion plasma, to a global version which fully includes radial temperature and density profiles as well as radial magnetic equilibrium variations. To this end, the gyrokinetic equations have been formulated for general magnetic geometry, keeping radial variations of equilibrium quantities, and considering field aligned coordinates, suitable for their numerical implementation. The numerical treatment of the radial direction has been modified from a Fourier representation in the local approach to real space in the global code. This has in particular required to adapt the radial derivatives, the field solver, and to implement a real space dealiasing scheme for the treatment of the nonlinearity. A heat source was in addition introduced to allow for steady state global nonlinear simulations. An important part of
Atomic size effects on local coordination and medium range order in molten trivalent metal chlorides
International Nuclear Information System (INIS)
Tatlipinar, H.; Akdeniz, Z.; Pastore, G.
1992-08-01
Structural correlations in molten trivalent metal chlorides are evaluated as functions of the metal ion size R M across the range from LaCl 3 (R M approx. 1.4 A) to AlCl 3 (R M approx. 0.8 A), using a charged soft-sphere model and the hypernetted chain approximation. Main attention is given to trends in the local liquid structure (partial radial distribution functions, coordination numbers and bond lengths) and in the intermediate range order (first sharp diffraction peak in the number-number and partial structure factors). The trend towards fourfold local coordination of the metal ions, the stabilization of their first-neighbour chlorine cage and the growth of medium range order are found to proceed in parallel as the size of the metal ion is allowed to decrease at constant number density and temperature. A tendency to molecular-type local structure and liquid-vapour phase separation is found within the hypernetted chain scheme at small metal ion sizes corresponding to AlCl 3 and is emphasized by decreasing the number density of the fluid. The predicted molecular units are rather strongly distorted Al 2 Cl 6 dimers, in agreement with observation. The calculated structural trends for other trichlorides are compared with diffraction and transport data. (author). 17 refs, 8 figs, 1 tab
DEFF Research Database (Denmark)
Krauss, M; Olsen, Lars; Antony, J
2002-01-01
Models of the metal ion binding sites of native ZnZn and of cadmium-substituted ZnCd and CdCd phosphotriesterase, including full amino acid side chains, were geometry optimized with quantum mechanical methods, with effective fragment potentials (EFP) representing the protein environment surroundi...... to the Od1 of the carboxylate of the first-shell aspartate designated M 1, but the energy difference between Cd1Zn2 and the lowest energy Zn1Cd2 structure is only about 2 kcal/mol and decreasing with the addition of water molecules. The Zn1Cd2 arrangement is found experimentally....
Local coordination of Eu(III) in organic/inorganic amine functionalized hybrids
International Nuclear Information System (INIS)
Carlos, L.D.; Sa Ferreira, R.A.; Goncalves, M.C.; Zea Bermudez, V. de
2004-01-01
The sol-gel method was used to prepare two families of organic/inorganic hybrids incorporating europium triflate, classed as di-urethanesils and aminosils. A siliceous network to which short polyether chains are covalently bonded through urethane linkages, composes the di-urethanesil host. A siliceous network containing pendant amine terminated propyl chains, forms the aminosils. The xerogels were investigated by photoluminescence, particularly the local interaction between the Eu 3+ ions and the host matrix. The Eu 3+ local coordination was modelled in terms of a local-field perturbation representing the ion's nearest ligands interaction potential. While for the aminosils the Eu 3+ ions occupy one low-symmetry local site--crystal-field strength of ca. 760.5 cm -1 and 5 D 0 lifetime of 0.6-0.7 ms--two local Eu 3+ environments with distinct point symmetry group, 5 D 0 lifetimes (ca. 0.2-0.3 and 1.4-1.8 ms, respectively) and covalent nature--crystal-field strengths of ca. 540 and 740-780 cm -1 , respectively--were identified in the di-urethanesils
Iterative Object Localization Algorithm Using Visual Images with a Reference Coordinate
Directory of Open Access Journals (Sweden)
We-Duke Cho
2008-09-01
Full Text Available We present a simplified algorithm for localizing an object using multiple visual images that are obtained from widely used digital imaging devices. We use a parallel projection model which supports both zooming and panning of the imaging devices. Our proposed algorithm is based on a virtual viewable plane for creating a relationship between an object position and a reference coordinate. The reference point is obtained from a rough estimate which may be obtained from the preestimation process. The algorithm minimizes localization error through the iterative process with relatively low-computational complexity. In addition, nonlinearity distortion of the digital image devices is compensated during the iterative process. Finally, the performances of several scenarios are evaluated and analyzed in both indoor and outdoor environments.
Directory of Open Access Journals (Sweden)
Ya-Juan Hao
2013-01-01
Full Text Available The main object of this paper is to investigate the Helmholtz and diffusion equations on the Cantor sets involving local fractional derivative operators. The Cantor-type cylindrical-coordinate method is applied to handle the corresponding local fractional differential equations. Two illustrative examples for the Helmholtz and diffusion equations on the Cantor sets are shown by making use of the Cantorian and Cantor-type cylindrical coordinates.
Effect of interior geometry on local climate inside an electronic device enclosure
DEFF Research Database (Denmark)
Joshy, Salil; Jellesen, Morten Stendahl; Ambat, Rajan
2017-01-01
Electronic enclosure design and the internal arrangement of PCBs and components influence microclimate inside the enclosure. This work features a general electronic unit with parallel PCBs. One of the PCB is considered to have heat generating components on it. The humidity and temperature profiles...... geometry of the device and related enclosure design parameters on the humidity and temperature profiles inside the electronic device enclosure....
Retrieval-based Face Annotation by Weak Label Regularized Local Coordinate Coding.
Wang, Dayong; Hoi, Steven C H; He, Ying; Zhu, Jianke; Mei, Tao; Luo, Jiebo
2013-08-02
Retrieval-based face annotation is a promising paradigm of mining massive web facial images for automated face annotation. This paper addresses a critical problem of such paradigm, i.e., how to effectively perform annotation by exploiting the similar facial images and their weak labels which are often noisy and incomplete. In particular, we propose an effective Weak Label Regularized Local Coordinate Coding (WLRLCC) technique, which exploits the principle of local coordinate coding in learning sparse features, and employs the idea of graph-based weak label regularization to enhance the weak labels of the similar facial images. We present an efficient optimization algorithm to solve the WLRLCC task. We conduct extensive empirical studies on two large-scale web facial image databases: (i) a Western celebrity database with a total of $6,025$ persons and $714,454$ web facial images, and (ii)an Asian celebrity database with $1,200$ persons and $126,070$ web facial images. The encouraging results validate the efficacy of the proposed WLRLCC algorithm. To further improve the efficiency and scalability, we also propose a PCA-based approximation scheme and an offline approximation scheme (AWLRLCC), which generally maintains comparable results but significantly saves much time cost. Finally, we show that WLRLCC can also tackle two existing face annotation tasks with promising performance.
Kan, Jinglan; Wang, Hailong; Sun, Wei; Cao, Wei; Tao, Jun; Jiang, Jianzhuang
2013-08-05
Employment of the raise-by-one step method starting from M(TClPP)(acac) (acac = monoanion of acetylacetone) and [Pc(OPh)8]M'[Pc(OPh)8] led to the isolation and free modulation of the two rare-earth ions in the series of four mixed tetrapyrrole dysprosium sandwich complexes {(TClPP)M[Pc(OPh)8]M'[Pc(OPh)8]} [1-4; TClPP = dianion of meso-tetrakis(4-chlorophenyl)porphyrin; Pc(OPh)8 = dianion of 2,3,9,10,16,17,23,24-octa(phenoxyl)phthalocyanine; M-M' = Dy-Dy, Y-Dy, Dy-Y, and Y-Y]. Single-crystal X-ray diffraction analysis reveals different octacoordination geometries for the two metal ions in terms of the twist angle (defined as the rotation angle of one coordination square away from the eclipsed conformation with the other) between the two neighboring tetrapyrrole rings for the three dysprosium-containing isostructural triple-decker compounds, with the metal ion locating between an inner phthalocyanine ligand and an outer porphyrin ligand with a twist angle of 9.64-9.90° and the one between two phthalocyanine ligands of 25.12-25.30°. Systematic and comparative studies over the magnetic properties reveal magnetic-field-induced single-molecule magnet (SMM), SMM, and non-SMM nature for 1-3, respectively, indicating the dominant effect of the coordination geometry of the spin carrier, instead of the f-f interaction, on the magnetic properties. The present result will be helpful for the future design and synthesis of tetrapyrrole lanthanide SMMs with sandwich molecular structures.
International Nuclear Information System (INIS)
Kobzar, L.L.; Oleksyuk, D.A.
2001-01-01
The results of experiments executed in RRC 'Kurchatov Institute on the thermal-physical critical facility SVD are presented herein. The experiments modeled the drawing of two fuel rods to each other till touching WWER-1000 reactor in FA. The experimental model is a 7-rod bundle with the heated length of 1 m. The primary goal of experiments was to acquire the quantitative factors of the reduction in the critical heat fluxes as contrasted to the basic model (without disturbances of FA geometry) at the expense of local disturbance of a rod bundle geometry. As it follows from the experiment, the effect of decrease of the critical heat rate depends on combination of regime parameters and it makes 15% in the most unfavorable case (Authors)
Fujii, Keisuke; Isaka, Tadao; Kouzaki, Motoki; Yamamoto, Yuji
2015-11-01
Humans interact by changing their actions, perceiving other’s actions and executing solutions in conflicting situations. Using oscillator models, nonlinear dynamics have been considered for describing these complex human movements as an emergence of self-organisation. However, these frameworks cannot explain the hierarchical structures of complex behaviours between conflicting inter-agent and adapting intra-agent systems, especially in sport competitions wherein mutually quick decision making and execution are required. Here we adopt a hybrid multiscale approach to model an attack-and-defend game during which both players predict the opponent’s movement and move with a delay. From both simulated and measured data, one synchronous outcome between two-agent (i.e. successful defence) can be described as one attractor. In contrast, the other coordination-breaking outcome (i.e. successful attack) cannot be explained using gradient dynamics because the asymmetric interaction cannot always assume a conserved physical quantity. Instead, we provide the asymmetric and asynchronous hierarchical dynamical models to discuss two-agent competition. Our framework suggests that possessing information about an opponent and oneself in local-coordinative and global-competitive scale enables us to gain a deeper understanding of sports competitions. We anticipate developments in the scientific fields of complex movement adapting to such uncontrolled environments.
Matsumoto, Akihiro; Tachibana, Masao
2017-01-01
Even when the body is stationary, the whole retinal image is always in motion by fixational eye movements and saccades that move the eye between fixation points. Accumulating evidence indicates that the brain is equipped with specific mechanisms for compensating for the global motion induced by these eye movements. However, it is not yet fully understood how the retina processes global motion images during eye movements. Here we show that global motion images evoke novel coordinated firing in retinal ganglion cells (GCs). We simultaneously recorded the firing of GCs in the goldfish isolated retina using a multi-electrode array, and classified each GC based on the temporal profile of its receptive field (RF). A moving target that accompanied the global motion (simulating a saccade following a period of fixational eye movements) modulated the RF properties and evoked synchronized and correlated firing among local clusters of the specific GCs. Our findings provide a novel concept for retinal information processing during eye movements.
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
Local differential geometry of null curves in conformally flat space-time
International Nuclear Information System (INIS)
Urbantke, H.
1989-01-01
The conformally invariant differential geometry of null curves in conformally flat space-times is given, using the six-vector formalism which has generalizations to higher dimensions. This is then paralleled by a twistor description, with a twofold merit: firstly, sometimes the description is easier in twistor terms, sometimes in six-vector terms, which leads to a mutual enlightenment of both; and secondly, the case of null curves in timelike pseudospheres or 2+1 Minkowski space we were only able to treat twistorially, making use of an invariant differential found by Fubini and Cech. The result is the expected one: apart from stated exceptional cases there is a conformally invariant parameter and two conformally invariant curvatures which, when specified in terms of this parameter, serve to characterize the curve up to conformal transformations. 12 refs. (Author)
International Nuclear Information System (INIS)
Robinson, I.; Trautman, A.
1988-01-01
The geometry of classical physics is Lorentzian; but weaker geometries are often more appropriate: null geodesics and electromagnetic fields, for example, are well known to be objects of conformal geometry. To deal with a single null congruence, or with the radiative electromagnetic fields associated with it, even less is needed: flag geometry for the first, optical geometry, with which this paper is chiefly concerned, for the second. The authors establish a natural one-to-one correspondence between optical geometries, considered locally, and three-dimensional Cauchy-Riemann structures. A number of Lorentzian geometries are shown to be equivalent from the optical point of view. For example the Goedel universe, the Taub-NUT metric and Hauser's twisting null solution have an optical geometry isomorphic to the one underlying the Robinson congruence in Minkowski space. The authors present general results on the problem of lifting a CR structure to a Lorentz manifold and, in particular, to Minkowski space; and exhibit the relevance of the deviation form to this problem
Acharya, S.; Kaplan, D. A.; Casey, S.; Cohen, M. J.; Jawitz, J. W.
2015-05-01
Self-organized landscape patterning can arise in response to multiple processes. Discriminating among alternative patterning mechanisms, particularly where experimental manipulations are untenable, requires process-based models. Previous modeling studies have attributed patterning in the Everglades (Florida, USA) to sediment redistribution and anisotropic soil hydraulic properties. In this work, we tested an alternate theory, the self-organizing-canal (SOC) hypothesis, by developing a cellular automata model that simulates pattern evolution via local positive feedbacks (i.e., facilitation) coupled with a global negative feedback based on hydrology. The model is forced by global hydroperiod that drives stochastic transitions between two patch types: ridge (higher elevation) and slough (lower elevation). We evaluated model performance using multiple criteria based on six statistical and geostatistical properties observed in reference portions of the Everglades landscape: patch density, patch anisotropy, semivariogram ranges, power-law scaling of ridge areas, perimeter area fractal dimension, and characteristic pattern wavelength. Model results showed strong statistical agreement with reference landscapes, but only when anisotropically acting local facilitation was coupled with hydrologic global feedback, for which several plausible mechanisms exist. Critically, the model correctly generated fractal landscapes that had no characteristic pattern wavelength, supporting the invocation of global rather than scale-specific negative feedbacks.
Alford, W. A.; Kawamura, Kazuhiko; Wilkes, Don M.
1997-12-01
This paper discusses the problem of integrating human intelligence and skills into an intelligent manufacturing system. Our center has jointed the Holonic Manufacturing Systems (HMS) Project, an international consortium dedicated to developing holonic systems technologies. One of our contributions to this effort is in Work Package 6: flexible human integration. This paper focuses on one activity, namely, human integration into motion guidance and coordination. Much research on intelligent systems focuses on creating totally autonomous agents. At the Center for Intelligent Systems (CIS), we design robots that interact directly with a human user. We focus on using the natural intelligence of the user to simplify the design of a robotic system. The problem is finding ways for the user to interact with the robot that are efficient and comfortable for the user. Manufacturing applications impose the additional constraint that the manufacturing process should not be disturbed; that is, frequent interacting with the user could degrade real-time performance. Our research in human-robot interaction is based on a concept called human directed local autonomy (HuDL). Under this paradigm, the intelligent agent selects and executes a behavior or skill, based upon directions from a human user. The user interacts with the robot via speech, gestures, or other media. Our control software is based on the intelligent machine architecture (IMA), an object-oriented architecture which facilitates cooperation and communication among intelligent agents. In this paper we describe our research testbed, a dual-arm humanoid robot and human user, and the use of this testbed for a human directed sorting task. We also discuss some proposed experiments for evaluating the integration of the human into the robot system. At the time of this writing, the experiments have not been completed.
Ukwatta, T. N.; Linnemann, J. T.; Tollefson, K.; Abeysekara, A. U.; Bhat, P. N.; Sonbas, E.; Gehrels, N.
2011-01-01
We investigate the feasibility of implementing a system that will coordinate ground-based optical telescopes to cover the Fermi GBM Error Circle (EC). The aim of the system is to localize GBM detected GRBs and facilitate multi-wavelength follow-up from space and ground. This system will optimize the observing locations in the GBM EC based on individual telescope location, Field of View (FoV) and sensitivity. The proposed system will coordinate GBM EC scanning by professional as well as amateur astronomers around the world. The results of a Monte Carlo simulation to investigate the feasibility of the project are presented.
Spinning geometry = Twisted geometry
International Nuclear Information System (INIS)
Freidel, Laurent; Ziprick, Jonathan
2014-01-01
It is well known that the SU(2)-gauge invariant phase space of loop gravity can be represented in terms of twisted geometries. These are piecewise-linear-flat geometries obtained by gluing together polyhedra, but the resulting geometries are not continuous across the faces. Here we show that this phase space can also be represented by continuous, piecewise-flat three-geometries called spinning geometries. These are composed of metric-flat three-cells glued together consistently. The geometry of each cell and the manner in which they are glued is compatible with the choice of fluxes and holonomies. We first remark that the fluxes provide each edge with an angular momentum. By studying the piecewise-flat geometries which minimize edge lengths, we show that these angular momenta can be literally interpreted as the spin of the edges: the geometries of all edges are necessarily helices. We also show that the compatibility of the gluing maps with the holonomy data results in the same conclusion. This shows that a spinning geometry represents a way to glue together the three-cells of a twisted geometry to form a continuous geometry which represents a point in the loop gravity phase space. (paper)
International Nuclear Information System (INIS)
Moeller, R.; Tschoeke, H.; Kolodziej, M.
1980-12-01
The operating reliability of nuclear reactors calls for a reliable strength analysis of the highly loaded core elements, one of its prerequisites being the reliable determination of the three-dimensional velocity and temperature fields. To verify thermohydraulics computer programs, extensive local temperature measurements in the rod claddings of the critical bundle zone were performed on a heated 19-rod bundle model with sodium flow and provided with spacer grids (P/D = 1.30; W/D = 1.19). These are the essential results obtained: Outside the spacer grids the azimuthal temperature variations of the side and corner rods are greater by approximately the factor 10 in the bundle geometry under consideration as compared to rods in the central bundle zone. The spacer grids investigated give rise to great local temperature peaks and correspondingly great temperature gradients in the axial and azimuthal directions immediately around the support points. Continuous reduction of a subchannel by rod bowing results in substantial rises of temperature which, however, are limited to the adjacent cladding tube zones. (orig.) [de
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...
Energy Technology Data Exchange (ETDEWEB)
Hanson-Heine, Magnus W. D., E-mail: magnus.hansonheine@nottingham.ac.uk [School of Chemistry, University of Nottingham, University Park, Nottingham NG7 2RD (United Kingdom)
2015-10-28
Carefully choosing a set of optimized coordinates for performing vibrational frequency calculations can significantly reduce the anharmonic correlation energy from the self-consistent field treatment of molecular vibrations. However, moving away from normal coordinates also introduces an additional source of correlation energy arising from mode-coupling at the harmonic level. The impact of this new component of the vibrational energy is examined for a range of molecules, and a method is proposed for correcting the resulting self-consistent field frequencies by adding the full coupling energy from connected pairs of harmonic and pseudoharmonic modes, termed vibrational self-consistent field (harmonic correlation). This approach is found to lift the vibrational degeneracies arising from coordinate optimization and provides better agreement with experimental and benchmark frequencies than uncorrected vibrational self-consistent field theory without relying on traditional correlated methods.
Goren, Liran; Castelltort, Sébastien; Klinger, Yann
2016-04-01
Partitioning of horizontal deformation between localized and distributed modes in regions of oblique tectonic convergence is, in many cases, hard to quantify. As a case study, we consider the Dead Sea Fault System that changes its orientation across Lebanon and forms a restraining bend. The oblique deformation along the Lebanese restraining bend is characterized by a complex suite of tectonic structures, among which, the Yammouneh fault, is believed to be the main strand that relays deformation from the southern section to the northern section of the Dead Sea Fault System. However, uncertainties regarding slip rates along the Yammouneh fault and strain partitioning in Lebanon still prevail. In the current work we use the geometry and topology of river basins together with numerical modeling to evaluate modes and rates of the horizontal deformation in Mount Lebanon that is associated with the Arabia-Sinai relative plate motion. We focus on river basins that drain Mount Lebanon to the Mediterranean and originate close to the Yammouneh fault. We quantify a systematic counterclockwise rotation of these basins and evaluate drainage area disequilibrium using an application of the χ mapping technique, which aims at estimating the degree of geometrical and topological disequilibrium in river networks. The analysis indicates a systematic spatial pattern whereby tributaries of the rotated basins appear to experience drainage area loss or gain with respect to channel length. A kinematic model that is informed by river basin geometry reveals that since the late Miocene, about a quarter of the relative plate motion parallel to the plate boundary has been distributed along a wide band of deformation to the west of the Yammouneh fault. Taken together with previous, shorter-term estimates, the model indicates little variation of slip rate along the Yammouneh fault since the late Miocene. Kinematic model results are compatible with late Miocene paleomagnetic rotations in western
Directory of Open Access Journals (Sweden)
Filipiak Daria
2015-02-01
Full Text Available Electronic tacheometers are currently the standard instruments used in geodetic work, including also geodetic engineering measurements. The main advantage connected with this equipment is among others high accuracy of the measurement and thus high accuracy of the final determinations represented for example by the points’ coordinates. One of many applications of the tacheometers is the measurement of crane rail axes. This measurement is based on polar method and it allows to get the spatial coordinates of points in 3D local system. The standard technology of measurement of crane rail axes and development of its calculations’ results is well-known and widely presented in the subject literature. At the same time new methods of observations results evaluation are developing.
Directory of Open Access Journals (Sweden)
Ristić Kornelija T.
2016-01-01
Full Text Available The most commonly used method for establishing the mathematical basis of surveying and spatial data collection is the method of Global Navigation Satellite Positioning System (GNSS. However, these data relate to the World Geodetic Date WGS84 which is different from the State geodetic network,. As a part of realization the project of determining spatial local reference network Mrkonjić Grad the GNSS observations on 15 trigonometric points whose position is known to the State system of coordinates (x, y, h were made. For the purpose of coordinate transformation between the two system two different transformation models were anlyzed. Beside the most commonly used Helmert seven parameter transformation, afina nine parametric transformation was tested. Comparing the two transformations models, conclusion was made that showes some benefits of using affina nine parameter transformation models in Republic of Serpska.
Directory of Open Access Journals (Sweden)
Олексій Павлович Федотов
2016-06-01
Based on the results of the study the author notes that the interaction of the Ukrainian SFS customs offices and local state administrations with local self-government bodies is an inherent quality, link and component of the Ukrainian SFS Customs offices functioning organization, which aims to improve the state customs service implementation standards by the Ukrainian SFS customs houses and to ensure the said implementation efficiency. However, in the course of interaction of the Ukrainian SFS customs with local state administrations and local self-government bodies each of the mentioned organizations specializes in solving their specific tasks in accordance with their subject expertise, and forms a clear organizational system. The complementarity of such kind helps to improve the state customs affairs conductance quality and is realized through the coordination of performance of the Ukrainian SFS customs offices, local state administrations and local self-government bodies as the interaction subjects through normative, informational and analytical provision for the interaction and concretization of the activities of each subject within the planned activities.
Directory of Open Access Journals (Sweden)
Filipiak-Kowszyk Daria
2018-01-01
Full Text Available Geodetic control measurements play an important part because they provide information about the current state of repair of the construction, which has a direct impact on the safety assessment of its exploitation. Authors in this paper have focused on control measurements of the elevator shaft. The article discusses the problem of determining the deviation of elevator shaft walls from the vertical plane in the local 3D coordinate system. It presents a concept of estimation of measurements results base on the parametric method with conditions on parameters. The simulated measurement results were used to verify the concept presented in the paper.
Directory of Open Access Journals (Sweden)
Wen Liu
2016-12-01
Full Text Available Indoor positioning technologies has boomed recently because of the growing commercial interest in indoor location-based service (ILBS. Due to the absence of satellite signal in Global Navigation Satellite System (GNSS, various technologies have been proposed for indoor applications. Among them, Wi-Fi fingerprinting has been attracting much interest from researchers because of its pervasive deployment, flexibility and robustness to dense cluttered indoor environments. One challenge, however, is the deployment of Access Points (AP, which would bring a significant influence on the system positioning accuracy. This paper concentrates on WLAN based fingerprinting indoor location by analyzing the AP deployment influence, and studying the advantages of coordinate-based clustering compared to traditional RSS-based clustering. A coordinate-based clustering method for indoor fingerprinting location, named Smallest-Enclosing-Circle-based (SEC, is then proposed aiming at reducing the positioning error lying in the AP deployment and improving robustness to dense cluttered environments. All measurements are conducted in indoor public areas, such as the National Center For the Performing Arts (as Test-bed 1 and the XiDan Joy City (Floors 1 and 2, as Test-bed 2, and results show that SEC clustering algorithm can improve system positioning accuracy by about 32.7% for Test-bed 1, 71.7% for Test-bed 2 Floor 1 and 73.7% for Test-bed 2 Floor 2 compared with traditional RSS-based clustering algorithms such as K-means.
Liu, Wen; Fu, Xiao; Deng, Zhongliang
2016-12-02
Indoor positioning technologies has boomed recently because of the growing commercial interest in indoor location-based service (ILBS). Due to the absence of satellite signal in Global Navigation Satellite System (GNSS), various technologies have been proposed for indoor applications. Among them, Wi-Fi fingerprinting has been attracting much interest from researchers because of its pervasive deployment, flexibility and robustness to dense cluttered indoor environments. One challenge, however, is the deployment of Access Points (AP), which would bring a significant influence on the system positioning accuracy. This paper concentrates on WLAN based fingerprinting indoor location by analyzing the AP deployment influence, and studying the advantages of coordinate-based clustering compared to traditional RSS-based clustering. A coordinate-based clustering method for indoor fingerprinting location, named Smallest-Enclosing-Circle-based (SEC), is then proposed aiming at reducing the positioning error lying in the AP deployment and improving robustness to dense cluttered environments. All measurements are conducted in indoor public areas, such as the National Center For the Performing Arts (as Test-bed 1) and the XiDan Joy City (Floors 1 and 2, as Test-bed 2), and results show that SEC clustering algorithm can improve system positioning accuracy by about 32.7% for Test-bed 1, 71.7% for Test-bed 2 Floor 1 and 73.7% for Test-bed 2 Floor 2 compared with traditional RSS-based clustering algorithms such as K-means.
Gardner, Karen; Yen, Laurann; Banfield, Michelle; Gillespie, James; McRae, Ian; Wells, Robert
2013-02-01
The terms coordination and integration refer to a wide range of interventions, from strategies aimed at coordinating clinical care for individuals to organizational and system interventions such as managed care, which contract medical and support services. Ongoing debate about whether financial and organizational integration are needed to achieve clinical integration is evident in policy debates over several decades, from a focus through the 1990s on improving coordination through structural reform and the use of market mechanisms to achieve allocative efficiencies (better overall service mix) to more recent attention on system performance to improve coordination and quality. We examine this shift in Australia and ask how has changing the policy driver affected efforts to achieve coordination? Care planning, fund pooling and purchasing are still important planks in coordination. Evidence suggests that financial strategies can be used to drive improvements for particular patient groups, but these are unlikely to improve outcomes without being linked to clinical strategies that support coordination through multidisciplinary teamwork, IT, disease management guidelines and audit and feedback. Meso level organizational strategies might align the various elements to improve coordination. Changing the policy driver has refocused research and policy over the last two decades from a focus on achieving allocative efficiencies to achieving quality and value for money. Research is yet to develop theoretical approaches that can deal with the implications for assessing effectiveness. Efforts need to identify intervention mechanisms, plausible relationships between these and their measurable outcomes and the components of contexts that support the emergence of intervention attributes.
Van Es, S.H.J.; Kolstein, M.H.; Pijpers, R.J.M.; Bijlaard, F.S.K.
2014-01-01
This paper presents the results of extensive measurements on weld toe geometry of as-welded and TIG-dressed butt welded connections in high strength steels S460, S690 and very high strength steels S890 and S1100. Descriptions of the measurement techniques and data analysis are presented. Four weld
Es, S.H.J. van; Kolstein, M.H.; Pijpers, R.J.M.; Bijlaard, F.S.K.
2013-01-01
This paper presents the results of extensive measurements on weld toe geometry of as-welded and TIG-dressed butt welded connections in high strength steels S460, S690 and very high strength steels S890 and S1100. Descriptions of the measurement techniques and data analysis are presented. Four weld
New approach to isometric transformations in oblique local coordinate systems of reference
Directory of Open Access Journals (Sweden)
Stępień Grzegorz
2017-12-01
Full Text Available The research article describes a method of isometric transformation and determining an exterior orientation of a measurement instrument. The method is based on a designation of a “virtual” translation of two relative oblique orthogonal systems to a common, known in the both systems, point. The relative angle orientation of the systems does not change as each of the systems is moved along its axis. The next step is the designation of the three rotation angles (e.g. Tait-Bryan or Euler angles, transformation of the system convoluted at the calculated angles and moving the system to the initial position where the primary coordinate system was. This way eliminates movements of the systems from the calculations and makes it possible to calculate angles of mutual rotation angles of two orthogonal systems primarily involved in the movement. The research article covers laboratory calculations for simulated data. The accuracy of the results is 10-6 m (10-3 regarding the accuracy of the input data. This confi rmed the correctness of the assumed calculation method. In the following step the method was verifi ed under fi eld conditions, where the accuracy of the method raised to 0.003 m. The proposed method enabled to make the measurements with the oblique and uncentered instrument, e.g. total station instrument set over an unknown point. This is the reason why the method was named by the authors as Total Free Station - TFS. The method may be also used for isometric transformations for photogrammetric purposes.
Stephens, Susanna L; Bittner, Dror M; Mikhailov, Victor A; Mizukami, Wataru; Tew, David P; Walker, Nicholas R; Legon, Anthony C
2014-10-06
The molecular geometries of isolated complexes in which a single molecule of C2H4 or C2H2 is bound to CuCl have been determined through pure rotational spectroscopy and ab-initio calculations. The C2H2···CuCl and C2H4···CuCl complexes are generated through laser vaporization of a copper rod in the presence of a gas sample undergoing supersonic expansion and containing C2H2 (or C2H4), CCl4, and Ar. Results are presented for five isotopologues of C2H2···CuCl and six isotopologues of C2H4···CuCl. Both of these complexes adopt C(2v), T-shaped geometries in which the hydrocarbon binds to the copper atom through its π electrons such that the metal is equidistant from all H atoms. The linear and planar geometries of free C2H2 and C2H4, respectively, are observed to distort significantly on attachment to the CuCl unit, and the various changes are quantified. The ∠(*-C-H) parameter in C2H2 (where * indicates the midpoint of the C≡C bond) is measured to be 192.4(7)° in the r0 geometry of the complex representing a significant change from the linear geometry of the free molecule. This distortion of the linear geometry of C2H2 involves the hydrogen atoms moving away from the copper atom within the complex. Ab-initio calculations at the CCSD(T)(F12*)/AVTZ level predict a dihedral ∠(HCCCu) angle of 96.05° in C2H4···CuCl, and the experimental results are consistent with such a distortion from planarity. The bonds connecting the carbon atoms within each of C2H2 and C2H4, respectively, extend by 0.027 and 0.029 Å relative to the bond lengths in the isolated molecules. Force constants, k(σ), and nuclear quadrupole coupling constants, χ(aa)(Cu), [χ(bb)(Cu) - χ(cc)(Cu)], χ(aa)(Cl), and [χ(bb)(Cl) - χ(cc)(Cl)], are independently determined for all isotopologues of C2H2···CuCl studied and for four isotopologues of C2H4···CuCl.
DEFF Research Database (Denmark)
Speedtsberg, Merete Brink; Christensen, Sofie Bouschinger; Stenum, Jan
2018-01-01
-posterior directions were recorded with a sternum mounted accelerometer at 256Hz. Short term local dynamic stability (λs), root mean square (RMS) and relative root mean square (RMSR) were calculated from measures of orthogonal trunk accelerations. Receiver operating characteristic curve (ROC) analysis was performed...... between children with DCD and TD children in any direction. The ROC analysis of λs in separate directions and in two dimensions showed an excellent accuracy of discriminating between children with DCD and TD children. Anterior-posterior direction in combination with medio-lateral or vertical showed best...
