2015-12-01
ARL-SR-0347 ● DEC 2015 US Army Research Laboratory An Investigation into Conversion from Non-Uniform Rational B-Spline Boundary...US Army Research Laboratory An Investigation into Conversion from Non-Uniform Rational B-Spline Boundary Representation Geometry to...from Non-Uniform Rational B-Spline Boundary Representation Geometry to Constructive Solid Geometry 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c
Exploration of solids based on representation systems
Directory of Open Access Journals (Sweden)
Publio Suárez Sotomonte
2011-01-01
Full Text Available This article refers to some of the findings of a research project implemented as a teaching strategy to generate environments for the learning of platonic and archimedean solids, with a group of eighth grade students. This strategy was based on the meaningful learning approach and on the use of representation systems using the ontosemiotic approach in mathematical education, as a framework for the construction of mathematical concepts. This geometry teaching strategy adopts the stages of exploration, representation-modeling, formal construction and study of applications. It uses concrete, physical and tangible materials for origami, die making, and structures for the construction of threedimensional solids considered external tangible solid representation systems, as well as computer based educational tools to design dynamic geometry environments as intangible external representation systems.These strategies support both the imagination and internal systems of representation, fundamental to the comprehension of geometry concepts.
International Nuclear Information System (INIS)
Davis, J. E.; Eddy, M. J.; Sutton, T. M.; Altomari, T. J.
2007-01-01
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. (authors)
Several (un) known representational environments in geometry
Czech Academy of Sciences Publication Activity Database
Roubíček, Filip
2006-01-01
Roč. 14, 1 (2006), s. 40-43 ISSN 1214-4681. [Creativity in Mathematics Education and the Education of Gifted Students. České Budějovice, 05.07.2006-08.07.2006] R&D Projects: GA ČR(CZ) GP406/03/D052; GA ČR GA406/05/2444 Institutional research plan: CEZ:AV0Z10190503 Keywords : teaching of geometry * representation * construction Subject RIV: AM - Education
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.
Numerically robust geometry engine for compound solid geometries
International Nuclear Information System (INIS)
Vlachoudis, V.; Sinuela-Pastor, D.
2013-01-01
Monte Carlo programs heavily rely on a fast and numerically robust solid geometry engines. However the success of solid modeling, depends on facilities for specifying and editing parameterized models through a user-friendly graphical front-end. Such a user interface has to be fast enough in order to be interactive for 2D and/or 3D displays, but at the same time numerically robust in order to display possible modeling errors at real time that could be critical for the simulation. The graphical user interface Flair for FLUKA currently employs such an engine where special emphasis has been given on being fast and numerically robust. The numerically robustness is achieved by a novel method of estimating the floating precision of the operations, which dynamically adapts all the decision operations accordingly. Moreover a predictive caching mechanism is ensuring that logical errors in the geometry description are found online, without compromising the processing time by checking all regions. (authors)
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...
Nonabelian Jacobian of projective surfaces geometry and representation theory
Reider, Igor
2013-01-01
The Jacobian of a smooth projective curve is undoubtedly one of the most remarkable and beautiful objects in algebraic geometry. This work is an attempt to develop an analogous theory for smooth projective surfaces - a theory of the nonabelian Jacobian of smooth projective surfaces. Just like its classical counterpart, our nonabelian Jacobian relates to vector bundles (of rank 2) on a surface as well as its Hilbert scheme of points. But it also comes equipped with the variation of Hodge-like structures, which produces a sheaf of reductive Lie algebras naturally attached to our Jacobian. This constitutes a nonabelian analogue of the (abelian) Lie algebra structure of the classical Jacobian. This feature naturally relates geometry of surfaces with the representation theory of reductive Lie algebras/groups. This work’s main focus is on providing an in-depth study of various aspects of this relation. It presents a substantial body of evidence that the sheaf of Lie algebras on the nonabelian Jacobian is an effic...
International Nuclear Information System (INIS)
Yang Xue; Satvat, Nader
2012-01-01
Highlight: ► A two-dimensional numerical code based on the method of characteristics is developed. ► The complex arbitrary geometries are represented by constructive solid geometry and decomposed by unstructured meshing. ► Excellent agreement between Monte Carlo and the developed code is observed. ► High efficiency is achieved by parallel computing. - Abstract: A transport theory code MOCUM based on the method of characteristics as the flux solver with an advanced general geometry processor has been developed for two-dimensional rectangular and hexagonal lattice and full core neutronics modeling. In the code, the core structure is represented by the constructive solid geometry that uses regularized Boolean operations to build complex geometries from simple polygons. Arbitrary-precision arithmetic is also used in the process of building geometry objects to eliminate the round-off error from the commonly used double precision numbers. Then, the constructed core frame will be decomposed and refined into a Conforming Delaunay Triangulation to ensure the quality of the meshes. The code is fully parallelized using OpenMP and is verified and validated by various benchmarks representing rectangular, hexagonal, plate type and CANDU reactor geometries. Compared with Monte Carlo and deterministic reference solution, MOCUM results are highly accurate. The mentioned characteristics of the MOCUM make it a perfect tool for high fidelity full core calculation for current and GenIV reactor core designs. The detailed representation of reactor physics parameters can enhance the safety margins with acceptable confidence levels, which lead to more economically optimized designs.
Preliminary investigation of solid target geometry
Energy Technology Data Exchange (ETDEWEB)
Haga, Katsuhiro; Kaminaga, Masanori; Hino, Ryutaro; Takada, Hiroshi [Japan Atomic Energy Research Inst., Tokai, Ibaraki (Japan). Tokai Research Establishment; Shafiqul, I.M.; Tsuji, Nobumasa; Okamoto, Hutoshi; Kumasaka, Katsuyuki; Hayashi, Katsumi
1997-11-01
In this report, we introduce the developing plan for a solid metal target structure. Supposing tantalum as the target material, the temperature distribution and the maximum thermal stress in a tantalum plate of a solid metal target was evaluated under a water cooling condition, using the heat generation rate calculated with the JAERI`s neutron transport code. The calculation results showed that the water velocity was higher than 10 m/s in order to cool the 3mm-thick target plate down to 200degC when the target surface was smooth and heat transfer rate was calculated with the Dittus-Boelter equation. In this case, the maximum thermal stress is 50 MPa at the target plate surface. The coolant water flow distribution in a target vessel was also evaluated for ISIS-type flow channels and the parallel flow channels. In the ISIS-type flow channels, at least 25mm height of the coolant plenum is needed for a uniform flow distribution. The maximum flow velocity difference between the flow gaps in the parallel flow channels was 30%. A heat transfer augmentation experiment was conducted using ribbed-surface flow channel. The heat transfer rate was confirmed to increase up to twice the value of that for a smooth surface. (author)
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.
An Integral Spectral Representation of the Propagator for the Wave Equation in the Kerr Geometry
Finster, F.; Kamran, N.; Smoller, J.; Yau, S.-T.
2005-12-01
We consider the scalar wave equation in the Kerr geometry for Cauchy data which is smooth and compactly supported outside the event horizon. We derive an integral representation which expresses the solution as a superposition of solutions of the radial and angular ODEs which arise in the separation of variables. In particular, we prove completeness of the solutions of the separated ODEs.
Path integral representation of Lorentzian spinfoam model, asymptotics and simplicial geometries
International Nuclear Information System (INIS)
Han, Muxin; Krajewski, Thomas
2014-01-01
A new path integral representation of Lorentzian Engle–Pereira–Rovelli–Livine spinfoam model is derived by employing the theory of unitary representation of SL(2,C). The path integral representation is taken as a starting point of semiclassical analysis. The relation between the spinfoam model and classical simplicial geometry is studied via the large-spin asymptotic expansion of the spinfoam amplitude with all spins uniformly large. More precisely, in the large-spin regime, there is an equivalence between the spinfoam critical configuration (with certain nondegeneracy assumption) and a classical Lorentzian simplicial geometry. Such an equivalence relation allows us to classify the spinfoam critical configurations by their geometrical interpretations, via two types of solution-generating maps. The equivalence between spinfoam critical configuration and simplical geometry also allows us to define the notion of globally oriented and time-oriented spinfoam critical configuration. It is shown that only at the globally oriented and time-oriented spinfoam critical configuration, the leading-order contribution of spinfoam large-spin asymptotics gives precisely an exponential of Lorentzian Regge action of General Relativity. At all other (unphysical) critical configurations, spinfoam large-spin asymptotics modifies the Regge action at the leading-order approximation. (paper)
Assadi, Amir H.
2001-11-01
Perceptual geometry is an emerging field of interdisciplinary research whose objectives focus on study of geometry from the perspective of visual perception, and in turn, apply such geometric findings to the ecological study of vision. Perceptual geometry attempts to answer fundamental questions in perception of form and representation of space through synthesis of cognitive and biological theories of visual perception with geometric theories of the physical world. Perception of form and space are among fundamental problems in vision science. In recent cognitive and computational models of human perception, natural scenes are used systematically as preferred visual stimuli. Among key problems in perception of form and space, we have examined perception of geometry of natural surfaces and curves, e.g. as in the observer's environment. Besides a systematic mathematical foundation for a remarkably general framework, the advantages of the Gestalt theory of natural surfaces include a concrete computational approach to simulate or recreate images whose geometric invariants and quantities might be perceived and estimated by an observer. The latter is at the very foundation of understanding the nature of perception of space and form, and the (computer graphics) problem of rendering scenes to visually invoke virtual presence.
Sossinsky, A B
2012-01-01
The book is an innovative modern exposition of geometry, or rather, of geometries; it is the first textbook in which Felix Klein's Erlangen Program (the action of transformation groups) is systematically used as the basis for defining various geometries. The course of study presented is dedicated to the proposition that all geometries are created equal--although some, of course, remain more equal than others. The author concentrates on several of the more distinguished and beautiful ones, which include what he terms "toy geometries", the geometries of Platonic bodies, discrete geometries, and classical continuous geometries. The text is based on first-year semester course lectures delivered at the Independent University of Moscow in 2003 and 2006. It is by no means a formal algebraic or analytic treatment of geometric topics, but rather, a highly visual exposition containing upwards of 200 illustrations. The reader is expected to possess a familiarity with elementary Euclidean geometry, albeit those lacking t...
Directory of Open Access Journals (Sweden)
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”.
Indian Academy of Sciences (India)
. In the previous article we looked at the origins of synthetic and analytic geometry. More practical minded people, the builders and navigators, were studying two other aspects of geometry- trigonometry and integral calculus. These are actually ...
Energy Technology Data Exchange (ETDEWEB)
Millman, D. L. [Dept. of Computer Science, Univ. of North Carolina at Chapel Hill (United States); Griesheimer, D. P.; Nease, B. R. [Bechtel Marine Propulsion Corporation, Bertis Atomic Power Laboratory (United States); Snoeyink, J. [Dept. of Computer Science, Univ. of North Carolina at Chapel Hill (United States)
2012-07-01
In this paper we consider a new generalized algorithm for the efficient calculation of component object volumes given their equivalent constructive solid geometry (CSG) definition. The new method relies on domain decomposition to recursively subdivide the original component into smaller pieces with volumes that can be computed analytically or stochastically, if needed. Unlike simpler brute-force approaches, the proposed decomposition scheme is guaranteed to be robust and accurate to within a user-defined tolerance. The new algorithm is also fully general and can handle any valid CSG component definition, without the need for additional input from the user. The new technique has been specifically optimized to calculate volumes of component definitions commonly found in models used for Monte Carlo particle transport simulations for criticality safety and reactor analysis applications. However, the algorithm can be easily extended to any application which uses CSG representations for component objects. The paper provides a complete description of the novel volume calculation algorithm, along with a discussion of the conjectured error bounds on volumes calculated within the method. In addition, numerical results comparing the new algorithm with a standard stochastic volume calculation algorithm are presented for a series of problems spanning a range of representative component sizes and complexities. (authors)
International Nuclear Information System (INIS)
Millman, D. L.; Griesheimer, D. P.; Nease, B. R.; Snoeyink, J.
2012-01-01
In this paper we consider a new generalized algorithm for the efficient calculation of component object volumes given their equivalent constructive solid geometry (CSG) definition. The new method relies on domain decomposition to recursively subdivide the original component into smaller pieces with volumes that can be computed analytically or stochastically, if needed. Unlike simpler brute-force approaches, the proposed decomposition scheme is guaranteed to be robust and accurate to within a user-defined tolerance. The new algorithm is also fully general and can handle any valid CSG component definition, without the need for additional input from the user. The new technique has been specifically optimized to calculate volumes of component definitions commonly found in models used for Monte Carlo particle transport simulations for criticality safety and reactor analysis applications. However, the algorithm can be easily extended to any application which uses CSG representations for component objects. The paper provides a complete description of the novel volume calculation algorithm, along with a discussion of the conjectured error bounds on volumes calculated within the method. In addition, numerical results comparing the new algorithm with a standard stochastic volume calculation algorithm are presented for a series of problems spanning a range of representative component sizes and complexities. (authors)
Prasolov, V V
2015-01-01
This book provides a systematic introduction to various geometries, including Euclidean, affine, projective, spherical, and hyperbolic geometries. Also included is a chapter on infinite-dimensional generalizations of Euclidean and affine geometries. A uniform approach to different geometries, based on Klein's Erlangen Program is suggested, and similarities of various phenomena in all geometries are traced. An important notion of duality of geometric objects is highlighted throughout the book. The authors also include a detailed presentation of the theory of conics and quadrics, including the theory of conics for non-Euclidean geometries. The book contains many beautiful geometric facts and has plenty of problems, most of them with solutions, which nicely supplement the main text. With more than 150 figures illustrating the arguments, the book can be recommended as a textbook for undergraduate and graduate-level courses in geometry.
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…
Effect of Geometry on Electrokinetic Characterization of Solid Surfaces.
Kumar, Abhijeet; Kleinen, Jochen; Venzmer, Joachim; Gambaryan-Roisman, Tatiana
2017-08-01
An analytical approach is presented to describe pressure-driven streaming current (I str ) and streaming potential (U str ) generation in geometrically complex samples, for which the classical Helmholtz-Smoluchowski (H-S) equation is known to be inaccurate. The new approach is valid under the same prerequisite conditions that are used for the development of the H-S equation, that is, the electrical double layers (EDLs) are sufficiently thin and surface conductivity and electroviscous effects are negligible. The analytical methodology is developed using linear velocity profiles to describe liquid flow inside of EDLs and using simplifying approximations to describe macroscopic flow. At first, a general expression is obtained to describe the I str generated in different cross sections of an arbitrarily shaped sample. Thereafter, assuming that the generated U str varies only along the pressure-gradient direction, an expression describing the variation of generated U str along the sample length is obtained. These expressions describing I str and U str generation constitute the theoretical foundation of this work, which is first applied to a set of three nonuniform cross-sectional capillaries and thereafter to a square array of cylindrical fibers (model porous media) for both parallel and transverse fiber orientation cases. Although analytical solutions cannot be obtained for real porous substrates because of their random structure, the new theory provides useful insights into the effect of important factors such as fiber orientation, sample porosity, and sample dimensions. The solutions obtained for the model porous media are used to device strategies for more accurate zeta potential determination of porous fiber plugs. The new approach could be thus useful in resolving the long-standing problem of sample geometry dependence of zeta potential measurements.
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
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.
Herold, Elisabeth; Hellmann, Robert; Wagner, Joachim
2017-11-01
We provide analytical expressions for the second virial coefficients of differently shaped hard solids of revolution in dependence on their aspect ratio. The second virial coefficients of convex hard solids, which are the orientational averages of the mutual excluded volume, are derived from volume, surface, and mean radii of curvature employing the Isihara-Hadwiger theorem. Virial coefficients of both prolate and oblate hard solids of revolution are investigated in dependence on their aspect ratio. The influence of one- and two-dimensional removable singularities of the surface curvature to the mutual excluded volume is analyzed. The virial coefficients of infinitely thin oblate and infinitely long prolate particles are compared, and analytical expressions for their ratios are derived. Beyond their dependence on the aspect ratio, the second virial coefficients are influenced by the detailed geometry of the particles.
Room acoustics modeling using a point-cloud representation of the room geometry
DEFF Research Database (Denmark)
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...... level of user immersion by a real time acoustical simulation of a dynamic scenes....
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…
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.
Analysis of students’ spatial thinking in geometry: 3D object into 2D representation
Fiantika, F. R.; Maknun, C. L.; Budayasa, I. K.; Lukito, A.
2018-05-01
The aim of this study is to find out the spatial thinking process of students in transforming 3-dimensional (3D) object to 2-dimensional (2D) representation. Spatial thinking is helpful in using maps, planning routes, designing floor plans, and creating art. The student can engage geometric ideas by using concrete models and drawing. Spatial thinking in this study is identified through geometrical problems of transforming a 3-dimensional object into a 2-dimensional object image. The problem was resolved by the subject and analyzed by reference to predetermined spatial thinking indicators. Two representative subjects of elementary school were chosen based on mathematical ability and visual learning style. Explorative description through qualitative approach was used in this study. The result of this study are: 1) there are different representations of spatial thinking between a boy and a girl object, 2) the subjects has their own way to invent the fastest way to draw cube net.
Pop, Flavia; Lewis, William; Amabilino, David B.
2016-01-01
Mono- and di-alkylated 1,4-diketo-3,6-dithiophenylpyrrolo[3-4-c]pyrrole derivatives (TDPPs) have been synthesised and their solid state packing and absorption properties have been correlated. In this library of compounds the bulkier substituents distort the geometry of the chromophores and shift the lowest energy absorption band as a consequence of reduced π–π stacking and inter-chromophore overlap. Longitudinal displacement of the conjugated core is affected by donor–acceptor intermolecular ...
Anomalous ortho-para conversion of solid hydrogen in constrained geometries
International Nuclear Information System (INIS)
Rall, M.; Brison, J.P.; Sullivan, N.S.
1991-01-01
Using cw NMR techniques, we have measured the ortho-para conversion of solid hydrogen constrained to the interior of the molecular cages of zeolite. The conversion observed in the constrained geometry is very different from that of bulk solid hydrogen. Two distinct conversion rates were observed for short and long times. An apparently bimolecular conversion rate of 0.43% h -1 (one-fourth of the bulk value) dominates during the first 500 h, and the rate then increases to 2.2% h -1 . The initial slow rate is explained in terms of a reduced number of nearest neighbors and possible wall effects, and the fast rate is attributed to the formation of small ortho-H 2 Rclusters at later times. Surface effects due to magnetic impurities do not appear to determine the conversion rate in the samples studied
Jurco, B; Jurco, B; Schlieker, M
1995-01-01
In this paper we construct explicitly natural (from the geometrical point of view) Fock space representations (contragradient Verma modules) of the quantized enveloping algebras. In order to do so, we start from the Gauss decomposition of the quantum group and introduce the differential operators on the corresponding q-deformed flag manifold (asuumed as a left comodule for the quantum group) by a projection to it of the right action of the quantized enveloping algebra on the quantum group. Finally, we express the representatives of the elements of the quantized enveloping algebra corresponding to the left-invariant vector fields on the quantum group as first-order differential operators on the q-deformed flag manifold.
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.
National Research Council Canada - National Science Library
Little, Daniel
2006-01-01
...). The reason this is so is due to hierarchies that we take for granted. By hierarchies I mean that there is a layer of representation of us as individuals, as military professional, as members of a military unit and as citizens of an entire nation...
Theoretical concepts of fractal geometry semkow by radon emanation in solids
International Nuclear Information System (INIS)
Cruz G, H.
1996-01-01
The objective of this work is to introduce the fractal geometry concept to the study of gaseous emanations in solids, specially with reference to radon emission in mineral grains. The basic elements of fractals theory are developed. A fractal is defined as an auto similar subassembly, which fractal dimension is greater than the topological dimension. Starting from this, and making a brief description of the physicals basis of radon emission in solids, a model between emanation power (E R ) and the ratio s/v (surface to volume), is founded. A Gaussian model is assumed for extent of recoil from alpha decay of Ra-226. Using the results of Pfeifer it is obtained that distribution of pore size is scaled like Br -D-1 , where D: fractal[dimension, B: constant and r: pore radius. After an adequate mathematics expansion, it is found that the expression for emanation power is scaled like r 0 D-3 (r 0 grain radius). We may concluded that if we have a logarithmic graph of E R vs size of grain we can deduce the fractal dimension of the emanation surface. The experimental data of different materials provides an interval into fractal dimension D , between 2.1 to 2.86. (author). 5 refs., 1 tab
2006-09-01
two weeks to arrive. Source: http://beergame.mit.edu/ Permission Granted – MIT Supply Chain Forum 2005 Professor Sterman –Sloan School of...Management - MITSource: http://web.mit.edu/jsterman/www/ SDG /beergame.html Rules of Engagement The MIT Beer Game Simulation 04-04 Slide Number 10 Professor...Sterman –Sloan School of Management - MITSource: http://web.mit.edu/jsterman/www/ SDG /beergame.html What is the Significance of Representation
International Nuclear Information System (INIS)
Atanasov, Victor; Saxena, Avadh
2010-12-01
Adopting a purely two dimensional relativistic equation for graphene's carriers contradicts the Heisenberg uncertainty principle since it requires setting off-the-surface coordinate of a three-dimensional wavefunction to zero. Here we present a theoretical framework for describing graphene's massless relativistic carriers in accordance with this most fundamental of all quantum principles. A gradual confining procedure is used to restrict the dynamics onto a surface and in the process the embedding of this surface into the three dimensional world is accounted for. As a result an invariant geometric potential arises which scales linearly with the Mean curvature and shifts the Fermi energy of the material proportional to bending. Strain induced modification of the electronic properties or 'straintronics' is clearly an important field of study in graphene. This opens a venue to producing electronic devices, MEMS and NEMS where the electronic properties are controlled by geometric means and no additional alteration of graphene is necessary. The appearance of this geometric potential also provides us with clues as to how quantum dynamics looks like in the curved space-time of general relativity. In this context, we explore a two-dimensional cross-section of the wormhole geometry realized with graphene as a solid state thought experiment. (author)
Gong, Lunkun; Chen, Xiong; Musa, Omer; Yang, Haitao; Zhou, Changsheng
2017-12-01
Numerical and experimental investigation on the solid-fuel ramjet was carried out to study the effect of geometry on combustion characteristics. The two-dimensional axisymmetric program developed in the present study adopted finite rate chemistry and second-order moment turbulence-chemistry models, together with k-ω shear stress transport (SST) turbulence model. Experimental data were obtained by burning cylindrical polyethylene using a connected pipe facility. The simulation results show that a fuel-rich zone near the solid fuel surface and an air-rich zone in the core exist in the chamber, and the chemical reactions occur mainly in the interface of this two regions; The physical reasons for the effect of geometry on regression rate is the variation of turbulent viscosity due to the geometry change. Port-to-inlet diameter ratio is the main parameter influencing the turbulent viscosity, and a linear relationship between port-to-inlet diameter and regression rate were obtained. The air mass flow rate and air-fuel ratio are the main influencing factors on ramjet performances. Based on the simulation results, the correlations between geometry and air-fuel ratio were obtained, and the effect of geometry on ramjet performances was analyzed according to the correlation. Three-dimensional regression rate contour obtained experimentally indicates that the regression rate which shows axisymmetric distribution due to the symmetry structure increases sharply, followed by slow decrease in axial direction. The radiation heat transfer in recirculation zone cannot be ignored. Compared with the experimental results, the deviations of calculated average regression rate and characteristic velocity are about 5%. Concerning the effect of geometry on air-fuel ratio, the deviations between experimental and theoretical results are less than 10%.
International Nuclear Information System (INIS)
Bottoni, M.; Lyczkowski, R.; Ahuja, S.
1995-01-01
Numerical simulation of subcooled boiling in one-dimensional geometry with the Homogeneous Equilibrium Model (HEM) may yield difficulties related to the very low sonic velocity associated with the HEM. These difficulties do not arise with subcritical flow. Possible solutions of the problem include introducing a relaxation of the vapor production rate. Three-dimensional simulations of subcooled boiling in bundle geometry typical of fast reactors can be performed by using two systems of conservation equations, one for the HEM and the other for a Separated Phases Model (SPM), with a smooth transition between the two models
Solid-state nanopores of controlled geometry fabricated in a transmission electron microscope
Qian, Hui; Egerton, Ray F.
2017-11-01
Energy-filtered transmission electron microscopy and electron tomography were applied to in situ studies of the formation, shape, and diameter of nanopores formed in a silicon nitride membrane in a transmission electron microscope. The nanopore geometry was observed in three dimensions by electron tomography. Drilling conditions, such as probe current, beam convergence angle, and probe position, affect the formation rate and the geometry of the pores. With a beam convergence semi-angle of α = 22 mrad, a conical shaped nanopore is formed but at α = 45 mrad, double-cone (hourglass-shaped) nanopores were produced. Nanopores with an effective diameter between 10 nm and 1.8 nm were fabricated by controlling the drilling time.
2017-10-01
ENGINEERING CENTER GRAIN EVALUATION SOFTWARE TO NUMERICALLY PREDICT LINEAR BURN REGRESSION FOR SOLID PROPELLANT GRAIN GEOMETRIES Brian...distribution is unlimited. AD U.S. ARMY ARMAMENT RESEARCH, DEVELOPMENT AND ENGINEERING CENTER Munitions Engineering Technology Center Picatinny...U.S. ARMY ARMAMENT RESEARCH, DEVELOPMENT AND ENGINEERING CENTER GRAIN EVALUATION SOFTWARE TO NUMERICALLY PREDICT LINEAR BURN REGRESSION FOR SOLID
Concept of Quantum Geometry in Optoelectronic Processes in Solids: Application to Solar Cells.
Nagaosa, Naoto; Morimoto, Takahiro
2017-07-01
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. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Influence of Geometry and Velocity of Rotating Solids on Hydrodynamics of a Confined Volume
Directory of Open Access Journals (Sweden)
Ignacio Carvajal-Mariscal
2017-01-01
Full Text Available Three cylinder-based geometries were evaluated at five different rotating speeds (ω = 20.94, 62.83, 94.25, 125.66, and 157.08 rad·s−1 to obtain the fluid flow pattern in nonsteady conditions. Two of the models were modified at the lower region, also known as tip section, by means of inverted and right truncated cone geometries, respectively. The experimental technique used a visualization cell and a Particle Imaging Velocimetry installation to obtain the vector field at the central plane of the volume. The Line Integral Convolution Method was used to obtain the fluid motion at the plane. In addition, the scalar kinetic energy and the time series were calculated to perform the normal probability plot. This procedure was used to determine the nonlinear fluid flow pattern. It was also used to identify two different flow regimens in physical and numerical results. As the rotation speed increased, the turbulent regions were placed together and moved. The process makes experimental observation difficult. The biphasic and turbulence constitutive equations were solved with the Computational Fluid Dynamics technique. Numerical results were compared with physical experiments for validation. The model with the inverted truncated cone tip presented better stability in the fluid flow pattern along the rotation speed range.
International Nuclear Information System (INIS)
Whitcher, Ralph
2007-01-01
1 - Description of program or function: SACALC2B calculates the average solid angle subtended by a rectangular or circular detector window to a coaxial or non-coaxial rectangular, circular or point source, including where the source and detector planes are not parallel. SACALC C YL calculates the average solid angle subtended by a cylinder to a rectangular or circular source, plane or thick, at any location and orientation. This is needed, for example, in calculating the intrinsic gamma efficiency of a detector such as a GM tube. The program also calculates the number of hits on the cylinder side and on each end, and the average path length through the detector volume (assuming no scattering or absorption). Point sources can be modelled by using a circular source of zero radius. NEA-1688/03: Documentation has been updated (January 2006). 2 - Methods: The program uses a Monte Carlo method to calculate average solid angle for source-detector geometries that are difficult to analyse by analytical methods. The values of solid angle are calculated to accuracies of typically better than 0.1%. The calculated values from the Monte Carlo method agree closely with those produced by polygon approximation and numerical integration by Gardner and Verghese, and others. 3 - Restrictions on the complexity of the problem: The program models a circular or rectangular detector in planes that are not necessarily coaxial, nor parallel. Point sources can be modelled by using a circular source of zero radius. The sources are assumed to be uniformly distributed. NEA-1688/04: In SACALC C YL, to avoid rounding errors, differences less than 1 E-12 are assumed to be zero
Energy Technology Data Exchange (ETDEWEB)
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)
International Nuclear Information System (INIS)
Tayal, M.
1987-01-01
Structures often operate at elevated temperatures. Temperature calculations are needed so that the design can accommodate thermally induced stresses and material changes. A finite element computer called FEAT has been developed to calculate temperatures in solids of arbitrary shapes. FEAT solves the classical equation for steady state conduction of heat. The solution is obtained for two-dimensional (plane or axisymmetric) or for three-dimensional problems. Gap elements are use to simulate interfaces between neighbouring surfaces. The code can model: conduction; internal generation of heat; prescribed convection to a heat sink; prescribed temperatures at boundaries; prescribed heat fluxes on some surfaces; and temperature-dependence of material properties like thermal conductivity. The user has a option of specifying the detailed variation of thermal conductivity with temperature. For convenience to the nuclear fuel industry, the user can also opt for pre-coded values of thermal conductivity, which are obtained from the MATPRO data base (sponsored by the U.S. Nuclear Regulatory Commission). The finite element method makes FEAT versatile, and enables it to accurately accommodate complex geometries. The optional link to MATPRO makes it convenient for the nuclear fuel industry to use FEAT, without loss of generality. Special numerical techniques make the code inexpensive to run, for the type of material non-linearities often encounter in the analysis of nuclear fuel. The code, however, is general, and can be used for other components of the reactor, or even for non-nuclear systems. The predictions of FEAT have been compared against several analytical solutions. The agreement is usually better than 5%. Thermocouple measurements show that the FEAT predictions are consistent with measured changes in temperatures in simulated pressure tubes. FEAT was also found to predict well, the axial variations in temperatures in the end-pellets(UO 2 ) of two fuel elements irradiated
Apseudo-fluid representation of vertical liquid–coarse solids flow
Directory of Open Access Journals (Sweden)
ZORANA ARSENIJEVIC
2005-05-01
Full Text Available The pseudo–fluid concept has been applied for the prediction of the pressure gradient and voidage in vertical liquid-coarse solids flow. Treating the flowing mixture as a single homogenous fluid, the correlation for the friction coefficient of the suspension–wall was developed, as was the correlation between the true voidage and the apparent (volumetric voidage in the transport tube. Experiments were performed using water and spherical glass particles 1.20, 1.94 and 2.98 mm in diameter in a transport tube of 24 mm in diameter. The loading ratio (Gp/Gf was varied between 0.05 and 1.05 and the fluid superficial velocity was between 0.4 Ut and 4.95 Ut where Ut represents the single particle terminal velocity. The voidage ranged from 0.648 to 0.951 for these ratios. Experimental data for the pressure gradient and voidage from the literature agree well with the proposed correlations.
