Reverse engineering: algebraic boundary representations to constructive solid geometry.
Buchele, S. F.; Ellingson, W. A.
1997-12-17
Recent advances in reverse engineering have focused on recovering a boundary representation (b-rep) of an object, often for integration with rapid prototyping. This boundary representation may be a 3-D point cloud, a triangulation of points, or piecewise algebraic or parametric surfaces. This paper presents work in progress to develop an algorithm to extend the current state of the art in reverse engineering of mechanical parts. This algorithm will take algebraic surface representations as input and will produce a constructive solid geometry (CSG) description that uses solid primitives such as rectangular block, pyramid, sphere, cylinder, and cone. The proposed algorithm will automatically generate a CSG solid model of a part given its algebraic b-rep, thus allowing direct input into a CAD system and subsequent CSG model generation.
Christensen, Noel C.; Emery, James D.; Smith, Maurice L.
1988-04-05
A system converts from the boundary representation of an object to the constructive solid geometry representation thereof. The system converts the boundary representation of the object into elemental atomic geometrical units or I-bodies which are in the shape of stock primitives or regularized intersections of stock primitives. These elemental atomic geometrical units are then represented in symbolic form. The symbolic representations of the elemental atomic geometrical units are then assembled heuristically to form a constructive solid geometry representation of the object usable for manufacturing thereof. Artificial intelligence is used to determine the best constructive solid geometry representation from the boundary representation of the object. Heuristic criteria are adapted to the manufacturing environment for which the device is to be utilized. The surface finish, tolerance, and other information associated with each surface of the boundary representation of the object are mapped onto the constructive solid geometry representation of the object to produce an enhanced solid geometry representation, particularly useful for computer-aided manufacture of the object.
2015-12-01
Island Boolean Hierarchy 12 7. Raytracing -Based Validation 13 8. Performance Implications 14 9. Conclusions and Future Work 15 10. References 16...Visualization provided by NIST, b) right is the same model imported and raytraced in BRL- CAD...geometry which, although providing a definite step forward, is typically slow compared to CSG raytracing . In general, there has been relatively little
Solid T-spline Construction from Boundary Representations for Genus-Zero Geometry
2011-11-14
isogeometric analysis [10, 2], which utilizes NURBS ∗ Corresponding author: Y. Zhang. E-mail address: jessicaz@andrew.cmu.edu. Tel: (412) 268-5332; Fax...in [1] to generate NURBS parameterizations of swept volumes via sweep- ing a closed curve and isogeometric analysis was applied to the generated NURBS ...model. In [23], an approach was proposed to construct solid NURBS for patient-specific vascular geometric mod- els from image data for use in
Integral geometry and representation theory
Gel'fand, I M; Vilenkin, N Ya
1966-01-01
Generalized Functions, Volume 5: Integral Geometry and Representation Theory is devoted to the theory of representations, focusing on the group of two-dimensional complex matrices of determinant one.This book emphasizes that the theory of representations is a good example of the use of algebraic and geometric methods in functional analysis, in which transformations are performed not on the points of a space, but on the functions defined on it. The topics discussed include Radon transform on a real affine space, integral transforms in the complex domain, and representations of the group of comp
Davis JE, Eddy MJ, Sutton TM, Altomari TJ
2007-03-01
Solid modeling computer software systems provide for the design of three-dimensional solid models used in the design and analysis of physical components. The current state-of-the-art in solid modeling representation uses a boundary representation format in which geometry and topology are used to form three-dimensional boundaries of the solid. The geometry representation used in these systems is cubic B-spline curves and surfaces--a network of cubic B-spline functions in three-dimensional Cartesian coordinate space. Many Monte Carlo codes, however, use a geometry representation in which geometry units are specified by intersections and unions of half-spaces. This paper describes an algorithm for converting from a boundary representation to a half-space representation.
Configuration spaces geometry, topology and representation theory
Cohen, Frederick; Concini, Corrado; Feichtner, Eva; Gaiffi, Giovanni; Salvetti, Mario
2016-01-01
This book collects the scientific contributions of a group of leading experts who took part in the INdAM Meeting held in Cortona in September 2014. With combinatorial techniques as the central theme, it focuses on recent developments in configuration spaces from various perspectives. It also discusses their applications in areas ranging from representation theory, toric geometry and geometric group theory to applied algebraic topology.
Continuum representations of cellular solids
Neilsen, M.K.
1993-09-01
Cellular materials consist of interconnected struts or plates which form cells. The struts or plates are constructed from a variety of metals, polymers, ceramics and wood products. Cellular materials are often used in impact limiters for shipping containers to protect the contents from accidental impact events. These materials exhibit a variety of complex behavior when subjected to crushing loads. This research focuses on the development of continuum representations of cellular solids that can be used in the finite element analysis of shipping container accidents. A significant portion of this work is the development of a new methodology to relate localized deformations to appropriate constitutive descriptions. This methodology provides the insight needed to select constitutive descriptions for cellular solids that capture the localized deformations that are observed experimentally. Constitutive relations are developed for two different cellular materials, aluminum honeycomb and polyurethane foam. These constitutive relations are based on plasticity and continuum damage theories. Plasticity is used to describe the permanent deformation exhibited by both aluminum honeycomb and polyurethane foam. Continuum damage is needed to capture the change in elastic parameters due to cracking of the polyurethane cell wall materials. The new constitutive description of polyurethane foam is implemented in both static and dynamic finite element codes, and analytical and numerical predictions are compared with available experimental data.
Graph-based representation for multiview image geometry.
Maugey, Thomas; Ortega, Antonio; Frossard, Pascal
2015-05-01
In this paper, we propose a new geometry representation method for multiview image sets. Our approach relies on graphs to describe the multiview geometry information in a compact and controllable way. The links of the graph connect pixels in different images and describe the proximity between pixels in 3D space. These connections are dependent on the geometry of the scene and provide the right amount of information that is necessary for coding and reconstructing multiple views. Our multiview image representation is very compact and adapts the transmitted geometry information as a function of the complexity of the prediction performed at the decoder side. To achieve this, our graph-based representation (GBR) carefully selects the amount of geometry information needed before coding. This is in contrast with depth coding, which directly compresses with losses the original geometry signal, thus making it difficult to quantify the impact of coding errors on geometry-based interpolation. We present the principles of this GBR and we build an efficient coding algorithm to represent it. We compare our GBR approach to classical depth compression methods and compare their respective view synthesis qualities as a function of the compactness of the geometry description. We show that GBR can achieve significant gains in geometry coding rate over depth-based schemes operating at similar quality. Experimental results demonstrate the potential of this new representation.
Quadric solids and computational geometry
Emery, J.D.
1980-07-25
As part of the CAD-CAM development project, this report discusses the mathematics underlying the program QUADRIC, which does computations on objects modeled as Boolean combinations of quadric half-spaces. Topics considered include projective space, quadric surfaces, polars, affine transformations, the construction of solids, shaded image, the inertia tensor, moments, volume, surface integrals, Monte Carlo integration, and stratified sampling. 1 figure.
Buchele, S.F. [Univ. of Texas, Austin, TX (United States). Computer Sciences Dept.; Ellingson, W.A. [Argonne National Lab., IL (United States)
1997-06-01
Recent advances in reverse engineering have focused on recovering a boundary representation (b-rep) of an object, often for integration with rapid prototyping. This boundary representation may be a 3-D point cloud, a triangulation of points, or piecewise algebraic or parametric surfaces. This paper presents work in progress to develop an algorithm to extend the current state of the art in reverse engineering of mechanical parts. This algorithm will take algebraic surface representations as input and will produce a constructive solid geometry (CSG) description that uses solid primitives such as rectangular block, pyramid, sphere, cylinder, and cone. The proposed algorithm will automatically generate a CSG solid model of a part given its algebraic b-rep, thus allowing direct input into a CAD system and subsequent CSG model generation.
Laws of granular solids: geometry and topology.
DeGiuli, Eric; McElwaine, Jim
2011-10-01
In a granular solid, mechanical equilibrium requires a delicate balance of forces at the disordered grain scale. To understand how macroscopic rigidity can emerge in this amorphous solid, it is crucial that we understand how Newton's laws pass from the disordered grain scale to the laboratory scale. In this work, we introduce an exact discrete calculus, in which Newton's laws appear as differential relations at the scale of a single grain. Using this calculus, we introduce gauge variables that describe identically force- and torque-balanced configurations. In a first, intrinsic formulation, we use the topology of the contact network, but not its geometry. In a second, extrinsic formulation, we introduce geometry with the Delaunay triangulation. These formulations show, with exact methods, how topology and geometry in a disordered medium are related by constraints. In particular, we derive Airy's expression for a divergence-free, symmetric stress tensor in two and three dimensions.
Conjugate Representations and Characterizing Escort Expectations in Information Geometry
Tatsuaki Wada
2017-06-01
Full Text Available Based on the maximum entropy (MaxEnt principle for a generalized entropy functional and the conjugate representations introduced by Zhang, we have reformulated the method of information geometry. For a set of conjugate representations, the associated escort expectation is naturally introduced and characterized by the generalized score function which has zero-escort expectation. Furthermore, we show that the escort expectation induces a conformal divergence.
Flag varieties an interplay of geometry, combinatorics, and representation theory
Lakshmibai, V
2009-01-01
Flag varieties are important geometric objects and their study involves an interplay of geometry, combinatorics, and representation theory. This book is detailed account of this interplay. In the area of representation theory, the book presents a discussion of complex semisimple Lie algebras and of semisimple algebraic groups; in addition, the representation theory of symmetric groups is also discussed. In the area of algebraic geometry, the book gives a detailed account of the Grassmannian varieties, flag varieties, and their Schubert subvarieties. Because of the connections with root systems, many of the geometric results admit elegant combinatorial description, a typical example being the description of the singular locus of a Schubert variety. This is shown to be a consequence of standard monomial theory (abbreviated SMT). Thus the book includes SMT and some important applications - singular loci of Schubert varieties, toric degenerations of Schubert varieties, and the relationship between Schubert variet...
Noncommutative differential geometry, and the matrix representations of generalised algebras
Gratus, J.
1998-05-01
The underly ing algebra I or a noncummutative geometry is taken to be a matrix algebra, and the set of derivatives the ad joint of a subset of traceless matrices. This is sufficient to calculate the dual 1-forms, and show that the space of 1-firms is at free module over the algebra of matrices. The concept of a generalised algebra is delined and it is shown that this is required in order for the space of 2-forms to exist, The exterior derivative is generalised for higher-order forms and these are also shown to he free modules over the matrix algebra. Examples of mappings that preserve the differential Structure are peen, Also giken are four examples of matrix generalised algebras, and the corresponding noncommutntive geometries, including the cases where the generalised algebra corresponds to a representation of a Lie algebra or a q-deformed algebra.
Generation of high order geometry representations in Octree meshes
Harald G. Klimach
2015-11-01
Full Text Available We propose a robust method to convert triangulated surface data into polynomial volume data. Such polynomial representations are required for high-order partial differential solvers, as low-order surface representations would diminish the accuracy of their solution. Our proposed method deploys a first order spatial bisection algorithm to find robustly an approximation of given geometries. The resulting voxelization is then used to generate Legendre polynomials of arbitrary degree. By embedding the locally defined polynomials in cubical elements of a coarser mesh, this method can reliably approximate even complex structures, like porous media. It thereby is possible to provide appropriate material definitions for high order discontinuous Galerkin schemes. We describe the method to construct the polynomial and how it fits into the overall mesh generation. Our discussion includes numerical properties of the method and we show some results from applying it to various geometries. We have implemented the described method in our mesh generator Seeder, which is publically available under a permissive open-source license.
Finsler geometry of nonlinear elastic solids with internal structure
Clayton, J. D.
2017-02-01
Concepts from Finsler differential geometry are applied towards a theory of deformable continua with internal structure. The general theory accounts for finite deformation, nonlinear elasticity, and various kinds of structural features in a solid body. The general kinematic structure of the theory includes macroscopic and microscopic displacement fields-i.e., a multiscale representation-whereby the latter are represented mathematically by the director vector of pseudo-Finsler space, not necessarily of unit magnitude. A physically appropriate fundamental (metric) tensor is introduced, leading to affine and nonlinear connections. A deformation gradient tensor is defined via differentiation of the macroscopic motion field, and another metric indicative of strain in the body is a function of this gradient. A total energy functional of strain, referential microscopic coordinates, and horizontal covariant derivatives of the latter is introduced. Variational methods are applied to derive Euler-Lagrange equations and Neumann boundary conditions. The theory is shown to encompass existing continuum physics models such as micromorphic, micropolar, strain gradient, phase field, and conventional nonlinear elasticity models, and it can reduce to such models when certain assumptions on geometry, kinematics, and energy functionals are imposed. The theory is applied to analyze two physical problems in crystalline solids: shear localization/fracture in a two-dimensional body and cavitation in a spherical body. In these examples, a conformal or Weyl-type transformation of the fundamental tensor enables a description of dilatation associated, respectively, with cleavage surface roughness and nucleation of voids or vacancies. For the shear localization problem, the Finsler theory is able to accurately reproduce the surface energy of Griffith's fracture mechanics, and it predicts dilatation-induced toughening as observed in experiments on brittle crystals. For the cavitation problem
Transcendental Representations with Applications to Solids and Fluids
Campos, Luis Manuel Braga de Costa
2012-01-01
Building on the author's previous book in the series, Complex Analysis with Applications to Flows and Fields (CRC Press, 2010), Transcendental Representations with Applications to Solids and Fluids focuses on four infinite representations: series expansions, series of fractions for meromorphic functions, infinite products for functions with infinitely many zeros, and continued fractions as alternative representations. This book also continues the application of complex functions to more classes of fields, including incompressible rotational flows, compressible irrotational flows, unsteady flow
Discrete Scale Axis Representations for 3D Geometry
Miklos, Balint; Giesen, Joachim; Pauly, Mark
2010-01-01
This paper addresses the fundamental problem of computing stable medial representations of 3D shapes. We propose a spatially adaptive classification of geometric features that yields a robust algorithm for generating medial representations at different levels of abstraction. The recently introduced continuous scale axis transform serves as the mathematical foundation of our algorithm. We show how geometric and topological properties of the continuous setting carry over to discrete shape repre...
Three-dimensional representation of complex muscle architectures and geometries.
Blemker, Silvia S; Delp, Scott L
2005-05-01
Almost all computer models of the musculoskeletal system represent muscle geometry using a series of line segments. This simplification (i) limits the ability of models to accurately represent the paths of muscles with complex geometry and (ii) assumes that moment arms are equivalent for all fibers within a muscle (or muscle compartment). The goal of this work was to develop and evaluate a new method for creating three-dimensional (3D) finite-element models that represent complex muscle geometry and the variation in moment arms across fibers within a muscle. We created 3D models of the psoas, iliacus, gluteus maximus, and gluteus medius muscles from magnetic resonance (MR) images. Peak fiber moment arms varied substantially among fibers within each muscle (e.g., for the psoas the peak fiber hip flexion moment arms varied from 2 to 3 cm, and for the gluteus maximus the peak fiber hip extension moment arms varied from 1 to 7 cm). Moment arms from the literature were generally within the range of fiber moment arms predicted by the 3D models. The models accurately predicted changes in muscle surface geometry over a 55 degrees range of hip flexion, as compared to changes in shape predicted from MR images (average errors between the model and measured surfaces were between 1.7 and 5.2 mm). This new framework for representing muscle will enhance the accuracy of computer models of the musculoskeletal system.
Generalized functions, volume 5 integral geometry and representation theory
Gel′fand, I M; Vilenkin, N Ya; Vilenkin, N Ya
2016-01-01
The first systematic theory of generalized functions (also known as distributions) was created in the early 1950s, although some aspects were developed much earlier, most notably in the definition of the Green's function in mathematics and in the work of Paul Dirac on quantum electrodynamics in physics. The six-volume collection, Generalized Functions, written by I. M. Gel′fand and co-authors and published in Russian between 1958 and 1966, gives an introduction to generalized functions and presents various applications to analysis, PDE, stochastic processes, and representation theory. The unif
Leikin, Mark; Waisman, Ilana; Shaul, Shelley; Leikin, Roza
2014-03-01
This paper presents a small part of a larger interdisciplinary study that investigates brain activity (using event related potential methodology) of male adolescents when solving mathematical problems of different types. The study design links mathematics education research with neurocognitive studies. In this paper we performed a comparative analysis of brain activity associated with the translation from visual to symbolic representations of mathematical objects in algebra and geometry. Algebraic tasks require translation from graphical to symbolic representation of a function, whereas tasks in geometry require translation from a drawing of a geometric figure to a symbolic representation of its property. The findings demonstrate that electrical activity associated with the performance of geometrical tasks is stronger than that associated with solving algebraic tasks. Additionally, we found different scalp topography of the brain activity associated with algebraic and geometric tasks. Based on these results, we argue that problem solving in algebra and geometry is associated with different patterns of brain activity.
Nonassociative geometry in quasi-Hopf representation categories II: Connections and curvature
Barnes, Gwendolyn E; Szabo, Richard J
2015-01-01
We continue our systematic development of noncommutative and nonassociative differential geometry internal to the representation category of a quasitriangular quasi-Hopf algebra. We describe derivations, differential operators, differential calculi and connections using universal categorical constructions to capture algebraic properties such as Leibniz rules. Our main result is the construction of morphisms which provide prescriptions for lifting connections to tensor products and to internal homomorphisms. We describe the curvatures of connections within our formalism, and also the formulation of Einstein-Cartan geometry as a putative framework for a nonassociative theory of gravity.
Nonassociative geometry in quasi-Hopf representation categories II: Connections and curvature
Barnes, Gwendolyn E.; Schenkel, Alexander; Szabo, Richard J.
2016-08-01
We continue our systematic development of noncommutative and nonassociative differential geometry internal to the representation category of a quasitriangular quasi-Hopf algebra. We describe derivations, differential operators, differential calculi and connections using universal categorical constructions to capture algebraic properties such as Leibniz rules. Our main result is the construction of morphisms which provide prescriptions for lifting connections to tensor products and to internal homomorphisms. We describe the curvatures of connections within our formalism, and also the formulation of Einstein-Cartan geometry as a putative framework for a nonassociative theory of gravity.
Zhang, Dake; Wang, Qiu; Ding, Yi; Liu, Jeremy Jian
2014-01-01
According to the National Council of Teachers of Mathematics, geometry and spatial sense are fundamental components of mathematics learning. However, learning disabilities (LD) research has shown that many K-12 students encounter particular geometry difficulties (GD). This study examined the effect of an integrated object representation (IOR)…
Barnes, Gwendolyn E; Szabo, Richard J
2014-01-01
We systematically study noncommutative and nonassociative algebras A and their bimodules as algebras and bimodules internal to the representation category of a quasitriangular quasi-Hopf algebra. We enlarge the morphisms of the monoidal category of A-bimodules by internal homomorphisms, and describe explicitly their evaluation and composition morphisms. For braided commutative algebras A the full subcategory of symmetric A-bimodule objects is a braided closed monoidal category, from which we obtain an internal tensor product operation on internal homomorphisms. We describe how these structures deform under cochain twisting of the quasi-Hopf algebra, and apply the formalism to the example of deformation quantization of equivariant vector bundles over a smooth manifold. Our constructions set up the basic ingredients for the systematic development of differential geometry internal to the quasi-Hopf representation category, which will be tackled in the sequels to this paper, together with applications to models o...
Ping Lu; Xudong Jiang; Wei Lu; Ran Wei; Bin Sheng
2015-01-01
Regularized Boolean operations have been widely used in 3D modeling systems. However, evaluating Boolean operations may be quite numerically unstable and time consuming, espe⁃cially for iterated set operations. A novel and unified tech⁃nique is proposed in this paper for computing single and iter⁃ated set operations efficiently, robustly and exactly. An adap⁃tive octree is combined with a nested constructive solid geom⁃etry (CSG) tree by this technique. The intersection handling is restricted to the cells in the octree where intersection actu⁃ally occurs. Within those cells, a CSG tree template is in⁃stanced by the surfaces and the tree is converted to plane⁃based binary space partitioning (BSP) for set evaluation;More⁃over, the surface classification is restricted to the cells in the octree where the surfaces only come from a model and are within the bounding⁃boxes of other polyhedrons. These two ways bring about the efficiency and scalability of the opera⁃tions, in terms of runtime and memory. As all surfaces in such a cell have the same classification relation, they are clas⁃sified as a whole. Robustness and exactness are achieved by integrating plane⁃based geometry representation with adaptive geometry predicate technique in intersection handling, and by applying divide⁃and⁃conquer arithmetic on surface classifica⁃tion. Experimental results demonstrate that the proposed ap⁃proach can guarantee the robustness of Boolean computations and runs faster than other existing approaches.
Finsler Geometry of Nonlinear Elastic Solids with Internal Structure
2017-01-01
generality has resulted in its use in field-theoretical descriptions of nearly all branches of physics : general relativity [1], gravitation [2], quantum ...John D Clayton A reprint from the Journal of Geometry and Physics . 2017;112:118–146. Approved for public release...Materials Research Directorate, ARL A reprint from the Journal of Geometry and Physics . 2017;112:118–146. Approved for
Jun Zhang
2013-12-01
Full Text Available Divergence functions are the non-symmetric “distance” on the manifold, Μθ, of parametric probability density functions over a measure space, (Χ,μ. Classical information geometry prescribes, on Μθ: (i a Riemannian metric given by the Fisher information; (ii a pair of dual connections (giving rise to the family of α-connections that preserve the metric under parallel transport by their joint actions; and (iii a family of divergence functions ( α-divergence defined on Μθ x Μθ, which induce the metric and the dual connections. Here, we construct an extension of this differential geometric structure from Μθ (that of parametric probability density functions to the manifold, Μ, of non-parametric functions on X, removing the positivity and normalization constraints. The generalized Fisher information and α-connections on M are induced by an α-parameterized family of divergence functions, reflecting the fundamental convex inequality associated with any smooth and strictly convex function. The infinite-dimensional manifold, M, has zero curvature for all these α-connections; hence, the generally non-zero curvature of M can be interpreted as arising from an embedding of Μθ into Μ. Furthermore, when a parametric model (after a monotonic scaling forms an affine submanifold, its natural and expectation parameters form biorthogonal coordinates, and such a submanifold is dually flat for α = ± 1, generalizing the results of Amari’s α-embedding. The present analysis illuminates two different types of duality in information geometry, one concerning the referential status of a point (measurable function expressed in the divergence function (“referential duality” and the other concerning its representation under an arbitrary monotone scaling (“representational duality”.
Conformal Solid T-spline Construction from Boundary T-spline Representations
2012-07-01
idea of isogeo- metric analysis [6, 2], one challenge is to automatically cre- ate a conformal solid NURBS /T-spline model with the given spline...solid NURBS construction method for patient-specific vas- cular geometric models was presented. In [1], a swept vol- ume parameterization was built for...representations. A general methodology for constructing a conformal solid T-spline from boundary T-spline/ NURBS representations is 2 Yongjie Zhang et al. (a
Hwang, Wu-Yuin; Hu, Shih-Shin
2013-01-01
Learning geometry emphasizes the importance of exploring different representations such as virtual manipulatives, written math formulas, and verbal explanations, which help students build math concepts and develop critical thinking. Besides helping individuals construct math knowledge, peer interaction also plays a crucial role in promoting an…
Lazar, Markus, E-mail: lazar@fkp.tu-darmstadt.de [Heisenberg Research Group, Department of Physics, Darmstadt University of Technology, Hochschulstr. 6, D-64289 Darmstadt (Germany); Po, Giacomo [Mechanical and Aerospace Engineering, University of California, Los Angeles, Los Angeles, CA 90095 (United States)
2014-01-24
A representation of the solid angle and the Burgers formula as line integral is derived in the framework of the theory of gradient elasticity of Helmholtz type. The gradient version of the Eshelby–deWit representation of the Burgers formula of a closed dislocation loop is given. Such a form is suitable for the numerical implementation in 3D dislocation dynamics (DD).
Defined solid-angle counter with variable geometry
Garcia-Torano, E. [Laboratorio de Metrologia de Radiaciones Ionizantes, CIEMAT, Avda. Complutense 22, 28040 Madrid (Spain)], E-mail: e.garciatorano@ciemat.es; Duran Ramiro, T. [Laboratorio de Metrologia de Radiaciones Ionizantes, CIEMAT, Avda. Complutense 22, 28040 Madrid (Spain); Burgos, C. [Division de Infraestrutura General Tecnica, CIEMAT, Madrid (Spain); Begona Ahedo, M. [Unidad de Ingenieria y Obras, CIEMAT, Madrid (Spain)
2008-06-15
We describe a defined solid-angle counter for the standardization of radioactive sources of alpha-particle emitters. It has been built with the aim of combining good counting efficiencies, low uncertainties and flexibility of operation. The distance between source and detector can be changed in a continuous way with a precision guide and a ball screw from 8 to 19 cm, which correspond to counting efficiencies between 0.023 and 0.004 for small size sources. A linear encoder allows the accurate determination of the source position. Alpha spectra of the sources are measured with an implanted silicon detector with an active area of 2000 mm{sup 2}. Uncertainties, excluding counting statistics, are below 0.1%.
Graph Representation for Configurational Properties of Crystalline Solids
Yuge, Koretaka
2017-02-01
We propose representation of configurational physical quantities and microscopic structures for multicomponent system on lattice, by extending a concept of generalized Ising model (GIM) to graph theory. We construct graph Laplacian (and adjacency matrix) composed of symmetry-equivalent neighboring edges, whose landscape of spectrum explicitly represents GIM description of structures as well as low-dimensional topological information in terms of graph. The proposed representation indicates the importance of linear combination of graph to further investigate the role of spatial constraint on equilibrium properties in classical systems. We demonstrate that spectrum for such linear combination of graph can find out additional characteristic microscopic structures compared with GIM-based descriptions for given set of figures on the same low-dimensional configuration space, coming from the proposed representation explicitly having more structural information for, e.g., higher-order closed links of selected element. Statistical interdependence for density of microscopic states including graph representation for structures is also examined, which exhibits similar behavior that has been seen for GIM description of the microscopic structures.
Zhang, Dake; Wang, Qiu; Ding, Yi; Liu, Jeremy Jian
2014-01-01
According to the National Council of Teachers of Mathematics, geometry and spatial sense are fundamental components of mathematics learning. However, learning disabilities (LD) research has shown that many K-12 students encounter particular geometry difficulties (GD). This study examined the effect of an integrated object representation (IOR) accommodation on the test performance of students with GD compared to students without GD. Participants were 118 elementary students who took a researcher-developed geometry problem solving test under both a standard testing condition and an IOR accommodation condition. A total of 36 students who were classified with GD scored below 40% correct in the geometry problem solving test in the standard testing condition, and 82 students who were classified without GD scored equal to or above 40% correct in the same test and condition. All students were tested in both standard testing condition and IOR accommodation condition. The results from both ANOVA and regression discontinuity (RD) analyses suggested that students with GD benefited more than students without GD from the IOR accommodation. Implications of the study are discussed in terms of providing accommodations for students with mathematics learning difficulties and recommending RD design in LD research.
Lin, Hao-Chiang Koong; Chen, Mei-Chi; Chang, Chih-Kai
2015-01-01
This study integrates augmented reality (AR) technology into teaching activities to design a learning system that assists junior high-school students in learning solid geometry. The following issues are addressed: (1) the relationship between achievements in mathematics and performance in spatial perception; (2) whether system-assisted learning…
Lin, Hao-Chiang Koong; Chen, Mei-Chi; Chang, Chih-Kai
2015-01-01
This study integrates augmented reality (AR) technology into teaching activities to design a learning system that assists junior high-school students in learning solid geometry. The following issues are addressed: (1) the relationship between achievements in mathematics and performance in spatial perception; (2) whether system-assisted learning…
Tomaschewski, Fernanda K.; Segatto, Cynthia F., E-mail: fernandasls_89@hotmail.com, E-mail: cynthia.segatto@ufrgs.br [Universidade Federal do Rio Grande do Sul (UFRS), Porto Alegre, RS (Brazil). Programa de Pos-Graduacao em Matematica Aplicada; Barros, Ricardo C., E-mail: rcbarros@pq.cnpq.br [Universidade do Estado do Rio de Janeiro (UERJ), Nova Friburgo, RJ (Brazil). Departamento de Modelagem Computacional
2015-07-01
Presented here is a decomposition method based on series representation of the group angular fluxes and delayed neutron precursors in smoothly continuous functions for energy multigroups, slab-geometry discrete ordinates kinetics equations supplemented with a prescribed number of delayed neutron precursors. Numerical results to a non-reflected sub-critical slab stabilized by steady-state sources are given to illustrate the accuracy and efficiency of the o offered method. (author)
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
Kring, J.; Gyekenyesi, J.; Mendelson, A.
1977-01-01
The line method of analysis is applied to the Navier-Cauchy equations of elastic equilibrium to calculate the displacement fields in finite geometry bars containing central, surface, and double-edge cracks under extensionally applied uniform loading. The application of this method to these equations leads to coupled sets of simultaneous ordinary differential equations whose solutions are obtained along sets of lines in a discretized region. Normal stresses and the stress intensity factor variation along the crack periphery are calculated using the obtained displacement field. The reported results demonstrate the usefulness of this method in calculating stress intensity factors for commonly encountered crack geometries in finite solids.
Mali, Kunal S; Zöphel, Lukas; Ivasenko, Oleksandr; Müllen, Klaus; De Feyter, Steven
2013-10-01
In this work, we provide evidence for multiple non-planar adsorption geometries of a novel pyrenocyanine derivative at the liquid-solid interface under ambient conditions. When adsorbed at the organic liquid-solid interface, lead pyrenocyanine forms well-ordered monolayers that exhibit peculiar non-periodic contrast variation. The different contrast of the adsorbed molecules is attributed to dissimilar adsorption geometries which arise from the non-planar conformation of the molecules. The non-planarity of the molecular backbone in turn arises due to a combination of the angularly extended pyrene subunits and the presence of the large lead ion, which is too big to fit inside the central cavity and thus is located out of the aromatic plane. The two possible locations of the lead atom, namely below and above the aromatic plane, could be identified as depression and protrusion in the central cavity, respectively. The manifestation of such multiple adsorption geometries on the structure of the resultant monolayer is discussed in detail. The packing density of these 2D arrays of molecules could be tuned by heating of the sample wherein the molecular packing changes from a low-density, pseudo six-fold symmetric to a high-density, two-fold symmetric arrangement. Finally, a well-ordered two-component system could be constructed by incorporating C60 molecules in the adlayer of lead pyrenocyanine at the liquid-solid interface.
Room acoustics modeling using a point-cloud representation of the room geometry
Markovic, Milos; Olesen, Søren Krarup; Hammershøi, Dorte
2013-01-01
Room acoustics modeling is usually based on the room geometry that is parametrically described prior to a sound transmission calculation. This is a highly room-specific task and rather time consuming if a complex geometry is to be described. Here, a run time generic method for an arbitrary room...... geometry acquisition is presented. The method exploits a depth sensor of the Kinect device that provides a point based information of a scanned room interior. After post-processing of the Kinect output data, a 3D point-cloud model of the room is obtained. Sound transmission between two selected points...... within the room is simulated using a 3D point-cloud model to define a room geometry and a discrete ray-tracing method to calculate sound propagation paths within the enclosure. Based on a 3D point-cloud room model a voxel grid is created and each voxel has been assigned certain properties...
Finster, Felix
2016-01-01
The massive Dirac equation is considered in the non-extreme Kerr geometry in horizon-penetrating Eddington-Finkelstein-type coordinates. We derive an integral representation for the Dirac propagator involving the solutions of the ODEs which arise in Chandrasekhar's separation of variables. This integral representation describes the dynamics of Dirac waves outside and across the event horizon, up to the Cauchy horizon. For the proof, we write the Dirac equation in Hamiltonian form. One of the main difficulties is that the time evolution is not unitary, because the wave may "hit" the singularity. This problem is resolved by imposing suitable Dirichlet-type boundary conditions inside the Cauchy horizon, having no effect on the outside dynamics. Another main difficulty is that the Dirac Hamiltonian fails to be elliptic at the horizons. Combining the theory of symmetric hyperbolic systems with elliptic methods near the boundary, we construct a self-adjoint extension of the resulting Hamiltonian. We finally apply S...
SPH-DCDEM model for arbitrary geometries in free surface solid-fluid flows
Canelas, Ricardo B.; Crespo, Alejandro J. C.; Domínguez, Jose M.; Ferreira, Rui M. L.; Gómez-Gesteira, Moncho
2016-05-01
A unified discretization of rigid solids and fluids is introduced, allowing for resolved simulations of fluid-solid phases within a meshless framework. The numerical solution, attained by Smoothed Particle Hydrodynamics (SPH) and a variation of Discrete Element Method (DEM), the Distributed Contact Discrete Element Method (DCDEM) discretization, is achieved by directly considering solid-solid and solid-fluid interactions. The novelty of the work is centred on the generalization of the coupling of the DEM and SPH methodologies for resolved simulations, allowing for state-of-the-art contact mechanics theories to be used in arbitrary geometries, while fluid to solid and vice versa momentum transfers are accurately described. The methods are introduced, analysed and discussed. Initial validations on the DCDEM and the fluid coupling are presented, drawing from test cases in the literature. An experimental campaign serves as a validation point for complex, large scale solid-fluid flows, where a set of blocks in several configurations is subjected to a dam-break wave. Blocks are tracked and positions are then compared between experimental data and the numerical solutions. A Particle Image Velocimetry (PIV) technique allows for the quantification of the flow field and direct comparison with numerical data. The results show that the model is accurate and is capable of treating highly complex interactions, such as transport of debris or hydrodynamic actions on structures, if relevant scales are reproduced.
The representation of manipulable solid objects in a relational database
Bahler, D.
1984-01-01
This project is concerned with the interface between database management and solid geometric modeling. The desirability of integrating computer-aided design, manufacture, testing, and management into a coherent system is by now well recognized. One proposed configuration for such a system uses a relational database management system as the central focus; the various other functions are linked through their use of a common data repesentation in the data manager, rather than communicating pairwise to integrate a geometric modeling capability with a generic relational data managemet system in such a way that well-formed questions can be posed and answered about the performance of the system as a whole. One necessary feature of any such system is simplification for purposes of anaysis; this and system performance considerations meant that a paramount goal therefore was that of unity and simplicity of the data structures used.
Comparison of solid shapes geometry derived by a laser scanner and a total station
Sidiropoulos, Andreas; Lakakis, Konstantinos
2016-08-01
The laser scanning technology has become a common method for the daily applications of a large variety of scientists and professionals. Even for more sophisticated projects, laser scanners have been proved a very useful tool at researchers' and engineers' disposal. In this paper, we investigated the ability of a laser scanner compared to the ability of a total station to provide the geometry of solids. The tests were made in the laboratory facilities of the Aristotle University of Thessaloniki, in a variety of distances between the measuring instrument and the object. The solids that were used differ in shape, material and color. The objects are a wooden cube, a metal cube and a wooden pyramid. The absolute dimensions of the solid shapes were provided by the use of a caliper and were compared to the dimensions that were calculated by the coordinates produced by the total station and laser scanner measurements.
Zhang, Dake; Ding, Yi; Stegall, Joanna; Mo, Lei
2012-01-01
Students who struggle with learning mathematics often have difficulties with geometry problem solving, which requires strong visual imagery skills. These difficulties have been correlated with deficiencies in visual working memory. Cognitive psychology has shown that chunking of visual items accommodates students' working memory deficits. This…
Room acoustics modeling using a point-cloud representation of the room geometry
Markovic, Milos; Olesen, Søren Krarup; Hammershøi, Dorte
2013-01-01
within the room is simulated using a 3D point-cloud model to define a room geometry and a discrete ray-tracing method to calculate sound propagation paths within the enclosure. Based on a 3D point-cloud room model a voxel grid is created and each voxel has been assigned certain properties...