Energy Technology Data Exchange (ETDEWEB)
Bo, Maolin [Key Laboratory of Low-Dimensional Materials and Application Technologies, Ministry of Education, Xiangtan University, Xiangtan, Hunan 411105 (China); Wang, Yan [Key Laboratory of Low-Dimensional Materials and Application Technologies, Ministry of Education, Xiangtan University, Xiangtan, Hunan 411105 (China); School of Information and Electronic Engineering, Hunan University of Science and Technology, Xiangtan, Hunan 411201 (China); Huang, Yongli, E-mail: huangyongli@xtu.edu.cn [Key Laboratory of Low-Dimensional Materials and Application Technologies, Ministry of Education, Xiangtan University, Xiangtan, Hunan 411105 (China); Yang, Xuexian [Department of Physics, Jishou University, Jishou, Hunan 416000 (China); Yang, Yezi [Key Laboratory of Low-Dimensional Materials and Application Technologies, Ministry of Education, Xiangtan University, Xiangtan, Hunan 411105 (China); Li, Can [Center for Coordination Bond Engineering, School of Materials Science and Engineering, China Jiliang University, Hangzhou 330018 (China); Sun, Chang Q., E-mail: ecqsun@ntu.edu.sg [Key Laboratory of Low-Dimensional Materials and Application Technologies, Ministry of Education, Xiangtan University, Xiangtan, Hunan 411105 (China); NOVITAS, School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798 (Singapore)
2014-11-30
Highlights: • Cohesive energy of the representative bond determines the core-level shift. • XPS derives the energy level of an isolated atom and its bulk shift. • XPS derives the local bond length, bond energy, binding energy density. • Thermal XPS resolves the Debye temperature and atomic cohesive energy. - Abstract: Numerical reproduction of the measured 4f{sub 7/2} energy shift of Ir(1 0 0), (1 1 1), and (2 1 0) solid skins turns out the following: (i) the 4f{sub 7/2} level of an isolated Ir atom shifts from 56.367 eV to 60.332 eV by 3.965 eV upon bulk formation; (ii) the local energy density increases by up to 130% and the atomic cohesive energy decreases by 70% in the skin region compared with the bulk values. Numerical match to observation of the temperature dependent energy shift derives the Debye temperature that varies from 285.2 K (Surface) to 315.2 K (Bulk). We clarified that the shorter and stronger bonds between under-coordinated atoms cause local densification and quantum entrapment of electron binding energy, which perturbs the Hamiltonian and the core shifts in the skin region.
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.
Iversen, Birger
1992-01-01
Although it arose from purely theoretical considerations of the underlying axioms of geometry, the work of Einstein and Dirac has demonstrated that hyperbolic geometry is a fundamental aspect of modern physics
van den Broek, P.M.
1984-01-01
The aim of this paper is to give a detailed exposition of the relation between the geometry of twistor space and the geometry of Minkowski space. The paper has a didactical purpose; no use has been made of differential geometry and cohomology.
International Nuclear Information System (INIS)
Pastore, G.; Tosi, M.P.
1995-11-01
Earlier work has identified the metal ion size R M as a relevant parameter in determining the evolution of the liquid structure of trivalent metal chlorides across the series from LaCl 3 (R M approx. 1.4 A) to AlCl 3 (R M approx. 0.8 A). Here we highlight the structural role of the chlorines by contrasting the structure of fully equilibrated melts with that of disordered systems obtained by quenching the chlorine component. Main attention is given to how the suppression of screening of the polyvalent ions by the chlorines changes trends in the local liquid structure (first neighbour coordination and partial radial distribution functions) and in the intermediate range order (first sharp diffraction peak in the partial structure factors). The main microscopic consequences of structural quenching of the chlorine component are a reduction in short range order and an enhancement of intermediate range order in the metal ion component, as well as the suppression of a tendency to molecular-type states at the lower end of the range of R M . (author). 23 refs, 6 figs
Hu, Zhiyong; Zhao, Meng; Su, Jian; Xu, Shasha; Hu, Lei; Liu, Hui; Zhang, Qiong; Zhang, Jun; Wu, Jieying; Tian, Yupeng
2018-02-01
Three novel coordination polymers, [Zn(μ2-HTCA)(Phen)]n (1), {[Cd(μ3-HTCA)(Phen)]·2H2O}n (2), [Mn(μ2-HTCA)(Phen)(H2O)]n (3) were prepared by hydrothermal synthesis from the 4, 4', 4''-nitrilotribenzoicacid (H3TCA) and 1, 10-phenanthroline monohydrate (Phen) with different transition metal salts, which were characterized by elemental analysis, IR spectra, powder and single-crystal X-ray diffraction and thermogravimetric analysis. The photophysical properties of the complexes were investigated by solid-state diffuse reflectance spectra, photoluminescent properties, lifetime and quantum yield. For these complexes, it was found that the band gaps follow the order: 3 ＜ 2 ＜ 1 ＜ 2.80 eV, fluorescence intensity order: 1 ＞ H3TCA ＞ 2 ＞ 3; quantum yield order: H3TCA ＞ 1 ＞ 2 ＞ 3; while the lifetime order: 1 ＞ 2 ＞ H3TCA ＞ 3.
International Nuclear Information System (INIS)
Moeller, R.; Tschoeke, H.
1980-01-01
The operating reliability of nuclear reactors calls for a reliable strength analysis of the highly loaded core elements, one of its prerequisites being the reliable determination of the three-dimensional velocity and temperature fields. To verify thermohydraulics computer programs, extensive local temperature measurements in the rod claddings of the critical bundle zone were performed on a heated 19-rod bundle model with sodium flow and provided with spacer grids (P/D = 1.30; W/D = 1.19). The essential results are: - Outside the spacer grids, the azimuthal temperature variations of the side and corner rods are approximately 10-fold those of rods in the central bundle zone. - The spacer grids investigated give rise to great local temperature peaks and correspondingly great temperature gradients in the axial and azimuthal directions immediately around the support points. - Continuous reduction of a subchannel by rod bowing results in substantial rises of temperature which, however, are limited to adjacent cladding tubes. (orig.)
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
De Virgiliis, Andres; Vink, Richard L C; Horbach, Jürgen; Binder, Kurt
2008-10-01
Monte Carlo simulations of the Asakura-Oosawa model for colloid-polymer mixtures confined between two parallel repulsive structureless walls are presented and analyzed in the light of current theories on capillary condensation and interface localization transitions. Choosing a polymer-to-colloid size ratio of q=0.8 and studying ultrathin films in the range of D=3 to D=10 colloid diameters thickness, grand canonical Monte Carlo methods are used; phase transitions are analyzed via finite size scaling, as in previous work on bulk systems and under confinement between identical types of walls. Unlike the latter work, inequivalent walls are used here: While the left wall has a hard-core repulsion for both polymers and colloids, at the right-hand wall an additional square-well repulsion of variable strength acting only on the colloids is present. We study how the phase separation into colloid-rich and colloid-poor phases occurring already in the bulk is modified by such a confinement. When the asymmetry of the wall-colloid interaction increases, the character of the transition smoothly changes from capillary condensation type to interface localization type. For very thin films (i.e., for D=3 ) and a suitable choice of the wall-colloid interactions, evidence is found that the critical behavior falls in the universality class of the two-dimensional Ising model. Otherwise, we observe crossover scaling between different universality classes (namely, the crossover from the three-dimensional to the two-dimensional Ising model universality class). The colloid and polymer density profiles across the film in the various phases are discussed, as well as the correlation of interfacial fluctuations in the direction parallel to the confining walls. The broadening of the interface between the coexisting colloid-rich and polymer-rich phases (located parallel to the confining walls) is understood in terms of capillary wave fluctuations. The experimental observability of all these
Definition of treatment geometry in radiation therapy
International Nuclear Information System (INIS)
Aaltonen, P.
1996-01-01
When accurate systems for quality assurance and treatment optimization are employed, a precise system for fixation and dosimetric and portal verification are as important as a continued and standardized code of practice for dosimetry and patient follow-up, including registration of tumour responses and acute and late normal tissue reactions. To improve the accuracy of existing dose response relations in order to improve future therapy the treatment geometry and dose delivery concepts have to be accurately defined and uniformly employed. A Nordic working group was set up in 1991 (by Nordic Association of Clinica Physics) to standardize the concepts and quantities used during the whole radiotherapy process in the Nordic countries. Now the group is finalizing its report ''Specification of Dose Delivery in Radiation Therapy''. The report emphasizes that the treatment geometry shall be consistent with the geometry used during the diagnostic work up. The patient fixation is of importance early in the diagnostic phase to ensure that the same reference points and patients position will be used both during the diagnostic work up, simulation and treatment execution. Reference Coordinate System of the patient is a concept based on defined anatomic reference points. This Patient Reference System is a local system which has validity for the tissues, organs and volumes defined during radiotherapy. The reference points of the Patient Reference System should in turn be used for beam set-up. The treatment geometry is then defined by using different concepts describing tissues which are mobile in the Patient Reference System, and finally, volumes which are fixed in this coordinate system. A Set-up Margin has to be considered for movements of the volumes defined in the Reference Coordinate System of the Patient in relation to the radiation beam. The Set-up Margin is dependent on the treatment technique and it is needed in the treatment planning procedure to ensure that the prescribed
Definition of treatment geometry in radiation therapy
Energy Technology Data Exchange (ETDEWEB)
Aaltonen, P [Finnish Centre for Radiation and Nuclear Safety (STUK), Helsinki (Finland)
1996-08-01
When accurate systems for quality assurance and treatment optimization are employed, a precise system for fixation and dosimetric and portal verification are as important as a continued and standardized code of practice for dosimetry and patient follow-up, including registration of tumour responses and acute and late normal tissue reactions. To improve the accuracy of existing dose response relations in order to improve future therapy the treatment geometry and dose delivery concepts have to be accurately defined and uniformly employed. A Nordic working group was set up in 1991 to standardize the concepts and quantities used during the whole radiotherapy process in the Nordic countries. Now the group is finalizing its report ``Specification of Dose Delivery in Radiation Therapy``. The report emphasizes that the treatment geometry shall be consistent with the geometry used during the diagnostic work up. The patient fixation is of importance early in the diagnostic phase to ensure that the same reference points and patients position will be used both during the diagnostic work up, simulation and treatment execution. Reference Coordinate System of the patient is a concept based on defined anatomic reference points. This Patient Reference System is a local system which has validity for the tissues, organs and volumes defined during radiotherapy. The reference points of the Patient Reference System should in turn be used for beam set-up. The treatment geometry is then defined by using different concepts describing tissues which are mobile in the Patient Reference System, and finally, volumes which are fixed in this coordinate system. A Set-up Margin has to be considered for movements of the volumes defined in the Reference Coordinate System of the Patient in relation to the radiation beam. The Set-up Margin is dependent on the treatment technique and it is needed in the treatment planning procedure to ensure that the prescribed dose to the Target Volume is delivered.
Pottmann, Helmut; Eigensatz, Michael; Vaxman, Amir; Wallner, Johannes
2014-01-01
Around 2005 it became apparent in the geometry processing community that freeform architecture contains many problems of a geometric nature to be solved, and many opportunities for optimization which however require geometric understanding. This area of research, which has been called architectural geometry, meanwhile contains a great wealth of individual contributions which are relevant in various fields. For mathematicians, the relation to discrete differential geometry is significant, in particular the integrable system viewpoint. Besides, new application contexts have become available for quite some old-established concepts. Regarding graphics and geometry processing, architectural geometry yields interesting new questions but also new objects, e.g. replacing meshes by other combinatorial arrangements. Numerical optimization plays a major role but in itself would be powerless without geometric understanding. Summing up, architectural geometry has become a rewarding field of study. We here survey the main directions which have been pursued, we show real projects where geometric considerations have played a role, and we outline open problems which we think are significant for the future development of both theory and practice of architectural geometry.
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.
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
Kemnitz, Arnfried
Der Grundgedanke der Analytischen Geometrie besteht darin, dass geometrische Untersuchungen mit rechnerischen Mitteln geführt werden. Geometrische Objekte werden dabei durch Gleichungen beschrieben und mit algebraischen Methoden untersucht.
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.
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...
A Note on the Dipole Coordinates
Kageyama, Akira; Sugiyama, Tooru; Watanabe, Kunihiko; Sato, Tetsuya
2004-01-01
A couple of orthogonal coordinates for dipole geometry are proposed for numerical simulations of plasma geophysics in the Earth's dipole magnetic field. These coordinates have proper metric profiles along field lines in contrast to the standard dipole coordinate system that is commonly used in analytical studies for dipole geometry.
Weaver, Brian T; Braman, Jerrod E; Haut, Roger C
2016-06-01
A direct method to express the center of pressure (CoP) measured by an insole pressure sensor system (IPSS) into a known coordinate system measured by motion tracking equipment is presented. A custom probe was constructed with reflective markers to allow its tip to be precisely tracked with motion tracking equipment. This probe was utilized to activate individual sensors on an IPSS that was placed in a shoe fitted with reflective markers used to establish a local shoe coordinate system. When pressed onto the IPSS the location of the probe's tip was coincident with the CoP measured by the IPSS (IPSS-CoP). Two separate pushes (i.e., data points) were used to develop vectors in each respective coordinate system. Simple vector mathematics determined the rotational and translational components of the transformation matrix needed to express the IPSS-CoP into the local shoe coordinate system. Validation was performed by comparing IPSS-CoP with an embedded force plate measured CoP (FP-CoP) from data gathered during kinematic trials. Six male subjects stood on an embedded FP and performed anterior/posterior (AP) sway, internal rotation, and external rotation of the body relative to a firmly planted foot. The IPSS-CoP was highly correlated with the FP-CoP for all motions, root mean square errors (RMSRRs) were comparable to other research, and there were no statistical differences between the displacement of the IPSS-CoP and FP-CoP for both the AP and medial/lateral (ML) axes, respectively. The results demonstrated that this methodology could be utilized to determine the transformation variables need to express IPSS-CoP into a known coordinate system measured by motion tracking equipment and that these variables can be determined outside the laboratory anywhere motion tracking equipment is available.
Czech Academy of Sciences Publication Activity Database
Nachtigall, Petr; Frolich, K.; Drobná, H.; Bludský, Ota; Nachtigallová, Dana; Bulánek, R.
2007-01-01
Roč. 111, č. 30 (2007), s. 11353-11362 ISSN 1932-7447 R&D Projects: GA MŠk LC512; GA ČR GA203/06/0324; GA ČR GD203/03/H140 Institutional research plan: CEZ:AV0Z40550506 Keywords : zeolite * adsorption * coordination Subject RIV: CF - Physical ; Theoretical Chemistry
2010-01-01
... 10 Energy 3 2010-01-01 2010-01-01 false Grant awards for units of local government, public care... CONSERVATION GRANT PROGRAMS FOR SCHOOLS AND HOSPITALS AND BUILDINGS OWNED BY UNITS OF LOCAL GOVERNMENT AND PUBLIC CARE INSTITUTIONS Grant Awards § 455.141 Grant awards for units of local government, public care...
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...
International Nuclear Information System (INIS)
Jonsson, Rickard; Westman, Hans
2006-01-01
We show that by employing the standard projected curvature as a measure of spatial curvature, we can make a certain generalization of optical geometry (Abramowicz M A and Lasota J-P 1997 Class. Quantum Grav. A 14 23-30). This generalization applies to any spacetime that admits a hypersurface orthogonal shearfree congruence of worldlines. This is a somewhat larger class of spacetimes than the conformally static spacetimes assumed in standard optical geometry. In the generalized optical geometry, which in the generic case is time dependent, photons move with unit speed along spatial geodesics and the sideways force experienced by a particle following a spatially straight line is independent of the velocity. Also gyroscopes moving along spatial geodesics do not precess (relative to the forward direction). Gyroscopes that follow a curved spatial trajectory precess according to a very simple law of three-rotation. We also present an inertial force formalism in coordinate representation for this generalization. Furthermore, we show that by employing a new sense of spatial curvature (Jonsson R 2006 Class. Quantum Grav. 23 1)) closely connected to Fermat's principle, we can make a more extensive generalization of optical geometry that applies to arbitrary spacetimes. In general this optical geometry will be time dependent, but still geodesic photons move with unit speed and follow lines that are spatially straight in the new sense. Also, the sideways experienced (comoving) force on a test particle following a line that is straight in the new sense will be independent of the velocity
Zhang, Yi; Wu, Yulong; Yan, Jianguo; Wang, Haoran; Rodriguez, J. Alexis P.; Qiu, Yue
2018-04-01
In this paper, we propose an inverse method for full gravity gradient tensor data in the spherical coordinate system. As opposed to the traditional gravity inversion in the Cartesian coordinate system, our proposed method takes the curvature of the Earth, the Moon, or other planets into account, using tesseroid bodies to produce gravity gradient effects in forward modeling. We used both synthetic and observed datasets to test the stability and validity of the proposed method. Our results using synthetic gravity data show that our new method predicts the depth of the density anomalous body efficiently and accurately. Using observed gravity data for the Mare Smythii area on the moon, the density distribution of the crust in this area reveals its geological structure. These results validate the proposed method and potential application for large area data inversion of planetary geological structures.[Figure not available: see fulltext.
International Nuclear Information System (INIS)
Nomura, Kenji; Ohta, Hiromichi; Hirano, Masahiro; Kamiya, Toshio; Uruga, Tomoya; Hosono, Hideo
2007-01-01
Ionic amorphous oxide semiconductors (IAOSs) are new materials for flexible thin film transistors that exhibit field-effect mobilities of ∼10 cm 2 V -1 s -1 [K. Nomura et al., Nature 488, 432 (2004)]. The local coordination structure in an IAOS, In-Ga-Zn-O (a-IGZO), was examined using extended x-ray absorption fine structure analysis combined with ab initio calculations. The short-range ordering and coordination structures in a-IGZO are similar to those in the corresponding crystalline phase, InGaZnO 4 , and edge-sharing structures consisting of In-O polyhedra remain in the amorphous structure. The In 3+ 5s orbitals form an extended state with a band effective mass of ∼0.2m e at the conduction band bottom
Berger, Marcel
2010-01-01
Both classical geometry and modern differential geometry have been active subjects of research throughout the 20th century and lie at the heart of many recent advances in mathematics and physics. The underlying motivating concept for the present book is that it offers readers the elements of a modern geometric culture by means of a whole series of visually appealing unsolved (or recently solved) problems that require the creation of concepts and tools of varying abstraction. Starting with such natural, classical objects as lines, planes, circles, spheres, polygons, polyhedra, curves, surfaces,
Connes, Alain
1994-01-01
This English version of the path-breaking French book on this subject gives the definitive treatment of the revolutionary approach to measure theory, geometry, and mathematical physics developed by Alain Connes. Profusely illustrated and invitingly written, this book is ideal for anyone who wants to know what noncommutative geometry is, what it can do, or how it can be used in various areas of mathematics, quantization, and elementary particles and fields.Key Features* First full treatment of the subject and its applications* Written by the pioneer of this field* Broad applications in mathemat
International Nuclear Information System (INIS)
Soufi, M; Arimura, H; Toyofuku, F; Nakamura, K; Hirose, T; Umezu, Y; Shioyama, Y
2016-01-01
Purpose: To propose a computerized framework for localization of anatomical feature points on the patient surface in infrared-ray based range images by using differential geometry (curvature) features. Methods: The general concept was to reconstruct the patient surface by using a mathematical modeling technique for the computation of differential geometry features that characterize the local shapes of the patient surfaces. A region of interest (ROI) was firstly extracted based on a template matching technique applied on amplitude (grayscale) images. The extracted ROI was preprocessed for reducing temporal and spatial noises by using Kalman and bilateral filters, respectively. Next, a smooth patient surface was reconstructed by using a non-uniform rational basis spline (NURBS) model. Finally, differential geometry features, i.e. the shape index and curvedness features were computed for localizing the anatomical feature points. The proposed framework was trained for optimizing shape index and curvedness thresholds and tested on range images of an anthropomorphic head phantom. The range images were acquired by an infrared ray-based time-of-flight (TOF) camera. The localization accuracy was evaluated by measuring the mean of minimum Euclidean distances (MMED) between reference (ground truth) points and the feature points localized by the proposed framework. The evaluation was performed for points localized on convex regions (e.g. apex of nose) and concave regions (e.g. nasofacial sulcus). Results: The proposed framework has localized anatomical feature points on convex and concave anatomical landmarks with MMEDs of 1.91±0.50 mm and 3.70±0.92 mm, respectively. A statistically significant difference was obtained between the feature points on the convex and concave regions (P<0.001). Conclusion: Our study has shown the feasibility of differential geometry features for localization of anatomical feature points on the patient surface in range images. The proposed
Energy Technology Data Exchange (ETDEWEB)
Soufi, M; Arimura, H; Toyofuku, F [Kyushu University, Fukuoka, Fukuoka (Japan); Nakamura, K [Hamamatsu University School of Medicine, Hamamatsu, Shizuoka (Japan); Hirose, T; Umezu, Y [Kyushu University Hospital, Fukuoka, Fukuoka (Japan); Shioyama, Y [Saga Heavy Ion Medical Accelerator in Tosu, Tosu, Saga (Japan)
2016-06-15
Purpose: To propose a computerized framework for localization of anatomical feature points on the patient surface in infrared-ray based range images by using differential geometry (curvature) features. Methods: The general concept was to reconstruct the patient surface by using a mathematical modeling technique for the computation of differential geometry features that characterize the local shapes of the patient surfaces. A region of interest (ROI) was firstly extracted based on a template matching technique applied on amplitude (grayscale) images. The extracted ROI was preprocessed for reducing temporal and spatial noises by using Kalman and bilateral filters, respectively. Next, a smooth patient surface was reconstructed by using a non-uniform rational basis spline (NURBS) model. Finally, differential geometry features, i.e. the shape index and curvedness features were computed for localizing the anatomical feature points. The proposed framework was trained for optimizing shape index and curvedness thresholds and tested on range images of an anthropomorphic head phantom. The range images were acquired by an infrared ray-based time-of-flight (TOF) camera. The localization accuracy was evaluated by measuring the mean of minimum Euclidean distances (MMED) between reference (ground truth) points and the feature points localized by the proposed framework. The evaluation was performed for points localized on convex regions (e.g. apex of nose) and concave regions (e.g. nasofacial sulcus). Results: The proposed framework has localized anatomical feature points on convex and concave anatomical landmarks with MMEDs of 1.91±0.50 mm and 3.70±0.92 mm, respectively. A statistically significant difference was obtained between the feature points on the convex and concave regions (P<0.001). Conclusion: Our study has shown the feasibility of differential geometry features for localization of anatomical feature points on the patient surface in range images. The proposed
Indian Academy of Sciences (India)
mathematicians are trained to use very precise language, and so find it hard to simplify and state .... thing. If you take a plane on which there are two such triangles which enjoy the above ... within this geometry to simplify things if needed.
Geometry -----------~--------------RESONANCE
Indian Academy of Sciences (India)
Parallel: A pair of lines in a plane is said to be parallel if they do not meet. Mathematicians were at war ... Subsequently, Poincare, Klein, Beltrami and others refined non-. Euclidean geometry. ... plane divides the plane into two half planes and.
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
Differential geometry of curves and surfaces
Banchoff, Thomas F
2010-01-01
Students and professors of an undergraduate course in differential geometry will appreciate the clear exposition and comprehensive exercises in this book that focuses on the geometric properties of curves and surfaces, one- and two-dimensional objects in Euclidean space. The problems generally relate to questions of local properties (the properties observed at a point on the curve or surface) or global properties (the properties of the object as a whole). Some of the more interesting theorems explore relationships between local and global properties. A special feature is the availability of accompanying online interactive java applets coordinated with each section. The applets allow students to investigate and manipulate curves and surfaces to develop intuition and to help analyze geometric phenomena.
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 ...
Functional integration over geometries
International Nuclear Information System (INIS)
Mottola, E.
1995-01-01
The geometric construction of the functional integral over coset spaces M/G is reviewed. The inner product on the cotangent space of infinitesimal deformations of M defines an invariant distance and volume form, or functional integration measure on the full configuration space. Then, by a simple change of coordinates parameterizing the gauge fiber G, the functional measure on the coset space M/G is deduced. This change of integration variables leads to a Jacobian which is entirely equivalent to the Faddeev--Popov determinant of the more traditional gauge fixed approach in non-abelian gauge theory. If the general construction is applied to the case where G is the group of coordinate reparameterizations of spacetime, the continuum functional integral over geometries, i.e. metrics modulo coordinate reparameterizations may be defined. The invariant functional integration measure is used to derive the trace anomaly and effective action for the conformal part of the metric in two and four dimensional spacetime. In two dimensions this approach generates the Polyakov--Liouville action of closed bosonic non-critical string theory. In four dimensions the corresponding effective action leads to novel conclusions on the importance of quantum effects in gravity in the far infrared, and in particular, a dramatic modification of the classical Einstein theory at cosmological distance scales, signaled first by the quantum instability of classical de Sitter spacetime. Finite volume scaling relations for the functional integral of quantum gravity in two and four dimensions are derived, and comparison with the discretized dynamical triangulation approach to the integration over geometries are discussed. Outstanding unsolved problems in both the continuum definition and the simplicial approach to the functional integral over geometries are highlighted
General Geometry and Geometry of Electromagnetism
Shahverdiyev, Shervgi S.
2002-01-01
It is shown that Electromagnetism creates geometry different from Riemannian geometry. General geometry including Riemannian geometry as a special case is constructed. It is proven that the most simplest special case of General Geometry is geometry underlying Electromagnetism. Action for electromagnetic field and Maxwell equations are derived from curvature function of geometry underlying Electromagnetism. And it is shown that equation of motion for a particle interacting with electromagnetic...
Hughes, H Velocity; Lisher, John P; Hardy, Gail G; Kysela, David T; Arnold, Randy J; Giedroc, David P; Brun, Yves V
2013-12-01
Organelles with specialized form and function occur in diverse bacteria. Within the Alphaproteobacteria, several species extrude thin cellular appendages known as stalks, which function in nutrient uptake, buoyancy and reproduction. Consistent with their specialization, stalks maintain a unique molecular composition compared with the cell body, but how this is achieved remains to be fully elucidated. Here we dissect the mechanism of localization of StpX, a stalk-specific protein in Caulobacter crescentus. Using a forward genetics approach, we identify a penicillin-binding-protein, PbpC, which is required for the localization of StpX in the stalk. We show that PbpC acts at the stalked cell pole to anchor StpX to rigid components of the outer membrane of the elongating stalk, concurrent with stalk synthesis. Stalk-localized StpX in turn functions in cellular responses to copper and zinc, suggesting that the stalk may contribute to metal homeostasis in Caulobacter. Together, these results identify a novel role for a penicillin-binding-protein in compartmentalizing a bacterial organelle it itself helps create, raising the possibility that cell wall-synthetic enzymes may broadly serve not only to synthesize the diverse shapes of bacteria, but also to functionalize them at the molecular level. © 2013 John Wiley & Sons Ltd.
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
Shi, Yiquan; Wolfensteller, Uta; Schubert, Torsten; Ruge, Hannes
2018-02-01
Cognitive flexibility is essential to cope with changing task demands and often it is necessary to adapt to combined changes in a coordinated manner. The present fMRI study examined how the brain implements such multi-level adaptation processes. Specifically, on a "local," hierarchically lower level, switching between two tasks was required across trials while the rules of each task remained unchanged for blocks of trials. On a "global" level regarding blocks of twelve trials, the task rules could reverse or remain the same. The current task was cued at the start of each trial while the current task rules were instructed before the start of a new block. We found that partly overlapping and partly segregated neural networks play different roles when coping with the combination of global rule reversal and local task switching. The fronto-parietal control network (FPN) supported the encoding of reversed rules at the time of explicit rule instruction. The same regions subsequently supported local task switching processes during actual implementation trials, irrespective of rule reversal condition. By contrast, a cortico-striatal network (CSN) including supplementary motor area and putamen was increasingly engaged across implementation trials and more so for rule reversal than for nonreversal blocks, irrespective of task switching condition. Together, these findings suggest that the brain accomplishes the coordinated adaptation to multi-level demand changes by distributing processing resources either across time (FPN for reversed rule encoding and later for task switching) or across regions (CSN for reversed rule implementation and FPN for concurrent task switching). © 2017 Wiley Periodicals, Inc.
Ben-Shimon, Lilach; Paul, Viktoria D; David-Kadoch, Galit; Volpe, Marina; Stümpfig, Martin; Bill, Eckhard; Mühlenhoff, Ulrich; Lill, Roland; Ben-Aroya, Shay
2018-05-30
Fe-S clusters act as co-factors of proteins with diverse functions, e.g. in DNA repair. Down-regulation of the cytosolic iron-sulfur protein assembly (CIA) machinery promotes genomic instability by the inactivation of multiple DNA repair pathways. Furthermore, CIA deficiencies are associated with so far unexplained mitotic defects. Here, we show that CIA2B and MMS19, constituents of the CIA targeting complex involved in facilitating Fe-S cluster insertion into cytosolic and nuclear target proteins, co-localize with components of the mitotic machinery. Down-regulation of CIA2B and MMS19 impairs the mitotic cycle. We identify the chromokinesin KIF4A as a mitotic component involved in these effects. KIF4A binds a Fe-S cluster in vitro through its conserved cysteine-rich domain. We demonstrate in vivo that this domain is required for the mitosis-related KIF4A localization and for the mitotic defects associated with KIF4A knockout. KIF4A is the first identified mitotic component carrying such a post-translational modification. These findings suggest that the lack of Fe-S clusters in KIF4A upon down-regulation of the CIA targeting complex contributes to the mitotic defects. © 2018. Published by The Company of Biologists Ltd.
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.
Borgia, Alessandro; Wensley, Beth G.; Soranno, Andrea; Nettels, Daniel; Borgia, Madeleine B.; Hoffmann, Armin; Pfeil, Shawn H.; Lipman, Everett A.; Clarke, Jane; Schuler, Benjamin
2012-01-01
Theory, simulations and experimental results have suggested an important role of internal friction in the kinetics of protein folding. Recent experiments on spectrin domains provided the first evidence for a pronounced contribution of internal friction in proteins that fold on the millisecond timescale. However, it has remained unclear how this contribution is distributed along the reaction and what influence it has on the folding dynamics. Here we use a combination of single-molecule Förster resonance energy transfer, nanosecond fluorescence correlation spectroscopy, microfluidic mixing and denaturant- and viscosity-dependent protein-folding kinetics to probe internal friction in the unfolded state and at the early and late transition states of slow- and fast-folding spectrin domains. We find that the internal friction affecting the folding rates of spectrin domains is highly localized to the early transition state, suggesting an important role of rather specific interactions in the rate-limiting conformational changes. PMID:23149740
Energy Technology Data Exchange (ETDEWEB)
Bo, Maolin; Huang, Yongli; Zhang, Ting [Key Laboratory of Low-Dimensional Materials and Application Technologies, Xiangtan University, Hunan 411105 (China); Wang, Yan, E-mail: ywang8@hnust.edu.cn, E-mail: ecqsun@ntu.edu.sg [Key Laboratory of Low-Dimensional Materials and Application Technologies, Xiangtan University, Hunan 411105 (China); School of Information and Electronic Engineering, Hunan University of Science and Technology, Hunan 411201 (China); Zhang, Xi [School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798 (Singapore); Li, Can [Center for Coordination Bond Engineering, School of Materials Science and Engineering, China Jiliang University, Hangzhou 330018 (China); Sun, Chang Q., E-mail: ywang8@hnust.edu.cn, E-mail: ecqsun@ntu.edu.sg [Key Laboratory of Low-Dimensional Materials and Application Technologies, Xiangtan University, Hunan 411105 (China); School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798 (Singapore); Center for Coordination Bond Engineering, School of Materials Science and Engineering, China Jiliang University, Hangzhou 330018 (China)
2014-04-14
Consistency between x-ray photoelectron spectroscopy measurements and density-function theory calculations confirms our bond order-length-strength notation-incorporated tight-binding theory predictions on the quantum entrapment of Si solid skin and atomic clusters. It has been revealed that bond-order deficiency shortens and strengthens the Si-Si bond, which results in the local densification and quantum entrapment of the core and valence electrons. Unifying Si clusters and Si(001) and (111) skins, this mechanism has led to quantification of the 2p binding energy of 96.089 eV for an isolated Si atom, and their bulk shifts of 2.461 eV. Findings evidence the significance of atomic undercoordination that is of great importance to device performance.