Spinning geometry = Twisted geometry
International Nuclear Information System (INIS)
Freidel, Laurent; Ziprick, Jonathan
2014-01-01
It is well known that the SU(2)-gauge invariant phase space of loop gravity can be represented in terms of twisted geometries. These are piecewise-linear-flat geometries obtained by gluing together polyhedra, but the resulting geometries are not continuous across the faces. Here we show that this phase space can also be represented by continuous, piecewise-flat three-geometries called spinning geometries. These are composed of metric-flat three-cells glued together consistently. The geometry of each cell and the manner in which they are glued is compatible with the choice of fluxes and holonomies. We first remark that the fluxes provide each edge with an angular momentum. By studying the piecewise-flat geometries which minimize edge lengths, we show that these angular momenta can be literally interpreted as the spin of the edges: the geometries of all edges are necessarily helices. We also show that the compatibility of the gluing maps with the holonomy data results in the same conclusion. This shows that a spinning geometry represents a way to glue together the three-cells of a twisted geometry to form a continuous geometry which represents a point in the loop gravity phase space. (paper)
Karpilovsky, G
1994-01-01
This third volume can be roughly divided into two parts. The first part is devoted to the investigation of various properties of projective characters. Special attention is drawn to spin representations and their character tables and to various correspondences for projective characters. Among other topics, projective Schur index and projective representations of abelian groups are covered. The last topic is investigated by introducing a symplectic geometry on finite abelian groups. The second part is devoted to Clifford theory for graded algebras and its application to the corresponding theory
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
Symplectic geometry and Fourier analysis
Wallach, Nolan R
2018-01-01
Suitable for graduate students in mathematics, this monograph covers differential and symplectic geometry, homogeneous symplectic manifolds, Fourier analysis, metaplectic representation, quantization, Kirillov theory. Includes Appendix on Quantum Mechanics by Robert Hermann. 1977 edition.
Boundary representation modelling techniques
2006-01-01
Provides the most complete presentation of boundary representation solid modelling yet publishedOffers basic reference information for software developers, application developers and users Includes a historical perspective as well as giving a background for modern research.
Iversen, Birger
1992-01-01
Although it arose from purely theoretical considerations of the underlying axioms of geometry, the work of Einstein and Dirac has demonstrated that hyperbolic geometry is a fundamental aspect of modern physics
van den Broek, P.M.
1984-01-01
The aim of this paper is to give a detailed exposition of the relation between the geometry of twistor space and the geometry of Minkowski space. The paper has a didactical purpose; no use has been made of differential geometry and cohomology.
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
or the middle range of dimensions (in the non-Shimura variety case), the systems of Hecke eigenvalues that appear are all Eisenstein ...characteristic p coecients of GLn(Q) is Eisenstein . (The characteristic zero analogue follows directly from Borel’s proof of stability of cohomology with
Introduction to representation theory
Etingof, Pavel; Hensel, Sebastian; Liu, Tiankai; Schwendner, Alex
2011-01-01
Very roughly speaking, representation theory studies symmetry in linear spaces. It is a beautiful mathematical subject which has many applications, ranging from number theory and combinatorics to geometry, probability theory, quantum mechanics, and quantum field theory. The goal of this book is to give a "holistic" introduction to representation theory, presenting it as a unified subject which studies representations of associative algebras and treating the representation theories of groups, Lie algebras, and quivers as special cases. Using this approach, the book covers a number of standard topics in the representation theories of these structures. Theoretical material in the book is supplemented by many problems and exercises which touch upon a lot of additional topics; the more difficult exercises are provided with hints. The book is designed as a textbook for advanced undergraduate and beginning graduate students. It should be accessible to students with a strong background in linear algebra and a basic k...
International Nuclear Information System (INIS)
Robinson, I.; Trautman, A.
1988-01-01
The geometry of classical physics is Lorentzian; but weaker geometries are often more appropriate: null geodesics and electromagnetic fields, for example, are well known to be objects of conformal geometry. To deal with a single null congruence, or with the radiative electromagnetic fields associated with it, even less is needed: flag geometry for the first, optical geometry, with which this paper is chiefly concerned, for the second. The authors establish a natural one-to-one correspondence between optical geometries, considered locally, and three-dimensional Cauchy-Riemann structures. A number of Lorentzian geometries are shown to be equivalent from the optical point of view. For example the Goedel universe, the Taub-NUT metric and Hauser's twisting null solution have an optical geometry isomorphic to the one underlying the Robinson congruence in Minkowski space. The authors present general results on the problem of lifting a CR structure to a Lorentz manifold and, in particular, to Minkowski space; and exhibit the relevance of the deviation form to this problem
Pottmann, Helmut; Eigensatz, Michael; Vaxman, Amir; Wallner, Johannes
2014-01-01
Around 2005 it became apparent in the geometry processing community that freeform architecture contains many problems of a geometric nature to be solved, and many opportunities for optimization which however require geometric understanding. This area of research, which has been called architectural geometry, meanwhile contains a great wealth of individual contributions which are relevant in various fields. For mathematicians, the relation to discrete differential geometry is significant, in particular the integrable system viewpoint. Besides, new application contexts have become available for quite some old-established concepts. Regarding graphics and geometry processing, architectural geometry yields interesting new questions but also new objects, e.g. replacing meshes by other combinatorial arrangements. Numerical optimization plays a major role but in itself would be powerless without geometric understanding. Summing up, architectural geometry has become a rewarding field of study. We here survey the main directions which have been pursued, we show real projects where geometric considerations have played a role, and we outline open problems which we think are significant for the future development of both theory and practice of architectural geometry.
Pottmann, Helmut
2014-11-26
Around 2005 it became apparent in the geometry processing community that freeform architecture contains many problems of a geometric nature to be solved, and many opportunities for optimization which however require geometric understanding. This area of research, which has been called architectural geometry, meanwhile contains a great wealth of individual contributions which are relevant in various fields. For mathematicians, the relation to discrete differential geometry is significant, in particular the integrable system viewpoint. Besides, new application contexts have become available for quite some old-established concepts. Regarding graphics and geometry processing, architectural geometry yields interesting new questions but also new objects, e.g. replacing meshes by other combinatorial arrangements. Numerical optimization plays a major role but in itself would be powerless without geometric understanding. Summing up, architectural geometry has become a rewarding field of study. We here survey the main directions which have been pursued, we show real projects where geometric considerations have played a role, and we outline open problems which we think are significant for the future development of both theory and practice of architectural geometry.
Maor, Eli
2014-01-01
If you've ever thought that mathematics and art don't mix, this stunning visual history of geometry will change your mind. As much a work of art as a book about mathematics, Beautiful Geometry presents more than sixty exquisite color plates illustrating a wide range of geometric patterns and theorems, accompanied by brief accounts of the fascinating history and people behind each. With artwork by Swiss artist Eugen Jost and text by acclaimed math historian Eli Maor, this unique celebration of geometry covers numerous subjects, from straightedge-and-compass constructions to intriguing configur
International Nuclear Information System (INIS)
Jonsson, Rickard; Westman, Hans
2006-01-01
We show that by employing the standard projected curvature as a measure of spatial curvature, we can make a certain generalization of optical geometry (Abramowicz M A and Lasota J-P 1997 Class. Quantum Grav. A 14 23-30). This generalization applies to any spacetime that admits a hypersurface orthogonal shearfree congruence of worldlines. This is a somewhat larger class of spacetimes than the conformally static spacetimes assumed in standard optical geometry. In the generalized optical geometry, which in the generic case is time dependent, photons move with unit speed along spatial geodesics and the sideways force experienced by a particle following a spatially straight line is independent of the velocity. Also gyroscopes moving along spatial geodesics do not precess (relative to the forward direction). Gyroscopes that follow a curved spatial trajectory precess according to a very simple law of three-rotation. We also present an inertial force formalism in coordinate representation for this generalization. Furthermore, we show that by employing a new sense of spatial curvature (Jonsson R 2006 Class. Quantum Grav. 23 1)) closely connected to Fermat's principle, we can make a more extensive generalization of optical geometry that applies to arbitrary spacetimes. In general this optical geometry will be time dependent, but still geodesic photons move with unit speed and follow lines that are spatially straight in the new sense. Also, the sideways experienced (comoving) force on a test particle following a line that is straight in the new sense will be independent of the velocity
Kemnitz, Arnfried
Der Grundgedanke der Analytischen Geometrie besteht darin, dass geometrische Untersuchungen mit rechnerischen Mitteln geführt werden. Geometrische Objekte werden dabei durch Gleichungen beschrieben und mit algebraischen Methoden untersucht.
Lefschetz, Solomon
2005-01-01
An introduction to algebraic geometry and a bridge between its analytical-topological and algebraical aspects, this text for advanced undergraduate students is particularly relevant to those more familiar with analysis than algebra. 1953 edition.
Ay, Nihat; Lê, Hông Vân; Schwachhöfer, Lorenz
2017-01-01
The book provides a comprehensive introduction and a novel mathematical foundation of the field of information geometry with complete proofs and detailed background material on measure theory, Riemannian geometry and Banach space theory. Parametrised measure models are defined as fundamental geometric objects, which can be both finite or infinite dimensional. Based on these models, canonical tensor fields are introduced and further studied, including the Fisher metric and the Amari-Chentsov tensor, and embeddings of statistical manifolds are investigated. This novel foundation then leads to application highlights, such as generalizations and extensions of the classical uniqueness result of Chentsov or the Cramér-Rao inequality. Additionally, several new application fields of information geometry are highlighted, for instance hierarchical and graphical models, complexity theory, population genetics, or Markov Chain Monte Carlo. The book will be of interest to mathematicians who are interested in geometry, inf...
Moritz enhancements for visualization of complicated geometry models
International Nuclear Information System (INIS)
Van Riper, K. A.
2009-01-01
We describe new features implemented in the Moritz geometry editing and visualization program to enhance the accuracy and efficiency of viewing complex geometry models. The 3D display is based on OpenGL and requires conversion of the combinatorial surface and solid body geometry used by MCNP and other transport codes to a set of polygons. Calculation of those polygons can take many minutes for complex models. Once calculated, the polygons can be saved to a file and reused when the same or a derivative model is loaded; the file can be read and processed in under a second. A cell can be filled with a collection of other cells constituting a universe. A new option bypasses use of the filled cell's boundaries when calculating the polygons for the filling universe. This option, when applicable, speeds processing, improves the 3D image, and permits reuse of the universe's polygons when other cells are filled with transformed instances of the universe. Surfaces and solid bodies used in a cell description must be converted to polygons before calculating the polygonal representation of a cell; this conversion requires truncation of infinite surfaces. A new method for truncating transformed surfaces ensures the finite surface intersects the entire model. When a surface or solid body is processed in a cell description, an optional test detects when that object does not contribute additional polygons; if so, that object May be extraneous for the cell description. (authors)
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...
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.
Learners engaging with transformation geometry
African Journals Online (AJOL)
participants engaged in investigative semi-structured interviews with the resear- chers. ... Keywords: analysis; conversions; transformation geometry; transformations; treatments .... semiotic systems of representation is not only to designate mathematical objects or to com- municate but also to ... Research design. We believe ...
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
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,
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
Connes, Alain
1994-01-01
This English version of the path-breaking French book on this subject gives the definitive treatment of the revolutionary approach to measure theory, geometry, and mathematical physics developed by Alain Connes. Profusely illustrated and invitingly written, this book is ideal for anyone who wants to know what noncommutative geometry is, what it can do, or how it can be used in various areas of mathematics, quantization, and elementary particles and fields.Key Features* First full treatment of the subject and its applications* Written by the pioneer of this field* Broad applications in mathemat
Indian Academy of Sciences (India)
mathematicians are trained to use very precise language, and so find it hard to simplify and state .... thing. If you take a plane on which there are two such triangles which enjoy the above ... within this geometry to simplify things if needed.
Geometry -----------~--------------RESONANCE
Indian Academy of Sciences (India)
Parallel: A pair of lines in a plane is said to be parallel if they do not meet. Mathematicians were at war ... Subsequently, Poincare, Klein, Beltrami and others refined non-. Euclidean geometry. ... plane divides the plane into two half planes and.
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...
International Nuclear Information System (INIS)
Strominger, A.
1990-01-01
A special manifold is an allowed target manifold for the vector multiplets of D=4, N=2 supergravity. These manifolds are of interest for string theory because the moduli spaces of Calabi-Yau threefolds and c=9, (2,2) conformal field theories are special. Previous work has given a local, coordinate-dependent characterization of special geometry. A global description of special geometries is given herein, and their properties are studied. A special manifold M of complex dimension n is characterized by the existence of a holomorphic Sp(2n+2,R)xGL(1,C) vector bundle over M with a nowhere-vanishing holomorphic section Ω. The Kaehler potential on M is the logarithm of the Sp(2n+2,R) invariant norm of Ω. (orig.)
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
Directory of Open Access Journals (Sweden)
Roberto De Rubertis
2012-06-01
Full Text Available This article will discuss about the physiological genesis of representation and then it will illustrate the developments, especially in evolutionary perspective, and it will show how these are mainly a result of accidental circumstances, rather than of deliberate intention of improvement. In particular, it will be argue that the representation has behaved like a meme that has arrived to its own progressive evolution coming into symbiosis with the different cultures in which it has spread, and using in this activity human work “unconsciously”. Finally it will be shown how in this action the geometry is an element key, linked to representation both to construct images using graphics operations and to erect buildings using concrete operations.
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
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
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
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
Manipulation of volumetric solids with applications to sculpting
DEFF Research Database (Denmark)
Bærentzen, Jakob Andreas
2002-01-01
that it is reasonable to classify the tools in a sculpting system according to whether the tools tend to deform the sculpted object or work according to the paradigm of Constructive Solid Geometry (CSG). Existing volume sculpting systems are surveyed, and it is found that almost all systems provide sculpting tools...... representation where the meaning of a voxel is shortest distance. The deformative tools are based on a specialization of the Level Set Method. The main advantage of using the Level Set Method is that it is a very generic technique as opposed to methods previously proposed. The main task here has been to restrict....... The most important disadvantage of the volume representation is its lack of support for features at different scales. By choosing a volume representation, we implicitly choose a scale, and features that are very small with respect to that scale are essentially un-representable. As a solution, I propose...
DEFF Research Database (Denmark)
Wulf-Andersen, Trine Østergaard
2012-01-01
, 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...
Guide to Computational Geometry Processing
DEFF Research Database (Denmark)
Bærentzen, Jakob Andreas; Gravesen, Jens; Anton, François
be processed before it is useful. This Guide to Computational Geometry Processing reviews the algorithms for processing geometric data, with a practical focus on important techniques not covered by traditional courses on computer vision and computer graphics. This is balanced with an introduction...... to the theoretical and mathematical underpinnings of each technique, enabling the reader to not only implement a given method, but also to understand the ideas behind it, its limitations and its advantages. Topics and features: Presents an overview of the underlying mathematical theory, covering vector spaces......, metric space, affine spaces, differential geometry, and finite difference methods for derivatives and differential equations Reviews geometry representations, including polygonal meshes, splines, and subdivision surfaces Examines techniques for computing curvature from polygonal meshes Describes...
Nonperturbative quantum geometries
International Nuclear Information System (INIS)
Jacobson, T.; California Univ., Santa Barbara; Smolin, L.; California Univ., Santa Barbara
1988-01-01
Using the self-dual representation of quantum general relativity, based on Ashtekar's new phase space variables, we present an infinite dimensional family of quantum states of the gravitational field which are exactly annihilated by the hamiltonian constraint. These states are constructed from Wilson loops for Ashtekar's connection (which is the spatial part of the left handed spin connection). We propose a new regularization procedure which allows us to evaluate the action of the hamiltonian constraint on these states. Infinite linear combinations of these states which are formally annihilated by the diffeomorphism constraints as well are also described. These are explicit examples of physical states of the gravitational field - and for the compact case are exact zero eigenstates of the hamiltonian of quantum general relativity. Several different approaches to constructing diffeomorphism invariant states in the self dual representation are also described. The physical interpretation of the states described here is discussed. However, as we do not yet know the physical inner product, any interpretation is at this stage speculative. Nevertheless, this work suggests that quantum geometry at Planck scales might be much simpler when explored in terms of the parallel transport of left-handed spinors than when explored in terms of the three metric. (orig.)
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
CAD-based automatic modeling method for Geant4 geometry model through MCAM
International Nuclear Information System (INIS)
Wang, D.; Nie, F.; Wang, G.; Long, P.; LV, Z.
2013-01-01
The full text of publication follows. Geant4 is a widely used Monte Carlo transport simulation package. Before calculating using Geant4, the calculation model need be established which could be described by using Geometry Description Markup Language (GDML) or C++ language. However, it is time-consuming and error-prone to manually describe the models by GDML. Automatic modeling methods have been developed recently, but there are some problems that exist in most present modeling programs, specially some of them were not accurate or adapted to specifically CAD format. To convert the GDML format models to CAD format accurately, a Geant4 Computer Aided Design (CAD) based modeling method was developed for automatically converting complex CAD geometry model into GDML geometry model. The essence of this method was dealing with CAD model represented with boundary representation (B-REP) and GDML model represented with constructive solid geometry (CSG). At first, CAD model was decomposed to several simple solids which had only one close shell. And then the simple solid was decomposed to convex shell set. Then corresponding GDML convex basic solids were generated by the boundary surfaces getting from the topological characteristic of a convex shell. After the generation of these solids, GDML model was accomplished with series boolean operations. This method was adopted in CAD/Image-based Automatic Modeling Program for Neutronics and Radiation Transport (MCAM), and tested with several models including the examples in Geant4 install package. The results showed that this method could convert standard CAD model accurately, and can be used for Geant4 automatic modeling. (authors)
Weyl geometry and the nonlinear mechanics of distributed point defects
Yavari, A.; Goriely, A.
2012-01-01
The residual stress field of a nonlinear elastic solid with a spherically symmetric distribution of point defects is obtained explicitly using methods from differential geometry. The material manifold of a solid with distributed point defects
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.
DEFF Research Database (Denmark)
Photography not only represents space. Space is produced photographically. Since its inception in the 19th century, photography has brought to light a vast array of represented subjects. Always situated in some spatial order, photographic representations have been operatively underpinned by social...... 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...... possibilities, and genre distinctions. Presenting several distinct ways of producing space photographically, this book opens a new and important field of inquiry for photography research....
DEFF Research Database (Denmark)
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...
International Nuclear Information System (INIS)
Hook, D W
2008-01-01
applications of the geometric approach. The first four chapters contain the standard mathematics required to understand the rest of the material presented: specific areas in colour theory, set theory, probability theory, differential geometry and projective geometry are all covered with an eye to the material that follows. Chapter 5 starts the first real discussion of quantum theory in GQS and serves as an elegant, succinct introduction to the geometry which underlies quantum theory. This may be the most worthwhile chapter for the casual reader who wants to understand the key ideas in this field. Chapter 6 builds on the discussion in Chapter 5, introducing a group theoretic approach to understand coherent states and Chapter 7 describes a geometric tool in the form of an approach to complex projective geometry called 'the stellar representation'. Chapter 8 returns to a more purely quantum mechanical discussion as the authors turn to study the space of density matrices. This chapter completes the discussion which started in Chapter 5. Chapter 9 begins the part of the book concerned with applications of the geometric approach. From this point on the book aims, specifically, to prepare the reader for the material in Chapter 15 beginning with a discussion on the purification of mixed quantum states. In the succeeding chapters a definite choice has been made to present a geometric approach to certain quantum information problems. For example, Chapter 10 contains an extremely well formulated discussion of measurement and positive operator-valued measures with several well illustrated examples and Chapter 11 reopens the discussion of density matrices. Entropy and majorization are again revisited in Chapter 12 in much greater detail than in previous chapters. Chapters 13 and 14 concern themselves with a discussion of various metrics and their relation to the problem of distinguishing between probability distributions and their suitability as probability measures. (book review)
Silva, Alessandro
1993-01-01
The papers in this wide-ranging collection report on the results of investigations from a number of linked disciplines, including complex algebraic geometry, complex analytic geometry of manifolds and spaces, and complex differential geometry.
Eisenhart, Luther Pfahler
2005-01-01
This concise text by a prominent mathematician deals chiefly with manifolds dominated by the geometry of paths. Topics include asymmetric and symmetric connections, the projective geometry of paths, and the geometry of sub-spaces. 1927 edition.
International Nuclear Information System (INIS)
Gurevich, L.Eh.; Gliner, Eh.B.
1978-01-01
Problems of investigating the Universe space-time geometry are described on a popular level. Immediate space-time geometries, corresponding to three cosmologic models are considered. Space-time geometry of a closed model is the spherical Riemann geonetry, of an open model - is the Lobachevskij geometry; and of a plane model - is the Euclidean geometry. The Universe real geometry in the contemporary epoch of development is based on the data testifying to the fact that the Universe is infinitely expanding
Fast rendering of scanned room geometries
DEFF Research Database (Denmark)
Olesen, Søren Krarup; Markovic, Milos; Hammershøi, Dorte
2014-01-01
Room acoustics are rendered in Virtual Realities based on models of the real world. These are typically rather coarse representations of the true geometry resulting in room impulse responses with a lack of natural detail. This problem can be overcome by using data scanned by sensors, such as e...
Geometry of supersymmetric gauge theories
International Nuclear Information System (INIS)
Gieres, F.
1988-01-01
This monograph gives a detailed and pedagogical account of the geometry of rigid superspace and supersymmetric Yang-Mills theories. While the core of the text is concerned with the classical theory, the quantization and anomaly problem are briefly discussed following a comprehensive introduction to BRS differential algebras and their field theoretical applications. Among the treated topics are invariant forms and vector fields on superspace, the matrix-representation of the super-Poincare group, invariant connections on reductive homogeneous spaces and the supermetric approach. Various aspects of the subject are discussed for the first time in textbook and are consistently presented in a unified geometric formalism
DEFF Research Database (Denmark)
Mullins, Michael
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...... 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...... representation? How is virtual reality used in public participation and how do virtual environments affect participatory decision making? How does VR thus affect the physical world of built environment? Given the practical collaborative possibilities of immersive technology, how can they best be implemented...
Computer aided surface representation
Energy Technology Data Exchange (ETDEWEB)
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.
Granular flows in constrained geometries
Murthy, Tejas; Viswanathan, Koushik
Confined geometries are widespread in granular processing applications. The deformation and flow fields in such a geometry, with non-trivial boundary conditions, determine the resultant mechanical properties of the material (local porosity, density, residual stresses etc.). We present experimental studies of deformation and plastic flow of a prototypical granular medium in different nontrivial geometries- flat-punch compression, Couette-shear flow and a rigid body sliding past a granular half-space. These geometries represent simplified scaled-down versions of common industrial configurations such as compaction and dredging. The corresponding granular flows show a rich variety of flow features, representing the entire gamut of material types, from elastic solids (beam buckling) to fluids (vortex-formation, boundary layers) and even plastically deforming metals (dead material zone, pile-up). The effect of changing particle-level properties (e.g., shape, size, density) on the observed flows is also explicitly demonstrated. Non-smooth contact dynamics particle simulations are shown to reproduce some of the observed flow features quantitatively. These results showcase some central challenges facing continuum-scale constitutive theories for dynamic granular flows.
Computational geometry for reactor applications
International Nuclear Information System (INIS)
Brown, F.B.; Bischoff, F.G.
1988-01-01
Monte Carlo codes for simulating particle transport involve three basic computational sections: a geometry package for locating particles and computing distances to regional boundaries, a physics package for analyzing interactions between particles and problem materials, and an editing package for determining event statistics and overall results. This paper describes the computational geometry methods in RACER, a vectorized Monte Carlo code used for reactor physics analysis, so that comparisons may be made with techniques used in other codes. The principal applications for RACER are eigenvalue calculations and power distributions associated with reactor core physics analysis. Successive batches of neutrons are run until convergence and acceptable confidence intervals are obtained, with typical problems involving >10 6 histories. As such, the development of computational geometry methods has emphasized two basic needs: a flexible but compact geometric representation that permits accurate modeling of reactor core details and efficient geometric computation to permit very large numbers of histories to be run. The current geometric capabilities meet these needs effectively, supporting a variety of very large and demanding applications
Meyer, Walter J
2006-01-01
Meyer''s Geometry and Its Applications, Second Edition, combines traditional geometry with current ideas to present a modern approach that is grounded in real-world applications. It balances the deductive approach with discovery learning, and introduces axiomatic, Euclidean geometry, non-Euclidean geometry, and transformational geometry. The text integrates applications and examples throughout and includes historical notes in many chapters. The Second Edition of Geometry and Its Applications is a significant text for any college or university that focuses on geometry''s usefulness in other disciplines. It is especially appropriate for engineering and science majors, as well as future mathematics teachers.* Realistic applications integrated throughout the text, including (but not limited to): - Symmetries of artistic patterns- Physics- Robotics- Computer vision- Computer graphics- Stability of architectural structures- Molecular biology- Medicine- Pattern recognition* Historical notes included in many chapters...
Indian Academy of Sciences (India)
algebraic geometry but also in related fields like number theory. ... every vector bundle on the affine space is trivial. (equivalently ... les on a compact Riemann surface to unitary rep- ... tial geometry and topology and was generalised in.
International Nuclear Information System (INIS)
Sloane, Peter
2007-01-01
We adapt the spinorial geometry method introduced in [J. Gillard, U. Gran and G. Papadopoulos, 'The spinorial geometry of supersymmetric backgrounds,' Class. Quant. Grav. 22 (2005) 1033 [ (arXiv:hep-th/0410155)
Energy Technology Data Exchange (ETDEWEB)
Sloane, Peter [Department of Mathematics, King' s College, University of London, Strand, London WC2R 2LS (United Kingdom)
2007-09-15
We adapt the spinorial geometry method introduced in [J. Gillard, U. Gran and G. Papadopoulos, 'The spinorial geometry of supersymmetric backgrounds,' Class. Quant. Grav. 22 (2005) 1033 [ (arXiv:hep-th/0410155)
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.
Geometry essentials for dummies
Ryan, Mark
2011-01-01
Just the critical concepts you need to score high in geometry This practical, friendly guide focuses on critical concepts taught in a typical geometry course, from the properties of triangles, parallelograms, circles, and cylinders, to the skills and strategies you need to write geometry proofs. Geometry Essentials For Dummies is perfect for cramming or doing homework, or as a reference for parents helping kids study for exams. Get down to the basics - get a handle on the basics of geometry, from lines, segments, and angles, to vertices, altitudes, and diagonals Conque
Arithmetic noncommutative geometry
Marcolli, Matilde
2005-01-01
Arithmetic noncommutative geometry denotes the use of ideas and tools from the field of noncommutative geometry, to address questions and reinterpret in a new perspective results and constructions from number theory and arithmetic algebraic geometry. This general philosophy is applied to the geometry and arithmetic of modular curves and to the fibers at archimedean places of arithmetic surfaces and varieties. The main reason why noncommutative geometry can be expected to say something about topics of arithmetic interest lies in the fact that it provides the right framework in which the tools of geometry continue to make sense on spaces that are very singular and apparently very far from the world of algebraic varieties. This provides a way of refining the boundary structure of certain classes of spaces that arise in the context of arithmetic geometry, such as moduli spaces (of which modular curves are the simplest case) or arithmetic varieties (completed by suitable "fibers at infinity"), by adding boundaries...
International Nuclear Information System (INIS)
Choi, Sung Hoon; Kwark, Min Su; Shim, Hyung Jin
2012-01-01
As The Monte Carlo (MC) particle transport analysis for a complex system such as research reactor, accelerator, and fusion facility may require accurate modeling of the complicated geometry. Its manual modeling by using the text interface of a MC code to define the geometrical objects is tedious, lengthy and error-prone. This problem can be overcome by taking advantage of modeling capability of the computer aided design (CAD) system. There have been two kinds of approaches to develop MC code systems utilizing the CAD data: the external format conversion and the CAD kernel imbedded MC simulation. The first approach includes several interfacing programs such as McCAD, MCAM, GEOMIT etc. which were developed to automatically convert the CAD data into the MCNP geometry input data. This approach makes the most of the existing MC codes without any modifications, but implies latent data inconsistency due to the difference of the geometry modeling system. In the second approach, a MC code utilizes the CAD data for the direct particle tracking or the conversion to an internal data structure of the constructive solid geometry (CSG) and/or boundary representation (B-rep) modeling with help of a CAD kernel. MCNP-BRL and OiNC have demonstrated their capabilities of the CAD-based MC simulations. Recently we have developed a CAD-based geometry processing module for the MC particle simulation by using the OpenCASCADE (OCC) library. In the developed module, CAD data can be used for the particle tracking through primitive CAD surfaces (hereafter the CAD-based tracking) or the internal conversion to the CSG data structure. In this paper, the performances of the text-based model, the CAD-based tracking, and the internal CSG conversion are compared by using an in-house MC code, McSIM, equipped with the developed CAD-based geometry processing module
Attention and Representational Momentum
Hayes, Amy; Freyd, Jennifer J
1995-01-01
Representational momentum, the tendency for memory to be distorted in the direction of an implied transformation, suggests that dynamics are an intrinsic part of perceptual representations. We examined the effect of attention on dynamic representation by testing for representational momentum under conditions of distraction. Forward memory shifts increase when attention is divided. Attention may be involved in halting but not in maintaining dynamic representations.
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.