Shin, Sunghwan; Kang, Hani; Kim, Jun Soo; Kang, Heon
2014-11-26
We investigated the phase transformations of amorphous solid acetone under confined geometry by preparing acetone films trapped in amorphous solid water (ASW) or CCl4. Reflection absorption infrared spectroscopy (RAIRS) and temperature-programmed desorption (TPD) were used to monitor the phase changes of the acetone sample with increasing temperature. An acetone film trapped in ASW shows an abrupt change in the RAIRS features of the acetone vibrational bands during heating from 80 to 100 K, which indicates the transformation of amorphous solid acetone to a molecularly aligned crystalline phase. Further heating of the sample to 140 K produces an isotropic solid phase, and eventually a fluid phase near 157 K, at which the acetone sample is probably trapped in a pressurized, superheated condition inside the ASW matrix. Inside a CCl4 matrix, amorphous solid acetone crystallizes into a different, isotropic structure at ca. 90 K. We propose that the molecularly aligned crystalline phase formed in ASW is created by heterogeneous nucleation at the acetone-water interface, with resultant crystal growth, whereas the isotropic crystalline phase in CCl4 is formed by homogeneous crystal growth starting from the bulk region of the acetone sample.
Domain Decomposition of a Constructive Solid Geometry Monte Carlo Transport Code
O' Brien, M J; Joy, K I; Procassini, R J; Greenman, G M
2008-12-07
Domain decomposition has been implemented in a Constructive Solid Geometry (CSG) Monte Carlo neutron transport code. Previous methods to parallelize a CSG code relied entirely on particle parallelism; but in our approach we distribute the geometry as well as the particles across processors. This enables calculations whose geometric description is larger than what could fit in memory of a single processor, thus it must be distributed across processors. In addition to enabling very large calculations, we show that domain decomposition can speed up calculations compared to particle parallelism alone. We also show results of a calculation of the proposed Laser Inertial-Confinement Fusion-Fission Energy (LIFE) facility, which has 5.6 million CSG parts.
Gyekenyesi, J. P.; Mendelson, A.
1977-01-01
The line method of analysis is applied to the Navier-Cauchy equations of elastic equilibrium to calculate the displacement field in a finite geometry bar containing a variable depth rectangular surface crack under extensionally applied uniform loading. The application of this method to these equations leads to coupled sets of simultaneous ordinary differential equations whose solutions are obtained along sets of lines in a discretized region. Using the obtained displacement field, normal stresses, and the stress-intensity factor variation along the crack periphery are calculated for different crack depth to bar thickness ratios. Crack opening displacements and stress-intensity factors are also obtained for a through-thickness, center-cracked bar with variable thickness. The reported results show a considerable potential for using this method in calculating stress-intensity factors for commonly encountered surface crack geometries in finite solids
Gyekenyesi, J. P.; Mendelson, A.
1975-01-01
The line method of analysis is applied to the Navier-Cauchy equations of elastic equilibrium to calculate the displacement field in a finite geometry bar containing a variable depth rectangular surface crack under extensionally applied uniform loading. The application of this method to these equations leads to coupled sets of simultaneous ordinary differential equations whose solutions are obtained along sets of lines in a discretized region. Using the obtained displacement field, normal stresses and the stress intensity factor variation along the crack periphery are calculated for different crack depth to bar thickness ratios. Crack opening displacements and stress intensity factors are also obtained for a through-thickness, center cracked bar with variable thickness. The reported results show a considerable potential for using this method in calculating stress intensity factors for commonly encountered surface crack geometries in finite solids.
Majkic, M. D.; Nedeljkovic, N. N.; Galijas, S. M. D.
2010-07-01
We elaborated the time-symmetric, two-state vector model to investigate the intermediate stages of the electron capture into the Rydberg states of multiply charged ions interacting with solid surface under the grazing incidence geometry. The neutralization distances for the ions XeZ+ interacting with Al-surface are calculated, for core charges Z ?[5,30]. The corresponding mean neutralization distances are in agreement with the data deduced from the measured kinetic energy gain due to the image acceleration of the ions.
Yang-Mills Field from Quaternion Space Geometry, and its Klein-Gordon Representation
Yefremov A.
2007-07-01
Full Text Available Analysis of covariant derivatives of vectors in quaternion (Q- spaces performed using Q-unit spinor-splitting technique and use of SL(2C-invariance of quaternion multiplication reveals close connexion of Q-geometry objects and Yang-Mills (YM field principle characteristics. In particular, it is shown that Q-connexion (with quaternion non-metricity and related curvature of 4 dimensional (4D space-times with 3D Q-space sections are formally equivalent to respectively YM-field potential and strength, traditionally emerging from the minimal action assumption. Plausible links between YM field equation and Klein-Gordon equation, in particular via its known isomorphism with Duffin-Kemmer equation, are also discussed.
The physics of solid-state neutron detector materials and geometries.
Caruso, A N
2010-11-10
Detection of neutrons, at high total efficiency, with greater resolution in kinetic energy, time and/or real-space position, is fundamental to the advance of subfields within nuclear medicine, high-energy physics, non-proliferation of special nuclear materials, astrophysics, structural biology and chemistry, magnetism and nuclear energy. Clever indirect-conversion geometries, interaction/transport calculations and modern processing methods for silicon and gallium arsenide allow for the realization of moderate- to high-efficiency neutron detectors as a result of low defect concentrations, tuned reaction product ranges, enhanced effective omnidirectional cross sections and reduced electron-hole pair recombination from more physically abrupt and electronically engineered interfaces. Conversely, semiconductors with high neutron cross sections and unique transduction mechanisms capable of achieving very high total efficiency are gaining greater recognition despite the relative immaturity of their growth, lithographic processing and electronic structure understanding. This review focuses on advances and challenges in charged-particle-based device geometries, materials and associated mechanisms for direct and indirect transduction of thermal to fast neutrons within the context of application. Calorimetry- and radioluminescence-based intermediate processes in the solid state are not included.
A smooth dissipative particle dynamics method for domains with arbitrary-geometry solid boundaries
Gatsonis, Nikolaos A.; Potami, Raffaele; Yang, Jun
2014-01-01
A smooth dissipative particle dynamics method with dynamic virtual particle allocation (SDPD-DV) for modeling and simulation of mesoscopic fluids in wall-bounded domains is presented. The physical domain in SDPD-DV may contain external and internal solid boundaries of arbitrary geometries, periodic inlets and outlets, and the fluid region. The SDPD-DV method is realized with fluid particles, boundary particles, and dynamically allocated virtual particles. The internal or external solid boundaries of the domain can be of arbitrary geometry and are discretized with a surface grid. These boundaries are represented by boundary particles with assigned properties. The fluid domain is discretized with fluid particles of constant mass and variable volume. Conservative and dissipative force models due to virtual particles exerted on a fluid particle in the proximity of a solid boundary supplement the original SDPD formulation. The dynamic virtual particle allocation approach provides the density and the forces due to virtual particles. The integration of the SDPD equations is accomplished with a velocity-Verlet algorithm for the momentum and a Runge-Kutta for the entropy equation. The velocity integrator is supplemented by a bounce-forward algorithm in cases where the virtual particle force model is not able to prevent particle penetration. For the incompressible isothermal systems considered in this work, the pressure of a fluid particle is obtained by an artificial compressibility formulation for liquids and the ideal gas law for gases. The self-diffusion coefficient is obtained by an implementation of the generalized Einstein and the Green-Kubo relations. Field properties are obtained by sampling SDPD-DV outputs on a post-processing grid that allows harnessing the particle information on desired spatiotemporal scales. The SDPD-DV method is verified and validated with simulations in bounded and periodic domains that cover the hydrodynamic and mesoscopic regimes for
The symplectic geometry of the Gel'fand--Cetlin--Molev basis for representations of $Sp(2n,\\C)$
Harada, Megumi
2006-01-01
Gel'fand and Cetlin [I. Gel'fand and M. Tsetlin, Finite-dimensional representations of the group of orthogonal matrices, Dokl. Akad. Nauk SSSR 17 (1950), 1017--1020; I. Gel'fand and M. Tsetlin, Finite-dimensional representations of the group of unimodular matrices. Dokl. Akad. Nauk SSSR 71 (1950), 825--828.] constructed in the 1950s a canonical basis for a finite-dimensional representation $V(\\lambda)$ of $U(n,\\C)$ by successive decompositions of the representation by a chai...
LI Shao-jing; Soichiroh INOUE; Tohru KANADA
2013-01-01
Descriptive geometry is very important and recognized as a basic skill and knowledge for mechanical engineering student. In this study, PC-based electronic teaching/learning materials for descriptive geometry are created using Flash®, which is a typical animation creator. Furthermore, several axonometric representations, created by 3D-CAD, SolidWorks®, for 3D objects are auxiliary materials to promote understanding of descriptive geometry. The axonometric representations in 3D-CAD are also dynamic, in other words, a viewpoint can be moved free. The movement of 3D model in a PC monitor can be recorded using a normal function of SolidWorks and replayed by typical animation software. The developed materials are excellent at accuracy of drawing, repeatability of self-study and visual attraction in comparison to oral presentation using still image and inaccurate drawing on a textbook or blackboard in a classroom. Actually, questionnaire survey results present favorable impressions from student-users, although they point out the further improvement in the replaying speed. The replaying speed can be controlled easily by using a normal function of Flash®. In addition, usual playback software for animation has functions of pause and replay on demand and, thus, it is not contro-versial.
SETOR: hardware-lighted three-dimensional solid model representations of macromolecules.
Evans, S V
1993-06-01
SETOR is designed to exploit the hardware lighting capabilities of the IRIS-4D series graphics workstations to render high-quality raster images of macromolecules that can undergo rotation and translation interactively. SETOR can render standard all-atom and backbone models of proteins or nucleic acids, but focuses on displaying protein molecules by highlighting elements of secondary structure. The program has a very friendly user interface that minimizes the number of input files by allowing the user to interactively edit parameters, such as colors, lighting coefficients, and descriptions of secondary structure via mouse activated dialogue boxes. The choice of polymer chain representation can be varied from standard vector models and van der Waal models, to a B-spline fit of polymer backbones that yields a smooth ribbon that approximates the polymer chain, to strict Cardinal splines that interpolate the smoothest curve possible that will precisely follow the polymer chain. The program provides a photograph mode, save/restore facilities, and efficient generation of symmetry-related molecules and packing diagrams. Additionally, SETOR is designed to accept commands and model coordinates from the standard input stream, and to control standard output. Ancillary programs provide a method to interactively edit hardcopy plots of all vector and many solid models generated by SETOR, and to produce standard HPGL or PostScript files. Examples of figures rendered by SETOR of a number of macromolecules of various classes are presented.
Nedeljković, N. N.; Majkić, M. D.; Božanić, D. K.; Dojčilović, R. J.
2016-06-01
We consider the population dynamics of the intermediate Rydberg states of highly charged ions (core charge Z\\gg 1, principal quantum number {n}{{A}}\\gg 1) interacting with solid surfaces at arbitrary collision geometry. The recently developed resonant two-state vector model for the grazing incidence (2012 J. Phys. B: At. Mol. Opt. Phys. 45 215202) is extended to the quasi-resonant case and arbitrary angle of incidence. According to the model, the population probabilities depend both on the projectile parallel and perpendicular velocity components, in a complementary way. A cascade neutralization process for {{{Xe}}}Z+ ions, for Z=15{--}45, interacting with a conductive-surface is considered by taking into account the population dynamics. For an arbitrary collision geometry and given range of ionic velocities, a micro-staircase model for the simultaneous calculation of the kinetic energy gain and the charge state of the ion in front of the surface is proposed. The relevance of the obtained results for the explanation of the formation of nanostructures on solid surfaces by slow highly charged ions for normal incidence geometry is briefly discussed.
Ahn, Sung-Jin; Kim, Yong-Bum; Moon, Jooho [Department of Materials Science and Engineering, Yonsei University, Seoul 120-749 (Korea); Lee, Jong-Ho; Kim, Joosun [Nano-Materials Research Center, KIST, Seoul 136-791 (Korea)
2007-09-27
Co-planar, single-chamber, solid oxide fuel cells (SC-SOFCs) with linearly patterned electrode structures on one surface of the electrolyte are fabricated via a robo-dispensing method. The SC-SOFCs with various electrode patterns are prepared to investigate the relationship between electrode geometry and cell performance. The open-circuit voltage (OCV) for cells with a single electrode pair is unaffected by the anode-to-cathode distance. By contrast, for cells with multiple electrode pairs, increasing the number of electrode pairs leads to a gradual decrease in OCV. These observations confirm that the inter-mixing of product gases causes a loss in OCV and power density, which in turn reduces the oxygen partial pressure gradient between the anode and cathode. Keeping the electrode pairs apart by {proportional_to}4 mm permits cells with complex electrode geometry to exhibit higher OCVs and power densities. (author)
Ahn, Sung-Jin; Kim, Yong-Bum; Moon, Jooho; Lee, Jong-Ho; Kim, Joosun
Co-planar, single-chamber, solid oxide fuel cells (SC-SOFCs) with linearly patterned electrode structures on one surface of the electrolyte are fabricated via a robo-dispensing method. The SC-SOFCs with various electrode patterns are prepared to investigate the relationship between electrode geometry and cell performance. The open-circuit voltage (OCV) for cells with a single electrode pair is unaffected by the anode-to-cathode distance. By contrast, for cells with multiple electrode pairs, increasing the number of electrode pairs leads to a gradual decrease in OCV. These observations confirm that the inter-mixing of product gases causes a loss in OCV and power density, which in turn reduces the oxygen partial pressure gradient between the anode and cathode. Keeping the electrode pairs apart by ∼4 mm permits cells with complex electrode geometry to exhibit higher OCVs and power densities.
The so(d+2,2) Minimal Representation and Ambient Tractors: the Conformal Geometry of Momentum Space
Gover, A R
2009-01-01
Tractor Calculus is a powerful tool for analyzing Weyl invariance; although fundamentally linked to the Cartan connection, it may also be arrived at geometrically by viewing a conformal manifold as the space of null rays in a Lorentzian ambient space. For dimension d conformally flat manifolds we show that the (d+2)-dimensional Fefferman--Graham ambient space corresponds to the momentum space of a massless scalar field. Hence on the one hand the null cone parameterizes physical momentum excitations, while on the other hand, null rays correspond to points in the underlying conformal manifold. This allows us to identify a fundamental set of tractor operators with the generators of conformal symmetries of a scalar field theory in a momentum representation. Moreover, these constitute the minimal representation of the non-compact conformal Lie symmetry algebra of the scalar field with Kostant--Kirillov dimension d+1. Relaxing the conformally flat requirement, we find that while the conformal Lie algebra of tractor...
Concept of Quantum Geometry in Optoelectronic Processes in Solids: Application to Solar Cells.
Nagaosa, Naoto; Morimoto, Takahiro
2017-03-20
The concept of topology is becoming more and more relevant to the properties and functions of electronic materials including various transport phenomena and optical responses. A pedagogical introduction is given here to the basic ideas and their applications to optoelectronic processes in solids.
Ablation and geometry change study of solid armature in a railgun
Zhang, Ya-Dong; Ruan, Jiang-Jun; Hu, Yuan-Chao; Gong, Ruo-Han; Wen, Wu
2013-08-01
Armature plays an important role in the electromagnetic launch process. Due to the skin effect, the current density distribution is neither uniform on the rail, nor on the armature. High current density centralization in one part could lead to a partial high temperature and make the armature material melt down and be ablated, especially at low velocity. In this paper we try to change the geometry of a Cshaped armature to improve the current density distribution and reduce the ablation. Four variants of C-shaped armatures are designed to study the specific features, including a conventional C-shaped armature (CCA), a rounded leading edge C-shaped armature (LCA), a rounded trailing edge C-shaped armature (TCA), and a rounded incorporate edge C-shaped armature (ICA). A novel low-speed experiment is constructed and tested. The armatures are ablated and recovered to compare the improved effects. Then finite element simulations according to the experimental results are performed to further analyze the experimental results. It is proved that the current density and hence the temperature distribution can be immensely improved by simply changing the armature geometry. LCA and ICA show that the erosion is more uniform on the contact surface due to the rounded leading edge. The curved trailing edge could improve the uniformity of the current on the interface. ICA which combines the effects of LCA and TCA is the best option in the four armatures. How much the leading edge and the trailing edge should be curved involves the geometry of CCA and the posture of the interface on the rail. A saddle shape is a good option to improve the current density and temperature distribution in the throat. Erosion mechanism is analyzed finally. The experiments and simulations support the erosion and transition mechanism. A detailed description of the experiments and simulations is also presented in this paper.
Guggenheimer, Heinrich W
1977-01-01
This is a text of local differential geometry considered as an application of advanced calculus and linear algebra. The discussion is designed for advanced undergraduate or beginning graduate study, and presumes of readers only a fair knowledge of matrix algebra and of advanced calculus of functions of several real variables. The author, who is a Professor of Mathematics at the Polytechnic Institute of New York, begins with a discussion of plane geometry and then treats the local theory of Lie groups and transformation groups, solid differential geometry, and Riemannian geometry, leading to a
A. V. Voroneckii
2016-01-01
Full Text Available The paper deals with various theoretical approaches to the mathematical modeling of the operating process in solid propellant ramjets (SPRJ that use highly metalized solid propellant. It introduces a new method (combustion operating law method that allows us to carry out comparative analysis of combustion efficiency in SPRJ arbitrary geometry ram-burners (RB when there is no accurate information on the combustion law of condensed fuel particles. To illustrate an application of the proposed method, mathematical modeling of the operating process was conducted for three SPRJ ram-burners with three different air intakes (AI, for which distribution fields of main parameters of gas and fuel particles have been obtained. Most complete combustion of fuel particles and the lowest level of particles buildup are registered for RB180 (180 degree angle between AIs. The results of a comparative analysis show that the relative (compared to RB180 efficiency of the particle burning process equals 0.64 and 0.6, respectively, for RB90 (90 degree angle between AIs and RB60 (60 degree angle between AIs. The proposed method may be applied to solve the most difficult problems of mathematical modeling when the optimization development of the solid propellant and ramjet structure are fulfilled simultaneously, i.e. when designers do not have the complete information about the combustion law of the condensed fuel particles.
Sabio, E.; Zamora, F.; González-García, C. M.; Ledesma, B.; Álvarez-Murillo, A.; Román, S.
2016-12-01
In this work, the adsorption kinetics of p-nitrophenol (PNP) onto several commercial activated carbons (ACs) with different textural and geometrical characteristics was studied. For this aim, a homogeneous diffusion solid model (HDSM) was used, which does take the adsorbent shape into account. The HDSM was solved by means of the finite element method (FEM) using the commercial software COMSOL. The different kinetic patterns observed in the experiments carried out can be described by the developed model, which shows that the sharp drop of adsorption rate observed in some samples is caused by the formation of a concentration wave. The model allows one to visualize the changes in concentration taking place in both liquid and solid phases, which enables us to link the kinetic behaviour with the main features of the carbon samples.
Ablation and geometry change study of solid armature in a railgun
Zhang Ya-Dong; Ruan Jiang-Jun; Hu Yuan-Chao; Gong Ruo-Han; Wen Wu
2013-01-01
Armature plays an important role in the electromagnetic launch process.Due to the skin effect,the current density distribution is neither uniform on the rail,nor on the armature.High current density centralization in one part could lead to a partial high temperature and make the armature material melt down and be ablated,especially at low velocity.In this paper we try to change the geometry of a Cshaped armature to improve the current density distribution and reduce the ablation.Four variants of C-shaped armatures are designed to study the specific features,including a conventional C-shaped armature (CCA),a rounded leading edge C-shaped armature (LCA),a rounded trailing edge C-shaped armature (TCA),and a rounded incorporate edge C-shaped armature (ICA).A novel low-speed experiment is constructed and tested.The armatures are ablated and recovered to compare the improved effects.Then finite element simulations according to the experimental results are performed to further analyze the experimental results.It is proved that the current density and hence the temperature distribution can be immensely improved by simply changing the armature geometry.LCA and ICA show that the erosion is more uniform on the contact surface due to the rounded leading edge.The curved trailing edge could improve the uniformity of the current on the interface.ICA which combines the effects of LCA and TCA is the best option in the four armatures.How much the leading edge and the trailing edge should be curved involves the geometry of CCA and the posture of the interface on the rail.A saddle shape is a good option to improve the current density and temperature distribution in the throat.Erosion mechanism is analyzed finally.The experiments and simulations support the erosion and transition mechanism.A detailed description of the experiments and simulations is also presented in this paper.
Fernandes, Julio C.L.; Vilhena, Marco T.; Bodmann, Bardo E.J., E-mail: julio.lombaldo@ufrgs.br, E-mail: mtmbvilhena@gmail.com, E-mail: bardo.bodmann@ufrgs.br [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Dept. de Matematica Pura e Aplicada; Dulla, Sandra; Ravetto, Piero, E-mail: sandra.dulla@polito.it, E-mail: piero.ravetto@polito.it [Dipartimento di Energia, Politecnico di Torino, Piemonte (Italy)
2015-07-01
In this work we generalize the solution of the one-dimensional neutron transport equation to a multi- group approach in planar geometry. The basic idea of this work consists in consider the hierarchical construction of a solution for a generic number G of energy groups, starting from a mono-energetic solution. The hierarchical method follows the reasoning of the decomposition method. More specifically, the additional terms from adding energy groups is incorporated into the recursive scheme as source terms. This procedure leads to an analytical representation for the solution with G energy groups. The recursion depth is related to the accuracy of the solution, that may be evaluated after each recursion step. The authors present a heuristic analysis of stability for the results. Numerical simulations for a specific example with four energy groups and a localized pulsed source. (author)
A Unified Representation Scheme for Solid Geometric Objects Using B-splines (extended Abstract)
Bahler, D.
1985-01-01
A geometric representation scheme called the B-spline cylinder, which consists of interpolation between pairs of uniform periodic cubic B-spline curves is discussed. This approach carries a number of interesting implications. For one, a single relatively simple database schema can be used to represent a reasonably large class of objects, since the spline representation is flexible enough to allow a large domain of representable objects at very little cost in data complexity. The model is thus very storage-efficient. A second feature of such a system is that it reduces to one the number of routines which the system must support to perform a given operation on objects. Third, the scheme enables easy conversion to and from other representations. The formal definition of the cylinder entity is given. In the geometric properties of the entity are explored and several operations on such objects are defined. Some general purpose criteria for evaluating any geometric representation scheme are introduced and the B-spline cylinder scheme according to these criteria is evaluated.
Zhang, Shan-Lin; Li, Cheng-Xin; Liu, Shuai; Li, Chang-Jiu; Yang, Guan-Jun; He, Peng-Jiang; Yun, Liang-Liang; Song, Bo; Xie, Ying-Xin
2017-02-01
In this study, we develop a large tubular solid oxide fuel cells design with several cells in series on a porous cermet support, which has many characteristics such as self-sealing, low Ohmic loss, high strength, and good thermal expansion coefficient matching. Here, we investigate aspects of the cell design, manufacture, performance, and application. Firstly, the cell length and number of cells in series are optimized by theoretical analysis. Then, thermal spraying is applied as a cost-effective method to prepare all the cell components. Finally, the performance of different types of cells and two types of stacks is characterized. The maximum output power of one tube, which had 20 cells in series, reaches 31 and 40.5 W at 800 and 900 °C, respectively. Moreover, the output power of a stack assembled with 56 tubes, each with ten cells in series, reaches 800 W at 830 °C. The excellent single tube and cell stack performance suggest that thermally sprayed tubular SOFCs have significant potential for commercialized application.
Zhang, Shan-Lin; Li, Cheng-Xin; Liu, Shuai; Li, Chang-Jiu; Yang, Guan-Jun; He, Peng-Jiang; Yun, Liang-Liang; Song, Bo; Xie, Ying-Xin
2017-01-01
In this study, we develop a large tubular solid oxide fuel cells design with several cells in series on a porous cermet support, which has many characteristics such as self-sealing, low Ohmic loss, high strength, and good thermal expansion coefficient matching. Here, we investigate aspects of the cell design, manufacture, performance, and application. Firstly, the cell length and number of cells in series are optimized by theoretical analysis. Then, thermal spraying is applied as a cost-effective method to prepare all the cell components. Finally, the performance of different types of cells and two types of stacks is characterized. The maximum output power of one tube, which had 20 cells in series, reaches 31 and 40.5 W at 800 and 900 °C, respectively. Moreover, the output power of a stack assembled with 56 tubes, each with ten cells in series, reaches 800 W at 830 °C. The excellent single tube and cell stack performance suggest that thermally sprayed tubular SOFCs have significant potential for commercialized application.
Advanced Geometric Modeler with Hybrid Representation
杨长贵; 陈玉健; 等
1996-01-01
An advanced geometric modeler GEMS4.0 has been developed,in which feature representation is used at the highest level abstraction of a product model.Boundary representation is used at the bottom level,while CSG model is adopted at the median level.A BRep data structure capable of modeling non-manifold is adopted.UNRBS representation is used for all curved surfaces,Quadric surfaces have dual representations consisting of their geometric data such as radius,center point,and center axis.Boundary representation of free form surfaces is easily built by sweeping and skinning method with NURBS geometry.Set operations on curved solids with boundary representation are performed by an evaluation process consisting of four steps.A file exchange facility is provided for the conversion between product data described by STEP and product information generated by GEMS4.0.
Direct space representation of metallicity and structural stability in SiO solids
Jenkins, Samantha [Department of Informatics and Mathematics, University of Trollhaettan/Uddevalla, PO Box 957, 461 29 Trollhaettan (Sweden)
2002-11-04
First principles calculations are performed on possible structures of silicon monoxide solids. The chemical character of all of the bonding interactions is systematically quantified in real space. It is found that the most stable SiO structure possesses the highest number of inequivalent bond paths. This process reveals a novel metallic Si-Si interaction and provides an explanation for the origin of the unexpectedly high conductivity in thin silicon oxide layers. In this paper a new measure for quantifying metallic character (in direct space) present in a bond has been introduced. Furthermore it has been possible to determine the directional properties of this metallic character in real space using the charge density. This finding is very important for future complementary metal oxide semiconductor technology.
Geometry from Information Geometry
Caticha, Ariel
2015-01-01
We use the method of maximum entropy to model physical space as a curved statistical manifold. It is then natural to use information geometry to explain the geometry of space. We find that the resultant information metric does not describe the full geometry of space but only its conformal geometry -- the geometry up to local changes of scale. Remarkably, this is precisely what is needed to model "physical" space in general relativity.
On the Application of Vector Method to Solid Geometry%向量法在立体几何中的应用
曾祥洲
2013-01-01
向量是一种最基本的，也是最重要的一种数学概念。通过向量的运用可以有效地解决几何问题。本文主要探讨向量在立体几何教学中的应用问题。%The vector is one of the most fundamental and most important mathematical concept. Through the use of the vector, we can effectively solve geometric problems. This paper mainly discusses the application of vector to the teaching of solid geome-try.
Adjoint-based shape optimization of fin geometry for enhanced solid/liquid phase-change process
Morimoto, Kenichi; Suzuki, Yuji
2015-11-01
In recent years, the control of heat transfer processes, which play a critical role in various engineering devices/systems, has gained renewed attention. The present study aims to establish an adjoint-based shape optimization method for high-performance heat transfer processes involving phase-change phenomena. A possible example includes the application to the thermal management technique using phase-change material. Adjoint-based shape optimization scheme is useful to optimal shape design and optimal control of systems, for which the base function of the solution is unknown and the solution includes an infinite number of degrees of freedom. Here we formulate the shape-optimization scheme based on adjoint heat conduction analyses, focusing on the shape optimization of fin geometry. In the computation of the developed scheme, a meshless local Petrov-Galerkin (MLPG) method that is suited for dealing with complex boundary geometry is employed, and the enthalpy method is adopted for analyzing the motion of the phase-change interface. We examine in detail the effect of the initial geometry and the node distribution in the MLPG analysis upon the final solution of the shape optimization. Also, we present a new strategy for the computation using bubble mesh.
Bowyer, Adrian
1983-01-01
A Programmer's Geometry provides a guide in programming geometric shapes. The book presents formulas and examples of computer representation and coding of geometry. Each of the nine chapters of the text deals with the representation and solution of a specific geometrical problem, such as areas, vectors, and volumes. The last chapter provides a brief discussion on generating image through a computer. The codes presented in the book are written in FORTRAN 77. The text will be of great use to programmers who are working on projects that involve geometric calculations.
Representation Discovery using Harmonic Analysis
Mahadevan, Sridhar
2008-01-01
Representations are at the heart of artificial intelligence (AI). This book is devoted to the problem of representation discovery: how can an intelligent system construct representations from its experience? Representation discovery re-parameterizes the state space - prior to the application of information retrieval, machine learning, or optimization techniques - facilitating later inference processes by constructing new task-specific bases adapted to the state space geometry. This book presents a general approach to representation discovery using the framework of harmonic analysis, in particu
2007-06-04
Flow Microfiltration ." Journal of Membrane Science 102(1-3): 31-42. 62 Hook, G. L., C. Jackson Lepage, et al. (2004). "Dynamic solid phase...Xia 2001) In another experiment, 1cm x 1cm and 1cm x 2cm sheets of thin PDMS membrane , with surface areas ~20 and ~40 times greater than a 100 μm...PDMS coated SPME fiber. The membranes were attached to a thin, deactivated stainless steel rod, in a configuration similar to a flag on a flagpole
Abedin Zafari
2012-11-01
Full Text Available Densiﬁcation of biomass feedstocks, such as pelletizing, can increase bulk density, improve storability, reduce transportation costs, and ease the handling of biomass using existing handling and storage equipment for grains. In order to study the pelletizing process, compost pellets were produced under controlled conditions. The aim of the work was to investigate the effect of raw material properties and the die geometry on the true density of formed pellets and also find the optimal conditions of the densification process for producing pellets with high density. Compost was extruded into cylindrical pellets utilizing open-end dies under axial stress from a vertical piston applied by a hydraulic press. The effects of independent variables, including the raw material moisture content (35 to 45% (wet basis, hammer mill screen size (0.3 to 1.5 mm, speed of piston (2 to 10 mm/s, and die length (8 to 12 mm on pellet density, were determined using response surface methodology. A quadratic model was proposed to predict the pellet density, which had high F and R2 values along with a low p value, indicating the predictability of the model. Moisture content, speed of piston, and particle size significantly affected (P 0.05.
Loop groups and noncommutative geometry
Carpi, Sebastiano
2015-01-01
We describe the representation theory of loop groups in terms of K-theory and noncommutative geometry. This is done by constructing suitable spectral triples associated with the level l projective unitary positive-energy representations of any given loop group LG. The construction is based on certain supersymmetric conformal field theory models associated with LG.
Tailwater recovery (TWR) systems are being implemented on agricultural landscapes to create an additional source of irrigation water. Existing studies have sampled TWR systems using grab samples; however, the applicability of solids and nutrient concentrations in these samples to water being irrigat...
Guide to Computational Geometry Processing
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......, 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...
Linear algebra and projective geometry
Baer, Reinhold
2005-01-01
Geared toward upper-level undergraduates and graduate students, this text establishes that projective geometry and linear algebra are essentially identical. The supporting evidence consists of theorems offering an algebraic demonstration of certain geometric concepts. These focus on the representation of projective geometries by linear manifolds, of projectivities by semilinear transformations, of collineations by linear transformations, and of dualities by semilinear forms. These theorems lead to a reconstruction of the geometry that constituted the discussion's starting point, within algebra
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.
Geometry in the Early Years: A Commentary
Dindyal, Jaguthsing
2015-01-01
The primary goal of this paper is to provide a commentary on the teaching and learning of geometry in the early years of schooling with the set of papers in this issue as a guiding factor. It is structured around issues about geometry education of young learners, such as: what should we teach in geometry and why; representation of geometrical…
Geometry in the Early Years: A Commentary
Dindyal, Jaguthsing
2015-01-01
The primary goal of this paper is to provide a commentary on the teaching and learning of geometry in the early years of schooling with the set of papers in this issue as a guiding factor. It is structured around issues about geometry education of young learners, such as: what should we teach in geometry and why; representation of geometrical…
Bengtsson, Ingemar; Zyczkowski, Karol
2007-12-01
Preface; 1. Convexity, colours and statistics; 2. Geometry of probability distributions; 3. Much ado about spheres; 4. Complex projective spaces; 5. Outline of quantum mechanics; 6. Coherent states and group actions; 7. The stellar representation; 8. The space of density matrices; 9. Purification of mixed quantum states; 10. Quantum operations; 11. Duality: maps versus states; 12. Density matrices and entropies; 13. Distinguishability measures; 14. Monotone metrics and measures; 15. Quantum entanglement; Epilogue; Appendices; References; Index.
Cecil, Thomas E
2015-01-01
This exposition provides the state-of-the art on the differential geometry of hypersurfaces in real, complex, and quaternionic space forms. Special emphasis is placed on isoparametric and Dupin hypersurfaces in real space forms as well as Hopf hypersurfaces in complex space forms. The book is accessible to a reader who has completed a one-year graduate course in differential geometry. The text, including open problems and an extensive list of references, is an excellent resource for researchers in this area. Geometry of Hypersurfaces begins with the basic theory of submanifolds in real space forms. Topics include shape operators, principal curvatures and foliations, tubes and parallel hypersurfaces, curvature spheres and focal submanifolds. The focus then turns to the theory of isoparametric hypersurfaces in spheres. Important examples and classification results are given, including the construction of isoparametric hypersurfaces based on representations of Clifford algebras. An in-depth treatment of Dupin hy...
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
Geometry, Representation Theory, and the Langlands Program
2013-04-01
April 2013 Final Report DISTRIBUTION A: Approved for public release. AIR FORCE RESEARCH LABORATORY AF OFFICE OF SCIENTIFIC RESEARCH ...following people, who did research at the Institute for Advanced Study: CHAUDOUARD, FARGUES, GORESKY, NAIR, and NGO. The mathematical context of the work was... Scientifiques de l’Ecole Normale Supérieure 45 (2012), 535-599. (14) (with Q. Lin) Highest weight modules at the critical level and noncommu- tative
Unit cell geometry of multiaxial preforms for structural composites
Ko, Frank; Lei, Charles; Rahman, Anisur; Du, G. W.; Cai, Yun-Jia
1993-01-01
The objective of this study is to investigate the yarn geometry of multiaxial preforms. The importance of multiaxial preforms for structural composites is well recognized by the industry but, to exploit their full potential, engineering design rules must be established. This study is a step in that direction. In this work the preform geometry for knitted and braided preforms was studied by making a range of well designed samples and studying them by photo microscopy. The structural geometry of the preforms is related to the processing parameters. Based on solid modeling and B-spline methodology a software package is developed. This computer code enables real time structural representations of complex fiber architecture based on the rule of preform manufacturing. The code has the capability of zooming and section plotting. These capabilities provide a powerful means to study the effect of processing variables on the preform geometry. the code also can be extended to an auto mesh generator for downstream structural analysis using finite element method. This report is organized into six sections. In the first section the scope and background of this work is elaborated. In section two the unit cell geometries of braided and multi-axial warp knitted preforms is discussed. The theoretical frame work of yarn path modeling and solid modeling is presented in section three. The thin section microscopy carried out to observe the structural geometry of the preforms is the subject in section four. The structural geometry is related to the processing parameters in section five. Section six documents the implementation of the modeling techniques into the computer code MP-CAD. A user manual for the software is also presented here. The source codes and published papers are listed in the Appendices.