Novel 3D Compression Methods for Geometry, Connectivity and Texture
Siddeq, M. M.; Rodrigues, M. A.
2016-06-01
A large number of applications in medical visualization, games, engineering design, entertainment, heritage, e-commerce and so on require the transmission of 3D models over the Internet or over local networks. 3D data compression is an important requirement for fast data storage, access and transmission within bandwidth limitations. The Wavefront OBJ (object) file format is commonly used to share models due to its clear simple design. Normally each OBJ file contains a large amount of data (e.g. vertices and triangulated faces, normals, texture coordinates and other parameters) describing the mesh surface. In this paper we introduce a new method to compress geometry, connectivity and texture coordinates by a novel Geometry Minimization Algorithm (GM-Algorithm) in connection with arithmetic coding. First, each vertex ( x, y, z) coordinates are encoded to a single value by the GM-Algorithm. Second, triangle faces are encoded by computing the differences between two adjacent vertex locations, which are compressed by arithmetic coding together with texture coordinates. We demonstrate the method on large data sets achieving compression ratios between 87 and 99 % without reduction in the number of reconstructed vertices and triangle faces. The decompression step is based on a Parallel Fast Matching Search Algorithm (Parallel-FMS) to recover the structure of the 3D mesh. A comparative analysis of compression ratios is provided with a number of commonly used 3D file formats such as VRML, OpenCTM and STL highlighting the performance and effectiveness of the proposed method.
Modern differential geometry for physicists
Isham, C J
1989-01-01
These notes are the content of an introductory course on modern, coordinate-free differential geometry which is taken by the first-year theoretical physics PhD students, or by students attending the one-year MSc course "Fundamental Fields and Forces" at Imperial College. The book is concerned entirely with mathematics proper, although the emphasis and detailed topics have been chosen with an eye to the way in which differential geometry is applied these days to modern theoretical physics. This includes not only the traditional area of general relativity but also the theory of Yang-Mills fields
Tropical geometry of statistical models.
Pachter, Lior; Sturmfels, Bernd
2004-11-16
This article presents a unified mathematical framework for inference in graphical models, building on the observation that graphical models are algebraic varieties. From this geometric viewpoint, observations generated from a model are coordinates of a point in the variety, and the sum-product algorithm is an efficient tool for evaluating specific coordinates. Here, we address the question of how the solutions to various inference problems depend on the model parameters. The proposed answer is expressed in terms of tropical algebraic geometry. The Newton polytope of a statistical model plays a key role. Our results are applied to the hidden Markov model and the general Markov model on a binary tree.
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
Optimization of strong and weak coordinates
Swart, M.; Bickelhaupt, F.M.
2006-01-01
We present a new scheme for the geometry optimization of equilibrium and transition state structures that can be used for both strong and weak coordinates. We use a screening function that depends on atom-pair distances to differentiate strong coordinates from weak coordinates. This differentiation
Amin, Elizabeth A; Truhlar, Donald G
2008-01-01
We present nonrelativistic and relativistic benchmark databases (obtained by coupled cluster calculations) of 10 Zn-ligand bond distances, 8 dipole moments, and 12 bond dissociation energies in Zn coordination compounds with O, S, NH3, H2O, OH, SCH3, and H ligands. These are used to test the predictions of 39 density functionals, Hartree-Fock theory, and seven more approximate molecular orbital theories. In the nonrelativisitic case, the M05-2X, B97-2, and mPW1PW functionals emerge as the most accurate ones for this test data, with unitless balanced mean unsigned errors (BMUEs) of 0.33, 0.38, and 0.43, respectively. The best local functionals (i.e., functionals with no Hartree-Fock exchange) are M06-L and τ-HCTH with BMUEs of 0.54 and 0.60, respectively. The popular B3LYP functional has a BMUE of 0.51, only slightly better than the value of 0.54 for the best local functional, which is less expensive. Hartree-Fock theory itself has a BMUE of 1.22. The M05-2X functional has a mean unsigned error of 0.008 Å for bond lengths, 0.19 D for dipole moments, and 4.30 kcal/mol for bond energies. The X3LYP functional has a smaller mean unsigned error (0.007 Å) for bond lengths but has mean unsigned errors of 0.43 D for dipole moments and 5.6 kcal/mol for bond energies. The M06-2X functional has a smaller mean unsigned error (3.3 kcal/mol) for bond energies but has mean unsigned errors of 0.017 Å for bond lengths and 0.37 D for dipole moments. The best of the semiempirical molecular orbital theories are PM3 and PM6, with BMUEs of 1.96 and 2.02, respectively. The ten most accurate functionals from the nonrelativistic benchmark analysis are then tested in relativistic calculations against new benchmarks obtained with coupled-cluster calculations and a relativistic effective core potential, resulting in M05-2X (BMUE = 0.895), PW6B95 (BMUE = 0.90), and B97-2 (BMUE = 0.93) as the top three functionals. We find significant relativistic effects (∼0.01 Å in bond lengths, ∼0
Czech Academy of Sciences Publication Activity Database
Klíma, Jiří; Frias-Ferrer, A.; González-Garcia, J.; Ludvík, Jiří; Sáez, V.; Iniesta, J.
2007-01-01
Roč. 14, č. 1 (2007), s. 19-28 ISSN 1350-4177 R&D Projects: GA MŠk(CZ) OC D32.001; GA MŠk 1P05OC074; GA AV ČR IAA4040304 Grant - others:Generalidad Valenciana(ES) GV05/104 Institutional research plan: CEZ:AV0Z40400503 Keywords : ultrasound * intensity distribution * cell geometry optimisation * wave equation Subject RIV: CG - Electrochemistry Impact factor: 2.434, year: 2007
Distance Adaptive Tensor Discriminative Geometry Preserving Projection for Face Recognition
Directory of Open Access Journals (Sweden)
Ziqiang Wang
2012-09-01
Full Text Available There is a growing interest in dimensionality reduction techniques for face recognition, however, the traditional dimensionality reduction algorithms often transform the input face image data into vectors before embedding. Such vectorization often ignores the underlying data structure and leads to higher computational complexity. To effectively cope with these problems, a novel dimensionality reduction algorithm termed distance adaptive tensor discriminative geometry preserving projection (DATDGPP is proposed in this paper. The key idea of DATDGPP is as follows: first, the face image data are directly encoded in high-order tensor structure so that the relationships among the face image data can be preserved; second, the data-adaptive tensor distance is adopted to model the correlation among different coordinates of tensor data; third, the transformation matrix which can preserve discrimination and local geometry information is obtained by an iteration algorithm. Experimental results on three face databases show that the proposed algorithm outperforms other representative dimensionality reduction algorithms.
On the formalism of local variational differential operators
Igonin, S.; Verbovetsky, A.V.; Vitolo, R.
2002-01-01
The calculus of local variational differential operators introduced by B. L. Voronov, I. V. Tyutin, and Sh. S. Shakhverdiev is studied in the context of jet super space geometry. In a coordinate-free way, we relate these operators to variational multivectors, for which we introduce and compute the
Carlton, Erik L; Singh, Simone Rauscher
2018-05-01
To examine the association between hospital-local health department (LHD) collaboration around community health needs assessments (CHNAs) and hospital investment in community health. We combined 2015 National Association of County and City Health Officials (NACCHO) Forces of Change, 2013 NACCHO Profile, and 2014-2015 Area Health Resource File data to identify a sample of LHDs (n = 439) across the United States. We included data on hospitals' community benefit from their 2014 tax filings (Internal Revenue Service Form 990, Schedule H). We used bivariate and multivariate regression analyses to examine LHDs' involvement in hospitals' CHNAs and implementation strategies and the relationship with hospital investment in community health. The LHDs that collaborated with hospitals around CHNAs were significantly more likely to be involved in joint implementation planning activities than were those that did not. Importantly, LHD involvement in hospitals' implementation strategies was associated with greater hospital investment in community health improvement initiatives. Joint CHNAs may improve coordination of community-wide health improvement efforts between hospitals and LHDs and encourage hospital investment in community health improvement activities. Public Health Implications. Policies that strengthen LHD-hospital collaboration around the CHNA may enhance hospital investments in community health.
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.
International Nuclear Information System (INIS)
Gurevich, L.Eh.; Gliner, Eh.B.
1978-01-01
Problems of investigating the Universe space-time geometry are described on a popular level. Immediate space-time geometries, corresponding to three cosmologic models are considered. Space-time geometry of a closed model is the spherical Riemann geonetry, of an open model - is the Lobachevskij geometry; and of a plane model - is the Euclidean geometry. The Universe real geometry in the contemporary epoch of development is based on the data testifying to the fact that the Universe is infinitely expanding
Directory of Open Access Journals (Sweden)
Abílio Amiguinho
2005-01-01
Full Text Available The process of socio-educational territorialisation in rural contexts is the topic of this text. The theme corresponds to a challenge to address it having as main axis of discussion either the problem of social exclusion or that of local development. The reasons to locate the discussion in this last field of analysis are discussed in the first part of the text. Theoretical and political reasons are there articulated because the question is about projects whose intentions and practices call for the political both in the theoretical debate and in the choices that anticipate intervention. From research conducted for several years, I use contributions that aim at discuss and enlighten how school can be a potential locus of local development. Its identification and recognition as local institution (either because of those that work and live in it or because of those that act in the surrounding context are crucial steps to progressively constitute school as a partner for development. The promotion of the local values and roots, the reconstruction of socio-personal and local identities, the production of sociabilities and the equation and solution of shared problems were the dimensions of a socio-educative intervention, markedly globalising. This scenario, as it is argued, was also, intentionally, one of transformation and of deliberate change of school and of the administration of the educative territoires.
Luminescent lanthanide coordination polymers
Energy Technology Data Exchange (ETDEWEB)
Ma, L.; Evans, O.R.; Foxman, B.M.; Lin, W.
1999-12-13
One-dimensional lanthanide coordination polymers with the formula Ln(isonicotinate){sub 3}(H{sub 2}O){sub 2} (Ln = Ce, Pr, Nd, Sm, Eu, Tb; 1a-f) were synthesized by treating nitrate or perchlorate salts of Ln(III) with 4-pyridinecarboxaldehyde under hydro(solvo)thermal conditions. Single-crystal and powder X-ray diffraction studies indicate that these lanthanide coordination polymers adopt two different structures. While Ce(III), Pr(III), and Nd(III) complexes adopt a chain structure with alternating Ln-(carboxylate){sub 2}-Ln and Ln-(carboxylate){sub 4}-Ln linkages, Sm(III), Eu(III), and Tb(III) complexes have a doubly carboxylate-bridged infinite-chain structure with one chelating carboxylate group on each metal center. In both structures, the lanthanide centers also bind to two water molecules to yield an eight-coordinate, square antiprismatic geometry. The pyridine nitrogen atoms of the isonicotinate groups do not coordinate to the metal centers in these lanthanide(III) complexes; instead, they direct the formation of Ln(III) coordination polymers via hydrogen bonding with coordinated water molecules. Photoluminescence measurements show that Tb(isonicotinate){sub 3}(H{sub 2}O){sub 2} is highly emissive at room temperature with a quantum yield of {approximately}90%. These results indicate that highly luminescent lanthanide coordination polymers can be assembled using a combination of coordination and hydrogen bonds. Crystal data for 1a: monoclinic space group P2{sub 1}/c, a = 9.712(2) {angstrom}, b = 19.833(4) {angstrom}, c = 11.616(2) {angstrom}, {beta} = 111.89(3){degree}, Z = 4. Crystal data for 1f: monoclinic space group C2/c, a = 20.253(4) {angstrom}, b = 11.584(2) {angstrom}, c = 9.839(2) {angstrom}, {beta} = 115.64(3){degree}, Z = 8.
Noncommutative geometry and twisted conformal symmetry
International Nuclear Information System (INIS)
Matlock, Peter
2005-01-01
The twist-deformed conformal algebra is constructed as a Hopf algebra with twisted coproduct. This allows for the definition of conformal symmetry in a noncommutative background geometry. The twisted coproduct is reviewed for the Poincare algebra and the construction is then extended to the full conformal algebra. The case of Moyal-type noncommutativity of the coordinates is considered. It is demonstrated that conformal invariance need not be viewed as incompatible with noncommutative geometry; the noncommutativity of the coordinates appears as a consequence of the twisting, as has been shown in the literature in the case of the twisted Poincare algebra
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
Tlig , Mohamed
2015-01-01
In this thesis, we focus on traffic coordination and optimization in road intersections, while accounting for intelligent autonomous vehicles. This thesis is organized in two parts. The first part focuses on the problem of sharing a one-lane road between two opposite flows of vehicles. The state of the art shows few studies addressing this issue. We propose two reactive coordination approaches that minimize vehicle delays and measure their performances statistically through simulations. The s...
Geometric Transformations in Engineering Geometry
Directory of Open Access Journals (Sweden)
I. F. Borovikov
2015-01-01
Full Text Available Recently, for business purposes, in view of current trends and world experience in training engineers, research and faculty staff there has been a need to transform traditional courses of descriptive geometry into the course of engineering geometry in which the geometrical transformations have to become its main section. On the basis of critical analysis the paper gives suggestions to improve a presentation technique of this section both in the classroom and in academic literature, extend an application scope of geometrical transformations to solve the position and metric tasks and simulation of surfaces, as well as to design complex engineering configurations, which meet a number of pre-specified conditions.The article offers to make a number of considerable amendments to the terms and definitions used in the existing courses of descriptive geometry. It draws some conclusions and makes the appropriate proposals on feasibility of coordination in teaching the movement transformation in the courses of analytical and descriptive geometry. This will provide interdisciplinary team teaching and allow students to be convinced that a combination of analytical and graphic ways to solve geometric tasks is useful and reasonable.The traditional sections of learning courses need to be added with a theory of projective and bi-rational transformations. In terms of application simplicity and convenience it is enough to consider the central transformations when solving the applied tasks. These transformations contain a beam of sub-invariant (low-invariant straight lines on which the invariant curve induces non-involution and involution projectivities. The expediency of nonlinear transformations application is shown in the article by a specific example of geometric modeling of the interfacing surface "spar-blade".Implementation of these suggestions will contribute to a real transformation of a traditional course of descriptive geometry to the engineering geometry
Li, Xian-Ying; Hu, Shi-Min
2013-02-01
Harmonic functions are the critical points of a Dirichlet energy functional, the linear projections of conformal maps. They play an important role in computer graphics, particularly for gradient-domain image processing and shape-preserving geometric computation. We propose Poisson coordinates, a novel transfinite interpolation scheme based on the Poisson integral formula, as a rapid way to estimate a harmonic function on a certain domain with desired boundary values. Poisson coordinates are an extension of the Mean Value coordinates (MVCs) which inherit their linear precision, smoothness, and kernel positivity. We give explicit formulas for Poisson coordinates in both continuous and 2D discrete forms. Superior to MVCs, Poisson coordinates are proved to be pseudoharmonic (i.e., they reproduce harmonic functions on n-dimensional balls). Our experimental results show that Poisson coordinates have lower Dirichlet energies than MVCs on a number of typical 2D domains (particularly convex domains). As well as presenting a formula, our approach provides useful insights for further studies on coordinates-based interpolation and fast estimation of harmonic functions.
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.)
Gauge symmetry, T-duality and doubled geometry
International Nuclear Information System (INIS)
Hull, C.M.
2007-11-01
String compactifications with T-duality twists are revisited and the gauge algebra of the dimensionally reduced theories calculated. These reductions can be viewed as string theory on T-fold backgrounds, and can be formulated in a 'doubled space' in which each circle is supplemented by a T-dual circle to construct a geometry which is a doubled torus bundle over a circle. We discuss a conjectured extension to include T-duality on the base circle, and propose the introduction of a dual base coordinate, to give a doubled space which is locally the group manifold of the gauge group. Special cases include those in which the doubled group is a Drinfel'd double. This gives a framework to discuss backgrounds that are not even locally geometric. (orig.)
Convection in Slab and Spheroidal Geometries
Porter, David H.; Woodward, Paul R.; Jacobs, Michael L.
2000-01-01
Three-dimensional numerical simulations of compressible turbulent thermally driven convection, in both slab and spheroidal geometries, are reviewed and analyzed in terms of velocity spectra and mixing-length theory. The same ideal gas model is used in both geometries, and resulting flows are compared. The piecewise-parabolic method (PPM), with either thermal conductivity or photospheric boundary conditions, is used to solve the fluid equations of motion. Fluid motions in both geometries exhibit a Kolmogorov-like k(sup -5/3) range in their velocity spectra. The longest wavelength modes are energetically dominant in both geometries, typically leading to one convection cell dominating the flow. In spheroidal geometry, a dipolar flow dominates the largest scale convective motions. Downflows are intensely turbulent and up drafts are relatively laminar in both geometries. In slab geometry, correlations between temperature and velocity fluctuations, which lead to the enthalpy flux, are fairly independent of depth. In spheroidal geometry this same correlation increases linearly with radius over the inner 70 percent by radius, in which the local pressure scale heights are a sizable fraction of the radius. The effects from the impenetrable boundary conditions in the slab geometry models are confused with the effects from non-local convection. In spheroidal geometry nonlocal effects, due to coherent plumes, are seen as far as several pressure scale heights from the lower boundary and are clearly distinguishable from boundary effects.
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.
Geometry, topology, and string theory
International Nuclear Information System (INIS)
Varadarajan, Uday
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
Energy Technology Data Exchange (ETDEWEB)
Miliordos, Evangelos; Aprà, Edoardo; Xantheas, Sotiris S.
2013-01-01
We report the first optimum geometries and harmonic vibrational frequencies for the ring pentamer and several water hexamer (prism, cage, cyclic and two book) at the CCSD(T)/aug-cc-pVDZ level of theory. All five hexamer isomer minima previously reported by MP2 are also minima on the CCSD(T) potential energy surface (PES). In addition, all CCSD(T) minimum energy structures for the n=2-6 cluster isomers are quite close to the ones previously obtained by MP2 on the respective PESs, as confirmed by a modified Procrustes analysis that quantifies the difference between any two cluster geometries. The CCSD(T) results confirm the cooperative effect of the homodromic ring networks (systematic contraction of the nearest-neighbor (nn) intermolecular separations with cluster size) previously reported by MP2, albeit with O-O distances shorter by ~0.02 Å, indicating that MP2 overcorrects this effect. The harmonic frequencies at the minimum geometries were obtained by the double differentiation of the CCSD(T) energy using an efficient scheme based on internal coordinates that reduces the number of required single point energy evaluations by ~15% when compared to the corresponding double differentiation using Cartesian coordinates. Negligible differences between MP2 and CCSD(T) are found for the librational modes, while uniform increases of ~15 and ~25 cm^{-1} are observed for the bending and “free” OH harmonic frequencies. The largest differences between MP2 and CCSD(T) are observed for the harmonic hydrogen bonded frequencies. The CCSD(T) red shifts from the monomer frequencies (Δω) are smaller than the MP2 ones, due to the fact that the former produces shorter elongations (ΔR) of the respective hydrogen bonded OH lengths from the monomer value with respect to the latter. Both the MP2 and CCSD(T) results for the hydrogen bonded frequencies were found to closely follow the relation - Δω = s · ΔR, with a rate of s = 20.3 cm^{-1} / 0.001 Å. The CCSD
International Nuclear Information System (INIS)
Huber, F.; Peppler, W.
1985-05-01
The consequences of local cooling disturbances in subassemblies of LMFBRs have been investigated out-of-pile at KfK. Flow and temperature distributions in the disturbed region as well as cooling under boiling conditions up to loss of cooling were investigated. Fission gas release was simulated by gas injection. A total of 16 different blockages in 20 test set-ups were used, four of them under sodium and the rest under water conditions. Mainly planar plates of different sizes and arrangements were used as blockages. In some of the experiments performed in water also porous blockages were investigated. The test sections consisted of electrically heated pin bundles with a thermal-hydraulic characteristic corresponding to that of an SNR 300 subassembly. With different parameter settings the single-phase tests in water furnished a multitude of test results on flow and temperature fields and on the behaviour of gas in the recirculation zone. In the experiments involving boiling two boiling patterns were observed: steady-state boiling and oscillating boiling. With increasing boiling intensity the boiling region grew to some extent, but it remained always confined to the blocked zone because of the relatively cold sodium flow around this zone. In the experiments simulating fission gas release it was found that under certain conditions gas accumulates in the reverse flow region behind a blockage and leads to loss of cooling. (orig./GL) [de
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...
Indian Academy of Sciences (India)
algebraic geometry but also in related fields like number theory. ... every vector bundle on the affine space is trivial. (equivalently ... les on a compact Riemann surface to unitary rep- ... tial geometry and topology and was generalised in.
International Nuclear Information System (INIS)
Sloane, Peter
2007-01-01
We adapt the spinorial geometry method introduced in [J. Gillard, U. Gran and G. Papadopoulos, 'The spinorial geometry of supersymmetric backgrounds,' Class. Quant. Grav. 22 (2005) 1033 [ (arXiv:hep-th/0410155)
Energy Technology Data Exchange (ETDEWEB)
Sloane, Peter [Department of Mathematics, King' s College, University of London, Strand, London WC2R 2LS (United Kingdom)
2007-09-15
We adapt the spinorial geometry method introduced in [J. Gillard, U. Gran and G. Papadopoulos, 'The spinorial geometry of supersymmetric backgrounds,' Class. Quant. Grav. 22 (2005) 1033 [ (arXiv:hep-th/0410155)
Hyperunified field theory and gravitational gauge-geometry duality
International Nuclear Information System (INIS)
Wu, Yue-Liang
2018-01-01
A hyperunified field theory is built in detail based on the postulates of gauge invariance and coordinate independence along with the conformal scaling symmetry. All elementary particles are merged into a single hyper-spinor field and all basic forces are unified into a fundamental interaction governed by the hyper-spin gauge symmetry SP(1, D h - 1). The dimension D h of hyper-spacetime is conjectured to have a physical origin in correlation with the hyper-spin charge of elementary particles. The hyper-gravifield fiber bundle structure of biframe hyper-spacetime appears naturally with the globally flat Minkowski hyper-spacetime as a base spacetime and the locally flat hyper-gravifield spacetime as a fiber that is viewed as a dynamically emerged hyper-spacetime characterized by a non-commutative geometry. The gravitational origin of gauge symmetry is revealed with the hyper-gravifield that plays an essential role as a Goldstone-like field. The gauge-gravity and gravity-geometry correspondences bring about the gravitational gauge-geometry duality. The basic properties of hyperunified field theory and the issue on the fundamental scale are analyzed within the framework of quantum field theory, which allows us to describe the laws of nature in deriving the gauge gravitational equation with the conserved current and the geometric gravitational equations of Einstein-like type and beyond. (orig.)
Hyperunified field theory and gravitational gauge-geometry duality
Energy Technology Data Exchange (ETDEWEB)
Wu, Yue-Liang [International Centre for Theoretical Physics Asia-Pacific (ICTP-AP), Beijing (China); Chinese Academy of Sciences, Institute of Theoretical Physics, Beijing (China); University of Chinese Academy of Sciences (UCAS), Beijing (China)
2018-01-15
A hyperunified field theory is built in detail based on the postulates of gauge invariance and coordinate independence along with the conformal scaling symmetry. All elementary particles are merged into a single hyper-spinor field and all basic forces are unified into a fundamental interaction governed by the hyper-spin gauge symmetry SP(1, D{sub h} - 1). The dimension D{sub h} of hyper-spacetime is conjectured to have a physical origin in correlation with the hyper-spin charge of elementary particles. The hyper-gravifield fiber bundle structure of biframe hyper-spacetime appears naturally with the globally flat Minkowski hyper-spacetime as a base spacetime and the locally flat hyper-gravifield spacetime as a fiber that is viewed as a dynamically emerged hyper-spacetime characterized by a non-commutative geometry. The gravitational origin of gauge symmetry is revealed with the hyper-gravifield that plays an essential role as a Goldstone-like field. The gauge-gravity and gravity-geometry correspondences bring about the gravitational gauge-geometry duality. The basic properties of hyperunified field theory and the issue on the fundamental scale are analyzed within the framework of quantum field theory, which allows us to describe the laws of nature in deriving the gauge gravitational equation with the conserved current and the geometric gravitational equations of Einstein-like type and beyond. (orig.)
Hyperunified field theory and gravitational gauge-geometry duality
Wu, Yue-Liang
2018-01-01
A hyperunified field theory is built in detail based on the postulates of gauge invariance and coordinate independence along with the conformal scaling symmetry. All elementary particles are merged into a single hyper-spinor field and all basic forces are unified into a fundamental interaction governed by the hyper-spin gauge symmetry SP(1, D_h-1). The dimension D_h of hyper-spacetime is conjectured to have a physical origin in correlation with the hyper-spin charge of elementary particles. The hyper-gravifield fiber bundle structure of biframe hyper-spacetime appears naturally with the globally flat Minkowski hyper-spacetime as a base spacetime and the locally flat hyper-gravifield spacetime as a fiber that is viewed as a dynamically emerged hyper-spacetime characterized by a non-commutative geometry. The gravitational origin of gauge symmetry is revealed with the hyper-gravifield that plays an essential role as a Goldstone-like field. The gauge-gravity and gravity-geometry correspondences bring about the gravitational gauge-geometry duality. The basic properties of hyperunified field theory and the issue on the fundamental scale are analyzed within the framework of quantum field theory, which allows us to describe the laws of nature in deriving the gauge gravitational equation with the conserved current and the geometric gravitational equations of Einstein-like type and beyond.
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.
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
Arithmetic noncommutative geometry
Marcolli, Matilde
2005-01-01
Arithmetic noncommutative geometry denotes the use of ideas and tools from the field of noncommutative geometry, to address questions and reinterpret in a new perspective results and constructions from number theory and arithmetic algebraic geometry. This general philosophy is applied to the geometry and arithmetic of modular curves and to the fibers at archimedean places of arithmetic surfaces and varieties. The main reason why noncommutative geometry can be expected to say something about topics of arithmetic interest lies in the fact that it provides the right framework in which the tools of geometry continue to make sense on spaces that are very singular and apparently very far from the world of algebraic varieties. This provides a way of refining the boundary structure of certain classes of spaces that arise in the context of arithmetic geometry, such as moduli spaces (of which modular curves are the simplest case) or arithmetic varieties (completed by suitable "fibers at infinity"), by adding boundaries...
Needle decompositions in Riemannian geometry
Klartag, Bo'az
2017-01-01
The localization technique from convex geometry is generalized to the setting of Riemannian manifolds whose Ricci curvature is bounded from below. In a nutshell, the author's method is based on the following observation: When the Ricci curvature is non-negative, log-concave measures are obtained when conditioning the Riemannian volume measure with respect to a geodesic foliation that is orthogonal to the level sets of a Lipschitz function. The Monge mass transfer problem plays an important role in the author's analysis.
Geometry Dependence of Stellarator Turbulence
International Nuclear Information System (INIS)
Mynick, H.E.; Xanthopoulos, P.; Boozer, A.H.
2009-01-01
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
Superbanana orbits in stellarator geometries
International Nuclear Information System (INIS)
Derr, J.A.; Shohet, J.L.
1979-04-01
The presence of superbanana orbit types localized to either the interior or the exterior of stellarators and torsatrons is numerically investigated for 3.5 MeV alpha particles. The absence of the interior superbanana in both geometries is found to be due to non-conservation of the action. Exterior superbananas are found in the stellarator only, as a consequence of the existence of closed helical magnetic wells. No superbananas of either type are found in the torsatron
Czech Academy of Sciences Publication Activity Database
Steiner, Jakub
-, č. 274 (2005), s. 1-26 ISSN 1211-3298 Institutional research plan: CEZ:AV0Z70850503 Keywords : coordination * crises * cycles and fluctuations Subject RIV: AH - Economics http://www.cerge-ei.cz/pdf/wp/Wp274.pdf
Czech Academy of Sciences Publication Activity Database
Steiner, Jakub
2008-01-01
Roč. 63, č. 1 (2008), s. 308-327 ISSN 0899-8256 Institutional research plan: CEZ:AV0Z70850503 Keywords : global games * coordination * crises * cycles and fluctuations Subject RIV: AH - Economics Impact factor: 1.333, year: 2008
Geometry of superspace and local supersymmetry
International Nuclear Information System (INIS)
Gates, S.J. Jr.
1978-01-01
We briefly review the theory of general relativity in superspace and show how the theory may be interpreted from the view of a superfiber bundle. It is shown that this superfiber, however, does not possess, as its structural group, the fourteen-parameter group of global supersymmetry, the super Poincare group. Starting from an ansatz which is suggested by superspace general relativity, a second superfiber bundle theory is constructed which does possess the super Poincare group as its structural group
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.
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 ...
Granular flows in constrained geometries
Murthy, Tejas; Viswanathan, Koushik
Confined geometries are widespread in granular processing applications. The deformation and flow fields in such a geometry, with non-trivial boundary conditions, determine the resultant mechanical properties of the material (local porosity, density, residual stresses etc.). We present experimental studies of deformation and plastic flow of a prototypical granular medium in different nontrivial geometries- flat-punch compression, Couette-shear flow and a rigid body sliding past a granular half-space. These geometries represent simplified scaled-down versions of common industrial configurations such as compaction and dredging. The corresponding granular flows show a rich variety of flow features, representing the entire gamut of material types, from elastic solids (beam buckling) to fluids (vortex-formation, boundary layers) and even plastically deforming metals (dead material zone, pile-up). The effect of changing particle-level properties (e.g., shape, size, density) on the observed flows is also explicitly demonstrated. Non-smooth contact dynamics particle simulations are shown to reproduce some of the observed flow features quantitatively. These results showcase some central challenges facing continuum-scale constitutive theories for dynamic granular flows.
Algorithms in Algebraic Geometry
Dickenstein, Alicia; Sommese, Andrew J
2008-01-01
In the last decade, there has been a burgeoning of activity in the design and implementation of algorithms for algebraic geometric computation. Some of these algorithms were originally designed for abstract algebraic geometry, but now are of interest for use in applications and some of these algorithms were originally designed for applications, but now are of interest for use in abstract algebraic geometry. The workshop on Algorithms in Algebraic Geometry that was held in the framework of the IMA Annual Program Year in Applications of Algebraic Geometry by the Institute for Mathematics and Its
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
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.
Energy Technology Data Exchange (ETDEWEB)
Anon.
1986-07-15
While physics Laboratories are having to absorb cuts in resources, the machines they rely on are becoming more and more complex, requiring increasingly sophisticated systems. Rather than being a resourceful engineer or physicist able to timber together solutions in his 'backyard', the modern controls specialist has become a professional in his own right. Because of possible conflicts between increasing sophistication on one hand and scarcer resources on the other, there was felt a need for more contacts among controls specialists to exchange experiences, coordinate development and discuss 'family problems', away from meetings where the main interest is on experimental physics.
DEFF Research Database (Denmark)
Timmermans, Bram; Zabala-Iturriagagoitia, Jon Mikel
2013-01-01
Public procurement for innovation is a matter of using public demand to trigger innovation. Empirical studies have demonstrated that demand-based policy instruments can be considered to be a powerful tool in stimulating innovative processes among existing firms; however, the existing literature has...... not focused on the role this policy instrument can play in the promotion of (knowledge-intensive) entrepreneurship. This paper investigates this link in more detail and introduces the concept of coordinated unbundling as a strategy that can facilitate this purpose. We also present a framework on how...