METHODS FOR THE REPRESENTATION OF THE HELICOIDAL SURFACE
Directory of Open Access Journals (Sweden)
SCURTU Liviu-Iacob
2017-05-01
Full Text Available In this paper there are presented the graphical methods to determine the parameters of an helicoidal stairs. The first part of this paper shows the used methods to generate the helicoidal curves using descriptive geometry methods. It has represented the state of the art of the generation of a helical surface studies. The second part of this study shows the helical stairs surface representation using descriptive geometry methods. For the representation of the helicoidal stairs are used two projections, the front and top view. A method of the stairs representation is solved using CAD modelling dedicated software. Following the helical surface representation in both methods, has been achieved a comparative study by using two representation methods. Conclusions about these two representation methods are presented in the end of this paper.
Algorithms in Algebraic Geometry
Dickenstein, Alicia; Sommese, Andrew J
2008-01-01
In the last decade, there has been a burgeoning of activity in the design and implementation of algorithms for algebraic geometric computation. Some of these algorithms were originally designed for abstract algebraic geometry, but now are of interest for use in applications and some of these algorithms were originally designed for applications, but now are of interest for use in abstract algebraic geometry. The workshop on Algorithms in Algebraic Geometry that was held in the framework of the IMA Annual Program Year in Applications of Algebraic Geometry by the Institute for Mathematics and Its
O'Leary, Michael
2010-01-01
Guides readers through the development of geometry and basic proof writing using a historical approach to the topic. In an effort to fully appreciate the logic and structure of geometric proofs, Revolutions of Geometry places proofs into the context of geometry's history, helping readers to understand that proof writing is crucial to the job of a mathematician. Written for students and educators of mathematics alike, the book guides readers through the rich history and influential works, from ancient times to the present, behind the development of geometry. As a result, readers are successfull
Fundamental concepts of geometry
Meserve, Bruce E
1983-01-01
Demonstrates relationships between different types of geometry. Provides excellent overview of the foundations and historical evolution of geometrical concepts. Exercises (no solutions). Includes 98 illustrations.
Developments in special geometry
International Nuclear Information System (INIS)
Mohaupt, Thomas; Vaughan, Owen
2012-01-01
We review the special geometry of N = 2 supersymmetric vector and hypermultiplets with emphasis on recent developments and applications. A new formulation of the local c-map based on the Hesse potential and special real coordinates is presented. Other recent developments include the Euclidean version of special geometry, and generalizations of special geometry to non-supersymmetric theories. As applications we discuss the proof that the local r-map and c-map preserve geodesic completeness, and the construction of four- and five-dimensional static solutions through dimensional reduction over time. The shared features of the real, complex and quaternionic version of special geometry are stressed throughout.
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 of multihadron production
Energy Technology Data Exchange (ETDEWEB)
Bjorken, J.D.
1994-10-01
This summary talk only reviews a small sample of topics featured at this symposium: Introduction; The Geometry and Geography of Phase space; Space-Time Geometry and HBT; Multiplicities, Intermittency, Correlations; Disoriented Chiral Condensate; Deep Inelastic Scattering at HERA; and Other Contributions.
1996-01-01
Designs and Finite Geometries brings together in one place important contributions and up-to-date research results in this important area of mathematics. Designs and Finite Geometries serves as an excellent reference, providing insight into some of the most important research issues in the field.
Geometry of multihadron production
International Nuclear Information System (INIS)
Bjorken, J.D.
1994-10-01
This summary talk only reviews a small sample of topics featured at this symposium: Introduction; The Geometry and Geography of Phase space; Space-Time Geometry and HBT; Multiplicities, Intermittency, Correlations; Disoriented Chiral Condensate; Deep Inelastic Scattering at HERA; and Other Contributions
Morris, Barbara H.
2004-01-01
This article describes a geometry project that used the beauty of stained-glass-window designs to teach middle school students about geometric figures and concepts. Three honors prealgebra teachers and a middle school mathematics gifted intervention specialist created a geometry project that covered the curriculum and also assessed students'…
Energy Technology Data Exchange (ETDEWEB)
Grotz, Andreas
2011-10-07
In this thesis, a formulation of a Lorentzian quantum geometry based on the framework of causal fermion systems is proposed. After giving the general definition of causal fermion systems, we deduce space-time as a topological space with an underlying causal structure. Restricting attention to systems of spin dimension two, we derive the objects of our quantum geometry: the spin space, the tangent space endowed with a Lorentzian metric, connection and curvature. In order to get the correspondence to classical differential geometry, we construct examples of causal fermion systems by regularizing Dirac sea configurations in Minkowski space and on a globally hyperbolic Lorentzian manifold. When removing the regularization, the objects of our quantum geometry reduce to the common objects of spin geometry on Lorentzian manifolds, up to higher order curvature corrections.
Methods of information geometry
Amari, Shun-Ichi
2000-01-01
Information geometry provides the mathematical sciences with a new framework of analysis. It has emerged from the investigation of the natural differential geometric structure on manifolds of probability distributions, which consists of a Riemannian metric defined by the Fisher information and a one-parameter family of affine connections called the \\alpha-connections. The duality between the \\alpha-connection and the (-\\alpha)-connection together with the metric play an essential role in this geometry. This kind of duality, having emerged from manifolds of probability distributions, is ubiquitous, appearing in a variety of problems which might have no explicit relation to probability theory. Through the duality, it is possible to analyze various fundamental problems in a unified perspective. The first half of this book is devoted to a comprehensive introduction to the mathematical foundation of information geometry, including preliminaries from differential geometry, the geometry of manifolds or probability d...
International Nuclear Information System (INIS)
Grotz, Andreas
2011-01-01
In this thesis, a formulation of a Lorentzian quantum geometry based on the framework of causal fermion systems is proposed. After giving the general definition of causal fermion systems, we deduce space-time as a topological space with an underlying causal structure. Restricting attention to systems of spin dimension two, we derive the objects of our quantum geometry: the spin space, the tangent space endowed with a Lorentzian metric, connection and curvature. In order to get the correspondence to classical differential geometry, we construct examples of causal fermion systems by regularizing Dirac sea configurations in Minkowski space and on a globally hyperbolic Lorentzian manifold. When removing the regularization, the objects of our quantum geometry reduce to the common objects of spin geometry on Lorentzian manifolds, up to higher order curvature corrections.
Geometry on the space of geometries
International Nuclear Information System (INIS)
Christodoulakis, T.; Zanelli, J.
1988-06-01
We discuss the geometric structure of the configuration space of pure gravity. This is an infinite dimensional manifold, M, where each point represents one spatial geometry g ij (x). The metric on M is dictated by geometrodynamics, and from it, the Christoffel symbols and Riemann tensor can be found. A ''free geometry'' tracing a geodesic on the manifold describes the time evolution of space in the strong gravity limit. In a regularization previously introduced by the authors, it is found that M does not have the same dimensionality, D, everywhere, and that D is not a scalar, although it is covariantly constant. In this regularization, it is seen that the path integral measure can be absorbed in a renormalization of the cosmological constant. (author). 19 refs
International Nuclear Information System (INIS)
Fonseca, Gabriel Paiva; Yoriyaz, Hélio; Landry, Guillaume; White, Shane; Reniers, Brigitte; Verhaegen, Frank; D’Amours, Michel; Beaulieu, Luc
2014-01-01
Accounting for brachytherapy applicator attenuation is part of the recommendations from the recent report of AAPM Task Group 186. To do so, model based dose calculation algorithms require accurate modelling of the applicator geometry. This can be non-trivial in the case of irregularly shaped applicators such as the Fletcher Williamson gynaecological applicator or balloon applicators with possibly irregular shapes employed in accelerated partial breast irradiation (APBI) performed using electronic brachytherapy sources (EBS). While many of these applicators can be modelled using constructive solid geometry (CSG), the latter may be difficult and time-consuming. Alternatively, these complex geometries can be modelled using tessellated geometries such as tetrahedral meshes (mesh geometries (MG)). Recent versions of Monte Carlo (MC) codes Geant4 and MCNP6 allow for the use of MG. The goal of this work was to model a series of applicators relevant to brachytherapy using MG. Applicators designed for 192 Ir sources and 50 kV EBS were studied; a shielded vaginal applicator, a shielded Fletcher Williamson applicator and an APBI balloon applicator. All applicators were modelled in Geant4 and MCNP6 using MG and CSG for dose calculations. CSG derived dose distributions were considered as reference and used to validate MG models by comparing dose distribution ratios. In general agreement within 1% for the dose calculations was observed for all applicators between MG and CSG and between codes when considering volumes inside the 25% isodose surface. When compared to CSG, MG required longer computation times by a factor of at least 2 for MC simulations using the same code. MCNP6 calculation times were more than ten times shorter than Geant4 in some cases. In conclusion we presented methods allowing for high fidelity modelling with results equivalent to CSG. To the best of our knowledge MG offers the most accurate representation of an irregular APBI balloon applicator. (paper)
Factorizations and physical representations
International Nuclear Information System (INIS)
Revzen, M; Khanna, F C; Mann, A; Zak, J
2006-01-01
A Hilbert space in M dimensions is shown explicitly to accommodate representations that reflect the decomposition of M into prime numbers. Representations that exhibit the factorization of M into two relatively prime numbers: the kq representation (Zak J 1970 Phys. Today 23 51), and related representations termed q 1 q 2 representations (together with their conjugates) are analysed, as well as a representation that exhibits the complete factorization of M. In this latter representation each quantum number varies in a subspace that is associated with one of the prime numbers that make up M
The Kerr geometry, complex world lines and hyperbolic strings
International Nuclear Information System (INIS)
Burinskii, A.Ya.
1994-01-01
In the Lind-Newman representation the Kerr geometry is created by a source moving along an analytical complex world line. An equivalence of the complex world line and complex (hyperbolic) string is considered. Therefore the hyperbolic string may play the role of the complex source of the Kerr geometry. The Kerr solution with the complex string source acquires Regge behavior of the angular momentum. (orig.)
Complex and symplectic geometry
Medori, Costantino; Tomassini, Adriano
2017-01-01
This book arises from the INdAM Meeting "Complex and Symplectic Geometry", which was held in Cortona in June 2016. Several leading specialists, including young researchers, in the field of complex and symplectic geometry, present the state of the art of their research on topics such as the cohomology of complex manifolds; analytic techniques in Kähler and non-Kähler geometry; almost-complex and symplectic structures; special structures on complex manifolds; and deformations of complex objects. The work is intended for researchers in these areas.
Kulczycki, Stefan
2008-01-01
This accessible approach features two varieties of proofs: stereometric and planimetric, as well as elementary proofs that employ only the simplest properties of the plane. A short history of geometry precedes a systematic exposition of the principles of non-Euclidean geometry.Starting with fundamental assumptions, the author examines the theorems of Hjelmslev, mapping a plane into a circle, the angle of parallelism and area of a polygon, regular polygons, straight lines and planes in space, and the horosphere. Further development of the theory covers hyperbolic functions, the geometry of suff
Teacher spatial skills are linked to differences in geometry instruction.
Otumfuor, Beryl Ann; Carr, Martha
2017-12-01
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.
Geometry of the Mesopotamian "ecliptic"
Kurtik, G. E.
2018-02-01
The article deals with the history of ecliptic as an element of the mathematical astronomy in Ancient Mesopotamia. It contains data from the cuneiform sources of the 2nd - 1st millennia BC and from the modern studies shedding light on the following three questions: 1) the idea of the celestial sphere in Mesopotamian astronomy; 2) the geometric representations associated with the ecliptic; 3) the positions of the ecliptic relative to the fixed stars and to the Sun. It is shown that although we do not have solid evidences, however, there are serious reasons to believe that in the Seleucid period in the mathematical astronomy and astrology the ecliptic was conceived geometrically as a circle divided into 12 equal parts. It is also shown that in this period the ecliptic was not yet identified with the projection of annual path of the Sun to the celestial sphere.
Roe, John
2003-01-01
Coarse geometry is the study of spaces (particularly metric spaces) from a 'large scale' point of view, so that two spaces that look the same from a great distance are actually equivalent. This point of view is effective because it is often true that the relevant geometric properties of metric spaces are determined by their coarse geometry. Two examples of important uses of coarse geometry are Gromov's beautiful notion of a hyperbolic group and Mostow's proof of his famous rigidity theorem. The first few chapters of the book provide a general perspective on coarse structures. Even when only metric coarse structures are in view, the abstract framework brings the same simplification as does the passage from epsilons and deltas to open sets when speaking of continuity. The middle section reviews notions of negative curvature and rigidity. Modern interest in large scale geometry derives in large part from Mostow's rigidity theorem and from Gromov's subsequent 'large scale' rendition of the crucial properties of n...
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...
Kollár, János
1997-01-01
This volume contains the lectures presented at the third Regional Geometry Institute at Park City in 1993. The lectures provide an introduction to the subject, complex algebraic geometry, making the book suitable as a text for second- and third-year graduate students. The book deals with topics in algebraic geometry where one can reach the level of current research while starting with the basics. Topics covered include the theory of surfaces from the viewpoint of recent higher-dimensional developments, providing an excellent introduction to more advanced topics such as the minimal model program. Also included is an introduction to Hodge theory and intersection homology based on the simple topological ideas of Lefschetz and an overview of the recent interactions between algebraic geometry and theoretical physics, which involve mirror symmetry and string theory.
DEFF Research Database (Denmark)
Kokkendorff, Simon Lyngby
2002-01-01
The subject of this Ph.D.-thesis is somewhere in between continuous and discrete geometry. Chapter 2 treats the geometry of finite point sets in semi-Riemannian hyperquadrics,using a matrix whose entries are a trigonometric function of relative distances in a given point set. The distance...... to the geometry of a simplex in a semi-Riemannian hyperquadric. In chapter 3 we study which finite metric spaces that are realizable in a hyperbolic space in the limit where curvature goes to -∞. We show that such spaces are the so called leaf spaces, the set of degree 1 vertices of weighted trees. We also...... establish results on the limiting geometry of such an isometrically realized leaf space simplex in hyperbolic space, when curvature goes to -∞. Chapter 4 discusses negative type of metric spaces. We give a measure theoretic treatment of this concept and related invariants. The theory developed...
Busemann, Herbert
2005-01-01
A comprehensive approach to qualitative problems in intrinsic differential geometry, this text examines Desarguesian spaces, perpendiculars and parallels, covering spaces, the influence of the sign of the curvature on geodesics, more. 1955 edition. Includes 66 figures.
Tabachnikov, Serge
2005-01-01
Mathematical billiards describe the motion of a mass point in a domain with elastic reflections off the boundary or, equivalently, the behavior of rays of light in a domain with ideally reflecting boundary. From the point of view of differential geometry, the billiard flow is the geodesic flow on a manifold with boundary. This book is devoted to billiards in their relation with differential geometry, classical mechanics, and geometrical optics. The topics covered include variational principles of billiard motion, symplectic geometry of rays of light and integral geometry, existence and nonexistence of caustics, optical properties of conics and quadrics and completely integrable billiards, periodic billiard trajectories, polygonal billiards, mechanisms of chaos in billiard dynamics, and the lesser-known subject of dual (or outer) billiards. The book is based on an advanced undergraduate topics course (but contains more material than can be realistically taught in one semester). Although the minimum prerequisit...
Introduction to tropical geometry
Maclagan, Diane
2015-01-01
Tropical geometry is a combinatorial shadow of algebraic geometry, offering new polyhedral tools to compute invariants of algebraic varieties. It is based on tropical algebra, where the sum of two numbers is their minimum and the product is their sum. This turns polynomials into piecewise-linear functions, and their zero sets into polyhedral complexes. These tropical varieties retain a surprising amount of information about their classical counterparts. Tropical geometry is a young subject that has undergone a rapid development since the beginning of the 21st century. While establishing itself as an area in its own right, deep connections have been made to many branches of pure and applied mathematics. This book offers a self-contained introduction to tropical geometry, suitable as a course text for beginning graduate students. Proofs are provided for the main results, such as the Fundamental Theorem and the Structure Theorem. Numerous examples and explicit computations illustrate the main concepts. Each of t...
Rudiments of algebraic geometry
Jenner, WE
2017-01-01
Aimed at advanced undergraduate students of mathematics, this concise text covers the basics of algebraic geometry. Topics include affine spaces, projective spaces, rational curves, algebraic sets with group structure, more. 1963 edition.
Implosions and hypertoric geometry
DEFF Research Database (Denmark)
Dancer, A.; Kirwan, F.; Swann, A.
2013-01-01
The geometry of the universal hyperkahler implosion for SU (n) is explored. In particular, we show that the universal hyperkahler implosion naturally contains a hypertoric variety described in terms of quivers. Furthermore, we discuss a gauge theoretic approach to hyperkahler implosion.......The geometry of the universal hyperkahler implosion for SU (n) is explored. In particular, we show that the universal hyperkahler implosion naturally contains a hypertoric variety described in terms of quivers. Furthermore, we discuss a gauge theoretic approach to hyperkahler implosion....
Intermediate algebra & analytic geometry
Gondin, William R
1967-01-01
Intermediate Algebra & Analytic Geometry Made Simple focuses on the principles, processes, calculations, and methodologies involved in intermediate algebra and analytic geometry. The publication first offers information on linear equations in two unknowns and variables, functions, and graphs. Discussions focus on graphic interpretations, explicit and implicit functions, first quadrant graphs, variables and functions, determinate and indeterminate systems, independent and dependent equations, and defective and redundant systems. The text then examines quadratic equations in one variable, system
Ceresole, Anna; Gnecchi, Alessandra; Marrani, Alessio
2013-01-01
We analyze some properties of the four dimensional supergravity theories which originate from five dimensions upon reduction. They generalize to N>2 extended supersymmetries the d-geometries with cubic prepotentials, familiar from N=2 special K\\"ahler geometry. We emphasize the role of a suitable parametrization of the scalar fields and the corresponding triangular symplectic basis. We also consider applications to the first order flow equations for non-BPS extremal black holes.
International Nuclear Information System (INIS)
Osborne, I; Brownson, E; Eulisse, G; Jones, C D; Sexton-Kennedy, E; Lange, D J
2014-01-01
CMS faces real challenges with upgrade of the CMS detector through 2020 and beyond. One of the challenges, from the software point of view, is managing upgrade simulations with the same software release as the 2013 scenario. We present the CMS geometry description software model, its integration with the CMS event setup and core software. The CMS geometry configuration and selection is implemented in Python. The tools collect the Python configuration fragments into a script used in CMS workflow. This flexible and automated geometry configuration allows choosing either transient or persistent version of the same scenario and specific version of the same scenario. We describe how the geometries are integrated and validated, and how we define and handle different geometry scenarios in simulation and reconstruction. We discuss how to transparently manage multiple incompatible geometries in the same software release. Several examples are shown based on current implementation assuring consistent choice of scenario conditions. The consequences and implications for multiple/different code algorithms are discussed.
Software Geometry in Simulations
Alion, Tyler; Viren, Brett; Junk, Tom
2015-04-01
The Long Baseline Neutrino Experiment (LBNE) involves many detectors. The experiment's near detector (ND) facility, may ultimately involve several detectors. The far detector (FD) will be significantly larger than any other Liquid Argon (LAr) detector yet constructed; many prototype detectors are being constructed and studied to motivate a plethora of proposed FD designs. Whether it be a constructed prototype or a proposed ND/FD design, every design must be simulated and analyzed. This presents a considerable challenge to LBNE software experts; each detector geometry must be described to the simulation software in an efficient way which allows for multiple authors to easily collaborate. Furthermore, different geometry versions must be tracked throughout their use. We present a framework called General Geometry Description (GGD), written and developed by LBNE software collaborators for managing software to generate geometries. Though GGD is flexible enough to be used by any experiment working with detectors, we present it's first use in generating Geometry Description Markup Language (GDML) files to interface with LArSoft, a framework of detector simulations, event reconstruction, and data analyses written for all LAr technology users at Fermilab. Brett is the other of the framework discussed here, the General Geometry Description (GGD).
Introduction to combinatorial geometry
International Nuclear Information System (INIS)
Gabriel, T.A.; Emmett, M.B.
1985-01-01
The combinatorial geometry package as used in many three-dimensional multimedia Monte Carlo radiation transport codes, such as HETC, MORSE, and EGS, is becoming the preferred way to describe simple and complicated systems. Just about any system can be modeled using the package with relatively few input statements. This can be contrasted against the older style geometry packages in which the required input statements could be large even for relatively simple systems. However, with advancements come some difficulties. The users of combinatorial geometry must be able to visualize more, and, in some instances, all of the system at a time. Errors can be introduced into the modeling which, though slight, and at times hard to detect, can have devastating effects on the calculated results. As with all modeling packages, the best way to learn the combinatorial geometry is to use it, first on a simple system then on more complicated systems. The basic technique for the description of the geometry consists of defining the location and shape of the various zones in terms of the intersections and unions of geometric bodies. The geometric bodies which are generally included in most combinatorial geometry packages are: (1) box, (2) right parallelepiped, (3) sphere, (4) right circular cylinder, (5) right elliptic cylinder, (6) ellipsoid, (7) truncated right cone, (8) right angle wedge, and (9) arbitrary polyhedron. The data necessary to describe each of these bodies are given. As can be easily noted, there are some subsets included for simplicity
Geometry of the Borel - de Siebenthal discrete series
DEFF Research Database (Denmark)
Ørsted, Bent; Wolf, Joseph A
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...... 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...
Global aspects of complex geometry
Catanese, Fabrizio; Huckleberry, Alan T
2006-01-01
Present an overview of developments in Complex Geometry. This book covers topics that range from curve and surface theory through special varieties in higher dimensions, moduli theory, Kahler geometry, and group actions to Hodge theory and characteristic p-geometry.
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
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...
Parameterized combinatorial geometry modeling in Moritz
International Nuclear Information System (INIS)
Van Riper, K.A.
2005-01-01
We describe the use of named variables as surface and solid body coefficients in the Moritz geometry editing program. Variables can also be used as material numbers, cell densities, and transformation values. A variable is defined as a constant or an arithmetic combination of constants and other variables. A variable reference, such as in a surface coefficient, can be a single variable or an expression containing variables and constants. Moritz can read and write geometry models in MCNP and ITS ACCEPT format; support for other codes will be added. The geometry can be saved with either the variables in place, for modifying the models in Moritz, or with the variables evaluated for use in the transport codes. A program window shows a list of variables and provides fields for editing them. Surface coefficients and other values that use a variable reference are shown in a distinctive style on object property dialogs; associated buttons show fields for editing the reference. We discuss our use of variables in defining geometry models for shielding studies in PET clinics. When a model is parameterized through the use of variables, changes such as room dimensions, shielding layer widths, and cell compositions can be quickly achieved by changing a few numbers without requiring knowledge of the input syntax for the transport code or the tedious and error prone work of recalculating many surface or solid body coefficients. (author)
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…
Difference sets connecting algebra, combinatorics, and geometry
Moore, Emily H
2013-01-01
Difference sets belong both to group theory and to combinatorics. Studying them requires tools from geometry, number theory, and representation theory. This book lays a foundation for these topics, including a primer on representations and characters of finite groups. It makes the research literature on difference sets accessible to students who have studied linear algebra and abstract algebra, and it prepares them to do their own research. This text is suitable for an undergraduate capstone course, since it illuminates the many links among topics that the students have already studied. To this end, almost every chapter ends with a coda highlighting the main ideas and emphasizing mathematical connections. This book can also be used for self-study by anyone interested in these connections and concrete examples. An abundance of exercises, varying from straightforward to challenging, invites the reader to solve puzzles, construct proofs, and investigate problems--by hand or on a computer. Hints and solutions are...
Chemical thermodynamic representation of
International Nuclear Information System (INIS)
Lindemer, T.B.; Besmann, T.M.
1984-01-01
The entire data base for the dependence of the nonstoichiometry, x, on temperature and chemical potential of oxygen (oxygen potential) was retrieved from the literature and represented. This data base was interpreted by least-squares analysis using equations derived from the classical thermodynamic theory for the solid solution of a solute in a solvent. For hyperstoichiometric oxide at oxygen potentials more positive than -266700 + 16.5T kJ/mol, the data were best represented by a [UO 2 ]-[U 3 O 7 ] solution. For O/U ratios above 2 and oxygen potentials below this boundary, a [UO 2 ]-[U 2 O 4 . 5 ] solution represented the data. The data were represented by a [UO 2 ]-[U 1 / 3 ] solution. The resulting equations represent the experimental ln(PO 2 ) - ln(x) behavior and can be used in thermodynamic calculations to predict phase boundary compositions consistent with the literature. Collectively, the present analysis permits a mathematical representation of the behavior of the total data base
Computational synthetic geometry
Bokowski, Jürgen
1989-01-01
Computational synthetic geometry deals with methods for realizing abstract geometric objects in concrete vector spaces. This research monograph considers a large class of problems from convexity and discrete geometry including constructing convex polytopes from simplicial complexes, vector geometries from incidence structures and hyperplane arrangements from oriented matroids. It turns out that algorithms for these constructions exist if and only if arbitrary polynomial equations are decidable with respect to the underlying field. Besides such complexity theorems a variety of symbolic algorithms are discussed, and the methods are applied to obtain new mathematical results on convex polytopes, projective configurations and the combinatorics of Grassmann varieties. Finally algebraic varieties characterizing matroids and oriented matroids are introduced providing a new basis for applying computer algebra methods in this field. The necessary background knowledge is reviewed briefly. The text is accessible to stud...
Discrete and computational geometry
Devadoss, Satyan L
2011-01-01
Discrete geometry is a relatively new development in pure mathematics, while computational geometry is an emerging area in applications-driven computer science. Their intermingling has yielded exciting advances in recent years, yet what has been lacking until now is an undergraduate textbook that bridges the gap between the two. Discrete and Computational Geometry offers a comprehensive yet accessible introduction to this cutting-edge frontier of mathematics and computer science. This book covers traditional topics such as convex hulls, triangulations, and Voronoi diagrams, as well as more recent subjects like pseudotriangulations, curve reconstruction, and locked chains. It also touches on more advanced material, including Dehn invariants, associahedra, quasigeodesics, Morse theory, and the recent resolution of the Poincaré conjecture. Connections to real-world applications are made throughout, and algorithms are presented independently of any programming language. This richly illustrated textbook also fe...
Ochiai, T.; Nacher, J. C.
2011-09-01
Recently, the application of geometry and conformal mappings to artificial materials (metamaterials) has attracted the attention in various research communities. These materials, characterized by a unique man-made structure, have unusual optical properties, which materials found in nature do not exhibit. By applying the geometry and conformal mappings theory to metamaterial science, it may be possible to realize so-called "Harry Potter cloaking device". Although such a device is still in the science fiction realm, several works have shown that by using such metamaterials it may be possible to control the direction of the electromagnetic field at will. We could then make an object hidden inside of a cloaking device. Here, we will explain how to design invisibility device using differential geometry and conformal mappings.
2002-01-01
Discrete geometry investigates combinatorial properties of configurations of geometric objects. To a working mathematician or computer scientist, it offers sophisticated results and techniques of great diversity and it is a foundation for fields such as computational geometry or combinatorial optimization. This book is primarily a textbook introduction to various areas of discrete geometry. In each area, it explains several key results and methods, in an accessible and concrete manner. It also contains more advanced material in separate sections and thus it can serve as a collection of surveys in several narrower subfields. The main topics include: basics on convex sets, convex polytopes, and hyperplane arrangements; combinatorial complexity of geometric configurations; intersection patterns and transversals of convex sets; geometric Ramsey-type results; polyhedral combinatorics and high-dimensional convexity; and lastly, embeddings of finite metric spaces into normed spaces. Jiri Matousek is Professor of Com...
Zheng, Fangyang
2002-01-01
The theory of complex manifolds overlaps with several branches of mathematics, including differential geometry, algebraic geometry, several complex variables, global analysis, topology, algebraic number theory, and mathematical physics. Complex manifolds provide a rich class of geometric objects, for example the (common) zero locus of any generic set of complex polynomials is always a complex manifold. Yet complex manifolds behave differently than generic smooth manifolds; they are more coherent and fragile. The rich yet restrictive character of complex manifolds makes them a special and interesting object of study. This book is a self-contained graduate textbook that discusses the differential geometric aspects of complex manifolds. The first part contains standard materials from general topology, differentiable manifolds, and basic Riemannian geometry. The second part discusses complex manifolds and analytic varieties, sheaves and holomorphic vector bundles, and gives a brief account of the surface classifi...
Poincare ball embeddings of the optical geometry
International Nuclear Information System (INIS)
Abramowicz, M A; Bengtsson, I; Karas, V; Rosquist, K
2002-01-01
It is shown that the optical geometry of the Reissner-Nordstroem exterior metric can be embedded in a hyperbolic space all the way down to its outer horizon. The adopted embedding procedure removes a breakdown of flat-space embeddings which occurs outside the horizon, at and below the Buchdahl-Bondi limit (R/M=9/4 in the Schwarzschild case). In particular, the horizon can be captured in the optical geometry embedding diagram. Moreover, by using the compact Poincare ball representation of the hyperbolic space, the embedding diagram can cover the whole extent of radius from spatial infinity down to the horizon. Attention is drawn to the advantages of such embeddings in an appropriately curved space: this approach gives compact embeddings and it clearly distinguishes the case of an extremal black hole from a non-extremal one in terms of the topology of the embedded horizon
Stages as models of scene geometry.
Nedović, Vladimir; Smeulders, Arnold W M; Redert, André; Geusebroek, Jan-Mark
2010-09-01
Reconstruction of 3D scene geometry is an important element for scene understanding, autonomous vehicle and robot navigation, image retrieval, and 3D television. We propose accounting for the inherent structure of the visual world when trying to solve the scene reconstruction problem. Consequently, we identify geometric scene categorization as the first step toward robust and efficient depth estimation from single images. We introduce 15 typical 3D scene geometries called stages, each with a unique depth profile, which roughly correspond to a large majority of broadcast video frames. Stage information serves as a first approximation of global depth, narrowing down the search space in depth estimation and object localization. We propose different sets of low-level features for depth estimation, and perform stage classification on two diverse data sets of television broadcasts. Classification results demonstrate that stages can often be efficiently learned from low-dimensional image representations.