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
Graustein, William C
2006-01-01
This first course in differential geometry presents the fundamentals of the metric differential geometry of curves and surfaces in a Euclidean space of three dimensions. Written by an outstanding teacher and mathematician, it explains the material in the most effective way, using vector notation and technique. It also provides an introduction to the study of Riemannian geometry.Suitable for advanced undergraduates and graduate students, the text presupposes a knowledge of calculus. The first nine chapters focus on the theory, treating the basic properties of curves and surfaces, the mapping of
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...
The Common Geometry Module (CGM).
Tautges, Timothy James
2004-12-01
The Common Geometry Module (CGM) is a code library which provides geometry functionality used for mesh generation and other applications. This functionality includes that commonly found in solid modeling engines, like geometry creation, query and modification; CGM also includes capabilities not commonly found in solid modeling engines, like geometry decomposition tools and support for shared material interfaces. CGM is built upon the ACIS solid modeling engine, but also includes geometry capability developed beside and on top of ACIS. CGM can be used as-is to provide geometry functionality for codes needing this capability. However, CGM can also be extended using derived classes in C++, allowing the geometric model to serve as the basis for other applications, for example mesh generation. CGM is supported on Sun Solaris, SGI, HP, IBM, DEC, Linux and Windows NT platforms. CGM also includes support for loading ACIS models on parallel computers, using MPI-based communication. Future plans for CGM are to port it to different solid modeling engines, including Pro/Engineer or SolidWorks. CGM is being released into the public domain under an LGPL license; the ACIS-based engine is available to ACIS licensees on request.
Saleem, Zain Hamid
In this thesis we study a special class of black hole geometries called subtracted geometries. Subtracted geometry black holes are obtained when one omits certain terms from the warp factor of the metric of general charged rotating black holes. The omission of these terms allows one to write the wave equation of the black hole in a completely separable way and one can explicitly see that the wave equation of a massless scalar field in this slightly altered background of a general multi-charged rotating black hole acquires an SL(2, R) x SL(2, R) x SO(3) symmetry. The "subtracted limit" is considered an appropriate limit for studying the internal structure of the non-subtracted black holes because new 'subtracted' black holes have the same horizon area and periodicity of the angular and time coordinates in the near horizon regions as the original black hole geometry it was constructed from. The new geometry is asymptotically conical and is physically similar to that of a black hole in an asymptotically confining box. We use the different nice properties of these geometries to understand various classically and quantum mechanically important features of general charged rotating black holes.
Geometry, structure and randomness in combinatorics
Nešetřil, Jaroslav; Pellegrini, Marco
2014-01-01
This book collects some surveys on current trends in discrete mathematics and discrete geometry. The areas covered include: graph representations, structural graphs theory, extremal graph theory, Ramsey theory and constrained satisfaction problems.
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...
Core foundations of abstract geometry.
Dillon, Moira R; Huang, Yi; Spelke, Elizabeth S
2013-08-27
Human adults from diverse cultures share intuitions about the points, lines, and figures of Euclidean geometry. Do children develop these intuitions by drawing on phylogenetically ancient and developmentally precocious geometric representations that guide their navigation and their analysis of object shape? In what way might these early-arising representations support later-developing Euclidean intuitions? To approach these questions, we investigated the relations among young children's use of geometry in tasks assessing: navigation; visual form analysis; and the interpretation of symbolic, purely geometric maps. Children's navigation depended on the distance and directional relations of the surface layout and predicted their use of a symbolic map with targets designated by surface distances. In contrast, children's analysis of visual forms depended on the size-invariant shape relations of objects and predicted their use of the same map but with targets designated by corner angles. Even though the two map tasks used identical instructions and map displays, children's performance on these tasks showed no evidence of integrated representations of distance and angle. Instead, young children flexibly recruited geometric representations of either navigable layouts or objects to interpret the same spatial symbols. These findings reveal a link between the early-arising geometric representations that humans share with diverse animals and the flexible geometric intuitions that give rise to human knowledge at its highest reaches. Although young children do not appear to integrate core geometric representations, children's use of the abstract geometry in spatial symbols such as maps may provide the earliest clues to the later construction of Euclidean geometry.
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,
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
Pottmann, Helmut; Eigensatz, Michael; Vaxman, A.; Wallner, Johannes
2015-01-01
Around 2005 it became apparent in the geometry processing community that freeform architecture contains many problems of a geometric nature to be solved, and many opportunities for optimization which however require geometric understanding. This area of research, which has been called architectural
Pottmann, Helmut; Eigensatz, Michael; Vaxman, A.; Wallner, Johannes
2015-01-01
Around 2005 it became apparent in the geometry processing community that freeform architecture contains many problems of a geometric nature to be solved, and many opportunities for optimization which however require geometric understanding. This area of research, which has been called architectural
Representation Theory of Algebraic Groups and Quantum Groups
Gyoja, A; Shinoda, K-I; Shoji, T; Tanisaki, Toshiyuki
2010-01-01
Invited articles by top notch expertsFocus is on topics in representation theory of algebraic groups and quantum groupsOf interest to graduate students and researchers in representation theory, group theory, algebraic geometry, quantum theory and math physics
Geometry of time-spaces non-commutative algebraic geometry, applied to quantum theory
Landau, Olav Arnfinn
2011-01-01
This is a monograph about non-commutative algebraic geometry, and its application to physics. The main mathematical inputs are the non-commutative deformation theory, moduli theory of representations of associative algebras, a new non-commutative theory o
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...
Guide to Computational Geometry Processing
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......Optical scanning is rapidly becoming ubiquitous. From industrial laser scanners to medical CT, MR and 3D ultrasound scanners, numerous organizations now have easy access to optical acquisition devices that provide huge volumes of image data. However, the raw geometry data acquired must first......, 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...
Kreyszig, Erwin
1991-01-01
An introductory textbook on the differential geometry of curves and surfaces in three-dimensional Euclidean space, presented in its simplest, most essential form, but with many explanatory details, figures and examples, and in a manner that conveys the theoretical and practical importance of the different concepts, methods and results involved. With problems at the end of each section, and solutions listed at the end of the book. Includes 99 illustrations.
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...
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
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.
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
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
Foucault, Heather M; Bryce, David L; Fogg, Deryn E
2006-12-11
Reaction of RuCl2(PPh3)3 with LiNN' (NN' = 2-[(2,6-diisopropylphenyl)imino]pyrrolide) affords a single product, with the empirical formula RuCl[(2,6-iPr2C6H3)N=CHC4H3N](PPh3)2. We identify this species as a sigma-pyrrolato complex, [Ru(NN')(PPh3)2]2(mu-Cl)2 (3b), rather than mononuclear RuCl(NN')(PPh3)2 (3a), on the basis of detailed 1D and 2D NMR characterization in solution and in the solid state. Retention of the chelating, sigma-bound iminopyrrolato unit within 3b, despite the presence of labile (dative) chloride and PPh3 donors, indicates that the chelate effect is sufficient to inhibit sigma --> pi isomerization of 3b to a piano-stool, pi-pyrrolato structure. 2D COSY, SECSY, and J-resolved solid-state 31P NMR experiments confirm that the PPh3 ligands on each metal center are magnetically and crystallographically inequivalent, and 31P CP/MAS NMR experiments reveal the largest 99Ru-31P spin-spin coupling constant (1J(99Ru,31P) = 244 +/- 20 Hz) yet measured. Finally, 31P dipolar-chemical shift spectroscopy is applied to determine benchmark phosphorus chemical shift tensors for phosphine ligands in hexacoordinate ruthenium complexes.
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
Geometry of Knowledge for Intelligent Systems
Resconi, Germano
2013-01-01
The book is on the geometry of agent knowledge. The important concept studied in this book is the Field and its Geometric Representation. To develop a geometric image of the gravity , Einstein used Tensor Calculus but this is very different from the knowledge instruments used now, as for instance techniques of data mining , neural networks , formal concept analysis ,quantum computer and other topics. The aim of this book is to rebuild the tensor calculus in order to give a geometric representation of agent knowledge. By using a new geometry of knowledge we can unify all the topics that have been studied in recent years to create a bridge between the geometric representation of the physical phenomena and the geometric representation of the individual and subjective knowledge of the agents.
Schiffler, Ralf
2014-01-01
This book is intended to serve as a textbook for a course in Representation Theory of Algebras at the beginning graduate level. The text has two parts. In Part I, the theory is studied in an elementary way using quivers and their representations. This is a very hands-on approach and requires only basic knowledge of linear algebra. The main tool for describing the representation theory of a finite-dimensional algebra is its Auslander-Reiten quiver, and the text introduces these quivers as early as possible. Part II then uses the language of algebras and modules to build on the material developed before. The equivalence of the two approaches is proved in the text. The last chapter gives a proof of Gabriel’s Theorem. The language of category theory is developed along the way as needed.
Wulf-Andersen, Trine Østergaard
2012-01-01
This article is based on a Danish research project with young people in vulnerable positions. Young people are involved throughout the research process, including the interpretation of material produced through interviews, and discussions on how reflections and conclusions from the research should......, and dialogue, of situated participants. The article includes a lengthy example of a poetic representation of one participant’s story, and the author comments on the potentials of ‘doing’ poetic representations as an example of writing in ways that challenges what sometimes goes unasked in participative social...
Rasmussen, Majken Kirkegaard; Petersen, Marianne Graves
2011-01-01
Stereotypic presumptions about gender affect the design process, both in relation to how users are understood and how products are designed. As a way to decrease the influence of stereotypic presumptions in design process, we propose not to disregard the aspect of gender in the design process......, as the perspective brings valuable insights on different approaches to technology, but instead to view gender through a value lens. Contributing to this perspective, we have developed Value Representations as a design-oriented instrument for staging a reflective dialogue with users. Value Representations...
Petersson, Dag; Dahlgren, Anna; Vestberg, Nina Lager
to the enterprises of the medium. This is the subject of Representational Machines: How photography enlists the workings of institutional technologies in search of establishing new iconic and social spaces. Together, the contributions to this edited volume span historical epochs, social environments, technological...
The field representation language.
Tsafnat, Guy
2008-02-01
The complexity of quantitative biomedical models, and the rate at which they are published, is increasing to a point where managing the information has become all but impossible without automation. International efforts are underway to standardise representation languages for a number of mathematical entities that represent a wide variety of physiological systems. This paper presents the Field Representation Language (FRL), a portable representation of values that change over space and/or time. FRL is an extensible mark-up language (XML) derivative with support for large numeric data sets in Hierarchical Data Format version 5 (HDF5). Components of FRL can be reused through unified resource identifiers (URI) that point to external resources such as custom basis functions, boundary geometries and numerical data. To demonstrate the use of FRL as an interchange we present three models that study hyperthermia cancer treatment: a fractal model of liver tumour microvasculature; a probabilistic model simulating the deposition of magnetic microspheres throughout it; and a finite element model of hyperthermic treatment. The microsphere distribution field was used to compute the heat generation rate field around the tumour. We used FRL to convey results from the microsphere simulation to the treatment model. FRL facilitated the conversion of the coordinate systems and approximated the integral over regions of the microsphere deposition field.
Beyond core knowledge: Natural geometry
Spelke, Elizabeth; Lee, Sang Ah; Izard, Véronique
2010-01-01
For many centuries, philosophers and scientists have pondered the origins and nature of human intuitions about the properties of points, lines, and figures on the Euclidean plane, with most hypothesizing that a system of Euclidean concepts either is innate or is assembled by general learning processes. Recent research from cognitive and developmental psychology, cognitive anthropology, animal cognition, and cognitive neuroscience suggests a different view. Knowledge of geometry may be founded on at least two distinct, evolutionarily ancient, core cognitive systems for representing the shapes of large-scale, navigable surface layouts and of small-scale, movable forms and objects. Each of these systems applies to some but not all perceptible arrays and captures some but not all of the three fundamental Euclidean relationships of distance (or length), angle, and direction (or sense). Like natural number (Carey, 2009), Euclidean geometry may be constructed through the productive combination of representations from these core systems, through the use of uniquely human symbolic systems. PMID:20625445
Tolerance analysis and variational solid geometry
Watterberg, P. [Sandia National Labs., Albuquerque, NM (United States). Intelligent Systems and Robotics Center
1998-01-01
The fields of tolerancing and assembly analysis have depended for decades on ad hoc, shop floor methods. This causes serious problems when subjected toleranced designs to automated, analytical methods. This project attempted to further the formalization and mathematization of tolerancing by extending the concept of the Maximum Material Part. A software system was envisioned that would guide designers in the use of appropriate tolerance specifications and then create software models of Maximum Material Parts from the toleranced nominal parts.
3DHZETRN: Inhomogeneous Geometry Issues
Wilson, John W.; Slaba, Tony C.; Badavi, Francis F.
2017-01-01
Historical methods for assessing radiation exposure inside complicated geometries for space applications were limited by computational constraints and lack of knowledge associated with nuclear processes occurring over a broad range of particles and energies. Various methods were developed and utilized to simplify geometric representations and enable coupling with simplified but efficient particle transport codes. Recent transport code development efforts, leading to 3DHZETRN, now enable such approximate methods to be carefully assessed to determine if past exposure analyses and validation efforts based on those approximate methods need to be revisited. In this work, historical methods of representing inhomogeneous spacecraft geometry for radiation protection analysis are first reviewed. Two inhomogeneous geometry cases, previously studied with 3DHZETRN and Monte Carlo codes, are considered with various levels of geometric approximation. Fluence, dose, and dose equivalent values are computed in all cases and compared. It is found that although these historical geometry approximations can induce large errors in neutron fluences up to 100 MeV, errors on dose and dose equivalent are modest (<10%) for the cases studied here.
Octree Representation and Its Applications in CAD
唐泽圣
1992-01-01
In this paper,a survey of octree representation and its applications in CAD is presented.The octree representation may be categorized as pure octree representation and polytree(or extended octree),and the latter is actually a boundary representation decomposed by octree.Linear octree which is a variant of regular octree representation has the advantage of saving memory space.The mapping between Cartesian coordinates and node addresses in linear octree is discussed.Then,algorithms for converting a boundary representation of 3D object into an octree are investiged and major approaches for transforming an octree encoded object are presented.After that,some of the applications of octree representation in CAD are listed,in particular,the applications in solid modeling,in accelerating ray tracing and in generating meshes for FEM.
Bär, Christian; Schwarz, Matthias
2012-01-01
This volume contains a collection of well-written surveys provided by experts in Global Differential Geometry to give an overview over recent developments in Riemannian Geometry, Geometric Analysis and Symplectic Geometry. The papers are written for graduate students and researchers with a general interest in geometry, who want to get acquainted with the current trends in these central fields of modern mathematics.
Cukier, Mimi; Asdourian, Tony; Thakker, Anand
2012-01-01
Geometry provides a natural window into what it is like to do mathematics. In the world of geometry, playful experimentation is often more fruitful than following a procedure, and logic plus a few axioms can open new worlds. Nonetheless, teaching a geometry course in a way that combines both rigor and play can be difficult. Many geometry courses…
Computer aided surface representation
Barnhill, R.E.
1990-02-19
The central research problem of this project is the effective representation, computation, and display of surfaces interpolating to information in three or more dimensions. If the given information is located on another surface, then the problem is to construct a surface defined on a surface''. Sometimes properties of an already defined surface are desired, which is geometry processing''. Visualization of multivariate surfaces is possible by means of contouring higher dimensional surfaces. These problems and more are discussed below. The broad sweep from constructive mathematics through computational algorithms to computer graphics illustrations is utilized in this research. The breadth and depth of this research activity makes this research project unique.
Mahé, Louis; Roy, Marie-Françoise
1992-01-01
Ten years after the first Rennes international meeting on real algebraic geometry, the second one looked at the developments in the subject during the intervening decade - see the 6 survey papers listed below. Further contributions from the participants on recent research covered real algebra and geometry, topology of real algebraic varieties and 16thHilbert problem, classical algebraic geometry, techniques in real algebraic geometry, algorithms in real algebraic geometry, semialgebraic geometry, real analytic geometry. CONTENTS: Survey papers: M. Knebusch: Semialgebraic topology in the last ten years.- R. Parimala: Algebraic and topological invariants of real algebraic varieties.- Polotovskii, G.M.: On the classification of decomposing plane algebraic curves.- Scheiderer, C.: Real algebra and its applications to geometry in the last ten years: some major developments and results.- Shustin, E.L.: Topology of real plane algebraic curves.- Silhol, R.: Moduli problems in real algebraic geometry. Further contribu...
Digital Differential Geometry Processing
Xin-Guo Liu; Hu-Jun Bao; Qun-Sheng Peng
2006-01-01
The theory and methods of digital geometry processing has been a hot research area in computer graphics, as geometric models serves as the core data for 3D graphics applications. The purpose of this paper is to introduce some recent advances in digital geometry processing, particularly mesh fairing, surface parameterization and mesh editing, that heavily use differential geometry quantities. Some related concepts from differential geometry, such as normal, curvature, gradient,Laplacian and their counterparts on digital geometry are also reviewed for understanding the strength and weakness of various digital geometry processing methods.
Mullins, Michael
elements into the process of design. Through its immersive properties, virtual reality allows access to a spatial experience of a computer model very different to both screen based simulations as well as traditional forms of architectural representation. The dissertation focuses on processes of the current......Contemporary communicational and informational processes contribute to the shaping of our physical environment by having a powerful influence on the process of design. Applications of virtual reality (VR) are transforming the way architecture is conceived and produced by introducing dynamic...... by ‘professionals’ to ‘laypeople’. The thesis articulates problems in VR’s current application, specifically the CAVE and Panorama theatres, and seeks an understanding of how these problems may be addressed. The central questions that have motivated this research project are thus: What is architectural VR...
Minimal representations, geometric quantization, and unitarity.
Brylinski, R; Kostant, B
1994-06-21
In the framework of geometric quantization we explicitly construct, in a uniform fashion, a unitary minimal representation pio of every simply-connected real Lie group Go such that the maximal compact subgroup of Go has finite center and Go admits some minimal representation. We obtain algebraic and analytic results about pio. We give several results on the algebraic and symplectic geometry of the minimal nilpotent orbits and then "quantize" these results to obtain the corresponding representations. We assume (Lie Go)C is simple.
Geometric Algebra Model of Distributed Representations
Patyk, Agnieszka
2010-01-01
Formalism based on GA is an alternative to distributed representation models developed so far --- Smolensky's tensor product, Holographic Reduced Representations (HRR) and Binary Spatter Code (BSC). Convolutions are replaced by geometric products, interpretable in terms of geometry which seems to be the most natural language for visualization of higher concepts. This paper recalls the main ideas behind the GA model and investigates recognition test results using both inner product and a clipped version of matrix representation. The influence of accidental blade equality on recognition is also studied. Finally, the efficiency of the GA model is compared to that of previously developed models.
Effect of geometry on hydrodynamic film thickness
Brewe, D. E.; Hamrock, B. J.; Taylor, C. M.
1978-01-01
The influence of geometry on the isothermal hydrodynamic film separating two rigid solids was investigated. Pressure-viscosity effects were not considered. The minimum film thickness is derived for fully flooded conjunctions by using the Reynolds boundary conditions. It was found that the minimum film thickness had the same speed, viscosity, and load dependence as Kapitza's classical solution. However, the incorporation of Reynolds boundary conditions resulted in an additional geometry effect. Solutions using the parabolic film approximation are compared with those using the exact expression for the film in the analysis. Contour plots are shown that indicate in detail the pressure developed between the solids.
A spectral invariant representation of spectral reflectance
Ibrahim, Abdelhameed; Tominaga, Shoji; Horiuchi, Takahiko
2011-03-01
Spectral image acquisition as well as color image is affected by several illumination factors such as shading, gloss, and specular highlight. Spectral invariant representations for these factors were proposed for the standard dichromatic reflection model of inhomogeneous dielectric materials. However, these representations are inadequate for other characteristic materials like metal. This paper proposes a more general spectral invariant representation for obtaining reliable spectral reflectance images. Our invariant representation is derived from the standard dichromatic reflection model for dielectric materials and the extended dichromatic reflection model for metals. We proof that the invariant formulas for spectral images of natural objects preserve spectral information and are invariant to highlights, shading, surface geometry, and illumination intensity. It is proved that the conventional spectral invariant technique can be applied to metals in addition to dielectric objects. Experimental results show that the proposed spectral invariant representation is effective for image segmentation.
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...
GUO Enli; MO Xiaohuan
2006-01-01
In this paper,a survey on Riemann-Finsler geometry is given.Non-trivial examples of Finsler metrics satisfying different curvature conditions are presented.Local and global results in Finsler geometry are analyzed.
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.
Noncommutative geometry and Cayley-Smooth orders
Le Bruyn, Lieven
2007-01-01
Preface Introduction Noncommutative algebra Noncommutative geometryNoncommutative desingularizationsCayley-Hamilton Algebras Conjugacy classes of matrices Simultaneous conjugacy classesMatrix invariants and necklaces The trace algebraThe symmetric group Necklace relations Trace relations Cayley-Hamilton algebrasReconstructing Algebras Representation schemes Some algebraic geometry The Hilbert criterium Semisimple modules Some invariant theory Geometric reconstruction The Gerstenhaber-Hesselink theoremThe real moment mapÉtale Technology Étale topologyCentral simple algebrasSpectral sequencesTse
Representations of Subgroups of Universal Triangle Groups
Jianguo Xia
2007-01-01
Let G be a universal triangle group, and H a subgroup of G such that the chamber system △H is a tight triangle geometryThen H, which is canonically isomorphic to the topological fundamental group π1(△H) of △ H, is a finitely presented group.For some H we give their representations.
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
Introduction to projective geometry
Wylie, C R
2008-01-01
This lucid introductory text offers both an analytic and an axiomatic approach to plane projective geometry. The analytic treatment builds and expands upon students' familiarity with elementary plane analytic geometry and provides a well-motivated approach to projective geometry. Subsequent chapters explore Euclidean and non-Euclidean geometry as specializations of the projective plane, revealing the existence of an infinite number of geometries, each Euclidean in nature but characterized by a different set of distance- and angle-measurement formulas. Outstanding pedagogical features include w
Affine and Projective Geometry
Bennett, M K
1995-01-01
An important new perspective on AFFINE AND PROJECTIVE GEOMETRY. This innovative book treats math majors and math education students to a fresh look at affine and projective geometry from algebraic, synthetic, and lattice theoretic points of view. Affine and Projective Geometry comes complete with ninety illustrations, and numerous examples and exercises, covering material for two semesters of upper-level undergraduate mathematics. The first part of the book deals with the correlation between synthetic geometry and linear algebra. In the second part, geometry is used to introduce lattice theory
Symplectic geometries on supermanifolds
Lavrov, P M
2007-01-01
Extension of symplectic geometry on manifolds to the supersymmetric case is considered. In the even case it leads to the even symplectic geometry (or, equivalently, to the geometry on supermanifolds endowed with an non-degenerate Poisson bracket) or to the geometry on an even Fedosov supermanifolds. It is proven that in the odd case there are two different scalar symplectic structures (namely, an odd closed differential 2-form and the antibracket) which can be used for construction of different symplectic geometries on supermanifolds.
Gualtieri, Marco
2010-01-01
Generalized Kahler geometry is the natural analogue of Kahler geometry, in the context of generalized complex geometry. Just as we may require a complex structure to be compatible with a Riemannian metric in a way which gives rise to a symplectic form, we may require a generalized complex structure to be compatible with a metric so that it defines a second generalized complex structure. We explore the fundamental aspects of this geometry, including its equivalence with the bi-Hermitian geometry on the target of a 2-dimensional sigma model with (2,2) supersymmetry, as well as the relation to holomorphic Dirac geometry and the resulting derived deformation theory. We also explore the analogy between pre-quantum line bundles and gerbes in the context of generalized Kahler geometry.
Methods for euclidean geometry
Byer, Owen; Smeltzer, Deirdre L
2010-01-01
Euclidean plane geometry is one of the oldest and most beautiful topics in mathematics. Instead of carefully building geometries from axiom sets, this book uses a wealth of methods to solve problems in Euclidean geometry. Many of these methods arose where existing techniques proved inadequate. In several cases, the new ideas used in solving specific problems later developed into independent areas of mathematics. This book is primarily a geometry textbook, but studying geometry in this way will also develop students' appreciation of the subject and of mathematics as a whole. For instance, despite the fact that the analytic method has been part of mathematics for four centuries, it is rarely a tool a student considers using when faced with a geometry problem. Methods for Euclidean Geometry explores the application of a broad range of mathematical topics to the solution of Euclidean problems.
Interactive graphics for geometry modeling
Wozny, M. J.
1984-01-01
An interactive vector capability to create geometry and a raster color shaded rendering capability to sample and verify interim geometric design steps through color snapshots is described. The development is outlined of the underlying methodology which facilitates computer aided engineering and design. At present, raster systems cannot match the interactivity and line-drawing capability of refresh vector systems. Consequently, an intermediate step in mechanical design is used to create objects interactively on the vector display and then scan convert the wireframe model to render it as a color shaded object on a raster display. Several algorithms are presented for rendering such objects. Superquadric solid primitive extend the class of primitives normally used in solid modelers.
Noncommutative geometry with graded differential Lie algebras
Wulkenhaar, Raimar
1997-06-01
Starting with a Hilbert space endowed with a representation of a unitary Lie algebra and an action of a generalized Dirac operator, we develop a mathematical concept towards gauge field theories. This concept shares common features with the Connes-Lott prescription of noncommutative geometry, differs from that, however, by the implementation of unitary Lie algebras instead of associative * -algebras. The general scheme is presented in detail and is applied to functions ⊗ matrices.
Automatically extracting sheet-metal features from solid model
刘志坚; 李建军; 王义林; 李材元; 肖祥芷
2004-01-01
With the development of modern industry,sheet-metal parts in mass production have been widely applied in mechanical,communication,electronics,and light industries in recent decades; but the advances in sheet-metal part design and manufacturing remain too slow compared with the increasing importance of sheet-metal parts in modern industry. This paper proposes a method for automatically extracting features from an arbitrary solid model of sheet-metal parts; whose characteristics are used for classification and graph-based representation of the sheet-metal features to extract the features embodied in a sheet-metal part. The extracting feature process can be divided for valid checking of the model geometry,feature matching,and feature relationship. Since the extracted features include abundant geometry and engineering information,they will be effective for downstream application such as feature rebuilding and stamping process planning.
Automatically extracting sheet-metal features from solid model
刘志坚; 李建军; 王义林; 李材元; 肖祥芷
2004-01-01
With the development of modern industry, sheet-metal parts in mass production have been widely applied in mechanical, communication, electronics, and light industries in recent decades; but the advances in sheet-metal part design and manufacturing remain too slow compared with the increasing importance of sheet-metal parts in modern industry. This paper proposes a method for automatically extracting features from an arbitrary solid model of sheet-metal parts; whose characteristics are used for classification and graph-based representation of the sheet-metal features to extract the features embodied in a sheet-metal part. The extracting feature process can be divided for valid checking of the model geometry, feature matching, and feature relationship. Since the extracted features include abundant geometry and engineering information, they will be effective for downstream application such as feature rebuilding and stamping process planning.
The Convex Geometry of Linear Inverse Problems
2010-12-02
equator. Via elementary trigonometry , the solid angle that K subtends is given by π/2− sin−1(h). Hence, if h(β) is the largest number such that β caps of...1107–1130. [34] Harris, J., Algebraic Geometry: A First Course . Springer. [35] Haupt, J., Bajwa, W., Raz, G., and Nowak, R. (2008). Toeplitz
Hessian geometry and entanglement thermodynamics
Matsueda, Hiroaki
2015-01-01
We reconstruct entanglement thermodynamics by means of Hessian geometry, since this method exactly generalizes thermodynamics into much wider exponential family cases including quantum entanglement. Starting with the correct first law of entanglement thermodynamics, we derive that a proper choice of the Hessian potential leads to both of the entanglement entropy scaling for quantum critical systems and hyperbolic metric (or AdS space with imaginary time). We also derive geometric representation of the entanglement entropy in which the entropy is described as integration of local conserved current of information flowing across an entangling surface. We find that the entangling surface is equivalent to the domain boundary of the Hessian potential. This feature originates in a special property of critical systems in which we can identify the entanglement entropy with the Hessian potential after the second derivative by the canonical parameters, and this identification guarantees violation of extensive nature of ...
Categorification in geometry, topology, and physics
Beliakova, Anna
2017-01-01
The emergent mathematical philosophy of categorification is reshaping our view of modern mathematics by uncovering a hidden layer of structure in mathematics, revealing richer and more robust structures capable of describing more complex phenomena. Categorification is a powerful tool for relating various branches of mathematics and exploiting the commonalities between fields. It provides a language emphasizing essential features and allowing precise relationships between vastly different fields. This volume focuses on the role categorification plays in geometry, topology, and physics. These articles illustrate many important trends for the field including geometric representation theory, homotopical methods in link homology, interactions between higher representation theory and gauge theory, and double affine Hecke algebra approaches to link homology. The companion volume (Contemporary Mathematics, Volume 683) is devoted to categorification and higher representation theory.
Geometry and Coarse-Grained Representations of Landscapes
Qin, Jing; Stadler, Peter; Klemm, Konstantin
2014-01-01
Recent Advances in the Theory and Application of Fitness Landscapes Emergence, Complexity and ComputationVolume 6, 2014, pp 153-176......Recent Advances in the Theory and Application of Fitness Landscapes Emergence, Complexity and ComputationVolume 6, 2014, pp 153-176...
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.
Landscape as a model: the importance of geometry.
Holland, E Penelope; Aegerter, James N; Dytham, Calvin; Smith, Graham C
2007-10-01
In all models, but especially in those used to predict uncertain processes (e.g., climate change and nonnative species establishment), it is important to identify and remove any sources of bias that may confound results. This is critical in models designed to help support decisionmaking. The geometry used to represent virtual landscapes in spatially explicit models is a potential source of bias. The majority of spatial models use regular square geometry, although regular hexagonal landscapes have also been used. However, there are other ways in which space can be represented in spatially explicit models. For the first time, we explicitly compare the range of alternative geometries available to the modeller, and present a mechanism by which uncertainty in the representation of landscapes can be incorporated. We test how geometry can affect cell-to-cell movement across homogeneous virtual landscapes and compare regular geometries with a suite of irregular mosaics. We show that regular geometries have the potential to systematically bias the direction and distance of movement, whereas even individual instances of landscapes with irregular geometry do not. We also examine how geometry can affect the gross representation of real-world landscapes, and again show that individual instances of regular geometries will always create qualitative and quantitative errors. These can be reduced by the use of multiple randomized instances, though this still creates scale-dependent biases. In contrast, virtual landscapes formed using irregular geometries can represent complex real-world landscapes without error. We found that the potential for bias caused by regular geometries can be effectively eliminated by subdividing virtual landscapes using irregular geometry. The use of irregular geometry appears to offer spatial modellers other potential advantages, which are as yet underdeveloped. We recommend their use in all spatially explicit models, but especially for predictive models
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
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.
O'Leary, Michael
2010-01-01
Guides readers through the development of geometry and basic proof writing using a historical approach to the topic. In an effort to fully appreciate the logic and structure of geometric proofs, Revolutions of Geometry places proofs into the context of geometry's history, helping readers to understand that proof writing is crucial to the job of a mathematician. Written for students and educators of mathematics alike, the book guides readers through the rich history and influential works, from ancient times to the present, behind the development of geometry. As a result, readers are successfull
Euclidean geometry and transformations
Dodge, Clayton W
1972-01-01
This introduction to Euclidean geometry emphasizes transformations, particularly isometries and similarities. Suitable for undergraduate courses, it includes numerous examples, many with detailed answers. 1972 edition.
Introduction to finite geometries
Kárteszi, F
1976-01-01
North-Holland Texts in Advanced Mathematics: Introduction to Finite Geometries focuses on the advancements in finite geometries, including mapping and combinatorics. The manuscript first offers information on the basic concepts on finite geometries and Galois geometries. Discussions focus on linear mapping of a given quadrangle onto another given quadrangle; point configurations of order 2 on a Galois plane of even order; canonical equation of curves of the second order on the Galois planes of even order; and set of collineations mapping a Galois plane onto itself. The text then ponders on geo
Geometry and the Quantum: Basics
Chamseddine, Ali H; Mukhanov, Viatcheslav
2014-01-01
Motivated by the construction of spectral manifolds in noncommutative geometry, we introduce a higher degree Heisenberg commutation relation involving the Dirac operator and the Feynman slash of scalar fields. This commutation relation appears in two versions, one sided and two sided. It implies the quantization of the volume. In the one-sided case it implies that the manifold decomposes into a disconnected sum of spheres which will represent quanta of geometry. The two sided version in dimension 4 predicts the two algebras M_2(H) and M_4(C) which are the algebraic constituents of the Standard Model of particle physics. This taken together with the non-commutative algebra of functions allows one to reconstruct, using the spectral action, the Lagrangian of gravity coupled with the Standard Model. We show that any connected Riemannian Spin 4-manifold with quantized volume >4 (in suitable units) appears as an irreducible representation of the two-sided commutation relations in dimension 4 and that these represen...
Euclidean Geometry via Programming.
Filimonov, Rossen; Kreith, Kurt
1992-01-01
Describes the Plane Geometry System computer software developed at the Educational Computer Systems laboratory in Sofia, Bulgaria. The system enables students to use the concept of "algorithm" to correspond to the process of "deductive proof" in the development of plane geometry. Provides an example of the software's capability and compares it to…
Supersymmetric Sigma Model Geometry
Ulf Lindström
2012-01-01
This is a review of how sigma models formulated in Superspace have become important tools for understanding geometry. Topics included are: The (hyper)k\\"ahler reduction; projective superspace; the generalized Legendre construction; generalized K\\"ahler geometry and constructions of hyperk\\"ahler metrics on Hermitean symmetric spaces.
Geometry of multihadron production
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.
Supersymmetric Sigma Model geometry
Lindström, Ulf
2012-01-01
This is a review of how sigma models formulated in Superspace have become important tools for understanding geometry. Topics included are: The (hyper)k\\"ahler reduction; projective superspace; the generalized Legendre construction; generalized K\\"ahler geometry and constructions of hyperk\\"ahler metrics on Hermitean symmetric spaces.
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.
Foundations of algebraic geometry
Weil, A
1946-01-01
This classic is one of the cornerstones of modern algebraic geometry. At the same time, it is entirely self-contained, assuming no knowledge whatsoever of algebraic geometry, and no knowledge of modern algebra beyond the simplest facts about abstract fields and their extensions, and the bare rudiments of the theory of ideals.
Bergshoeff, Eric A.; Riccioni, Fabio; Alvarez-Gaumé, L.
2011-01-01
We probe doubled geometry with dual fundamental branes. i.e. solitons. Restricting ourselves first to solitonic branes with more than two transverse directions we find that the doubled geometry requires an effective wrapping rule for the solitonic branes which is dual to the wrapping rule for fundam
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.
STUDY ON THE REPRESENTATION OF THE PLÜCKER CONOID
DRAGAN Delia
2008-07-01
Full Text Available The architecture and construction related design requires an in-depth knowledge of all the systems of representation of solids and surfaces. This paper presents a comparative study on the representation of the Plücker conoid using the three systems of representation, i.e. axonometry, the orthogonal projection on two planes of projection and the projection with elevation. Each of these representation systems has its own advantages and disadvantages. They relate to the practical aspect of measuring the true lengths, respectively sizes of angles and surfaces. Then, the way in which the representation is perceived spatially by specialists or non-specialists is also of importance.
Teacher spatial skills are linked to differences in geometry instruction.