International Nuclear Information System (INIS)
Anon.
1986-01-01
While physics Laboratories are having to absorb cuts in resources, the machines they rely on are becoming more and more complex, requiring increasingly sophisticated systems. Rather than being a resourceful engineer or physicist able to timber together solutions in his 'backyard', the modern controls specialist has become a professional in his own right. Because of possible conflicts between increasing sophistication on one hand and scarcer resources on the other, there was felt a need for more contacts among controls specialists to exchange experiences, coordinate development and discuss 'family problems', away from meetings where the main interest is on experimental physics
Geometry of multihadron production
Energy Technology Data Exchange (ETDEWEB)
Bjorken, J.D.
1994-10-01
This summary talk only reviews a small sample of topics featured at this symposium: Introduction; The Geometry and Geography of Phase space; Space-Time Geometry and HBT; Multiplicities, Intermittency, Correlations; Disoriented Chiral Condensate; Deep Inelastic Scattering at HERA; and Other Contributions.
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.
Geometry of multihadron production
International Nuclear Information System (INIS)
Bjorken, J.D.
1994-10-01
This summary talk only reviews a small sample of topics featured at this symposium: Introduction; The Geometry and Geography of Phase space; Space-Time Geometry and HBT; Multiplicities, Intermittency, Correlations; Disoriented Chiral Condensate; Deep Inelastic Scattering at HERA; and Other Contributions
Morris, Barbara H.
2004-01-01
This article describes a geometry project that used the beauty of stained-glass-window designs to teach middle school students about geometric figures and concepts. Three honors prealgebra teachers and a middle school mathematics gifted intervention specialist created a geometry project that covered the curriculum and also assessed students'…
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.
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...
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.
Methods of information geometry
Amari, Shun-Ichi
2000-01-01
Information geometry provides the mathematical sciences with a new framework of analysis. It has emerged from the investigation of the natural differential geometric structure on manifolds of probability distributions, which consists of a Riemannian metric defined by the Fisher information and a one-parameter family of affine connections called the \\alpha-connections. The duality between the \\alpha-connection and the (-\\alpha)-connection together with the metric play an essential role in this geometry. This kind of duality, having emerged from manifolds of probability distributions, is ubiquitous, appearing in a variety of problems which might have no explicit relation to probability theory. Through the duality, it is possible to analyze various fundamental problems in a unified perspective. The first half of this book is devoted to a comprehensive introduction to the mathematical foundation of information geometry, including preliminaries from differential geometry, the geometry of manifolds or probability d...
International Nuclear Information System (INIS)
Grotz, Andreas
2011-01-01
In this thesis, a formulation of a Lorentzian quantum geometry based on the framework of causal fermion systems is proposed. After giving the general definition of causal fermion systems, we deduce space-time as a topological space with an underlying causal structure. Restricting attention to systems of spin dimension two, we derive the objects of our quantum geometry: the spin space, the tangent space endowed with a Lorentzian metric, connection and curvature. In order to get the correspondence to classical differential geometry, we construct examples of causal fermion systems by regularizing Dirac sea configurations in Minkowski space and on a globally hyperbolic Lorentzian manifold. When removing the regularization, the objects of our quantum geometry reduce to the common objects of spin geometry on Lorentzian manifolds, up to higher order curvature corrections.
2010-07-01
... 40 Protection of Environment 21 2010-07-01 2010-07-01 false Coordination. 109.6 Section 109.6 Protection of Environment ENVIRONMENTAL PROTECTION AGENCY (CONTINUED) WATER PROGRAMS CRITERIA FOR STATE, LOCAL AND REGIONAL OIL REMOVAL CONTINGENCY PLANS § 109.6 Coordination. For the purposes of coordination...
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...
Geometry on the space of geometries
International Nuclear Information System (INIS)
Christodoulakis, T.; Zanelli, J.
1988-06-01
We discuss the geometric structure of the configuration space of pure gravity. This is an infinite dimensional manifold, M, where each point represents one spatial geometry g ij (x). The metric on M is dictated by geometrodynamics, and from it, the Christoffel symbols and Riemann tensor can be found. A ''free geometry'' tracing a geodesic on the manifold describes the time evolution of space in the strong gravity limit. In a regularization previously introduced by the authors, it is found that M does not have the same dimensionality, D, everywhere, and that D is not a scalar, although it is covariantly constant. In this regularization, it is seen that the path integral measure can be absorbed in a renormalization of the cosmological constant. (author). 19 refs
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…
International Nuclear Information System (INIS)
Gervais, J.L.
1993-01-01
By analyzing the extrinsic geometry of two dimensional surfaces chirally embedded in C P n (the C P n W-surface), we give exact treatments in various aspects of the classical W-geometry in the conformal gauge: First, the basis of tangent and normal vectors are defined at regular points of the surface, such that their infinitesimal displacements are given by connections which coincide with the vector potentials of the (conformal) A n -Toda Lax pair. Since the latter is known to be intrinsically related with the W symmetries, this gives the geometrical meaning of the A n W-Algebra. Second, W-surfaces are put in one-to-one correspondence with solutions of the conformally-reduced WZNW model, which is such that the Toda fields give the Cartan part in the Gauss decomposition of its solutions. Third, the additional variables of the Toda hierarchy are used as coordinates of C P n . This allows us to show that W-transformations may be extended as particular diffeomorphisms of this target-space. Higher-dimensional generalizations of the WZNW equations are derived and related with the Zakharov-Shabat equations of the Toda hierarchy. Fourth, singular points are studied from a global viewpoint, using our earlier observation that W-surfaces may be regarded as instantons. The global indices of the W-geometry, which are written in terms of the Toda fields, are shown to be the instanton numbers for associated mappings of W-surfaces into the Grassmannians. The relation with the singularities of W-surface is derived by combining the Toda equations with the Gauss-Bonnet theorem. (orig.)
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...
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.
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
Geometry of physical dispersion relations
International Nuclear Information System (INIS)
Raetzel, Dennis; Rivera, Sergio; Schuller, Frederic P.
2011-01-01
To serve as a dispersion relation, a cotangent bundle function must satisfy three simple algebraic properties. These conditions are derived from the inescapable physical requirements that local matter field dynamics must be predictive and allow for an observer-independent notion of positive energy. Possible modifications of the standard relativistic dispersion relation are thereby severely restricted. For instance, the dispersion relations associated with popular deformations of Maxwell theory by Gambini-Pullin or Myers-Pospelov are not admissible. Dispersion relations passing the simple algebraic checks derived here correspond to physically admissible Finslerian refinements of Lorentzian geometry.
How Do Teachers Coordinate Their Work? A Framing Approach
Dumay, Xavier
2014-01-01
Since the 1970s, schools have been characterized as loosely coupled systems, meaning that the teachers' work is weakly coordinated at the local level. Nonetheless, few studies have focused on the local variations of coordination modes, their sources and their nature. In this article, the process of local coordination of the teachers' work is…
Directory of Open Access Journals (Sweden)
Bernard G. Hounmenou
2003-10-01
Full Text Available Les politiques de développement en cours dans plusieurs pays du sud, notamment dans ceux de l’Afrique sub-saharienne ont amorcé un nouveau tournant à partir de la fin des années 1980. A la faveur de l’instauration du climat de démocratie dans plusieurs de ces pays à partir de cette période, nombre d’entre eux ont procédé à de profondes réformes, donnant à la société civile et aux populations à la base, un droit de regard plus important dans la conduite des affaires les concernant. L’une des manifestations les plus importantes de ces réformes se traduit par la mise en œuvre de la décentralisation. Ce processus vise entre autres, la prise en compte des réalités locales et la responsabilisation des communautés à la base dans la gestion de leur développement. Il s’agit en d’autres termes, de favoriser le renforcement des capacités des populations locales, en vue de leur permettre de prendre en charge de façon durable, la gestion de leurs propres affaires dans le cadre de la gouvernance participative. Amorcé en janvier 1993, avec les états généraux de l’administration territoriale, le processus de la décentralisation au Bénin n’a connu sa phase de concrétisation qu’avec les élections et l’installation des élus locaux en début 2003. En prélude à l’avènement de la décentralisation, plusieurs localités béninoises font l’objet, depuis le milieu des années 1990, d’expériences d’appui au développement des communautés locales. C’est le cas notamment, des villages des départements de l’Atlantique et des Collines. A travers ces expériences, se mettent en place, divers dispositifs de gouvernance locale au sein des systèmes locaux d’action publique relatifs aux localités rurales. Il s’agit notamment, des comités villageois de suivi ou de gestion, des dispositifs de comités villageois de développement dans le département de l’Atlantique, et du dispositif des projets de
Roe, John
2003-01-01
Coarse geometry is the study of spaces (particularly metric spaces) from a 'large scale' point of view, so that two spaces that look the same from a great distance are actually equivalent. This point of view is effective because it is often true that the relevant geometric properties of metric spaces are determined by their coarse geometry. Two examples of important uses of coarse geometry are Gromov's beautiful notion of a hyperbolic group and Mostow's proof of his famous rigidity theorem. The first few chapters of the book provide a general perspective on coarse structures. Even when only metric coarse structures are in view, the abstract framework brings the same simplification as does the passage from epsilons and deltas to open sets when speaking of continuity. The middle section reviews notions of negative curvature and rigidity. Modern interest in large scale geometry derives in large part from Mostow's rigidity theorem and from Gromov's subsequent 'large scale' rendition of the crucial properties of n...
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.
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...
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.
Tabachnikov, Serge
2005-01-01
Mathematical billiards describe the motion of a mass point in a domain with elastic reflections off the boundary or, equivalently, the behavior of rays of light in a domain with ideally reflecting boundary. From the point of view of differential geometry, the billiard flow is the geodesic flow on a manifold with boundary. This book is devoted to billiards in their relation with differential geometry, classical mechanics, and geometrical optics. The topics covered include variational principles of billiard motion, symplectic geometry of rays of light and integral geometry, existence and nonexistence of caustics, optical properties of conics and quadrics and completely integrable billiards, periodic billiard trajectories, polygonal billiards, mechanisms of chaos in billiard dynamics, and the lesser-known subject of dual (or outer) billiards. The book is based on an advanced undergraduate topics course (but contains more material than can be realistically taught in one semester). Although the minimum prerequisit...
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...
Rudiments of algebraic geometry
Jenner, WE
2017-01-01
Aimed at advanced undergraduate students of mathematics, this concise text covers the basics of algebraic geometry. Topics include affine spaces, projective spaces, rational curves, algebraic sets with group structure, more. 1963 edition.
Implosions and hypertoric geometry
DEFF Research Database (Denmark)
Dancer, A.; Kirwan, F.; Swann, A.
2013-01-01
The geometry of the universal hyperkahler implosion for SU (n) is explored. In particular, we show that the universal hyperkahler implosion naturally contains a hypertoric variety described in terms of quivers. Furthermore, we discuss a gauge theoretic approach to hyperkahler implosion.......The geometry of the universal hyperkahler implosion for SU (n) is explored. In particular, we show that the universal hyperkahler implosion naturally contains a hypertoric variety described in terms of quivers. Furthermore, we discuss a gauge theoretic approach to hyperkahler implosion....
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
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.
International Nuclear Information System (INIS)
Osborne, I; Brownson, E; Eulisse, G; Jones, C D; Sexton-Kennedy, E; Lange, D J
2014-01-01
CMS faces real challenges with upgrade of the CMS detector through 2020 and beyond. One of the challenges, from the software point of view, is managing upgrade simulations with the same software release as the 2013 scenario. We present the CMS geometry description software model, its integration with the CMS event setup and core software. The CMS geometry configuration and selection is implemented in Python. The tools collect the Python configuration fragments into a script used in CMS workflow. This flexible and automated geometry configuration allows choosing either transient or persistent version of the same scenario and specific version of the same scenario. We describe how the geometries are integrated and validated, and how we define and handle different geometry scenarios in simulation and reconstruction. We discuss how to transparently manage multiple incompatible geometries in the same software release. Several examples are shown based on current implementation assuring consistent choice of scenario conditions. The consequences and implications for multiple/different code algorithms are discussed.
Software Geometry in Simulations
Alion, Tyler; Viren, Brett; Junk, Tom
2015-04-01
The Long Baseline Neutrino Experiment (LBNE) involves many detectors. The experiment's near detector (ND) facility, may ultimately involve several detectors. The far detector (FD) will be significantly larger than any other Liquid Argon (LAr) detector yet constructed; many prototype detectors are being constructed and studied to motivate a plethora of proposed FD designs. Whether it be a constructed prototype or a proposed ND/FD design, every design must be simulated and analyzed. This presents a considerable challenge to LBNE software experts; each detector geometry must be described to the simulation software in an efficient way which allows for multiple authors to easily collaborate. Furthermore, different geometry versions must be tracked throughout their use. We present a framework called General Geometry Description (GGD), written and developed by LBNE software collaborators for managing software to generate geometries. Though GGD is flexible enough to be used by any experiment working with detectors, we present it's first use in generating Geometry Description Markup Language (GDML) files to interface with LArSoft, a framework of detector simulations, event reconstruction, and data analyses written for all LAr technology users at Fermilab. Brett is the other of the framework discussed here, the General Geometry Description (GGD).
Introduction to combinatorial geometry
International Nuclear Information System (INIS)
Gabriel, T.A.; Emmett, M.B.
1985-01-01
The combinatorial geometry package as used in many three-dimensional multimedia Monte Carlo radiation transport codes, such as HETC, MORSE, and EGS, is becoming the preferred way to describe simple and complicated systems. Just about any system can be modeled using the package with relatively few input statements. This can be contrasted against the older style geometry packages in which the required input statements could be large even for relatively simple systems. However, with advancements come some difficulties. The users of combinatorial geometry must be able to visualize more, and, in some instances, all of the system at a time. Errors can be introduced into the modeling which, though slight, and at times hard to detect, can have devastating effects on the calculated results. As with all modeling packages, the best way to learn the combinatorial geometry is to use it, first on a simple system then on more complicated systems. The basic technique for the description of the geometry consists of defining the location and shape of the various zones in terms of the intersections and unions of geometric bodies. The geometric bodies which are generally included in most combinatorial geometry packages are: (1) box, (2) right parallelepiped, (3) sphere, (4) right circular cylinder, (5) right elliptic cylinder, (6) ellipsoid, (7) truncated right cone, (8) right angle wedge, and (9) arbitrary polyhedron. The data necessary to describe each of these bodies are given. As can be easily noted, there are some subsets included for simplicity
A geometry calibration method for rotation translation trajectory
International Nuclear Information System (INIS)
Zhang Jun; Yan Bin; Li Lei; Lu Lizhong; Zhang Feng
2013-01-01
In cone-beam CT imaging system, it is difficult to directly measure the geometry parameters. In this paper, a geometry calibration method for rotation translation trajectory is proposed. Intrinsic parameters are solved from the relationship built on geometry parameter of the system and projection trajectory of calibration object. Parameters of rotation axis are extrapolated from the unified intrinsic parameter, and geometry parameters of the idle trajectory are acquired too. The calibration geometry can be analytically determined using explicit formulae, it can avoid getting into local optimum in iterative way. Simulation experiments are carried out on misaligned geometry, experiment results indicate that geometry artifacts due to misaligned geometry are effectively depressed by the proposed method, and the image quality is enhanced. (authors)
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...
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...
Global aspects of complex geometry
Catanese, Fabrizio; Huckleberry, Alan T
2006-01-01
Present an overview of developments in Complex Geometry. This book covers topics that range from curve and surface theory through special varieties in higher dimensions, moduli theory, Kahler geometry, and group actions to Hodge theory and characteristic p-geometry.
Directory of Open Access Journals (Sweden)
H. J. Opgenoorth
Full Text Available On 14 January 2001, the four Cluster spacecraft passed through the northern magnetospheric mantle in close conjunction to the EISCAT Svalbard Radar (ESR and approached the post-noon dayside magnetopause over Green-land between 13:00 and 14:00 UT. During that interval, a sudden reorganisation of the high-latitude dayside convection pattern occurred after 13:20 UT, most likely caused by a direction change of the Solar wind magnetic field. The result was an eastward and poleward directed flow-channel, as monitored by the SuperDARN radar network and also by arrays of ground-based magnetometers in Canada, Greenland and Scandinavia. After an initial eastward and later poleward expansion of the flow-channel between 13:20 and 13:40 UT, the four Cluster spacecraft, and the field line footprints covered by the eastward looking scan cycle of the Söndre Strömfjord incoherent scatter radar were engulfed by cusp-like precipitation with transient magnetic and electric field signatures. In addition, the EISCAT Svalbard Radar detected strong transient effects of the convection reorganisation, a poleward moving precipitation, and a fast ion flow-channel in association with the auroral structures that suddenly formed to the west and north of the radar. From a detailed analysis of the coordinated Cluster and ground-based data, it was found that this extraordinary transient convection pattern, indeed, had moved the cusp precipitation from its former pre-noon position into the late post-noon sector, allowing for the first and quite unexpected encounter of the cusp by the Cluster spacecraft. Our findings illustrate the large amplitude of cusp dynamics even in response to moderate solar wind forcing. The global ground-based data proves to be an invaluable tool to monitor the dynamics and width of the affected magnetospheric regions.
Key words. Magnetospheric cusp, ionosphere, reconnection, convection flow-channel, Cluster, ground-based observations
Pratihar, Subha; Chandra, Amalendu
2008-07-14
The microsolvation structures and energetics of water-ammonia mixed clusters containing a lithium atom, i.e., Li(H(2)O)(n)(NH(3)), n = 1-5, are investigated by means of ab initio theoretical calculations. Several structural aspects such as the solvent coordination to the metal ion and binding motifs of the free valence electron of the metal are investigated. We also study the energetics aspects such as the dependence of vertical ionization energies on the cluster size, and all these structural and energetics aspects are compared to the corresponding results of previously studied anionic water-ammonia clusters without a metal ion. It is found that the Li-O and Li-N interactions play a very important role in stabilizing the lithium-water-ammonia clusters, and the presence of these metal ion-solvent interactions also affect the characteristics of electron solvation in these clusters. This is seen from the spatial distribution of the singly occupied molecular orbital (SOMO) which holds the ejected valence electron of the Li atom. For very small clusters, SOMO electron density is found to exist mainly at the vicinity of the Li atom, whereas for larger clusters, it is distributed outside the first solvation shell. The free dangling hydrogens of water and ammonia molecules are involved in capturing the SOMO electron density. In some of the conformers, OH{e}HO and OH{e}HN types of interactions are found to be present. The presence of the metal ion at the center of the cluster ensures that the ejected electron is solvated at a surface state only, whereas both surface and interiorlike states were found for the free electron in the corresponding anionic clusters without a metal ion. The vertical ionization energies of the present clusters are found to be higher than the vertical detachment energies of the corresponding anionic clusters which signify a relatively stronger binding of the free electron in the presence of the positive metal counterion. The shifts in different
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...
Coordinated School Health and the Contribution of a District Wellness Coordinator
Westrich, Lisa; Sanchez, Monika; Strobel, Karen
2015-01-01
Background: A San Francisco Bay Area school health initiative was established in fall 2010 to improve wellness programs in 4 local school districts using the Coordinated School Health (CSH) model. This study examines the role of district-wide wellness coordinators and the ways in which they contribute to intentional coordination of health and…
Computational synthetic geometry
Bokowski, Jürgen
1989-01-01
Computational synthetic geometry deals with methods for realizing abstract geometric objects in concrete vector spaces. This research monograph considers a large class of problems from convexity and discrete geometry including constructing convex polytopes from simplicial complexes, vector geometries from incidence structures and hyperplane arrangements from oriented matroids. It turns out that algorithms for these constructions exist if and only if arbitrary polynomial equations are decidable with respect to the underlying field. Besides such complexity theorems a variety of symbolic algorithms are discussed, and the methods are applied to obtain new mathematical results on convex polytopes, projective configurations and the combinatorics of Grassmann varieties. Finally algebraic varieties characterizing matroids and oriented matroids are introduced providing a new basis for applying computer algebra methods in this field. The necessary background knowledge is reviewed briefly. The text is accessible to stud...
Discrete and computational geometry
Devadoss, Satyan L
2011-01-01
Discrete geometry is a relatively new development in pure mathematics, while computational geometry is an emerging area in applications-driven computer science. Their intermingling has yielded exciting advances in recent years, yet what has been lacking until now is an undergraduate textbook that bridges the gap between the two. Discrete and Computational Geometry offers a comprehensive yet accessible introduction to this cutting-edge frontier of mathematics and computer science. This book covers traditional topics such as convex hulls, triangulations, and Voronoi diagrams, as well as more recent subjects like pseudotriangulations, curve reconstruction, and locked chains. It also touches on more advanced material, including Dehn invariants, associahedra, quasigeodesics, Morse theory, and the recent resolution of the Poincaré conjecture. Connections to real-world applications are made throughout, and algorithms are presented independently of any programming language. This richly illustrated textbook also fe...
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.
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...
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...
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
Directory of Open Access Journals (Sweden)
Luís D. Carlos
2001-08-01
Full Text Available Eu3+ luminescence and EXAFS (Extended X-ray Absorption Fine Structure results are presented for organic-inorganic hybrid gel hosts composed of a siliceous network to which small chains of oxyethylene units are covalently grafted by means of urea bridges. Coordination numbers for Eu3+ ions range from 12.8 to 9.7 with increasing Eu3+ concentration while the Eu3+-first neighbours mean distance is found to be constant at 2.48-2.49 Å in the same concentration range. Emission spectra display a broad band in the green/blue spectral region superposed to narrow lines appearing in the yellow/red region in such a way that for the eyes emission appears white. The broad band is assigned to intrinsic NH groups emission and also to electron-hole recombination in the nanosised siliceous domains. The narrow lines are assigned to intra-4f6, 5D0->7F0-4 Eu3+ transitions and from the energy position of the 7F0-4 levels a mean distance could be calculated for the Eu3+-first neighbours. The calculated results are in good agreement with the experimental ones obtained from EXAFS analysis.
On the geometry of fracture and frustration
Koning, Vinzenz
2014-01-01
Geometric frustration occurs when local order cannot propagate through space. A common example is the surface of a soccer ball, which cannot be tiled with hexaganons only. Geometric frustration can also be present in materials. In fact, geometry can act as an instrument to design the mechanical,
Arbitrariness of geometry and the aether
International Nuclear Information System (INIS)
Browne, P.F.
1976-01-01
As emphasized by Milne, an observer ultimately depends on the transmission and reception of light signals for the measurement of natural lengths and periods remote from his world point. The laws of geometry which are obeyed when these lengths and periods are plotted on a space--time depend, inevitably, on assumptions concerning the dependence of light velocity on the spatial and temporal coordinates. A convention regarding light velocity fixes the geometry, and conversely. However, the convention of flat space--time implies nonintegrable ''radar distances'' unless the concept of coordinate-dependent units of measure is employed. Einstein's space--time has the advantage of admitting a special reference system R with respect to which the aether fluid is at rest and the total gravitational field vanishes. A holonomic transformation from R to another reference system R belonging to the same space--time introduces a nonpermanent gravitational field and holonomic aether motion. A nonholonomic transformation from R to a reference system R* which belongs to a different space--time introduces a permanent gravitational field and nonholonomic aether motion. The arbitrariness of geometry is expressed by extending covariance to include the latter transformation. By means of a nonholonomic (or units) transformation it is possible, with the aid of the principle of equivalence, to obtain the Schwarzschild and de Sitter metrics from the Newtonian fields that would arise in a flat space--time description. Some light is thrown on the interpretation of cosmological models
Towards relativistic quantum geometry
Energy Technology Data Exchange (ETDEWEB)
Ridao, Luis Santiago [Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Mar del Plata (Argentina); Bellini, Mauricio, E-mail: mbellini@mdp.edu.ar [Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata, Funes 3350, C.P. 7600, Mar del Plata (Argentina); Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Mar del Plata (Argentina)
2015-12-17
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.
Multiplicity in difference geometry
Tomasic, Ivan
2011-01-01
We prove a first principle of preservation of multiplicity in difference geometry, paving the way for the development of a more general intersection theory. In particular, the fibres of a \\sigma-finite morphism between difference curves are all of the same size, when counted with correct multiplicities.
Spacetime and Euclidean geometry
Brill, Dieter; Jacobson, Ted
2006-04-01
Using only the principle of relativity and Euclidean geometry we show in this pedagogical article that the square of proper time or length in a two-dimensional spacetime diagram is proportional to the Euclidean area of the corresponding causal domain. We use this relation to derive the Minkowski line element by two geometric proofs of the spacetime Pythagoras theorem.
International Nuclear Information System (INIS)
Konopleva, N.P.
2009-01-01
The basic ideas of description methods of physical fields and elementary particle interactions are discussed. One of such ideas is the conception of space-time geometry. In this connection experimental measurement methods are analyzed. It is shown that measure procedures are the origin of geometrical axioms. The connection between space symmetry properties and the conservation laws is considered
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…
MacKeown, P. K.
1984-01-01
Clarifies two concepts of gravity--those of a fictitious force and those of how space and time may have geometry. Reviews the position of Newton's theory of gravity in the context of special relativity and considers why gravity (as distinct from electromagnetics) lends itself to Einstein's revolutionary interpretation. (JN)
DEFF Research Database (Denmark)
Booss-Bavnbek, Bernhelm
2011-01-01
This paper applies I.M. Gelfand's distinction between adequate and non-adequate use of mathematical language in different contexts to the newly opened window of model-based measurements of intracellular dynamics. The specifics of geometry and dynamics on the mesoscale of cell physiology are elabo...
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.
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.
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.
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.
International Nuclear Information System (INIS)
Ezin, J.P.
1988-08-01
The lectures given at the ''5th Symposium of Mathematics in Abidjan: Differential Geometry and Mechanics'' are presented. They are divided into four chapters: Riemannian metric on a differential manifold, curvature tensor fields on a Riemannian manifold, some classical functionals on Riemannian manifolds and questions. 11 refs
Motivic amplitudes and cluster coordinates
International Nuclear Information System (INIS)
Golden, J.K.; Goncharov, A.B.; Spradlin, M.; Vergu, C.; Volovich, A.
2014-01-01
In this paper we study motivic amplitudes — objects which contain all of the essential mathematical content of scattering amplitudes in planar SYM theory in a completely canonical way, free from the ambiguities inherent in any attempt to choose particular functional representatives. We find that the cluster structure on the kinematic configuration space Conf n (ℙ 3 ) underlies the structure of motivic amplitudes. Specifically, we compute explicitly the coproduct of the two-loop seven-particle MHV motivic amplitude A 7,2 M and find that like the previously known six-particle amplitude, it depends only on certain preferred coordinates known in the mathematics literature as cluster X-coordinates on Conf n (ℙ 3 ). We also find intriguing relations between motivic amplitudes and the geometry of generalized associahedrons, to which cluster coordinates have a natural combinatoric connection. For example, the obstruction to A 7,2 M being expressible in terms of classical polylogarithms is most naturally represented by certain quadrilateral faces of the appropriate associahedron. We also find and prove the first known functional equation for the trilogarithm in which all 40 arguments are cluster X-coordinates of a single algebra. In this respect it is similar to Abel’s 5-term dilogarithm identity
Geometry of isotropic convex bodies
Brazitikos, Silouanos; Valettas, Petros; Vritsiou, Beatrice-Helen
2014-01-01
The study of high-dimensional convex bodies from a geometric and analytic point of view, with an emphasis on the dependence of various parameters on the dimension stands at the intersection of classical convex geometry and the local theory of Banach spaces. It is also closely linked to many other fields, such as probability theory, partial differential equations, Riemannian geometry, harmonic analysis and combinatorics. It is now understood that the convexity assumption forces most of the volume of a high-dimensional convex body to be concentrated in some canonical way and the main question is whether, under some natural normalization, the answer to many fundamental questions should be independent of the dimension. The aim of this book is to introduce a number of well-known questions regarding the distribution of volume in high-dimensional convex bodies, which are exactly of this nature: among them are the slicing problem, the thin shell conjecture and the Kannan-Lov�sz-Simonovits conjecture. This book prov...
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.
Special Geometry and Automorphic Forms
Berglund, P; Wyllard, N; Berglund, Per; Henningson, Mans; Wyllard, Niclas
1997-01-01
We consider special geometry of the vector multiplet moduli space in compactifications of the heterotic string on $K3 \\times T^2$ or the type IIA string on $K3$-fibered Calabi-Yau threefolds. In particular, we construct a modified dilaton that is invariant under $SO(2, n; Z)$ T-duality transformations at the non-perturbative level and regular everywhere on the moduli space. The invariant dilaton, together with a set of other coordinates that transform covariantly under $SO(2, n; Z)$, parameterize the moduli space. The construction involves a meromorphic automorphic function of $SO(2, n; Z)$, that also depends on the invariant dilaton. In the weak coupling limit, the divisor of this automorphic form is an integer linear combination of the rational quadratic divisors where the gauge symmetry is enhanced classically. We also show how the non-perturbative prepotential can be expressed in terms of meromorphic automorphic forms, by expanding a T-duality invariant quantity both in terms of the standard special coord...
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
Hopf algebras in noncommutative geometry
International Nuclear Information System (INIS)
Varilly, Joseph C.
2001-10-01
We give an introductory survey to the use of Hopf algebras in several problems of non- commutative geometry. The main example, the Hopf algebra of rooted trees, is a graded, connected Hopf algebra arising from a universal construction. We show its relation to the algebra of transverse differential operators introduced by Connes and Moscovici in order to compute a local index formula in cyclic cohomology, and to the several Hopf algebras defined by Connes and Kreimer to simplify the combinatorics of perturbative renormalization. We explain how characteristic classes for a Hopf module algebra can be obtained from the cyclic cohomology of the Hopf algebra which acts on it. Finally, we discuss the theory of non- commutative spherical manifolds and show how they arise as homogeneous spaces of certain compact quantum groups. (author)
Seesaw mechanism in warped geometry
International Nuclear Information System (INIS)
Huber, S.J.; Shafi, Q.
2003-09-01
We show how the seesaw mechanism for neutrino masses can be realized within a five dimensional (5D) warped geometry framework. Intermediate scale standard model (SM) singlet neutrino masses, needed to explain the atmospheric and solar neutrino oscillations, are shown to be proportional to M P1 .exp((2c-1)πkR), where c denotes the coefficient of the 5D Dirac mass term for the singlet neutrino which also has a Planck scale Majorana mass localized on the Planck-brane, and kR∼11 in order to resolve the gauge hierarchy problem. The case with a bulk 5D Majorana mass term for the singlet neutrino is briefly discussed. (orig.)
Seesaw mechanism in warped geometry
International Nuclear Information System (INIS)
Huber, Stephan J.; Shafi, Qaisar
2004-01-01
We show how the seesaw mechanism for neutrino masses can be realized within a five-dimensional (5D) warped geometry framework. Intermediate scale standard model (SM) singlet neutrino masses, needed to explain the atmospheric and solar neutrino oscillations, are shown to be proportional to M Pl exp((2c-1)πkR), where c denotes the coefficient of the 5D Dirac mass term for the singlet neutrino which also has a Planck scale Majorana mass localized on the Planck-brane, and kR∼11 in order to resolve the gauge hierarchy problem. The case with a bulk 5D Majorana mass term for the singlet neutrino is briefly discussed
Multivariate calculus and geometry
Dineen, Seán
2014-01-01
Multivariate calculus can be understood best by combining geometric insight, intuitive arguments, detailed explanations and mathematical reasoning. This textbook has successfully followed this programme. It additionally provides a solid description of the basic concepts, via familiar examples, which are then tested in technically demanding situations. In this new edition the introductory chapter and two of the chapters on the geometry of surfaces have been revised. Some exercises have been replaced and others provided with expanded solutions. Familiarity with partial derivatives and a course in linear algebra are essential prerequisites for readers of this book. Multivariate Calculus and Geometry is aimed primarily at higher level undergraduates in the mathematical sciences. The inclusion of many practical examples involving problems of several variables will appeal to mathematics, science and engineering students.