Webb, Jason C.; Lauret, Jerome; Perevoztchikov, Victor
2012-12-01
Increasingly detailed descriptions of complex detector geometries are required for the simulation and analysis of today's high-energy and nuclear physics experiments. As new tools for the representation of geometry models become available during the course of an experiment, a fundamental challenge arises: how best to migrate from legacy geometry codes developed over many runs to the new technologies, such as the ROOT/TGeo [1] framework, without losing touch with years of development, tuning and validation. One approach, which has been discussed within the community for a number of years, is to represent the geometry model in a higher-level language independent of the concrete implementation of the geometry. The STAR experiment has used this approach to successfully migrate its legacy GEANT 3-era geometry to an Abstract geometry Modelling Language (AgML), which allows us to create both native GEANT 3 and ROOT/TGeo implementations. The language is supported by parsers and a C++ class library which enables the automated conversion of the original source code to AgML, supports export back to the original AgSTAR[5] representation, and creates the concrete ROOT/TGeo geometry implementation used by our track reconstruction software. In this paper we present our approach, design and experience and will demonstrate physical consistency between the original AgSTAR and new AgML geometry representations.
Rumelhart, David E.; Norman, Donald A.
This paper reviews work on the representation of knowledge from within psychology and artificial intelligence. The work covers the nature of representation, the distinction between the represented world and the representing world, and significant issues concerned with propositional, analogical, and superpositional representations. Specific topics…
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
Galileo symmetries in polymer particle representation
International Nuclear Information System (INIS)
Chiou, D-W
2007-01-01
To illustrate the conceptual problems for the low-energy symmetries in the continuum of spacetime emerging from the discrete quantum geometry, Galileo symmetries are investigated in the polymer particle representation of a non-relativistic particle as a simple toy model. The complete Galileo transformations (translation, rotation and Galileo boost) are naturally defined in the polymer particle Hilbert space and Galileo symmetries are recovered with highly suppressed deviations in the low-energy regime from the underlying polymer particle description
Topics in Cubic Special Geometry
Bellucci, Stefano; Roychowdhury, Raju
2011-01-01
We reconsider the sub-leading quantum perturbative corrections to N=2 cubic special Kaehler geometries. Imposing the invariance under axion-shifts, all such corrections (but the imaginary constant one) can be introduced or removed through suitable, lower unitriangular symplectic transformations, dubbed Peccei-Quinn (PQ) transformations. Since PQ transformations do not belong to the d=4 U-duality group G4, in symmetric cases they generally have a non-trivial action on the unique quartic invariant polynomial I4 of the charge representation R of G4. This leads to interesting phenomena in relation to theory of extremal black hole attractors; namely, the possibility to make transitions between different charge orbits of R, with corresponding change of the supersymmetry properties of the supported attractor solutions. Furthermore, a suitable action of PQ transformations can also set I4 to zero, or vice versa it can generate a non-vanishing I4: this corresponds to transitions between "large" and "small" charge orbit...
Perception of global facial geometry is modulated through experience
Directory of Open Access Journals (Sweden)
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.
Exploring the Structure of Spatial Representations
Madl, Tamas; Franklin, Stan; Chen, Ke; Trappl, Robert; Montaldi, Daniela
2016-01-01
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. PMID:27347681
Towards relativistic quantum geometry
Energy Technology Data Exchange (ETDEWEB)
Ridao, Luis Santiago [Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Mar del Plata (Argentina); Bellini, Mauricio, E-mail: mbellini@mdp.edu.ar [Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata, Funes 3350, C.P. 7600, Mar del Plata (Argentina); Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Mar del Plata (Argentina)
2015-12-17
We obtain a gauge-invariant relativistic quantum geometry by using a Weylian-like manifold with a geometric scalar field which provides a gauge-invariant relativistic quantum theory in which the algebra of the Weylian-like field depends on observers. An example for a Reissner–Nordström black-hole is studied.
Multiplicity in difference geometry
Tomasic, Ivan
2011-01-01
We prove a first principle of preservation of multiplicity in difference geometry, paving the way for the development of a more general intersection theory. In particular, the fibres of a \\sigma-finite morphism between difference curves are all of the same size, when counted with correct multiplicities.
Spacetime and Euclidean geometry
Brill, Dieter; Jacobson, Ted
2006-04-01
Using only the principle of relativity and Euclidean geometry we show in this pedagogical article that the square of proper time or length in a two-dimensional spacetime diagram is proportional to the Euclidean area of the corresponding causal domain. We use this relation to derive the Minkowski line element by two geometric proofs of the spacetime Pythagoras theorem.
International Nuclear Information System (INIS)
Konopleva, N.P.
2009-01-01
The basic ideas of description methods of physical fields and elementary particle interactions are discussed. One of such ideas is the conception of space-time geometry. In this connection experimental measurement methods are analyzed. It is shown that measure procedures are the origin of geometrical axioms. The connection between space symmetry properties and the conservation laws is considered
Wares, Arsalan; Elstak, Iwan
2017-01-01
The purpose of this paper is to describe the mathematics that emanates from the construction of an origami box. We first construct a simple origami box from a rectangular sheet and then discuss some of the mathematical questions that arise in the context of geometry and algebra. The activity can be used as a context for illustrating how algebra…
MacKeown, P. K.
1984-01-01
Clarifies two concepts of gravity--those of a fictitious force and those of how space and time may have geometry. Reviews the position of Newton's theory of gravity in the context of special relativity and considers why gravity (as distinct from electromagnetics) lends itself to Einstein's revolutionary interpretation. (JN)
DEFF Research Database (Denmark)
Booss-Bavnbek, Bernhelm
2011-01-01
This paper applies I.M. Gelfand's distinction between adequate and non-adequate use of mathematical language in different contexts to the newly opened window of model-based measurements of intracellular dynamics. The specifics of geometry and dynamics on the mesoscale of cell physiology are elabo...
Diophantine geometry an introduction
Hindry, Marc
2000-01-01
This is an introduction to diophantine geometry at the advanced graduate level. The book contains a proof of the Mordell conjecture which will make it quite attractive to graduate students and professional mathematicians. In each part of the book, the reader will find numerous exercises.
Sliding vane geometry turbines
Sun, Harold Huimin; Zhang, Jizhong; Hu, Liangjun; Hanna, Dave R
2014-12-30
Various systems and methods are described for a variable geometry turbine. In one example, a turbine nozzle comprises a central axis and a nozzle vane. The nozzle vane includes a stationary vane and a sliding vane. The sliding vane is positioned to slide in a direction substantially tangent to an inner circumference of the turbine nozzle and in contact with the stationary vane.
Boyer, Carl B
2012-01-01
Designed as an integrated survey of the development of analytic geometry, this study presents the concepts and contributions from before the Alexandrian Age through the eras of the great French mathematicians Fermat and Descartes, and on through Newton and Euler to the "Golden Age," from 1789 to 1850.
Coxeter, HSM
1965-01-01
This textbook introduces non-Euclidean geometry, and the third edition adds a new chapter, including a description of the two families of 'mid-lines' between two given lines and an elementary derivation of the basic formulae of spherical trigonometry and hyperbolic trigonometry, and other new material.
International Nuclear Information System (INIS)
Ezin, J.P.
1988-08-01
The lectures given at the ''5th Symposium of Mathematics in Abidjan: Differential Geometry and Mechanics'' are presented. They are divided into four chapters: Riemannian metric on a differential manifold, curvature tensor fields on a Riemannian manifold, some classical functionals on Riemannian manifolds and questions. 11 refs
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 ...
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.
Transformational plane geometry
Umble, Ronald N
2014-01-01
Axioms of Euclidean Plane Geometry The Existence and Incidence Postulates The Distance and Ruler Postulates The Plane Separation Postulate The Protractor Postulate The Side-Angle-Side Postulate and the Euclidean Parallel Postulate Theorems of Euclidean Plane Geometry The Exterior Angle Theorem Triangle Congruence Theorems The Alternate Interior Angles Theorem and the Angle Sum Theorem Similar Triangles Introduction to Transformations, Isometries, and Similarities Transformations Isometries and SimilaritiesAppendix: Proof of Surjectivity Translations, Rotations, and Reflections Translations Rotations Reflections Appendix: Geometer's Sketchpad Commands Required by Exploratory Activities Compositions of Translations, Rotations, and Reflections The Three Points Theorem Rotations as Compositions of Two Reflections Translations as Compositions of Two Halfturns or Two Reflections The Angle Addition Theorem Glide Reflections Classification of Isometries The Fundamental Theorem and Congruence Classification of Isometr...
Multilevel geometry optimization
Rodgers, Jocelyn M.; Fast, Patton L.; Truhlar, Donald G.
2000-02-01
Geometry optimization has been carried out for three test molecules using six multilevel electronic structure methods, in particular Gaussian-2, Gaussian-3, multicoefficient G2, multicoefficient G3, and two multicoefficient correlation methods based on correlation-consistent basis sets. In the Gaussian-2 and Gaussian-3 methods, various levels are added and subtracted with unit coefficients, whereas the multicoefficient Gaussian-x methods involve noninteger parameters as coefficients. The multilevel optimizations drop the average error in the geometry (averaged over the 18 cases) by a factor of about two when compared to the single most expensive component of a given multilevel calculation, and in all 18 cases the accuracy of the atomization energy for the three test molecules improves; with an average improvement of 16.7 kcal/mol.
Multilevel geometry optimization
Energy Technology Data Exchange (ETDEWEB)
Rodgers, Jocelyn M. [Department of Chemistry and Supercomputer Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431 (United States); Fast, Patton L. [Department of Chemistry and Supercomputer Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431 (United States); Truhlar, Donald G. [Department of Chemistry and Supercomputer Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431 (United States)
2000-02-15
Geometry optimization has been carried out for three test molecules using six multilevel electronic structure methods, in particular Gaussian-2, Gaussian-3, multicoefficient G2, multicoefficient G3, and two multicoefficient correlation methods based on correlation-consistent basis sets. In the Gaussian-2 and Gaussian-3 methods, various levels are added and subtracted with unit coefficients, whereas the multicoefficient Gaussian-x methods involve noninteger parameters as coefficients. The multilevel optimizations drop the average error in the geometry (averaged over the 18 cases) by a factor of about two when compared to the single most expensive component of a given multilevel calculation, and in all 18 cases the accuracy of the atomization energy for the three test molecules improves; with an average improvement of 16.7 kcal/mol. (c) 2000 American Institute of Physics.
Krauss, Lawrence M.; Turner, Michael S.
1999-01-01
The recognition that the cosmological constant may be non-zero forces us to re-evaluate standard notions about the connection between geometry and the fate of our Universe. An open Universe can recollapse, and a closed Universe can expand forever. As a corollary, we point out that there is no set of cosmological observations we can perform that will unambiguously allow us to determine what the ultimate destiny of the Universe will be.
DEFF Research Database (Denmark)
Tamke, Martin; Ramsgaard Thomsen, Mette; Riiber Nielsen, Jacob
2009-01-01
The versatility of wood constructions and traditional wood joints for the production of non standard elements was in focus of a design based research. Herein we established a seamless process from digital design to fabrication. A first research phase centered on the development of a robust...... parametric model and a generic design language a later explored the possibilities to construct complex shaped geometries with self registering joints on modern wood crafting machines. The research was carried out as collaboration with industrial partners....
International Nuclear Information System (INIS)
Lepora, N.; Kibble, T.
1999-01-01
We analyse symmetry breaking in the Weinberg-Salam model paying particular attention to the underlying geometry of the theory. In this context we find two natural metrics upon the vacuum manifold: an isotropic metric associated with the scalar sector, and a squashed metric associated with the gauge sector. Physically, the interplay between these metrics gives rise to many of the non-perturbative features of Weinberg-Salam theory. (author)
International Nuclear Information System (INIS)
Hull, C.M.
1993-01-01
The geometric structure of theories with gauge fields of spins two and higher should involve a higher spin generalisation of Riemannian geometry. Such geometries are discussed and the case of W ∝ -gravity is analysed in detail. While the gauge group for gravity in d dimensions is the diffeomorphism group of the space-time, the gauge group for a certain W-gravity theory (which is W ∝ -gravity in the case d=2) is the group of symplectic diffeomorphisms of the cotangent bundle of the space-time. Gauge transformations for W-gravity gauge fields are given by requiring the invariance of a generalised line element. Densities exist and can be constructed from the line element (generalising √detg μν ) only if d=1 or d=2, so that only for d=1,2 can actions be constructed. These two cases and the corresponding W-gravity actions are considered in detail. In d=2, the gauge group is effectively only a subgroup of the symplectic diffeomorphisms group. Some of the constraints that arise for d=2 are similar to equations arising in the study of self-dual four-dimensional geometries and can be analysed using twistor methods, allowing contact to be made with other formulations of W-gravity. While the twistor transform for self-dual spaces with one Killing vector reduces to a Legendre transform, that for two Killing vectors gives a generalisation of the Legendre transform. (orig.)
Integral geometry and valuations
Solanes, Gil
2014-01-01
Valuations are finitely additive functionals on the space of convex bodies. Their study has become a central subject in convexity theory, with fundamental applications to integral geometry. In the last years there has been significant progress in the theory of valuations, which in turn has led to important achievements in integral geometry. This book originated from two courses delivered by the authors at the CRM and provides a self-contained introduction to these topics, covering most of the recent advances. The first part, by Semyon Alesker, is devoted to the theory of convex valuations, with emphasis on the latest developments. A special focus is put on the new fundamental structures of the space of valuations discovered after Alesker's irreducibility theorem. Moreover, the author describes the newly developed theory of valuations on manifolds. In the second part, Joseph H. G. Fu gives a modern introduction to integral geometry in the sense of Blaschke and Santaló, based on the notions and tools presented...
CBM RICH geometry optimization
Energy Technology Data Exchange (ETDEWEB)
Mahmoud, Tariq; Hoehne, Claudia [II. Physikalisches Institut, Giessen Univ. (Germany); Collaboration: CBM-Collaboration
2016-07-01
The Compressed Baryonic Matter (CBM) experiment at the future FAIR complex will investigate the phase diagram of strongly interacting matter at high baryon density and moderate temperatures in A+A collisions from 2-11 AGeV (SIS100) beam energy. The main electron identification detector in the CBM experiment will be a RICH detector with a CO{sub 2} gaseous-radiator, focusing spherical glass mirrors, and MAPMT photo-detectors being placed on a PMT-plane. The RICH detector is located directly behind the CBM dipole magnet. As the final magnet geometry is now available, some changes in the RICH geometry become necessary. In order to guarantee a magnetic field of 1 mT at maximum in the PMT plane for effective operation of the MAPMTs, two measures have to be taken: The PMT plane is moved outwards of the stray field by tilting the mirrors by 10 degrees and shielding boxes have been designed. In this contribution the results of the geometry optimization procedure are presented.
Understanding representations in design
DEFF Research Database (Denmark)
Bødker, Susanne
1998-01-01
Representing computer applications and their use is an important aspect of design. In various ways, designers need to externalize design proposals and present them to other designers, users, or managers. This article deals with understanding design representations and the work they do in design....... The article is based on a series of theoretical concepts coming out of studies of scientific and other work practices and on practical experiences from design of computer applications. The article presents alternatives to the ideas that design representations are mappings of present or future work situations...... and computer applications. It suggests that representations are primarily containers of ideas and that representation is situated at the same time as representations are crossing boundaries between various design and use activities. As such, representations should be carriers of their own contexts regarding...
Introducing geometry concept based on history of Islamic geometry
Maarif, S.; Wahyudin; Raditya, A.; Perbowo, K. S.
2018-01-01
Geometry is one of the areas of mathematics interesting to discuss. Geometry also has a long history in mathematical developments. Therefore, it is important integrated historical development of geometry in the classroom to increase’ knowledge of how mathematicians earlier finding and constructing a geometric concept. Introduction geometrical concept can be started by introducing the Muslim mathematician who invented these concepts so that students can understand in detail how a concept of geometry can be found. However, the history of mathematics development, especially history of Islamic geometry today is less popular in the world of education in Indonesia. There are several concepts discovered by Muslim mathematicians that should be appreciated by the students in learning geometry. Great ideas of mathematicians Muslim can be used as study materials to supplement religious character values taught by Muslim mathematicians. Additionally, by integrating the history of geometry in teaching geometry are expected to improve motivation and geometrical understanding concept.
Two lectures on D-geometry and noncommutative geometry
International Nuclear Information System (INIS)
Douglas, M.R.
1999-01-01
This is a write-up of lectures given at the 1998 Spring School at the Abdus Salam ICTP. We give a conceptual introduction to D-geometry, the study of geometry as seen by D-branes in string theory, and to noncommutative geometry as it has appeared in D-brane and Matrix theory physics. (author)
Finsler geometry, relativity and gauge theories
International Nuclear Information System (INIS)
Asanov, G.S.
1985-01-01
This book provides a self-contained account of the Finslerian techniques which aim to synthesize the ideas of Finslerian metrical generalization of Riemannian geometry to merge with the primary physical concepts of general relativity and gauge field theories. The geometrization of internal symmetries in terms of Finslerian geometry, as well as the formulation of Finslerian generalization of gravitational field equations and equations of motion of matter, are two key points used to expound the techniques. The Clebsch representation of the canonical momentum field is used to formulate the Hamilton-Jacobi theory for homogeneous Lagrangians of classical mechanics. As an auxillary mathematical apparatus, the author uses invariance identities which systematically reflect the covariant properties of geometrical objects. The results of recent studies of special Finsler spaces are also applied. The book adds substantially to the mathematical monographs by Rund (1959) and Rund and Bear (1972), all basic results of the latter being reflected. It is the author's hope that thorough exploration of the materrial presented will tempt the reader to revise the habitual physical concepts supported conventionally by Riemannian geometry. (Auth.)
Indian Academy of Sciences (India)
IAS Admin
Sphere–Cylinder Theorem, vol- ume and surface area of the torus, volume and surface area of a slice of a solid sphere. The author earned his PhD degree in mathematics. (topology), in 2000, from. Panjab University,. Chandigarh and since then he has been teaching analysis, algebra, calculus and discrete mathematics at.
Scanlon, Regina M.
2003-01-01
Describes an engaging project in which students have to design and construct a three-dimensional candy box that would appeal to children. Requires students to make the box out of prisms, pyramids, or cylinders, determine the surface area and volume of the solids, and write a persuasive business letter. (YDS)
Indian Academy of Sciences (India)
Sphere–Cylinder Theorem; volume and surface area of the torus; volume and surface area of a slice of a solid sphere. Author Affiliations. Keeri Vardhan Madahar1. Assistant Professor in Mathematics (DES) Panjab University Chandigarh, India. Resonance – Journal of Science Education. Current Issue : Vol. 23, Issue 4.
Functional integration over geometries
International Nuclear Information System (INIS)
Mottola, E.
1995-01-01
The geometric construction of the functional integral over coset spaces M/G is reviewed. The inner product on the cotangent space of infinitesimal deformations of M defines an invariant distance and volume form, or functional integration measure on the full configuration space. Then, by a simple change of coordinates parameterizing the gauge fiber G, the functional measure on the coset space M/G is deduced. This change of integration variables leads to a Jacobian which is entirely equivalent to the Faddeev--Popov determinant of the more traditional gauge fixed approach in non-abelian gauge theory. If the general construction is applied to the case where G is the group of coordinate reparameterizations of spacetime, the continuum functional integral over geometries, i.e. metrics modulo coordinate reparameterizations may be defined. The invariant functional integration measure is used to derive the trace anomaly and effective action for the conformal part of the metric in two and four dimensional spacetime. In two dimensions this approach generates the Polyakov--Liouville action of closed bosonic non-critical string theory. In four dimensions the corresponding effective action leads to novel conclusions on the importance of quantum effects in gravity in the far infrared, and in particular, a dramatic modification of the classical Einstein theory at cosmological distance scales, signaled first by the quantum instability of classical de Sitter spacetime. Finite volume scaling relations for the functional integral of quantum gravity in two and four dimensions are derived, and comparison with the discretized dynamical triangulation approach to the integration over geometries are discussed. Outstanding unsolved problems in both the continuum definition and the simplicial approach to the functional integral over geometries are highlighted
Dooner, David B
2012-01-01
Building on the first edition published in 1995 this new edition of Kinematic Geometry of Gearing has been extensively revised and updated with new and original material. This includes the methodology for general tooth forms, radius of torsure', cylinder of osculation, and cylindroid of torsure; the author has also completely reworked the '3 laws of gearing', the first law re-written to better parallel the existing 'Law of Gearing" as pioneered by Leonard Euler, expanded from Euler's original law to encompass non-circular gears and hypoid gears, the 2nd law of gearing describing a unique relat
Flegg, H Graham
2001-01-01
This excellent introduction to topology eases first-year math students and general readers into the subject by surveying its concepts in a descriptive and intuitive way, attempting to build a bridge from the familiar concepts of geometry to the formalized study of topology. The first three chapters focus on congruence classes defined by transformations in real Euclidean space. As the number of permitted transformations increases, these classes become larger, and their common topological properties become intuitively clear. Chapters 4-12 give a largely intuitive presentation of selected topics.
Torsional heterotic geometries
International Nuclear Information System (INIS)
Becker, Katrin; Sethi, Savdeep
2009-01-01
We construct new examples of torsional heterotic backgrounds using duality with orientifold flux compactifications. We explain how duality provides a perturbative solution to the type I/heterotic string Bianchi identity. The choice of connection used in the Bianchi identity plays an important role in the construction. We propose the existence of a much larger landscape of compact torsional geometries using string duality. Finally, we present some quantum exact metrics that correspond to NS5-branes placed on an elliptic space. These metrics describe how torus isometries are broken by NS flux.
Geometrie verstehen: statisch - kinematisch
Kroll, Ekkehard
Dem Allgemeinen steht begrifflich das Besondere gegenüber. In diesem Sinne sind allgemeine Überlegungen zum Verstehen von Mathematik zu ergänzen durch Untersuchungen hinsichtlich des Verstehens der einzelnen mathematischen Disziplinen, insbesondere der Geometrie. Hier haben viele Schülerinnen und Schüler Probleme. Diese rühren hauptsächlich daher, dass eine fertige geometrische Konstruktion in ihrer statischen Präsentation auf Papier nicht mehr die einzelnen Konstruktionsschritte erkennen lässt; zum Nachvollzug müssen sie daher ergänzend in einer Konstruktionsbeschreibung festgehalten werden.
Kendig, Keith
2015-01-01
Designed to make learning introductory algebraic geometry as easy as possible, this text is intended for advanced undergraduates and graduate students who have taken a one-year course in algebra and are familiar with complex analysis. This newly updated second edition enhances the original treatment's extensive use of concrete examples and exercises with numerous figures that have been specially redrawn in Adobe Illustrator. An introductory chapter that focuses on examples of curves is followed by a more rigorous and careful look at plane curves. Subsequent chapters explore commutative ring th
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
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
Graded geometry and Poisson reduction
Cattaneo, A S; Zambon, M
2009-01-01
The main result of [2] extends the Marsden-Ratiu reduction theorem [4] in Poisson geometry, and is proven by means of graded geometry. In this note we provide the background material about graded geometry necessary for the proof in [2]. Further, we provide an alternative algebraic proof for the main result. ©2009 American Institute of Physics
DEFF Research Database (Denmark)
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...
International Nuclear Information System (INIS)
Aspinwall, P.S.; Luetken, C.A.
1991-01-01
We analyze the mirror manifold hypothesis in one and three dimensions using the simplest available representations of the N = 2 superconformal algebra. The symmetries of these tensor models can be divided out to give an explicit representation of the mirror, and we give a simple group theoretical algorithm for determining which symmetries should be used. We show that the mirror of a superconformal field theory does not always have a geometrical interpretation, but when it does, deformations of complex structure of one manifold are reflected in deformations of the Kaehler form of the mirror manifold, and we show how the large radius limit of a manifold corresponds to a large complex structure limit in the mirror manifold. The mirror of the Tian-Yau three generation model is constructed both as a conformal field theory and as an algebraic variety with Euler number six. The Hodge numbers of this manifolds are fixed, but the intersection numbes are highly ambiguous, presumably reflected a rich structure of multicritical points in the moduli space of the field theory. (orig.)
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...
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
Dependence of displacement fields on the damage cluster nucleus geometry
International Nuclear Information System (INIS)
Grigor'ev, A.N.; Zabela, A.G.; Nikolajchuk, L.I.; Prokhorenko, E.M.; Khizhnyak, N.A.
1988-01-01
Displacement fields in doped crystals of cubic and hexagonal structures containing extended defects are studied. The numerical results are presented depending on the damage cluster nucleus geometry. All calculations are based on analytical representations of displacement fields in an integral form using elasticity theory equations. The investigation results are vital for radiation physics as they permit to predict and calculate both the character and geometry of distortions near damaged region cluster and determine cluster parameters on the basis of the known structure of distortions. Dependences are obtained for the following monocrystals: Mg, ZnO, CdS, W, Au. 6 refs.; 3 figs
Covariant representations of nuclear *-algebras
International Nuclear Information System (INIS)
Moore, S.M.
1978-01-01
Extensions of the Csup(*)-algebra theory for covariant representations to nuclear *-algebra are considered. Irreducible covariant representations are essentially unique, an invariant state produces a covariant representation with stable vacuum, and the usual relation between ergodic states and covariant representations holds. There exist construction and decomposition theorems and a possible relation between derivations and covariant representations
Bochnak, Jacek; Roy, Marie-Françoise
1998-01-01
This book is a systematic treatment of real algebraic geometry, a subject that has strong interrelation with other areas of mathematics: singularity theory, differential topology, quadratic forms, commutative algebra, model theory, complexity theory etc. The careful and clearly written account covers both basic concepts and up-to-date research topics. It may be used as text for a graduate course. The present edition is a substantially revised and expanded English version of the book "Géometrie algébrique réelle" originally published in French, in 1987, as Volume 12 of ERGEBNISSE. Since the publication of the French version the theory has made advances in several directions. Many of these are included in this English version. Thus the English book may be regarded as a completely new treatment of the subject.
Critique of information geometry
International Nuclear Information System (INIS)
Skilling, John
2014-01-01
As applied to probability, information geometry fails because probability distributions do not form a metric space. Probability theory rests on a compelling foundation of elementary symmetries, which also support information (aka minus entropy, Kullback-Leibler) H(p;q) as the unique measure of divergence from source probability distribution q to destination p. Because the only compatible connective H is from≠to asymmetric, H(p;q)≠H(q;p), there can be no compatible geometrical distance (which would necessarily be from=to symmetric). Hence there is no distance relationship compatible with the structure of probability theory. Metrics g and densities sqrt(det(g)) interpreted as prior probabilities follow from the definition of distance, and must fail likewise. Various metrics and corresponding priors have been proposed, Fisher's being the most popular, but all must behave unacceptably. This is illustrated with simple counter-examples
International Nuclear Information System (INIS)
Correa, Diego H.; Silva, Guillermo A.
2008-01-01
We discuss how geometrical and topological aspects of certain (1/2)-BPS type IIB geometries are captured by their dual operators in N = 4 Super Yang-Mills theory. The type IIB solutions are characterized by arbitrary droplet pictures in a plane and we consider, in particular, axially symmetric droplets. The 1-loop anomalous dimension of the dual gauge theory operators probed with single traces is described by some bosonic lattice Hamiltonians. These Hamiltonians are shown to encode the topology of the droplets. In appropriate BMN limits, the Hamiltonians spectrum reproduces the spectrum of near-BPS string excitations propagating along each of the individual edges of the droplet. We also study semiclassical regimes for the Hamiltonians. For droplets having disconnected constituents, the Hamiltonian admits different complimentary semiclassical descriptions, each one replicating the semiclassical description for closed strings extending in each of the constituents
Emergent geometry of membranes
Energy Technology Data Exchange (ETDEWEB)
Badyn, Mathias Hudoba de; Karczmarek, Joanna L.; Sabella-Garnier, Philippe; Yeh, Ken Huai-Che [Department of Physics and Astronomy, University of British Columbia,6224 Agricultural Road, Vancouver (Canada)
2015-11-13
In work http://dx.doi.org/10.1103/PhysRevD.86.086001, a surface embedded in flat ℝ{sup 3} is associated to any three hermitian matrices. We study this emergent surface when the matrices are large, by constructing coherent states corresponding to points in the emergent geometry. We find the original matrices determine not only shape of the emergent surface, but also a unique Poisson structure. We prove that commutators of matrix operators correspond to Poisson brackets. Through our construction, we can realize arbitrary noncommutative membranes: for example, we examine a round sphere with a non-spherically symmetric Poisson structure. We also give a natural construction for a noncommutative torus embedded in ℝ{sup 3}. Finally, we make remarks about area and find matrix equations for minimal area surfaces.
Geometry through history Euclidean, hyperbolic, and projective geometries
Dillon, Meighan I
2018-01-01
Presented as an engaging discourse, this textbook invites readers to delve into the historical origins and uses of geometry. The narrative traces the influence of Euclid’s system of geometry, as developed in his classic text The Elements, through the Arabic period, the modern era in the West, and up to twentieth century mathematics. Axioms and proof methods used by mathematicians from those periods are explored alongside the problems in Euclidean geometry that lead to their work. Students cultivate skills applicable to much of modern mathematics through sections that integrate concepts like projective and hyperbolic geometry with representative proof-based exercises. For its sophisticated account of ancient to modern geometries, this text assumes only a year of college mathematics as it builds towards its conclusion with algebraic curves and quaternions. Euclid’s work has affected geometry for thousands of years, so this text has something to offer to anyone who wants to broaden their appreciation for the...
International Nuclear Information System (INIS)
Qiu, S.; Amano, H.; Kasai, A.
1988-01-01
The solid angle in extended alpha source measurement for a series of counting geometries has been obtained by two methods: (1) calculated by means of the Nelson Blachmen series; (2) interpolated from the data table given by Gardner. A particular consequence of the application of the Nelson Blachmen series was deduced which was different from that given by the original author. The applicability of these two methods, as well as an experimentally measured method, is also evaluated. (author)
On organizing principles of discrete differential geometry. Geometry of spheres
International Nuclear Information System (INIS)
Bobenko, Alexander I; Suris, Yury B
2007-01-01
Discrete differential geometry aims to develop discrete equivalents of the geometric notions and methods of classical differential geometry. This survey contains a discussion of the following two fundamental discretization principles: the transformation group principle (smooth geometric objects and their discretizations are invariant with respect to the same transformation group) and the consistency principle (discretizations of smooth parametrized geometries can be extended to multidimensional consistent nets). The main concrete geometric problem treated here is discretization of curvature-line parametrized surfaces in Lie geometry. Systematic use of the discretization principles leads to a discretization of curvature-line parametrization which unifies circular and conical nets.