Otumfuor, Beryl Ann; Carr, Martha
2017-08-31
Spatial skills have been linked to better performance in mathematics. The purpose of this study was to examine the relationship between teacher spatial skills and their instruction, including teacher content and pedagogical knowledge, use of pictorial representations, and use of gestures during geometry instruction. Fifty-six middle school teachers participated in the study. The teachers were administered spatial measures of mental rotations and spatial visualization. Next, a single geometry class was videotaped. Correlational analyses revealed that spatial skills significantly correlate with teacher's use of representational gestures and content and pedagogical knowledge during instruction of geometry. Spatial skills did not independently correlate with the use of pointing gestures or the use of pictorial representations. However, an interaction term between spatial skills and content and pedagogical knowledge did correlate significantly with the use of pictorial representations. Teacher experience as measured by the number of years of teaching and highest degree did not appear to affect the relationships among the variables with the exception of the relationship between spatial skills and teacher content and pedagogical knowledge. Teachers with better spatial skills are also likely to use representational gestures and to show better content and pedagogical knowledge during instruction. Spatial skills predict pictorial representation use only as a function of content and pedagogical knowledge. © 2017 The British Psychological Society.
Riemann-Finsler Geometry with Applications to Information Geometry
无
2006-01-01
Information geometry is a new branch in mathematics, originated from the applications of differential geometry to statistics. In this paper we briefly introduce RiemannFinsler geometry, by which we establish Information Geometry on a much broader base,so that the potential applications of Information Geometry will be beyond statistics.
Geometry of the Borel - de Siebenthal discrete series
Ørsted, Bent; Wolf, Joseph A
system”. There is a lot of fascinating geometry associated to the corresponding “Borel – de Siebenthal discrete series” representations of G0. In this paper we explore some of those geometric aspects and we work out the K0–spectra of the Borel – de Siebenthal discrete series representations. This has......Let G0 be a connected, simply connected real simple Lie group. Suppose that G0 has a compact Cartan subgroup T0, so it has discrete series representations. Relative to T0 there is a distinguished positive root system + for which there is a unique noncompact simple root , the “Borel – de Siebenthal...
Representation as the representation of experience
Ankersmit, FR
This essay deals, mainly, with the notion of representation. Representation is associated with texts and, as such, is contrasted to the true singular statement. It is argued that the relationship between the text and what the text represents can never be modeled on the relationship between the true
Ariwahjoedi, Seramika; Kosasih, Jusak Sali; Rovelli, Carlo; Zen, Freddy Permana
2016-01-01
Following our earlier work, we construct statistical discrete geometry by applying statistical mechanics to discrete (Regge) gravity. We propose a coarse-graining method for discrete geometry under the assumptions of atomism and background independence. To maintain these assumptions, restrictions are given to the theory by introducing cut-offs, both in ultraviolet and infrared regime. Having a well-defined statistical picture of discrete Regge geometry, we take the infinite degrees of freedom (large n) limit. We argue that the correct limit consistent with the restrictions and the background independence concept is not the continuum limit of statistical mechanics, but the thermodynamical limit.
Bonola, Roberto
2010-01-01
This is an excellent historical and mathematical view by a renowned Italian geometer of the geometries that have risen from a rejection of Euclid's parallel postulate. Students, teachers and mathematicians will find here a ready reference source and guide to a field that has now become overwhelmingly important.Non-Euclidean Geometry first examines the various attempts to prove Euclid's parallel postulate-by the Greeks, Arabs, and mathematicians of the Renaissance. Then, ranging through the 17th, 18th and 19th centuries, it considers the forerunners and founders of non-Euclidean geometry, such
Santo, J
1999-01-01
The ALICE Geometry Database project consists of the development of a set of data structures to store the geometrical information of the ALICE Detector. This Database will be used in Simulation, Reconstruction and Visualisation and will interface with existing CAD systems and Geometrical Modellers.At the present time, we are able to read a complete GEANT3 geometry, to store it in our database and to visualise it. On disk, we store different geometry files in hierarchical fashion, and all the nodes, materials, shapes, configurations and transformations distributed in this tree structure. The present status of the prototype and its future evolution will be presented.
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 a
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
Lu, Shufang; Jin, Xiaogang; Jaffer, Aubrey; Gao, Fei; Mao, Xiaoyang
2016-05-25
Years of research have been devoted to computer-generated two-dimensional marbling. However, three-dimensional marbling has yet to be explored. In this paper, we present mathematical marbling of three-dimensional solids which supports a compact random-access vector representation. Our solid marbling textures are created by composing closed-form 3D pattern tool functions. These tool functions are an injection function and five deformation functions. The injection function is used to generate basic patterns, and the deformation functions are responsible for transforming the basic pattern into complex marbling effects. The resulting representation is feature preserving and resolution-independent. Our approach can render high-quality images preserving both the sharp features and the smooth color variations of a solid texture. When implemented on the GPU, our representation enables efficient color evaluation during the real-time solid marbling texture mapping. The color of a point in the volume space is computed by the 3D pattern tool functions from its coordinates. Our method consumes very little memory because only the mathematical functions and their corresponding parameters are stored. In addition, we develop an intuitive user interface and a genetic algorithm to facilitate the solid marbling texture authoring process. We demonstrate the effectiveness of our approach through various solid marbling textures and 3D objects carved from them.
Core systems of geometry in animal minds.
Spelke, Elizabeth S; Lee, Sang Ah
2012-10-05
Research on humans from birth to maturity converges with research on diverse animals to reveal foundational cognitive systems in human and animal minds. The present article focuses on two such systems of geometry. One system represents places in the navigable environment by recording the distance and direction of the navigator from surrounding, extended surfaces. The other system represents objects by detecting the shapes of small-scale forms. These two systems show common signatures across animals, suggesting that they evolved in distant ancestral species. As children master symbolic systems such as maps and language, they come productively to combine representations from the two core systems of geometry in uniquely human ways; these combinations may give rise to abstract geometric intuitions. Studies of the ontogenetic and phylogenetic sources of abstract geometry therefore are illuminating of both human and animal cognition. Research on animals brings simpler model systems and richer empirical methods to bear on the analysis of abstract concepts in human minds. In return, research on humans, relating core cognitive capacities to symbolic abilities, sheds light on the content of representations in animal minds.
Elementary differential geometry
Pressley, Andrew
2001-01-01
Curves and surfaces are objects that everyone can see, and many of the questions that can be asked about them are natural and easily understood Differential geometry is concerned with the precise mathematical formulation of some of these questions, and with trying to answer them using calculus techniques It is a subject that contains some of the most beautiful and profound results in mathematics yet many of these are accessible to higher-level undergraduates Elementary Differential Geometry presents the main results in the differential geometry of curves and surfaces while keeping the prerequisites to an absolute minimum Nothing more than first courses in linear algebra and multivariate calculus are required, and the most direct and straightforward approach is used at all times Numerous diagrams illustrate both the ideas in the text and the examples of curves and surfaces discussed there The book will provide an invaluable resource to all those taking a first course in differential geometry, for their lecture...
Chern, Shiing-Shen
1990-01-01
Discussed are the major historical developments of geometry. Euclid, Descartes, Klein's Erlanger Program, Gaus and Riemann, globalization, topology, Elie Cartan, and an application to molecular biology are included as topics. (KR)
Kumaresan, S
2005-01-01
Including Affine and projective classification of Conics, 2 point homogeneity's of the planes, essential isometrics, non euclidean plan geometrics, in this book, the treatment of Geometry goes beyond the Kleinian views.
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...
Emenaker, Charles E.
1999-01-01
Describes a sixth-grade interdisciplinary geometry unit based on Charles Dickens's "A Christmas Carol". Focuses on finding area, volume, and perimeter, and working with estimation, decimals, and fractions in the context of making gingerbread houses. (ASK)
Geometry of differential equations
Khovanskiĭ, A; Vassiliev, V
1998-01-01
This volume contains articles written by V. I. Arnold's colleagues on the occasion of his 60th birthday. The articles are mostly devoted to various aspects of geometry of differential equations and relations to global analysis and Hamiltonian mechanics.
Facilitating Understandings of Geometry.
Pappas, Christine C.; Bush, Sara
1989-01-01
Illustrates some learning encounters for facilitating first graders' understanding of geometry. Describes some of children's approaches using Cuisenaire rods and teacher's intervening. Presents six problems involving various combinations of Cuisenaire rods and cubes. (YP)
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...
Melzak, Z A
2008-01-01
Intended for students of many different backgrounds with only a modest knowledge of mathematics, this text features self-contained chapters that can be adapted to several types of geometry courses. 1983 edition.
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.
Derived logarithmic geometry I
Steffen, Sagave; Timo, Schurg; Gabriele, Vezzosi
2016-01-01
In order to develop the foundations of logarithmic derived geometry, we introduce a model category of logarithmic simplicial rings and a notion of derived log \\'etale maps and use this to define derived log stacks.
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.
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...
Hohmann, Manuel
2014-01-01
From general relativity we have learned the principles of general covariance and local Lorentz invariance, which follow from the fact that we consider observables as tensors on a spacetime manifold whose geometry is modeled by a Lorentzian metric. Approaches to quantum gravity, however, hint towards a breaking of these symmetries and the possible existence of more general, non-tensorial geometric structures. Possible implications of these approaches are non-tensorial transformation laws between different observers and an observer-dependent notion of geometry. In this work we review two different frameworks for observer dependent geometries, which may provide hints towards a quantization of gravity and possible explanations for so far unexplained phenomena: Finsler spacetimes and Cartan geometry on observer space. We discuss their definitions, properties and applications to observers, field theories and gravity.
An introduction to algebraic geometry and algebraic groups
Geck, Meinolf
2003-01-01
An accessible text introducing algebraic geometries and algebraic groups at advanced undergraduate and early graduate level, this book develops the language of algebraic geometry from scratch and uses it to set up the theory of affine algebraic groups from first principles.Building on the background material from algebraic geometry and algebraic groups, the text provides an introduction to more advanced and specialised material. An example is the representation theory of finite groups of Lie type.The text covers the conjugacy of Borel subgroups and maximal tori, the theory of algebraic groups
Implosions and hypertoric geometry
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
Schreiber, Urs
2016-01-01
This is a survey of motivations, constructions and applications of higher prequantum geometry. In section 1 we highlight the open problem of prequantizing local field theory in a local and gauge invariant way, and we survey how a solution to this problem exists in higher differential geometry. In section 2 we survey examples and problems of interest. In section 3 we survey the abstract cohesive homotopy theory that serves to make all this precise and tractable.
Punzi, Raffaele; Wohlfarth, Mattias N R
2008-01-01
We reveal the non-metric geometry underlying omega-->0 Brans-Dicke theory by unifying the metric and scalar field into a single geometric structure. Taking this structure seriously as the geometry to which matter universally couples, we show that the theory is fully consistent with solar system tests. This is in striking constrast with the standard metric coupling, which grossly violates post-Newtonian experimental constraints.
Punzi, Raffaele [Zentrum fuer Mathematische Physik und II. Institut fuer Theoretische Physik, Universitaet Hamburg, Luruper Chaussee 149, 22761 Hamburg (Germany)], E-mail: raffaele.punzi@desy.de; Schuller, Frederic P. [Max Planck Institut fuer Gravitationsphysik, Albert Einstein Institut, Am Muehlenberg 1, 14467 Potsdam (Germany)], E-mail: fps@aei.mpg.de; Wohlfarth, Mattias N.R. [Zentrum fuer Mathematische Physik und II. Institut fuer Theoretische Physik, Universitaet Hamburg, Luruper Chaussee 149, 22761 Hamburg (Germany)], E-mail: mattias.wohlfarth@desy.de
2008-12-11
We reveal the non-metric geometry underlying {omega}{yields}0 Brans-Dicke theory by unifying the metric and scalar field into a single geometric structure. Taking this structure seriously as the geometry to which matter universally couples, we show that the theory is fully consistent with solar system tests. This is in striking contrast with the standard metric coupling, which grossly violates post-Newtonian experimental constraints.
McAteer, R. T. J.
2013-06-01
When Mandelbrot, the father of modern fractal geometry, made this seemingly obvious statement he was trying to show that we should move out of our comfortable Euclidean space and adopt a fractal approach to geometry. The concepts and mathematical tools of fractal geometry provides insight into natural physical systems that Euclidean tools cannot do. The benet from applying fractal geometry to studies of Self-Organized Criticality (SOC) are even greater. SOC and fractal geometry share concepts of dynamic n-body interactions, apparent non-predictability, self-similarity, and an approach to global statistics in space and time that make these two areas into naturally paired research techniques. Further, the iterative generation techniques used in both SOC models and in fractals mean they share common features and common problems. This chapter explores the strong historical connections between fractal geometry and SOC from both a mathematical and conceptual understanding, explores modern day interactions between these two topics, and discusses how this is likely to evolve into an even stronger link in the near future.
First-order Dyson coordinates and geometry.
Hermes, Matthew R; Hirata, So
2013-08-15
The mathematical constructs of the Dyson coordinates and geometry are introduced. The former are a unitary transformation of the normal coordinates and the anharmonic vibrational counterpart of the Dyson orbitals in electronic structure theory. The first-order Dyson coordinates bring the sums of the harmonic force constants and their first-order diagrammatic perturbation corrections (the first-order Dyson self-energy) to a diagonal form. The first-order Dyson geometry has no counterpart in electronic structure theory. It is the point on the potential energy surface at which the sums of the energy gradients and their first-order diagrammatic perturbation corrections vanish. It agrees with the vibrationally averaged geometry of vibrational self-consistent field (VSCF) theory in the bulk limit. These constructs provide a unified view of the relationship of VSCF and its diagrammatically size-consistent modifications as well as the self-consistent phonon method widely used in solid-state physics.
Some Remarks on Navajo Geometry and Piagetian Genetic Theory.
Pinxten, Rik
1991-01-01
Examines aspects of Navajo cosmology relevant to understanding Navajo spatial representations. Compares Navajo children's spatial knowledge with Piaget's findings about the development of geometric concepts in Swiss children. Describes classroom activities whereby Navajo children explore the geometry inherent in their cultural and physical…
Some Remarks on Navajo Geometry and Piagetian Genetic Theory.
Pinxten, Rik
1991-01-01
Examines aspects of Navajo cosmology relevant to understanding Navajo spatial representations. Compares Navajo children's spatial knowledge with Piaget's findings about the development of geometric concepts in Swiss children. Describes classroom activities whereby Navajo children explore the geometry inherent in their cultural and physical…
Computer aided surface representation
Barnhill, R.E.
1989-02-09
The central research problem of this project is the effective representation and display of surfaces, interpolating to given information, in three or more dimensions. In a typical problem, we wish to create a surface from some discrete information. If this information is itself on another surface, the problem is to determine a surface defined on a surface,'' which is discussed below. Often, properties of an already constructed surface are desired: such geometry processing'' is described below. The Summary of Proposed Research from our original proposal describes the aims of this research project. This Summary and the Table of Contents from the original proposal are enclosed as an Appendix to this Progress Report. The broad sweep from constructive mathematics through algorithms and computer graphics displays is utilized in the research. The wide range of activity, directed in both theory and applications, makes this project unique. Last month in the first Ardent Titan delivered in the State of Arizona came to our group, funded by the DOE and Arizona State University. Although the Titan is a commercial product, its newness requires our close collaboration with Ardent to maximize results. During the past year, four faculty members and several graduate research assistants have worked on this DOE project. The gaining of new professionals is an important aspect of this project. A listing of the students and their topics is given in the Appendix. The most significant publication during the past year is the book, Curves and Surfaces for Computer Aided Geometric Design, by Dr. Gerald Farin. This 300 page volume helps fill a considerable gap in the subject and includes many new results on Bernstein-Bezier curves and surfaces.
Exploring the Structure of Spatial Representations.
Tamas Madl
Full Text Available It has been suggested that the map-like representations that support human spatial memory are fragmented into sub-maps with local reference frames, rather than being unitary and global. However, the principles underlying the structure of these 'cognitive maps' are not well understood. We propose that the structure of the representations of navigation space arises from clustering within individual psychological spaces, i.e. from a process that groups together objects that are close in these spaces. Building on the ideas of representational geometry and similarity-based representations in cognitive science, we formulate methods for learning dissimilarity functions (metrics characterizing participants' psychological spaces. We show that these learned metrics, together with a probabilistic model of clustering based on the Bayesian cognition paradigm, allow prediction of participants' cognitive map structures in advance. Apart from insights into spatial representation learning in human cognition, these methods could facilitate novel computational tools capable of using human-like spatial concepts. We also compare several features influencing spatial memory structure, including spatial distance, visual similarity and functional similarity, and report strong correlations between these dimensions and the grouping probability in participants' spatial representations, providing further support for clustering in spatial memory.
The Spectrum of Static Subtracted Geometries
Andrade, Tomas; Cohen-Maldonado, Diego
2016-01-01
Subtracted geometries are black hole solutions of the four dimensional STU model with rather interesting ties to asymptotically flat black holes. In addition, a peculiar feature is that the solutions to the Klein-Gordon equation on this subtracted background can be organized according to representations of the conformal group $SO(2,2)$. We test if this behavior persists for the linearized fluctuations of gravitational and matter fields on static, electrically charged backgrounds of this kind. We find that there is a subsector of the modes that do display conformal symmetry, while some modes do not. We also discuss two different effective actions that describe these subtracted geometries and how the spectrum of quasinormal modes is dramatically different depending upon the action used.
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...
Perception of global facial geometry is modulated through experience
Meike Ramon
2015-03-01
Full Text Available Identification of personally familiar faces is highly efficient across various viewing conditions. While the presence of robust facial representations stored in memory is considered to aid this process, the mechanisms underlying invariant identification remain unclear. Two experiments tested the hypothesis that facial representations stored in memory are associated with differential perceptual processing of the overall facial geometry. Subjects who were personally familiar or unfamiliar with the identities presented discriminated between stimuli whose overall facial geometry had been manipulated to maintain or alter the original facial configuration (see Barton, Zhao & Keenan, 2003. The results demonstrate that familiarity gives rise to more efficient processing of global facial geometry, and are interpreted in terms of increased holistic processing of facial information that is maintained across viewing distances.
Students Discovering Spherical Geometry Using Dynamic Geometry Software
Guven, Bulent; Karatas, Ilhan
2009-01-01
Dynamic geometry software (DGS) such as Cabri and Geometers' Sketchpad has been regularly used worldwide for teaching and learning Euclidean geometry for a long time. The DGS with its inductive nature allows students to learn Euclidean geometry via explorations. However, with respect to non-Euclidean geometries, do we need to introduce them to…
Students Discovering Spherical Geometry Using Dynamic Geometry Software
Guven, Bulent; Karatas, Ilhan
2009-01-01
Dynamic geometry software (DGS) such as Cabri and Geometers' Sketchpad has been regularly used worldwide for teaching and learning Euclidean geometry for a long time. The DGS with its inductive nature allows students to learn Euclidean geometry via explorations. However, with respect to non-Euclidean geometries, do we need to introduce them to…
Emergent Complex Network Geometry
Wu, Zhihao; Rahmede, Christoph; Bianconi, Ginestra
2014-01-01
Networks are mathematical structures that are universally used to describe a large variety of complex systems such as the brain or the Internet. Characterizing the geometrical properties of these networks has become increasingly relevant for routing problems, inference and data mining. In real growing networks, topological, structural and geometrical properties emerge spontaneously from their dynamical rules. Nevertheless we still miss a model in which networks develop an emergent complex geometry. Here we show that a single two parameter network model, the growing geometrical network, can generate complex network geometries with non-trivial distribution of curvatures, combining exponential growth and small-world properties with finite spectral dimensionality. In one limit, the non-equilibrium dynamical rules of these networks can generate scale-free networks with clustering and communities, in another limit planar random geometries with non-trivial modularity. Finally we find that these properties of the geo...
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...
Supersymmetry and noncommutative geometry
Beenakker, Wim; Suijlekom, Walter D van
2016-01-01
In this work the question whether noncommutative geometry allows for supersymmetric theories is addressed. Noncommutative geometry has seen remarkable applications in high energy physics, viz. the geometrical interpretation of the Standard Model, however such a question has not been answered in a conclusive way so far. The book starts with a systematic analysis of the possibilities for so-called almost-commutative geometries on a 4-dimensional, flat background to exhibit not only a particle content that is eligible for supersymmetry, but also have a supersymmetric action. An approach is proposed in which the basic `building blocks' of potentially supersymmetric theories and the demands for their action to be supersymmetric are identified. It is then described how a novel kind of soft supersymmetry breaking Lagrangian arises naturally from the spectral action. Finally, the above formalism is applied to explore the existence of a noncommutative version of the minimal supersymmetric Standard Model. This book is ...
Wetterich, C
2012-01-01
In models of emergent gravity the metric arises as the expectation value of some collective field. Usually, many different collective fields with appropriate tensor properties are candidates for a metric. Which collective field describes the "physical geometry"? We resolve this "metric ambiguity" by an investigation of the most general form of the quantum effective action for several metrics. In the long-distance limit the physical metric is universal and accounts for a massless graviton. Other degrees of freedom contained in the various metric candidates describe very massive scalars and symmetric second rank tensors. They only play a role at microscopic distances, typically around the Planck length. The universality of geometry at long distances extends to the vierbein and the connection. On the other hand, for distances and time intervals of Planck size geometry looses its universal meaning. Time is born with the big bang.
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...
Integral Geometry and Holography
Czech, Bartlomiej; McCandlish, Samuel; Sully, James
2015-01-01
We present a mathematical framework which underlies the connection between information theory and the bulk spacetime in the AdS$_3$/CFT$_2$ correspondence. A key concept is kinematic space: an auxiliary Lorentzian geometry whose metric is defined in terms of conditional mutual informations and which organizes the entanglement pattern of a CFT state. When the field theory has a holographic dual obeying the Ryu-Takayanagi proposal, kinematic space has a direct geometric meaning: it is the space of bulk geodesics studied in integral geometry. Lengths of bulk curves are computed by kinematic volumes, giving a precise entropic interpretation of the length of any bulk curve. We explain how basic geometric concepts -- points, distances and angles -- are reflected in kinematic space, allowing one to reconstruct a large class of spatial bulk geometries from boundary entanglement entropies. In this way, kinematic space translates between information theoretic and geometric descriptions of a CFT state. As an example, we...
2002-01-01
Discrete geometry investigates combinatorial properties of configurations of geometric objects. To a working mathematician or computer scientist, it offers sophisticated results and techniques of great diversity and it is a foundation for fields such as computational geometry or combinatorial optimization. This book is primarily a textbook introduction to various areas of discrete geometry. In each area, it explains several key results and methods, in an accessible and concrete manner. It also contains more advanced material in separate sections and thus it can serve as a collection of surveys in several narrower subfields. The main topics include: basics on convex sets, convex polytopes, and hyperplane arrangements; combinatorial complexity of geometric configurations; intersection patterns and transversals of convex sets; geometric Ramsey-type results; polyhedral combinatorics and high-dimensional convexity; and lastly, embeddings of finite metric spaces into normed spaces. Jiri Matousek is Professor of Com...
Ochiai, T.; Nacher, J. C.
2011-09-01
Recently, the application of geometry and conformal mappings to artificial materials (metamaterials) has attracted the attention in various research communities. These materials, characterized by a unique man-made structure, have unusual optical properties, which materials found in nature do not exhibit. By applying the geometry and conformal mappings theory to metamaterial science, it may be possible to realize so-called "Harry Potter cloaking device". Although such a device is still in the science fiction realm, several works have shown that by using such metamaterials it may be possible to control the direction of the electromagnetic field at will. We could then make an object hidden inside of a cloaking device. Here, we will explain how to design invisibility device using differential geometry and conformal mappings.
The Geometry of Conventionality
Weatherall, James Owen
2013-01-01
Hans Reichenbach famously argued that the geometry of spacetime is conventional in relativity theory, in the sense that one can freely choose the spacetime metric so long as one is willing to postulate a "universal force field". Here we make precise a sense in which the field Reichenbach defines fails to be a "force". We then argue that there is an interesting and perhaps tenable sense in which geometry is conventional in classical spacetimes. We conclude with a no-go result showing that the variety of conventionalism available in classical spacetimes does not extend to relativistic spacetimes.
Yale, Paul B
2012-01-01
This book is an introduction to the geometry of Euclidean, affine, and projective spaces with special emphasis on the important groups of symmetries of these spaces. The two major objectives of the text are to introduce the main ideas of affine and projective spaces and to develop facility in handling transformations and groups of transformations. Since there are many good texts on affine and projective planes, the author has concentrated on the n-dimensional cases.Designed to be used in advanced undergraduate mathematics or physics courses, the book focuses on ""practical geometry,"" emphasi
Eisenhart, L P
1927-01-01
The use of the differential geometry of a Riemannian space in the mathematical formulation of physical theories led to important developments in the geometry of such spaces. The concept of parallelism of vectors, as introduced by Levi-Civita, gave rise to a theory of the affine properties of a Riemannian space. Covariant differentiation, as developed by Christoffel and Ricci, is a fundamental process in this theory. Various writers, notably Eddington, Einstein and Weyl, in their efforts to formulate a combined theory of gravitation and electromagnetism, proposed a simultaneous generalization o
Staircase-free finite-difference time-domain formulation for general materials in complex geometries
Dridi, Kim; Hesthaven, J.S.; Ditkowski, A.
2001-01-01
A stable Cartesian grid staircase-free finite-difference time-domain formulation for arbitrary material distributions in general geometries is introduced. It is shown that the method exhibits higher accuracy than the classical Yee scheme for complex geometries since the computational representation...
Clifford algebras geometric modelling and chain geometries with application in kinematics
Klawitter, Daniel
2015-01-01
After revising known representations of the group of Euclidean displacements Daniel Klawitter gives a comprehensive introduction into Clifford algebras. The Clifford algebra calculus is used to construct new models that allow descriptions of the group of projective transformations and inversions with respect to hyperquadrics. Afterwards, chain geometries over Clifford algebras and their subchain geometries are examined. The author applies this theory and the developed methods to the homogeneous Clifford algebra model corresponding to Euclidean geometry. Moreover, kinematic mappings for special Cayley-Klein geometries are developed. These mappings allow a description of existing kinematic mappings in a unifying framework. Contents Models and representations of classical groups Clifford algebras, chain geometries over Clifford algebras Kinematic mappings for Pin and Spin groups Cayley-Klein geometries Target Groups Researchers and students in the field of mathematics, physics, and mechanical engineering About...
Universal correlators from geometry
Dijkgraaf, Robbert [Institute for Theoretical Physics, University of Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam (Netherlands); Korteweg-de Vries Institute for Mathematics, University of Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam (Netherlands); Temuerhan, Mine; Sinkovics, Annamaria [Institute for Theoretical Physics, University of Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam (Netherlands)]. E-mail: sinkovic@science.uva.nl
2004-11-01
Matrix model correlators show universal behaviour at short distances. We provide a derivation for these universal correlators by inserting probe branes in the underlying effective geometry. We generalize these results to study correlators of branes and their universal behaviour in the Calabi-Yau crystals, where we find a role for a generalized brane insertion. (author)
Universal Correlators from Geometry
Dijkgraaf, Robbert; Sinkovics, Annamaria; Temurhan, Mine
2004-11-01
Matrix model correlators show universal behaviour at short distances. We provide a derivation for these universal correlators by inserting probe branes in the underlying effective geometry. We generalize these results to study correlators of branes and their universal behaviour in the Calabi-Yau crystals, where we find a role for a generalized brane insertion.
Universal Correlators from Geometry
Dijkgraaf, R; Temurhan, M; Dijkgraaf, Robbert; Sinkovics, Annamaria; Temurhan, Mine
2004-01-01
Matrix model correlators show universal behaviour at short distances. We provide a derivation for these universal correlators by inserting probe branes in the underlying effective geometry. We generalize these results to study correlators of branes and their universal behaviour in the Calabi-Yau crystals, where we find a role for a generalized brane insertion.
Atiyah, Michael; Dijkgraaf, Robbert; Hitchin, Nigel
2010-01-01
We review the remarkably fruitful interactions between mathematics and quantum physics in the past decades, pointing out some general trends and highlighting several examples, such as the counting of curves in algebraic geometry, invariants of knots and four-dimensional topology. PMID:20123740
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.
Diophantine geometry an introduction
Hindry, Marc
2000-01-01
This is an introduction to diophantine geometry at the advanced graduate level. The book contains a proof of the Mordell conjecture which will make it quite attractive to graduate students and professional mathematicians. In each part of the book, the reader will find numerous exercises.
Towards relativistic quantum geometry
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.
Advanced geometries and regimes
Bulanov, S. S. [Univeristy of California, Berkeley, CA, 94720 (United States); Bulanov, S. V. [Kansai Photon Science Institute, JAEA, Kizugawa, Kyoto 619-0215 (Japan); Turchetti, G. [Dipartimento di Fisica, Università di Bologna and INFN Sezione di Bologna, Via Irnerio, 46-I-40126 Bologna (Italy); Limpouch, J.; Klimo, O.; Psikal, J. [Institute of Physics of the ASCR, ELI-Beamlines/HiLASE project, Na Slovance 2, 18221 Prague, Czech Republic and Czech Technical University in Prague, FNSPE, Brehova 7, 115 19 Prague (Czech Republic); Antici, P. [Dipartimento di Energetica ed INFM, Università di Roma, La Sapienza, 00165 Roma (Italy); Margarone, D.; Korn, G. [Institute of Physics of the ASCR, ELI-Beamlines/HiLASE project, Na Slovance 2, 18221 Prague (Czech Republic)
2013-07-26
We review and discuss different schemes of laser ion acceleration as well as advanced target geometries in connection with the development of the laser-driven proton source for hadron therapy of oncological diseases, which is a part of the ELIMED project.
Emergent Hyperbolic Network Geometry
Bianconi, Ginestra; Rahmede, Christoph
2017-02-01
A large variety of interacting complex systems are characterized by interactions occurring between more than two nodes. These systems are described by simplicial complexes. Simplicial complexes are formed by simplices (nodes, links, triangles, tetrahedra etc.) that have a natural geometric interpretation. As such simplicial complexes are widely used in quantum gravity approaches that involve a discretization of spacetime. Here, by extending our knowledge of growing complex networks to growing simplicial complexes we investigate the nature of the emergent geometry of complex networks and explore whether this geometry is hyperbolic. Specifically we show that an hyperbolic network geometry emerges spontaneously from models of growing simplicial complexes that are purely combinatorial. The statistical and geometrical properties of the growing simplicial complexes strongly depend on their dimensionality and display the major universal properties of real complex networks (scale-free degree distribution, small-world and communities) at the same time. Interestingly, when the network dynamics includes an heterogeneous fitness of the faces, the growing simplicial complex can undergo phase transitions that are reflected by relevant changes in the network geometry.
Spacetime and Euclidean Geometry
Brill, D R; Brill, Dieter; Jacobson, Ted
2004-01-01
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".
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.
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...
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…
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 ...
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.
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…
Thermal analysis on motorcycle disc brake geometry
W. M. Zurin W., S.; Talib, R. J.; Ismail, N. I.
2017-08-01
Braking is a phase of slowing and stop the movement of motorcycle. During braking, the frictional heat was generated and the energy was ideally should be faster dissipated to surrounding to prevent the built up of the excessive temperature which may lead to brake fluid vaporization, thermoelastic deformation at the contact surface, material degradation and failure. In this paper, solid and ventilated type of motorcycle disc brake are being analyse using Computational Fluid Dynamic (CFD) software. The main focus of the analysis is the thermal behaviour during braking for solid and ventilated disc brake. A comparison between both geometries is being discussed to determine the better braking performance in term of temperature distribution. It is found that ventilated disc brake is having better braking performance in terms of heat transfer compare to solid disc.
An introduction to Minkowski geometries
Farnsworth, David L.
2016-07-01
The fundamental ideas of Minkowski geometries are presented. Learning about Minkowski geometries can sharpen our students' understanding of concepts such as distance measurement. Many of its ideas are important and accessible to undergraduate students. Following a brief overview, distance and orthogonality in Minkowski geometries are thoroughly discussed and many illustrative examples and applications are supplied. Suggestions for further study of these geometries are given. Indeed, Minkowski geometries are an excellent source of topics for undergraduate research and independent study.
Social representations of women
Álvaro Estramiana, José Luis
2006-05-01
Full Text Available Social Representations is one of the most important theories in contemporary social psychology. Since the social psychologist Serge Moscovici developed his theory of social representations to explain how a scientific theory such as the psychoanalysis turns into a common sense knowledge many studies have been done by different social psychologists. The analysis of the social representations of women as represented in myths and popular beliefs is an excellent opportunity to study how this theory can be applied to this representational field. At the same time it makes possible to understand the formation of attitudes towards women
Noncommutative algebra and geometry
De Concini, Corrado; Vavilov, Nikolai 0
2005-01-01
Finite Galois Stable Subgroups of Gln. Derived Categories for Nodal Rings and Projective Configurations. Crowns in Profinite Groups and Applications. The Galois Structure of Ambiguous Ideals in Cyclic Extensions of Degree 8. An Introduction to Noncommutative Deformations of Modules. Symmetric Functions, Noncommutative Symmetric Functions and Quasisymmetric Functions II. Quotient Grothendieck Representations. On the Strong Rigidity of Solvable Lie Algebras. The Role of Bergman in Invesigating Identities in Matrix Algebras with Symplectic Involution. The Triangular Structure of Ladder Functors.
Leone, María J; Fernandez Slezak, Diego; Cecchi, Guillermo A; Sigman, Mariano
2014-01-01
Theories of expertise based on the acquisition of chunk and templates suggest a differential geometric organization of perception between experts and novices. It is implied that expert representation is less anchored by spatial (Euclidean) proximity and may instead be dictated by the intrinsic relation in the structure and grammar of the specific domain of expertise. Here we set out to examine this hypothesis. We used the domain of chess which has been widely used as a tool to study human expertise. We reasoned that the movement of an opponent piece to a specific square constitutes an external cue and the reaction of the player to this "perturbation" should reveal his internal representation of proximity. We hypothesized that novice players will tend to respond by moving a piece in closer squares than experts. Similarly, but now in terms of object representations, we hypothesized weak players will more likely focus on a specific piece and hence produce sequence of actions repeating movements of the same piece. We capitalized on a large corpus of data obtained from internet chess servers. Results showed that, relative to experts, weaker players tend to (1) produce consecutive moves in proximal board locations, (2) move more often the same piece and (3) reduce the number of remaining pieces more rapidly, most likely to decrease cognitive load and mental effort. These three principles might reflect the effect of expertise on human actions in complex setups.
A toolbox for representational similarity analysis.
Hamed Nili
2014-04-01
Full Text Available Neuronal population codes are increasingly being investigated with multivariate pattern-information analyses. A key challenge is to use measured brain-activity patterns to test computational models of brain information processing. One approach to this problem is representational similarity analysis (RSA, which characterizes a representation in a brain or computational model by the distance matrix of the response patterns elicited by a set of stimuli. The representational distance matrix encapsulates what distinctions between stimuli are emphasized and what distinctions are de-emphasized in the representation. A model is tested by comparing the representational distance matrix it predicts to that of a measured brain region. RSA also enables us to compare representations between stages of processing within a given brain or model, between brain and behavioral data, and between individuals and species. Here, we introduce a Matlab toolbox for RSA. The toolbox supports an analysis approach that is simultaneously data- and hypothesis-driven. It is designed to help integrate a wide range of computational models into the analysis of multichannel brain-activity measurements as provided by modern functional imaging and neuronal recording techniques. Tools for visualization and inference enable the user to relate sets of models to sets of brain regions and to statistically test and compare the models using nonparametric inference methods. The toolbox supports searchlight-based RSA, to continuously map a measured brain volume in search of a neuronal population code with a specific geometry. Finally, we introduce the linear-discriminant t value as a measure of representational discriminability that bridges the gap between linear decoding analyses and RSA. In order to demonstrate the capabilities of the toolbox, we apply it to both simulated and real fMRI data. The key functions are equally applicable to other modalities of brain-activity measurement. The
Cylindrical geometry hall thruster
Raitses, Yevgeny; Fisch, Nathaniel J.