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...
Multilevel geometry optimization
Rodgers, Jocelyn M.; Fast, Patton L.; Truhlar, Donald G.
2000-02-01
Geometry optimization has been carried out for three test molecules using six multilevel electronic structure methods, in particular Gaussian-2, Gaussian-3, multicoefficient G2, multicoefficient G3, and two multicoefficient correlation methods based on correlation-consistent basis sets. In the Gaussian-2 and Gaussian-3 methods, various levels are added and subtracted with unit coefficients, whereas the multicoefficient Gaussian-x methods involve noninteger parameters as coefficients. The multilevel optimizations drop the average error in the geometry (averaged over the 18 cases) by a factor of about two when compared to the single most expensive component of a given multilevel calculation, and in all 18 cases the accuracy of the atomization energy for the three test molecules improves; with an average improvement of 16.7 kcal/mol.
Multilevel geometry optimization
Energy Technology Data Exchange (ETDEWEB)
Rodgers, Jocelyn M. [Department of Chemistry and Supercomputer Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431 (United States); Fast, Patton L. [Department of Chemistry and Supercomputer Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431 (United States); Truhlar, Donald G. [Department of Chemistry and Supercomputer Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431 (United States)
2000-02-15
Geometry optimization has been carried out for three test molecules using six multilevel electronic structure methods, in particular Gaussian-2, Gaussian-3, multicoefficient G2, multicoefficient G3, and two multicoefficient correlation methods based on correlation-consistent basis sets. In the Gaussian-2 and Gaussian-3 methods, various levels are added and subtracted with unit coefficients, whereas the multicoefficient Gaussian-x methods involve noninteger parameters as coefficients. The multilevel optimizations drop the average error in the geometry (averaged over the 18 cases) by a factor of about two when compared to the single most expensive component of a given multilevel calculation, and in all 18 cases the accuracy of the atomization energy for the three test molecules improves; with an average improvement of 16.7 kcal/mol. (c) 2000 American Institute of Physics.
Polygons, Pillars and Pavilions: Discovering Connections between Geometry and Architecture
Madden, Sean Patrick
2017-01-01
Crowning the second semester of geometry, taught within a Catholic middle school, the author's students explored connections between the geometry of regular polygons and architecture of local buildings. They went on to explore how these principles apply famous buildings around the world such as the monuments of Washington, D.C. and the elliptical…
Krauss, Lawrence M.; Turner, Michael S.
1999-01-01
The recognition that the cosmological constant may be non-zero forces us to re-evaluate standard notions about the connection between geometry and the fate of our Universe. An open Universe can recollapse, and a closed Universe can expand forever. As a corollary, we point out that there is no set of cosmological observations we can perform that will unambiguously allow us to determine what the ultimate destiny of the Universe will be.
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...... 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....
International Nuclear Information System (INIS)
Lepora, N.; Kibble, T.
1999-01-01
We analyse symmetry breaking in the Weinberg-Salam model paying particular attention to the underlying geometry of the theory. In this context we find two natural metrics upon the vacuum manifold: an isotropic metric associated with the scalar sector, and a squashed metric associated with the gauge sector. Physically, the interplay between these metrics gives rise to many of the non-perturbative features of Weinberg-Salam theory. (author)
International Nuclear Information System (INIS)
Hull, C.M.
1993-01-01
The geometric structure of theories with gauge fields of spins two and higher should involve a higher spin generalisation of Riemannian geometry. Such geometries are discussed and the case of W ∝ -gravity is analysed in detail. While the gauge group for gravity in d dimensions is the diffeomorphism group of the space-time, the gauge group for a certain W-gravity theory (which is W ∝ -gravity in the case d=2) is the group of symplectic diffeomorphisms of the cotangent bundle of the space-time. Gauge transformations for W-gravity gauge fields are given by requiring the invariance of a generalised line element. Densities exist and can be constructed from the line element (generalising √detg μν ) only if d=1 or d=2, so that only for d=1,2 can actions be constructed. These two cases and the corresponding W-gravity actions are considered in detail. In d=2, the gauge group is effectively only a subgroup of the symplectic diffeomorphisms group. Some of the constraints that arise for d=2 are similar to equations arising in the study of self-dual four-dimensional geometries and can be analysed using twistor methods, allowing contact to be made with other formulations of W-gravity. While the twistor transform for self-dual spaces with one Killing vector reduces to a Legendre transform, that for two Killing vectors gives a generalisation of the Legendre transform. (orig.)
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...
CBM RICH geometry optimization
Energy Technology Data Exchange (ETDEWEB)
Mahmoud, Tariq; Hoehne, Claudia [II. Physikalisches Institut, Giessen Univ. (Germany); Collaboration: CBM-Collaboration
2016-07-01
The Compressed Baryonic Matter (CBM) experiment at the future FAIR complex will investigate the phase diagram of strongly interacting matter at high baryon density and moderate temperatures in A+A collisions from 2-11 AGeV (SIS100) beam energy. The main electron identification detector in the CBM experiment will be a RICH detector with a CO{sub 2} gaseous-radiator, focusing spherical glass mirrors, and MAPMT photo-detectors being placed on a PMT-plane. The RICH detector is located directly behind the CBM dipole magnet. As the final magnet geometry is now available, some changes in the RICH geometry become necessary. In order to guarantee a magnetic field of 1 mT at maximum in the PMT plane for effective operation of the MAPMTs, two measures have to be taken: The PMT plane is moved outwards of the stray field by tilting the mirrors by 10 degrees and shielding boxes have been designed. In this contribution the results of the geometry optimization procedure are presented.
Introducing geometry concept based on history of Islamic geometry
Maarif, S.; Wahyudin; Raditya, A.; Perbowo, K. S.
2018-01-01
Geometry is one of the areas of mathematics interesting to discuss. Geometry also has a long history in mathematical developments. Therefore, it is important integrated historical development of geometry in the classroom to increase’ knowledge of how mathematicians earlier finding and constructing a geometric concept. Introduction geometrical concept can be started by introducing the Muslim mathematician who invented these concepts so that students can understand in detail how a concept of geometry can be found. However, the history of mathematics development, especially history of Islamic geometry today is less popular in the world of education in Indonesia. There are several concepts discovered by Muslim mathematicians that should be appreciated by the students in learning geometry. Great ideas of mathematicians Muslim can be used as study materials to supplement religious character values taught by Muslim mathematicians. Additionally, by integrating the history of geometry in teaching geometry are expected to improve motivation and geometrical understanding concept.
Functions locally dependent on finitely many coordinates
Czech Academy of Sciences Publication Activity Database
Hájek, Petr Pavel; Zizler, Václav
2006-01-01
Roč. 100, č. 2 (2006), s. 147-154 ISSN 1578-7303 R&D Projects: GA AV ČR(CZ) IAA100190502; GA ČR(CZ) GA201/04/0090 Institutional research plan: CEZ:AV0Z10190503 Keywords : smoothness * renormings * higher smoothness Subject RIV: BA - General Mathematics
Mathematical model of geometry and fibrous structure of the heart.
Nielsen, P M; Le Grice, I J; Smaill, B H; Hunter, P J
1991-04-01
We developed a mathematical representation of ventricular geometry and muscle fiber organization using three-dimensional finite elements referred to a prolate spheroid coordinate system. Within elements, fields are approximated using basis functions with associated parameters defined at the element nodes. Four parameters per node are used to describe ventricular geometry. The radial coordinate is interpolated using cubic Hermite basis functions that preserve slope continuity, while the angular coordinates are interpolated linearly. Two further nodal parameters describe the orientation of myocardial fibers. The orientation of fibers within coordinate planes bounded by epicardial and endocardial surfaces is interpolated linearly, with transmural variation given by cubic Hermite basis functions. Left and right ventricular geometry and myocardial fiber orientations were characterized for a canine heart arrested in diastole and fixed at zero transmural pressure. The geometry was represented by a 24-element ensemble with 41 nodes. Nodal parameters fitted using least squares provided a realistic description of ventricular epicardial [root mean square (RMS) error less than 0.9 mm] and endocardial (RMS error less than 2.6 mm) surfaces. Measured fiber fields were also fitted (RMS error less than 17 degrees) with a 60-element, 99-node mesh obtained by subdividing the 24-element mesh. These methods provide a compact and accurate anatomic description of the ventricles suitable for use in finite element stress analysis, simulation of cardiac electrical activation, and other cardiac field modeling problems.
Two lectures on D-geometry and noncommutative geometry
International Nuclear Information System (INIS)
Douglas, M.R.
1999-01-01
This is a write-up of lectures given at the 1998 Spring School at the Abdus Salam ICTP. We give a conceptual introduction to D-geometry, the study of geometry as seen by D-branes in string theory, and to noncommutative geometry as it has appeared in D-brane and Matrix theory physics. (author)
The Schwarzschild metric: It's the coordinates, stupid!
Fromholz, Pierre; Poisson, Eric; Will, Clifford M.
2014-04-01
Every general relativity textbook emphasizes that coordinates have no physical meaning. Nevertheless, a coordinate choice must be made in order to carry out real calculations, and that choice can make the difference between a calculation that is simple and one that is a mess. We give a concrete illustration of the maxim that "coordinates matter" using the exact Schwarzschild solution for a vacuum, static spherical spacetime. We review the standard textbook derivation, Schwarzschild's original 1916 derivation, and a derivation using the Landau-Lifshitz formulation of the Einstein field equations. The last derivation is much more complicated, has one aspect for which we have been unable to find a solution, and gives an explicit illustration of the fact that the Schwarzschild geometry can be described in infinitely many coordinate systems.
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...
International Nuclear Information System (INIS)
Hook, D W
2008-01-01
A geometric framework for quantum mechanics arose during the mid 1970s when authors such as Cantoni explored the notion of generalized transition probabilities, and Kibble promoted the idea that the space of pure quantum states provides a natural quantum mechanical analogue for classical phase space. This central idea can be seen easily since the projection of Schroedinger's equation from a Hilbert space into the space of pure spaces is a set of Hamilton's equations. Over the intervening years considerable work has been carried out by a variety of authors and a mature description of quantum mechanics in geometric terms has emerged with many applications. This current offering would seem ideally placed to review the last thirty years of progress and relate this to the most recent work in quantum entanglement. Bengtsson and Zyczkowski's beautifully illustrated volume, Geometry of Quantum States (referred to as GQS from now on) attempts to cover considerable ground in its 466 pages. Its topics range from colour theory in Chapter 1 to quantum entanglement in Chapter 15-to say that this is a whirlwind tour is, perhaps, no understatement. The use of the work 'introduction' in the subtitle of GQS, might suggest to the reader that this work be viewed as a textbook and I think that this interpretation would be incorrect. The authors have chosen to present a survey of different topics with the specific aim to introduce entanglement in geometric terms-the book is not intended as a pedagogical introduction to the geometric approach to quantum mechanics. Each of the fifteen chapters is a short, and mostly self-contained, essay on a particular aspect or application of geometry in the context of quantum mechanics with entanglement being addressed specifically in the final chapter. The chapters fall into three classifications: those concerned with the mathematical background, those which discuss quantum theory and the foundational aspects of the geometric framework, and
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
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.
Torsional heterotic geometries
International Nuclear Information System (INIS)
Becker, Katrin; Sethi, Savdeep
2009-01-01
We construct new examples of torsional heterotic backgrounds using duality with orientifold flux compactifications. We explain how duality provides a perturbative solution to the type I/heterotic string Bianchi identity. The choice of connection used in the Bianchi identity plays an important role in the construction. We propose the existence of a much larger landscape of compact torsional geometries using string duality. Finally, we present some quantum exact metrics that correspond to NS5-branes placed on an elliptic space. These metrics describe how torus isometries are broken by NS flux.
Geometrie verstehen: statisch - kinematisch
Kroll, Ekkehard
Dem Allgemeinen steht begrifflich das Besondere gegenüber. In diesem Sinne sind allgemeine Überlegungen zum Verstehen von Mathematik zu ergänzen durch Untersuchungen hinsichtlich des Verstehens der einzelnen mathematischen Disziplinen, insbesondere der Geometrie. Hier haben viele Schülerinnen und Schüler Probleme. Diese rühren hauptsächlich daher, dass eine fertige geometrische Konstruktion in ihrer statischen Präsentation auf Papier nicht mehr die einzelnen Konstruktionsschritte erkennen lässt; zum Nachvollzug müssen sie daher ergänzend in einer Konstruktionsbeschreibung festgehalten werden.
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
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
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
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
KENO-IV/CG, the combinatorial geometry version of the KENO Monte Carlo criticality safety program
International Nuclear Information System (INIS)
West, J.T.; Petrie, L.M.; Fraley, S.K.
1979-09-01
KENO-IV/CG was developed to merge the simple geometry input description utilized by combinatorial geometry with the repeating lattice feature of the original KENO geometry package. The result is a criticality code with the ability to model a complex system of repeating rectangular lattices inside a complicated three-dimensional geometry system. Furthermore, combinatorial geometry was modified to differentiate between combinatorial zones describing a particular KENO BOX to be repeated in a KENO array and those combinatorial zones describing geometry external to an array. This allows the user to maintain a simple coordinate system without any geometric conflict due to spatial overlap. Several difficult criticality design problems have been solved with the new geometry package in KENO-IV/CG, thus illustrating the power of the code to model difficult geometries with a minimum of effort
Rare earth niobate coordination polymers
Muniz, Collin N.; Patel, Hiral; Fast, Dylan B.; Rohwer, Lauren E. S.; Reinheimer, Eric W.; Dolgos, Michelle; Graham, Matt W.; Nyman, May
2018-03-01
Rare-earth (RE) coordination polymers are infinitely tailorable to yield luminescent materials for various applications. Here we described the synthesis of a heterometallic rare-earth coordination compound ((CH3)2SO)3(RE)NbO(C2O4)3((CH3)2SO) = dimethylsulfoxide, DMSO, (C2O2= oxalate), (RE=La, Ce, Pr, Nd, Sm, Eu, Gd, Tb). The structure was obtained from single crystal X-ray diffraction of the La analogue. The Nb˭O and DMSO terminal-bonding character guides assembly of an open framework structure with noncentrosymmetric RE-coordination geometry, and large spacing between the RE centers. A second structure was observed by PXRD for the smaller rare earths (Dy, Ho, Er, Yb); this structure has not yet been determined. The materials were further characterized using FTIR, and photoluminescence measurements. Characteristic excitation and emission transitions were observed for RE = Nd, Sm, Eu, and Tb. Quantum yield (QY) measurements were performed by exciting Eu and Tb analoges at 394 nm (QY 66%) and 464 nm (QY 71%) for Eu; and 370 nm (QY=40%) for Tb. We attribute the high QY and bright luminescence to two main structure-function properties of the system; namely the absence of water in the structure, and absence of concentration quenching.
Non-Perturbative Quantum Geometry III
Krefl, Daniel
2016-08-02
The Nekrasov-Shatashvili limit of the refined topological string on toric Calabi-Yau manifolds and the resulting quantum geometry is studied from a non-perturbative perspective. The quantum differential and thus the quantum periods exhibit Stockes phenomena over the combined string coupling and quantized Kaehler moduli space. We outline that the underlying formalism of exact quantization is generally applicable to points in moduli space featuring massless hypermultiplets, leading to non-perturbative band splitting. Our prime example is local P1xP1 near a conifold point in moduli space. In particular, we will present numerical evidence that in a Stockes chamber of interest the string based quantum geometry reproduces the non-perturbative corrections for the Nekrasov-Shatashvili limit of 4d supersymmetric SU(2) gauge theory at strong coupling found in the previous part of this series. A preliminary discussion of local P2 near the conifold point in moduli space is also provided.
coordination polymers derived from two different bis-pyridyl-bis-am
Indian Academy of Sciences (India)
Abstract. Three new Ni(II) coordination polymers exhibiting different 1D and 2D framework structures ... separation, magnetism, ion exchange and so on.5 8 ... of the coordination geometries of metal ions, which ... Cu(II)/Co(II)/Cd(II) coordination polymers containing ..... tion, the concentration of MB and RhB (C) versus reac-.
The Generation of Three-Dimensional Body-Fitted Coordinate Systems for Viscous Flow Problems.
1982-07-01
Geometries," NASA TM X-3206, 1975. iq p] Papers Written Under The Contract 1. "Basic Differential Models For Coordinate Generation ", Z . U. A. Warsi...8217 Ii (C) (4’) p Figure 1. Coordinate Surfaces fr. I • BASIC DIFFERENTIAL MODELS FOR COORDINATE GENERATION Z . U. A. WARSI* Department of Aerospace
International Nuclear Information System (INIS)
Merkulov, S.A.
1987-01-01
Geometry of local supertwistors is investigated. It is proved that the Yang-Mills equations for the introduced ansatz for supertwistor connection are equivalent to free bach equations, describing the dynamics of N=1 conformal supergravity. Analogous interpretation of the dynamics of N=1 conformal supergravity coupled to a vector superfield is proposed. It is proved that any complex conformally right or left flat superspace automatically satisfies the Bach equations
The G2 spinorial geometry of supersymmetric IIB backgrounds
International Nuclear Information System (INIS)
Gran, U; Gutowski, J; Papadopoulos, G
2006-01-01
We solve the Killing spinor equations of supersymmetric IIB backgrounds which admit one supersymmetry and the Killing spinor has stability subgroup G 2 in Spin(9, 1) x U(1). We find that such backgrounds admit a timelike Killing vector field and the geometric structure of the spacetime reduces from Spin(9, 1) x U(1) to G 2 . We determine the type of G 2 structure that the spacetime admits by computing the covariant derivatives of the spacetime forms associated with the Killing spinor bilinears. We also solve the Killing spinor equations of backgrounds with two supersymmetries and Spin(7) x R 8 -invariant spinors, and four supersymmetries with SU(4) x R 8 - and with G 2 -invariant spinors. We show that the Killing spinor equations factorize in two sets, one involving the geometry and the 5-form flux, and the other the 3-form flux and the scalars. In the Spin(7) x R 8 and SU(4) x R 8 cases, the spacetime admits a parallel null vector field and so the spacetime metric can be locally described in terms of Penrose coordinates adapted to the associated rotation free, null, geodesic congruence. The transverse space of the congruence is a Spin(7) and a SU(4) holonomy manifold, respectively. In the G 2 case, all the fluxes vanish and the spacetime is the product of a three-dimensional Minkowski space with a holonomy G 2 manifold
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.
Critique of information geometry
International Nuclear Information System (INIS)
Skilling, John
2014-01-01
As applied to probability, information geometry fails because probability distributions do not form a metric space. Probability theory rests on a compelling foundation of elementary symmetries, which also support information (aka minus entropy, Kullback-Leibler) H(p;q) as the unique measure of divergence from source probability distribution q to destination p. Because the only compatible connective H is from≠to asymmetric, H(p;q)≠H(q;p), there can be no compatible geometrical distance (which would necessarily be from=to symmetric). Hence there is no distance relationship compatible with the structure of probability theory. Metrics g and densities sqrt(det(g)) interpreted as prior probabilities follow from the definition of distance, and must fail likewise. Various metrics and corresponding priors have been proposed, Fisher's being the most popular, but all must behave unacceptably. This is illustrated with simple counter-examples
International Nuclear Information System (INIS)
Correa, Diego H.; Silva, Guillermo A.
2008-01-01
We discuss how geometrical and topological aspects of certain (1/2)-BPS type IIB geometries are captured by their dual operators in N = 4 Super Yang-Mills theory. The type IIB solutions are characterized by arbitrary droplet pictures in a plane and we consider, in particular, axially symmetric droplets. The 1-loop anomalous dimension of the dual gauge theory operators probed with single traces is described by some bosonic lattice Hamiltonians. These Hamiltonians are shown to encode the topology of the droplets. In appropriate BMN limits, the Hamiltonians spectrum reproduces the spectrum of near-BPS string excitations propagating along each of the individual edges of the droplet. We also study semiclassical regimes for the Hamiltonians. For droplets having disconnected constituents, the Hamiltonian admits different complimentary semiclassical descriptions, each one replicating the semiclassical description for closed strings extending in each of the constituents
Emergent geometry of membranes
Energy Technology Data Exchange (ETDEWEB)
Badyn, Mathias Hudoba de; Karczmarek, Joanna L.; Sabella-Garnier, Philippe; Yeh, Ken Huai-Che [Department of Physics and Astronomy, University of British Columbia,6224 Agricultural Road, Vancouver (Canada)
2015-11-13
In work http://dx.doi.org/10.1103/PhysRevD.86.086001, a surface embedded in flat ℝ{sup 3} is associated to any three hermitian matrices. We study this emergent surface when the matrices are large, by constructing coherent states corresponding to points in the emergent geometry. We find the original matrices determine not only shape of the emergent surface, but also a unique Poisson structure. We prove that commutators of matrix operators correspond to Poisson brackets. Through our construction, we can realize arbitrary noncommutative membranes: for example, we examine a round sphere with a non-spherically symmetric Poisson structure. We also give a natural construction for a noncommutative torus embedded in ℝ{sup 3}. Finally, we make remarks about area and find matrix equations for minimal area surfaces.
A coordination language for databases
DEFF Research Database (Denmark)
Li, Ximeng; Wu, Xi; Lluch Lafuente, Alberto
2017-01-01
We present a coordination language for the modeling of distributed database applications. The language, baptized Klaim-DB, borrows the concepts of localities and nets of the coordination language Klaim but re-incarnates the tuple spaces of Klaim as databases. It provides high-level abstractions...... and primitives for the access and manipulation of structured data, with integrity and atomicity considerations. We present the formal semantics of Klaim-DB and develop a type system that avoids potential runtime errors such as certain evaluation errors and mismatches of data format in tables, which are monitored...... in the semantics. The use of the language is illustrated in a scenario where the sales from different branches of a chain of department stores are aggregated from their local databases. Raising the abstraction level and encapsulating integrity checks in the language primitives have benefited the modeling task...
Improving Information Exchange and Coordination Amongst Homeland Security Organizations
National Research Council Canada - National Science Library
Goan, Terrance; Mayk, Israel
2005-01-01
Command and Control for coordinated response to domestic terrorist attack will require the ability of Federal, state, and local agencies to maintain awareness of the status, capabilities, requirements...
Geometry through history Euclidean, hyperbolic, and projective geometries
Dillon, Meighan I
2018-01-01
Presented as an engaging discourse, this textbook invites readers to delve into the historical origins and uses of geometry. The narrative traces the influence of Euclid’s system of geometry, as developed in his classic text The Elements, through the Arabic period, the modern era in the West, and up to twentieth century mathematics. Axioms and proof methods used by mathematicians from those periods are explored alongside the problems in Euclidean geometry that lead to their work. Students cultivate skills applicable to much of modern mathematics through sections that integrate concepts like projective and hyperbolic geometry with representative proof-based exercises. For its sophisticated account of ancient to modern geometries, this text assumes only a year of college mathematics as it builds towards its conclusion with algebraic curves and quaternions. Euclid’s work has affected geometry for thousands of years, so this text has something to offer to anyone who wants to broaden their appreciation for the...
Howangyin, Kiave-Yune; Zlatanova, Ivana; Pinto, Cristina; Ngkelo, Anta; Cochain, Clément; Rouanet, Marie; Vilar, José; Lemitre, Mathilde; Stockmann, Christian; Fleischmann, Bernd K; Mallat, Ziad; Silvestre, Jean-Sébastien
2016-03-01
In infarcted heart, improper clearance of dying cells by activated neighboring phagocytes may precipitate the transition to heart failure. We analyzed the coordinated role of 2 major mediators of efferocytosis, the myeloid-epithelial-reproductive protein tyrosine kinase (Mertk) and the milk fat globule epidermal growth factor (Mfge8), in directing cardiac remodeling by skewing the inflammatory response after myocardial infarction. We generated double-deficient mice for Mertk and Mfge8 (Mertk(-/-)/Mfge8(-/-)) and challenged them with acute coronary ligature. Compared with wild-type, Mertk-deficient (Mertk(-/-)), or Mfge8-deficient (Mfge8(-/-)) animals, Mertk(-/-)/Mfge8(-/-) mice displayed greater alteration in cardiac function and remodeling. Mertk and Mfge8 were expressed mainly by cardiac Ly6C(High and Low) monocytes and macrophages. In parallel, Mertk(-/-)/Mfge8(-/-) bone marrow chimeras manifested increased accumulation of apoptotic cells, enhanced fibrotic area, and larger infarct size, as well as reduced angiogenesis. We found that the abrogation of efferocytosis affected neither the ability of circulating monocytes to infiltrate cardiac tissue nor the number of resident Ly6C(High) and Ly6C(How) monocytes/macrophages populating the infarcted milieu. In contrast, combined Mertk and Mfge8 deficiency in Ly6C(High)/Ly6C(Low) monocytes/macrophages either obtained from in vitro differentiation of bone marrow cells or isolated from infarcted hearts altered their capacity of efferocytosis and subsequently blunted vascular endothelial growth factor A (VEGFA) release. Using LysMCre(+)/VEGFA(fl/fl) mice, we further identified an important role for myeloid-derived VEGFA in improving cardiac function and angiogenesis. After myocardial infarction, Mertk- and Mfge8-expressing monocyte/macrophages synergistically engage the clearance of injured cardiomyocytes, favoring the secretion of VEGFA to locally repair the dysfunctional heart. © 2016 The Authors.
On organizing principles of discrete differential geometry. Geometry of spheres
International Nuclear Information System (INIS)
Bobenko, Alexander I; Suris, Yury B
2007-01-01
Discrete differential geometry aims to develop discrete equivalents of the geometric notions and methods of classical differential geometry. This survey contains a discussion of the following two fundamental discretization principles: the transformation group principle (smooth geometric objects and their discretizations are invariant with respect to the same transformation group) and the consistency principle (discretizations of smooth parametrized geometries can be extended to multidimensional consistent nets). The main concrete geometric problem treated here is discretization of curvature-line parametrized surfaces in Lie geometry. Systematic use of the discretization principles leads to a discretization of curvature-line parametrization which unifies circular and conical nets.
Higher geometry an introduction to advanced methods in analytic geometry
Woods, Frederick S
2005-01-01
For students of mathematics with a sound background in analytic geometry and some knowledge of determinants, this volume has long been among the best available expositions of advanced work on projective and algebraic geometry. Developed from Professor Woods' lectures at the Massachusetts Institute of Technology, it bridges the gap between intermediate studies in the field and highly specialized works.With exceptional thoroughness, it presents the most important general concepts and methods of advanced algebraic geometry (as distinguished from differential geometry). It offers a thorough study
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...
Transformation procedures in 3D terrestrial coordinate systems
Directory of Open Access Journals (Sweden)
Sedlák Vladimír
2001-12-01
Full Text Available Transformation procedures belong to the main tasks of surveyor working in a field of geodesy, for example in satellite geodesy or astronomical geodesy. It is necessary to know transformation procedures in 3D terrestrial (Earth coordinate systems. Increasingly a dynamic advance growth of application of satellite navigation systems, for example GPS (Global Positioning System into engineering surveying, real estate register and others spheres of applied geodesy and geo-surveying (mine surveying exacts knowledge of these transformation procedures between coordinates in various coordinate systems. These tasks are common for daily work for various practical surveyors too, not only for theoretical scientific working surveyors.Conventional Terrestrial System is 3D coordinate system what is the most important coordinate system in global geodesy. Conventional Terrestrial System is an approximation of the nature coordinate system of the Earth. The origin of this coordinate system is placed in the earth substantial centre of gravity and in the centre of geoid. Conventional Terrestrial System is the Cartesian right-handed coordinate system, i.e. positive one. The Local Astronomical System is 3D coordinate system too and it belongs to an important coordinate system in geodesy from its practical point of view. Many geodetic measurements are realized in this coordinate system. Designation of this coordinate system as astronomical system expresses its sticking to a normal line to an equipotential plane, i.e. to a vertical. Local Astronomical system is the left-handed cartesian coordinate system.Transformation procedures in 3D terrestrial coordinate systems with theory of these systems are presented in the paper. Transformation in the local astronomical coordinate system presents common transformation in a frame of an adjustment of various local geodetic networks. In a case of satellite measurements (GPS, satellite altimetry, etc. transformation between local and
International Nuclear Information System (INIS)
Buescher, R.
2005-01-01
Casimir interactions are interactions induced by quantum vacuum fluctuations and thermal fluctuations of the electromagnetic field. Using a path integral quantization for the gauge field, an effective Gaussian action will be derived which is the starting point to compute Casimir forces between macroscopic objects analytically and numerically. No assumptions about the independence of the material and shape dependent contributions to the interaction are made. We study the limit of flat surfaces in further detail and obtain a concise derivation of Lifshitz' theory of molecular forces. For the case of ideally conducting boundaries, the Gaussian action will be calculated explicitly. Both limiting cases are also discussed within the framework of a scalar field quantization approach, which is applicable for translationally invariant geometries. We develop a non-perturbative approach to calculate the Casimir interaction from the Gaussian action for periodically deformed and ideally conducting objects numerically. The obtained results reveal two different scaling regimes for the Casimir force as a function of the distance between the objects, their deformation wavelength and -amplitude. The results confirm that the interaction is non-additive, especially in the presence of strong geometric deformations. Furthermore, the numerical approach is extended to calculate lateral Casimir forces. The results are consistent with the results of the proximity-force approximation for large deformation wavelengths. A qualitatively different behaviour between the normal and lateral force is revealed. We also establish a relation between the boundary induced change of the of the density of states for the scalar Helmholtz equation and the Casimir interaction using the path integral method. For statically deformed boundaries, this relation can be expressed as a novel trace formula, which is formally similar to the so-called Krein-Friedel-Lloyd formula. While the latter formula describes the
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
Nonlinear gyrokinetic Maxwell-Vlasov equations using magnetic coordinates
International Nuclear Information System (INIS)
Brizard, A.
1988-09-01
A gyrokinetic formalism using magnetic coordinates is used to derive self-consistent, nonlinear Maxwell-Vlasov equations that are suitable for particle simulation studies of finite-β tokamak microturbulence and its associated anomalous transport. The use of magnetic coordinates is an important feature of this work as it introduces the toroidal geometry naturally into our gyrokinetic formalism. The gyrokinetic formalism itself is based on the use of the Action-variational Lie perturbation method of Cary and Littlejohn, and preserves the Hamiltonian structure of the original Maxwell-Vlasov system. Previous nonlinear gyrokinetic sets of equations suitable for particle simulation analysis have considered either electrostatic and shear-Alfven perturbations in slab geometry, or electrostatic perturbations in toroidal geometry. In this present work, fully electromagnetic perturbations in toroidal geometry are considered. 26 refs
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.
Nonperturbative quantum geometries
International Nuclear Information System (INIS)
Jacobson, T.; California Univ., Santa Barbara; Smolin, L.; California Univ., Santa Barbara
1988-01-01
Using the self-dual representation of quantum general relativity, based on Ashtekar's new phase space variables, we present an infinite dimensional family of quantum states of the gravitational field which are exactly annihilated by the hamiltonian constraint. These states are constructed from Wilson loops for Ashtekar's connection (which is the spatial part of the left handed spin connection). We propose a new regularization procedure which allows us to evaluate the action of the hamiltonian constraint on these states. Infinite linear combinations of these states which are formally annihilated by the diffeomorphism constraints as well are also described. These are explicit examples of physical states of the gravitational field - and for the compact case are exact zero eigenstates of the hamiltonian of quantum general relativity. Several different approaches to constructing diffeomorphism invariant states in the self dual representation are also described. The physical interpretation of the states described here is discussed. However, as we do not yet know the physical inner product, any interpretation is at this stage speculative. Nevertheless, this work suggests that quantum geometry at Planck scales might be much simpler when explored in terms of the parallel transport of left-handed spinors than when explored in terms of the three metric. (orig.)
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.