Higher geometry an introduction to advanced methods in analytic geometry
Woods, Frederick S
2005-01-01
For students of mathematics with a sound background in analytic geometry and some knowledge of determinants, this volume has long been among the best available expositions of advanced work on projective and algebraic geometry. Developed from Professor Woods' lectures at the Massachusetts Institute of Technology, it bridges the gap between intermediate studies in the field and highly specialized works.With exceptional thoroughness, it presents the most important general concepts and methods of advanced algebraic geometry (as distinguished from differential geometry). It offers a thorough study
The Prints: A Picture Book for Pre-Formal Geometry
Skoumpourdi, Chrysanthi; Mpakopoulou, Ifigenia
2011-01-01
A pre-test questionnaire was conducted in a kindergarten and it showed that, although the children were able to give various examples of objects, from their everyday lives, that are similar to solid shapes, the examples they gave for plane figures were also tangible objects. Since it is suggested that geometry instruction has to begin early,…
Czech Academy of Sciences Publication Activity Database
Koťátko, Petr
2014-01-01
Roč. 21, č. 3 (2014), s. 282-302 ISSN 1335-0668 Institutional support: RVO:67985955 Keywords : representation * proposition * truth-conditions * belief-ascriptions * reference * externalism * fiction Subject RIV: AA - Philosophy ; Religion
Wigner's Symmetry Representation Theorem
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 19; Issue 10. Wigner's Symmetry Representation Theorem: At the Heart of Quantum Field Theory! Aritra Kr Mukhopadhyay. General Article Volume 19 Issue 10 October 2014 pp 900-916 ...
Polynomial representations of GLn
Green, James A; Erdmann, Karin
2007-01-01
The first half of this book contains the text of the first edition of LNM volume 830, Polynomial Representations of GLn. This classic account of matrix representations, the Schur algebra, the modular representations of GLn, and connections with symmetric groups, has been the basis of much research in representation theory. The second half is an Appendix, and can be read independently of the first. It is an account of the Littelmann path model for the case gln. In this case, Littelmann's 'paths' become 'words', and so the Appendix works with the combinatorics on words. This leads to the repesentation theory of the 'Littelmann algebra', which is a close analogue of the Schur algebra. The treatment is self- contained; in particular complete proofs are given of classical theorems of Schensted and Knuth.
Polynomial representations of GLN
Green, James A
1980-01-01
The first half of this book contains the text of the first edition of LNM volume 830, Polynomial Representations of GLn. This classic account of matrix representations, the Schur algebra, the modular representations of GLn, and connections with symmetric groups, has been the basis of much research in representation theory. The second half is an Appendix, and can be read independently of the first. It is an account of the Littelmann path model for the case gln. In this case, Littelmann's 'paths' become 'words', and so the Appendix works with the combinatorics on words. This leads to the repesentation theory of the 'Littelmann algebra', which is a close analogue of the Schur algebra. The treatment is self- contained; in particular complete proofs are given of classical theorems of Schensted and Knuth.
Procedural Media Representation
Henrysson, Anders
2002-01-01
We present a concept for using procedural techniques to represent media. Procedural methods allow us to represent digital media (2D images, 3D environments etc.) with very little information and to render it photo realistically. Since not all kind of content can be created procedurally, traditional media representations (bitmaps, polygons etc.) must be used as well. We have adopted an object-based media representation where an object can be represented either with a procedure or with its trad...
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...
International Nuclear Information System (INIS)
Buescher, R.
2005-01-01
Casimir interactions are interactions induced by quantum vacuum fluctuations and thermal fluctuations of the electromagnetic field. Using a path integral quantization for the gauge field, an effective Gaussian action will be derived which is the starting point to compute Casimir forces between macroscopic objects analytically and numerically. No assumptions about the independence of the material and shape dependent contributions to the interaction are made. We study the limit of flat surfaces in further detail and obtain a concise derivation of Lifshitz' theory of molecular forces. For the case of ideally conducting boundaries, the Gaussian action will be calculated explicitly. Both limiting cases are also discussed within the framework of a scalar field quantization approach, which is applicable for translationally invariant geometries. We develop a non-perturbative approach to calculate the Casimir interaction from the Gaussian action for periodically deformed and ideally conducting objects numerically. The obtained results reveal two different scaling regimes for the Casimir force as a function of the distance between the objects, their deformation wavelength and -amplitude. The results confirm that the interaction is non-additive, especially in the presence of strong geometric deformations. Furthermore, the numerical approach is extended to calculate lateral Casimir forces. The results are consistent with the results of the proximity-force approximation for large deformation wavelengths. A qualitatively different behaviour between the normal and lateral force is revealed. We also establish a relation between the boundary induced change of the of the density of states for the scalar Helmholtz equation and the Casimir interaction using the path integral method. For statically deformed boundaries, this relation can be expressed as a novel trace formula, which is formally similar to the so-called Krein-Friedel-Lloyd formula. While the latter formula describes the
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
The Koslowski-Sahlmann representation: quantum configuration space
Campiglia, Miguel; Varadarajan, Madhavan
2014-09-01
The Koslowski-Sahlmann (KS) representation is a generalization of the representation underlying the discrete spatial geometry of loop quantum gravity (LQG), to accommodate states labelled by smooth spatial geometries. As shown recently, the KS representation supports, in addition to the action of the holonomy and flux operators, the action of operators which are the quantum counterparts of certain connection dependent functions known as ‘background exponentials’. Here we show that the KS representation displays the following properties which are the exact counterparts of LQG ones: (i) the abelian * algebra of SU(2) holonomies and ‘U(1)’ background exponentials can be completed to a C* algebra, (ii) the space of semianalytic SU(2) connections is topologically dense in the spectrum of this algebra, (iii) there exists a measure on this spectrum for which the KS Hilbert space is realized as the space of square integrable functions on the spectrum, (iv) the spectrum admits a characterization as a projective limit of finite numbers of copies of SU(2) and U(1), (v) the algebra underlying the KS representation is constructed from cylindrical functions and their derivations in exactly the same way as the LQG (holonomy-flux) algebra except that the KS cylindrical functions depend on the holonomies and the background exponentials, this extra dependence being responsible for the differences between the KS and LQG algebras. While these results are obtained for compact spaces, they are expected to be of use for the construction of the KS representation in the asymptotically flat case.
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
Directory of Open Access Journals (Sweden)
Šárka Nedomová
2013-01-01
Full Text Available Precise quantification of the profile of egg can provide a powerful tool for the analysis of egg shape for various biological problems. A new approach to the geometry of a Ostrich’s egg profile is presented here using an analysing the egg’s digital photo by edge detection techniques. The obtained points on the eggshell counter are fitted by the Fourier series. The obtained equations describing an egg profile have been used to calculate radii of curvature. The radii of the curvature at the important point of the egg profile (sharp end, blunt end and maximum thickness are independent on the egg shape index. The exact values of the egg surface and the egg volume have been obtained. These quantities are also independent on the egg shape index. These quantities can be successively estimated on the basis of simplified equations which are expressed in terms of the egg length, L¸ and its width, B. The surface area of the eggshells also exhibits good correlation with the egg long circumference length. Some limitations of the most used procedures have been also shown.
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.
Knowledge representation and use. II. Representations
Energy Technology Data Exchange (ETDEWEB)
Lauriere, J L
1982-03-01
The use of computers is less and less restricted to numerical and data processing. On the other hand, current software mostly contains algorithms on universes with complete information. The paper discusses a different family of programs: expert systems are designed as aids in human reasoning in various specific areas. Symbolic knowledge manipulation, uncertain and incomplete deduction capabilities, natural communication with humans in non-procedural ways are their essential features. This part is mainly a reflection and a debate about the various modes of acquisition and representation of human knowledge. 32 references.
Comparison of Microinstability Properties for Stellarator Magnetic Geometries
International Nuclear Information System (INIS)
Rewoldt, G.; Ku, L.-P.; Tang, W.M.
2005-01-01
The microinstability properties of seven distinct magnetic geometries corresponding to different operating and planned stellarators with differing symmetry properties are compared. Specifically, the kinetic stability properties (linear growth rates and real frequencies) of toroidal microinstabilities (driven by ion temperature gradients and trapped-electron dynamics) are compared, as parameters are varied. The familiar ballooning representation is used to enable efficient treatment of the spatial variations along the equilibrium magnetic field lines. These studies provide useful insights for understanding the differences in the relative strengths of the instabilities caused by the differing localizations of good and bad magnetic curvature and of the presence of trapped particles. The associated differences in growth rates due to magnetic geometry are large for small values of the temperature gradient parameter n identical to d ln T/d ln n, whereas for large values of n, the mode is strongly unstable for all of the different magnetic geometries
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, ...
Spin, statistics, and geometry of random walks
International Nuclear Information System (INIS)
Jaroszewicz, T.; Kurzepa, P.S.
1991-01-01
The authors develop and unify two complementary descriptions of propagation of spinning particles: the directed random walk representation and the spin factor approach. Working in an arbitrary number of dimensions D, they first represent the Dirac propagator in terms of a directed random walk. They then derive the general and explicit form of the gauge connection describing parallel transport of spin and investigate the resulting quantum-mechanical problem of a particle moving on a sphere in the field of a nonabelian SO(D-1) monopole. This construction, generalizing Polyakov's results, enables them to prove the equivalence of the random walk and path-integral (spin factor) representation. As an alternative, they construct and discuss various Wess-Zumino-Witten forms of the spin factor. They clarify the role played by the coupling between the particle's spin and translational degrees of freedom in establishing the geometrical properties of particle's paths in spacetime. To this end, they carefully define and evaluate Hausdorff dimensions of bosonic and fermionic sample paths, in the covariant as well as nonrelativistic formulations. Finally, as an application of the developed formalism, they give an intuitive spacetime interpretation of chiral anomalies in terms of the geometry of fermion trajectories
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
Operator representations of frames
DEFF Research Database (Denmark)
Christensen, Ole; Hasannasab, Marzieh
2017-01-01
of the properties of the operator T requires more work. For example it is a delicate issue to obtain a representation with a bounded operator, and the availability of such a representation not only depends on the frame considered as a set, but also on the chosen indexing. Using results from operator theory we show......The purpose of this paper is to consider representations of frames {fk}k∈I in a Hilbert space ℋ of the form {fk}k∈I = {Tkf0}k∈I for a linear operator T; here the index set I is either ℤ or ℒ0. While a representation of this form is available under weak conditions on the frame, the analysis...... that by embedding the Hilbert space ℋ into a larger Hilbert space, we can always represent a frame via iterations of a bounded operator, composed with the orthogonal projection onto ℋ. The paper closes with a discussion of an open problem concerning representations of Gabor frames via iterations of a bounded...
GPS: Geometry, Probability, and Statistics
Field, Mike
2012-01-01
It might be said that for most occupations there is now less of a need for mathematics than there was say fifty years ago. But, the author argues, geometry, probability, and statistics constitute essential knowledge for everyone. Maybe not the geometry of Euclid, but certainly geometrical ways of thinking that might enable us to describe the world…
Surrogate Modeling for Geometry Optimization
DEFF Research Database (Denmark)
Rojas Larrazabal, Marielba de la Caridad; Abraham, Yonas; Holzwarth, Natalie
2009-01-01
A new approach for optimizing the nuclear geometry of an atomic system is described. Instead of the original expensive objective function (energy functional), a small number of simpler surrogates is used.......A new approach for optimizing the nuclear geometry of an atomic system is described. Instead of the original expensive objective function (energy functional), a small number of simpler surrogates is used....
Kaehler geometry and SUSY mechanics
International Nuclear Information System (INIS)
Bellucci, Stefano; Nersessian, Armen
2001-01-01
We present two examples of SUSY mechanics related with Kaehler geometry. The first system is the N = 4 supersymmetric one-dimensional sigma-model proposed in hep-th/0101065. Another system is the N = 2 SUSY mechanics whose phase space is the external algebra of an arbitrary Kaehler manifold. The relation of these models with antisymplectic geometry is discussed
A prediction for bubbling geometries
Okuda, Takuya
2007-01-01
We study the supersymmetric circular Wilson loops in N=4 Yang-Mills theory. Their vacuum expectation values are computed in the parameter region that admits smooth bubbling geometry duals. The results are a prediction for the supergravity action evaluated on the bubbling geometries for Wilson loops.
Molecular motion in restricted geometries
Indian Academy of Sciences (India)
Molecular dynamics in restricted geometries is known to exhibit anomalous behaviour. Diffusion, translational or rotational, of molecules is altered significantly on confinement in restricted geometries. Quasielastic neutron scattering (QENS) offers a unique possibility of studying molecular motion in such systems. Both time ...
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.
Finsler Geometry of Nonlinear Elastic Solids with Internal Structure
2017-01-01
the locally relaxed intermediate state of the crystal, following earlier classical differential–geometric treatments by the Japanese school [24]. Kondo...Remark 8. Components of F and f are defined in an identical fashion by Bejancu [12]. Tensor definitions (2.39) and (2.40) potentially differ in two ways...transformations (i.e., push-forwards and pull-backs) of vectors and tensors to be calculated in a completely analogous fashion to transformations between
Optical geometry across the horizon
International Nuclear Information System (INIS)
Jonsson, Rickard
2006-01-01
In a recent paper (Jonsson and Westman 2006 Class. Quantum Grav. 23 61), a generalization of optical geometry, assuming a non-shearing reference congruence, is discussed. Here we illustrate that this formalism can be applied to (a finite four-volume) of any spherically symmetric spacetime. In particular we apply the formalism, using a non-static reference congruence, to do optical geometry across the horizon of a static black hole. While the resulting geometry in principle is time dependent, we can choose the reference congruence in such a manner that an embedding of the geometry always looks the same. Relative to the embedded geometry the reference points are then moving. We discuss the motion of photons, inertial forces and gyroscope precession in this framework
Poincaré Embeddings for Learning Hierarchical Representations
CERN. Geneva
2018-01-01
Abstracts: Representation learning has become an invaluable approach for learning from symbolic data such as text and graphs. However, while complex symbolic datasets often exhibit a latent hierarchical structure, state-of-the-art methods typically do not account for this property. In this talk, I will discuss a new approach for learning hierarchical representations of symbolic data by embedding them into hyperbolic space -- or more precisely into an n-dimensional Poincaré ball. Due to the underlying hyperbolic geometry, this allows us to learn parsimonious representations of symbolic data by simultaneously capturing hierarchy and similarity. We introduce an efficient algorithm to learn the embeddings based on Riemannian optimization and show experimentally that Poincaré embeddings outperform Euclidean embeddings significantly on data with latent hierarchies, both in terms of representation capacity and in terms of generalization ability. &...
Mobilities and Representations
DEFF Research Database (Denmark)
Thelle, Mikkel
2017-01-01
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......As the centerpiece of the eighth T2M yearbook, the following interview about representations of mobility signals a new and exciting focus area for Mobility in History. In future issues we hope to include reviews that grapple more with how mobilities have been imagined and represented in the arts......, 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...
Post-representational cartography
Directory of Open Access Journals (Sweden)
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.
Introduction to computer data representation
Fenwick, Peter
2014-01-01
Introduction to Computer Data Representation introduces readers to the representation of data within computers. Starting from basic principles of number representation in computers, the book covers the representation of both integer and floating point numbers, and characters or text. It comprehensively explains the main techniques of computer arithmetic and logical manipulation. The book also features chapters covering the less usual topics of basic checksums and 'universal' or variable length representations for integers, with additional coverage of Gray Codes, BCD codes and logarithmic repre
Multiple-view, Multiple-selection Visualization of Simulation Geometry in CMS
International Nuclear Information System (INIS)
Bauerdick, L A T; Eulisse, G; Jones, C; McCauley, T; Osborne, I; Kovalskyi, D; Mrak Tadel, A; Tadel, M; Yagil, A
2012-01-01
Fireworks, the event-display program of CMS, was extended with an advanced geometry visualization package. ROOT's TGeo geometry is used as internal representation, shared among several geometry views. Each view is represented by a GUI list-tree widget, implemented as a flat vector to allow for fast searching, selection, and filtering by material type, node name, and shape type. Display of logical and physical volumes is supported. Color, transparency, and visibility flags can be modified for each node or for a selection of nodes. Further operations, like opening of a new view or changing of the root node, can be performed via a context menu. Node selection and graphical properties determined by the list-tree view can be visualized in any 3D graphics view of Fireworks. As each 3D view can display any number of geometry views, a user is free to combine different geometry-view selections within the same 3D view. Node-selection by proximity to a given point is possible. A visual clipping box can be set for each geometry view to limit geometry drawing into a specified region. Visualization of geometric overlaps, as detected by TGeo, is also supported. The geometry visualization package is used for detailed inspection and display of simulation geometry with or without the event data. It also serves as a tool for geometry debugging and inspection, facilitating development of geometries for CMS detector upgrades and for SLHC.
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
Energy Technology Data Exchange (ETDEWEB)
Hoff da Silva, J.M.; Rogerio, R.J.B. [Universidade Estadual Paulista, Departamento de Fisica e Quimica, Guaratingueta, SP (Brazil); Villalobos, C.H.C. [Universidade Estadual Paulista, Departamento de Fisica e Quimica, Guaratingueta, SP (Brazil); Universidade Federal Fluminense, Instituto de Fisica, Niteroi, RJ (Brazil); Rocha, Roldao da [Universidade Federal do ABC-UFABC, Centro de Matematica, Computacao e Cognicao, Santo Andre (Brazil)
2017-07-15
A systematic study of the spinor representation by means of the fermionic physical space is accomplished and implemented. The spinor representation space is shown to be constrained by the Fierz-Pauli-Kofink identities among the spinor bilinear covariants. A robust geometric and topological structure can be manifested from the spinor space, wherein the first and second homotopy groups play prominent roles on the underlying physical properties, associated to fermionic fields. The mapping that changes spinor fields classes is then exemplified, in an Einstein-Dirac system that provides the spacetime generated by a fermion. (orig.)
Complex analysis and CR geometry
Zampieri, Giuseppe
2008-01-01
Cauchy-Riemann (CR) geometry is the study of manifolds equipped with a system of CR-type equations. Compared to the early days when the purpose of CR geometry was to supply tools for the analysis of the existence and regularity of solutions to the \\bar\\partial-Neumann problem, it has rapidly acquired a life of its own and has became an important topic in differential geometry and the study of non-linear partial differential equations. A full understanding of modern CR geometry requires knowledge of various topics such as real/complex differential and symplectic geometry, foliation theory, the geometric theory of PDE's, and microlocal analysis. Nowadays, the subject of CR geometry is very rich in results, and the amount of material required to reach competence is daunting to graduate students who wish to learn it. However, the present book does not aim at introducing all the topics of current interest in CR geometry. Instead, an attempt is made to be friendly to the novice by moving, in a fairly relaxed way, f...
The geometry description markup language
International Nuclear Information System (INIS)
Chytracek, R.
2001-01-01
Currently, a lot of effort is being put on designing complex detectors. A number of simulation and reconstruction frameworks and applications have been developed with the aim to make this job easier. A very important role in this activity is played by the geometry description of the detector apparatus layout and its working environment. However, no real common approach to represent geometry data is available and such data can be found in various forms starting from custom semi-structured text files, source code (C/C++/FORTRAN), to XML and database solutions. The XML (Extensible Markup Language) has proven to provide an interesting approach for describing detector geometries, with several different but incompatible XML-based solutions existing. Therefore, interoperability and geometry data exchange among different frameworks is not possible at present. The author introduces a markup language for geometry descriptions. Its aim is to define a common approach for sharing and exchanging of geometry description data. Its requirements and design have been driven by experience and user feedback from existing projects which have their geometry description in XML
Going beyond representational anthropology
DEFF Research Database (Denmark)
Winther, Ida Wentzel
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...
Reflection on Political Representation
DEFF Research Database (Denmark)
Kusche, Isabel
2017-01-01
This article compares how Members of Parliament in the United Kingdom and Ireland reflect on constituency service as an aspect of political representation. It differs from existing research on the constituency role of MPs in two regards. First, it approaches the question from a sociological viewp...
Social representations about cancer
Directory of Open Access Journals (Sweden)
Andreja Cirila Škufca
2003-09-01
Full Text Available In this article we are presenting the results of the comparison study on social representations and causal attributions about cancer. We compared a breast cancer survivors group and control group without own experience of cancer of their own. Although social representations about cancer differ in each group, they are closely related to the concept of suffering, dying and death. We found differences in causal attribution of cancer. In both groups we found a category of risky behavior, which attributes a responsibility for a disease to an individual. Besides these factors we found predominate stress and psychological influences in cancer survivors group. On the other hand control group indicated factors outside the ones control e.g. heredity and environmental factors. Representations about a disease inside person's social space are important in co-shaping the individual process of coping with own disease. Since these representations are not always coherent with the knowledge of modern medicine their knowledge and appreciation in the course of treatment is of great value. We find the findingss of applied social psychology important as starting points in the therapeutic work with patients.
Tervo, Juuso
2012-01-01
In "Postphysical Vision: Art Education's Challenge in an Age of Globalized Aesthetics (AMondofesto)" (2008) and "Beyond Aesthetics: Returning Force and Truth to Art and Its Education" (2009), jan jagodzinski argued for politics that go "beyond" representation--a project that radically questions visual culture…
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.
Fallow), Stray
2009-01-01
Having trouble with geometry? Do Pi, The Pythagorean Theorem, and angle calculations just make your head spin? Relax. With Head First 2D Geometry, you'll master everything from triangles, quads and polygons to the time-saving secrets of similar and congruent angles -- and it'll be quick, painless, and fun. Through entertaining stories and practical examples from the world around you, this book takes you beyond boring problems. You'll actually use what you learn to make real-life decisions, like using angles and parallel lines to crack a mysterious CSI case. Put geometry to work for you, and
Differential geometry curves, surfaces, manifolds
Kohnel, Wolfgang
2002-01-01
This carefully written book is an introduction to the beautiful ideas and results of differential geometry. The first half covers the geometry of curves and surfaces, which provide much of the motivation and intuition for the general theory. Special topics that are explored include Frenet frames, ruled surfaces, minimal surfaces and the Gauss-Bonnet theorem. The second part is an introduction to the geometry of general manifolds, with particular emphasis on connections and curvature. The final two chapters are insightful examinations of the special cases of spaces of constant curvature and Einstein manifolds. The text is illustrated with many figures and examples. The prerequisites are undergraduate analysis and linear algebra.
Conformal-Based Surface Morphing and Multi-Scale Representation
Directory of Open Access Journals (Sweden)
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.
PENILAIAN PEMAHAMAN REPRESENTASI GRAFIK MATERI OPTIKA GEOMETRI MENGGUNAKAN TES DIAGNOSTIK
Directory of Open Access Journals (Sweden)
Wawan Bunawan
2015-06-01
Full Text Available Abstrak: Tujuan penelitian adalah mengembangkan dan menerapkan tes diagnostik pilihan ganda tiga tingkat untuk mengukur pemahaman representasi grafik mahasiswa terkait esensi inkuiri sains dan materi optika geometri. Penelitian menggunakan metode campuran melibatkan 83 mahasiswa calon guru fisika di satu LPTK Sumatera Utara. Instrumen tes diagnostik terlebih dahulu didesain kemudian disempurnakan selama proses, direvisi, dan digunakan untuk mendeteksi dan menilai pemahaman representasi grafik mahasiswa calon guru fisika. Instrumen tes telah dikembangkan untuk dapat mendiagnosis dan memperbaiki kesalahan-kesalahan yang dilakukan calon guru fisika terkait dengan keterampilan mengonstruk grafik, menemukan kesulitan-kesulitan dalam membaca dan menginterpretasi grafik. Analisis data dilakukan secara kualitatif dan kuantitatif. Hasil studi menunjukkan pembacaan grafik dan keterampilan menginterpretasi grafik calon guru fisika masih belum memadai dan juga kemahiran dalam menganalisis grafik bergantung pada jenis grafik dan level atau tipe pertanyaan yang dikembangkan. Kata Kunci: representasi grafik, optik geometri, diagnostik tes ASSESSING OF UNDERSTANDING GRAPHICAL REPRESENTATION CONTENT GEOMETRICAL OPTIC USING DIAGNOSTIC TEST Abstract: The purpose of this study is to develop and apply three tier multiple choice diagnostic test to measure student’s understanding of graphical representation about essential features of inquiry and content geometrical optic. The study was conducted using mixed methods and carried out with 83 prephysics teachers at a University of Teachers Education in North Sumatera. The diagnostic instrument was designed and then progressively refined, revised, and implemented to detect and assess student’s understanding of graphical representation. Test instrument was developed to diagnose and correct the mistakes made by pre-service physics teachers about construction graphic skills, difficulties in the reading and interpretation
Advances in discrete differential geometry
2016-01-01
This is one of the first books on a newly emerging field of discrete differential geometry and an excellent way to access this exciting area. It surveys the fascinating connections between discrete models in differential geometry and complex analysis, integrable systems and applications in computer graphics. The authors take a closer look at discrete models in differential geometry and dynamical systems. Their curves are polygonal, surfaces are made from triangles and quadrilaterals, and time is discrete. Nevertheless, the difference between the corresponding smooth curves, surfaces and classical dynamical systems with continuous time can hardly be seen. This is the paradigm of structure-preserving discretizations. Current advances in this field are stimulated to a large extent by its relevance for computer graphics and mathematical physics. This book is written by specialists working together on a common research project. It is about differential geometry and dynamical systems, smooth and discrete theories, ...
Hyperbolic Metamaterials with Complex Geometry
DEFF Research Database (Denmark)
Lavrinenko, Andrei; Andryieuski, Andrei; Zhukovsky, Sergei
2016-01-01
We investigate new geometries of hyperbolic metamaterialssuch as highly corrugated structures, nanoparticle monolayer assemblies, super-structured or vertically arranged multilayersand nanopillars. All structures retain basic propertiesof hyperbolic metamaterials, but have functionality improved...
An introduction to differential geometry
Willmore, T J
2012-01-01
This text employs vector methods to explore the classical theory of curves and surfaces. Topics include basic theory of tensor algebra, tensor calculus, calculus of differential forms, and elements of Riemannian geometry. 1959 edition.
Topology and geometry for physicists
Nash, Charles
1983-01-01
Differential geometry and topology are essential tools for many theoretical physicists, particularly in the study of condensed matter physics, gravity, and particle physics. Written by physicists for physics students, this text introduces geometrical and topological methods in theoretical physics and applied mathematics. It assumes no detailed background in topology or geometry, and it emphasizes physical motivations, enabling students to apply the techniques to their physics formulas and research. ""Thoroughly recommended"" by The Physics Bulletin, this volume's physics applications range fr
Spectral dimension of quantum geometries
International Nuclear Information System (INIS)
Calcagni, Gianluca; Oriti, Daniele; Thürigen, Johannes
2014-01-01
The spectral dimension is an indicator of geometry and topology of spacetime and a tool to compare the description of quantum geometry in various approaches to quantum gravity. This is possible because it can be defined not only on smooth geometries but also on discrete (e.g., simplicial) ones. In this paper, we consider the spectral dimension of quantum states of spatial geometry defined on combinatorial complexes endowed with additional algebraic data: the kinematical quantum states of loop quantum gravity (LQG). Preliminarily, the effects of topology and discreteness of classical discrete geometries are studied in a systematic manner. We look for states reproducing the spectral dimension of a classical space in the appropriate regime. We also test the hypothesis that in LQG, as in other approaches, there is a scale dependence of the spectral dimension, which runs from the topological dimension at large scales to a smaller one at short distances. While our results do not give any strong support to this hypothesis, we can however pinpoint when the topological dimension is reproduced by LQG quantum states. Overall, by exploring the interplay of combinatorial, topological and geometrical effects, and by considering various kinds of quantum states such as coherent states and their superpositions, we find that the spectral dimension of discrete quantum geometries is more sensitive to the underlying combinatorial structures than to the details of the additional data associated with them. (paper)
Absorbing CAD system geometries into GEANT
International Nuclear Information System (INIS)
Womersley, J.; Dragovitsch, P.; Youssef, S.
1991-01-01
The simulation community has for many years discussed the possibility of direct conversion of geometrical detector models from computer- aided design and engineering systems (CAD systems) to the simulation packages (which we shall assume means GEANT). This would allow fast and simultaneous optimization of the physics performance and structural integrity of detector designs. The benefit that this would offer is the avoidance of such problems as the late discovery of the rather thick cryostats in the D-Zero detector. Recent progress in the absorption of CAD geometries into GEANT models is reviewed, including descriptions of the additions to the I-DEAS solid modeller package developed for the EMPACT SSC proposal, the COGENT CAD-to-GEANT interpreter developed by Quantum Research Services, and the OCTAGON package for representing arbitrary shapes in GEANT. Likely future directions of development are described. 2 refs., 7 figs
On Finsler Geometry and Applications in Mechanics: Review and New Perspectives
Directory of Open Access Journals (Sweden)
J. D. Clayton
2015-01-01
direction as well as position, and a number of connections emerge associated with various covariant derivatives involving affine and nonlinear coefficients. Finsler geometry encompasses Riemannian, Euclidean, and Minkowskian geometries as special cases, and thus it affords great generality for describing a number of phenomena in physics. Here, descriptions of finite deformation of continuous media are of primary focus. After a review of necessary mathematical definitions and derivations, prior work involving application of Finsler geometry in continuum mechanics of solids is reviewed. A new theoretical description of continua with microstructure is then outlined, merging concepts from Finsler geometry and phase field theories of materials science.
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.
Constructing visual representations
DEFF Research Database (Denmark)
Huron, Samuel; Jansen, Yvonne; Carpendale, Sheelagh
2014-01-01
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 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...