2002-01-01
An apparatus and method for thrusting plasma, utilizing a Hall thruster with a cylindrical geometry, wherein ions are accelerated in substantially the axial direction. The apparatus is suitable for operation at low power. It employs small size thruster components, including a ceramic channel, with the center pole piece of the conventional annular design thruster eliminated or greatly reduced. Efficient operation is accomplished through magnetic fields with a substantial radial component. The propellant gas is ionized at an optimal location in the thruster. A further improvement is accomplished by segmented electrodes, which produce localized voltage drops within the thruster at optimally prescribed locations. The apparatus differs from a conventional Hall thruster, which has an annular geometry, not well suited to scaling to small size, because the small size for an annular design has a great deal of surface area relative to the volume.
Lee, Jeongseog; Safdi, Benjamin R
2014-01-01
Entanglement entropy in even dimensional conformal field theories (CFTs) contains well-known universal terms arising from the conformal anomaly. Renyi entropies are natural generalizations of the entanglement entropy that are much less understood. Above two spacetime dimensions, the universal terms in the Renyi entropies are unknown for general entangling geometries. We conjecture a new structure in the dependence of the four-dimensional Renyi entropies on the intrinsic and extrinsic geometry of the entangling surface. We provide evidence for this conjecture by direct numerical computations in the free scalar and fermion field theories. The computation involves relating the four-dimensional free massless Renyi entropies across cylindrical entangling surfaces to corresponding three-dimensional massive Renyi entropies across circular entangling surfaces. Our numerical technique also allows us to directly probe other interesting aspects of three-dimensional Renyi entropy, including the massless renormalized Reny...
Spectral Geometry and Causality
Kopf, T
1996-01-01
For a physical interpretation of a theory of quantum gravity, it is necessary to recover classical spacetime, at least approximately. However, quantum gravity may eventually provide classical spacetimes by giving spectral data similar to those appearing in noncommutative geometry, rather than by giving directly a spacetime manifold. It is shown that a globally hyperbolic Lorentzian manifold can be given by spectral data. A new phenomenon in the context of spectral geometry is observed: causal relationships. The employment of the causal relationships of spectral data is shown to lead to a highly efficient description of Lorentzian manifolds, indicating the possible usefulness of this approach. Connections to free quantum field theory are discussed for both motivation and physical interpretation. It is conjectured that the necessary spectral data can be generically obtained from an effective field theory having the fundamental structures of generalized quantum mechanics: a decoherence functional and a choice of...
Algebra, Arithmetic, and Geometry
Tschinkel, Yuri
2009-01-01
The two volumes of "Algebra, Arithmetic, and Geometry: In Honor of Y.I. Manin" are composed of invited expository articles and extensions detailing Manin's contributions to the subjects, and are in celebration of his 70th birthday. The well-respected and distinguished contributors include: Behrend, Berkovich, Bost, Bressler, Calaque, Carlson, Chambert-Loir, Colombo, Connes, Consani, Dabrowski, Deninger, Dolgachev, Donaldson, Ekedahl, Elsenhans, Enriques, Etingof, Fock, Friedlander, Geemen, Getzler, Goncharov, Harris, Iskovskikh, Jahnel, Kaledin, Kapranov, Katz, Kaufmann, Kollar, Kont
Differential geometry and thermodynamics
Quevedo, H
2003-01-01
In this work we present the first steps of a new approach to the study of thermodynamics in the context of differential geometry. We introduce a fundamental differential 1-form and a metric on a pseudo-Euclidean manifold coordinatized by means of the extensive thermodynamic variables. The study of the connection and the curvature of these objects is initialized in this work by using Cartan structure equations. (Author)
Krauss, L M; 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.
Inflation from quantum geometry.
Bojowald, Martin
2002-12-23
Quantum geometry predicts that a universe evolves through an inflationary phase at small volume before exiting gracefully into a standard Friedmann phase. This does not require the introduction of additional matter fields with ad hoc potentials; rather, it occurs because of a quantum gravity modification of the kinetic part of ordinary matter Hamiltonians. An application of the same mechanism can explain why the present day cosmological acceleration is so tiny.
Tamke, Martin; Ramsgaard Thomsen, Mette; Riiber Nielsen, Jacob
2009-01-01
The versatility of wood constructions and traditional wood joints for the production of non standard elements was in focus of a design based research. Herein we established a seamless process from digital design to fabrication. A first research phase centered on the development of a robust parame...... parametric model and a generic design language a later explored the possibilities to construct complex shaped geometries with self registering joints on modern wood crafting machines. The research was carried out as collaboration with industrial partners....
Invariant representation for spectral reflectance images and its application
Ibrahim Abdelhameed
2011-01-01
Full Text Available Abstract Spectral images as well as color images observed from object surfaces are much influenced by various illumination conditions such as shading and specular highlight. Several invariant representations were proposed for these conditions using the standard dichromatic reflection model of dielectric materials. However, these representations are inadequate for other materials like metal. This article proposes an invariant representation that is derived from the standard dichromatic reflection model for dielectric and the extended dichromatic reflection model for metal. We show that a normalized surface-spectral reflectance by the minimum reflectance is invariant to highlights, shading, surface geometry, and illumination intensity. Here the illumination spectrum and the spectral sensitivity functions of the imaging system are measured in a separate way. As an application of the proposed invariant representation, a segmentation algorithm based on the proposed representation is presented for effectively segmenting spectral images of natural scenes and bare circuit boards.
Extensions of tempered representations
Opdam, E.; Solleveld, M.
2013-01-01
Let π, π′ be irreducible tempered representations of an affine Hecke algebra H with positive parameters. We compute the higher extension groups Ext nH(π,π′) explicitly in terms of the representations of analytic R-groups corresponding to π and π′. The result has immediate applications to the computa
Multiple sparse representations classification
E. Plenge (Esben); S.K. Klein (Stefan); W.J. Niessen (Wiro); E. Meijering (Erik)
2015-01-01
textabstractSparse representations classification (SRC) is a powerful technique for pixelwise classification of images and it is increasingly being used for a wide variety of image analysis tasks. The method uses sparse representation and learned redundant dictionaries to classify image pixels. In t
Embedded Data Representations.
Willett, Wesley; Jansen, Yvonne; Dragicevic, Pierre
2017-01-01
We introduce embedded data representations, the use of visual and physical representations of data that are deeply integrated with the physical spaces, objects, and entities to which the data refers. Technologies like lightweight wireless displays, mixed reality hardware, and autonomous vehicles are making it increasingly easier to display data in-context. While researchers and artists have already begun to create embedded data representations, the benefits, trade-offs, and even the language necessary to describe and compare these approaches remain unexplored. In this paper, we formalize the notion of physical data referents - the real-world entities and spaces to which data corresponds - and examine the relationship between referents and the visual and physical representations of their data. We differentiate situated representations, which display data in proximity to data referents, and embedded representations, which display data so that it spatially coincides with data referents. Drawing on examples from visualization, ubiquitous computing, and art, we explore the role of spatial indirection, scale, and interaction for embedded representations. We also examine the tradeoffs between non-situated, situated, and embedded data displays, including both visualizations and physicalizations. Based on our observations, we identify a variety of design challenges for embedded data representation, and suggest opportunities for future research and applications.
Ankersmit, F.R.
2010-01-01
This essay focuses on the historical text as a whole. It does so by conceiving of the historical text as representation - in the way the we may say of a photo or a painting that it represents the person depicted on it. It is argued that representation cannot be properly understood by modelling it on
Integral geometry and holography
Czech, Bartłomiej; Lamprou, Lampros; McCandlish, Samuel; Sully, James
2015-10-01
We present a mathematical framework which underlies the connection between information theory and the bulk spacetime in the AdS3/CFT2 correspondence. A key concept is kinematic space: an auxiliary Lorentzian geometry whose metric is defined in terms of conditional mutual informations and which organizes the entanglement pattern of a CFT state. When the field theory has a holographic dual obeying the Ryu-Takayanagi proposal, kinematic space has a direct geometric meaning: it is the space of bulk geodesics studied in integral geometry. Lengths of bulk curves are computed by kinematic volumes, giving a precise entropic interpretation of the length of any bulk curve. We explain how basic geometric concepts — points, distances and angles — are reflected in kinematic space, allowing one to reconstruct a large class of spatial bulk geometries from boundary entanglement entropies. In this way, kinematic space translates between information theoretic and geometric descriptions of a CFT state. As an example, we discuss in detail the static slice of AdS3 whose kinematic space is two-dimensional de Sitter space.
Hilbert, completeness and geometry
Giorgio Venturi
2011-11-01
Full Text Available This paper aims to show how the mathematical content of Hilbert's Axiom of Completeness consists in an attempt to solve the more general problem of the relationship between intuition and formalization. Hilbert found the accordance between these two sides of mathematical knowledge at a logical level, clarifying the necessary and sufficient conditions for a good formalization of geometry. We will tackle the problem of what is, for Hilbert, the definition of geometry. The solution of this problem will bring out how Hilbert's conception of mathematics is not as innovative as his conception of the axiomatic method. The role that the demonstrative tools play in Hilbert's foundational reflections will also drive us to deal with the problem of the purity of methods, explicitly addressed by Hilbert. In this respect Hilbert's position is very innovative and deeply linked to his modern conception of the axiomatic method. In the end we will show that the role played by the Axiom of Completeness for geometry is the same as the Axiom of Induction for arithmetic and of Church-Turing thesis for computability theory. We end this paper arguing that set theory is the right context in which applying the axiomatic method to mathematics and we postpone to a sequel of this work the attempt to offer a solution similar to Hilbert's for the completeness of set theory.
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...
Generalised Geometry and Flux Vacua
Larfors, Magdalena
2015-01-01
This note discusses the connection between generalised geometry and flux compactifications of string theory. Firstly, we explain in a pedestrian manner how the supersymmetry constraints of type II ${\\mathcal{N}}=1$ flux compactifications can be restated as integrability constraints on certain generalised complex structures. This reformulation uses generalised complex geometry, a mathematical framework that geometrizes the B-field. Secondly, we discuss how exceptional generalised geometry may provide a similar geometrization of the RR fields. Thirdly, we examine the connection between generalised geometry and non-geometry, and finally we present recent developments where generalised geometry is used to construct explicit examples of flux compactifications to flat space.
Group and representation theory
Vergados, J D
2017-01-01
This volume goes beyond the understanding of symmetries and exploits them in the study of the behavior of both classical and quantum physical systems. Thus it is important to study the symmetries described by continuous (Lie) groups of transformations. We then discuss how we get operators that form a Lie algebra. Of particular interest to physics is the representation of the elements of the algebra and the group in terms of matrices and, in particular, the irreducible representations. These representations can be identified with physical observables. This leads to the study of the classical Lie algebras, associated with unitary, unimodular, orthogonal and symplectic transformations. We also discuss some special algebras in some detail. The discussion proceeds along the lines of the Cartan-Weyl theory via the root vectors and root diagrams and, in particular, the Dynkin representation of the roots. Thus the representations are expressed in terms of weights, which are generated by the application of the elemen...
Willett, Wesley; Jansen, Yvonne; Dragicevic, Pierre
2017-01-01
We introduce embedded data representations, the use of visual and physical representations of data that are deeply integrated with the physical spaces, objects, and entities to which the data refers. Technologies like lightweight wireless displays, mixed reality hardware, and autonomous vehicles...... are making it increasingly easier to display data in-context. While researchers and artists have already begun to create embedded data representations, the benefits, trade-offs, and even the language necessary to describe and compare these approaches remain unexplored. In this paper, we formalize the notion...... of physical data referents – the real-world entities and spaces to which data corresponds – and examine the relationship between referents and the visual and physical representations of their data. We differentiate situated representations, which display data in proximity to data referents, and embedded...
Determining Fault Geometries From Surface Displacements
Volkov, D.; Voisin, C.; Ionescu, I. R.
2017-02-01
We introduce a new algorithm for determining the geometry of active parts of faults. This algorithm uses surface measurements of displacement fields and local modeling of the Earth's crust as a half-space elastic medium. The numerical method relies on iterations alternating non-linear steps for recovering the geometry and linear steps for reconstructing slip fields. Our algorithm greatly improves upon past attempts at reconstructing fault profiles. We argue that these past attempts suffered from either the restrictive assumption that the geometry of faults can be derived using only uniformly constant slips or that they relied on arbitrary assumptions on the statistics of the reconstruction error. We test this algorithm on the 2006 Guerrero, Mexico, slow slip event (SSE) and on the 2009 SSE for the same region. These events occurred on a relatively well-known subduction zone, whose geometry was derived from seismicity and gravimetric techniques, see Kostoglodov et al. (Geophys Res Lett 23(23):3385-3388, 1996), Pardo and Suarez (J Geophys Res 100(B7):357-373, 1995), Singh and Pardo (Geophys Res Lett 20(14):1483-1486, 1993), so our results can be compared to known benchmarks. Our derived geometry is found to be consistent with these benchmarks regarding dip and strike angles and the positioning of the North American Trench. In addition, our derived slip distribution is also consistent with previous studies (all done with an assumed fixed geometry), see Larson et al. (Geophys Res Lett 34(13), 2007), Bekaert et al. (J Geophys Res: Solid Earth 120(2):1357-1375, 2015), Radiguet et al. (Geophys J Int 184(2):816-828, 2011, J Geophys Res 2012), Rivet et al. (Geophys Res Lett 38(8), 2011), Vergnolle et al. (J Geophys Res: Solid Earth 115(B8), 2010), Walpersdorf et al. Geophys Res Lett 38(15), 2011), to name a few. We believe that the new computational inverse method introduced in this paper holds great promise for applications to blind inversion cases, where both geometry and
SU (N ) Heisenberg model with multicolumn representations
Okubo, Tsuyoshi; Harada, Kenji; Lou, Jie; Kawashima, Naoki
2015-10-01
The SU (N ) symmetric antiferromagnetic Heisenberg model with multicolumn representations on the two-dimensional square lattice is investigated by quantum Monte Carlo simulations. For the representation of a Young diagram with two columns, we confirm that a valence-bond solid (VBS) order appears as soon as the Néel order disappears at N =10 , indicating no intermediate phase. In the case of the representation with three columns, there is no evidence for either the Néel or the VBS ordering for N ≥15 . This is actually consistent with the large-N theory, which predicts that the VBS state immediately follows the Néel state, because the expected spontaneous order is too weak to be detected.
Twisted geometries, twistors and conformal transformations
Långvik, Miklos
2016-01-01
The twisted geometries of spin network states are described by simple twistors, isomorphic to null twistors with a time-like direction singled out. The isomorphism depends on the Immirzi parameter, and reduces to the identity when the parameter goes to infinity. Using this twistorial representation we study the action of the conformal group SU(2,2) on the classical phase space of loop quantum gravity, described by twisted geometry. The generators of translations and conformal boosts do not preserve the geometric structure, whereas the dilatation generator does. It corresponds to a 1-parameter family of embeddings of T*SL(2,C) in twistor space, and its action preserves the intrinsic geometry while changing the extrinsic one - that is the boosts among polyhedra. We discuss the implication of this action from a dynamical point of view, and compare it with a discretisation of the dilatation generator of the continuum phase space, given by the Lie derivative of the group character. At leading order in the continuu...
Introductory non-Euclidean geometry
Manning, Henry Parker
1963-01-01
This fine and versatile introduction begins with the theorems common to Euclidean and non-Euclidean geometry, and then it addresses the specific differences that constitute elliptic and hyperbolic geometry. 1901 edition.
Geometry for the Secondary School
Moalem, D.
1977-01-01
A sequential but non-axiomatic high school geometry course which includes Euclidean, transformation, and analytic geometry and vectors and matrices, and emphasizes the invariance property of transformations, is outlined. Sample problems, solutions, and comments are included. (MN)
Linear connections on matrix geometries
Madore, J; Mourad, J; Madore, John; Masson, Thierry; Mourad, Jihad
1994-01-01
A general definition of a linear connection in noncommutative geometry has been recently proposed. Two examples are given of linear connections in noncommutative geometries which are based on matrix algebras. They both possess a unique metric connection.
Differential geometry basic notions and physical examples
Epstein, Marcelo
2014-01-01
Differential Geometry offers a concise introduction to some basic notions of modern differential geometry and their applications to solid mechanics and physics. Concepts such as manifolds, groups, fibre bundles and groupoids are first introduced within a purely topological framework. They are shown to be relevant to the description of space-time, configuration spaces of mechanical systems, symmetries in general, microstructure and local and distant symmetries of the constitutive response of continuous media. Once these ideas have been grasped at the topological level, the differential structure needed for the description of physical fields is introduced in terms of differentiable manifolds and principal frame bundles. These mathematical concepts are then illustrated with examples from continuum kinematics, Lagrangian and Hamiltonian mechanics, Cauchy fluxes and dislocation theory. This book will be useful for researchers and graduate students in science and engineering.
The Role of Visual Representations for Structuring Classroom Mathematical Activity
David, Maria Manuela; Tomaz, Vanessa Sena
2012-01-01
It is our presupposition that there is still a need for more research about how classroom practices can exploit the use and power of visualization in mathematics education. The aim of this article is to contribute in this direction, investigating how visual representations can structure geometry activity in the classroom and discussing teaching…
The topo-approach to spatial representation and reasoning
Aiello, Marco
2003-01-01
Commonsense knowledge about the surrounding physical world and quantitative theories of space, such as metric geometry, can be viewed as two extremes on how human beings relate to space. Qualitative spatial representation and reasoning places itself in between these two approaches. Qualitative spati
Editors, LearningExpress
2010-01-01
Whether you're new to geometry or just looking for a refresher, this completely revised and updated third edition of Geometry Success in 20 Minutes a Day offers a 20-step lesson plan that provides quick and thorough instruction in practical, critical skills. Stripped of unnecessary math jargon but bursting with geometry essentials, Geometry Success in 20 Minutes a Day is an invaluable resource for both students and adults.
Differential geometry the mathematical works of J. H. C. Whitehead
James, I M
1962-01-01
The Mathematical Works of J. H. C. Whitehead, Volume 1: Differential Geometry contains all of Whitehead's published work on differential geometry, along with some papers on algebras. Most of these were written in the period 1929-1937, but a few later articles are included. The book begins with a list of Whitehead's works, in chronological order of writing as well as a biographical note by M. H. A. Newman and Barbara Whitehead, and a mathematical appreciation by John Milnor. This is followed by separate chapters on topics such as linear connections; a method of obtaining normal representations
Integral representations on supermanifolds: super Hodge duals, PCOs and Liouville forms
Castellani, Leonardo; Catenacci, Roberto; Grassi, Pietro Antonio
2016-11-01
We present a few types of integral transforms and integral representations that are very useful for extending to supergeometry many familiar concepts of differential geometry. Among them we discuss the construction of the super Hodge dual, the integral representation of picture changing operators of string theories and the construction of the super-Liouville form of a symplectic supermanifold.
Integral representations in supermanifolds: super Hodge duals, PCOs and Liouville forms
Catenacci, L Castellani R
2016-01-01
We present few types of integral transforms and integral representations that are very useful for extending to supergeometry many familiar concepts of differential geometry. Among them we discuss the construction of the super Hodge dual, the integral representation of picture changing operators of string theories and the construction of the super-Liouville form of a symplectic supermanifold.
Teaching of Geometry in Bulgaria
Bankov, Kiril
2013-01-01
Geometry plays an important role in the school mathematics curriculum all around the world. Teaching of geometry varies a lot (Hoyls, Foxman, & Kuchemann, 2001). Many countries revise the objectives, the content, and the approaches to the geometry in school. Studies of the processes show that there are not common trends of these changes…
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
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
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.
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
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
Hyperfinite Representation of Distributions
J Sousa Pinto; R F Hoskins
2000-11-01
Hyperfinite representation of distributions is studied following the method introduced by Kinoshita [2, 3], although we use a different approach much in the vein of [4]. Products and Fourier transforms of representatives of distributions are also analysed.
Income, Ideology, and Representation
Chris Tausanovitch
2016-11-01
Full Text Available Do legislators represent the rich better than they represent the poor? Recent work provides mixed support for this proposition. I test the hypothesis of differential representation using a data set on the political preferences of 318,537 individuals. Evidence of differential representation in the House of Representatives is weak. Support for differential representation is stronger in the Senate. In recent years, representation has occurred primarily through the selection of a legislator from the appropriate party. Although the preferences of higher-income constituents account for more of the variation in legislator voting behavior, higher-income constituents also account for much more of the variation in district preferences. In light of the low level of overall responsiveness, differential responsiveness appears small.
Ordering ambiguity versus representation
Souza de Dutra, A [Abdus Salam ICTP, Strada Costiera 11, 34014 Trieste (Italy); UNESP-Campus de Guaratingueta-DFQ , Av. Dr. Ariberto Pereira da Cunha, 333, C.P. 205, 12516-410 Guaratingueta SP (Brazil)
2006-01-06
In this work we show that the ordering ambiguity on quantization depends on the representation choice. This property is then used to solve unambiguously some particular systems. Finally, we speculate on the consequences for more involved cases.
MORPHOLOGICAL REPRESENTATION AND SEMANTIC ...
The morphological representation assigned to a complex word must provide the formal structure .... This brings us to the cases where, on Williams's (1981a:258) analysis, the compositional notion ...... Die en moda Ii tei t . Kaaps tad: Ba 1 kema.
Function, anticipation, representation
Bickhard, Mark. H.
2001-06-01
Function emerges in certain kinds of far-from-equilibrium systems. One important kind of function is that of interactive anticipation, an adaptedness to temporal complexity. Interactive anticipation is the locus of the emergence of normative representational content, and, thus, of representation in general: interactive anticipation is the naturalistic core of the evolution of cognition. Higher forms of such anticipation are involved in the subsequent macro-evolutionary sequence of learning, emotions, and reflexive consciousness.
Boolean operations with implicit and parametric representation of primitives using R-functions.
Fougerolle, Yohan D; Gribok, Andrei; Foufou, Sebti; Truchetet, Frédéric; Abidi, Mongi A
2005-01-01
We present a new and efficient algorithm to accurately polygonize an implicit surface generated by multiple Boolean operations with globally deformed primitives. Our algorithm is special in the sense that it can be applied to objects with both an implicit and a parametric representation, such as superquadrics, supershapes, and Dupin cyclides. The input is a Constructive Solid Geometry tree (CSG tree) that contains the Boolean operations, the parameters of the primitives, and the global deformations. At each node of the CSG tree, the implicit formulations of the subtrees are used to quickly determine the parts to be transmitted to the parent node, while the primitives' parametric definition are used to refine an intermediary mesh around the intersection curves. The output is both an implicit equation and a mesh representing its solution. For the resulting object, an implicit equation with guaranteed differential properties is obtained by simple combinations of the primitives' implicit equations using R-functions. Depending on the chosen R-function, this equation is continuous and can be differentiable everywhere. The primitives' parametric representations are used to directly polygonize the resulting surface by generating vertices that belong exactly to the zero-set of the resulting implicit equation. The proposed approach has many potential applications, ranging from mechanical engineering to shape recognition and data compression. Examples of complex objects are presented and commented on to show the potential of our approach for shape modeling.
Solid Propellant Grain Structural Integrity Analysis
1973-01-01
The structural properties of solid propellant rocket grains were studied to determine the propellant resistance to stresses. Grain geometry, thermal properties, mechanical properties, and failure modes are discussed along with design criteria and recommended practices.
Byron, S.
1985-03-01
The low pressure gas-filled thyratron is scalable in the long dimension. Internally the tube is formed as a tetrode, with an auxiliary grid placed between the cathode and the control grid. A dc or pulsed power source drives the auxiliary grid both to insure uniform cathode emission and to provide a grid-cathode plasma prior to commutation. The high voltage holdoff structure consists of the anode, the control grid and its electrostatic shielding baffles, and a main quartz insulator. A small gas flow supply and exhaust system is used that eliminates the need for a hydrogen reservoir and permits other gases, such as helium, to be used. The thyratron provides a low inductance, high current, long lifetime switch configuration: useful for switch-on applications involving large scale lasers and other similar loads that are distributed in a linear geometry.
Critique of information geometry
Skilling, John, E-mail: skilling@eircom.net [Maximum Entropy Data Consultants Ltd, Kenmare (Ireland)
2014-12-05
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.
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.
Covariant Macroscopic Quantum Geometry
Hogan, Craig J
2012-01-01
A covariant noncommutative algebra of position operators is presented, and interpreted as the macroscopic limit of a geometry that describes a collective quantum behavior of the positions of massive bodies in a flat emergent space-time. The commutator defines a quantum-geometrical relationship between world lines that depends on their separation and relative velocity, but on no other property of the bodies, and leads to a transverse uncertainty of the geometrical wave function that increases with separation. The number of geometrical degrees of freedom in a space-time volume scales holographically, as the surface area in Planck units. Ongoing branching of the wave function causes fluctuations in transverse position, shared coherently among bodies with similar trajectories. The theory can be tested using appropriately configured Michelson interferometers.
Advanced geometries and regimes
Bulanov, S. S.; Bulanov, S. V.; Turchetti, G.; Limpouch, J.; Klimo, O.; Psikal, J.; Stockem, A.; Fiuza, F.; Silva, L. O.; Antici, P.; Margarone, D.; Korn, G.
2013-08-01
We review and discuss different schemes of laser ion acceleration as well as advanced target geometries in connection with the development of the laser-driven proton source for hadron therapy of oncological diseases, which is a part of the ELIMED project. At the request of the Proceedings Editors and Dr. Stepan Bulanov, University of California, Berkeley, the above article has been updated to include three additional authors: A. Stockem, F. Fiuza, and L. O. Silva. All additional authors have consented to their name being added to the paper. Furthermore, the updated article PDF contains amendments to a number of references as detailed within the pages attached to the end of the updated article PDF file. The updated article was re-published on 8 August 2013.
Magnetism in curved geometries
Streubel, Robert; Fischer, Peter; Kronast, Florian; Kravchuk, Volodymyr P.; Sheka, Denis D.; Gaididei, Yuri; Schmidt, Oliver G.; Makarov, Denys
2016-09-01
Extending planar two-dimensional structures into the three-dimensional space has become a general trend in multiple disciplines, including electronics, photonics, plasmonics and magnetics. This approach provides means to modify conventional or to launch novel functionalities by tailoring the geometry of an object, e.g. its local curvature. In a generic electronic system, curvature results in the appearance of scalar and vector geometric potentials inducing anisotropic and chiral effects. In the specific case of magnetism, even in the simplest case of a curved anisotropic Heisenberg magnet, the curvilinear geometry manifests two exchange-driven interactions, namely effective anisotropy and antisymmetric exchange, i.e. Dzyaloshinskii-Moriya-like interaction. As a consequence, a family of novel curvature-driven effects emerges, which includes magnetochiral effects and topologically induced magnetization patterning, resulting in theoretically predicted unlimited domain wall velocities, chirality symmetry breaking and Cherenkov-like effects for magnons. The broad range of altered physical properties makes these curved architectures appealing in view of fundamental research on e.g. skyrmionic systems, magnonic crystals or exotic spin configurations. In addition to these rich physics, the application potential of three-dimensionally shaped objects is currently being explored as magnetic field sensorics for magnetofluidic applications, spin-wave filters, advanced magneto-encephalography devices for diagnosis of epilepsy or for energy-efficient racetrack memory devices. These recent developments ranging from theoretical predictions over fabrication of three-dimensionally curved magnetic thin films, hollow cylinders or wires, to their characterization using integral means as well as the development of advanced tomography approaches are in the focus of this review.
Stereo Orthogonal Axonometric Perspective for the Teaching of Descriptive Geometry
Méxas, José Geraldo Franco; Guedes, Karla Bastos; Tavares, Ronaldo da Silva
2015-01-01
Purpose: The purpose of this paper is to present the development of a software for stereo visualization of geometric solids, applied to the teaching/learning of Descriptive Geometry. Design/methodology/approach: The paper presents the traditional method commonly used in computer graphic stereoscopic vision (implemented in C language) and the…
Stereo Orthogonal Axonometric Perspective for the Teaching of Descriptive Geometry
Méxas, José Geraldo Franco; Guedes, Karla Bastos; Tavares, Ronaldo da Silva
2015-01-01
Purpose: The purpose of this paper is to present the development of a software for stereo visualization of geometric solids, applied to the teaching/learning of Descriptive Geometry. Design/methodology/approach: The paper presents the traditional method commonly used in computer graphic stereoscopic vision (implemented in C language) and the…
The Bell states in noncommutative algebraic geometry
Beil, Charlie
2014-10-01
We introduce new mathematical aspects of the Bell states using matrix factorizations, non-noetherian singularities, and noncommutative blowups. A matrix factorization of a polynomial p consists of two matrices ϕ1, ϕ2 such that ϕ1ϕ2 = ϕ2ϕ1 = p id. Using this notion, we show how the Bell states emerge from the separable product of two mixtures, by defining pure states over complex matrices rather than just the complex numbers. We then show in an idealized algebraic setting that pure states are supported on non-noetherian singularities. Moreover, we find that the collapse of a Bell state is intimately related to the representation theory of the noncommutative blowup along its singular support. This presents an exchange in geometry: the nonlocal commutative spacetime of the entangled state emerges from an underlying local noncommutative spacetime.
Klein geometries, parabolic geometries and differential equations of finite type
Abadoglu, Ender
2009-01-01
We define the infinitesimal and geometric orders of an effective Klein geometry G/H. Using these concepts, we prove i) For any integer m>1, there exists an effective Klein geometry G/H of infinitesimal order m such that G/H is a projective variety (Corollary 9). ii) An effective Klein geometry G/H of geometric order M defines a differential equation of order M+1 on G/H whose global solution space is G (Proposition 18).
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
Representation Elements of Spatial Thinking
Fiantika, F. R.
2017-04-01
This paper aims to add a reference in revealing spatial thinking. There several definitions of spatial thinking but it is not easy to defining it. We can start to discuss the concept, its basic a forming representation. Initially, the five sense catch the natural phenomenon and forward it to memory for processing. Abstraction plays a role in processing information into a concept. There are two types of representation, namely internal representation and external representation. The internal representation is also known as mental representation; this representation is in the human mind. The external representation may include images, auditory and kinesthetic which can be used to describe, explain and communicate the structure, operation, the function of the object as well as relationships. There are two main elements, representations properties and object relationships. These elements play a role in forming a representation.
A Topological Representation for Taking Cities as a Coherent Whole
Jiang, Bin
2016-01-01
A city is a whole, as are all cities in a country. Within a whole, individual cities possess different degrees of wholeness, defined by Christopher Alexander as a life-giving order or simply a living structure. To characterize the wholeness and in particular to advocate for wholeness as an effective design principle, this paper develops a geographic representation that views cities as a whole. This geographic representation is topology-oriented, so fundamentally differs from existing geometry-based geographic representations. With the topological representation, all cities are abstracted as individual points and put into different hierarchical levels, according to their sizes and based on head/tail breaks - a classification scheme and visualization tool for data with a heavy tailed distribution. These points of different hierarchical levels are respectively used to create Thiessen polygons. Based on polygon-polygon relationships, we set up a complex network. In this network, small polygons point to adjacent l...
Representation, interaction, and intersubjectivity.
Alterman, Richard
2007-09-10
What the participants share, their common "sense" of the world, creates a foundation, a framing, an orientation that enables human actors to see and act in coordination with one another. For recurrent activities, the methods the participants use to understand each other as they act change, making the intersubjective space in which actors operate richer and easier to produce. This article works through some of the issues that emerge from a close examination of intersubjectivity as it is managed through representation and interaction. The data that are presented document, in detail, a sequence of related interactions, within and across episodes of cooperation, where continuity and change can be observed. The emergence of conversational structure and coordinating representations are significant milestones in the long-term development of a representational practice that support the runtime co-construction of intersubjective space. Conversational structures emerge interactively to mediate recurrent points of coordination in the domain activity, and only secondarily the conversation itself. Coordinating representations change the representational practice of the participants by making it easier to manage their "shared view" of the collective work, enabling the participants to make progress, expand the field of the common activity, while exhibiting more control of if and when explicit grounding occurs.
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...
段毅文; 陈丽萍; 斯钦达莱
2002-01-01
分形学是一个十分重要的自然分支.为了描述一个真实多孔固体催化剂颗粒中等温扩散催化反应的特性,分形几何对称模型的分形参数m是至关重要的.单颗粒化学反应模型参数m的一个关系已被得到.而且这个模型参数m的一些影响因素也已经搞清楚.%Fractals is a very important natural science branch.The fractal parameter m in fractal geometry symmetry model is a very important one in order to describe the fractal characteristics for isothermal diffusion catalysis reactions within a porous solid catalyst particle.A relationship,that for the parameter m in single particle chemical reaction engineering,has been obtained.And some influence factors on the parameter m have been made clear.
王靖宇
2011-01-01
清末新学制的颁布有力地促进了教育由传统向近代的转化,国人开始自行翻译和编译新式的中小学教科书.介绍了清末新学制颁布后第一套新式教科书之一——《最新中学教科书几何学·立体部》的编译者谢洪赉的生平,阐述了新式立体几何教科书的编译背景、编写理念、编排形式、主要内容和名词术语,以及该书的编写特点.%The promulgation of the new educational system in the late Qing Dynasty stimulated greatly the transformation of Chinese education from traditional to modern, so that some new primary and secondary school textbooks were compiled or translated. This paper deals with The latest middle school Solid geometry text book, which was one of the first new textbooks for high school students after the new educational system issued in late Qing dynasty,studying the background of writing the textbook,and its compilation idea, its content, symbols and the characteristics,as well as the author Xie Honglai's lifetime.
NUMERICAL SIMULATION OF THE GEOMETRY OF LOGS FOR SAWING INDUSTRIES
R. DANWE,
2011-02-01
Full Text Available Currently, the majority of wood sawing industries in Cameroun have as a concern the search for an optimization of the production. It is a question of having a good output matter during the cutting up. Thisproblem passes by knowledge of the geometry of the wood log, the strategies of cutting up and the quality of output. In this paper we develop a tool able to represent the log geometry with an aim at carrying out an optimal cutting up. We used representation by the analytical equations of the geometry of the external structure of the log ; that enables us to obtain an algorithm which helps to numerically generate the external structure of the wood.
3rd International Conference on Computational Mathematics and Computational Geometry
Ravindran, Anton
2016-01-01
This volume presents original research contributed to the 3rd Annual International Conference on Computational Mathematics and Computational Geometry (CMCGS 2014), organized and administered by Global Science and Technology Forum (GSTF). Computational Mathematics and Computational Geometry are closely related subjects, but are often studied by separate communities and published in different venues. This volume is unique in its combination of these topics. After the conference, which took place in Singapore, selected contributions chosen for this volume and peer-reviewed. The section on Computational Mathematics contains papers that are concerned with developing new and efficient numerical algorithms for mathematical sciences or scientific computing. They also cover analysis of such algorithms to assess accuracy and reliability. The parts of this project that are related to Computational Geometry aim to develop effective and efficient algorithms for geometrical applications such as representation and computati...