Geometric control theory and sub-Riemannian geometry
Boscain, Ugo; Gauthier, Jean-Paul; Sarychev, Andrey; Sigalotti, Mario
2014-01-01
This volume presents recent advances in the interaction between Geometric Control Theory and sub-Riemannian geometry. On the one hand, Geometric Control Theory used the differential geometric and Lie algebraic language for studying controllability, motion planning, stabilizability and optimality for control systems. The geometric approach turned out to be fruitful in applications to robotics, vision modeling, mathematical physics etc. On the other hand, Riemannian geometry and its generalizations, such as sub-Riemannian, Finslerian geometry etc., have been actively adopting methods developed in the scope of geometric control. Application of these methods has led to important results regarding geometry of sub-Riemannian spaces, regularity of sub-Riemannian distances, properties of the group of diffeomorphisms of sub-Riemannian manifolds, local geometry and equivalence of distributions and sub-Riemannian structures, regularity of the Hausdorff volume.
Trufanov, Aleksandr N.; Trufanov, Nikolay A.; Semenov, Nikita V.
2016-09-01
The experimental data analysis of the stress applying rod section geometry for the PANDA-type polarization maintaining optical fiber has been performed. The dependencies of the change in the radial dimensions of the preform and the doping boundary on the angular coordinate have been obtained. The original algorithm of experimental data statistic analysis, which enables determination of the specimens' characteristic form of section, has been described. The influence of actual doped zone geometry on the residual stress fields formed during the stress rod preform fabrication has been investigated. It has been established that the deviation of the boundary between pure silica and the doped zone from the circular shape results in dissymmetry and local concentrations of the residual stress fields along the section, which can cause preforms destruction at high degrees of doping. The observed geometry deviations of up to 10% lead to the increase of the maximum stress intensity value by over 20%.
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....
Kaehler geometry and SUSY mechanics
International Nuclear Information System (INIS)
Bellucci, Stefano; Nersessian, Armen
2001-01-01
We present two examples of SUSY mechanics related with Kaehler geometry. The first system is the N = 4 supersymmetric one-dimensional sigma-model proposed in hep-th/0101065. Another system is the N = 2 SUSY mechanics whose phase space is the external algebra of an arbitrary Kaehler manifold. The relation of these models with antisymplectic geometry is discussed
A prediction for bubbling geometries
Okuda, Takuya
2007-01-01
We study the supersymmetric circular Wilson loops in N=4 Yang-Mills theory. Their vacuum expectation values are computed in the parameter region that admits smooth bubbling geometry duals. The results are a prediction for the supergravity action evaluated on the bubbling geometries for Wilson loops.
Molecular motion in restricted geometries
Indian Academy of Sciences (India)
Molecular dynamics in restricted geometries is known to exhibit anomalous behaviour. Diffusion, translational or rotational, of molecules is altered significantly on confinement in restricted geometries. Quasielastic neutron scattering (QENS) offers a unique possibility of studying molecular motion in such systems. Both time ...
Stages as models of scene geometry.
Nedović, Vladimir; Smeulders, Arnold W M; Redert, André; Geusebroek, Jan-Mark
2010-09-01
Reconstruction of 3D scene geometry is an important element for scene understanding, autonomous vehicle and robot navigation, image retrieval, and 3D television. We propose accounting for the inherent structure of the visual world when trying to solve the scene reconstruction problem. Consequently, we identify geometric scene categorization as the first step toward robust and efficient depth estimation from single images. We introduce 15 typical 3D scene geometries called stages, each with a unique depth profile, which roughly correspond to a large majority of broadcast video frames. Stage information serves as a first approximation of global depth, narrowing down the search space in depth estimation and object localization. We propose different sets of low-level features for depth estimation, and perform stage classification on two diverse data sets of television broadcasts. Classification results demonstrate that stages can often be efficiently learned from low-dimensional image representations.
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...
Optical geometry across the horizon
International Nuclear Information System (INIS)
Jonsson, Rickard
2006-01-01
In a recent paper (Jonsson and Westman 2006 Class. Quantum Grav. 23 61), a generalization of optical geometry, assuming a non-shearing reference congruence, is discussed. Here we illustrate that this formalism can be applied to (a finite four-volume) of any spherically symmetric spacetime. In particular we apply the formalism, using a non-static reference congruence, to do optical geometry across the horizon of a static black hole. While the resulting geometry in principle is time dependent, we can choose the reference congruence in such a manner that an embedding of the geometry always looks the same. Relative to the embedded geometry the reference points are then moving. We discuss the motion of photons, inertial forces and gyroscope precession in this framework
Noncommutative geometry and fluid dynamics
International Nuclear Information System (INIS)
Das, Praloy; Ghosh, Subir
2016-01-01
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.)
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.)
Energy Technology Data Exchange (ETDEWEB)
Basiuk, Vladimir A., E-mail: basiuk@nucleares.unam.mx [Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Circuito Exterior C.U., 04510 México D.F. (Mexico); Department of Chemistry,Tufts University, 62 Talbot Avenue, Medford, MA 02155 (United States); Alzate-Carvajal, Natalia [Centro de Ciencias Aplicadas y Desarrollo Tecnológico, Universidad Nacional Autónoma de México, Circuito Exterior C.U., 04510 México D.F. (Mexico); Henao-Holguín, Laura V. [Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Circuito Exterior C.U., 04510 México D.F. (Mexico); Rybak-Akimova, Elena V. [Department of Chemistry,Tufts University, 62 Talbot Avenue, Medford, MA 02155 (United States); Basiuk, Elena V., E-mail: elbg1111@gmail.com [Department of Chemistry,Tufts University, 62 Talbot Avenue, Medford, MA 02155 (United States); Centro de Ciencias Aplicadas y Desarrollo Tecnológico, Universidad Nacional Autónoma de México, Circuito Exterior C.U., 04510 México D.F. (Mexico)
2016-05-15
Highlights: • [Ni(cyclam)]{sup 2+} and [Ni(tet b)]{sup 2+} cations coordinate to carboxylic groups of GO. • The coordination takes place under basic conditions in aqueous-based medium. • The coordination results in the conversion from low-spin to high-spin Ni(II). • Functionalized GO samples were characterized by various instrumental techniques. - Abstract: We describe a novel approach to functionalization of graphene oxide (GO) which allows for a facile generation of paramagnetic centers from two diamagnetic components. Coordination attachment of [Ni(cyclam)]{sup 2+} or [Ni(tet b)]{sup 2+} tetraazamacrocyclic cations to carboxylic groups of GO takes place under basic conditions in aqueous-based reaction medium. The procedure is very straightforward and does not require high temperatures or other harsh conditions. Changing the coordination geometry of Ni(II) from square-planar tetracoordinated to pseudooctahedral hexacoordinated brings about the conversion from low-spin to high-spin state of the metal centers. Even though the content of tetraazamacrocyclic complexes in functionalized GO samples was found to be relatively low (nickel content of ca. 1 wt%, as determined by thermogravimetric analysis, elemental analysis and energy dispersive X-ray spectroscopy), room temperature magnetic susceptibility measurements easily detected the appearance of paramagnetic properties in GO + [Ni(cyclam)] and GO + [Ni(tet b)] nanohybrids, with effective magnetic moments of 1.95 BM and 2.2 BM for, respectively. According to density functional theory calculations, the main spin density is localized at the macrocyclic complexes, without considerable extension to graphene sheet, which suggests insignificant ferromagnetic coupling in the nanohybrids, in agreement with the results of magnetic susceptibility measurements. The coordination attachment of Ni(II) tetraazamacrocycles to GO results in considerable changes in Fourier-transform infrared and X-ray photoelectron spectra
FENICIA: a generic plasma simulation code using a flux-independent field-aligned coordinate approach
International Nuclear Information System (INIS)
Hariri, Farah
2013-01-01
The primary thrust of this work is the development and implementation of a new approach to the problem of field-aligned coordinates in magnetized plasma turbulence simulations called the FCI approach (Flux-Coordinate Independent). The method exploits the elongated nature of micro-instability driven turbulence which typically has perpendicular scales on the order of a few ion gyro-radii, and parallel scales on the order of the machine size. Mathematically speaking, it relies on local transformations that align a suitable coordinate to the magnetic field to allow efficient computation of the parallel derivative. However, it does not rely on flux coordinates, which permits discretizing any given field on a regular grid in the natural coordinates such as (x, y, z) in the cylindrical limit. The new method has a number of advantages over methods constructed starting from flux coordinates, allowing for more flexible coding in a variety of situations including X-point configurations. In light of these findings, a plasma simulation code FENICIA has been developed based on the FCI approach with the ability to tackle a wide class of physical models. The code has been verified on several 3D test models. The accuracy of the approach is tested in particular with respect to the question of spurious radial transport. Tests on 3D models of the drift wave propagation and of the Ion Temperature Gradient (ITG) instability in cylindrical geometry in the linear regime demonstrate again the high quality of the numerical method. Finally, the FCI approach is shown to be able to deal with an X-point configuration such as one with a magnetic island with good convergence and conservation properties. (author) [fr
Methodology for wind turbine blade geometry optimization
Energy Technology Data Exchange (ETDEWEB)
Perfiliev, D.
2013-11-01
Nowadays, the upwind three bladed horizontal axis wind turbine is the leading player on the market. It has been found to be the best industrial compromise in the range of different turbine constructions. The current wind industry innovation is conducted in the development of individual turbine components. The blade constitutes 20-25% of the overall turbine budget. Its optimal operation in particular local economic and wind conditions is worth investigating. The blade geometry, namely the chord, twist and airfoil type distributions along the span, responds to the output measures of the blade performance. Therefore, the optimal wind blade geometry can improve the overall turbine performance. The objectives of the dissertation are focused on the development of a methodology and specific tool for the investigation of possible existing wind blade geometry adjustments. The novelty of the methodology presented in the thesis is the multiobjective perspective on wind blade geometry optimization, particularly taking simultaneously into account the local wind conditions and the issue of aerodynamic noise emissions. The presented optimization objective approach has not been investigated previously for the implementation in wind blade design. The possibilities to use different theories for the analysis and search procedures are investigated and sufficient arguments derived for the usage of proposed theories. The tool is used for the test optimization of a particular wind turbine blade. The sensitivity analysis shows the dependence of the outputs on the provided inputs, as well as its relative and absolute divergences and instabilities. The pros and cons of the proposed technique are seen from the practical implementation, which is documented in the results, analysis and conclusion sections. (orig.)
Explicitly computing geodetic coordinates from Cartesian coordinates
Zeng, Huaien
2013-04-01
This paper presents a new form of quartic equation based on Lagrange's extremum law and a Groebner basis under the constraint that the geodetic height is the shortest distance between a given point and the reference ellipsoid. A very explicit and concise formulae of the quartic equation by Ferrari's line is found, which avoids the need of a good starting guess for iterative methods. A new explicit algorithm is then proposed to compute geodetic coordinates from Cartesian coordinates. The convergence region of the algorithm is investigated and the corresponding correct solution is given. Lastly, the algorithm is validated with numerical experiments.
Control Coordination of Large Scale Hereditary Systems.
1985-07-01
Theory - A Hilbert Space Approach, (Academic Press, New York, 1982). [4] W. Findeisen , F. N. Bailey, M. Brdys, K Malinowski, P. Tatjewski and A. Wozniak... Findeisen et al. (1980), in the sense that local models are used in the design of component control laws and a higher level coordination problem is...Vol. 1, pp. 590-591, 1985. 3. W. Findeisen , F.N. Bailley, M. Brdys, K. Malinowski, P. Tatjewski and A. Wozniak, Control Coordination in Hierarchical
Cieslinski, Jan L.; Ferapontov, Eugene V.; Kitaev, Alexander V.; Nimmo, Jonathan J. C.
2009-10-01
-component dispersionless Boussinesq-type system. T E Kouloukas and V G Papageorgiou introduce a family of nonparametric Yang-Baxter maps obtained by re-factorization of matrix polynomials of first degree. These maps are Poisson with respect to the Sklyanin bracket, and their degenerations are connected to known integrable systems on quad-graphs. S V Manakov and P M Santini apply a novel version of the inverse scattering transform based on Lax pairs in multidimensional commuting vector fields to the heavenly and Pavlov equations, establishing that their localized solutions evolve without breaking, and constructing the long-time behaviour of the corresponding Cauchy problems. Discretizations of integrable geometric models depend heavily on the coordinates used. M Nieszporski and A Sym show how to discretize Bianchi surfaces (associated with an elliptic version of the Ernst equation) in arbitrary parametrization. C Rogers and A Szereszewski study the Bäcklund transformation for L-isothermic surfaces in the original Bianchi formulation. They establish a connection between this transformation and a nonhomogeneous linear Schrödinger equation and construct a class of generalized Dupin cyclides. W K Schief, A Szereszewski and C Rogers study a classical system of equilibrium equations for shell membranes. Various examples of viable membrane geometries lead to remarkable geometric configurations such as generalized Dupin cyclides and L-minimal surfaces. A Sergyeyev constructs infinite hierarchies of nonlocal higher symmetries for the oriented associativity equations using the spectral problem. The hierarchies in question generalize those constructed by Chen, Kontsevich and Schwarz for the WDVV equations. J Shiraishi and Y Tutiya study an integro-differential equation which generalizes the periodic intermediate long wave equation. The kernel of the singular integral involved is a second order difference of the Weierstrass ζ-function. Using Sato's formulation, the authors
Helliwell, John R.; Tanley, Simon W. M.; Schreurs, Antoine M. M.; Kroon - Batenburg, Louise
2016-01-01
Following the interest of L Messori and A Merlino 2016 Coordination Chemistry Reviews in the platinum ions coordination geometries in our PDB entries 4dd4 and 4dd6 we have extended our original analyses.
Complex analysis and CR geometry
Zampieri, Giuseppe
2008-01-01
Cauchy-Riemann (CR) geometry is the study of manifolds equipped with a system of CR-type equations. Compared to the early days when the purpose of CR geometry was to supply tools for the analysis of the existence and regularity of solutions to the \\bar\\partial-Neumann problem, it has rapidly acquired a life of its own and has became an important topic in differential geometry and the study of non-linear partial differential equations. A full understanding of modern CR geometry requires knowledge of various topics such as real/complex differential and symplectic geometry, foliation theory, the geometric theory of PDE's, and microlocal analysis. Nowadays, the subject of CR geometry is very rich in results, and the amount of material required to reach competence is daunting to graduate students who wish to learn it. However, the present book does not aim at introducing all the topics of current interest in CR geometry. Instead, an attempt is made to be friendly to the novice by moving, in a fairly relaxed way, f...
The geometry description markup language
International Nuclear Information System (INIS)
Chytracek, R.
2001-01-01
Currently, a lot of effort is being put on designing complex detectors. A number of simulation and reconstruction frameworks and applications have been developed with the aim to make this job easier. A very important role in this activity is played by the geometry description of the detector apparatus layout and its working environment. However, no real common approach to represent geometry data is available and such data can be found in various forms starting from custom semi-structured text files, source code (C/C++/FORTRAN), to XML and database solutions. The XML (Extensible Markup Language) has proven to provide an interesting approach for describing detector geometries, with several different but incompatible XML-based solutions existing. Therefore, interoperability and geometry data exchange among different frameworks is not possible at present. The author introduces a markup language for geometry descriptions. Its aim is to define a common approach for sharing and exchanging of geometry description data. Its requirements and design have been driven by experience and user feedback from existing projects which have their geometry description in XML
Complex geometry and quantum string theory
International Nuclear Information System (INIS)
Belavin, A.A.; Knizhnik, V.G.
1986-01-01
Summation over closed oriented surfaces of genus p ≥ 2 (p - loop vacuum amplitudes in boson string theory) in a critical dimensions D=26 is reduced to integration over M p space of complex structures of Riemann surfaces of genus p. The analytic properties of the integration measure as a function of the complex coordinates on M p are studied. It is shown that the measure multiplied by (det Im τ-circumflex) 13 (τ-circumflex is the surface period matrix) is the square of the modulus of a function which is holomorphic on M p and does not vanish anywhere. The function has a second order pole at infinity of compactified space of moduli M p . These properties define the measure uniquely up to a constant multiple and this permits one to set up explicitformulae for p=2,3 in terms of the theta-constants. Power and logarithmic divergences connected with renormalization of the tachyon wave function and of the slope respectively are involved in the theory. Quantum geometry of critical strings turns out to be a complex geometry
PREFACE: Algebra, Geometry, and Mathematical Physics 2010
Stolin, A.; Abramov, V.; Fuchs, J.; Paal, E.; Shestopalov, Y.; Silvestrov, S.
2012-02-01
This proceedings volume presents results obtained by the participants of the 6th Baltic-Nordic workshop 'Algebra, Geometry, and Mathematical Physics (AGMP-6)' held at the Sven Lovén Centre for Marine Sciences in Tjärnö, Sweden on October 25-30, 2010. The Baltic-Nordic Network AGMP 'Algebra, Geometry, and Mathematical Physics' http://www.agmp.eu was created in 2005 on the initiative of two Estonian universities and two Swedish universities: Tallinn University of Technology represented by Eugen Paal (coordinator of the network), Tartu University represented by Viktor Abramov, Lund University represented by Sergei Silvestrov, and Chalmers University of Technology and the University of Gothenburg represented by Alexander Stolin. The goal was to promote international and interdisciplinary cooperation between scientists and research groups in the countries of the Baltic-Nordic region in mathematics and mathematical physics, with special emphasis on the important role played by algebra and geometry in modern physics, engineering and technologies. The main activities of the AGMP network consist of a series of regular annual international workshops, conferences and research schools. The AGMP network also constitutes an important educational forum for scientific exchange and dissimilation of research results for PhD students and Postdocs. The network has expanded since its creation, and nowadays its activities extend beyond countries in the Baltic-Nordic region to universities in other European countries and participants from elsewhere in the world. As one of the important research-dissimilation outcomes of its activities, the network has a tradition of producing high-quality research proceedings volumes after network events, publishing them with various international publishers. The PDF also contains the following: List of AGMP workshops and other AGMP activities Main topics discussed at AGMP-6 Review of AGMP-6 proceedings Acknowledgments List of Conference Participants
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
Differential geometry curves, surfaces, manifolds
Kohnel, Wolfgang
2002-01-01
This carefully written book is an introduction to the beautiful ideas and results of differential geometry. The first half covers the geometry of curves and surfaces, which provide much of the motivation and intuition for the general theory. Special topics that are explored include Frenet frames, ruled surfaces, minimal surfaces and the Gauss-Bonnet theorem. The second part is an introduction to the geometry of general manifolds, with particular emphasis on connections and curvature. The final two chapters are insightful examinations of the special cases of spaces of constant curvature and Einstein manifolds. The text is illustrated with many figures and examples. The prerequisites are undergraduate analysis and linear algebra.
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 lin...
Secant cumulants and toric geometry
Michalek, M.; Oeding, L.; Zwiernik, P.W.
2012-01-01
We study the secant line variety of the Segre product of projective spaces using special cumulant coordinates adapted for secant varieties. We show that the secant variety is covered by open normal toric varieties. We prove that in cumulant coordinates its ideal is generated by binomial quadrics. We
International Nuclear Information System (INIS)
Merkulov, S.A.
1987-01-01
The geometry of local supertwistors is investigated. An ansatz on the form of the supertwistor superconnection is introduced. Because of this restriction on the form of such a superconnection the Yang-Mills equations for the superconnection turn out to be equivalent to the free Bach equations describing the dynamics of simple conformal supergravity. It is shown that the equations of motion of conformal supergravity interacting with a vector superfield admit an analogous interpretation. It is proved that an arbitrary conformally right-flat or left-flat superspace is automatically a solution of the Bach equations
DEFF Research Database (Denmark)
De Chiffre, Leonardo
This document is used in connection with three exercises of 2 hours duration as a part of the course GEOMETRICAL METROLOGY AND MACHINE TESTING. The exercises concern three aspects of coordinate measuring: 1) Measuring and verification of tolerances on coordinate measuring machines, 2) Traceabilit...... and uncertainty during coordinate measurements, 3) Digitalisation and Reverse Engineering. This document contains a short description of each step in the exercise and schemes with room for taking notes of the results.......This document is used in connection with three exercises of 2 hours duration as a part of the course GEOMETRICAL METROLOGY AND MACHINE TESTING. The exercises concern three aspects of coordinate measuring: 1) Measuring and verification of tolerances on coordinate measuring machines, 2) Traceability...
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, ...
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...
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.
Symplectic geometry and Fourier analysis
Wallach, Nolan R
2018-01-01
Suitable for graduate students in mathematics, this monograph covers differential and symplectic geometry, homogeneous symplectic manifolds, Fourier analysis, metaplectic representation, quantization, Kirillov theory. Includes Appendix on Quantum Mechanics by Robert Hermann. 1977 edition.
Topology and geometry for physicists
Nash, Charles
1983-01-01
Differential geometry and topology are essential tools for many theoretical physicists, particularly in the study of condensed matter physics, gravity, and particle physics. Written by physicists for physics students, this text introduces geometrical and topological methods in theoretical physics and applied mathematics. It assumes no detailed background in topology or geometry, and it emphasizes physical motivations, enabling students to apply the techniques to their physics formulas and research. ""Thoroughly recommended"" by The Physics Bulletin, this volume's physics applications range fr
Bainbridge, Hannah E; Menten, Martin J; Fast, Martin F; Nill, Simeon; Oelfke, Uwe; McDonald, Fiona
2017-11-01
This study investigates the feasibility and potential benefits of radiotherapy with a 1.5T MR-Linac for locally advanced non-small cell lung cancer (LA NSCLC) patients. Ten patients with LA NSCLC were retrospectively re-planned six times: three treatment plans were created according to a protocol for conventionally fractionated radiotherapy and three treatment plans following guidelines for isotoxic target dose escalation. In each case, two plans were designed for the MR-Linac, either with standard (∼7mm) or reduced (∼3mm) planning target volume (PTV) margins, while one conventional linac plan was created with standard margins. Treatment plan quality was evaluated using dose-volume metrics or by quantifying dose escalation potential. All generated treatment plans fulfilled their respective planning constraints. For conventionally fractionated treatments, MR-Linac plans with standard margins had slightly increased skin dose when compared to conventional linac plans. Using reduced margins alleviated this issue and decreased exposure of several other organs-at-risk (OAR). Reduced margins also enabled increased isotoxic target dose escalation. It is feasible to generate treatment plans for LA NSCLC patients on a 1.5T MR-Linac. Margin reduction, facilitated by an envisioned MRI-guided workflow, enables increased OAR sparing and isotoxic target dose escalation for the respective treatment approaches. Copyright © 2017 The Authors. Published by Elsevier B.V. All rights reserved.
Emergent Geometry from Entropy and Causality
Engelhardt, Netta
In this thesis, we investigate the connections between the geometry of spacetime and aspects of quantum field theory such as entanglement entropy and causality. This work is motivated by the idea that spacetime geometry is an emergent phenomenon in quantum gravity, and that the physics responsible for this emergence is fundamental to quantum field theory. Part I of this thesis is focused on the interplay between spacetime and entropy, with a special emphasis on entropy due to entanglement. In general spacetimes, there exist locally-defined surfaces sensitive to the geometry that may act as local black hole boundaries or cosmological horizons; these surfaces, known as holographic screens, are argued to have a connection with the second law of thermodynamics. Holographic screens obey an area law, suggestive of an association with entropy; they are also distinguished surfaces from the perspective of the covariant entropy bound, a bound on the total entropy of a slice of the spacetime. This construction is shown to be quite general, and is formulated in both classical and perturbatively quantum theories of gravity. The remainder of Part I uses the Anti-de Sitter/ Conformal Field Theory (AdS/CFT) correspondence to both expand and constrain the connection between entanglement entropy and geometry. The AdS/CFT correspondence posits an equivalence between string theory in the "bulk" with AdS boundary conditions and certain quantum field theories. In the limit where the string theory is simply classical General Relativity, the Ryu-Takayanagi and more generally, the Hubeny-Rangamani-Takayanagi (HRT) formulae provide a way of relating the geometry of surfaces to entanglement entropy. A first-order bulk quantum correction to HRT was derived by Faulkner, Lewkowycz and Maldacena. This formula is generalized to include perturbative quantum corrections in the bulk at any (finite) order. Hurdles to spacetime emergence from entanglement entropy as described by HRT and its quantum
Spectral dimension of quantum geometries
International Nuclear Information System (INIS)
Calcagni, Gianluca; Oriti, Daniele; Thürigen, Johannes
2014-01-01
The spectral dimension is an indicator of geometry and topology of spacetime and a tool to compare the description of quantum geometry in various approaches to quantum gravity. This is possible because it can be defined not only on smooth geometries but also on discrete (e.g., simplicial) ones. In this paper, we consider the spectral dimension of quantum states of spatial geometry defined on combinatorial complexes endowed with additional algebraic data: the kinematical quantum states of loop quantum gravity (LQG). Preliminarily, the effects of topology and discreteness of classical discrete geometries are studied in a systematic manner. We look for states reproducing the spectral dimension of a classical space in the appropriate regime. We also test the hypothesis that in LQG, as in other approaches, there is a scale dependence of the spectral dimension, which runs from the topological dimension at large scales to a smaller one at short distances. While our results do not give any strong support to this hypothesis, we can however pinpoint when the topological dimension is reproduced by LQG quantum states. Overall, by exploring the interplay of combinatorial, topological and geometrical effects, and by considering various kinds of quantum states such as coherent states and their superpositions, we find that the spectral dimension of discrete quantum geometries is more sensitive to the underlying combinatorial structures than to the details of the additional data associated with them. (paper)
Location Discovery Based on Fuzzy Geometry in Passive Sensor Networks
Directory of Open Access Journals (Sweden)
Rui Wang
2011-01-01
Full Text Available Location discovery with uncertainty using passive sensor networks in the nation's power grid is known to be challenging, due to the massive scale and inherent complexity. For bearings-only target localization in passive sensor networks, the approach of fuzzy geometry is introduced to investigate the fuzzy measurability for a moving target in R2 space. The fuzzy analytical bias expressions and the geometrical constraints are derived for bearings-only target localization. The interplay between fuzzy geometry of target localization and the fuzzy estimation bias for the case of fuzzy linear observer trajectory is analyzed in detail in sensor networks, which can realize the 3-dimensional localization including fuzzy estimate position and velocity of the target by measuring the fuzzy azimuth angles at intervals of fixed time. Simulation results show that the resulting estimate position outperforms the traditional least squares approach for localization with uncertainty.
Unusual Coordination Behavior of Cr3+ in Microporous Aluminophosphates
Beale, AM; Grandjean, D; Kornatowski, J; Glatzel, P; de Groot, FMF; Weckhuysen, BM
2006-01-01
A CrAPO-5 molecular sieve has been investigated with X-ray absorption spectroscopy (EXAFS-XANES) as dehydrated material and after loading with water and ammonia to unravel the coordination geometries of Cr3+ in the framework of a microporous crystalline aluminophosphate, more particularly of the
Analytical geometry of three dimensions
McCrea, William Hunter
1947-01-01
Brief but rigorous, this text is geared toward advanced undergraduates and graduate students. It covers the coordinate system, planes and lines, spheres, homogeneous coordinates, general equations of the second degree, quadric in Cartesian coordinates, and intersection of quadrics.Mathematician, physicist, and astronomer, William H. McCrea conducted research in many areas and is best known for his work on relativity and cosmology. McCrea studied and taught at universities around the world, and this book is based on a series of his lectures.
Topology, Geometry, and Mechanics of Z -Plasty
Matsumoto, Elisabetta A.; Liang, Haiyi; Mahadevan, L.
2018-02-01
Reconstructive surgeries often use topological manipulation of tissue to minimize postoperative scarring. The most common version of this, Z -plasty, involves modifying a straight line cut into a Z shape, followed by a rotational transposition of the resulting triangular pedicle flaps, and a final restitching of the wound. This locally reorients the anisotropic stress field and reduces the potential for scarring. We analyze the planar geometry and mechanics of the Z -plasty to quantify the rotation of the overall stress field and the local forces on the restitched cut using theory, simulations, and simple physical Z -plasty experiments with foam sheets that corroborate each other. Our study rationalizes the most typical surgical choice of this angle, and opens the way for a range of surgical decisions by characterizing the stresses along the cut.
Geometries inherent to N=1 supergravities
International Nuclear Information System (INIS)
Galperin, A.S.; Ogievetsky, V.I.; Sokatchev, E.S.
1981-01-01
The first part of the talk is devoted to a consideration of linearized N=1 supergravities. The second main part deals with complex geometries inherent to different N=1 supergravities. A special attention is paid to a new version with local symmetry. It is connected to the special nonminimal case (n=0) having a remarkable property of supervolume preservation in Csup(4.4) superspace. Therefore the superdeterminant of change of variables from left to right-handed Rsup(4.4) parametrization is a dimensionless scalar. This geometric invariant has to be constrained to obtain an action. Solving such a constraint on vector and spinor prepotentials in Wess-Zumino gauge one obtains the new supergravity with 12+12 fields and local symmetry. A possible relaxation of this constraint is briefly considered (16+16 fields version) [ru
Coordination control of distributed systems
Villa, Tiziano
2015-01-01
This book describes how control of distributed systems can be advanced by an integration of control, communication, and computation. The global control objectives are met by judicious combinations of local and nonlocal observations taking advantage of various forms of communication exchanges between distributed controllers. Control architectures are considered according to increasing degrees of cooperation of local controllers: fully distributed or decentralized control, control with communication between controllers, coordination control, and multilevel control. The book covers also topics bridging computer science, communication, and control, like communication for control of networks, average consensus for distributed systems, and modeling and verification of discrete and of hybrid systems. Examples and case studies are introduced in the first part of the text and developed throughout the book. They include: control of underwater vehicles, automated-guided vehicles on a container terminal, contro...
Movement constraints on interpersonal coordination and communication.
Tolston, Michael T; Shockley, Kevin; Riley, Michael A; Richardson, Michael J
2014-10-01
The present study investigated how constraining movement affects interpersonal coordination and joint cognitive performance. Pairs of participants worked cooperatively to solve picture-puzzle tasks in which they conversed to identify differences between pictures in 3 degree-of-constraint conditions: both participants were free to move their hands (free-free; FF); both participants' hands were restrained (restrained-restrained; RR); and the hands of 1 participant were free while the hands of the other participant were restrained (free-restrained; FR). Eye tracking data were collected, and movement was measured at the waist, hand, and head. Data were analyzed using Cross-Recurrence Quantification Analysis (CRQ). Postural sway coordination, gaze coordination, and task performance were predicted to be highest in FF, followed by RR, and then by FR. Results showed the asymmetric FR condition generally exhibited lesser degrees of coordination than the symmetric Conditions FF and RR, and that the patterning of coordination in the symmetric conditions varied across the measured body segments. These results demonstrate that movement restraints affect not only interpersonal postural coordination, but also joint attention. Additionally, significant positive relationships were found between task performance and total amount of anterior-posterior movement measured at the head, hand and waist; number of utterances; and number of differences pairs found in the puzzles. These findings indicate a relationship between movement and task performance consistent with the hypotheses that both interpersonal coordination and cognitive performance are sensitive to local action constraints.
Regional transit coordination guidebook.
2009-01-01
Constant growth in rural areas and extensive suburban development have contributed to increasingly more people needing seamless and adequate public transportation into and from nearby cities. Coordinating existing services or determining the need for...
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...
Developmental coordination disorder
Developmental coordination disorder can lead to: Learning problems Low self-esteem resulting from poor ability at sports and teasing by other children Repeated injuries Weight gain as a result of not wanting to participate ...