Naturalising Representational Content
Shea, Nicholas
2014-01-01
This paper sets out a view about the explanatory role of representational content and advocates one approach to naturalising content – to giving a naturalistic account of what makes an entity a representation and in virtue of what it has the content it does. It argues for pluralism about the metaphysics of content and suggests that a good strategy is to ask the content question with respect to a variety of predictively successful information processing models in experimental psychology and cognitive neuroscience; and hence that data from psychology and cognitive neuroscience should play a greater role in theorising about the nature of content. Finally, the contours of the view are illustrated by drawing out and defending a surprising consequence: that individuation of vehicles of content is partly externalist. PMID:24563661
Knowledge Representation and Ontologies
Grimm, Stephan
Knowledge representation and reasoning aims at designing computer systems that reason about a machine-interpretable representation of the world. Knowledge-based systems have a computational model of some domain of interest in which symbols serve as surrogates for real world domain artefacts, such as physical objects, events, relationships, etc. [1]. The domain of interest can cover any part of the real world or any hypothetical system about which one desires to represent knowledge for com-putational purposes. A knowledge-based system maintains a knowledge base, which stores the symbols of the computational model in the form of statements about the domain, and it performs reasoning by manipulating these symbols. Applications can base their decisions on answers to domain-relevant questions posed to a knowledge base.
Europe representations in textbooks
Brennetot , Arnaud
2011-01-01
This EuroBroadMap working paper presents an analysis of textbooks dealing with the representations of Europe and European Union. In most of these textbooks from secondary school, the teaching of the geography of Europe precedes the evocation of the EU. Europe is often depicted as a given object, reduced to a number of structural aspects (relief, climate, demography, traditional cultures, economic activities, etc.) whose only common point is their location within conventional boundaries. Such ...
DEFF Research Database (Denmark)
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...
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.
Functional representations for quantized fields
International Nuclear Information System (INIS)
Jackiw, R.
1988-01-01
This paper provides information on Representing transformations in quantum theory bosonic quantum field theories: Schrodinger Picture; Represnting Transformations in Bosonic Quantum Field Theory; Two-Dimensional Conformal Transformations, Schrodinger picture representation, Fock space representation, Inequivalent Schrodinger picture representations; Discussion, Self-Dual and Other Models; Field Theory in de Sitter Space. Fermionic Quantum Field Theories: Schroedinger Picture; Schrodinger Picture Representation for Two-Dimensional; Conformal Transformations; Fock Space Dynamics in the Schrodinger Picture; Fock Space Evaluation of Anomalous Current and Conformal Commutators
Chemical thermodynamic representations of and
International Nuclear Information System (INIS)
Besmann, T.M.; Lindemer, T.B.
1985-01-01
All available oxygen potential-temperature-composition data for the calcium fluorite-structure sup(**) phase were retrieved from the literature and utilized in the development of a binary solid solution representation of the phase. The data and phase relations are found to be best described by a solution of [Pusub(4/3)O 2 ] and [PuO 2 ] with a temperature dependent interaction energy. The fluorite-structure is assumed to be represented by a combination of the binaries and , and thus treated as a solution of [Pusub(4/3)O 2 ], [PuO 2 ], [UO 2 ], and either [U 2 Osub(4.5)] or [U 3 O 7 ]. The resulting equations well reproduce the large amount of oxygen potential-temperature-composition data for the mixed oxide system, all of which were also retrieved from the literature. These models are the first that appear to display the appropriate oxygen potential-temperature-composition and phase relation behavior over the entire range of existence for the phases. (orig.)
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...
Cohen-Macaulay representations
Leuschke, Graham J
2012-01-01
This book is a comprehensive treatment of the representation theory of maximal Cohen-Macaulay (MCM) modules over local rings. This topic is at the intersection of commutative algebra, singularity theory, and representations of groups and algebras. Two introductory chapters treat the Krull-Remak-Schmidt Theorem on uniqueness of direct-sum decompositions and its failure for modules over local rings. Chapters 3-10 study the central problem of classifying the rings with only finitely many indecomposable MCM modules up to isomorphism, i.e., rings of finite CM type. The fundamental material--ADE/simple singularities, the double branched cover, Auslander-Reiten theory, and the Brauer-Thrall conjectures--is covered clearly and completely. Much of the content has never before appeared in book form. Examples include the representation theory of Artinian pairs and Burban-Drozd's related construction in dimension two, an introduction to the McKay correspondence from the point of view of maximal Cohen-Macaulay modules, Au...
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.
The Search for Fidelity in Geometry Apps: An Exercise in Futility?
Larkin, Kevin
2015-01-01
As the use of mathematics apps in classrooms becomes more prevalent, robust research into their effectiveness is required to inform best practice regarding their use. This is particularly the case for Geometry apps where accurate and dynamic representations are critical in enhancing mathematical learning. This paper provides findings from an…
Prediction of the weld pool geometry of TIG arc welding by using ...
African Journals Online (AJOL)
Prediction of the weld pool geometry of TIG arc welding by using fuzzy logic controller. ... The experimental data were then used for building a fuzzy logic model to predict the effects of control factors on the responses. A graphical mapping scheme was employed for the graphical representation of the macrostructure zones' ...
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…
Investigation of Surface Phenomena in Shocked Tin in Converging Geometry
Energy Technology Data Exchange (ETDEWEB)
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.
Variable geometry Darrieus wind machine
Pytlinski, J. T.; Serrano, D.
1983-08-01
A variable geometry Darrieus wind machine is proposed. The lower attachment of the blades to the rotor can move freely up and down the axle allowing the blades of change shape during rotation. Experimental data for a 17 m. diameter Darrieus rotor and a theoretical model for multiple streamtube performance prediction were used to develop a computer simulation program for studying parameters that affect the machine's performance. This new variable geometry concept is described and interrelated with multiple streamtube theory through aerodynamic parameters. The computer simulation study shows that governor behavior of a Darrieus turbine can not be attained by a standard turbine operating within normally occurring rotational velocity limits. A second generation variable geometry Darrieus wind turbine which uses a telescopic blade is proposed as a potential improvement on the studied concept.
Flux compactifications and generalized geometries
International Nuclear Information System (INIS)
Grana, Mariana
2006-01-01
Following the lectures given at CERN Winter School 2006, we present a pedagogical overview of flux compactifications and generalized geometries, concentrating on closed string fluxes in type II theories. We start by reviewing the supersymmetric flux configurations with maximally symmetric four-dimensional spaces. We then discuss the no-go theorems (and their evasion) for compactifications with fluxes. We analyse the resulting four-dimensional effective theories for Calabi-Yau and Calabi-Yau orientifold compactifications, concentrating on the flux-induced superpotentials. We discuss the generic mechanism of moduli stabilization and illustrate with two examples: the conifold in IIB and a T 6 /(Z 3 x Z 3 ) torus in IIA. We finish by studying the effective action and flux vacua for generalized geometries in the context of generalized complex geometry
Flux compactifications and generalized geometries
Energy Technology Data Exchange (ETDEWEB)
Grana, Mariana [Service de Physique Theorique, CEA/Saclay, 91191 Gif-sur-Yvette Cedex (France)
2006-11-07
Following the lectures given at CERN Winter School 2006, we present a pedagogical overview of flux compactifications and generalized geometries, concentrating on closed string fluxes in type II theories. We start by reviewing the supersymmetric flux configurations with maximally symmetric four-dimensional spaces. We then discuss the no-go theorems (and their evasion) for compactifications with fluxes. We analyse the resulting four-dimensional effective theories for Calabi-Yau and Calabi-Yau orientifold compactifications, concentrating on the flux-induced superpotentials. We discuss the generic mechanism of moduli stabilization and illustrate with two examples: the conifold in IIB and a T{sup 6} /(Z{sub 3} x Z{sub 3}) torus in IIA. We finish by studying the effective action and flux vacua for generalized geometries in the context of generalized complex geometry.
Euclidean geometry and its subgeometries
Specht, Edward John; Calkins, Keith G; Rhoads, Donald H
2015-01-01
In this monograph, the authors present a modern development of Euclidean geometry from independent axioms, using up-to-date language and providing detailed proofs. The axioms for incidence, betweenness, and plane separation are close to those of Hilbert. This is the only axiomatic treatment of Euclidean geometry that uses axioms not involving metric notions and that explores congruence and isometries by means of reflection mappings. The authors present thirteen axioms in sequence, proving as many theorems as possible at each stage and, in the process, building up subgeometries, most notably the Pasch and neutral geometries. Standard topics such as the congruence theorems for triangles, embedding the real numbers in a line, and coordinatization of the plane are included, as well as theorems of Pythagoras, Desargues, Pappas, Menelaus, and Ceva. The final chapter covers consistency and independence of axioms, as well as independence of definition properties. There are over 300 exercises; solutions to many of the...
Electrodynamics and Spacetime Geometry: Foundations
Cabral, Francisco; Lobo, Francisco S. N.
2017-02-01
We explore the intimate connection between spacetime geometry and electrodynamics. This link is already implicit in the constitutive relations between the field strengths and excitations, which are an essential part of the axiomatic structure of electromagnetism, clearly formulated via integration theory and differential forms. We review the foundations of classical electromagnetism based on charge and magnetic flux conservation, the Lorentz force and the constitutive relations. These relations introduce the conformal part of the metric and allow the study of electrodynamics for specific spacetime geometries. At the foundational level, we discuss the possibility of generalizing the vacuum constitutive relations, by relaxing the fixed conditions of homogeneity and isotropy, and by assuming that the symmetry properties of the electro-vacuum follow the spacetime isometries. The implications of this extension are briefly discussed in the context of the intimate connection between electromagnetism and the geometry (and causal structure) of spacetime.
Dayside merging and cusp geometry
International Nuclear Information System (INIS)
Crooker, N.U.
1979-01-01
Geometrical considerations are presented to show that dayside magnetic merging when constrained to act only where the fields are antiparallel results in lines of merging that converge at the polar cusps. An important consequence of this geometry is that no accelerated flows are predicted across the dayside magnetopause. Acceleration owing to merging acts in opposition to the magnetosheath flow at the merging point and produces the variably directed, slower-than-magnetosheath flows observed in the entry layer. Another consequence of the merging geometry is that much of the time closed field lines constitute the subsolar region of the magnetopause. The manner in which the polar cap convection patterns predicted by the proposed geometry change as the interplanetary field is rotated through 360 0 provides a unifying description of how the observed single circular vortex and the crescent-shaped double vortex patterns mutually evolve under the influence of a single operating principle
DOGBONE GEOMETRY FOR RECIRCULATING ACCELERATORS
International Nuclear Information System (INIS)
BERG, J.S.; JOHNSTONE, C.; SUMMERS, D.
2001-01-01
Most scenarios for accelerating muons require recirculating acceleration. A racetrack shape for the accelerator requires particles with lower energy in early passes to traverse almost the same length of arc as particles with the highest energy. This extra arc length may lead to excess decays and excess cost. Changing the geometry to a dogbone shape, where there is a single linac and the beam turns completely around at the end of the linac, returning to the same end of the linac from which it exited, addresses this problem. In this design, the arc lengths can be proportional to the particle's momentum. This paper proposes an approximate cost model for a recirculating accelerator, attempts to make cost-optimized designs for both racetrack and dogbone geometries, and demonstrates that the dogbone geometry does appear to be more cost effective
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...
Geometric Transformations in Engineering Geometry
Directory of Open Access Journals (Sweden)
I. F. Borovikov
2015-01-01
Full Text Available Recently, for business purposes, in view of current trends and world experience in training engineers, research and faculty staff there has been a need to transform traditional courses of descriptive geometry into the course of engineering geometry in which the geometrical transformations have to become its main section. On the basis of critical analysis the paper gives suggestions to improve a presentation technique of this section both in the classroom and in academic literature, extend an application scope of geometrical transformations to solve the position and metric tasks and simulation of surfaces, as well as to design complex engineering configurations, which meet a number of pre-specified conditions.The article offers to make a number of considerable amendments to the terms and definitions used in the existing courses of descriptive geometry. It draws some conclusions and makes the appropriate proposals on feasibility of coordination in teaching the movement transformation in the courses of analytical and descriptive geometry. This will provide interdisciplinary team teaching and allow students to be convinced that a combination of analytical and graphic ways to solve geometric tasks is useful and reasonable.The traditional sections of learning courses need to be added with a theory of projective and bi-rational transformations. In terms of application simplicity and convenience it is enough to consider the central transformations when solving the applied tasks. These transformations contain a beam of sub-invariant (low-invariant straight lines on which the invariant curve induces non-involution and involution projectivities. The expediency of nonlinear transformations application is shown in the article by a specific example of geometric modeling of the interfacing surface "spar-blade".Implementation of these suggestions will contribute to a real transformation of a traditional course of descriptive geometry to the engineering geometry
The SUSY oscillator from local geometry: Dynamics and coherent states
International Nuclear Information System (INIS)
Thienel, H.P.
1994-01-01
The choice of a coordinate chart on an analytical R n (R a n ) provides a representation of the n-dimensional SUSY oscillator. The corresponding Hilbert space is Cartan's exterior algebra endowed with a suitable scalar product. The exterior derivative gives rise to the algebra of the n-dimensional SUSY oscillator. Its euclidean dynamics is an inherent consequence of the geometry imposed by the Lie derivative generating the dilations, i.e. evolution of the quantum system corresponds to parametrization of a sequence of charts by euclidean time. Coherent states emerge as a natural structure related to the Lie derivative generating the translations. (orig.)
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.
KEMAJUAN BELAJAR SISWA PADA GEOMETRI TRANSFORMASI MENGGUNAKAN AKTIVITAS REFLEKSI GEOMETRI
Directory of Open Access Journals (Sweden)
Irkham Ulil Albab
2014-10-01
Full Text Available Abstrak: Penelitian ini bertujuan untuk mendeskripsikan kemajuan belajar siswa pada materi geometri transformasi yang didukung dengan serangkaian aktivitas belajar berdasarkan Pendidikan Matematika Realistik Indonesia. Penelitian didesain melalui tiga tahap, yaitu tahapan perancangan desain awal, pengujian desain melalui pembelajaran awal dan pembelajaran eksperimental, dan tahap analisis retrospektif. Dalam penelitian ini, Hypothetical Learning Trajectory, HLT (HLT berperan penting sebagai desain pembelajaran sekaligus instrumen penelitian. HLT diujikan terhadap 26 siswa kelas VII. Data dikumpulkan dengan teknik wawancara, pengamatan, dan catatan lapangan. Hasil penelitian menunjukkan bahwa desain pembelajaran ini mampu menstimulasi siswa untuk memberikan karakteristik refleksi dan transformasi geometri lainnya secara informal, mengklasifikasikannya dalam transformasi isometri pada level kedua, dan menemukan garis bantuan refleksi pada level yang lebih formal. Selain itu, garis bantuan refleksi digunakan oleh siswa untuk menggambar bayangan refleksi dan pola pencerminan serta memahami bentuk rotasi dan translasi sebagai kombinasi refleksi adalah level tertinggi. Keyword: transformasi geometri, kombinasi refleksi, rotasi, translasi, design research, HLT STUDENTS’ LEARNING PROGRESS ON TRANSFORMATION GEOMETRY USING THE GEOMETRY REFLECTION ACTIVITIES Abstract: This study was aimed at describing the students’ learning progress on transformation geometry supported by a set of learning activities based on Indonesian Realistic Mathematics Education. The study was designed into three stages, that is, the preliminary design stage, the design testing through initial instruction and experiment, and the restrospective analysis stage. In this study, Hypothetical Learning Trajectory (HLT played an important role as an instructional design and a research instrument. HLT was tested to 26 seventh grade students. The data were collected through interviews
Graphical debugging of combinational geometry
International Nuclear Information System (INIS)
Burns, T.J.; Smith, M.S.
1992-01-01
A graphical debugger for combinatorial geometry being developed at Oak Ridge National Laboratory is described. The prototype debugger consists of two parts: a FORTRAN-based ''view'' generator and a Microsoft Windows application for displaying the geometry. Options and features of both modules are discussed. Examples illustrating the various options available are presented. The potential for utilizing the images produced using the debugger as a visualization tool for the output of the radiation transport codes is discussed as is the future direction of the development
Lectures on Algebraic Geometry I
Harder, Gunter
2012-01-01
This book and the following second volume is an introduction into modern algebraic geometry. In the first volume the methods of homological algebra, theory of sheaves, and sheaf cohomology are developed. These methods are indispensable for modern algebraic geometry, but they are also fundamental for other branches of mathematics and of great interest in their own. In the last chapter of volume I these concepts are applied to the theory of compact Riemann surfaces. In this chapter the author makes clear how influential the ideas of Abel, Riemann and Jacobi were and that many of the modern metho
Combinatorial geometry in the plane
Hadwiger, Hugo; Klee, Victor
2014-01-01
Geared toward advanced undergraduates familiar with analysis and college geometry, this concise book discusses theorems on topics restricted to the plane such as convexity, coverings, and graphs. In addition to helping students cultivate rigorous thought, the text encourages the development of mathematical intuition and clarifies the nature of mathematical research.The two-part treatment begins with specific topics including integral distances, covering problems, point set geometry and convexity, simple paradoxes involving point sets, and pure combinatorics, among other subjects. The second pa
Modern differential geometry for physicists
Isham, C J
1989-01-01
These notes are the content of an introductory course on modern, coordinate-free differential geometry which is taken by the first-year theoretical physics PhD students, or by students attending the one-year MSc course "Fundamental Fields and Forces" at Imperial College. The book is concerned entirely with mathematics proper, although the emphasis and detailed topics have been chosen with an eye to the way in which differential geometry is applied these days to modern theoretical physics. This includes not only the traditional area of general relativity but also the theory of Yang-Mills fields
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
Geometry, topology, and string theory
Energy Technology Data Exchange (ETDEWEB)
Varadarajan, Uday [Univ. of California, Berkeley, CA (United States)
2003-01-01
A variety of scenarios are considered which shed light upon the uses and limitations of classical geometric and topological notions in string theory. The primary focus is on situations in which D-brane or string probes of a given classical space-time see the geometry quite differently than one might naively expect. In particular, situations in which extra dimensions, non-commutative geometries as well as other non-local structures emerge are explored in detail. Further, a preliminary exploration of such issues in Lorentzian space-times with non-trivial causal structures within string theory is initiated.
Spatial geometry and special relativity
DEFF Research Database (Denmark)
Kneubil, Fabiana Botelho
2016-01-01
In this work, it is shown the interplay of relative and absolute entities, which are present in both spatial geometry and special relativity. In order to strengthen the understanding of special relativity, we discuss firstly an instance of geometry and the existence of both frame......-dependent and frame-independent entities. We depart from a subject well known by students, which is the three-dimensional geometric space in order to compare, afterwards, with the treatment of four-dimensional space in the special relativity. The differences and similarities between these two subjects are also...
Stochastic geometry and its applications
Chiu, Sung Nok; Kendall, Wilfrid S; Mecke, Joseph
2013-01-01
An extensive update to a classic text Stochastic geometry and spatial statistics play a fundamental role in many modern branches of physics, materials sciences, engineering, biology and environmental sciences. They offer successful models for the description of random two- and three-dimensional micro and macro structures and statistical methods for their analysis. The previous edition of this book has served as the key reference in its field for over 18 years and is regarded as the best treatment of the subject of stochastic geometry, both as a subject with vital a
Introduction to topology and geometry
Stahl, Saul
2014-01-01
An easily accessible introduction to over three centuries of innovations in geometry Praise for the First Edition ". . . a welcome alternative to compartmentalized treatments bound to the old thinking. This clearly written, well-illustrated book supplies sufficient background to be self-contained." -CHOICE This fully revised new edition offers the most comprehensive coverage of modern geometry currently available at an introductory level. The book strikes a welcome balance between academic rigor and accessibility, providing a complete and cohesive picture of the science with an unparallele
Algebraic geometry and theta functions
Coble, Arthur B
1929-01-01
This book is the result of extending and deepening all questions from algebraic geometry that are connected to the central problem of this book: the determination of the tritangent planes of a space curve of order six and genus four, which the author treated in his Colloquium Lecture in 1928 at Amherst. The first two chapters recall fundamental ideas of algebraic geometry and theta functions in such fashion as will be most helpful in later applications. In order to clearly present the state of the central problem, the author first presents the better-known cases of genus two (Chapter III) and
Geometry, topology, and string theory
International Nuclear Information System (INIS)
Varadarajan, Uday
2003-01-01
A variety of scenarios are considered which shed light upon the uses and limitations of classical geometric and topological notions in string theory. The primary focus is on situations in which D-brane or string probes of a given classical space-time see the geometry quite differently than one might naively expect. In particular, situations in which extra dimensions, non-commutative geometries as well as other non-local structures emerge are explored in detail. Further, a preliminary exploration of such issues in Lorentzian space-times with non-trivial causal structures within string theory is initiated
Mathematical model of geometry and fibrous structure of the heart.
Nielsen, P M; Le Grice, I J; Smaill, B H; Hunter, P J
1991-04-01
We developed a mathematical representation of ventricular geometry and muscle fiber organization using three-dimensional finite elements referred to a prolate spheroid coordinate system. Within elements, fields are approximated using basis functions with associated parameters defined at the element nodes. Four parameters per node are used to describe ventricular geometry. The radial coordinate is interpolated using cubic Hermite basis functions that preserve slope continuity, while the angular coordinates are interpolated linearly. Two further nodal parameters describe the orientation of myocardial fibers. The orientation of fibers within coordinate planes bounded by epicardial and endocardial surfaces is interpolated linearly, with transmural variation given by cubic Hermite basis functions. Left and right ventricular geometry and myocardial fiber orientations were characterized for a canine heart arrested in diastole and fixed at zero transmural pressure. The geometry was represented by a 24-element ensemble with 41 nodes. Nodal parameters fitted using least squares provided a realistic description of ventricular epicardial [root mean square (RMS) error less than 0.9 mm] and endocardial (RMS error less than 2.6 mm) surfaces. Measured fiber fields were also fitted (RMS error less than 17 degrees) with a 60-element, 99-node mesh obtained by subdividing the 24-element mesh. These methods provide a compact and accurate anatomic description of the ventricles suitable for use in finite element stress analysis, simulation of cardiac electrical activation, and other cardiac field modeling problems.
DEFF Research Database (Denmark)
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...... Satan episode in Under Satan’s Sun is neither a break with the seriousness nor with the realism of the Catholic novel. On the basis of Tvetan Todorov’s definition of the traditional fantastic tale, the analysis shows that only the beginning of the fantastic episode follows Todorov’s definition...
DEFF Research Database (Denmark)
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...... Satan episode in Under Satan’s Sun is neither a break with the seriousness nor with the realism of the Catholic novel. On the basis of Tvetan Todorov’s definition of the traditional fantastic tale, the analysis shows that only the beginning of the fantastic episode follows Todorov’s definition...
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
Between Representation and Eternity
DEFF Research Database (Denmark)
Atzbach, Rainer
2016-01-01
This paper seeks to explore how prayer and praying practice are reflected in archaeological sources. Apart from objects directly involved in the personal act of praying, such as rosaries and praying books, churches and religious foundations played a major role in the medieval system of intercession....... 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...
Differential geometry of groups in string theory
International Nuclear Information System (INIS)
Schmidke, W.B. Jr.
1990-09-01
Techniques from differential geometry and group theory are applied to two topics from string theory. The first topic studied is quantum groups, with the example of GL (1|1). The quantum group GL q (1|1) is introduced, and an exponential description is derived. The algebra and coproduct are determined using the invariant differential calculus method introduced by Woronowicz and generalized by Wess and Zumino. An invariant calculus is also introduced on the quantum superplane, and a representation of the algebra of GL q (1|1) in terms of the super-plane coordinates is constructed. The second topic follows the approach to string theory introduced by Bowick and Rajeev. Here the ghost contribution to the anomaly of the energy-momentum tensor is calculated as the Ricci curvature of the Kaehler quotient space Diff(S 1 )/S 1 . We discuss general Kaehler quotient spaces and derive an expression for their Ricci curvatures. Application is made to the string and superstring diffeomorphism groups, considering all possible choices of subgroup. The formalism is extended to associated holomorphic vector bundles, where the Ricci curvature corresponds to the anomaly for different ghost sea levels. 26 refs
Noncommutative geometry and basic physics
International Nuclear Information System (INIS)
Kastler, D.
2000-01-01
The author describes spectral triples as generalized Dirac operators, the electroweak inner spectral triple, the application of the quantum Yang-Mills algorithm to the electroweak standard model sector, real spectral triples, the asymptotic heat-kernel expansion of the spectral action, tree approximation, the fermionic action, and the regular representation of the finite U q (sl2)
The Idea of Order at Geometry Class.
Rishel, Thomas
The idea of order in geometry is explored using the experience of assignments given to undergraduates in a college geometry course "From Space to Geometry." Discussed are the definition of geometry, and earth measurement using architecture, art, and common experience. This discussion concludes with a consideration of the question of whether…
Teaching Spatial Geometry in a Virtual World
DEFF Research Database (Denmark)
Förster, Klaus-Tycho
2017-01-01
Spatial geometry is one of the fundamental mathematical building blocks of any engineering education. However, it is overshadowed by planar geometry in the curriculum between playful early primary education and later analytical geometry, leaving a multi-year gap where spatial geometry is absent...
Non-uniform tube representation of proteins
DEFF Research Database (Denmark)
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....
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.
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...
Social Representations of Intelligence
Directory of Open Access Journals (Sweden)
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.
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…
Normal forms in Poisson geometry
Marcut, I.T.
2013-01-01
The structure of Poisson manifolds is highly nontrivial even locally. The first important result in this direction is Conn's linearization theorem around fixed points. One of the main results of this thesis (Theorem 2) is a normal form theorem in Poisson geometry, which is the Poisson-geometric
Exploring Bundling Theory with Geometry
Eckalbar, John C.
2006-01-01
The author shows how instructors might successfully introduce students in principles and intermediate microeconomic theory classes to the topic of bundling (i.e., the selling of two or more goods as a package, rather than separately). It is surprising how much students can learn using only the tools of high school geometry. To be specific, one can…
Stochastic Modelling of River Geometry
DEFF Research Database (Denmark)
Sørensen, John Dalsgaard; Schaarup-Jensen, K.
1996-01-01
Numerical hydrodynamic river models are used in a large number of applications to estimate critical events for rivers. These estimates are subject to a number of uncertainties. In this paper, the problem to evaluate these estimates using probabilistic methods is considered. Stochastic models for ...... for river geometries are formulated and a coupling between hydraulic computational methods and numerical reliability methods is presented....
Matter in toy dynamical geometries
Konopka, T.J.
2009-01-01
One of the objectives of theories describing quantum dynamical geometry is to compute expectation values of geometrical observables. The results of such computations can be affected by whether or not matter is taken into account. It is thus important to understand to what extent and to what effect
Ca??adas, Mar??a C.; Molina, Marta; Gallardo, Sandra; Mart??nez-Santaolalla, Manuel J.; Pe??as, Mar??a
2010-01-01
In this work we present an activity for High School students in which various mathematical concepts of plane and spatial geometry are involved. The final objective of the proposed tasks is constructing a particular polyhedron, the cube, by using a modality of origami called modular origami.
General Relativity: Geometry Meets Physics
Thomsen, Dietrick E.
1975-01-01
Observing the relationship of general relativity and the geometry of space-time, the author questions whether the rest of physics has geometrical explanations. As a partial answer he discusses current research on subatomic particles employing geometric transformations, and cites the existence of geometrical definitions of physical quantities such…
Multivariable calculus and differential geometry
Walschap, Gerard
2015-01-01
This text is a modern in-depth study of the subject that includes all the material needed from linear algebra. It then goes on to investigate topics in differential geometry, such as manifolds in Euclidean space, curvature, and the generalization of the fundamental theorem of calculus known as Stokes' theorem.
College geometry a unified development
Kay, David C
2011-01-01
""The book is a comprehensive textbook on basic geometry. … Key features of the book include numerous figures and many problems, more than half of which come with hints or even complete solutions. Frequent historical comments add to making the reading a pleasant one.""-Michael Joswig, Zentralblatt MATH 1273
International Nuclear Information System (INIS)
Gleiter, H.
1991-01-01
Nanocrystalline solids are polycrystals, the crystal size of which is a few (typically 1 to 10) nanometres so that 50% or more of the solid consists of incoherent interfaces between crystals of different orientations. Solids consisting primarily of internal interfaces represent a separate class of atomic structures because the atomic arrangement formed in the core of an interface is known to be an arrangement of minimum energy in the potential field of the two adjacent crystal lattices with different crystallographic orientations on either side of the boundary core. These boundary conditions result in atomic structures in the interfacial cores which cannot be formed elsewhere (e.g. in glasses or perfect crystals). Nanocrystalline solids are of interest for the following four reasons: (1) Nanocrystalline solids exhibit an atomic structure which differs from that of the two known solid states: the crystalline (with long-range order) and the glassy (with short-range order). (2) The properties of nanocrystalline solids differ (in some cases by several orders of magnitude) from those of glasses and/or crystals with the same chemical composition, which suggests that they may be utilized technologically in the future. (3) Nanocrystalline solids seem to permit the alloying of conventionally immiscible components. (4) If small (1 to 10 nm diameter) solid droplets with a glassy structure are consolidated (instead of small crystals), a new type of glass, called nanoglass, is obtained. Such glasses seem to differ structurally from conventional glasses. (orig.)
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
Mahaffey, Michael L.
One of a series of experimental units for children at the preschool level, this booklet deals with geometric concepts. A unit on volume and a unit on linear measurement are covered; for each unit a discussion of mathematical objectives, a list of materials needed, and a sequence of learning activities are provided. Directions are specified for the…
DEFF Research Database (Denmark)
Byg din egen boomerang, kast den, se den flyve, forstå hvorfor og hvordan den vender tilbage, og grib den. Det handler om opdriften på vingerne når du flyver, men det handler også og allermest om den mærkværdige gyroskop-effekt, du bruger til at holde balancen, når du kører på cykel. Vi vil bruge...
Discrete differential geometry. Consistency as integrability
Bobenko, Alexander I.; Suris, Yuri B.
2005-01-01
A new field of discrete differential geometry is presently emerging on the border between differential and discrete geometry. Whereas classical differential geometry investigates smooth geometric shapes (such as surfaces), and discrete geometry studies geometric shapes with finite number of elements (such as polyhedra), the discrete differential geometry aims at the development of discrete equivalents of notions and methods of smooth surface theory. Current interest in this field derives not ...