Conference on Number Theory and Arithmetic Geometry
Silverman, Joseph; Stevens, Glenn; Modular forms and Fermat’s last theorem
1997-01-01
This volume contains expanded versions of lectures given at an instructional conference on number theory and arithmetic geometry held August 9 through 18, 1995 at Boston University. Contributor's includeThe purpose of the conference, and of this book, is to introduce and explain the many ideas and techniques used by Wiles in his proof that every (semi-stable) elliptic curve over Q is modular, and to explain how Wiles' result can be combined with Ribet's theorem and ideas of Frey and Serre to show, at long last, that Fermat's Last Theorem is true. The book begins with an overview of the complete proof, followed by several introductory chapters surveying the basic theory of elliptic curves, modular functions, modular curves, Galois cohomology, and finite group schemes. Representation theory, which lies at the core of Wiles' proof, is dealt with in a chapter on automorphic representations and the Langlands-Tunnell theorem, and this is followed by in-depth discussions of Serre's conjectures, Galois deformations, ...
Finding Proofs in Tarskian Geometry
Beeson, Michael; Wos, Larry
2016-01-01
We report on a project to use a theorem prover to find proofs of the theorems in Tarskian geometry. These theorems start with fundamental properties of betweenness, proceed through the derivations of several famous theorems due to Gupta and end with the derivation from Tarski's axioms of Hilbert's 1899 axioms for geometry. They include the four challenge problems left unsolved by Quaife, who two decades ago found some \\Otter proofs in Tarskian geometry (solving challenges issued in Wos's 1998...
Phase structures in fuzzy geometries
Govindarajan, T R; Gupta, K S; Martin, X
2012-01-01
We study phase structures of quantum field theories in fuzzy geometries. Several examples of fuzzy geometries as well as QFT's on such geometries are considered. They are fuzzy spheres and beyond as well as noncommutative deformations of BTZ blackholes. Analysis is done analytically and through simulations. Several features like novel stripe phases as well as spontaneous symmetry breaking avoiding Colemen, Mermin, Wagner theorem are brought out. Also we establish that these phases are stable due to topological obstructions.
Thermodynamics of Asymptotically Conical Geometries.
Cvetič, Mirjam; Gibbons, Gary W; Saleem, Zain H
2015-06-12
We study the thermodynamical properties of a class of asymptotically conical geometries known as "subtracted geometries." We derive the mass and angular momentum from the regulated Komar integral and the Hawking-Horowitz prescription and show that they are equivalent. By deriving the asymptotic charges, we show that the Smarr formula and the first law of thermodynamics hold. We also propose an analog of Christodulou-Ruffini inequality. The analysis can be generalized to other asymptotically conical geometries.
Tsige-Tamirat, H. [Association FZK-Euratom, Forschungszentrum Karlsruhe, P.O. Box 3640, 76021 Karlsruhe (Germany)]. E-mail: tsige@irs.fzk.de; Fischer, U. [Association FZK-Euratom, Forschungszentrum Karlsruhe, P.O. Box 3640, 76021 Karlsruhe (Germany); Carman, P.P. [Euratom/UKAEA Fusion Association, Culham Science Center, Abingdon, Oxfordshire OX14 3DB (United Kingdom); Loughlin, M. [Euratom/UKAEA Fusion Association, Culham Science Center, Abingdon, Oxfordshire OX14 3DB (United Kingdom)
2005-11-15
The paper describes the automatic generation of a JET 3D neutronics model from data of computer aided design (CAD) system for Monte Carlo (MC) calculations. The applied method converts suitable CAD data into a representation appropriate for MC codes. The converted geometry is fully equivalent to the CAD geometry.
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
GBuilder—Computer Aided design of Detector Geometry
E.Tcherniasv; N.Smirnov
2001-01-01
Many tasks typical for High Energy Physics such as simulation,event display,maintenance of the geometry database of an experiment,require input of geometrical data.To simplify the process of preparation of such kinds of data an interactive graphica tool GBuilder is being develogped.Definition of the geometry model in GBuilder is based on the Constructive Solid Geometry approach where objects are defined using boolean operations on basic shapes.To provids parameterization of the model arithmetic expressions may be used in place of numbers,A wide list of predefined materials is also available.Different drivers allow to output the geometry model in a form suitable for specific simulation of visual analysis tools.
Seesaw geometry and leptogenesis
Di Bari, P
2005-01-01
The representation of the seesaw orthogonal matrix in the complex plane establishes a graphical correspondence between neutrino mass models and geometrical configurations, particularly useful to study relevant aspects of leptogenesis. We first derive the CP asymmetry bound for hierarchical heavy neutrinos and then an expression for the effective leptogenesis phase, determining the conditions for maximal phase and placing a lower bound on the phase suppression for generic models. Reconsidering the lower bounds on the lightest right-handed (RH) neutrino mass M_1 and on the reheating temperature T_{reh}, we find that models where the lightest neutrino mass m_1 is dominated by one of the two heavier right-handed (RH) neutrinos, typically arising from connections with quark masses, undergo both phase suppression and strong wash-out such that M_1 (T_{reh})\\gtrsim 1.5\\times 10^{11} (2x10^{10}) GeV. The window 10^9 GeV \\lesssim M_1,T_{reh}\\lesssim 10^{10} GeV is accessible only for a class of models where m_1 is domi...
Image-based BRDF Representation
Mihálik A.
2015-12-01
Full Text Available To acquire a certain level of photorealism in computer graphics, it is necessary to analyze, how the materials scatter the incident light. In this work, we propose the method to direct rendering of isotropic bidirectional reflectance function (BRDF from the small set of images. The image-based rendering is focused to synthesize as accurately as possible scenes composed of natural and artificial objects. The realistic image synthesis of BRDF data requires evaluation of radiance over the multiple directions of incident and scattered light from the surface. In our approach the images depict only the material reflectance, the shape is represented as the object geometry. We store the BRDF representation, acquired from the sample material, in a number of two-dimensional textures that contain images of spheres lit from the multiple directions. In order to render particular material, we interpolate between textures in the similar way the image morphing works. Our method allows the real-time rendering of tabulated BRDF data on low memory devices such as mobile phones.
Digital geometry in image processing
Mukhopadhyay, Jayanta
2013-01-01
Exploring theories and applications developed during the last 30 years, Digital Geometry in Image Processing presents a mathematical treatment of the properties of digital metric spaces and their relevance in analyzing shapes in two and three dimensions. Unlike similar books, this one connects the two areas of image processing and digital geometry, highlighting important results of digital geometry that are currently used in image analysis and processing. The book discusses different digital geometries in multi-dimensional integral coordinate spaces. It also describes interesting properties of
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
Towards Multimodal Content Representation
Bunt, Harry
2009-01-01
Multimodal interfaces, combining the use of speech, graphics, gestures, and facial expressions in input and output, promise to provide new possibilities to deal with information in more effective and efficient ways, supporting for instance: - the understanding of possibly imprecise, partial or ambiguous multimodal input; - the generation of coordinated, cohesive, and coherent multimodal presentations; - the management of multimodal interaction (e.g., task completion, adapting the interface, error prevention) by representing and exploiting models of the user, the domain, the task, the interactive context, and the media (e.g. text, audio, video). The present document is intended to support the discussion on multimodal content representation, its possible objectives and basic constraints, and how the definition of a generic representation framework for multimodal content representation may be approached. It takes into account the results of the Dagstuhl workshop, in particular those of the informal working group...
Post-representational cartography
Rob Kitchin
2010-03-01
Full Text Available Over the past decade there has been a move amongst critical cartographers to rethink maps from a post-representational perspective – that is, a vantage point that does not privilege representational modes of thinking (wherein maps are assumed to be mirrors of the world and automatically presumes the ontological security of a map as a map, but rather rethinks and destabilises such notions. This new theorisation extends beyond the earlier critiques of Brian Harley (1989 that argued maps were social constructions. For Harley a map still conveyed the truth of a landscape, albeit its message was bound within the ideological frame of its creator. He thus advocated a strategy of identifying the politics of representation within maps in order to circumnavigate them (to reveal the truth lurking underneath, with the ontology of cartographic practice remaining unquestioned.
Learning network representations
Moyano, Luis G.
2017-02-01
In this review I present several representation learning methods, and discuss the latest advancements with emphasis in applications to network science. Representation learning is a set of techniques that has the goal of efficiently mapping data structures into convenient latent spaces. Either for dimensionality reduction or for gaining semantic content, this type of feature embeddings has demonstrated to be useful, for example, for node classification or link prediction tasks, among many other relevant applications to networks. I provide a description of the state-of-the-art of network representation learning as well as a detailed account of the connections with other fields of study such as continuous word embeddings and deep learning architectures. Finally, I provide a broad view of several applications of these techniques to networks in various domains.
On a microscopic representation of space-time IV
Dahm, Rolf
2017-05-01
We summarize some previous work on SU(4) describing hadron representations and transformations as well as its noncompact "counterpart" SU*(4) being the complex embedding of SL(2,H). So after having related the 16-dim Dirac algebra to SU*(4), on the one hand we have access to real, complex, and quaternionic Lie group chains and their respective algebras, on the other hand it is of course possible to relate physical descriptions to the respective representations. With emphasis on the common maximal compact subgroup USp(4), we are led to projective geometry of the real 3-space and various transfer principles which we use to extend the previous work on the rank 3-algebras above. On real spaces, such considerations are governed by the groups SO( n, m) with n + m = 6. The central thread, however, focuses here on line and Complex geometry which finds its well-known counterparts in descriptions of electromagnetism and special relativity as well as—using transfer principles—in Dirac, gauge, and quantum field theory. We discuss a simple picture where Complexe of second grade play the major and dominant rôle to unify (real) projective geometry, complex representation theory and line/Complex representations in order to proceed to dynamics.
Intersecting Solitons, Amoeba and Tropical Geometry
Fujimori, Toshiaki; Ohta, Kazutoshi; Sakai, Norisuke; Yamazaki, Masahito
2008-01-01
We study generic intersection (or web) of vortices with instantons inside, which is a 1/4 BPS state in the Higgs phase of five-dimensional N=1 supersymmetric U(Nc) gauge theory on R_t \\times (C^\\ast)^2 \\simeq R^{2,1} \\times T^2 with Nf=Nc Higgs scalars in the fundamental representation. In the case of the Abelian-Higgs model (Nf=Nc=1), the intersecting vortex sheets can be beautifully understood in a mathematical framework of amoeba and tropical geometry, and we propose a dictionary relating solitons and gauge theory to amoeba and tropical geometry. A projective shape of vortex sheets is described by the amoeba. Vortex charge density is uniformly distributed among vortex sheets, and negative contribution to instanton charge density is understood as the complex Monge-Ampere measure with respect to a plurisubharmonic function on (C^\\ast)^2. The Wilson loops in T^2 are related with derivatives of the Ronkin function. The general form of the Kahler potential and the asymptotic metric of the moduli space of a vort...
Pulsar Emission Geometry and Accelerating Field Strength
DeCesar, Megan E.; Harding, Alice K.; Miller, M. Coleman; Kalapotharakos, Constantinos; Parent, Damien
2012-01-01
The high-quality Fermi LAT observations of gamma-ray pulsars have opened a new window to understanding the generation mechanisms of high-energy emission from these systems, The high statistics allow for careful modeling of the light curve features as well as for phase resolved spectral modeling. We modeled the LAT light curves of the Vela and CTA I pulsars with simulated high-energy light curves generated from geometrical representations of the outer gap and slot gap emission models. within the vacuum retarded dipole and force-free fields. A Markov Chain Monte Carlo maximum likelihood method was used to explore the phase space of the magnetic inclination angle, viewing angle. maximum emission radius, and gap width. We also used the measured spectral cutoff energies to estimate the accelerating parallel electric field dependence on radius. under the assumptions that the high-energy emission is dominated by curvature radiation and the geometry (radius of emission and minimum radius of curvature of the magnetic field lines) is determined by the best fitting light curves for each model. We find that light curves from the vacuum field more closely match the observed light curves and multiwavelength constraints, and that the calculated parallel electric field can place additional constraints on the emission geometry
Speziale, Simone
2013-01-01
We define and investigate a quantisation of null hypersurfaces in the context of loop quantum gravity on a fixed graph. The main tool we use is the parametrisation of the theory in terms of twistors, which has already proved useful in discussing the interpretation of spin networks as the quantization of twisted geometries. The classical formalism can be extended in a natural way to null hypersurfaces, with the Euclidean polyhedra replaced by null polyhedra with space-like faces, and SU(2) by the little group ISO(2). The main difference is that the simplicity constraints present in the formalims are all first class, and the symplectic reduction selects only the helicity subgroup of the little group. As a consequence, information on the shapes of the polyhedra is lost, and the result is a much simpler, abelian geometric picture. It can be described by an Euclidean singular structure on the 2-dimensional space-like surface defined by a foliation of space-time by null hypersurfaces. This geometric structure is na...
Bhatia, Rajendra
2013-01-01
This book is an outcome of the Indo-French Workshop on Matrix Information Geometries (MIG): Applications in Sensor and Cognitive Systems Engineering, which was held in Ecole Polytechnique and Thales Research and Technology Center, Palaiseau, France, in February 23-25, 2011. The workshop was generously funded by the Indo-French Centre for the Promotion of Advanced Research (IFCPAR). During the event, 22 renowned invited french or indian speakers gave lectures on their areas of expertise within the field of matrix analysis or processing. From these talks, a total of 17 original contribution or state-of-the-art chapters have been assembled in this volume. All articles were thoroughly peer-reviewed and improved, according to the suggestions of the international referees. The 17 contributions presented are organized in three parts: (1) State-of-the-art surveys & original matrix theory work, (2) Advanced matrix theory for radar processing, and (3) Matrix-based signal processing applications.
Functional integration over geometries
Mottola, E
1995-01-01
The geometric construction of the functional integral over coset spaces {\\cal M}/{\\cal G} is reviewed. The inner product on the cotangent space of infinitesimal deformations of \\cal 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 \\cal G, the functional measure on the coset space {\\cal M}/{\\cal 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 \\cal G is the group of coordinate reparametrizations of spacetime, the continuum functional integral over geometries, {\\it 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 me...
Itin, Yakov
2007-01-01
The possible extensions of GR for description of fermions on a curved space, for supergravity and for loop quantum gravity require a richer set of 16 independent variables. These variables can be assembled in a coframe field, i.e., a local set of four linearly independent 1-forms. In the ordinary formulation, the coframe gravity does not have any connection to a specific geometry even being constructed from the geometrical meaningful objects. A geometrization of the coframe gravity is an aim of this paper. We construct a complete class of the coframe connections which are linear in the first order derivatives of the coframe field on an $n$ dimensional manifolds with and without a metric. The subclasses of the torsion-free, metric-compatible and flat connections are derived. We also study the behavior of the geometrical structures under local transformations of the coframe. The remarkable fact is an existence of a subclass of connections which are invariant when the infinitesimal transformations satisfy the Ma...
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.
Geometries from field theories
Aoki, Sinya; Kikuchi, Kengo; Onogi, Tetsuya
2015-10-01
We propose a method to define a d+1-dimensional geometry from a d-dimensional quantum field theory in the 1/N expansion. We first construct a d+1-dimensional field theory from the d-dimensional one via the gradient-flow equation, whose flow time t represents the energy scale of the system such that trArr 0 corresponds to the ultraviolet and trArr infty to the infrared. We then define the induced metric from d+1-dimensional field operators. We show that the metric defined in this way becomes classical in the large-N limit, in the sense that quantum fluctuations of the metric are suppressed as 1/N due to the large-N factorization property. As a concrete example, we apply our method to the O(N) nonlinear σ model in two dimensions. We calculate the 3D induced metric, which is shown to describe an anti-de Sitter space in the massless limit. Finally, we discuss several open issues for future studies.
Optimum Stirling engine geometry
Senft, J.R. [University of Wisconsin, River Walls, WI (United States). Mathematics Dept.
2002-07-01
This paper combines the author's work on mechanical efficiency of reciprocating engines with the classic Schmidt thermodynamic model for Stirling engines and revisits the problem of identifying optimal engine geometry. All previous optimizations using the Schmidt theory focused on obtaining a maximal specific indicated cyclic work. This does not necessarily produce the highest shaft output. Indeed, some optima based upon indicated work would yield engines that cannot run at all due to excessive intrinsic mechanical losses. The analysis presented in this paper shows how to optimize for shaft or brake work output. Specifically, it presents solutions to the problem of finding the piston-to-displacer swept volume ratio and phase angle which will give the maximum brake output for a given total swept volume, given temperature extremes, a given mean operating pressure, and a given engine mechanism effectiveness. The paper covers the split-cylinder or gamma-type Stirling in detail, serving as a model for similar analysis of the other Stirling engine configurations. (author)
Mobilities and Representations
Thelle, Mikkel
2016-01-01
, literature, and film. Moreover, we hope the authors of future reviews will reflect on the ways they approached those representations. Such commentaries would provide valuable methodological insights, and we hope to begin that effort with this interview. We have asked four prominent mobility scholars...... to consider how they and their peers are currently confronting representations of mobility. This is particularly timely given the growing academic focus on practices, material mediation, and nonrepresentational theories, as well as on bodily reactions, emotions, and feelings that, according to those theories...
Additive and polynomial representations
Krantz, David H; Suppes, Patrick
1971-01-01
Additive and Polynomial Representations deals with major representation theorems in which the qualitative structure is reflected as some polynomial function of one or more numerical functions defined on the basic entities. Examples are additive expressions of a single measure (such as the probability of disjoint events being the sum of their probabilities), and additive expressions of two measures (such as the logarithm of momentum being the sum of log mass and log velocity terms). The book describes the three basic procedures of fundamental measurement as the mathematical pivot, as the utiliz
Spacetime, Geometry and Gravitation
Sharan, Pankaj
2009-01-01
This introductory textbook on the general theory of relativity presents a solid foundation for those who want to learn about relativity. The subject is presented in a physically intuitive, but mathematically rigorous style. The topic of relativity is covered in a broad and deep manner. Besides, the aim is that after reading the book a student should not feel discouraged when she opens advanced texts on general relativity for further reading. The book consists of three parts: An introduction to the general theory of relativity. Geometrical mathematical background material. Topics that include the action principle, weak gravitational fields and gravitational waves, Schwarzschild and Kerr solution, and the Friedman equation in cosmology. The book is suitable for advanced graduates and graduates, but also for established researchers wishing to be educated about the field.
On Maintenance of Inter-connectivity Among Multi-representations
WANG Yan-hui; MENG Hao; LIU Xiao-meng
2006-01-01
As the problems of conceptual and representational differences will arise among multi-representations, inter-connectivity maintenance among multi-representations exists as a foundational task in building multi-scale data model. Since the existing methods are still not satisfactory in practice, the inter-connectivity among multiple representations can be only achieved if the multi-scale model is capable of explicitly inter-relating them and dealing with their differences. So, this paper firstly explores the relation among multiple representations from the same entity, such as multi-semantic, multi-geometry, multi-attributes, hierarchical semantic relations and so on. Based on these, this paper proposes aggregation-based semantic hierarchical matching rules (ASHMR) as the basis of tackling inter-connectivity among multi-representations, and defines the available hierarchical semantic knowledge, namely semantically equal, semantically related and semantically irrelevant. According to different change among multi-representations from different types of objects, the applications and techniques of the corresponding hierarchy inter-connectivity matching criterion are explored. And taken the road intersections as examples, a case in point is given in details for describing the strategies of inter-connectivity maintenance, showing that this method is feasible to deal with inter-connectivity.
Reeve, W. D., Ed.
There are a number of recurring topics in the articles that comprise this yearbook, such as the nature of both informal and demonstrative geometry, the reasons for teaching both, and the extent of such courses. Other emphasized topics are use of the analytic method, whether to combine plane and solid geometry, the place of algebra and trigonometry…
Detecting Translation Errors in CAD Surfaces and Preparing Geometries for Mesh Generation
Petersson, N Anders; Chand, K K
2001-08-27
The authors have developed tools for the efficient preparation of CAD geometries for mesh generation. Geometries are read from IGES files and then maintained in a boundary-representation consisting of a patchwork of trimmed and untrimmed surfaces. Gross errors in the geometry can be identified and removed automatically while a user interface is provided for manipulating the geometry (such as correcting invalid trimming curves or removing unwanted details). Modifying the geometry by adding or deleting surfaces and/or sectioning it by arbitrary planes (e.g. symmetry planes) is also supported. These tools are used for robust and accurate geometry models for initial mesh generation and will be applied to in situ mesh generation requirements of moving and adaptive grid simulations.
Conformal-Based Surface Morphing and Multi-Scale Representation
Ka Chun Lam
2014-05-01
Full Text Available This paper presents two algorithms, based on conformal geometry, for the multi-scale representations of geometric shapes and surface morphing. A multi-scale surface representation aims to describe a 3D shape at different levels of geometric detail, which allows analyzing or editing surfaces at the global or local scales effectively. Surface morphing refers to the process of interpolating between two geometric shapes, which has been widely applied to estimate or analyze deformations in computer graphics, computer vision and medical imaging. In this work, we propose two geometric models for surface morphing and multi-scale representation for 3D surfaces. The basic idea is to represent a 3D surface by its mean curvature function, H, and conformal factor function λ, which uniquely determine the geometry of the surface according to Riemann surface theory. Once we have the (λ, H parameterization of the surface, post-processing of the surface can be done directly on the conformal parameter domain. In particular, the problem of multi-scale representations of shapes can be reduced to the signal filtering on the λ and H parameters. On the other hand, the surface morphing problem can be transformed to an interpolation process of two sets of (λ, H parameters. We test the proposed algorithms on 3D human face data and MRI-derived brain surfaces. Experimental results show that our proposed methods can effectively obtain multi-scale surface representations and give natural surface morphing results.
Surrogate Modeling for Geometry Optimization
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....
Analytic Geometry, A Tentative Guide.
Helwig, G. Alfred; And Others
This teacher's guide for a semester course in analytic geometry is based on the text "Analytic Geometry" by W. K. Morrill. Included is a daily schedule of suggested topics and homework assignments. Specific teaching hints are also given. The content of the course includes point and plane vectors, straight lines, point and space vectors, planes,…
Moment graphs and representations
Jantzen, Jens Carsten
2012-01-01
Moment graphs and sheaves on moment graphs are basically combinatorial objects that have be used to describe equivariant intersectiion cohomology. In these lectures we are going to show that they can be used to provide a direct link from this cohomology to the representation theory of simple Lie...
Compact Information Representations
2016-08-02
network traffic, information retrieval, and databases are faced with very large, inherently high-dimensional, or naturally streaming datasets. This...proposal aims at developing mathematically rigorous and general- purpose statistical methods based on stable random projections, to achieve compact...detections (e.g., DDoS attacks), machine learning, databases , and search. Fundamentally, compact data representations are highly beneficial because they
Representation and human reasoning
ter Meulen, Alice G.B.
2003-01-01
Interpretation and reasoning are two sides of sharing information. Representations of the context and common ground must capture the rich content of what has been said, by linking to situations in the world as well as to what has been said before, common sense and to the presuppositions and entailme
Moment graphs and representations
Jantzen, Jens Carsten
2012-01-01
Moment graphs and sheaves on moment graphs are basically combinatorial objects that have be used to describe equivariant intersectiion cohomology. In these lectures we are going to show that they can be used to provide a direct link from this cohomology to the representation theory of simple Lie...... algebras and of simple algebraic groups. The first section contains some background on equivariant cohomology....
Loddegaard, Anne
2009-01-01
out of place in a novel belonging to the serious combat literature of the Catholic Revival, and the direct representation of the supernatural is also surprising because previous Catholic Revival novelists, such as Léon Bloy and Karl-Joris Huysmans, maintain a realistic, non-magical world and deal...
Loddegaard, Anne
2012-01-01
out of place in a novel belonging to the serious combat literature of the Catholic Revival, and the direct representation of the supernatural is also surprising because previous Catholic Revival novelists, such as Léon Bloy and Karl-Joris Huysmans, maintain a realistic, non-magical world and deal...
Women and political representation.
Rathod, P B
1999-01-01
A remarkable progress in women's participation in politics throughout the world was witnessed in the final decade of the 20th century. According to the Inter-Parliamentary Union report, there were only eight countries with no women in their legislatures in 1998. The number of women ministers at the cabinet level worldwide doubled in a decade, and the number of countries without any women ministers dropped from 93 to 48 during 1987-96. However, this progress is far from satisfactory. Political representation of women, minorities, and other social groups is still inadequate. This may be due to a complex combination of socioeconomic, cultural, and institutional factors. The view that women's political participation increases with social and economic development is supported by data from the Nordic countries, where there are higher proportions of women legislators than in less developed countries. While better levels of socioeconomic development, having a women-friendly political culture, and higher literacy are considered favorable factors for women's increased political representation, adopting one of the proportional representation systems (such as a party-list system, a single transferable vote system, or a mixed proportional system with multi-member constituencies) is the single factor most responsible for the higher representation of women.
Sociocognitive Perspectives on Representation.
Jacob, Elin K.; Shaw, Debora
1998-01-01
Discusses research dealing with the cognitive aspects of formal systems of knowledge representation. Highlights include the origins and theoretical foundations of the cognitive viewpoint; cognition and information science; cognitivism, mentalism, and subjective individualism; categorization; mental models; and sociocognitive approaches to indexing…
Between Representation and Eternity
Atzbach, Rainer
2016-01-01
. At death, an indi- vidual’s corpse and burial primarily reflect the social act of representation during the funeral. The position of the arms, which have incorrectly been used as a chronological tool in Scandinavia, may indicate an evolution from a more collective act of prayer up to the eleventh century...
Sociocognitive Perspectives on Representation.
Jacob, Elin K.; Shaw, Debora
1998-01-01
Discusses research dealing with the cognitive aspects of formal systems of knowledge representation. Highlights include the origins and theoretical foundations of the cognitive viewpoint; cognition and information science; cognitivism, mentalism, and subjective individualism; categorization; mental models; and sociocognitive approaches to indexing…
Spectral representation of fingerprints
Xu, Haiyun; Bazen, Asker M.; Veldhuis, Raymond N.J.; Kevenaar, Tom A.M.; Akkermans, Anton H.M.
2007-01-01
Most fingerprint recognition systems are based on the use of a minutiae set, which is an unordered collection of minutiae locations and directions suffering from various deformations such as translation, rotation and scaling. The spectral minutiae representation introduced in this paper is a novel m
Index Theorems on Torsional Geometries
Kimura, Tetsuji
2007-01-01
We study various topological invariants on a differential geometry in the presence of a totally anti-symmetric torsion H under the closed condition dH=0. By using the identification between the Clifford algebra on a geometry and the canonical quantization condition of fermion in the quantum mechanics, we construct the N=1 quantum mechanical sigma model in the Hamiltonian formalism and extend this model to N=2 system, equipped with the totally anti-symmetric tensor associated with the torsion on the target space geometry. Next we construct transition elements in the Lagrangian path integral formalism and apply them to the analyses of the Witten indices in supersymmetric systems. We improve the formulation of the Dirac index on the torsional geometry which has already been studied. We also formulate the Euler characteristic and the Hirzebruch signature on the torsional geometry.
3D Cadastral Data Model Based on Conformal Geometry Algebra
Ji-yi Zhang
2016-02-01
Full Text Available Three-dimensional (3D cadastral data models that are based on Euclidean geometry (EG are incapable of providing a unified representation of geometry and topological relations for 3D spatial units in a cadastral database. This lack of unification causes problems such as complex expression structure and inefficiency in the updating of 3D cadastral objects. The inability of current cadastral data models to express cadastral objects in a unified manner can be attributed to the different expressions of dimensional objects. Because the hierarchical Grassmann structure corresponds to the hierarchical structure of dimensions in conformal geometric algebra (CGA, geometric objects in different dimensions can be constructed by outer products in a unified expression form, which enables the direct extension of two-dimensional (2D spatial representations to 3D spatial representations. The multivector structure in CGA can be employed to organize and store different dimensional objects in a multidimensional and unified manner. With the advantages of CGA in multidimensional expressions, a new 3D cadastral data model that is based on CGA is proposed in this paper. The geometries and topological relations of 3D spatial units can be represented in a unified form within the multivector structure. Detailed methods for 3D cadastral data model design based on CGA and data organization in CGA are introduced. The new cadastral data model is tested and analyzed with experimental data. The results indicate that the geometry and topological relations of 3D cadastral objects can be represented in a multidimensional manner with an intuitive topological structure and a unified dimensional expression.
Representations of Clifford algebras of ternary quartic forms
Coskun, Emer; Mustopa, Yusuf
2011-01-01
Given a nondegenerate ternary form $f=f(x_1,x_2,x_3)$ of degree 4 over an algebraically closed field of characteristic zero, we use the geometry of K3 surfaces to construct a certain positive-dimensional family of irreducible representations of the generalized Clifford algebra associated to $f.$ From this we obtain the existence of linear Pfaffian representations of the quartic surface $X_f=\\{w^4=f(x_1,x_2,x_3)\\},$ as well as information on the Brill-Noether theory of a general smooth curve in the linear system $|\\mathcal{O}_{X_f}(3)|.$
The Geometry Description Markup Language
RadovanChytracek
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.This article 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.
Realizations of the Canonical Representation
M K Vemuri
2008-02-01
A characterisation of the maximal abelian subalgebras of the bounded operators on Hilbert space that are normalised by the canonical representation of the Heisenberg group is given. This is used to classify the perfect realizations of the canonical representation.
Standard model of knowledge representation
Yin, Wensheng
2016-09-01
Knowledge representation is the core of artificial intelligence research. Knowledge representation methods include predicate logic, semantic network, computer programming language, database, mathematical model, graphics language, natural language, etc. To establish the intrinsic link between various knowledge representation methods, a unified knowledge representation model is necessary. According to ontology, system theory, and control theory, a standard model of knowledge representation that reflects the change of the objective world is proposed. The model is composed of input, processing, and output. This knowledge representation method is not a contradiction to the traditional knowledge representation method. It can express knowledge in terms of multivariate and multidimensional. It can also express process knowledge, and at the same time, it has a strong ability to solve problems. In addition, the standard model of knowledge representation provides a way to solve problems of non-precision and inconsistent knowledge.
Hamilton geometry: Phase space geometry from modified dispersion relations
Barcaroli, Leonardo; Gubitosi, Giulia; Loret, Niccoló; Pfeifer, Christian
2015-01-01
We describe the Hamilton geometry of the phase space of particles whose motion is characterised by general dispersion relations. In this framework spacetime and momentum space are naturally curved and intertwined, allowing for a simultaneous description of both spacetime curvature and non-trivial momentum space geometry. We consider as explicit examples two models for Planck-scale modified dispersion relations, inspired from the $q$-de Sitter and $\\kappa$-Poincar\\'e quantum groups. In the first case we find the expressions for the momentum and position dependent curvature of spacetime and momentum space, while for the second case the manifold is flat and only the momentum space possesses a nonzero, momentum dependent curvature. In contrast, for a dispersion relation that is induced by a spacetime metric, as in General Relativity, the Hamilton geometry yields a flat momentum space and the usual curved spacetime geometry with only position dependent geometric objects.
Representation type of local and two-vertex bocses
2009-01-01
Let κ be an algebraically closed field. It has been proved by Zhang and Xu that if a bocs is of tame representation type, then the degree of the diffierential of the first solid arrow must be less than or equal to 3. We will prove in the present paper that: The bocs is still wild when the degree of the diffierential of the first arrow is equal to 3. Especially, the bocs with only one solid arrow is of tame type if and only if the degree of the diffierential of the arrow is less than or equal to 2. Moreover, we classify in this case the growth problems of the representation category of the bocs and layout the sufficient and necessary conditions when the bocs is of finite representation type, tame domestic and tame exponential growth respectively.
Representation type of local and two-vertex bocses
ZHANG XueYing; ZHANG YingBo; ZHAO ShuangMei
2009-01-01
Let k be an algebraically closed field. It has been proved by Zhang and Xu that if a bocs is of tame representation type, then the degree of the differential of the first solid arrow must be less than or equal to 3. We will prove in the present paper that: The bocs is still wild when the degree of the differential of the first arrow is equal to 3. Especially, the bocs with only one solid arrow is of tame type if and only if the degree of the differential of the arrow is less than or equal to 2. Moreover, we classify in this case the growth problems of the representation category of the bocs and layout the sufficient and necessary conditions when the bocs is of finite representation type, tame domestic and tame exponential growth respectively.
Harmonic Analysis and Group Representation
Figa-Talamanca, Alessandro
2011-01-01
This title includes: Lectures - A. Auslander, R. Tolimeri - Nilpotent groups and abelian varieties, M Cowling - Unitary and uniformly bounded representations of some simple Lie groups, M. Duflo - Construction de representations unitaires d'un groupe de Lie, R. Howe - On a notion of rank for unitary representations of the classical groups, V.S. Varadarajan - Eigenfunction expansions of semisimple Lie groups, and R. Zimmer - Ergodic theory, group representations and rigidity; and, Seminars - A. Koranyi - Some applications of Gelfand pairs in classical analysis.
Hull, C. M.
1993-01-01
The higher-spin geometries of $W_\\infty$-gravity and $W_N$-gravity are analysed and used to derive the complete non-linear structure of the coupling to matter and its symmetries. The symmetry group is a subgroup of the symplectic diffeomorphisms of the cotangent bundle of the world-sheet, and the $W_N$ geometry is obtained from a non-linear truncation of the $W_\\infty$ geometry. Quantum W-gravity is briefly discussed. (Talk given at {\\it Pathways to Fundamental Interactions}, the 16th John Ho...
Linear algebra, geometry and transformation
Solomon, Bruce
2014-01-01
Vectors, Mappings and Linearity Numeric Vectors Functions Mappings and Transformations Linearity The Matrix of a Linear Transformation Solving Linear Systems The Linear SystemThe Augmented Matrix and RRE Form Homogeneous Systems in RRE Form Inhomogeneous Systems in RRE Form The Gauss-Jordan Algorithm Two Mapping Answers Linear Geometry Geometric Vectors Geometric/Numeric Duality Dot-Product Geometry Lines, Planes, and Hyperplanes System Geometry and Row/Column Duality The Algebra of Matrices Matrix Operations Special Matrices Matrix Inversion A Logical Digression The Logic of the Inversion Alg
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
Adler, Irving
1967-01-01
This richly detailed overview surveys the development and evolution of geometrical ideas and concepts from ancient times to the present. In addition to the relationship between physical and mathematical spaces, it examines the interactions of geometry, algebra, and calculus. The text proves many significant theorems and employs several important techniques. Chapters on non- Euclidean geometry and projective geometry form brief, self-contained treatments.More than 100 exercises with answers and 200 diagrams illuminate the text. Teachers, students (particularly those majoring in mathematics educa
Belogurov, S.; Berchun, Yu; Chernogorov, A.; Malzacher, P.; Ovcharenko, E.; Semennikov, A.
2011-12-01
Due to conceptual difference between geometry descriptions in Computer-Aided Design (CAD) systems and particle transport Monte Carlo (MC) codes direct conversion of detector geometry in either direction is not feasible. An original set of tools has been developed for building a GEANT4/ROOT compatible geometry in the CATIA CAD system and exchanging it with mentioned MC packages using GDML file format. A Special structure of a CATIA product tree, a wide range of primitives, different types of multiple volume instantiation, and supporting macros have been implemented.
Quantum Consequences of Parameterizing Geometry
Wanas, M. I.
2002-12-01
The marriage between geometrization and quantization is not successful, so far. It is well known that quantization of gravity , using known quantization schemes, is not satisfactory. It may be of interest to look for another approach to this problem. Recently, it is shown that geometries with torsion admit quantum paths. Such geometries should be parameterizied in order to preserve the quantum properties appeared in the paths. The present work explores the consequences of parameterizing such geometry. It is shown that quantum properties, appeared in the path equations, are transferred to other geometric entities.