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
Data Management Coordinators (DMC)
The Regional Data Management Coordinators (DMCs) were identified to serve as the primary contact for each region for all Water Quality Framework activities. They will facilitate and communicate information to the necessary individuals at the region and tra
Zlatkina, O. Yu
2018-04-01
There is a relationship between the service properties of component parts and their geometry; therefore, to predict and control the operational characteristics of parts and machines, it is necessary to measure their geometrical specifications. In modern production, a coordinate measuring machine is the advanced measuring instrument of the products geometrical specifications. The analysis of publications has shown that during the coordinate measurements the problems of choosing locating chart of parts and coordination have not been sufficiently studied. A special role in the coordination of the part is played by the coordinate axes informational content. Informational content is the sum of the degrees of freedom limited by the elementary item of a part. The coordinate planes of a rectangular coordinate system have different informational content (three, two, and one). The coordinate axes have informational content of four, two and zero. The higher the informational content of the coordinate plane or axis, the higher its priority for reading angular and linear coordinates is. The geometrical model production of the coordinate measurements object taking into account the information content of coordinate planes and coordinate axes allows us to clearly reveal the interrelationship of the coordinates of the deviations in location, sizes and deviations of their surfaces shape. The geometrical model helps to select the optimal locating chart of parts for bringing the machine coordinate system to the part coordinate system. The article presents an algorithm the model production of geometrical specifications using the example of the piston rod of a compressor.
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.
The generator coordinate method in nuclear physics
International Nuclear Information System (INIS)
Giraud, B.G.
1981-01-01
The generator coordinate method is introduced as a physical description of a N-body system in a subspace of a reduced number of degrees of freedom. Special attention is placed on the identification of these special, 'collective' degrees of freedom. It is shown in particular that the method has close links with the Born-Oppenheimer approximation and also that considerations of differential geometry are useful in the theory. A set of applications is discussed and in particular the case of nuclear collisions is considered. (Author) [pt
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....... Using the CSCW framework of coordination mechanisms, we have elicited six general factors influencing the integration of the groupware application in two situations....
Coordinate-invariant regularization
International Nuclear Information System (INIS)
Halpern, M.B.
1987-01-01
A general phase-space framework for coordinate-invariant regularization is given. The development is geometric, with all regularization contained in regularized DeWitt Superstructures on field deformations. Parallel development of invariant coordinate-space regularization is obtained by regularized functional integration of the momenta. As representative examples of the general formulation, the regularized general non-linear sigma model and regularized quantum gravity are discussed. copyright 1987 Academic Press, Inc
Coordinate transformations and matter waves cloaking
International Nuclear Information System (INIS)
Mohammadi, G.R.; Moghaddam, A.G.; Mohammadkhani, R.
2016-01-01
Transformation method provides an efficient tool to control wave propagation inside the materials. Using the coordinate transformation approach, we study invisibility cloaks with sphere, cylinder and ellipsoid structures for electronic waves propagation. The underlying physics behind this investigation is the fact that Schrödinger equation with position dependent mass tensor and potentials has a covariant form which follows the coordinate transformation. Using this technique we obtain the exact spatial form of the mass tensor and potentials for a variety of cloaks with different shapes. - Highlights: • Invisibility cloaks for matter waves with three different geometries. • Exact analytical form of the effective mass tensor and potential. • Analogy between cloaking for quantum mechanical waves with classical electromagnetic waves. • Possible experimental realization in engineered semiconducting structures.
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.
Nonlinear Methods in Riemannian and Kählerian Geometry
Jost, Jürgen
1991-01-01
In this book, I present an expanded version of the contents of my lectures at a Seminar of the DMV (Deutsche Mathematiker Vereinigung) in Düsseldorf, June, 1986. The title "Nonlinear methods in complex geometry" already indicates a combination of techniques from nonlinear partial differential equations and geometric concepts. In older geometric investigations, usually the local aspects attracted more attention than the global ones as differential geometry in its foundations provides approximations of local phenomena through infinitesimal or differential constructions. Here, all equations are linear. If one wants to consider global aspects, however, usually the presence of curvature Ieads to a nonlinearity in the equations. The simplest case is the one of geodesics which are described by a system of second ordernonlinear ODE; their linearizations are the Jacobi fields. More recently, nonlinear PDE played a more and more pro~inent röle in geometry. Let us Iist some of the most important ones: - harmonic maps ...
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.
Flux compactifications and generalized geometries
International Nuclear Information System (INIS)
Grana, Mariana
2006-01-01
Following the lectures given at CERN Winter School 2006, we present a pedagogical overview of flux compactifications and generalized geometries, concentrating on closed string fluxes in type II theories. We start by reviewing the supersymmetric flux configurations with maximally symmetric four-dimensional spaces. We then discuss the no-go theorems (and their evasion) for compactifications with fluxes. We analyse the resulting four-dimensional effective theories for Calabi-Yau and Calabi-Yau orientifold compactifications, concentrating on the flux-induced superpotentials. We discuss the generic mechanism of moduli stabilization and illustrate with two examples: the conifold in IIB and a T 6 /(Z 3 x Z 3 ) torus in IIA. We finish by studying the effective action and flux vacua for generalized geometries in the context of generalized complex geometry
Flux compactifications and generalized geometries
Energy Technology Data Exchange (ETDEWEB)
Grana, Mariana [Service de Physique Theorique, CEA/Saclay, 91191 Gif-sur-Yvette Cedex (France)
2006-11-07
Following the lectures given at CERN Winter School 2006, we present a pedagogical overview of flux compactifications and generalized geometries, concentrating on closed string fluxes in type II theories. We start by reviewing the supersymmetric flux configurations with maximally symmetric four-dimensional spaces. We then discuss the no-go theorems (and their evasion) for compactifications with fluxes. We analyse the resulting four-dimensional effective theories for Calabi-Yau and Calabi-Yau orientifold compactifications, concentrating on the flux-induced superpotentials. We discuss the generic mechanism of moduli stabilization and illustrate with two examples: the conifold in IIB and a T{sup 6} /(Z{sub 3} x Z{sub 3}) torus in IIA. We finish by studying the effective action and flux vacua for generalized geometries in the context of generalized complex geometry.
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...
Electrodynamics and Spacetime Geometry: Foundations
Cabral, Francisco; Lobo, Francisco S. N.
2017-02-01
We explore the intimate connection between spacetime geometry and electrodynamics. This link is already implicit in the constitutive relations between the field strengths and excitations, which are an essential part of the axiomatic structure of electromagnetism, clearly formulated via integration theory and differential forms. We review the foundations of classical electromagnetism based on charge and magnetic flux conservation, the Lorentz force and the constitutive relations. These relations introduce the conformal part of the metric and allow the study of electrodynamics for specific spacetime geometries. At the foundational level, we discuss the possibility of generalizing the vacuum constitutive relations, by relaxing the fixed conditions of homogeneity and isotropy, and by assuming that the symmetry properties of the electro-vacuum follow the spacetime isometries. The implications of this extension are briefly discussed in the context of the intimate connection between electromagnetism and the geometry (and causal structure) of spacetime.
Dayside merging and cusp geometry
International Nuclear Information System (INIS)
Crooker, N.U.
1979-01-01
Geometrical considerations are presented to show that dayside magnetic merging when constrained to act only where the fields are antiparallel results in lines of merging that converge at the polar cusps. An important consequence of this geometry is that no accelerated flows are predicted across the dayside magnetopause. Acceleration owing to merging acts in opposition to the magnetosheath flow at the merging point and produces the variably directed, slower-than-magnetosheath flows observed in the entry layer. Another consequence of the merging geometry is that much of the time closed field lines constitute the subsolar region of the magnetopause. The manner in which the polar cap convection patterns predicted by the proposed geometry change as the interplanetary field is rotated through 360 0 provides a unifying description of how the observed single circular vortex and the crescent-shaped double vortex patterns mutually evolve under the influence of a single operating principle
DOGBONE GEOMETRY FOR RECIRCULATING ACCELERATORS
International Nuclear Information System (INIS)
BERG, J.S.; JOHNSTONE, C.; SUMMERS, D.
2001-01-01
Most scenarios for accelerating muons require recirculating acceleration. A racetrack shape for the accelerator requires particles with lower energy in early passes to traverse almost the same length of arc as particles with the highest energy. This extra arc length may lead to excess decays and excess cost. Changing the geometry to a dogbone shape, where there is a single linac and the beam turns completely around at the end of the linac, returning to the same end of the linac from which it exited, addresses this problem. In this design, the arc lengths can be proportional to the particle's momentum. This paper proposes an approximate cost model for a recirculating accelerator, attempts to make cost-optimized designs for both racetrack and dogbone geometries, and demonstrates that the dogbone geometry does appear to be more cost effective
Stochastic Strategy Adjustment in Coordination Games
Kosfeld, M.
1999-01-01
We explore a model of equilibrium selection in coordination games, where agents stochastically adjust their strategies to changes in their local environment. Instead of playing perturbed best-response, we assume that agents follow a rule of "switching to better strategies more likely". We relate
Fault geometry and earthquake mechanics
Directory of Open Access Journals (Sweden)
D. J. Andrews
1994-06-01
Full Text Available Earthquake mechanics may be determined by the geometry of a fault system. Slip on a fractal branching fault surface can explain: 1 regeneration of stress irregularities in an earthquake; 2 the concentration of stress drop in an earthquake into asperities; 3 starting and stopping of earthquake slip at fault junctions, and 4 self-similar scaling of earthquakes. Slip at fault junctions provides a natural realization of barrier and asperity models without appealing to variations of fault strength. Fault systems are observed to have a branching fractal structure, and slip may occur at many fault junctions in an earthquake. Consider the mechanics of slip at one fault junction. In order to avoid a stress singularity of order 1/r, an intersection of faults must be a triple junction and the Burgers vectors on the three fault segments at the junction must sum to zero. In other words, to lowest order the deformation consists of rigid block displacement, which ensures that the local stress due to the dislocations is zero. The elastic dislocation solution, however, ignores the fact that the configuration of the blocks changes at the scale of the displacement. A volume change occurs at the junction; either a void opens or intense local deformation is required to avoid material overlap. The volume change is proportional to the product of the slip increment and the total slip since the formation of the junction. Energy absorbed at the junction, equal to confining pressure times the volume change, is not large enongh to prevent slip at a new junction. The ratio of energy absorbed at a new junction to elastic energy released in an earthquake is no larger than P/µ where P is confining pressure and µ is the shear modulus. At a depth of 10 km this dimensionless ratio has th value P/µ= 0.01. As slip accumulates at a fault junction in a number of earthquakes, the fault segments are displaced such that they no longer meet at a single point. For this reason the
KEMAJUAN BELAJAR SISWA PADA GEOMETRI TRANSFORMASI MENGGUNAKAN AKTIVITAS REFLEKSI GEOMETRI
Directory of Open Access Journals (Sweden)
Irkham Ulil Albab
2014-10-01
Full Text Available Abstrak: Penelitian ini bertujuan untuk mendeskripsikan kemajuan belajar siswa pada materi geometri transformasi yang didukung dengan serangkaian aktivitas belajar berdasarkan Pendidikan Matematika Realistik Indonesia. Penelitian didesain melalui tiga tahap, yaitu tahapan perancangan desain awal, pengujian desain melalui pembelajaran awal dan pembelajaran eksperimental, dan tahap analisis retrospektif. Dalam penelitian ini, Hypothetical Learning Trajectory, HLT (HLT berperan penting sebagai desain pembelajaran sekaligus instrumen penelitian. HLT diujikan terhadap 26 siswa kelas VII. Data dikumpulkan dengan teknik wawancara, pengamatan, dan catatan lapangan. Hasil penelitian menunjukkan bahwa desain pembelajaran ini mampu menstimulasi siswa untuk memberikan karakteristik refleksi dan transformasi geometri lainnya secara informal, mengklasifikasikannya dalam transformasi isometri pada level kedua, dan menemukan garis bantuan refleksi pada level yang lebih formal. Selain itu, garis bantuan refleksi digunakan oleh siswa untuk menggambar bayangan refleksi dan pola pencerminan serta memahami bentuk rotasi dan translasi sebagai kombinasi refleksi adalah level tertinggi. Keyword: transformasi geometri, kombinasi refleksi, rotasi, translasi, design research, HLT STUDENTS’ LEARNING PROGRESS ON TRANSFORMATION GEOMETRY USING THE GEOMETRY REFLECTION ACTIVITIES Abstract: This study was aimed at describing the students’ learning progress on transformation geometry supported by a set of learning activities based on Indonesian Realistic Mathematics Education. The study was designed into three stages, that is, the preliminary design stage, the design testing through initial instruction and experiment, and the restrospective analysis stage. In this study, Hypothetical Learning Trajectory (HLT played an important role as an instructional design and a research instrument. HLT was tested to 26 seventh grade students. The data were collected through interviews
Graphical debugging of combinational geometry
International Nuclear Information System (INIS)
Burns, T.J.; Smith, M.S.
1992-01-01
A graphical debugger for combinatorial geometry being developed at Oak Ridge National Laboratory is described. The prototype debugger consists of two parts: a FORTRAN-based ''view'' generator and a Microsoft Windows application for displaying the geometry. Options and features of both modules are discussed. Examples illustrating the various options available are presented. The potential for utilizing the images produced using the debugger as a visualization tool for the output of the radiation transport codes is discussed as is the future direction of the development
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
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
Comparison theorems in Riemannian geometry
Cheeger, Jeff
2008-01-01
The central theme of this book is the interaction between the curvature of a complete Riemannian manifold and its topology and global geometry. The first five chapters are preparatory in nature. They begin with a very concise introduction to Riemannian geometry, followed by an exposition of Toponogov's theorem-the first such treatment in a book in English. Next comes a detailed presentation of homogeneous spaces in which the main goal is to find formulas for their curvature. A quick chapter of Morse theory is followed by one on the injectivity radius. Chapters 6-9 deal with many of the most re
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 frame-independent entities. We depart from a subject well known by students, which is the three-dimensional geometric space in order to compare, afterwards, with the treatment of four-dimensional space in the special relativity. The differences and similarities between these two subjects are also...
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
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
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
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.
Classification of digital affine noncommutative geometries
Majid, Shahn; Pachoł, Anna
2018-03-01
It is known that connected translation invariant n-dimensional noncommutative differentials dxi on the algebra k[x1, …, xn] of polynomials in n-variables over a field k are classified by commutative algebras V on the vector space spanned by the coordinates. These data also apply to construct differentials on the Heisenberg algebra "spacetime" with relations [xμ, xν] = λΘμν, where Θ is an antisymmetric matrix, as well as to Lie algebras with pre-Lie algebra structures. We specialise the general theory to the field k =F2 of two elements, in which case translation invariant metrics (i.e., with constant coefficients) are equivalent to making V a Frobenius algebra. We classify all of these and their quantum Levi-Civita bimodule connections for n = 2, 3, with partial results for n = 4. For n = 2, we find 3 inequivalent differential structures admitting 1, 2, and 3 invariant metrics, respectively. For n = 3, we find 6 differential structures admitting 0, 1, 2, 3, 4, 7 invariant metrics, respectively. We give some examples for n = 4 and general n. Surprisingly, not all our geometries for n ≥ 2 have zero quantum Riemann curvature. Quantum gravity is normally seen as a weighted "sum" over all possible metrics but our results are a step towards a deeper approach in which we must also "sum" over differential structures. Over F2 we construct some of our algebras and associated structures by digital gates, opening up the possibility of "digital geometry."
The geometry of the super KP flows
International Nuclear Information System (INIS)
Rabin, J.M.
1991-01-01
A supersymmetric generalization of the Krichever map is used to construct algebro-geometric solutions to the various super Kadomtsev-Petviashvili (SKP) hierarchies. The geometric data required consist of a suitable algebraic supercurve of genus g (generally not a super Riemann surface) with a distinguished point and local coordinates (z, θ) there, and a generic line bundle of degree g-1 with a local trivialization near the point. The resulting solutions to the Manin-Radul SKP system describe coupled deformations of the line bundle and the supercurve itself, in contrast to the ordinary KP system which deforms line bundles but not curves. Two new SKP systems are introduced: An integrable 'Jacobian' system whose solutions describe genuine Jacobian flows, deforming the bundle but not the curve; and a nonintegrable 'maximal' system describing independent deformations of bundle and curve. The Kac-van de Leur SKP system describes the same deformations as the maximal system, but in a different parametrization. (orig.)
The Idea of Order at Geometry Class.
Rishel, Thomas
The idea of order in geometry is explored using the experience of assignments given to undergraduates in a college geometry course "From Space to Geometry." Discussed are the definition of geometry, and earth measurement using architecture, art, and common experience. This discussion concludes with a consideration of the question of whether…
Teaching Spatial Geometry in a Virtual World
DEFF Research Database (Denmark)
Förster, Klaus-Tycho
2017-01-01
Spatial geometry is one of the fundamental mathematical building blocks of any engineering education. However, it is overshadowed by planar geometry in the curriculum between playful early primary education and later analytical geometry, leaving a multi-year gap where spatial geometry is absent...
Power Generation and Distribution via Distributed Coordination Control
Kim, Byeong-Yeon; Oh, Kwang-Kyo; Ahn, Hyo-Sung
2014-01-01
This paper presents power coordination, power generation, and power flow control schemes for supply-demand balance in distributed grid networks. Consensus schemes using only local information are employed to generate power coordination, power generation and power flow control signals. For the supply-demand balance, it is required to determine the amount of power needed at each distributed power node. Also due to the different power generation capacities of each power node, coordination of pow...
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…
Exploring Bundling Theory with Geometry
Eckalbar, John C.
2006-01-01
The author shows how instructors might successfully introduce students in principles and intermediate microeconomic theory classes to the topic of bundling (i.e., the selling of two or more goods as a package, rather than separately). It is surprising how much students can learn using only the tools of high school geometry. To be specific, one can…
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....
Matter in toy dynamical geometries
Konopka, T.J.
2009-01-01
One of the objectives of theories describing quantum dynamical geometry is to compute expectation values of geometrical observables. The results of such computations can be affected by whether or not matter is taken into account. It is thus important to understand to what extent and to what effect
Ca??adas, Mar??a C.; Molina, Marta; Gallardo, Sandra; Mart??nez-Santaolalla, Manuel J.; Pe??as, Mar??a
2010-01-01
In this work we present an activity for High School students in which various mathematical concepts of plane and spatial geometry are involved. The final objective of the proposed tasks is constructing a particular polyhedron, the cube, by using a modality of origami called modular origami.
General Relativity: Geometry Meets Physics
Thomsen, Dietrick E.
1975-01-01
Observing the relationship of general relativity and the geometry of space-time, the author questions whether the rest of physics has geometrical explanations. As a partial answer he discusses current research on subatomic particles employing geometric transformations, and cites the existence of geometrical definitions of physical quantities such…
Learners engaging with transformation geometry
African Journals Online (AJOL)
participants engaged in investigative semi-structured interviews with the resear- chers. ... Keywords: analysis; conversions; transformation geometry; transformations; treatments .... semiotic systems of representation is not only to designate mathematical objects or to com- municate but also to ... Research design. We believe ...
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.
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
Energy Technology Data Exchange (ETDEWEB)
Thangavelu, Sonia G. [Department; Butcher, Ray J. [Department; Cahill, Christopher L. [Department
2015-06-09
Thiophene 2,5-dicarboxylic acid (TDC) was reacted with uranyl acetate dihydrate and one (or none) of six N-donor chelating ligands (2,2'-bipyridine (BPY), 4,4'-dimethyl-2,2'-bipyridine (4-MeBPY), 5,5'-dimethyl-2,2'-bipyridine (5-MeBPY), 6,6'-dimethyl-2,2'-bipyridine (6-MeBPY), 4,4',6,6'-tetramethyl-2,2'-bipyridine (4,6-MeBPY), and tetrakis(2-pyridyl)pyrazine (TPPZ) to result in the crystallization of seven uranyl coordination polymers, which were characterized by their crystal structures and luminescence properties. The seven coordination polymers, Na2[(UO2)2(C6H2O4S)3]·4H2O (1), [(UO2)4(C6H2O4S)5(C10H8N2)2]·C10H10N2·3H2O (2), [(UO2)(C6H2O4S)(C12H12N3)] (3), [(UO2)(C6H2O4S)(C12H12N3)]·H2O (4), [(UO2)2(C6H2O4S)3]·(C12H14N2)·5H2O (5), [(UO2)3(CH3CO2)(C6H2O4S)4](C14H17N2)3·(C14H16N2)·H2O (6), and [(UO2)2(C6H2O4S)3](C24H18N6) (7), consist of either uranyl hexagonal bipyramidal or pentagonal bipyramidal coordination geometries. In all structures, structural variations in the local and global structures of 1–7 are influenced by the positions (or number) of methyl groups or pyridyl rings on the N-donor species, thus resulting in a wide diversity of structures ranging from single chains, double chains, or 2-D sheets. Direct coordination of N-donor ligands to uranyl centers is observed in the chain structures of 2–4 using BPY, 4-MeBPY, and 5-MeBPY, whereas the N-donor species participate as guests (as either neutral or charge balancing species) in the chain and sheet structures of 5–7 using 6-MeBPY, 4,6-MeBPY, and TPPZ, respectively. Compound 1 is the only structure that does not contain any N-donor ligands and thus crystallizes as a 2-D interpenetrating sheet. The luminescent properties of 1–7 are influenced by the direct coordination or noncoordination of N-donor species to uranyl centers. Compounds 2–4 exhibit typical UO22+ emission upon direct coordination of N-donors, but its absence is observed in 1
Mahaffey, Michael L.
One of a series of experimental units for children at the preschool level, this booklet deals with geometric concepts. A unit on volume and a unit on linear measurement are covered; for each unit a discussion of mathematical objectives, a list of materials needed, and a sequence of learning activities are provided. Directions are specified for the…
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...
[Binocular coordination during reading].
Bassou, L; Granié, M; Pugh, A K; Morucci, J P
1992-01-01
Is there an effect on binocular coordination during reading of oculomotor imbalance (heterophoria, strabismus and inadequate convergence) and of functional lateral characteristics (eye preference and perceptually privileged visual laterality)? Recordings of the binocular eye-movements of ten-year-old children show that oculomotor imbalances occur most often among children whose left visual perceptual channel is privileged, and that these subjects can present optomotor dissociation and manifest lack of motor coordination. Close binocular motor coordination is far from being the norm in reading. The faster reader displays saccades of differing spatial amplitude and the slower reader an oculomotor hyperactivity, especially during fixations. The recording of binocular movements in reading appears to be an excellent means of diagnosing difficulties related to visual laterality and to problems associated with oculomotor imbalance.
Discrete differential geometry. Consistency as integrability
Bobenko, Alexander I.; Suris, Yuri B.
2005-01-01
A new field of discrete differential geometry is presently emerging on the border between differential and discrete geometry. Whereas classical differential geometry investigates smooth geometric shapes (such as surfaces), and discrete geometry studies geometric shapes with finite number of elements (such as polyhedra), the discrete differential geometry aims at the development of discrete equivalents of notions and methods of smooth surface theory. Current interest in this field derives not ...
Numerically robust geometry engine for compound solid geometries
International Nuclear Information System (INIS)
Vlachoudis, V.; Sinuela-Pastor, D.
2013-01-01
Monte Carlo programs heavily rely on a fast and numerically robust solid geometry engines. However the success of solid modeling, depends on facilities for specifying and editing parameterized models through a user-friendly graphical front-end. Such a user interface has to be fast enough in order to be interactive for 2D and/or 3D displays, but at the same time numerically robust in order to display possible modeling errors at real time that could be critical for the simulation. The graphical user interface Flair for FLUKA currently employs such an engine where special emphasis has been given on being fast and numerically robust. The numerically robustness is achieved by a novel method of estimating the floating precision of the operations, which dynamically adapts all the decision operations accordingly. Moreover a predictive caching mechanism is ensuring that logical errors in the geometry description are found online, without compromising the processing time by checking all regions. (authors)
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......). We employ nominal recurrence analysis (Orsucci et al 2005, Dale et al 2011) on the decision-making conversations between the participants. We report strong correlations between various indexes of recurrence and collective performance. We argue this method allows us to quantify the qualities...
Three-dimensional tracking of cardiac catheters using an inverse geometry x-ray fluoroscopy system
International Nuclear Information System (INIS)
Speidel, Michael A.; Tomkowiak, Michael T.; Raval, Amish N.; Van Lysel, Michael S.
2010-01-01
Purpose: Scanning beam digital x-ray (SBDX) is an inverse geometry fluoroscopic system with high dose efficiency and the ability to perform continuous real-time tomosynthesis at multiple planes. This study describes a tomosynthesis-based method for 3D tracking of high-contrast objects and present the first experimental investigation of cardiac catheter tracking using a prototype SBDX system. Methods: The 3D tracking algorithm utilizes the stack of regularly spaced tomosynthetic planes that are generated by SBDX after each frame period (15 frames/s). Gradient-filtered versions of the image planes are generated, the filtered images are segmented into object regions, and then a 3D coordinate is calculated for each object region. Two phantom studies of tracking performance were conducted. In the first study, an ablation catheter in a chest phantom was imaged as it was pulled along a 3D trajectory defined by a catheter sheath (10, 25, and 50 mm/s pullback speeds). SBDX tip tracking coordinates were compared to the 3D trajectory of the sheath as determined from a CT scan of the phantom after the registration of the SBDX and CT coordinate systems. In the second study, frame-to-frame tracking precision was measured for six different catheter configurations as a function of image noise level (662-7625 photons/mm 2 mean detected x-ray fluence at isocenter). Results: During catheter pullbacks, the 3D distance between the tracked catheter tip and the sheath centerline was 1.0±0.8 mm (mean ±one standard deviation). The electrode to centerline distances were comparable to the diameter of the catheter tip (2.3 mm), the confining sheath (4 mm outside diameter), and the estimated SBDX-to-CT registration error (±0.7 mm). The tip position was localized for all 332 image frames analyzed and 83% of tracked positions were inside the 3D sheath volume derived from CT. The pullback speeds derived from the catheter trajectories were within 5% of the programed pullback speeds. The
New geometries for black hole horizons
Energy Technology Data Exchange (ETDEWEB)
Armas, Jay [Physique Théorique et Mathématique,Université Libre de Bruxelles and International Solvay Institutes, ULB-Campus Plaine CP231, B-1050 Brussels (Belgium); Blau, Matthias [Albert Einstein Center for Fundamental Physics, University of Bern,Sidlerstrasse 5, 3012 Bern (Switzerland)
2015-07-10
We construct several classes of worldvolume effective actions for black holes by integrating out spatial sections of the worldvolume geometry of asymptotically flat black branes. This provides a generalisation of the blackfold approach for higher-dimensional black holes and yields a map between different effective theories, which we exploit by obtaining new hydrodynamic and elastic transport coefficients via simple integrations. Using Euclidean minimal surfaces in order to decouple the fluid dynamics on different sections of the worldvolume, we obtain local effective theories for ultraspinning Myers-Perry branes and helicoidal black branes, described in terms of a stress-energy tensor, particle currents and non-trivial boost vectors. We then study in detail and present novel compact and non-compact geometries for black hole horizons in higher-dimensional asymptotically flat space-time. These include doubly-spinning black rings, black helicoids and helicoidal p-branes as well as helicoidal black rings and helicoidal black tori in D≥6.
Non-Abelian bubbles in microstate geometries
Energy Technology Data Exchange (ETDEWEB)
Ramírez, Pedro F. [Instituto de Física Teórica UAM/CSIC,C/ Nicolás Cabrera, 13-15, C.University Cantoblanco, E-28049 Madrid (Spain); Institut de Physique Théorique, Université Paris Saclay, CEA, CNRS,Orme des Merisiers bâtiment 774, F-91191 Gif-sur-Yvette (France)
2016-11-24
We find the first smooth bubbling microstate geometries with non-Abelian fields. The solutions constitute an extension of the BPS three-charge smooth microstates. These consist in general families of regular supersymmetric solutions with non-trivial topology, i.e. bubbles, of N=1, d=5 Super-Einstein-Yang-Mills theory, having the asymptotic charges of a black hole or black ring but with no horizon. The non-Abelian fields make their presence at the very heart of the microstate structure: the physical size of the bubbles is affected by the non-Abelian topological charge they carry, which combines with the Abelian flux threading the bubbles to hold them up. Interestingly the non-Abelian fields carry a set of adjustable continuous parameters that do not alter the asymptotics of the solutions but modify the local geometry. This feature can be used to obtain a classically infinite number of microstate solutions with the asymptotics of a single black hole or black ring.
Global Differential Geometry and Global Analysis
Pinkall, Ulrich; Simon, Udo; Wegner, Berd
1991-01-01
All papers appearing in this volume are original research articles and have not been published elsewhere. They meet the requirements that are necessary for publication in a good quality primary journal. E.Belchev, S.Hineva: On the minimal hypersurfaces of a locally symmetric manifold. -N.Blasic, N.Bokan, P.Gilkey: The spectral geometry of the Laplacian and the conformal Laplacian for manifolds with boundary. -J.Bolton, W.M.Oxbury, L.Vrancken, L.M. Woodward: Minimal immersions of RP2 into CPn. -W.Cieslak, A. Miernowski, W.Mozgawa: Isoptics of a strictly convex curve. -F.Dillen, L.Vrancken: Generalized Cayley surfaces. -A.Ferrandez, O.J.Garay, P.Lucas: On a certain class of conformally flat Euclidean hypersurfaces. -P.Gauduchon: Self-dual manifolds with non-negative Ricci operator. -B.Hajduk: On the obstruction group toexistence of Riemannian metrics of positive scalar curvature. -U.Hammenstaedt: Compact manifolds with 1/4-pinched negative curvature. -J.Jost, Xiaowei Peng: The geometry of moduli spaces of stabl...
Aspects of non-geometry in string theory
International Nuclear Information System (INIS)
Patalong, Peter
2013-01-01
This thesis investigates various manifestations of non-geometry in string theory. It utilises different frameworks to study how non-geometry appears in the target space, how non-geometry and non-geometric fluxes are interconnected, how non-geometry can be captured in effective field theories and how a possible extension of the standard string worldsheet model can accommodate non-geometric setups. The first part provides an example that non-geometry can imply non-commutativity of the closed string coordinate fields. Three T-dual frames are investigated, the three-torus with constant H-flux, the twisted torus and the torus with non-geometric flux Q. Under the assumption of dilute flux, a mode expansion and the canonical quantisation are carried out in the second case up to linear order in the flux parameter. T-duality is then used to relate the commutators of the string expansion modes to the coordinate field commutator in the non-geometric third frame. Non-commutativity is found and related to the non-geometric flux Q and the string winding, it therefore appears as an intrinsically string theoretic feature. The second part investigates non-geometry in the context of ten-dimensional effective field theories, i.e. double field theory and supergravity. A field redefinition is implemented that takes the form of a T-duality transformation, it reveals an alternative set of field variables allowing to define non-geometric fluxes Q and R in higher dimensions. The perspective of double field theory provides a geometric interpretation of those by taking into account a new type of covariant winding derivative. The perspective of the ten-dimensional supergravity allows to investigate the interplay between non-geometric field configurations and non-geometric fluxes. For the three-torus example, a well-defined action can be found, and a simple dimensional reduction makes contact to the known four-dimensional potential. It thus proves the correct uplift of Q and R to higher
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.
Differential geometry of groups in string theory
International Nuclear Information System (INIS)
Schmidke, W.B. Jr.
1990-09-01
Techniques from differential geometry and group theory are applied to two topics from string theory. The first topic studied is quantum groups, with the example of GL (1|1). The quantum group GL q (1|1) is introduced, and an exponential description is derived. The algebra and coproduct are determined using the invariant differential calculus method introduced by Woronowicz and generalized by Wess and Zumino. An invariant calculus is also introduced on the quantum superplane, and a representation of the algebra of GL q (1|1) in terms of the super-plane coordinates is constructed. The second topic follows the approach to string theory introduced by Bowick and Rajeev. Here the ghost contribution to the anomaly of the energy-momentum tensor is calculated as the Ricci curvature of the Kaehler quotient space Diff(S 1 )/S 1 . We discuss general Kaehler quotient spaces and derive an expression for their Ricci curvatures. Application is made to the string and superstring diffeomorphism groups, considering all possible choices of subgroup. The formalism is extended to associated holomorphic vector bundles, where the Ricci curvature corresponds to the anomaly for different ghost sea levels. 26 refs
44 CFR 206.42 - Responsibilities of coordinating officers.
2010-10-01
... applications, and counsel individuals, families and businesses concerning available assistance; (3) Coordinate... their appropriate disaster assistance roles under their own legislative authorities and operational... and local disaster relief activities, and implementation of the State emergency plan. The functions...