A new experiment-independent mechanism to persistify and serve the detector geometry of ATLAS
Bianchi, Riccardo Maria; Boudreau, Joseph; Vukotic, Ilija
2017-10-01
The complex geometry of the whole detector of the ATLAS experiment at LHC is currently stored only in custom online databases, from which it is built on-the-fly on request. Accessing the online geometry guarantees accessing the latest version of the detector description, but requires the setup of the full ATLAS software framework “Athena”, which provides the online services and the tools to retrieve the data from the database. This operation is cumbersome and slows down the applications that need to access the geometry. Moreover, all applications that need to access the detector geometry need to be built and run on the same platform as the ATLAS framework, preventing the usage of the actual detector geometry in stand-alone applications. Here we propose a new mechanism to persistify (in software development in general, and in HEP computing in particular, persistifying means taking an object which lives in memory only - for example because it was built on-the-fly while processing the experimental data, - serializing it and storing it on disk as a persistent object) and serve the geometry of HEP experiments. The new mechanism is composed by a new file format and the modules to make use of it. The new file format allows to store the whole detector description locally in a file, and it is especially optimized to describe large complex detectors with the minimum file size, making use of shared instances and storing compressed representations of geometry transformations. Then, the detector description can be read back in, to fully restore the in-memory geometry tree. Moreover, a dedicated REST API is being designed and developed to serve the geometry in standard exchange formats like JSON, to let users and applications download specific partial geometry information. With this new geometry persistification a new generation of applications could be developed, which can use the actual detector geometry while being platform-independent and experiment-independent.
Parental representations of transsexuals.
Parker, G; Barr, R
1982-06-01
The parental representations of 30 male-to-female transsexuals were rated using a measure of fundamental parental dimensions and shown to be of acceptable validity as a measure both of perceived and actual parental characteristics. Scores on that measure were compared separately against scores returned by matched male and female controls. The transsexuals did not differ from the male controls in their scoring of their mothers but did score their fathers as less caring and more overprotective. These differences were weaker for the comparisons made against the female controls. Item analyses suggested that the greater paternal "overprotection" experienced by transsexuals was due to their fathers being perceived as offering less encouragement to their sons' independence and autonomy. Several interpretations of the findings are considered.
The representation of neutron polarization
International Nuclear Information System (INIS)
Byrne, J.
1979-01-01
Neutron beam polarization representation is discussed under the headings; transfer matrices, coherent parity violation for neutrons, neutron spin rotation in helical magnetic fields, polarization and interference. (UK)
Sinusoidal Representation of Acoustic Signals
Honda, Masaaki
Sinusoidal representation of acoustic signals has been an important tool in speech and music processing like signal analysis, synthesis and time scale or pitch modifications. It can be applicable to arbitrary signals, which is an important advantage over other signal representations like physical modeling of acoustic signals. In sinusoidal representation, acoustic signals are composed as sums of sinusoid (sine wave) with different amplitudes, frequencies and phases, which is based on the timedependent short-time Fourier transform (STFT). This article describes the principles of acoustic signal analysis/synthesis based on a sinusoid representation with focus on sine waves with rapidly varying frequency.
International Nuclear Information System (INIS)
1995-01-01
The article drawn up within the framework of 'the assessment of the state of the environment in Lebanon' provides an overview of solid waste management, and assesses future wastes volume and waste disposal issues.In particular it addresses the following concerns: - Long term projections of solid waste arisings (i.e. domestic, industrial, such commercial wastes, vehicle types, construction waste, waste oils, hazardous toxic wastes and finally hospital and clinical wastes) are described. - Appropriate disposal routes, and strategies for reducing volumes for final disposal - Balance between municipal and industrial solid waste generation and disposal/treatment and - environmental impacts (aesthetics, human health, natural environment )of existing dumps, and the potential impact of government plans for construction of solid waste facilities). Possible policies for institutional reform within the waste management sector are proposed. Tables provides estimations of generation rates and distribution of wastes in different regions of Lebanon. Laws related to solid waste management are summarized
Quantum logics and convex geometry
International Nuclear Information System (INIS)
Bunce, L.J.; Wright, J.D.M.
1985-01-01
The main result is a representation theorem which shows that, for a large class of quantum logics, a quantum logic, Q, is isomorphic to the lattice of projective faces in a suitable convex set K. As an application we extend our earlier results, which, subject to countability conditions, gave a geometric characterization of those quantum logics which are isomorphic to the projection lattice of a von Neumann algebra or a JBW-algebra. (orig.)
Code subspaces for LLM geometries
Berenstein, David; Miller, Alexandra
2018-03-01
We consider effective field theory around classical background geometries with a gauge theory dual, specifically those in the class of LLM geometries. These are dual to half-BPS states of N= 4 SYM. We find that the language of code subspaces is natural for discussing the set of nearby states, which are built by acting with effective fields on these backgrounds. This work extends our previous work by going beyond the strict infinite N limit. We further discuss how one can extract the topology of the state beyond N→∞ and find that, as before, uncertainty and entanglement entropy calculations provide a useful tool to do so. Finally, we discuss obstructions to writing down a globally defined metric operator. We find that the answer depends on the choice of reference state that one starts with. Therefore, within this setup, there is ambiguity in trying to write an operator that describes the metric globally.
Euclidean distance geometry an introduction
Liberti, Leo
2017-01-01
This textbook, the first of its kind, presents the fundamentals of distance geometry: theory, useful methodologies for obtaining solutions, and real world applications. Concise proofs are given and step-by-step algorithms for solving fundamental problems efficiently and precisely are presented in Mathematica®, enabling the reader to experiment with concepts and methods as they are introduced. Descriptive graphics, examples, and problems, accompany the real gems of the text, namely the applications in visualization of graphs, localization of sensor networks, protein conformation from distance data, clock synchronization protocols, robotics, and control of unmanned underwater vehicles, to name several. Aimed at intermediate undergraduates, beginning graduate students, researchers, and practitioners, the reader with a basic knowledge of linear algebra will gain an understanding of the basic theories of distance geometry and why they work in real life.
Fractal geometry and computer graphics
Sakas, Georgios; Peitgen, Heinz-Otto; Englert, Gabriele
1992-01-01
Fractal geometry has become popular in the last 15 years, its applications can be found in technology, science, or even arts. Fractal methods and formalism are seen today as a general, abstract, but nevertheless practical instrument for the description of nature in a wide sense. But it was Computer Graphics which made possible the increasing popularity of fractals several years ago, and long after their mathematical formulation. The two disciplines are tightly linked. The book contains the scientificcontributions presented in an international workshop in the "Computer Graphics Center" in Darmstadt, Germany. The target of the workshop was to present the wide spectrum of interrelationships and interactions between Fractal Geometry and Computer Graphics. The topics vary from fundamentals and new theoretical results to various applications and systems development. All contributions are original, unpublished papers.The presentations have been discussed in two working groups; the discussion results, together with a...
Differential geometry and mathematical physics
Rudolph, Gerd
Starting from an undergraduate level, this book systematically develops the basics of • Calculus on manifolds, vector bundles, vector fields and differential forms, • Lie groups and Lie group actions, • Linear symplectic algebra and symplectic geometry, • Hamiltonian systems, symmetries and reduction, integrable systems and Hamilton-Jacobi theory. The topics listed under the first item are relevant for virtually all areas of mathematical physics. The second and third items constitute the link between abstract calculus and the theory of Hamiltonian systems. The last item provides an introduction to various aspects of this theory, including Morse families, the Maslov class and caustics. The book guides the reader from elementary differential geometry to advanced topics in the theory of Hamiltonian systems with the aim of making current research literature accessible. The style is that of a mathematical textbook,with full proofs given in the text or as exercises. The material is illustrated by numerous d...
Grassmannian geometry of scattering amplitudes
Arkani-Hamed, Nima; Cachazo, Freddy; Goncharov, Alexander; Postnikov, Alexander; Trnka, Jaroslav
2016-01-01
Outlining a revolutionary reformulation of the foundations of perturbative quantum field theory, this book is a self-contained and authoritative analysis of the application of this new formulation to the case of planar, maximally supersymmetric Yang–Mills theory. The book begins by deriving connections between scattering amplitudes and Grassmannian geometry from first principles before introducing novel physical and mathematical ideas in a systematic manner accessible to both physicists and mathematicians. The principle players in this process are on-shell functions which are closely related to certain sub-strata of Grassmannian manifolds called positroids - in terms of which the classification of on-shell functions and their relations becomes combinatorially manifest. This is an essential introduction to the geometry and combinatorics of the positroid stratification of the Grassmannian and an ideal text for advanced students and researchers working in the areas of field theory, high energy physics, and the...
Foliation theory in algebraic geometry
McKernan, James; Pereira, Jorge
2016-01-01
Featuring a blend of original research papers and comprehensive surveys from an international team of leading researchers in the thriving fields of foliation theory, holomorphic foliations, and birational geometry, this book presents the proceedings of the conference "Foliation Theory in Algebraic Geometry," hosted by the Simons Foundation in New York City in September 2013. Topics covered include: Fano and del Pezzo foliations; the cone theorem and rank one foliations; the structure of symmetric differentials on a smooth complex surface and a local structure theorem for closed symmetric differentials of rank two; an overview of lifting symmetric differentials from varieties with canonical singularities and the applications to the classification of AT bundles on singular varieties; an overview of the powerful theory of the variety of minimal rational tangents introduced by Hwang and Mok; recent examples of varieties which are hyperbolic and yet the Green-Griffiths locus is the whole of X; and a classificati...
Groups and Geometries : Siena Conference
Kantor, William; Lunardon, Guglielmo; Pasini, Antonio; Tamburini, Maria
1998-01-01
On September 1-7, 1996 a conference on Groups and Geometries took place in lovely Siena, Italy. It brought together experts and interested mathematicians from numerous countries. The scientific program centered around invited exposi tory lectures; there also were shorter research announcements, including talks by younger researchers. The conference concerned a broad range of topics in group theory and geometry, with emphasis on recent results and open problems. Special attention was drawn to the interplay between group-theoretic methods and geometric and combinatorial ones. Expanded versions of many of the talks appear in these Proceedings. This volume is intended to provide a stimulating collection of themes for a broad range of algebraists and geometers. Among those themes, represented within the conference or these Proceedings, are aspects of the following: 1. the classification of finite simple groups, 2. the structure and properties of groups of Lie type over finite and algebraically closed fields of f...
Stochastic Geometry and Quantum Gravity: Some Rigorous Results
Zessin, H.
The aim of these lectures is a short introduction into some recent developments in stochastic geometry which have one of its origins in simplicial gravity theory (see Regge Nuovo Cimento 19: 558-571, 1961). The aim is to define and construct rigorously point processes on spaces of Euclidean simplices in such a way that the configurations of these simplices are simplicial complexes. The main interest then is concentrated on their curvature properties. We illustrate certain basic ideas from a mathematical point of view. An excellent representation of this area can be found in Schneider and Weil (Stochastic and Integral Geometry, Springer, Berlin, 2008. German edition: Stochastische Geometrie, Teubner, 2000). In Ambjørn et al. (Quantum Geometry Cambridge University Press, Cambridge, 1997) you find a beautiful account from the physical point of view. More recent developments in this direction can be found in Ambjørn et al. ("Quantum gravity as sum over spacetimes", Lect. Notes Phys. 807. Springer, Heidelberg, 2010). After an informal axiomatic introduction into the conceptual foundations of Regge's approach the first lecture recalls the concepts and notations used. It presents the fundamental zero-infinity law of stochastic geometry and the construction of cluster processes based on it. The second lecture presents the main mathematical object, i.e. Poisson-Delaunay surfaces possessing an intrinsic random metric structure. The third and fourth lectures discuss their ergodic behaviour and present the two-dimensional Regge model of pure simplicial quantum gravity. We terminate with the formulation of basic open problems. Proofs are given in detail only in a few cases. In general the main ideas are developed. Sufficiently complete references are given.
Hawke, Veronica; Gage, Peter; Manning, Ted
2007-01-01
ComGeom2, a tool developed to generate Common Geometry representation for multidisciplinary analysis, has been used to create a large set of geometries for use in a design study requiring analysis by two computational codes. This paper describes the process used to generate the large number of configurations and suggests ways to further automate the process and make it more efficient for future studies. The design geometry for this study is the launch abort system of the NASA Crew Launch Vehicle.
Needle decompositions in Riemannian geometry
Klartag, Bo'az
2017-01-01
The localization technique from convex geometry is generalized to the setting of Riemannian manifolds whose Ricci curvature is bounded from below. In a nutshell, the author's method is based on the following observation: When the Ricci curvature is non-negative, log-concave measures are obtained when conditioning the Riemannian volume measure with respect to a geodesic foliation that is orthogonal to the level sets of a Lipschitz function. The Monge mass transfer problem plays an important role in the author's analysis.
Systematics of IIB spinorial geometry
Gran, U.; Gutowski, J.; Papadopoulos, G.; Roest, D.
2005-01-01
We reduce the classification of all supersymmetric backgrounds of IIB supergravity to the evaluation of the Killing spinor equations and their integrability conditions, which contain the field equations, on five types of spinors. This extends the work of [hep-th/0503046] to IIB supergravity. We give the expressions of the Killing spinor equations on all five types of spinors. In this way, the Killing spinor equations become a linear system for the fluxes, geometry and spacetime derivatives of...
Geometry Dependence of Stellarator Turbulence
International Nuclear Information System (INIS)
Mynick, H.E.; Xanthopoulos, P.; Boozer, A.H.
2009-01-01
Using the nonlinear gyrokinetic code package GENE/GIST, we study the turbulent transport in a broad family of stellarator designs, to understand the geometry-dependence of the microturbulence. By using a set of flux tubes on a given flux surface, we construct a picture of the 2D structure of the microturbulence over that surface, and relate this to relevant geometric quantities, such as the curvature, local shear, and effective potential in the Schrodinger-like equation governing linear drift modes
Superbanana orbits in stellarator geometries
International Nuclear Information System (INIS)
Derr, J.A.; Shohet, J.L.
1979-04-01
The presence of superbanana orbit types localized to either the interior or the exterior of stellarators and torsatrons is numerically investigated for 3.5 MeV alpha particles. The absence of the interior superbanana in both geometries is found to be due to non-conservation of the action. Exterior superbananas are found in the stellarator only, as a consequence of the existence of closed helical magnetic wells. No superbananas of either type are found in the torsatron
Turtle geometry the Python way
Battle, S.
2014-01-01
An introduction to coding using Python’s on-screen ‘turtle’ that can be commanded with a few simple instructions including forward, backward, left and right. The turtle leaves a trace that can be used to draw geometric figures. This workshop is aimed at beginners of all ages. The aim is to learn a smattering of programming and a little bit of geometry in a fun way.
Topics in modern differential geometry
Verstraelen, Leopold
2017-01-01
A variety of introductory articles is provided on a wide range of topics, including variational problems on curves and surfaces with anisotropic curvature. Experts in the fields of Riemannian, Lorentzian and contact geometry present state-of-the-art reviews of their topics. The contributions are written on a graduate level and contain extended bibliographies. The ten chapters are the result of various doctoral courses which were held in 2009 and 2010 at universities in Leuven, Serbia, Romania and Spain.
Effective elastic properties of damaged isotropic solids
International Nuclear Information System (INIS)
Lee, U Sik
1998-01-01
In continuum damage mechanics, damaged solids have been represented by the effective elastic stiffness into which local damage is smoothly smeared. Similarly, damaged solids may be represented in terms of effective elastic compliances. By virtue of the effective elastic compliance representation, it may become easier to derive the effective engineering constants of damaged solids from the effective elastic compliances, all in closed form. Thus, in this paper, by using a continuum modeling approach based on both the principle of strain energy equivalence and the equivalent elliptical micro-crack representation of local damage, the effective elastic compliance and effective engineering constants are derived in terms of the undamaged (virgin) elastic properties and a scalar damage variable for both damaged two-and three-dimensional isotropic solids
Number theory III Diophantine geometry
1991-01-01
From the reviews of the first printing of this book, published as Volume 60 of the Encyclopaedia of Mathematical Sciences: "Between number theory and geometry there have been several stimulating influences, and this book records of these enterprises. This author, who has been at the centre of such research for many years, is one of the best guides a reader can hope for. The book is full of beautiful results, open questions, stimulating conjectures and suggestions where to look for future developments. This volume bears witness of the broad scope of knowledge of the author, and the influence of several people who have commented on the manuscript before publication ... Although in the series of number theory, this volume is on diophantine geometry, and the reader will notice that algebraic geometry is present in every chapter. ... The style of the book is clear. Ideas are well explained, and the author helps the reader to pass by several technicalities. Reading and rereading this book I noticed that the topics ...
Riemannian geometry and geometric analysis
Jost, Jürgen
2017-01-01
This established reference work continues to provide its readers with a gateway to some of the most interesting developments in contemporary geometry. It offers insight into a wide range of topics, including fundamental concepts of Riemannian geometry, such as geodesics, connections and curvature; the basic models and tools of geometric analysis, such as harmonic functions, forms, mappings, eigenvalues, the Dirac operator and the heat flow method; as well as the most important variational principles of theoretical physics, such as Yang-Mills, Ginzburg-Landau or the nonlinear sigma model of quantum field theory. The present volume connects all these topics in a systematic geometric framework. At the same time, it equips the reader with the working tools of the field and enables her or him to delve into geometric research. The 7th edition has been systematically reorganized and updated. Almost no page has been left unchanged. It also includes new material, for instance on symplectic geometry, as well as the B...
Donaldson invariants in algebraic geometry
International Nuclear Information System (INIS)
Goettsche, L.
2000-01-01
In these lectures I want to give an introduction to the relation of Donaldson invariants with algebraic geometry: Donaldson invariants are differentiable invariants of smooth compact 4-manifolds X, defined via moduli spaces of anti-self-dual connections. If X is an algebraic surface, then these moduli spaces can for a suitable choice of the metric be identified with moduli spaces of stable vector bundles on X. This can be used to compute Donaldson invariants via methods of algebraic geometry and has led to a lot of activity on moduli spaces of vector bundles and coherent sheaves on algebraic surfaces. We will first recall the definition of the Donaldson invariants via gauge theory. Then we will show the relation between moduli spaces of anti-self-dual connections and moduli spaces of vector bundles on algebraic surfaces, and how this makes it possible to compute Donaldson invariants via algebraic geometry methods. Finally we concentrate on the case that the number b + of positive eigenvalues of the intersection form on the second homology of the 4-manifold is 1. In this case the Donaldson invariants depend on the metric (or in the algebraic geometric case on the polarization) via a system of walls and chambers. We will study the change of the invariants under wall-crossing, and use this in particular to compute the Donaldson invariants of rational algebraic surfaces. (author)
Aspects of differential geometry II
Gilkey, Peter
2015-01-01
Differential Geometry is a wide field. We have chosen to concentrate upon certain aspects that are appropriate for an introduction to the subject; we have not attempted an encyclopedic treatment. Book II deals with more advanced material than Book I and is aimed at the graduate level. Chapter 4 deals with additional topics in Riemannian geometry. Properties of real analytic curves given by a single ODE and of surfaces given by a pair of ODEs are studied, and the volume of geodesic balls is treated. An introduction to both holomorphic and Kähler geometry is given. In Chapter 5, the basic properties of de Rham cohomology are discussed, the Hodge Decomposition Theorem, Poincaré duality, and the Künneth formula are proved, and a brief introduction to the theory of characteristic classes is given. In Chapter 6, Lie groups and Lie algebras are dealt with. The exponential map, the classical groups, and geodesics in the context of a bi-invariant metric are discussed. The de Rham cohomology of compact Lie groups an...
Algebraic Geometry and Number Theory Summer School
Sarıoğlu, Celal; Soulé, Christophe; Zeytin, Ayberk
2017-01-01
This lecture notes volume presents significant contributions from the “Algebraic Geometry and Number Theory” Summer School, held at Galatasaray University, Istanbul, June 2-13, 2014. It addresses subjects ranging from Arakelov geometry and Iwasawa theory to classical projective geometry, birational geometry and equivariant cohomology. Its main aim is to introduce these contemporary research topics to graduate students who plan to specialize in the area of algebraic geometry and/or number theory. All contributions combine main concepts and techniques with motivating examples and illustrative problems for the covered subjects. Naturally, the book will also be of interest to researchers working in algebraic geometry, number theory and related fields.
Geometry success in 20 minutes a day
LLC, LearningExpress
2014-01-01
Whether you're new to geometry or just looking for a refresher, Geometry Success in 20 Minutes a Day offers a 20-step lesson plan that provides quick and thorough instruction in practical, critical skills. Stripped of unnecessary math jargon but bursting with geometry essentials, Geometry Success in 20 Minutes a Day: Covers all vital geometry skills, from the basic building blocks of geometry to ratio, proportion, and similarity to trigonometry and beyond Provides hundreds of practice exercises in test format Applies geometr
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.
Mukta, K. N.; MacLaurin, J. N.; Robinson, P. A.
2017-11-01
Corticothalamic neural field theory is applied to a spherical geometry to better model neural activity in the human brain and is also compared with planar approximations. The frequency power spectrum, correlation, and coherence functions are computed analytically and numerically. The effects of cortical boundary conditions and resulting modal aspects of spherical corticothalamic dynamics are explored, showing that the results of spherical and finite planar geometries converge to those for the infinite planar geometry in the limit of large brain size. Estimates are made of the point at which modal series can be truncated and it is found that for physiologically plausible parameters only the lowest few spatial eigenmodes are needed for an accurate representation of macroscopic brain activity. A difference between the geometries is that there is a low-frequency 1 /f spectrum in the infinite planar geometry, whereas in the spherical geometry it is 1 /f2 . Another difference is that the alpha peak in the spherical geometry is sharper and stronger than in the planar geometry. Cortical modal effects can lead to a double alpha peak structure in the power spectrum, although the main determinant of the alpha peak is corticothalamic feedback. In the spherical geometry, the cross spectrum between two points is found to only depend on their relative distance apart. At small spatial separations the low-frequency cross spectrum is stronger than for an infinite planar geometry and the alpha peak is sharper and stronger due to the partitioning of the energy into discrete modes. In the spherical geometry, the coherence function between points decays monotonically as their separation increases at a fixed frequency, but persists further at resonant frequencies. The correlation between two points is found to be positive, regardless of the time lag and spatial separation, but decays monotonically as the separation increases at fixed time lag. At fixed distance the correlation has peaks
Solid-state disk amplifiers for fusion-laser systems
Energy Technology Data Exchange (ETDEWEB)
Martin, W.E.; Trenholme, J.B.; Linford, G.J.; Yarema, S.M.; Hurley, C.A.
1981-09-01
We review the design, performance, and operation of large-aperture (10 to 46 cm) solid-state disk amplifiers for use in laser systems. We present design data, prototype tests, simulations, and projections for conventional cylindrical pump-geometry amplifiers and rectangular pump-geometry disk amplifiers. The design of amplifiers for the Nova laser system is discussed.
Congruence properties of induced representations
DEFF Research Database (Denmark)
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...
Factorial representations of path groups
International Nuclear Information System (INIS)
Albeverio, S.; Hoegh-Krohn, R.; Testard, D.; Vershik, A.
1983-11-01
We give the reduction of the energy representation of the group of mappings from I = [ 0,1 ], S 1 , IRsub(+) or IR into a compact semi simple Lie group G. For G = SU(2) we prove the factoriality of the representation, which is of type III in the case I = IR
Using Integer Manipulatives: Representational Determinism
Bossé, Michael J.; Lynch-Davis, Kathleen; Adu-Gyamfi, Kwaku; Chandler, Kayla
2016-01-01
Teachers and students commonly use various concrete representations during mathematical instruction. These representations can be utilized to help students understand mathematical concepts and processes, increase flexibility of thinking, facilitate problem solving, and reduce anxiety while doing mathematics. Unfortunately, the manner in which some…
Knowledge Representation: A Brief Review.
Vickery, B. C.
1986-01-01
Reviews different structures and techniques of knowledge representation: structure of database records and files, data structures in computer programming, syntatic and semantic structure of natural language, knowledge representation in artificial intelligence, and models of human memory. A prototype expert system that makes use of some of these…
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…
Evaluation of tomographic-image based geometries with PENELOPE Monte Carlo
International Nuclear Information System (INIS)
Kakoi, A.A.Y.; Galina, A.C.; Nicolucci, P.
2009-01-01
The Monte Carlo method can be used to evaluate treatment planning systems or for the determination of dose distributions in radiotherapy planning due to its accuracy and precision. In Monte Carlo simulation packages typically used in radiotherapy, however, a realistic representation of the geometry of the patient can not be used, which compromises the accuracy of the results. In this work, an algorithm for the description of geometries based on CT images of patients, developed to be used with Monte Carlo simulation package PENELOPE, is tested by simulating the dose distribution produced by a photon beam of 10 MV. The geometry simulated was based on CT images of a planning of prostate cancer. The volumes of interest in the treatment were adequately represented in the simulation geometry, allowing the algorithm to be used in verification of doses in radiotherapy treatments. (author)
Network geometry with flavor: From complexity to quantum geometry
Bianconi, Ginestra; Rahmede, Christoph
2016-03-01
Network geometry is attracting increasing attention because it has a wide range of applications, ranging from data mining to routing protocols in the Internet. At the same time advances in the understanding of the geometrical properties of networks are essential for further progress in quantum gravity. In network geometry, simplicial complexes describing the interaction between two or more nodes play a special role. In fact these structures can be used to discretize a geometrical d -dimensional space, and for this reason they have already been widely used in quantum gravity. Here we introduce the network geometry with flavor s =-1 ,0 ,1 (NGF) describing simplicial complexes defined in arbitrary dimension d and evolving by a nonequilibrium dynamics. The NGF can generate discrete geometries of different natures, ranging from chains and higher-dimensional manifolds to scale-free networks with small-world properties, scale-free degree distribution, and nontrivial community structure. The NGF admits as limiting cases both the Bianconi-Barabási models for complex networks, the stochastic Apollonian network, and the recently introduced model for complex quantum network manifolds. The thermodynamic properties of NGF reveal that NGF obeys a generalized area law opening a new scenario for formulating its coarse-grained limit. The structure of NGF is strongly dependent on the dimensionality d . In d =1 NGFs grow complex networks for which the preferential attachment mechanism is necessary in order to obtain a scale-free degree distribution. Instead, for NGF with dimension d >1 it is not necessary to have an explicit preferential attachment rule to generate scale-free topologies. We also show that NGF admits a quantum mechanical description in terms of associated quantum network states. Quantum network states evolve by a Markovian dynamics and a quantum network state at time t encodes all possible NGF evolutions up to time t . Interestingly the NGF remains fully classical but
A generalized wavelet extrema representation
Energy Technology Data Exchange (ETDEWEB)
Lu, Jian; Lades, M.
1995-10-01
The wavelet extrema representation originated by Stephane Mallat is a unique framework for low-level and intermediate-level (feature) processing. In this paper, we present a new form of wavelet extrema representation generalizing Mallat`s original work. The generalized wavelet extrema representation is a feature-based multiscale representation. For a particular choice of wavelet, our scheme can be interpreted as representing a signal or image by its edges, and peaks and valleys at multiple scales. Such a representation is shown to be stable -- the original signal or image can be reconstructed with very good quality. It is further shown that a signal or image can be modeled as piecewise monotonic, with all turning points between monotonic segments given by the wavelet extrema. A new projection operator is introduced to enforce piecewise inonotonicity of a signal in its reconstruction. This leads to an enhancement to previously developed algorithms in preventing artifacts in reconstructed signal.
Multiple representations in physics education
Duit, Reinders; Fischer, Hans E
2017-01-01
This volume is important because despite various external representations, such as analogies, metaphors, and visualizations being commonly used by physics teachers, educators and researchers, the notion of using the pedagogical functions of multiple representations to support teaching and learning is still a gap in physics education. The research presented in the three sections of the book is introduced by descriptions of various psychological theories that are applied in different ways for designing physics teaching and learning in classroom settings. The following chapters of the book illustrate teaching and learning with respect to applying specific physics multiple representations in different levels of the education system and in different physics topics using analogies and models, different modes, and in reasoning and representational competence. When multiple representations are used in physics for teaching, the expectation is that they should be successful. To ensure this is the case, the implementati...
Differential geometry based solvation model II: Lagrangian formulation.
Chen, Zhan; Baker, Nathan A; Wei, G W
2011-12-01
Solvation is an elementary process in nature and is of paramount importance to more sophisticated chemical, biological and biomolecular processes. The understanding of solvation is an essential prerequisite for the quantitative description and analysis of biomolecular systems. This work presents a Lagrangian formulation of our differential geometry based solvation models. The Lagrangian representation of biomolecular surfaces has a few utilities/advantages. First, it provides an essential basis for biomolecular visualization, surface electrostatic potential map and visual perception of biomolecules. Additionally, it is consistent with the conventional setting of implicit solvent theories and thus, many existing theoretical algorithms and computational software packages can be directly employed. Finally, the Lagrangian representation does not need to resort to artificially enlarged van der Waals radii as often required by the Eulerian representation in solvation analysis. The main goal of the present work is to analyze the connection, similarity and difference between the Eulerian and Lagrangian formalisms of the solvation model. Such analysis is important to the understanding of the differential geometry based solvation model. The present model extends the scaled particle theory of nonpolar solvation model with a solvent-solute interaction potential. The nonpolar solvation model is completed with a Poisson-Boltzmann (PB) theory based polar solvation model. The differential geometry theory of surfaces is employed to provide a natural description of solvent-solute interfaces. The optimization of the total free energy functional, which encompasses the polar and nonpolar contributions, leads to coupled potential driven geometric flow and PB equations. Due to the development of singularities and nonsmooth manifolds in the Lagrangian representation, the resulting potential-driven geometric flow equation is embedded into the Eulerian representation for the purpose of
Islam and Media Representations
Directory of Open Access Journals (Sweden)
Mohamed Bensalah
2006-04-01
Full Text Available For the author of this article, the media’s treatment of Islam has raised numerous polymorphous questions and debates. Reactivated by the great scares of current events, the issue, though an ancient one, calls many things into question. By way of introduction, the author tries to analyse the complex processes of elaboration and perception of the representations that have prevailed during the past century. In referring to the semantic decoding of the abundant colonial literature and iconography, the author strives to translate the extreme xenophobic tensions and the identity crystallisations associated with the current media orchestration of Islam, both in theWest and the East. He then evokes the excesses of the media that are found at the origin of many amalgams wisely maintained between Islam, Islamism and Islamic terrorism, underscoring their duplicity and their willingness to put themselves, consciously, in service to deceivers and directors of awareness, who are very active at the heart of the politico-media sphere. After levelling a severe accusation against the harmful drifts of the media, especially in times of crisis and war, the author concludes by asserting that these tools of communication, once they are freed of their masks and invective apparatuses, can be re-appropriated by new words and bya true communication between peoples and cultures.