Hull, C M
1993-01-01
The higher-spin geometries of $W_\\infty$-gravity and $W_N$-gravity are analysed and used to derive the complete non-linear structure of the coupling to matter and its symmetries. The symmetry group is a subgroup of the symplectic diffeomorphisms of the cotangent bundle of the world-sheet, and the $W_N$ geometry is obtained from a non-linear truncation of the $W_\\infty$ geometry. Quantum W-gravity is briefly discussed. (Talk given at {\\it Pathways to Fundamental Interactions}, the 16th John Hopkins Workshop on Current Problems in Particle Theory, Gothenborg, 1992.)
Thermal Phase in Bubbling Geometries
LIU Chang-Yong
2008-01-01
We use matrix model to study thermal phase in bubbling half-BPS type IIB geometries with SO(4)×SO(4) symmetry.Near the horizon limit,we find that thermal vacua of bubbling geometries have disjoint parts,and each part is one kind of phase of the thermal system.We connect the thermal dynamics of bubbling geometries with one-dimensional fermions thermal system.Finally,we try to give a new possible way to resolve information loss puzzle.
An improved combinatorial geometry model for arbitrary geometry in DSMC
Kargaran, H.; Minuchehr, A.; Zolfaghari, A.
2017-03-01
This paper focuses on a new direct simulation Monte Carlo (DSMC) code based on combinatorial geometry (CG) for simulation of any rarefied gas flow. The developed code, called DgSMC-A, has been supplied with an improved CG modeling able to significantly optimize the particle-tracking process, resulting in a highly reduced runtime compared to the conventional codes. The improved algorithm inserts a grid over the geometry and saves those grid elements containing some part of the geometry border. Since only a small part of a grid is engaged with the geometry border, significant time can be saved using the proposed algorithm. Embedding the modified algorithm in the DgSMC-A resulted in a fast, robust and self-governing code needless to any mesh generator. The code completely handles complex geometries created with first-and second-order surfaces. In addition, we developed a new surface area calculator in the CG methodology for complex geometries based on the Monte Carlo method with acceptable accuracy. Several well-known test cases are examined to indicate the code ability to deal with a wide range of realistic problems. Results are also found to be in good agreement with references and experimental data.
Sannino, Francesco
2010-01-01
We uncover novel solutions of the 't Hooft anomaly matching conditions for scalarless gauge theories with matter transforming according to higher dimensional representations of the underlying gauge group. We argue that, if the duals exist, they are gauge theories with fermions transforming...... according to the defining representation of the dual gauge group. The resulting conformal windows match the one stemming from the all-orders beta function results when taking the anomalous dimension of the fermion mass to be unity which are also very close to the ones obtained using the Schwinger......-Dyson approximation. We use the solutions to gain useful insight on the conformal window of the associated electric theory. A consistent picture emerges corroborating previous results obtained via different analytic methods and in agreement with first principle lattice explorations....
Constructing visual representations
Huron, Samuel; Jansen, Yvonne; Carpendale, Sheelagh
2014-01-01
The accessibility of infovis authoring tools to a wide audience has been identified as a major research challenge. A key task in the authoring process is the development of visual mappings. While the infovis community has long been deeply interested in finding effective visual mappings......, comparatively little attention has been placed on how people construct visual mappings. In this paper, we present the results of a study designed to shed light on how people transform data into visual representations. We asked people to create, update and explain their own information visualizations using only...... tangible building blocks. We learned that all participants, most of whom had little experience in visualization authoring, were readily able to create and talk about their own visualizations. Based on our observations, we discuss participants’ actions during the development of their visual representations...
The Grassmannian variety geometric and representation-theoretic aspects
Lakshmibai, V
2015-01-01
This book gives a comprehensive treatment of the Grassmannian varieties and their Schubert subvarieties, focusing on the geometric and representation-theoretic aspects of Grassmannian varieties. Research of Grassmannian varieties is centered at the crossroads of commutative algebra, algebraic geometry, representation theory, and combinatorics. Therefore, this text uniquely presents an exciting playing field for graduate students and researchers in mathematics, physics, and computer science, to expand their knowledge in the field of algebraic geometry. The standard monomial theory (SMT) for the Grassmannian varieties and their Schubert subvarieties are introduced and the text presents some important applications of SMT including the Cohen–Macaulay property, normality, unique factoriality, Gorenstein property, singular loci of Schubert varieties, toric degenerations of Schubert varieties, and the relationship between Schubert varieties and classical invariant theory. This text would serve well as a refere...
MENTAL STATE REPRESENTATION: SPATIOTEMPORAL CHARACTERISTICS
Alexander Oktyabrinovich Prokhorov
2014-01-01
Full Text Available Since the time of statement of the problem of states in psychology, the study of “sensuous” tissue – the mental state representation-takes a fundamental meaning. The problem is concluded in the following questions: “How is mental state represented in the consciousness of an individual?”, “What is the specificity of the mental state representation as distinguished from the subject-matter representation?”, “What are the mechanisms of the mental state representation occurrence and the peculiarities of its dynamics? The study of the mental state representation will allow to explain its specificity and difference from the figurative representation, the peculiarities of state explication as a representation in the consciousness and its relation with other elements of consciousness, will allow to show the regularities of the mental state representation development and its dynamics, factors, which influence the specificity of its occurrence, the regulatory role of the state representation in the vital function. From these perspectives, the article presents the results of the study of spatiotemporal characteristics of the mental state representation; reveals the peculiar features of the spatiotemporal organization of mental state representations: Relieves, specificity, magnitude, variability of indicators, changes of structural characteristics in time spans; considers the age-specific peculiar features of the spatiotemporal organization of mental state representations in terms of organization, stability, coherence and differentiated nature of spatiotemporal structures with the representatives of certain age groups.
Comprehension and Representation in Translation
徐玉萍
2010-01-01
Transhfion is the faithful rcpresentation in one language of the thought, content, feeling and style written in another language. It involves two processes: comprehension and representation. Correct comprehension is the base for adequate representation. Criteria for good representation lies in two points: the version should be faithful to the original, and the version should be as intelligible as possible.
Learning Multisensory Representations
2016-05-23
AFRL-AFOSR-VA-TR-2016-0183 Learning Multisensory Representations Robert Jacobs UNIVERSITY OF ROCHESTER Final Report 05/23/2016 DISTRIBUTION A...DD-MM-YYYY) 16-05-2016 2. REPORT TYPE Final Performance Report 3. DATES COVERED (From - To) 01-09-2012 - 29-02-2016 4. TITLE AND SUBTITLE Learning ...perception; visual perception; haptic perception; auditory perception; perceptual learning ; perceptual decision making 16. SECURITY CLASSIFICATION OF
Jensen, Ole B.
2016-01-01
Dette kapitel gennemgår den såkaldte ”Non-Representational Theory” (NRT), der primært er kendt fra den Angelsaksiske humangeografi, og som særligt er blevet fremført af den engelske geograf Nigel Thrift siden midten af 2000 årtiet. Da positionen ikke kan siges at være specielt homogen vil kapitlet...
Digital Topology and Geometry in Medical Imaging: A Survey.
Saha, Punam K; Strand, Robin; Borgefors, Gunilla
2015-09-01
Digital topology and geometry refers to the use of topologic and geometric properties and features for images defined in digital grids. Such methods have been widely used in many medical imaging applications, including image segmentation, visualization, manipulation, interpolation, registration, surface-tracking, object representation, correction, quantitative morphometry etc. Digital topology and geometry play important roles in medical imaging research by enriching the scope of target outcomes and by adding strong theoretical foundations with enhanced stability, fidelity, and efficiency. This paper presents a comprehensive yet compact survey on results, principles, and insights of methods related to digital topology and geometry with strong emphasis on understanding their roles in various medical imaging applications. Specifically, this paper reviews methods related to distance analysis and path propagation, connectivity, surface-tracking, image segmentation, boundary and centerline detection, topology preservation and local topological properties, skeletonization, and object representation, correction, and quantitative morphometry. A common thread among the topics reviewed in this paper is that their theory and algorithms use the principle of digital path connectivity, path propagation, and neighborhood analysis.
Translation between representation languages
Vanbaalen, Jeffrey
1994-01-01
A capability for translating between representation languages is critical for effective knowledge base reuse. A translation technology for knowledge representation languages based on the use of an interlingua for communicating knowledge is described. The interlingua-based translation process consists of three major steps: translation from the source language into a subset of the interlingua, translation between subsets of the interlingua, and translation from a subset of the interlingua into the target language. The first translation step into the interlingua can typically be specified in the form of a grammar that describes how each top-level form in the source language translates into the interlingua. In cases where the source language does not have a declarative semantics, such a grammar is also a specification of a declarative semantics for the language. A methodology for building translators that is currently under development is described. A 'translator shell' based on this methodology is also under development. The shell has been used to build translators for multiple representation languages and those translators have successfully translated nontrivial knowledge bases.
[Time perceptions and representations].
Tordjman, S
2015-09-01
Representations of time and time measurements depend on subjective constructs that vary according to changes in our concepts, beliefs, societal needs and technical advances. Similarly, the past, the future and the present are subjective representations that depend on each individual's psychic time and biological time. Therefore, there is no single, one-size-fits-all time for everyone, but rather a different, subjective time for each individual. We need to acknowledge the existence of different inter-individual times but also intra-individual times, to which different functions and different rhythms are attached, depending on the system of reference. However, the construction of these time perceptions and representations is influenced by objective factors (physiological, physical and cognitive) related to neuroscience which will be presented and discussed in this article. Thus, studying representation and perception of time lies at the crossroads between neuroscience, human sciences and philosophy. Furthermore, it is possible to identify several constants among the many and various representations of time and their corresponding measures, regardless of the system of time reference. These include the notion of movements repeated in a stable rhythmic pattern involving the recurrence of the same interval of time, which enables us to define units of time of equal and invariable duration. This rhythmicity is also found at a physiological level and contributes through circadian rhythms, in particular the melatonin rhythm, to the existence of a biological time. Alterations of temporality in mental disorders will be also discussed in this article illustrated by certain developmental disorders such as autism spectrum disorders. In particular, the hypothesis will be developed that children with autism would need to create discontinuity out of continuity through stereotyped behaviors and/or interests. This discontinuity repeated at regular intervals could have been
Pioneers of representation theory
Curtis, Charles W
1999-01-01
The year 1897 was marked by two important mathematical events: the publication of the first paper on representations of finite groups by Ferdinand Georg Frobenius (1849-1917) and the appearance of the first treatise in English on the theory of finite groups by William Burnside (1852-1927). Burnside soon developed his own approach to representations of finite groups. In the next few years, working independently, Frobenius and Burnside explored the new subject and its applications to finite group theory. They were soon joined in this enterprise by Issai Schur (1875-1941) and some years later, by Richard Brauer (1901-1977). These mathematicians' pioneering research is the subject of this book. It presents an account of the early history of representation theory through an analysis of the published work of the principals and others with whom the principals' work was interwoven. Also included are biographical sketches and enough mathematics to enable readers to follow the development of the subject. An introductor...
Crystal Structure Representations for Machine Learning Models of Formation Energies
Faber, Felix; von Lilienfeld, O Anatole; Armiento, Rickard
2015-01-01
We introduce and evaluate a set of feature vector representations of crystal structures for machine learning (ML) models of formation energies of solids. ML models of atomization energies of organic molecules have been successful using a Coulomb matrix representation of the molecule. We consider three ways to generalize such representations to periodic systems: (i) a matrix where each element is related to the Ewald sum of the electrostatic interaction between two different atoms in the unit cell repeated over the lattice; (ii) an extended Coulomb-like matrix that takes into account a number of neighboring unit cells; and (iii) an Ansatz that mimics the periodicity and the basic features of the elements in the Ewald sum matrix by using a sine function of the crystal coordinates of the atoms. The representations are compared for a Laplacian kernel with Manhattan norm, trained to reproduce formation energies using a data set of 3938 crystal structures obtained from the Materials Project. For training sets consi...
Elliptic solid-on-solid model's partition function as a single determinant
Galleas, W
2016-01-01
In this work we express the partition function of the integrable elliptic solid-on-solid model with domain-wall boundary conditions as a single determinant. This representation appears naturally as the solution of a system of functional equations governing the model's partition function.
Hyperbolic Metamaterials with Complex Geometry
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...
Instability of supersymmetric microstate geometries
Eperon, Felicity C; Santos, Jorge E
2016-01-01
We investigate the classical stability of supersymmetric, asymptotically flat, microstate geometries with five non-compact dimensions. Such geometries admit an "evanescent ergosurface": a timelike hypersurface of infinite redshift. On such a surface, there are null geodesics with zero energy relative to infinity. These geodesics are stably trapped in the potential well near the ergosurface. We present a heuristic argument indicating that this feature is likely to lead to a nonlinear instability of these solutions. We argue that the precursor of such an instability can be seen in the behaviour of linear perturbations: nonlinear stability would require that all linear perturbations decay sufficiently rapidly but the stable trapping implies that some linear perturbation decay very slowly. We study this in detail for the most symmetric microstate geometries. By constructing quasinormal modes of these geometries we show that generic linear perturbations decay slower than any inverse power of time.
Molecular motion in restricted geometries
Siddharth Gautam; S Mitra; R Mukhopadhyay
2008-10-01
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 scales involved in the motion and the geometry of motion can be studied using QENS. Molecular dynamics (MD) simulation not only provides insight into the details of the different types of motion possible but also does not suffer limitations of the experimental set-up. Here we report the effect of confinement on molecular dynamics in various restricted geometries as studied by QENS and MD simulations: An example where the QENS technique provided direct evidence of phase transition associated with change in the dynamical behaviour of the molecules is also discussed.
Moment methods in extremal geometry
De Laat, D.
2016-01-01
In this thesis we develop techniques for solving problems in extremal geometry. We give an infinite dimensional generalization of moment techniques from polynomial optimization. We use this to construct semidefinite programming hierarchies for approximating optimal packing densities and ground state
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.
Instability of supersymmetric microstate geometries
Eperon, Felicity C.; Reall, Harvey S.; Santos, Jorge E. [Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA (United Kingdom)
2016-10-07
We investigate the classical stability of supersymmetric, asymptotically flat, microstate geometries with five non-compact dimensions. Such geometries admit an “evanescent ergosurface”: a timelike hypersurface of infinite redshift. On such a surface, there are null geodesics with zero energy relative to infinity. These geodesics are stably trapped in the potential well near the ergosurface. We present a heuristic argument indicating that this feature is likely to lead to a nonlinear instability of these solutions. We argue that the precursor of such an instability can be seen in the behaviour of linear perturbations: nonlinear stability would require that all linear perturbations decay sufficiently rapidly but the stable trapping implies that some linear perturbation decay very slowly. We study this in detail for the most symmetric microstate geometries. By constructing quasinormal modes of these geometries we show that generic linear perturbations decay slower than any inverse power of time.
Moment methods in extremal geometry
De Laat, D.
2016-01-01
In this thesis we develop techniques for solving problems in extremal geometry. We give an infinite dimensional generalization of moment techniques from polynomial optimization. We use this to construct semidefinite programming hierarchies for approximating optimal packing densities and ground state
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, ...
Children's schemes for anticipating the validity of nets for solids
Wright, Vince; Smith, Ken
2017-06-01
There is growing acknowledgement of the importance of spatial abilities to student achievement across a broad range of domains and disciplines. Nets are one way to connect three-dimensional shapes and their two-dimensional representations and are a common focus of geometry curricula. Thirty-four students at year 6 (upper primary school) were interviewed on two occasions about their anticipation of whether or not given nets for the cube- and square-based pyramid would fold to form the target solid. Vergnaud's (Journal of Mathematical Behavior, 17(2), 167-181, 1998, Human Development, 52, 83-94, 2009) four characteristics of schemes were used as a theoretical lens to analyse the data. Successful schemes depended on the interaction of operational invariants, such as strategic choice of the base, rules for action, particularly rotation of shapes, and anticipations of composites of polygons in the net forming arrangements of faces in the solid. Inferences were rare. These data suggest that students need teacher support to make inferences, in order to create transferable schemes.
Children's schemes for anticipating the validity of nets for solids
Wright, Vince; Smith, Ken
2017-09-01
There is growing acknowledgement of the importance of spatial abilities to student achievement across a broad range of domains and disciplines. Nets are one way to connect three-dimensional shapes and their two-dimensional representations and are a common focus of geometry curricula. Thirty-four students at year 6 (upper primary school) were interviewed on two occasions about their anticipation of whether or not given nets for the cube- and square-based pyramid would fold to form the target solid. Vergnaud's ( Journal of Mathematical Behavior, 17(2), 167-181, 1998, Human Development, 52, 83-94, 2009) four characteristics of schemes were used as a theoretical lens to analyse the data. Successful schemes depended on the interaction of operational invariants, such as strategic choice of the base, rules for action, particularly rotation of shapes, and anticipations of composites of polygons in the net forming arrangements of faces in the solid. Inferences were rare. These data suggest that students need teacher support to make inferences, in order to create transferable schemes.
Paper Interfaces for Learning Geometry
Bonnard, Quentin; Verma, Himanshu; Kaplan, Frédéric; Dillenbourg, Pierre
2012-01-01
Paper interfaces offer tremendous possibilities for geometry education in primary schools. Existing computer interfaces designed to learn geometry do not consider the integration of conventional school tools, which form the part of the curriculum. Moreover, most of computer tools are designed specifically for individual learning, some propose group activities, but most disregard classroom-level learning, thus impeding their adoption. We present an augmented reality based tabletop system with ...
Courant Algebroids in Parabolic Geometry
Armstrong, Stuart
2011-01-01
To a smooth manifold $M$, a parabolic geometry associates a principal bundle, which has a parabolic subgroup of a semisimple Lie group as its structure group, and a Cartan connection. We show that the adjoint tractor bundle of a regular normal parabolic geometry can be endowed with the structure of a Courant algebroid. This gives a class of examples of transitive Courant algebroids that are not exact.
Topology and geometry for physicists
Nash, Charles
2011-01-01
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
Higgs mass in noncommutative geometry
Devastato, A.; Martinetti, P. [Dipartimento di Fisica, Universita di Napoli Federico II, Via Cintia, 80126 Napoli (Italy); INFN, Sezione di Napoli, Via Cintia, 80126 Napoli (Italy); Lizzi, F. [Dipartimento di Fisica, Universita di Napoli Federico II, Via Cintia, 80126 Napoli (Italy); INFN, Sezione di Napoli, Via Cintia, 80126 Napoli (Italy); Departament de Estructura i Constituents de la Materia, Universitat de Barcelona, Marti y Franques, Barcelona, Catalonia (Spain)
2014-09-11
In the noncommutative geometry approach to the standard model, an extra scalar field σ - initially suggested by particle physicist to stabilize the electroweak vacuum - makes the computation of the Higgs mass compatible with the 126 GeV experimental value. We give a brief account on how to generate this field from the Majorana mass of the neutrino, following the principles of noncommutative geometry. (Copyright copyright 2014 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Effects of Blade Geometry on Performance of Wells Turbine for Wave Power Conversion
Taeho Kim; Toshiaki Setoguchi; Yoichi Kinoue; Kenji Kaneko
2001-01-01
An optimum design of the turbine would need a clear understanding of the influence of blade geometry on a Wells turbine performance. Practically, it is difficult to suggest the optimum geometry for the Wells turbine due to the complex interrelation among important parameters, the solidity, hub-to-tip ratio, aspect ratio, blade sweep of rotor, and so on.In the present study, the effect of blade geometry with the hub-to-tip and aspect ratios of rotor on the turbine performance was investigated with a numerical technique. As a result, the optimum blade geometry is as follows: the hub-to-tip ratio is about 0.7, and the aspect ratio about 0.5 under other constant important parameters, NACA0020 blade with blade sweep ratio of 0.35, and solidity of about 0.67. Furthermore, the detailed flow patterns for blade geometry were also shown and discussed in this paper.
Covariant representations of subproduct systems
Viselter, Ami
2010-01-01
A celebrated theorem of Pimsner states that a covariant representation $T$ of a $C^*$-correspondence $E$ extends to a $C^*$-representation of the Toeplitz algebra of $E$ if and only if $T$ is isometric. This paper is mainly concerned with finding conditions for a covariant representation of a \\emph{subproduct system} to extend to a $C^*$-representation of the Toeplitz algebra. This framework is much more general than the former. We are able to find sufficient conditions, and show that in important special cases, they are also necessary. Further results include the universality of the tensor algebra, dilations of completely contractive covariant representations, Wold decompositions and von Neumann inequalities.
Categorification and higher representation theory
Beliakova, Anna
2017-01-01
The emergent mathematical philosophy of categorification is reshaping our view of modern mathematics by uncovering a hidden layer of structure in mathematics, revealing richer and more robust structures capable of describing more complex phenomena. Categorified representation theory, or higher representation theory, aims to understand a new level of structure present in representation theory. Rather than studying actions of algebras on vector spaces where algebra elements act by linear endomorphisms of the vector space, higher representation theory describes the structure present when algebras act on categories, with algebra elements acting by functors. The new level of structure in higher representation theory arises by studying the natural transformations between functors. This enhanced perspective brings into play a powerful new set of tools that deepens our understanding of traditional representation theory. This volume exhibits some of the current trends in higher representation theory and the diverse te...
Ignitable solids having an arrayed structure and methods thereof
Adams, David P.; Reeves, Robert V.; Grubbs, Robert K.; Henry, Michael David
2017-08-08
The present invention relates to the design and manufacture of an ignitable solid, where the solid is composed of an array of ignitable regions. In some examples, the array provides a three-dimensional periodic arrangement of such ignitable regions. The ignitable region can have any useful geometry and geometric arrangement within the solid, and methods of making such regions are also described herein.
Holomorphic Cartan geometries and rational curves
Biswas, Indranil
2010-01-01
We prove that any compact K\\"ahler manifold bearing a holomorphic Cartan geometry contains a rational curve just when the Cartan geometry is inherited from a holomorphic Cartan geometry on a lower dimensional compact K\\"ahler manifold.
Use of B-Spline in the Finite Element Analysis: Comparison with ANCF Geometry
2011-02-04
formulations developed in this paper. 15. SUBJECT TERMS Geometric discontinuities; Finite element; Multibody systems; B-spline; NURBS 16. SECURITY...Keywords: Geometric discontinuities; Finite element; Multibody systems; B-spline; NURBS . UNCLAS: Dist A. Approved for public release 3 1...developed by computational geometry methods such as B- spline and NURBS (Non-Uniform Rational B-Splines) representations. This fact has motivated
Power Block Geometry Applied to the Building of Power Electronics Converters
dos Santos, E. C., Jr.; da Silva, E. R. C.
2013-01-01
This paper proposes a new methodology, Power Block Geometry (PBG), for the presentation of power electronics topologies that process ac voltage. PBG's strategy uses formal methods based on a geometrical representation with particular rules and defines a universe with axioms and conjectures to establish a formation law. It allows power…
Implementation of tetrahedral-mesh geometry in Monte Carlo radiation transport code PHITS
Furuta, Takuya; Sato, Tatsuhiko; Han, Min Cheol; Yeom, Yeon Soo; Kim, Chan Hyeong; Brown, Justin L.; Bolch, Wesley E.
2017-06-01
A new function to treat tetrahedral-mesh geometry was implemented in the particle and heavy ion transport code systems. To accelerate the computational speed in the transport process, an original algorithm was introduced to initially prepare decomposition maps for the container box of the tetrahedral-mesh geometry. The computational performance was tested by conducting radiation transport simulations of 100 MeV protons and 1 MeV photons in a water phantom represented by tetrahedral mesh. The simulation was repeated with varying number of meshes and the required computational times were then compared with those of the conventional voxel representation. Our results show that the computational costs for each boundary crossing of the region mesh are essentially equivalent for both representations. This study suggests that the tetrahedral-mesh representation offers not only a flexible description of the transport geometry but also improvement of computational efficiency for the radiation transport. Due to the adaptability of tetrahedrons in both size and shape, dosimetrically equivalent objects can be represented by tetrahedrons with a much fewer number of meshes as compared its voxelized representation. Our study additionally included dosimetric calculations using a computational human phantom. A significant acceleration of the computational speed, about 4 times, was confirmed by the adoption of a tetrahedral mesh over the traditional voxel mesh geometry.
Marsh, H. E., Jr.; Hutchison, J. J.
1972-01-01
The basic principles underlying propulsion by rocket motor are examined together with the configuration of a solid propellant motor. Solid propellants and their preparation are discussed, giving attention to homogeneous propellants, composite propellants, energetic considerations in choosing a solid propellant, the processing of composite propellants, and some examples of new developments. The performance of solid propellants is investigated, taking into account characteristics velocity, the specific impulse, and performance calculations. Aspects of propellant development considered include nonperformance requirements for solid propellants, the approach to development, propellant mechanical properties, and future trends.
A Novel Visualization of the Geometry of Special Relativity
Marr, John H
2015-01-01
The mathematical treatment and graphical representation of Special Relativity (SR) are well established, yet carry deep implications that remain hard to visualize. This paper presents a new graphical interpretation of the geometry of SR that may, by complementing the standard works, aid the understanding of SR and its fundamental principles in a more intuitive way. From the axiom that the velocity of light remains constant to any inertial observer, the geodesic is presented as a line of constant angle on the complex plane across a set of diverging reference frames. The resultant curve is a logarithmic spiral, and this view of the geodesic is extended to illustrate the relativistic Doppler effect, time dilation, length contraction, the twin paradox, and relativistic radar distance in an original way, whilst retaining the essential mathematical relationships of SR. Using a computer-generated graphical representation of photon trajectories allows a visual comparison between the relativistic relationships and the...
Representations of commonsense knowledge
Davis, Ernest
1990-01-01
Representations of Commonsense Knowledge provides a rich language for expressing commonsense knowledge and inference techniques for carrying out commonsense knowledge. This book provides a survey of the research on commonsense knowledge.Organized into 10 chapters, this book begins with an overview of the basic ideas on artificial intelligence commonsense reasoning. This text then examines the structure of logic, which is roughly analogous to that of a programming language. Other chapters describe how rules of universal validity can be applied to facts known with absolute certainty to deduce ot
Residual Representations of Spacetime
Saller, H
2001-01-01
Spacetime is modelled by binary relations - by the classes of the automorphisms $\\GL(\\C^2)$ of a complex 2-dimensional vector space with respect to the definite unitary subgroup $\\U(2)$. In extension of Feynman propagators for particle quantum fields representing only the tangent spacetime structure, global spacetime representations are given, formulated as residues using energy-momentum distributions with the invariants as singularities. The associatated quantum fields are characterized by two invariant masses - for time and position - supplementing the one mass for the definite unitary particle sector with another mass for the indefinite unitary interaction sector without asymptotic particle interpretation.
Boot, Inge; Pecher, Diane
2011-01-01
In the present study we investigated whether the mental representation of the concept categories is represented by the container image schema (Lakoff & Johnson, 1980). In two experiments participants decided whether two pictures were from the same category (animal or vehicle). Pictures were presented inside or outside a frame that should activate the container schema. We found that performance to pictures was influenced by the frame in congruence with the metaphorical mapping (same category—inside bounded region; different category—not in same bounded region). These results show that the concept categories is metaphorically represented by containers.
Lie groups, differential equations, and geometry advances and surveys
2017-01-01
This book collects a series of contributions addressing the various contexts in which the theory of Lie groups is applied. A preliminary chapter serves the reader both as a basic reference source and as an ongoing thread that runs through the subsequent chapters. From representation theory and Gerstenhaber algebras to control theory, from differential equations to Finsler geometry and Lepage manifolds, the book introduces young researchers in Mathematics to a wealth of different topics, encouraging a multidisciplinary approach to research. As such, it is suitable for students in doctoral courses, and will also benefit researchers who want to expand their field of interest.
Investigation of Surface Phenomena in Shocked Tin in Converging Geometry
Rousculp, Christopher L. [Los Alamos National Laboratory; Oro, David Michael [Los Alamos National Laboratory; Griego, Jeffrey Randall [Los Alamos National Laboratory; Turchi, Peter John [Los Alamos National Laboratory; Reinovsky, Robert Emil [Los Alamos National Laboratory; Bradley, Joseph Thomas [Los Alamos National Laboratory; Cheng, Baolian [Los Alamos National Laboratory; Freeman, Matthew Stouten [Los Alamos National Laboratory; Patten, Austin Randall [Los Alamos National Laboratory
2016-03-21
There is great interest in the behavior of the free surface of tin under shock loading. While it is known that meso-scale surface imperfections can seed the Richtmyer- Meshkov Instability (RMI) for a surface that is melted on release, much less is known about a tin surface that is solid, but plastically deforming. Here material properties such as shear and yield strength come into play especially in converging geometry. Previous experiments have been driven by direct contact HE. Usually a thin, flat target coupon is fielded with various single-mode, sinusoidal, machined, profiles on the free surface. The free surface is adjacent to either vacuum or an inert receiver gas. Most of these previous driver/target configurations have been nominal planer geometry. With modern HE it has been straightforward to shock tin into melt on release. However it has been challenging to achieve a low enough pressure for solid state on release. Here we propose to extend the existing base of knowledge to include the behavior of the free surface of tin in cylindrical converging geometry. By shock loading a cylindrical tin shell with a magnetically driven cylindrical liner impactor, the free surface evolution can be diagnosed with proton radiography. With the PHELIX capacitor bank, the drive can easily be varied to span the pressure range to achieve solid, mixed, and liquid states on release. A conceptual cylindrical liner and target is shown in Figure 1.
Investigation of Surface Phenomena in Shocked Tin in Converging Geometry
Rousculp, Christopher L. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Oro, David Michael [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Margolin, Len G. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Griego, Jeffrey Randall [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Reinovsky, Robert Emil [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Turchi, Peter John [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2015-08-06
There is great interest in the behavior of the free surface of tin under shock loading. While it is known that meso-scale surface imperfections can seed the Richtmyer-Meshkov Instability (RMI) for a surface that is melted on release, much less is known about a tin surface that is solid, but plastically deforming. Here material properties such as shear and yield strength come into play especially in converging geometry. Previous experiments have been driven by direct contact HE. Usually a thin, flat target coupon is fielded with various single-mode, sinusoidal, machined, profiles on the free surface. The free surface is adjacent to either vacuum or an inert receiver gas. Most of these previous driver/target configurations have been nominal planer geometry. With modern HE it has been straightforward to shock tin into melt on release. However it has been challenging to achieve a low enough pressure for solid state on release. Here we propose to extend the existing base of knowledge to include the behavior of the free surface of tin in cylindrical converging geometry. By shock loading a cylindrical tin shell with a magnetically driven cylindrical liner impactor, the free surface evolution can be diagnosed with proton radiography. With the PHELIX capacitor bank, the drive can easily be varied to span the pressure range to achieve solid, mixed, and liquid states on release.
Boolean representations of simplicial complexes and matroids
Rhodes, John
2015-01-01
This self-contained monograph explores a new theory centered around boolean representations of simplicial complexes leading to a new class of complexes featuring matroids as central to the theory. The book illustrates these new tools to study the classical theory of matroids as well as their important geometric connections. Moreover, many geometric and topological features of the theory of matroids find their counterparts in this extended context. Graduate students and researchers working in the areas of combinatorics, geometry, topology, algebra and lattice theory will find this monograph appealing due to the wide range of new problems raised by the theory. Combinatorialists will find this extension of the theory of matroids useful as it opens new lines of research within and beyond matroids. The geometric features and geometric/topological applications will appeal to geometers. Topologists who desire to perform algebraic topology computations will appreciate the algorithmic potential of boolean represent...
Non-Uniform Tube Representation of Proteins
Hansen, Mikael Sonne
Treating the full protein structure is often neither computationally nor physically possible. Instead one is forced to consider various reduced models capturing the properties of interest. Previous work have used tubular neighborhoods of the C-alpha backbone. However, assigning a unique radius...... might not correctly capture volume exclusion - of crucial importance when trying to understand a protein's 3d-structure. We propose a new reduced model treating the protein as a non-uniform tube with a radius reflecting the positions of atoms. The tube representation is well suited considering X......-ray crystallographic resolution ~ 3Å while a varying radius accounts for the different sizes of side chains. Such a non-uniform tube better captures the protein geometry and has numerous applications in structural/computational biology from the classification of protein structures to sequence-structure prediction....
Non-uniform tube representation of proteins
Hansen, Mikael Sonne
Treating the full protein structure is often neither computationally nor physically possible. Instead one is forced to consider various reduced models capturing the properties of interest. Previous work have used tubular neighborhoods of the C-alpha backbone. However, assigning a unique radius...... might not correctly capture volume exclusion - of crucial importance when trying to understand a proteins $3$d-structure. We propose a new reduced model treating the protein as a non-uniform tube with a radius reflecting the positions of atoms. The tube representation is well suited considering X......-ray crystallographic resolution ~ 3Å while a varying radius accounts for the different sizes of side chains. Such a non-uniform tube better capture the protein geometry and has numerous applications in structural/computational biology from the classification of protein structures to sequence-structure prediction....
Non-uniform tube representation of proteins
Hansen, Mikael Sonne
might not correctly capture volume exclusion - of crucial importance when trying to understand a proteins $3$d-structure. We propose a new reduced model treating the protein as a non-uniform tube with a radius reflecting the positions of atoms. The tube representation is well suited considering X......Treating the full protein structure is often neither computationally nor physically possible. Instead one is forced to consider various reduced models capturing the properties of interest. Previous work have used tubular neighborhoods of the C-alpha backbone. However, assigning a unique radius......-ray crystallographic resolution ~ 3Å while a varying radius accounts for the different sizes of side chains. Such a non-uniform tube better capture the protein geometry and has numerous applications in structural/computational biology from the classification of protein structures to sequence-structure prediction....
Non-Uniform Tube Representation of Proteins
Hansen, Mikael Sonne
might not correctly capture volume exclusion - of crucial importance when trying to understand a protein's 3d-structure. We propose a new reduced model treating the protein as a non-uniform tube with a radius reflecting the positions of atoms. The tube representation is well suited considering X......Treating the full protein structure is often neither computationally nor physically possible. Instead one is forced to consider various reduced models capturing the properties of interest. Previous work have used tubular neighborhoods of the C-alpha backbone. However, assigning a unique radius......-ray crystallographic resolution ~ 3Å while a varying radius accounts for the different sizes of side chains. Such a non-uniform tube better captures the protein geometry and has numerous applications in structural/computational biology from the classification of protein structures to sequence-structure prediction....
Quantum gravity momentum representation and maximum energy
Moffat, J. W.
2016-11-01
We use the idea of the symmetry between the spacetime coordinates xμ and the energy-momentum pμ in quantum theory to construct a momentum space quantum gravity geometry with a metric sμν and a curvature tensor Pλ μνρ. For a closed maximally symmetric momentum space with a constant 3-curvature, the volume of the p-space admits a cutoff with an invariant maximum momentum a. A Wheeler-DeWitt-type wave equation is obtained in the momentum space representation. The vacuum energy density and the self-energy of a charged particle are shown to be finite, and modifications of the electromagnetic radiation density and the entropy density of a system of particles occur for high frequencies.
Multidimensional integral representations problems of analytic continuation
Kytmanov, Alexander M
2015-01-01
The monograph is devoted to integral representations for holomorphic functions in several complex variables, such as Bochner-Martinelli, Cauchy-Fantappiè, Koppelman, multidimensional logarithmic residue etc., and their boundary properties. The applications considered are problems of analytic continuation of functions from the boundary of a bounded domain in C^n. In contrast to the well-known Hartogs-Bochner theorem, this book investigates functions with the one-dimensional property of holomorphic extension along complex lines, and includes the problems of receiving multidimensional boundary analogs of the Morera theorem. This book is a valuable resource for specialists in complex analysis, theoretical physics, as well as graduate and postgraduate students with an understanding of standard university courses in complex, real and functional analysis, as well as algebra and geometry.