Near horizon geometry of rotating black holes in five dimensions
International Nuclear Information System (INIS)
Cvetic, M.; Larsen, F.
1998-01-01
We interpret the general rotating black holes in five dimensions as rotating black strings in six dimensions. In the near-horizon limit the geometry is locally AdS 3 x S 3 , as in the non-rotating case. However, the global structure couples the AdS 3 and the S 3 , giving angular velocity to the S 3 . The asymptotic geometry is exploited to count the microstates and recover the precise value of the Bekenstein-Hawking entropy, with rotation taken properly into account. We discuss the perturbation spectrum of the rotating black hole, and its relation to the underlying conformal field theory. (orig.)
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....
Reusability of coordination programs
F. Arbab (Farhad); C.L. Blom (Kees); F.J. Burger (Freek); C.T.H. Everaars (Kees)
1996-01-01
textabstractIsolating computation and communication concerns into separate pure computation and pure coordination modules enhances modularity, understandability, and reusability of parallel and/or distributed software. This can be achieved by moving communication primitives (such as SendMessage and
[Civilian-military coordination].
de Montravel, G
2002-01-01
Current humanitarian emergencies create complex, mutidimensional situations that stimulate simultaneous responses from a wide variety of sources including governments, non-governmental organizations (NGO), United Nations agencies, and private individuals. As a result, it has become essential to establish a coherent framework in which each actor can contribute promptly and effectively to the overall effort. This is the role of the United Nations Office for the Coordination of Humanitarian Affairs. Regardless of the circumstances and level of coordination, cooperation and collaboration between humanitarian and military personnel, it is necessary to bear in mind their objectives. The purpose of humanitarian action is to reduce human suffering. The purpose of military intervention is to stop warfare. The author of this article will discuss the three major obstacles to civilian-military coordination (strategic, tactical, and operational). Operations cannot be conducted smoothly and differences cannot be ironed out without mutual respect between the two parties, an explicit definition of their respective duties and responsibilities, a clear understanding of their cultural differences, and the presence of an organization and facilities for coordination and arbitrage by a neutral referee.
Pesyna, Colin; Pundi, Krishna; Flanders, Martha
2011-03-09
The neural control of hand movement involves coordination of the sensory, motor, and memory systems. Recent studies have documented the motor coordinates for hand shape, but less is known about the corresponding patterns of somatosensory activity. To initiate this line of investigation, the present study characterized the sense of hand shape by evaluating the influence of differences in the amount of grasping or twisting force, and differences in forearm orientation. Human subjects were asked to use the left hand to report the perceived shape of the right hand. In the first experiment, six commonly grasped items were arranged on the table in front of the subject: bottle, doorknob, egg, notebook, carton, and pan. With eyes closed, subjects used the right hand to lightly touch, forcefully support, or imagine holding each object, while 15 joint angles were measured in each hand with a pair of wired gloves. The forces introduced by supporting or twisting did not influence the perceptual report of hand shape, but for most objects, the report was distorted in a consistent manner by differences in forearm orientation. Subjects appeared to adjust the intrinsic joint angles of the left hand, as well as the left wrist posture, so as to maintain the imagined object in its proper spatial orientation. In a second experiment, this result was largely replicated with unfamiliar objects. Thus, somatosensory and motor information appear to be coordinated in an object-based, spatial-coordinate system, sensitive to orientation relative to gravitational forces, but invariant to grasp forcefulness.
Koh, Kyoung Moo; Wong-Foy, Antek G; Matzger, Adam J; Benin, Annabelle I; Willis, Richard R
2012-11-13
The present invention provides compositions of crystalline coordination copolymers wherein multiple organic molecules are assembled to produce porous framework materials with layered or core-shell structures. These materials are synthesized by sequential growth techniques such as the seed growth technique. In addition, the invention provides a simple procedure for controlling functionality.
Insulin fibrillation: The influence and coordination of Zn2+
DEFF Research Database (Denmark)
Frankær, Christian Grundahl; Sønderby, Pernille; Bang, Maria Blanner
2017-01-01
fibrils has been debated for some years. We have therefore investigated the influence and binding geometry of zinc in fibrillated insulin using extended X-ray absorption fine-structure and X-ray absorption near-edge structure spectroscopy. The results were validated with fibre diffraction, Transmission...... Electron Microscopy and Thioflavin T fluorescence measurements. It is well-known that Zn2+ ions coordinate and stabilize the hexameric forms of insulin. However, this study is the first to show that zinc indeed binds to the insulin fibrils. Furthermore, zinc influences the kinetics and the morphology...... of the fibrils. It also shows that zinc coordinates to histidine residues in an environment, which is similar to the coordination seen in the insulin R6 hexamers, where three histidine residues and a chloride ion is coordinating the zinc....
Hydrodynamics of compressible superfluids in confined geometries
International Nuclear Information System (INIS)
Malmi-Kakkada, Abdul N; Valls, Oriol T; Dasgupta, Chandan
2014-01-01
We present a study of the hydrodynamics of compressible superfluids in confined geometries. We use a perturbative procedure in terms of the dimensionless expansion parameter (v/v s ) 2 where v is the typical speed of the flow and v s is the speed of sound. A zero value of this parameter corresponds to the incompressible limit. We apply the procedure to two specific problems: the case of a trapped superfluid with a Gaussian profile of the local density, and that of a superfluid confined in a rotating obstructed cylinder. We find that the corrections due to finite compressibility which are, as expected, negligible for liquid He, are important but amenable to the perturbative treatment for typical ultracold atomic systems. (paper)
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
International Nuclear Information System (INIS)
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
Coordination failure caused by sunspots
DEFF Research Database (Denmark)
Beugnot, Julie; Gürgüç, Zeynep; Øvlisen, Frederik Roose
2012-01-01
on the efficient equilibrium, we consider sunspots as a potential reason for coordination failure. We conduct an experiment with a three player 2x2x2 game in which coordination on the efficient equilibrium is easy and should normally occur. In the control session, we find almost perfect coordination on the payoff......-dominant equilibrium, but in the sunspot treatment, dis-coordination is frequent. Sunspots lead to significant inefficiency, and we conclude that sunspots can indeed cause coordination failure....
Code subspaces for LLM geometries
Berenstein, David; Miller, Alexandra
2018-03-01
We consider effective field theory around classical background geometries with a gauge theory dual, specifically those in the class of LLM geometries. These are dual to half-BPS states of N= 4 SYM. We find that the language of code subspaces is natural for discussing the set of nearby states, which are built by acting with effective fields on these backgrounds. This work extends our previous work by going beyond the strict infinite N limit. We further discuss how one can extract the topology of the state beyond N→∞ and find that, as before, uncertainty and entanglement entropy calculations provide a useful tool to do so. Finally, we discuss obstructions to writing down a globally defined metric operator. We find that the answer depends on the choice of reference state that one starts with. Therefore, within this setup, there is ambiguity in trying to write an operator that describes the metric globally.
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...
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...
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...
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...
Systematics of IIB spinorial geometry
Gran, U.; Gutowski, J.; Papadopoulos, G.; Roest, D.
2005-01-01
We reduce the classification of all supersymmetric backgrounds of IIB supergravity to the evaluation of the Killing spinor equations and their integrability conditions, which contain the field equations, on five types of spinors. This extends the work of [hep-th/0503046] to IIB supergravity. We give the expressions of the Killing spinor equations on all five types of spinors. In this way, the Killing spinor equations become a linear system for the fluxes, geometry and spacetime derivatives of...
Turtle geometry the Python way
Battle, S.
2014-01-01
An introduction to coding using Python’s on-screen ‘turtle’ that can be commanded with a few simple instructions including forward, backward, left and right. The turtle leaves a trace that can be used to draw geometric figures. This workshop is aimed at beginners of all ages. The aim is to learn a smattering of programming and a little bit of geometry in a fun way.
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.
Computational geometry for reactor applications
International Nuclear Information System (INIS)
Brown, F.B.; Bischoff, F.G.
1988-01-01
Monte Carlo codes for simulating particle transport involve three basic computational sections: a geometry package for locating particles and computing distances to regional boundaries, a physics package for analyzing interactions between particles and problem materials, and an editing package for determining event statistics and overall results. This paper describes the computational geometry methods in RACER, a vectorized Monte Carlo code used for reactor physics analysis, so that comparisons may be made with techniques used in other codes. The principal applications for RACER are eigenvalue calculations and power distributions associated with reactor core physics analysis. Successive batches of neutrons are run until convergence and acceptable confidence intervals are obtained, with typical problems involving >10 6 histories. As such, the development of computational geometry methods has emphasized two basic needs: a flexible but compact geometric representation that permits accurate modeling of reactor core details and efficient geometric computation to permit very large numbers of histories to be run. The current geometric capabilities meet these needs effectively, supporting a variety of very large and demanding applications
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 ...
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...
Donaldson invariants in algebraic geometry
International Nuclear Information System (INIS)
Goettsche, L.
2000-01-01
In these lectures I want to give an introduction to the relation of Donaldson invariants with algebraic geometry: Donaldson invariants are differentiable invariants of smooth compact 4-manifolds X, defined via moduli spaces of anti-self-dual connections. If X is an algebraic surface, then these moduli spaces can for a suitable choice of the metric be identified with moduli spaces of stable vector bundles on X. This can be used to compute Donaldson invariants via methods of algebraic geometry and has led to a lot of activity on moduli spaces of vector bundles and coherent sheaves on algebraic surfaces. We will first recall the definition of the Donaldson invariants via gauge theory. Then we will show the relation between moduli spaces of anti-self-dual connections and moduli spaces of vector bundles on algebraic surfaces, and how this makes it possible to compute Donaldson invariants via algebraic geometry methods. Finally we concentrate on the case that the number b + of positive eigenvalues of the intersection form on the second homology of the 4-manifold is 1. In this case the Donaldson invariants depend on the metric (or in the algebraic geometric case on the polarization) via a system of walls and chambers. We will study the change of the invariants under wall-crossing, and use this in particular to compute the Donaldson invariants of rational algebraic surfaces. (author)
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...
Fuzzy Geometry of Commutative Spaces and Quantum Dynamics
International Nuclear Information System (INIS)
Mayburov, S.N.
2016-01-01
Fuzzy topology and geometry considered as the possible mathematical framework for novel quantum-mechanical formalism. In such formalism the states of massive particle m correspond to the elements of fuzzy manifold called fuzzy points. Due to the manifold weak topology, m space coordinate x acquires principal uncertainty σ_x and described by the positive, normalized density w(r-vector , t) in 3-dimensional case. It’s shown that the evolution of m state on such 3-dimensional manifold corresponds to Shroedinger dynamics of massive quantum particle
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
Geometry and Framework Interactions of Zeolite-Encapsulated Copper(II)-Histidine Complexes
Weckhuysen, B.M.; Grommen, R.; Manikandan, P.; Gao, Y.; Shane, T.; Shane, J.J.; Schoonheydt, R.A.; Goldfarb, D.
2000-01-01
The coordination geometry of zeolite-encapsulated copper(II)-histidine (CuHis) complexes, prepared by ion exchange of the complexes from aqueous solutions into zeolite NaY, was determined by a combination of UV-vis-NIR diffuse reflectance spectroscopy (DRS), X-band EPR, electron-spin-echo envelope
Open problems in the geometry and analysis of Banach spaces
Guirao, Antonio J; Zizler, Václav
2016-01-01
This is a collection of some easily-formulated problems that remain open in the study of the geometry and analysis of Banach spaces. Assuming the reader has a working familiarity with the basic results of Banach space theory, the authors focus on concepts of basic linear geometry, convexity, approximation, optimization, differentiability, renormings, weak compact generating, Schauder bases and biorthogonal systems, fixed points, topology and nonlinear geometry. The main purpose of this work is to help convince young researchers in Functional Analysis that the theory of Banach spaces is a fertile field of research, full of interesting open problems. Inside the Banach space area, the text should help expose young researchers to the depth and breadth of the work that remains, and to provide the perspective necessary to choose a direction for further study. Some of the problems presented herein are longstanding open problems, some are recent, some are more important and some are only "local" problems. Some would ...
Comparison of Microinstability Properties for Stellarator Magnetic Geometries
International Nuclear Information System (INIS)
Rewoldt, G.; Ku, L.-P.; Tang, W.M.
2005-01-01
The microinstability properties of seven distinct magnetic geometries corresponding to different operating and planned stellarators with differing symmetry properties are compared. Specifically, the kinetic stability properties (linear growth rates and real frequencies) of toroidal microinstabilities (driven by ion temperature gradients and trapped-electron dynamics) are compared, as parameters are varied. The familiar ballooning representation is used to enable efficient treatment of the spatial variations along the equilibrium magnetic field lines. These studies provide useful insights for understanding the differences in the relative strengths of the instabilities caused by the differing localizations of good and bad magnetic curvature and of the presence of trapped particles. The associated differences in growth rates due to magnetic geometry are large for small values of the temperature gradient parameter n identical to d ln T/d ln n, whereas for large values of n, the mode is strongly unstable for all of the different magnetic geometries
Network geometry with flavor: From complexity to quantum geometry
Bianconi, Ginestra; Rahmede, Christoph
2016-03-01
Network geometry is attracting increasing attention because it has a wide range of applications, ranging from data mining to routing protocols in the Internet. At the same time advances in the understanding of the geometrical properties of networks are essential for further progress in quantum gravity. In network geometry, simplicial complexes describing the interaction between two or more nodes play a special role. In fact these structures can be used to discretize a geometrical d -dimensional space, and for this reason they have already been widely used in quantum gravity. Here we introduce the network geometry with flavor s =-1 ,0 ,1 (NGF) describing simplicial complexes defined in arbitrary dimension d and evolving by a nonequilibrium dynamics. The NGF can generate discrete geometries of different natures, ranging from chains and higher-dimensional manifolds to scale-free networks with small-world properties, scale-free degree distribution, and nontrivial community structure. The NGF admits as limiting cases both the Bianconi-Barabási models for complex networks, the stochastic Apollonian network, and the recently introduced model for complex quantum network manifolds. The thermodynamic properties of NGF reveal that NGF obeys a generalized area law opening a new scenario for formulating its coarse-grained limit. The structure of NGF is strongly dependent on the dimensionality d . In d =1 NGFs grow complex networks for which the preferential attachment mechanism is necessary in order to obtain a scale-free degree distribution. Instead, for NGF with dimension d >1 it is not necessary to have an explicit preferential attachment rule to generate scale-free topologies. We also show that NGF admits a quantum mechanical description in terms of associated quantum network states. Quantum network states evolve by a Markovian dynamics and a quantum network state at time t encodes all possible NGF evolutions up to time t . Interestingly the NGF remains fully classical but
On the Lorentz invariance of bit-string geometry
International Nuclear Information System (INIS)
Noyes, H.P.
1995-09-01
We construct the class of integer-sided triangles and tetrahedra that respectively correspond to two or three discriminately independent bit-strings. In order to specify integer coordinates in this space, we take one vertex of a regular tetrahedron whose common edge length is an even integer as the origin of a line of integer length to the open-quotes pointclose quotes and three integer distances to this open-quotes pointclose quotes from the three remaining vertices of the reference tetrahedron. This - usually chiral - integer coordinate description of bit-string geometry is possible because three discriminately independent bit-strings generate four more; the Hamming measures of these seven strings always allow this geometrical interpretation. On another occasion we intend to prove the rotational invariance of this coordinate description. By identifying the corners of these figures with the positions of recording counters whose clocks are synchronized using the Einstein convention, we define velocities in this space. This suggests that it may be possible to define boosts and discrete Lorentz transformations in a space of integer coordinates. We relate this description to our previous work on measurement accuracy and the discrete ordered calculus of Etter and Kauffman (DOC)
A Whirlwind Tour of Computational Geometry.
Graham, Ron; Yao, Frances
1990-01-01
Described is computational geometry which used concepts and results from classical geometry, topology, combinatorics, as well as standard algorithmic techniques such as sorting and searching, graph manipulations, and linear programing. Also included are special techniques and paradigms. (KR)
Optimizing solar-cell grid geometry
Crossley, A. P.
1969-01-01
Trade-off analysis and mathematical expressions calculate optimum grid geometry in terms of various cell parameters. Determination of the grid geometry provides proper balance between grid resistance and cell output to optimize the energy conversion process.
Improving Project Manufacturing Coordination
Directory of Open Access Journals (Sweden)
Korpivaara Ville
2014-09-01
Full Text Available The objective of this research is to develop firms’ project manufacturing coordination. The development will be made by centralizing the manufacturing information flows in one system. To be able to centralize information, a deep user need assessment is required. After user needs have been identified, the existing system will be developed to match these needs. The theoretical background is achieved through exploring the literature of project manufacturing, development project success factors and different frameworks and tools for development project execution. The focus of this research is rather in customer need assessment than in system’s technical expertise. To ensure the deep understanding of customer needs this study is executed by action research method. As a result of this research the information system for project manufacturing coordination was developed to respond revealed needs of the stakeholders. The new system improves the quality of the manufacturing information, eliminates waste in manufacturing coordination processes and offers a better visibility to the project manufacturing. Hence it provides a solid base for the further development of project manufacturing.
Universal mechatronics coordinator
Muir, Patrick F.
1999-11-01
Mechatronic systems incorporate multiple actuators and sensor which must be properly coordinated to achieve the desired system functionality. Many mechatronic systems are designed as one-of-a-kind custom projects without consideration for facilitating future system or alterations and extensions to the current syste. Thus, subsequent changes to the system are slow, different, and costly. It has become apparent that manufacturing processes, and thus the mechatronics which embody them, need to be agile in order to more quickly and easily respond to changing customer demands or market pressures. To achieve agility, both the hardware and software of the system need to be designed such that the creation of new system and the alteration and extension of current system is fast and easy. This paper describes the design of a Universal Mechatronics Coordinator (UMC) which facilitates agile setup and changeover of coordination software for mechatronic systems. The UMC is capable of sequencing continuous and discrete actions that are programmed as stimulus-response pairs, as state machines, or a combination of the two. It facilitates the modular, reusable programing of continuous actions such as servo control algorithms, data collection code, and safety checking routines; and discrete actions such as reporting achieved states, and turning on/off binary devices. The UMC has been applied to the control of a z- theta assembly robot for the Minifactory project and is applicable to a spectrum of widely differing mechatronic systems.
Energy Technology Data Exchange (ETDEWEB)
Lee, Kanghoon [Quantum Universe Center, Korea Institute for Advanced Study, Seoul (Korea, Republic of); Strickland-Constable, Charles [Institut de Physique Theorique, Universite Paris Saclay, CEA, CNRS, Gif-sur-Yvette (France); Waldram, Daniel [Department of Physics, Imperial College London (United Kingdom); Berkeley Center for Theoretical Physics, University of California, Berkeley, CA (United States)
2017-10-15
We discuss the possible realisation in string/M theory of the recently discovered family of four-dimensional maximal SO(8) gauged supergravities, and of an analogous family of seven-dimensional half-maximal SO(4) gauged supergravities. We first prove a no-go theorem that neither class of gaugings can be realised via a compactification that is locally described by ten- or eleven-dimensional supergravity. In the language of Double Field Theory and its M theory analogue, this implies that the section condition must be violated. Introducing the minimal number of additional coordinates possible, we then show that the standard S{sup 3} and S{sup 7} compactifications of ten- and eleven-dimensional supergravity admit a new class of section-violating generalised frames with a generalised Lie derivative algebra that reproduces the embedding tensor of the SO(4) and SO(8) gaugings respectively. The physical meaning, if any, of these constructions is unclear. They highlight a number of the issues that arise when attempting to apply the formalism of Double Field Theory to non-toroidal backgrounds. Using a naive brane charge quantisation to determine the periodicities of the additional coordinates restricts the SO(4) gaugings to an infinite discrete set and excludes all the SO(8) gaugings other than the standard one. (copyright 2017 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
International Nuclear Information System (INIS)
Lee, Kanghoon; Strickland-Constable, Charles; Waldram, Daniel
2017-01-01
We discuss the possible realisation in string/M theory of the recently discovered family of four-dimensional maximal SO(8) gauged supergravities, and of an analogous family of seven-dimensional half-maximal SO(4) gauged supergravities. We first prove a no-go theorem that neither class of gaugings can be realised via a compactification that is locally described by ten- or eleven-dimensional supergravity. In the language of Double Field Theory and its M theory analogue, this implies that the section condition must be violated. Introducing the minimal number of additional coordinates possible, we then show that the standard S 3 and S 7 compactifications of ten- and eleven-dimensional supergravity admit a new class of section-violating generalised frames with a generalised Lie derivative algebra that reproduces the embedding tensor of the SO(4) and SO(8) gaugings respectively. The physical meaning, if any, of these constructions is unclear. They highlight a number of the issues that arise when attempting to apply the formalism of Double Field Theory to non-toroidal backgrounds. Using a naive brane charge quantisation to determine the periodicities of the additional coordinates restricts the SO(4) gaugings to an infinite discrete set and excludes all the SO(8) gaugings other than the standard one. (copyright 2017 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
An improved tracking framework for ultrasound probe localization in image-guided radiosurgery
Directory of Open Access Journals (Sweden)
Ipsen Svenja
2016-09-01
Full Text Available Real-time target localization with ultrasound holds high potential for image guidance and motion compensation in radiosurgery due to its non-invasive image acquisition free from ionizing radiation. However, a two-step localization has to be performed when integrating ultrasound into the existing radiosurgery workflow. In addition to target localization inside the ultrasound volume, the probe itself has to be localized in order to transform the target position into treatment room coordinates. By adapting existing camera calibration tools, we have developed a method to extend the stereoscopic X-ray tracking system of a radiosurgery platform in order to locate objects such as marker geometries with six degrees of freedom. The calibration was performed with 0.1 mm reprojection error. By using the full area of the flat-panel detectors without pre-processing the extended software increased the tracking volume and resolution by up to 80%, substantially improving patient localization and marker detectability. Furthermore, marker-tracking showed sub-millimeter accuracy and rotational errors below 0.1°. This demonstrates that the developed extension framework can accurately localize marker geometries using an integrated X-ray system, establishing the link for the integration of real-time ultrasound image guidance into the existing system.
Sums over geometries and improvements on the mean field approximation
International Nuclear Information System (INIS)
Sacksteder, Vincent E. IV
2007-01-01
The saddle points of a Lagrangian due to Efetov are analyzed. This Lagrangian was originally proposed as a tool for calculating systematic corrections to the Bethe approximation, a mean-field approximation which is important in statistical mechanics, glasses, coding theory, and combinatorial optimization. Detailed analysis shows that the trivial saddle point generates a sum over geometries reminiscent of dynamically triangulated quantum gravity, which suggests new possibilities to design sums over geometries for the specific purpose of obtaining improved mean-field approximations to D-dimensional theories. In the case of the Efetov theory, the dominant geometries are locally treelike, and the sum over geometries diverges in a way that is similar to quantum gravity's divergence when all topologies are included. Expertise from the field of dynamically triangulated quantum gravity about sums over geometries may be able to remedy these defects and fulfill the Efetov theory's original promise. The other saddle points of the Efetov Lagrangian are also analyzed; the Hessian at these points is nonnormal and pseudo-Hermitian, which is unusual for bosonic theories. The standard formula for Gaussian integrals is generalized to nonnormal kernels
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.
Magnetoelectrostatic thruster physical geometry tests
Ramsey, W. D.
1981-01-01
Inert gas tests are conducted with several magnetoelectrostatic containment discharge chamber geometries. The configurations tested include three discharge chamber lengths; three boundary magnet patterns; two different flux density magnet materials; hemispherical and conical shaped thrusters having different surface-to-volume ratios; and two and three grid ion optics. Argon mass utilizations of 60 to 79% are attained at 210 to 280 eV/ion in different test configurations. Short hemi thruster configurations are found to produce 70 to 92% xenon mass utilization at 185 to 220 eV/ion.
Programming system for analytic geometry
International Nuclear Information System (INIS)
Raymond, Jacques
1970-01-01
After having outlined the characteristics of computing centres which do not comply with engineering tasks, notably the time required by all different tasks to be performed when developing a software (assembly, compilation, link edition, loading, run), and identified constraints specific to engineering, the author identifies the characteristics a programming system should have to suit engineering tasks. He discussed existing conversational systems and their programming language, and their main drawbacks. Then, he presents a system which aims at facilitating programming and addressing problems of analytic geometry and trigonometry
The geometry of special relativity
International Nuclear Information System (INIS)
Parizet, Jean
2008-01-01
This book for students in mathematics or physics shows the interest of geometry to understand special relativity as a consequence of invariance of Maxwell equations and of constancy of the speed of light. Space-time is actually provided with a geometrical structure and a physical interpretation: at each observer are associated his own time and his own physical space in which occur events he is concerned with. This leads to a natural approach to special relativity. The Lorentz group and its algebra are then studied by using matrices and the Pauli algebra. Quaternions are also addressed
Moduli spaces in algebraic geometry
International Nuclear Information System (INIS)
Goettsche, L.
2000-01-01
This volume of the new series of lecture notes of the Abdus Salam International Centre for Theoretical Physics contains the lecture notes of the School on Algebraic Geometry which took place at the Abdus Salam International Centre for Theoretical Physics from 26 July to 13 August 1999. The school consisted of 2 weeks of lecture courses and one week of conference. The topic of the school was moduli spaces. More specifically the lectures were divided into three subtopics: principal bundles on Riemann surfaces, moduli spaces of vector bundles and sheaves on projective varieties, and moduli spaces of curves
Worldsheet geometries of ambitwistor string
Energy Technology Data Exchange (ETDEWEB)
Ohmori, Kantaro [Department of Physics, the University of Tokyo,Hongo, Bunkyo-ku, Tokyo 133-0022 (Japan)
2015-06-12
Mason and Skinner proposed the ambitwistor string theory which directly reproduces the formulas for the amplitudes of massless particles proposed by Cachazo, He and Yuan. In this paper we discuss geometries of the moduli space of worldsheets associated to the bosonic or the RNS ambitwistor string. Further, we investigate the factorization properties of the amplitudes when an internal momentum is near on-shell in the abstract CFT language. Along the way, we propose the existence of the ambitwistor strings with three or four fermionic worldsheet currents.
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
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
Geometry of supersymmetric gauge theories
International Nuclear Information System (INIS)
Gieres, F.
1988-01-01
This monograph gives a detailed and pedagogical account of the geometry of rigid superspace and supersymmetric Yang-Mills theories. While the core of the text is concerned with the classical theory, the quantization and anomaly problem are briefly discussed following a comprehensive introduction to BRS differential algebras and their field theoretical applications. Among the treated topics are invariant forms and vector fields on superspace, the matrix-representation of the super-Poincare group, invariant connections on reductive homogeneous spaces and the supermetric approach. Various aspects of the subject are discussed for the first time in textbook and are consistently presented in a unified geometric formalism
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.
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
International Nuclear Information System (INIS)
Aziz, A.
1980-03-01
The research covered identification of radionuclides and measurement of their concentration in various environmental media and items of diet of the local population. Biomedia and items of diet selected for study were air, surface water, precipitation, vegetables, meat, poultry and fish etc. Radioactive assays under-taken were gross gamma activity measurements and gamma spectrometric analyses for the determination of gamma emitting radionuclides. These were followed by radiochemical analyses for the separation of Sr 90 and Pu 239. Radiometric measurements for Sr 90 and Pu 239 were performed by low back-ground beta counting and alpha spectrometric analyses respectively
Trends and developments in computational geometry
Berg, de M.
1997-01-01
This paper discusses some trends and achievements in computational geometry during the past five years, with emphasis on problems related to computer graphics. Furthermore, a direction of research in computational geometry is discussed that could help in bringing the fields of computational geometry
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.
"WGL," a Web Laboratory for Geometry
Quaresma, Pedro; Santos, Vanda; Maric, Milena
2018-01-01
The role of information and communication technologies (ICT) in education is nowadays well recognised. The "Web Geometry Laboratory," is an e-learning, collaborative and adaptive, Web environment for geometry, integrating a well known dynamic geometry system. In a collaborative session, teachers and students, engaged in solving…
Coordinating Interactions: The Event Coordination Notation
DEFF Research Database (Denmark)
Kindler, Ekkart
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...... for the local and the global behaviour define the overall behaviour of the domain. In this technical report, we discuss the main idea and philosophy of ECNO and its notation as well as all the subtle details and concepts - and we motivate the decisions made for its design. Moreover, we discuss the prototypical...... implementation of ECNO, which consists of a modelling environment based on Eclipse and the Eclipse Modeling Framework (EMF) and an execution engine, which fully supports all the concepts and features of ECNO discussed in this technical report. All the examples are based on EMF, but the ECNO Engine can be used...
National Research Council Canada - National Science Library
Goan, Terrance; Mayk, Israel
2005-01-01
Command and Control for coordinated response to domestic terrorist attack will require the ability of Federal, state, and local agencies to maintain awareness of the status, capabilities, requirements...
Jose, Abin; Haak, Daniel; Jonas, Stephan; Brandenburg, Vincent; Deserno, Thomas M.
2015-03-01
Photographic documentation and image-based wound assessment is frequently performed in medical diagnostics, patient care, and clinical research. To support quantitative assessment, photographic imaging is based on expensive and high-quality hardware and still needs appropriate registration and calibration. Using inexpensive consumer hardware such as smartphone-integrated cameras, calibration of geometry, color, and contrast is challenging. Some methods involve color calibration using a reference pattern such as a standard color card, which is located manually in the photographs. In this paper, we adopt the lattice detection algorithm by Park et al. from real world to medicine. At first, the algorithm extracts and clusters feature points according to their local intensity patterns. Groups of similar points are fed into a selection process, which tests for suitability as a lattice grid. The group which describes the largest probability of the meshes of a lattice is selected and from it a template for an initial lattice cell is extracted. Then, a Markov random field is modeled. Using the mean-shift belief propagation, the detection of the 2D lattice is solved iteratively as a spatial tracking problem. Least-squares geometric calibration of projective distortions and non-linear color calibration in RGB space is supported by 35 corner points of 24 color patches, respectively. The method is tested on 37 photographs taken from the German Calciphylaxis registry, where non-standardized photographic documentation is collected nationwide from all contributing trial sites. In all images, the reference card location is correctly identified. At least, 28 out of 35 lattice points were detected, outperforming the SIFT-based approach previously applied. Based on these coordinates, robust geometry and color registration is performed making the photographs comparable for quantitative analysis.
The heterogeneous response method in slab geometry
International Nuclear Information System (INIS)
Villarino, E.A.; Stamm'ler, R.J.J.
1984-01-01
The heterogeneous response method (HRM) has been developed to calculate the multigroup flux in a heterogeneous system, e.g. a fuel assembly, without having to resort to dubious homogenization recipes. Here, the method is described in slab geometry in a manner that facilitates its computerization. By dividing the system into subsystems or nodes, say pin cells, two levels of calculation are created, which define a set of local problems and a global problem, respectively. In the local problem, collision probabilities are used to obtain for a node in vacuum, its response fluxes caused by sources and in-currents. They preserve the heterogeneous character of the node. In the global problem, the nodes are coupled by cosine currents. A suitable transformation reduces the number of two unknown currents per interface to one unknown per node, its total transmitted in-current. The global equation system thus becomes a set of three-point relations, which can be solved efficiently. In cases typical of fuel-assembly situations, the HRM produces fluxes that compare very well with the direct solution of the entire system by collision probabilities, though at a fraction of the computer cost. Extension of the method to 2- and 3-D systems is discussed. (author)
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International Development Research Centre (IDRC) Digital Library (Canada)
The Coordinator, Translation Services coordinates the overall operations of the ... services in IDRC by acting as the main resource person for internal clients ... all operational issues in order to ensure good quality products delivered on time.
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 ...