Calabi-Yau Varieties: from Quiver Representations to Dessins d'Enfants
He, Yang-Hui
2016-01-01
The connections amongst (1) quivers whose representation varieties are Calabi-Yau, (2) the combinatorics of bipartite graphs on Riemann surfaces, and (3) the geometry of mirror symmetry have engendered a rich subject at whose heart is the physics of gauge/string theories. We review the various parts of this intricate story in some depth, for a mathematical audience without assumption of any knowledge of physics, emphasizing a plethora of results residing at the intersection between algebraic geometry, representation theory and number theory.
Social Representations of Intelligence
Elena Zubieta
2016-02-01
Full Text Available The article stresses the relationship between Explicit and Implicit theories of Intelligence. Following the line of common sense epistemology and the theory of Social Representations, a study was carried out in order to analyze naive’s explanations about Intelligence Definitions. Based on Mugny & Carugati (1989 research, a self-administered questionnaire was designed and filled in by 286 subjects. Results are congruent with the main hyphotesis postulated: A general overlap between explicit and implicit theories showed up. According to the results Intelligence appears as both, a social attribute related to social adaptation and as a concept defined in relation with contextual variables similar to expert’s current discourses. Nevertheless, conceptions based on “gifted ideology” still are present stressing the main axes of Intelligence debate: biological and sociological determinism. In the same sense, unfamiliarity and social identity are reaffirmed as organizing principles of social representation. The distance with the object -measured as the belief in intelligence differences as a solve/non solve problem- and the level of implication with the topic -teachers/no teachers- appear as discriminating elements at the moment of supporting specific dimensions.
Knowledge representation with SOA
Daniela Gotseva
2013-01-01
Full Text Available This paper addresses the problem of supporting the software development process through the artificial intelligence. The expert systems could advise the Domain Engineer in programming without the detailed experience in programming languages. He will use and integrate, with the help of deductive database and domain knowledge, the previously developed software components to new complex functionalities. The objective of this document is to provide the knowledge representation about atomic Web Services which will be registered as the facts in the deductive database. The author proposes to use the decision rules in decision tables for representing the service model which consists of semantic specification, interface description, service quality (QoS, non-functional properties. Also the use of Domain Specific Languages (DSL for modeling Domain Engineers re-quests to the expert system will be considered within this document. As the illustrative use case for described knowledge representation the author proposes the domain of SOA-based geographic information systems (GIS which represent a new branch of information and communication technologies.
Geometry definition and grid generation for a complete fighter aircraft
Edwards, Thomas A.
1986-01-01
Recent advances in computing power and numerical solution procedures have enabled computational fluid dynamicists to attempt increasingly difficult problems. In particular, efforts are focusing on computations of complex three-dimensional flow fields about realistic aerodynamic bodies. To perform such computations, a very accurate and detailed description of the surface geometry must be provided, and a three-dimensional grid must be generated in the space around the body. The geometry must be supplied in a format compatible with the grid generation requirements, and must be verified to be free of inconsistencies. A procedure for performing the geometry definition of a fighter aircraft that makes use of a commercial computer-aided design/computer-aided manufacturing system is presented. Furthermore, visual representations of the geometry are generated using a computer graphics system for verification of the body definition. Finally, the three-dimensional grids for fighter-like aircraft are generated by means of an efficient new parabolic grid generation method. This method exhibits good control of grid quality.
On Ruby's solid angle formula and some of its generalizations
Friot, Samuel
2014-01-01
Using the Mellin-Barnes representation, we show that Ruby's solid angle formula and some of its generalizations may be expressed in a compact way in terms of the Appell F4 and Lauricella Fc functions.
General Construction of Tubular Geometry
Mukhopadhyay, Partha
2016-01-01
We consider the problem of locally describing tubular geometry around a submanifold embedded in a (pseudo)Riemannian manifold in its general form. Given the geometry of ambient space in an arbitrary coordinate system and equations determining the submanifold in the same system, we compute the tubular expansion coefficients in terms of this {\\it a priori data}. This is done by using an indirect method that crucially applies the tubular expansion theorem for vielbein previously derived. With an explicit construction involving the relevant coordinate and non-coordinate frames we verify consistency of the whole method up to quadratic order in vielbein expansion. Furthermore, we perform certain (long and tedious) higher order computation which verifies the first non-trivial spin connection term in the expansion for the first time. Earlier a similar method was used to compute tubular geometry in loop space. We explain this work in the light of our general construction.
Quantum geometry and gravitational entropy
Simon, Joan; Balasubramanian, Vijay; Czech, Bart Iomiej; Larjo, Klaus; Marolf, Donald; Simon, Joan
2007-05-29
Most quantum states have wavefunctions that are widely spread over the accessible Hilbert space and hence do not have a good description in terms of a single classical geometry. In order to understand when geometric descriptions are possible, we exploit the AdS/CFT correspondence in the half-BPS sector of asymptotically AdS_5 x S5 universes. In this sector we devise a"coarse-grained metric operator" whose eigenstates are well described by a single spacetime topology and geometry. We show that such half-BPS universes have a non-vanishing entropy if and only if the metric is singular, and that the entropy arises from coarse-graining the geometry. Finally, we use our entropy formula to find the most entropic spacetimes with fixed asymptotic moments beyond the global charges.
Conventionalism and integrable Weyl geometry
Pucheu, M. L.
2015-03-01
Since the appearance of Einstein's general relativity, gravitation has been associated to the space-time curvature. This theory introduced a geometrodynamic language which became a convenient tool to predict matter behaviour. However, the properties of space-time itself cannot be measurable by experiments. Taking Poincaré idea that the geometry of space-time is merely a convention, we show that the general theory of relativity can be completely reformulated in a more general setting, a generalization of Riemannian geometry, namely, the Weyl integrable geometry. The choice of this new mathematical language implies, among other things, that the path of particles and light rays should now correspond to Weylian geodesies. Such modification in the dynamic of bodies brings a new perception of physical phenomena that we will explore.
Wave propagation on microstate geometries
Keir, Joseph
2016-01-01
Supersymmetric microstate geometries were recently conjectured to be nonlinearly unstable due to numerical and heuristic evidence, based on the existence of very slowly decaying solutions to the linear wave equation on these backgrounds. In this paper, we give a thorough mathematical treatment of the linear wave equation on both two and three charge supersymmetric microstate geometries, finding a number of surprising results. In both cases we prove that solutions to the wave equation have uniformly bounded local energy, despite the fact that three charge microstates possess an ergoregion; these geometries therefore avoid Friedman's "ergosphere instability". In fact, in the three charge case we are able to construct solutions to the wave equation with local energy that neither grows nor decays, although this data must have nontrivial dependence on the Kaluza-Klein coordinate. In the two charge case we construct quasimodes and use these to bound the uniform decay rate, showing that the only possible uniform dec...
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...
Geometry of black hole spacetimes
Andersson, Lars; Blue, Pieter
2016-01-01
These notes, based on lectures given at the summer school on Asymptotic Analysis in General Relativity, collect material on the Einstein equations, the geometry of black hole spacetimes, and the analysis of fields on black hole backgrounds. The Kerr model of a rotating black hole in vacuum is expected to be unique and stable. The problem of proving these fundamental facts provides the background for the material presented in these notes. Among the many topics which are relevant for the uniqueness and stability problems are the theory of fields on black hole spacetimes, in particular for gravitational perturbations of the Kerr black hole, and more generally, the study of nonlinear field equations in the presence of trapping. The study of these questions requires tools from several different fields, including Lorentzian geometry, hyperbolic differential equations and spin geometry, which are all relevant to the black hole stability problem.
Differential geometry of groups in string theory
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{vert bar}1). The quantum group GL{sub q}(1{vert bar}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{sub q}(1{vert bar}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{sup 1})/S{sup 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.
Geometric Transformations in Engineering Geometry
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
KEMAJUAN BELAJAR SISWA PADA GEOMETRI TRANSFORMASI MENGGUNAKAN AKTIVITAS REFLEKSI GEOMETRI
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
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
Geometry Design of Wooden Barrels
Ivan CISMARU
2010-12-01
Full Text Available The aim of this paper is to present a design methodology of the wooden barrel geometry, as an algorithm of successive calculations. Thus, starting from the required elements (volume, length, shape, maximum height of storage space the user will be able to define the geometry which must be obtained by processing. Based on these calculations, one can define the structure, size and shape of the staves in order to establish the processing technology of both components and subassemblies (jacket and bottoms which are to form the final product by their assembling using metal circles.
Geometry, topology, and string theory
Varadarajan, Uday
2003-07-10
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.
Spatial geometry and special relativity
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...
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
Lectures on classical differential geometry
Struik, Dirk J
1988-01-01
Elementary, yet authoritative and scholarly, this book offers an excellent brief introduction to the classical theory of differential geometry. It is aimed at advanced undergraduate and graduate students who will find it not only highly readable but replete with illustrations carefully selected to help stimulate the student's visual understanding of geometry. The text features an abundance of problems, most of which are simple enough for class use, and often convey an interesting geometrical fact. A selection of more difficult problems has been included to challenge the ambitious student.Writ
Gauging Geometry: A Didactic Lecture
Kannenberg, L
2016-01-01
Local inertial frame invariance is taken as the fundamental principle of physical geometry, where a local inertial frame is represented by a verbein. Invariance of the vierbein with respect to local Lorentz transformations then expresses local inertial frame invariance. The dynamics of physical geometry develops as a gauge theory of the verbein that is closely analogous to the Yang-Mills field provided the verbein connection and curvature correspond to the geometric potential and field respectively. The resulting theory is shown to be equivalent to Einstein's tensor form of relativistic gravitation.
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
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
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
Geometry Description Markup Language for Physics Simulation And Analysis Applications.
Chytracek, R.; /CERN; McCormick, J.; /SLAC; Pokorski, W.; /CERN; Santin, G.; /European Space Agency
2007-01-23
The Geometry Description Markup Language (GDML) is a specialized XML-based language designed as an application-independent persistent format for describing the geometries of detectors associated with physics measurements. It serves to implement ''geometry trees'' which correspond to the hierarchy of volumes a detector geometry can be composed of, and to allow to identify the position of individual solids, as well as to describe the materials they are made of. Being pure XML, GDML can be universally used, and in particular it can be considered as the format for interchanging geometries among different applications. In this paper we will present the current status of the development of GDML. After having discussed the contents of the latest GDML schema, which is the basic definition of the format, we will concentrate on the GDML processors. We will present the latest implementation of the GDML ''writers'' as well as ''readers'' for either Geant4 [2], [3] or ROOT [4], [10].
Sliney, Harold E.
1993-01-01
The state of knowledge of solid lubricants is reviewed. The results of research on solid lubricants from the 1940's to the present are presented from a historical perspective. Emphasis is placed largely, but not exclusively, on work performed at NASA Lewis Research Center with a natural focus on aerospace applications. However, because of the generic nature of the research, the information presented in this review is applicable to most areas where solid lubricant technology is useful.
Angelo, Joseph A
2011-01-01
Supported by a generous quantity of full-color illustrations and interesting sidebars, Solid Matter introduces the basic characteristics and properties of solid matter. It briefly describes the cosmic connection of the elements, leading readers through several key events in human pre-history that resulted in more advanced uses of matter in the solid state. Chapters include:. -Solid Matter: An Initial Perspective. -Physical Behavior of Matter. -The Gravity of Matter. -Fundamentals of Materials Science. -Rocks and Minerals. -Metals. -Building Materials. -Carbon Earth's Most Versatile Element. -S
Teaching Activity-Based Taxicab Geometry
Ada, Tuba
2013-01-01
This study aimed on the process of teaching taxicab geometry, a non-Euclidean geometry that is easy to understand and similar to Euclidean geometry with its axiomatic structure. In this regard, several teaching activities were designed such as measuring taxicab distance, defining a taxicab circle, finding a geometric locus in taxicab geometry, and…
Intentionality, Representation, and Anticipation
De Preester, Helena
2002-09-01
Both Brentano and Merleau-Ponty have developed an account of intentionality, which nevertheless differ profoundly in the following respect. According to Brentano, intentionality mainly is a matter of mental presentations. This marks the beginning of phenomenology's difficult relation with the nature of the intentional reference. Merleau-Ponty, on the other hand, has situated intentionality on the level of the body, a turn which has important implications for the nature of intentionality. Intentionality no longer is primarily based on having (re)presentations, but is rooted in the dynamics of the living body. To contrast those approaches enables us to make clear in what way intentionality is studied nowadays. On the one hand, intentionality is conceived of as a matter of formal-syntactical causality in cognitive science, and in particular in classical-computational theory. On the other hand, a interactivist approach offers a more Merleau-Ponty-like point of view, in which autonomy, embodiment and interaction are stressed.
Going beyond representational anthropology
Winther, Ida Wentzel
an education. There is a close connection between: 1) The dream and the desire for education; 2) Mobility (away from the family, home and friends in a very young age for getting an education; 3) Transforming a new and unknown site and space into a known place, where one can make one-self at home ('home one......Going beyond representational anthropology: Re-presenting bodily, emotional and virtual practices in everyday life. Separated youngsters and families in Greenland Greenland is a huge island, with a total of four high-schools. Many youngsters (age 16-18) move far away from home in order to get...... transformation work into the young people and their families. In this presentation I want to screen two sequences from the film, in order to show and clarify how mobility and transformation are made and dealt with both from the youngsters’ and their parents’ perspectives, but in asynchronous loups. I want...
Linear recursive distributed representations.
Voegtlin, Thomas; Dominey, Peter F
2005-09-01
Connectionist networks have been criticized for their inability to represent complex structures with systematicity. That is, while they can be trained to represent and manipulate complex objects made of several constituents, they generally fail to generalize to novel combinations of the same constituents. This paper presents a modification of Pollack's Recursive Auto-Associative Memory (RAAM), that addresses this criticism. The network uses linear units and is trained with Oja's rule, in which it generalizes PCA to tree-structured data. Learned representations may be linearly combined, in order to represent new complex structures. This results in unprecedented generalization capabilities. Capacity is orders of magnitude higher than that of a RAAM trained with back-propagation. Moreover, regularities of the training set are preserved in the new formed objects. The formation of new structures displays developmental effects similar to those observed in children when learning to generalize about the argument structure of verbs.
Monodromy of Galois representations and equal-rank subalgebra equivalence
Hui, Chun Yin
2012-01-01
Let K be a number field, P the set of prime numbers, and {\\rho_l}_{l\\in P} a compatible system (in the sense of Serre [17]) of semisimple, n-dimensional l-adic representations of Gal(\\bar{K}/K). Denote the Zariski closure of \\rho_l(Gal(\\bar{K}/K)) in GL_{n,Q_l} by G_l and its Lie algebra by g_l. We know that G_l^\\circ (the connected component) is reductive and the formal character of the tautological representation G_l^\\circ -> GL_{n,Q_l} is independent of l (Serre). We use the theory of abelian l-adic representations to prove that the formal character of the tautological representation of the derived group (G_l^\\circ)^der -> GL_{n,Q_l} is likewise independent of l. By investigating the geometry of weights of this representation, we prove that the semisimple parts of g_l\\otimes C satisfy an equal-rank subalgebra equivalence for all l. In particular, the number of A_n:=sl_{n+1,C} factors for n\\in {6,9,10,11,...} and the parity of the number of A_4 factors in g_l\\otimes C are independent of l.
Preschool Children's Participation in Representational and Non-Representational Activities
Braswell, Gregory S.
2017-01-01
The present study examined representational and non-representational activities in which children in a Head Start classroom participated. This was an investigation from the perspective of cultural-historical activity theory of how components (e.g. artifacts and division of labour) of classroom activities vary across and within types of activities.…
Differential geometry meets the cell.
Marshall, Wallace F
2013-07-18
A new study by Terasaki et al. highlights the role of physical forces in biological form by showing that connections between stacked endoplasmic reticulum cisternae have a shape well known in classical differential geometry, the helicoid, and that this shape is a predictable consequence of membrane physics.
Byrd, M.
1997-10-01
The group SU(3) is parameterized in terms of generalized {open_quotes}Euler angles{close_quotes}. The differential operators of SU(3) corresponding to the Lie Algebra elements are obtained, the invariant forms are found, the group invariant volume element is found, and some relevant comments about the geometry of the group manifold are made.
Fractal geometry and stochastics IV
Bandt, Christoph
2010-01-01
Over the years fractal geometry has established itself as a substantial mathematical theory in its own right. This book collects survey articles covering many of the developments, like Schramm-Loewner evolution, fractal scaling limits, exceptional sets for percolation, and heat kernels on fractals.
Signature geometry and quantum engineering
Samociuk, Stefan
2013-09-01
As the operating frequency of electromagnetic based devices increase, physical design geometry is playing an ever more important role. Evidence is considered in support of a relationship between the dimensionality of primitive geometric forms, such as transistors, and corresponding electromagnetic coupling efficiency. The industry of electronics is defined as the construction of devices by the patterning of primitive forms to physical materials. Examples are given to show the evolution of these primitives, down to nano scales, are requiring exacting geometry and three dimensional content. Consideration of microwave monolithic integrated circuits,(MMIC), photonics and metamaterials,(MM), support this trend and also add new requirements of strict geometric periodicity and multiplicity. Signature geometries,(SG), are characterized by distinctive attributes and examples are given. The transcendent form transcode algorithm, (TTA) is introduced as a multi dimensional SG and its use in designing photonic integrated circuits and metamaterials is discussed . A creative commons licensed research database, TRANSFORM, containing TTA geometries in OASIS file formats is described. An experimental methodology for using the database is given. Multidimensional SG and extraction of three dimensional cross sections as primitive forms is discussed as a foundation for quantum engineering and the exploitation of phenomena other than the electromagnetic.
Instructional Identities of Geometry Students
Aaron, Wendy Rose; Herbst, Patricio
2012-01-01
We inspect the hypothesis that geometry students may be oriented toward how they expect that the teacher will evaluate them as students or otherwise oriented to how they expect that their work will give them opportunities to do mathematics. The results reported here are based on a mixed-methods analysis of twenty-two interviews with high school…
The Basics of Information Geometry
Caticha, Ariel
2014-01-01
To what extent can we distinguish one probability distribution from another? Are there quantitative measures of distinguishability? The goal of this tutorial is to approach such questions by introducing the notion of the "distance" between two probability distributions and exploring some basic ideas of such an "information geometry".
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
Foucault pendulum through basic geometry
von Bergmann, Jens; von Bergmann, HsingChi
2007-10-01
We provide a thorough explanation of the Foucault pendulum that utilizes its underlying geometry on a level suitable for science students not necessarily familiar with calculus. We also explain how the geometrically understood Foucault pendulum can serve as a prototype for more advanced phenomena in physics known as Berry's phase or geometric phases.
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…
Open problems in algebraic geometry
Edixhoven, S.J.; Moonen, B.J.J.; Oort, F.
2000-01-01
The open problems presented here were collected on the occasion of a workshop on Arithmetic Geometry at the University ofUtrecht, 26{30 June, 2000. This workshop was organized by the editors of the present article, and was made possible by support of: | NWO, the Netherlands Organization for
Data Imprecision in Computational Geometry
Löffler, M.
2009-01-01
The field of computational geometry is concerned with the design and analysis of geometric algorithms. For such algorithms, correctness and efficiency proofs are constructed, or problems are proven to be hard when no correct and efficient algorithms exist. In order to be able to do this, several ass
GEOMETRY AND COMPLEXITY IN ARCHITECTURE
RUSU Maria Ana
2015-06-01
Full Text Available As Constantin Brancuși (1876-1956 said „Simplicity is complexity itself“, simplicity and regularity through the use of basic geometric forms has always played a central role in architectural design, during the 20th century. A diachronic perspective, shows as the use of geometry and mathematics to describe built form provided a common basis for communication between the processes of design, fabrication and stability. Classic ways of representing geometry, based on descriptive methods, favor precise language of bidimensionality easy to represent in a rectangular coordinate system. In recent years, the importance of geometry has been re-emphasized by significant advances in the digital age, where computers are increasingly used in design, fabrication and construction to explore the art of the possible. Contemporary architecture transcend the limitations of Euclidean geometry and create new forms that are emerging through the convergence of complex systems, computational design and robotic fabrication devices, but which can also achieve higher levels of performance. Freeform architectural shapes and structures play an increasingly important role in 21st century architectural design. Through a series of examples, the paper relates to contemporary architectural explorations of complex, curvilinear surfaces in the digital age and discusses how it has required rethinking the mode in which we traditionally operate as architects. The analysis creates the possibility of comparisons between original and current design.
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...
Geometric Representations of Interacting Maps
Tsuyoshi Kato
2010-01-01
Full Text Available Tropical geometry is a kind of dynamical scale transform which connects automata with real rational dynamics. Real rational dynamics are deeply studied from global analytic viewpoints. On the other hand, automata appear in various contexts in topology, combinatorics, and integrable systems. In this paper we study the analysis of these materials passing through tropical geometry. In particular we discover a new duality on the set of automata which arise from the projective duality in algebraic geometry.
A special irreducible matrix representation of the real Clifford algebra C(3,1)
Scharnhorst, K
1999-01-01
4x4 Dirac (gamma) matrices (irreducible matrix representations of the Clifford algebras C(3,1), C(1,3), C(4,0)) are an essential part of many calculations in quantum physics. Although the final physical results do not depend on any particular representation of the Dirac matrices (e.g. due to the invariance of traces of products of Dirac matrices), the appropriate choice of the representation used may facilitate the analysis. The present paper introduces a particularly symmetric real representation of 4x4 Dirac matrices (Majorana representation) which may prove useful in the future. The consideration is based on the role played by isoclinic 2-planes in the geometry of the real Clifford algebra C(3,0) which provide an invariant geometric frame for it.
Congruence properties of induced representations
Mayer, Dieter; Momeni, Arash; Venkov, Alexei
In this paper we study representations of the projective modular group induced from the Hecke congruence group of level 4 with Selberg's character. We show that the well known congruence properties of Selberg's character are equivalent to the congruence properties of the induced representations. ...
Representation of Fuzzy Symmetric Relations
1986-03-19
Std Z39-18 REPRESENTATION OF FUZZY SYMMETRIC RELATIONS L. Valverde Dept. de Matematiques i Estadistica Universitat Politecnica de Catalunya Avda...REPRESENTATION OF FUZZY SYMMETRIC RELATIONS L. "Valverde* Dept. de Matematiques i Estadistica Universitat Politecnica de Catalunya Avda. Diagonal, 649
Scientific Representation and Science Learning
Matta, Corrado
2014-01-01
In this article I examine three examples of philosophical theories of scientific representation with the aim of assessing which of these is a good candidate for a philosophical theory of scientific representation in science learning. The three candidate theories are Giere's intentional approach, Suárez's inferential approach and Lynch and…
Adjoint Functors and Representation Dimensions
Chang Chang XI
2006-01-01
We study the global dimensions of the coherent functors over two categories that are linked by a pair of adjoint functors. This idea is then exploited to compare the representation dimensions of two algebras. In particular, we show that if an Artin algebra is switched from the other, then they have the same representation dimension.
$\\alpha$-Representation for QCD
Tuan, Richard Hong
1998-01-01
An $\\alpha$-parameter representation is derived for gauge field theories.It involves, relative to a scalar field theory, only constants and derivatives with respect to the $\\alpha$-parameters. Simple rules are given to obtain the $\\alpha$-representation for a Feynman graph with an arbitrary number of loops in gauge theories in the Feynman gauge.
International agreements on commercial representation
Slanař, Jan
2014-01-01
The purpose of the thesis is to describe the possibilities for fixing the position of a company in the market through contracts for commercial representation with a focus to finding legal and economic impact on the company that contracted for exclusive representation.
Scientific Representation and Science Learning
Matta, Corrado
2014-01-01
In this article I examine three examples of philosophical theories of scientific representation with the aim of assessing which of these is a good candidate for a philosophical theory of scientific representation in science learning. The three candidate theories are Giere's intentional approach, Suárez's inferential approach and Lynch and…
Teachers’ representations of school indiscipline
Joe Garcia
2015-11-01
Full Text Available In this article we analyze a set of teachers’ representations of school indiscipline and its implications for pedagogical practices, particularly related to the resolution of problems in the classroom. Initially we explore three teachers’ representations on the genesis of school indiscipline. The first representation attributes prominence to the student as the singular subject in the production of indiscipline and who will be the center of the pedagogical intervention. The second representation attributes the genesis of the indiscipline to the context of the relations among the subjects in the classroom. The third representation suggests that the indiscipline would be something socially constructed in the schools, where it is intrinsically related to its nature and social function, and is an intrinsic part of its institutional culture. This third representation is distant of the previous ones, and provides an understanding of the indiscipline as a cultural message. In the second part of this article we analyze a set of implications of the teachers’ representations in relation to their pedagogical practices. At the ending of the text, we present some notes that put in evidence some issues that seems to be at the center in the study of the representations regarding to school indiscipline, in relation to the roles teachers are supposed to taken in contexts of indiscipline.
Revealing children's implicit spelling representations.
Critten, Sarah; Pine, Karen J; Messer, David J
2013-06-01
Conceptualizing the underlying representations and cognitive mechanisms of children's spelling development is a key challenge for literacy researchers. Using the Representational Redescription model (Karmiloff-Smith), Critten, Pine and Steffler (2007) demonstrated that the acquisition of phonological and morphological knowledge may be underpinned by increasingly explicit levels of spelling representation. However, their proposal that implicit representations may underlie early 'visually based' spelling remains unresolved. Children (N = 101, aged 4-6 years) were given a recognition task (Critten et al., 2007) and a novel production task, both involving verbal justifications of why spellings are correct/incorrect, strategy use and word pattern similarity. Results for both tasks supported an implicit level of spelling characterized by the ability to correctly recognize/produce words but the inability to explain operational strategies or generalize knowledge. Explicit levels and multiple representations were also in evidence across the two tasks. Implications for cognitive mechanisms underlying spelling development are discussed.
Fuzzy Morphological Polynomial Image Representation
Chin-Pan Huang
2010-01-01
Full Text Available A novel signal representation using fuzzy mathematical morphology is developed. We take advantage of the optimum fuzzy fitting and the efficient implementation of morphological operators to extract geometric information from signals. The new representation provides results analogous to those given by the polynomial transform. Geometrical decomposition of a signal is achieved by windowing and applying sequentially fuzzy morphological opening with structuring functions. The resulting representation is made to resemble an orthogonal expansion by constraining the results of opening to equate adapted structuring functions. Properties of the geometric decomposition are considered and used to calculate the adaptation parameters. Our procedure provides an efficient and flexible representation which can be efficiently implemented in parallel. The application of the representation is illustrated in data compression and fractal dimension estimation temporal signals and images.
Dual geometries and spacetime singularities
Quirós, I
2000-01-01
The concept of geometrical duality is disscused in the context of Brans-Dicke theory and extended to general relativity. It is shown, in some generic cases, that spacetime singularities that arise in usual Riemannian general relativity, may be avoided in its dual representation: Weyl-like general relativity, thus providing a singularity-free picture of the World that is physicaly equivalent to the canonical general relativistic one.
Environmental Geometry Aligns the Hippocampal Map during Spatial Reorientation.
Keinath, Alex T; Julian, Joshua B; Epstein, Russell A; Muzzio, Isabel A
2017-02-06
When a navigator's internal sense of direction is disrupted, she must rely on external cues to regain her bearings, a process termed spatial reorientation. Extensive research has demonstrated that the geometric shape of the environment exerts powerful control over reorientation behavior, but the neural and cognitive mechanisms underlying this phenomenon are not well understood. Whereas some theories claim that geometry controls behavior through an allocentric mechanism potentially tied to the hippocampus, others postulate that disoriented navigators reach their goals by using an egocentric view-matching strategy. To resolve this debate, we characterized hippocampal representations during reorientation. We first recorded from CA1 cells as disoriented mice foraged in chambers of various shapes. We found that the alignment of the recovered hippocampal map was determined by the geometry of the chamber, but not by nongeometric cues, even when these cues could be used to disambiguate geometric ambiguities. We then recorded hippocampal activity as disoriented mice performed a classical goal-directed spatial memory task in a rectangular chamber. Again, we found that the recovered hippocampal map aligned solely to the chamber geometry. Critically, we also found a strong correspondence between the hippocampal map alignment and the animal's behavior, making it possible to predict the search location of the animal from neural responses on a trial-by-trial basis. Together, these results demonstrate that spatial reorientation involves the alignment of the hippocampal map to local geometry. We hypothesize that geometry may be an especially salient cue for reorientation because it is an inherently stable aspect of the environment. Copyright © 2017 Elsevier Ltd. All rights reserved.
Archival Representation in the Digital Age
Zhang, Jane
2012-01-01
This study analyzes the representation systems of three digitized archival collections using the traditional archival representation framework of provenance, order, and content. The results of the study reveal a prominent role of provenance representation, a compromised role of order representation, and an active role of content representation in…
Archival Representation in the Digital Age
Zhang, Jane
2012-01-01
This study analyzes the representation systems of three digitized archival collections using the traditional archival representation framework of provenance, order, and content. The results of the study reveal a prominent role of provenance representation, a compromised role of order representation, and an active role of content representation in…
Geometric Entanglement of Symmetric States and the Majorana Representation
Aulbach, Martin; Murao, Mio
2010-01-01
Permutation-symmetric quantum states appear in a variety of physical situations, and they have been proposed for quantum information tasks. This article builds upon the results of [New J. Phys. 12, 073025 (2010)], where the maximally entangled symmetric states of up to twelve qubits were explored, and their amount of geometric entanglement determined by numeric and analytic means. For this the Majorana representation, a generalization of the Bloch sphere representation, can be employed to represent symmetric n qubit states by n points on the surface of a unit sphere. Symmetries of this point distribution simplify the determination of the entanglement, and enable the study of quantum states in novel ways. Here it is shown that the duality relationship of Platonic solids has a counterpart in the Majorana representation, and that in general maximally entangled symmetric states neither correspond to anticoherent spin states nor to spherical designs. The usability of symmetric states as resources for measurement-b...
Deep supervised, but not unsupervised, models may explain IT cortical representation.
Seyed-Mahdi Khaligh-Razavi
2014-11-01
Full Text Available Inferior temporal (IT cortex in human and nonhuman primates serves visual object recognition. Computational object-vision models, although continually improving, do not yet reach human performance. It is unclear to what extent the internal representations of computational models can explain the IT representation. Here we investigate a wide range of computational model representations (37 in total, testing their categorization performance and their ability to account for the IT representational geometry. The models include well-known neuroscientific object-recognition models (e.g. HMAX, VisNet along with several models from computer vision (e.g. SIFT, GIST, self-similarity features, and a deep convolutional neural network. We compared the representational dissimilarity matrices (RDMs of the model representations with the RDMs obtained from human IT (measured with fMRI and monkey IT (measured with cell recording for the same set of stimuli (not used in training the models. Better performing models were more similar to IT in that they showed greater clustering of representational patterns by category. In addition, better performing models also more strongly resembled IT in terms of their within-category representational dissimilarities. Representational geometries were significantly correlated between IT and many of the models. However, the categorical clustering observed in IT was largely unexplained by the unsupervised models. The deep convolutional network, which was trained by supervision with over a million category-labeled images, reached the highest categorization performance and also best explained IT, although it did not fully explain the IT data. Combining the features of this model with appropriate weights and adding linear combinations that maximize the margin between animate and inanimate objects and between faces and other objects yielded a representation that fully explained our IT data. Overall, our results suggest that explaining
Deep Supervised, but Not Unsupervised, Models May Explain IT Cortical Representation
Khaligh-Razavi, Seyed-Mahdi; Kriegeskorte, Nikolaus
2014-01-01
Inferior temporal (IT) cortex in human and nonhuman primates serves visual object recognition. Computational object-vision models, although continually improving, do not yet reach human performance. It is unclear to what extent the internal representations of computational models can explain the IT representation. Here we investigate a wide range of computational model representations (37 in total), testing their categorization performance and their ability to account for the IT representational geometry. The models include well-known neuroscientific object-recognition models (e.g. HMAX, VisNet) along with several models from computer vision (e.g. SIFT, GIST, self-similarity features, and a deep convolutional neural network). We compared the representational dissimilarity matrices (RDMs) of the model representations with the RDMs obtained from human IT (measured with fMRI) and monkey IT (measured with cell recording) for the same set of stimuli (not used in training the models). Better performing models were more similar to IT in that they showed greater clustering of representational patterns by category. In addition, better performing models also more strongly resembled IT in terms of their within-category representational dissimilarities. Representational geometries were significantly correlated between IT and many of the models. However, the categorical clustering observed in IT was largely unexplained by the unsupervised models. The deep convolutional network, which was trained by supervision with over a million category-labeled images, reached the highest categorization performance and also best explained IT, although it did not fully explain the IT data. Combining the features of this model with appropriate weights and adding linear combinations that maximize the margin between animate and inanimate objects and between faces and other objects yielded a representation that fully explained our IT data. Overall, our results suggest that explaining IT requires
Space Charge Effect in the Sheet and Solid Electron Beam
Song, Ho Young; Kim, Hyoung Suk; Ahn, Saeyoung
1998-11-01
We analyze the space charge effect of two different types of electron beam ; sheet and solid electron beam. Electron gun simulations are carried out using shadow and control grids for high and low perveance. Rectangular and cylindrical geometries are used for sheet and solid electron beam in planar and disk type cathode. The E-gun code is used to study the limiting current and space charge loading in each geometries.
Combinatorics of solvable lattice models, and modular representations of Hecke algebras
Foda, O E; Okado, M; Thibon, J Y; Welsh, Trevor A; Foda, Omar; Leclerc, Bernard; Okado, Masato; Thibon, Jean-Yves; Welsh, Trevor A.
1997-01-01
We review and motivate recently-observed relationships between exactly solvable lattice models and modular representations of Hecke algebras. Firstly, we describe how the set of $n$-regular partitions label both of the following classes of objects: 1. The spectrum of unrestricted solid-on-solid lattice models based on level-1 representations of the affine algebras $\\sl_n$, 2. The irreducible representations of type-A Hecke algebras at roots of unity: $H_m(\\sqrt[n]{1})$. Secondly, we show that a certain subset of the $n$-regular partitions label both of the following classes of objects: 1. The spectrum of restricted solid-on-solid lattice models based on cosets of affine algebras $(sl(n)^_1 \\times sl(n)^_1)/ sl(n)^_2$. 2. Jantzen-Seitz (JS) representations of $H_m(\\sqrt[n]{1})$: irreducible representations that remain irreducible under restriction to $H_{m-1}(\\sqrt[n]{1})$. Using the above relationships, we characterise the JS representations of $H_m(\\sqrt[n]{1})$ and show that the generating series that count...
Geometry of Membrane Sigma Models
Vysoky, Jan
2015-01-01
String theory still remains one of the promising candidates for a unification of the theory of gravity and quantum field theory. One of its essential parts is relativistic description of moving multi-dimensional objects called membranes (or p-branes) in a curved spacetime. On the classical field theory level, they are described by an action functional extremalising the volume of a manifold swept by a propagating membrane. This and related field theories are collectively called membrane sigma models. Differential geometry is an important mathematical tool in the study of string theory. It turns out that string and membrane backgrounds can be conveniently described using objects defined on a direct sum of tangent and cotangent bundles of the spacetime manifold. Mathematical field studying such object is called generalized geometry. Its integral part is the theory of Leibniz algebroids, vector bundles with a Leibniz algebra bracket on its module of smooth sections. Special cases of Leibniz algebroids are better ...