Modelling and simulation of gas explosions in complex geometries
Energy Technology Data Exchange (ETDEWEB)
Saeter, Olav
1998-12-31
This thesis presents a three-dimensional Computational Fluid Dynamics (CFD) code (EXSIM94) for modelling and simulation of gas explosions in complex geometries. It gives the theory and validates the following sub-models : (1) the flow resistance and turbulence generation model for densely packed regions, (2) the flow resistance and turbulence generation model for single objects, and (3) the quasi-laminar combustion model. It is found that a simple model for flow resistance and turbulence generation in densely packed beds is able to reproduce the medium and large scale MERGE explosion experiments of the Commission of European Communities (CEC) within a band of factor 2. The model for a single representation is found to predict explosion pressure in better agreement with the experiments with a modified k-{epsilon} model. This modification also gives a slightly improved grid independence for realistic gas explosion approaches. One laminar model is found unsuitable for gas explosion modelling because of strong grid dependence. Another laminar model is found to be relatively grid independent and to work well in harmony with the turbulent combustion model. The code is validated against 40 realistic gas explosion experiments. It is relatively grid independent in predicting explosion pressure in different offshore geometries. It can predict the influence of ignition point location, vent arrangements, different geometries, scaling effects and gas reactivity. The validation study concludes with statistical and uncertainty analyses of the code performance. 98 refs., 96 figs, 12 tabs.
A Whirlwind Tour of Computational Geometry.
Graham, Ron; Yao, Frances
1990-01-01
Described is computational geometry which used concepts and results from classical geometry, topology, combinatorics, as well as standard algorithmic techniques such as sorting and searching, graph manipulations, and linear programing. Also included are special techniques and paradigms. (KR)
Optimizing solar-cell grid geometry
Crossley, A. P.
1969-01-01
Trade-off analysis and mathematical expressions calculate optimum grid geometry in terms of various cell parameters. Determination of the grid geometry provides proper balance between grid resistance and cell output to optimize the energy conversion process.
Projective geometry solved problems and theory review
Fortuna, Elisabetta; Pardini, Rita
2016-01-01
This book starts with a concise but rigorous overview of the basic notions of projective geometry, using straightforward and modern language. The goal is not only to establish the notation and terminology used, but also to offer the reader a quick survey of the subject matter. In the second part, the book presents more than 200 solved problems, for many of which several alternative solutions are provided. The level of difficulty of the exercises varies considerably: they range from computations to harder problems of a more theoretical nature, up to some actual complements of the theory. The structure of the text allows the reader to use the solutions of the exercises both to master the basic notions and techniques and to further their knowledge of the subject, thus learning some classical results not covered in the first part of the book. The book addresses the needs of undergraduate and graduate students in the theoretical and applied sciences, and will especially benefit those readers with a solid grasp of ...
On a microscopic representation of space-time
International Nuclear Information System (INIS)
Dahm, R.
2012-01-01
We start from a noncompact Lie algebra isomorphic to the Dirac algebra and relate this Lie algebra in a brief review to low-energy hadron physics described by the compact group SU(4). This step permits an overall physical identification of the operator actions. Then we discuss the geometrical origin of this noncompact Lie algebra and “reduce” the geometry in order to introduce in each of these steps coordinate definitions which can be related to an algebraic representation in terms of the spontaneous symmetry breakdown along the Lie algebra chain su*(4) → usp(4) → su(2) × u(1). Standard techniques of Lie algebra decomposition(s) as well as the (physical) operator identification give rise to interesting physical aspects and lead to a rank-1 Riemannian space which provides an analytic representation and leads to a 5-dimensional hyperbolic space H 5 with SO(5, 1) isometries. The action of the (compact) symplectic group decomposes this (globally) hyperbolic space into H 2 ⊕ H 3 with SO(2, 1) and SO(3, 1) isometries, respectively, which we relate to electromagnetic (dynamically broken SU(2) isospin) and Lorentz transformations. Last not least, we attribute this symmetry pattern to the algebraic representation of a projective geometry over the division algebra H and subsequent coordinate restrictions.
Interactive three-dimensional visualization and creation of geometries for Monte Carlo calculations
International Nuclear Information System (INIS)
Theis, C.; Buchegger, K.H.; Brugger, M.; Forkel-Wirth, D.; Roesler, S.; Vincke, H.
2006-01-01
The implementation of three-dimensional geometries for the simulation of radiation transport problems is a very time-consuming task. Each particle transport code supplies its own scripting language and syntax for creating the geometries. All of them are based on the Constructive Solid Geometry scheme requiring textual description. This makes the creation a tedious and error-prone task, which is especially hard to master for novice users. The Monte Carlo code FLUKA comes with built-in support for creating two-dimensional cross-sections through the geometry and FLUKACAD, a custom-built converter to the commercial Computer Aided Design package AutoCAD, exists for 3D visualization. For other codes, like MCNPX, a couple of different tools are available, but they are often specifically tailored to the particle transport code and its approach used for implementing geometries. Complex constructive solid modeling usually requires very fast and expensive special purpose hardware, which is not widely available. In this paper SimpleGeo is presented, which is an implementation of a generic versatile interactive geometry modeler using off-the-shelf hardware. It is running on Windows, with a Linux version currently under preparation. This paper describes its functionality, which allows for rapid interactive visualization as well as generation of three-dimensional geometries, and also discusses critical issues regarding common CAD systems
Directory of Open Access Journals (Sweden)
Frédéric Barbaresco
2016-11-01
Full Text Available We introduce the symplectic structure of information geometry based on Souriau’s Lie group thermodynamics model, with a covariant definition of Gibbs equilibrium via invariances through co-adjoint action of a group on its moment space, defining physical observables like energy, heat, and moment as pure geometrical objects. Using geometric Planck temperature of Souriau model and symplectic cocycle notion, the Fisher metric is identified as a Souriau geometric heat capacity. The Souriau model is based on affine representation of Lie group and Lie algebra that we compare with Koszul works on G/K homogeneous space and bijective correspondence between the set of G-invariant flat connections on G/K and the set of affine representations of the Lie algebra of G. In the framework of Lie group thermodynamics, an Euler-Poincaré equation is elaborated with respect to thermodynamic variables, and a new variational principal for thermodynamics is built through an invariant Poincaré-Cartan-Souriau integral. The Souriau-Fisher metric is linked to KKS (Kostant–Kirillov–Souriau 2-form that associates a canonical homogeneous symplectic manifold to the co-adjoint orbits. We apply this model in the framework of information geometry for the action of an affine group for exponential families, and provide some illustrations of use cases for multivariate gaussian densities. Information geometry is presented in the context of the seminal work of Fréchet and his Clairaut-Legendre equation. The Souriau model of statistical physics is validated as compatible with the Balian gauge model of thermodynamics. We recall the precursor work of Casalis on affine group invariance for natural exponential families.
Deep supervised, but not unsupervised, models may explain IT cortical representation.
Directory of Open Access Journals (Sweden)
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
International Nuclear Information System (INIS)
Gervais, J.L.
1993-01-01
By analyzing the extrinsic geometry of two dimensional surfaces chirally embedded in C P n (the C P n W-surface), we give exact treatments in various aspects of the classical W-geometry in the conformal gauge: First, the basis of tangent and normal vectors are defined at regular points of the surface, such that their infinitesimal displacements are given by connections which coincide with the vector potentials of the (conformal) A n -Toda Lax pair. Since the latter is known to be intrinsically related with the W symmetries, this gives the geometrical meaning of the A n W-Algebra. Second, W-surfaces are put in one-to-one correspondence with solutions of the conformally-reduced WZNW model, which is such that the Toda fields give the Cartan part in the Gauss decomposition of its solutions. Third, the additional variables of the Toda hierarchy are used as coordinates of C P n . This allows us to show that W-transformations may be extended as particular diffeomorphisms of this target-space. Higher-dimensional generalizations of the WZNW equations are derived and related with the Zakharov-Shabat equations of the Toda hierarchy. Fourth, singular points are studied from a global viewpoint, using our earlier observation that W-surfaces may be regarded as instantons. The global indices of the W-geometry, which are written in terms of the Toda fields, are shown to be the instanton numbers for associated mappings of W-surfaces into the Grassmannians. The relation with the singularities of W-surface is derived by combining the Toda equations with the Gauss-Bonnet theorem. (orig.)
ORIGAMI -- The Oak Ridge Geometry Analysis and Modeling Interface
International Nuclear Information System (INIS)
Burns, T.J.
1996-01-01
A revised ''ray-tracing'' package which is a superset of the geometry specifications of the radiation transport codes MORSE, MASH (GIFT Versions 4 and 5), HETC, and TORT has been developed by ORNL. Two additional CAD-based formats are also included as part of the superset: the native format of the BRL-CAD system--MGED, and the solid constructive geometry subset of the IGES specification. As part of this upgrade effort, ORNL has designed an Xwindows-based utility (ORIGAMI) to facilitate the construction, manipulation, and display of the geometric models required by the MASH code. Since the primary design criterion for this effort was that the utility ''see'' the geometric model exactly as the radiation transport code does, ORIGAMI is designed to utilize the same ''ray-tracing'' package as the revised version of MASH. ORIGAMI incorporates the functionality of two previously developed graphical utilities, CGVIEW and ORGBUG, into a single consistent interface
Mutabaruka, Patrick; Kamrin, Ken
2018-04-01
A numerical method for particle-laden fluids interacting with a deformable solid domain and mobile rigid parts is proposed and implemented in a full engineering system. The fluid domain is modeled with a lattice Boltzmann representation, the particles and rigid parts are modeled with a discrete element representation, and the deformable solid domain is modeled using a Lagrangian mesh. The main issue of this work, since separately each of these methods is a mature tool, is to develop coupling and model-reduction approaches in order to efficiently simulate coupled problems of this nature, as in various geological and engineering applications. The lattice Boltzmann method incorporates a large eddy simulation technique using the Smagorinsky turbulence model. The discrete element method incorporates spherical and polyhedral particles for stiff contact interactions. A neo-Hookean hyperelastic model is used for the deformable solid. We provide a detailed description of how to couple the three solvers within a unified algorithm. The technique we propose for rubber modeling/coupling exploits a simplification that prevents having to solve a finite-element problem at each time step. We also developed a technique to reduce the domain size of the full system by replacing certain zones with quasi-analytic solutions, which act as effective boundary conditions for the lattice Boltzmann method. The major ingredients of the routine are separately validated. To demonstrate the coupled method in full, we simulate slurry flows in two kinds of piston valve geometries. The dynamics of the valve and slurry are studied and reported over a large range of input parameters.
Stochastic geometry for image analysis
Descombes, Xavier
2013-01-01
This book develops the stochastic geometry framework for image analysis purpose. Two main frameworks are described: marked point process and random closed sets models. We derive the main issues for defining an appropriate model. The algorithms for sampling and optimizing the models as well as for estimating parameters are reviewed. Numerous applications, covering remote sensing images, biological and medical imaging, are detailed. This book provides all the necessary tools for developing an image analysis application based on modern stochastic modeling.
Magnetoelectrostatic thruster physical geometry tests
Ramsey, W. D.
1981-01-01
Inert gas tests are conducted with several magnetoelectrostatic containment discharge chamber geometries. The configurations tested include three discharge chamber lengths; three boundary magnet patterns; two different flux density magnet materials; hemispherical and conical shaped thrusters having different surface-to-volume ratios; and two and three grid ion optics. Argon mass utilizations of 60 to 79% are attained at 210 to 280 eV/ion in different test configurations. Short hemi thruster configurations are found to produce 70 to 92% xenon mass utilization at 185 to 220 eV/ion.
Programming system for analytic geometry
International Nuclear Information System (INIS)
Raymond, Jacques
1970-01-01
After having outlined the characteristics of computing centres which do not comply with engineering tasks, notably the time required by all different tasks to be performed when developing a software (assembly, compilation, link edition, loading, run), and identified constraints specific to engineering, the author identifies the characteristics a programming system should have to suit engineering tasks. He discussed existing conversational systems and their programming language, and their main drawbacks. Then, he presents a system which aims at facilitating programming and addressing problems of analytic geometry and trigonometry
The geometry of special relativity
International Nuclear Information System (INIS)
Parizet, Jean
2008-01-01
This book for students in mathematics or physics shows the interest of geometry to understand special relativity as a consequence of invariance of Maxwell equations and of constancy of the speed of light. Space-time is actually provided with a geometrical structure and a physical interpretation: at each observer are associated his own time and his own physical space in which occur events he is concerned with. This leads to a natural approach to special relativity. The Lorentz group and its algebra are then studied by using matrices and the Pauli algebra. Quaternions are also addressed
Moduli spaces in algebraic geometry
International Nuclear Information System (INIS)
Goettsche, L.
2000-01-01
This volume of the new series of lecture notes of the Abdus Salam International Centre for Theoretical Physics contains the lecture notes of the School on Algebraic Geometry which took place at the Abdus Salam International Centre for Theoretical Physics from 26 July to 13 August 1999. The school consisted of 2 weeks of lecture courses and one week of conference. The topic of the school was moduli spaces. More specifically the lectures were divided into three subtopics: principal bundles on Riemann surfaces, moduli spaces of vector bundles and sheaves on projective varieties, and moduli spaces of curves
Worldsheet geometries of ambitwistor string
Energy Technology Data Exchange (ETDEWEB)
Ohmori, Kantaro [Department of Physics, the University of Tokyo,Hongo, Bunkyo-ku, Tokyo 133-0022 (Japan)
2015-06-12
Mason and Skinner proposed the ambitwistor string theory which directly reproduces the formulas for the amplitudes of massless particles proposed by Cachazo, He and Yuan. In this paper we discuss geometries of the moduli space of worldsheets associated to the bosonic or the RNS ambitwistor string. Further, we investigate the factorization properties of the amplitudes when an internal momentum is near on-shell in the abstract CFT language. Along the way, we propose the existence of the ambitwistor strings with three or four fermionic worldsheet currents.
Porous media geometry and transports
Adler, Pierre
1992-01-01
The goal of ""Porous Media: Geometry and Transports"" is to provide the basis of a rational and modern approach to porous media. This book emphasizes several geometrical structures (spatially periodic, fractal, and random to reconstructed) and the three major single-phase transports (diffusion, convection, and Taylor dispersion).""Porous Media"" serves various purposes. For students it introduces basic information on structure and transports. Engineers will find this book useful as a readily accessible assemblage of al the major experimental results pertaining to single-phase tr
Geometry of physical dispersion relations
International Nuclear Information System (INIS)
Raetzel, Dennis; Rivera, Sergio; Schuller, Frederic P.
2011-01-01
To serve as a dispersion relation, a cotangent bundle function must satisfy three simple algebraic properties. These conditions are derived from the inescapable physical requirements that local matter field dynamics must be predictive and allow for an observer-independent notion of positive energy. Possible modifications of the standard relativistic dispersion relation are thereby severely restricted. For instance, the dispersion relations associated with popular deformations of Maxwell theory by Gambini-Pullin or Myers-Pospelov are not admissible. Dispersion relations passing the simple algebraic checks derived here correspond to physically admissible Finslerian refinements of Lorentzian geometry.
Projective geometry and projective metrics
Busemann, Herbert
2005-01-01
The basic results and methods of projective and non-Euclidean geometry are indispensable for the geometer, and this book--different in content, methods, and point of view from traditional texts--attempts to emphasize that fact. Results of special theorems are discussed in detail only when they are needed to develop a feeling for the subject or when they illustrate a general method. On the other hand, an unusual amount of space is devoted to the discussion of the fundamental concepts of distance, motion, area, and perpendicularity.Topics include the projective plane, polarities and conic sectio
Tropical geometry of statistical models.
Pachter, Lior; Sturmfels, Bernd
2004-11-16
This article presents a unified mathematical framework for inference in graphical models, building on the observation that graphical models are algebraic varieties. From this geometric viewpoint, observations generated from a model are coordinates of a point in the variety, and the sum-product algorithm is an efficient tool for evaluating specific coordinates. Here, we address the question of how the solutions to various inference problems depend on the model parameters. The proposed answer is expressed in terms of tropical algebraic geometry. The Newton polytope of a statistical model plays a key role. Our results are applied to the hidden Markov model and the general Markov model on a binary tree.
Clustering in Hilbert simplex geometry
Nielsen, Frank
2017-04-03
Clustering categorical distributions in the probability simplex is a fundamental primitive often met in applications dealing with histograms or mixtures of multinomials. Traditionally, the differential-geometric structure of the probability simplex has been used either by (i) setting the Riemannian metric tensor to the Fisher information matrix of the categorical distributions, or (ii) defining the information-geometric structure induced by a smooth dissimilarity measure, called a divergence. In this paper, we introduce a novel computationally-friendly non-Riemannian framework for modeling the probability simplex: Hilbert simplex geometry. We discuss the pros and cons of those three statistical modelings, and compare them experimentally for clustering tasks.
An invitation to noncommutative geometry
Marcolli, Matilde
2008-01-01
This is the first existing volume that collects lectures on this important and fast developing subject in mathematics. The lectures are given by leading experts in the field and the range of topics is kept as broad as possible by including both the algebraic and the differential aspects of noncommutative geometry as well as recent applications to theoretical physics and number theory. Sample Chapter(s). A Walk in the Noncommutative Garden (1,639 KB). Contents: A Walk in the Noncommutative Garden (A Connes & M Marcolli); Renormalization of Noncommutative Quantum Field Theory (H Grosse & R Wulke
Trends and developments in computational geometry
Berg, de M.
1997-01-01
This paper discusses some trends and achievements in computational geometry during the past five years, with emphasis on problems related to computer graphics. Furthermore, a direction of research in computational geometry is discussed that could help in bringing the fields of computational geometry
Global affine differential geometry of hypersurfaces
Li, An-Min; Zhao, Guosong; Hu, Zejun
2015-01-01
This book draws a colorful and widespread picture of global affine hypersurface theory up to the most recent state. Moreover, the recent development revealed that affine differential geometry- as differential geometry in general- has an exciting intersection area with other fields of interest, like partial differential equations, global analysis, convex geometry and Riemann surfaces.
"WGL," a Web Laboratory for Geometry
Quaresma, Pedro; Santos, Vanda; Maric, Milena
2018-01-01
The role of information and communication technologies (ICT) in education is nowadays well recognised. The "Web Geometry Laboratory," is an e-learning, collaborative and adaptive, Web environment for geometry, integrating a well known dynamic geometry system. In a collaborative session, teachers and students, engaged in solving…
Geometrical setting of solid mechanics
International Nuclear Information System (INIS)
Fiala, Zdenek
2011-01-01
Highlights: → Solid mechanics within the Riemannian symmetric manifold GL (3, R)/O (3, R). → Generalized logarithmic strain. → Consistent linearization. → Incremental principle of virtual power. → Time-discrete approximation. - Abstract: The starting point in the geometrical setting of solid mechanics is to represent deformation process of a solid body as a trajectory in a convenient space with Riemannian geometry, and then to use the corresponding tools for its analysis. Based on virtual power of internal stresses, we show that such a configuration space is the (globally) symmetric space of symmetric positive-definite real matrices. From this unifying point of view, we shall analyse the logarithmic strain, the stress rate, as well as linearization and intrinsic integration of corresponding evolution equation.
Solid Mesh Registration for Radiotherapy Treatment Planning
DEFF Research Database (Denmark)
Noe, Karsten Østergaard; Sørensen, Thomas Sangild
2010-01-01
We present an algorithm for solid organ registration of pre-segmented data represented as tetrahedral meshes. Registration of the organ surface is driven by force terms based on a distance field representation of the source and reference shapes. Registration of internal morphology is achieved usi...
Computational geometry algorithms and applications
de Berg, Mark; Overmars, Mark; Schwarzkopf, Otfried
1997-01-01
Computational geometry emerged from the field of algorithms design and anal ysis in the late 1970s. It has grown into a recognized discipline with its own journals, conferences, and a large community of active researchers. The suc cess of the field as a research discipline can on the one hand be explained from the beauty of the problems studied and the solutions obtained, and, on the other hand, by the many application domains--computer graphics, geographic in formation systems (GIS), robotics, and others-in which geometric algorithms play a fundamental role. For many geometric problems the early algorithmic solutions were either slow or difficult to understand and implement. In recent years a number of new algorithmic techniques have been developed that improved and simplified many of the previous approaches. In this textbook we have tried to make these modem algorithmic solutions accessible to a large audience. The book has been written as a textbook for a course in computational geometry, but it can ...
Tearing modes in toroidal geometry
International Nuclear Information System (INIS)
Connor, J.W.; Cowley, S.C.; Hastie, R.J.; Hender, T.C.; Hood, A.; Martin, T.J.
1988-01-01
The separation of the cylindrical tearing mode stability problem into a resistive resonant layer calculation and an external marginal ideal magnetohydrodynamic (MHD) calculation (Δ' calculation) is generalized to axisymmetric toroidal geometry. The general structure of this separation is analyzed and the marginal ideal MHD information (the toroidal generalization of Δ') required to discuss stability is isolated. This can then, in principle, be combined with relevant resonant layer calculations to determine tearing mode growth rates in realistic situations. Two examples are given: the first is an analytic treatment of toroidally coupled (m = 1, n = 1) and (m = 2, n = 1) tearing modes in a large aspect ratio torus; the second, a numerical treatment of the toroidal coupling of three tearing modes through finite pressure effects in a large aspect ratio torus. In addition, the use of a coupling integral approach for determining the stability of coupled tearing modes is discussed. Finally, the possibility of using initial value resistive MHD codes in realistic toroidal geometry to determine the necessary information from the ideal MHD marginal solution is discussed
Foundations of arithmetic differential geometry
Buium, Alexandru
2017-01-01
The aim of this book is to introduce and develop an arithmetic analogue of classical differential geometry. In this new geometry the ring of integers plays the role of a ring of functions on an infinite dimensional manifold. The role of coordinate functions on this manifold is played by the prime numbers. The role of partial derivatives of functions with respect to the coordinates is played by the Fermat quotients of integers with respect to the primes. The role of metrics is played by symmetric matrices with integer coefficients. The role of connections (respectively curvature) attached to metrics is played by certain adelic (respectively global) objects attached to the corresponding matrices. One of the main conclusions of the theory is that the spectrum of the integers is "intrinsically curved"; the study of this curvature is then the main task of the theory. The book follows, and builds upon, a series of recent research papers. A significant part of the material has never been published before.
Geometry of isotropic convex bodies
Brazitikos, Silouanos; Valettas, Petros; Vritsiou, Beatrice-Helen
2014-01-01
The study of high-dimensional convex bodies from a geometric and analytic point of view, with an emphasis on the dependence of various parameters on the dimension stands at the intersection of classical convex geometry and the local theory of Banach spaces. It is also closely linked to many other fields, such as probability theory, partial differential equations, Riemannian geometry, harmonic analysis and combinatorics. It is now understood that the convexity assumption forces most of the volume of a high-dimensional convex body to be concentrated in some canonical way and the main question is whether, under some natural normalization, the answer to many fundamental questions should be independent of the dimension. The aim of this book is to introduce a number of well-known questions regarding the distribution of volume in high-dimensional convex bodies, which are exactly of this nature: among them are the slicing problem, the thin shell conjecture and the Kannan-Lov�sz-Simonovits conjecture. This book prov...
Differential geometry of group lattices
International Nuclear Information System (INIS)
Dimakis, Aristophanes; Mueller-Hoissen, Folkert
2003-01-01
In a series of publications we developed ''differential geometry'' on discrete sets based on concepts of noncommutative geometry. In particular, it turned out that first-order differential calculi (over the algebra of functions) on a discrete set are in bijective correspondence with digraph structures where the vertices are given by the elements of the set. A particular class of digraphs are Cayley graphs, also known as group lattices. They are determined by a discrete group G and a finite subset S. There is a distinguished subclass of ''bicovariant'' Cayley graphs with the property ad(S)S subset of S. We explore the properties of differential calculi which arise from Cayley graphs via the above correspondence. The first-order calculi extend to higher orders and then allow us to introduce further differential geometric structures. Furthermore, we explore the properties of ''discrete'' vector fields which describe deterministic flows on group lattices. A Lie derivative with respect to a discrete vector field and an inner product with forms is defined. The Lie-Cartan identity then holds on all forms for a certain subclass of discrete vector fields. We develop elements of gauge theory and construct an analog of the lattice gauge theory (Yang-Mills) action on an arbitrary group lattice. Also linear connections are considered and a simple geometric interpretation of the torsion is established. By taking a quotient with respect to some subgroup of the discrete group, generalized differential calculi associated with so-called Schreier diagrams are obtained
Geometry of anisotropic CO outflows
International Nuclear Information System (INIS)
Liseau, R.; Sandell, G.; Helsinki Univ., Observatory, Finland)
1986-01-01
A simple geometrical model for the space motions of the bipolar high-velocity CO outflows in regions of recent, active star formation is proposed. It is assumed that the velocity field of the neutral gas component can be represented by large-scale uniform motions. From observations of the spatial distribution and from the characteristics of the line shape of the high-velocity molecular gas emission the geometry of the line-emitting regions can be inferred, i.e., the direction in space and the collimating angle of the flow. The model has been applied to regions where a check on presently obtained results is provided by independent optical determinations of the motions of Herbig-Haro objects associated with the CO flows. These two methods are in good agreement and, furthermore, the results obtained provide convincingly strong evidence for the physical association of CO outflows and Herbig-Haro objects. This also supports the common view that a young stellar central source is responsible for the active phenomena observed in its environmental neighborhood. It is noteworthy that within the framework of the model the determination of the flow geometry of the high-velocity gas from CO measurements is independent of the distance to the source and, furthermore, can be done at relatively low spatial resolution. 32 references
FURNACE; a toroidal geometry neutronic program system method description and users manual
International Nuclear Information System (INIS)
Verschuur, K.A.
1984-12-01
The FURNACE program system performs neutronic and photonic calculations in 3D toroidal geometry for application to fusion reactors. The geometry description is quite general, allowing any torus cross section and any neutron source density distribution for the plasma, as well as simple parametric representations of circular, elliptic and D-shaped tori and plasmas. The numerical method is based on an approximate transport model that produces results with sufficient accuracy for reactor-design purposes, at acceptable calculational costs. A short description is given of the numerical method, and a user manual for the programs of the system: FURNACE, ANISN-PT, LIBRA, TAPEMA and DRAWER is presented
Canonical differential geometry of string backgrounds
International Nuclear Information System (INIS)
Schuller, Frederic P.; Wohlfarth, Mattias N.R.
2006-01-01
String backgrounds and D-branes do not possess the structure of Lorentzian manifolds, but that of manifolds with area metric. Area metric geometry is a true generalization of metric geometry, which in particular may accommodate a B-field. While an area metric does not determine a connection, we identify the appropriate differential geometric structure which is of relevance for the minimal surface equation in such a generalized geometry. In particular the notion of a derivative action of areas on areas emerges naturally. Area metric geometry provides new tools in differential geometry, which promise to play a role in the description of gravitational dynamics on D-branes
Solar-pumped solid state Nd lasers
Williams, M. D.; Zapata, L.
1985-01-01
Solid state neodymium lasers are considered candidates for space-based polar-pumped laser for continuous power transmission. Laser performance for three different slab laser configurations has been computed to show the excellent power capability of such systems if heat problems can be solved. Ideas involving geometries and materials are offered as potential solutions to the heat problem.
Abraham, Kuzhikalail M.; Alamgir, Mohamed
1993-06-15
This invention pertains to Li ion (Li.sup.+) conductive solid polymer electrolytes composed of solvates of Li salts immobilized (encapsulated) in a solid organic polymer matrix. In particular, this invention relates to solid polymer electrolytes derived by immobilizing complexes (solvates) formed between a Li salt such as LiAsF.sub.6, LiCF.sub.3 SO.sub.3 or LiClO.sub.4 and a mixture of aprotic organic solvents having high dielectric constants such as ethylene carbonate (EC) (dielectric constant=89.6) and propylene carbonate (PC) (dielectric constant=64.4) in a polymer matrix such as polyacrylonitrile, poly(tetraethylene glycol diacrylate), or poly(vinyl pyrrolidinone).
Vietnamese Document Representation and Classification
Nguyen, Giang-Son; Gao, Xiaoying; Andreae, Peter
Vietnamese is very different from English and little research has been done on Vietnamese document classification, or indeed, on any kind of Vietnamese language processing, and only a few small corpora are available for research. We created a large Vietnamese text corpus with about 18000 documents, and manually classified them based on different criteria such as topics and styles, giving several classification tasks of different difficulty levels. This paper introduces a new syllable-based document representation at the morphological level of the language for efficient classification. We tested the representation on our corpus with different classification tasks using six classification algorithms and two feature selection techniques. Our experiments show that the new representation is effective for Vietnamese categorization, and suggest that best performance can be achieved using syllable-pair document representation, an SVM with a polynomial kernel as the learning algorithm, and using Information gain and an external dictionary for feature selection.
Number theory via Representation theory
Indian Academy of Sciences (India)
2014-11-09
Number theory via Representation theory. Eknath Ghate. November 9, 2014. Eightieth Annual Meeting, Chennai. Indian Academy of Sciences1. 1. This is a non-technical 20 minute talk intended for a general Academy audience.
(Self)-representations on youtube
DEFF Research Database (Denmark)
Simonsen, Thomas Mosebo
This paper examines forms of self-representation on YouTube with specific focus on Vlogs (Video blogs). The analytical scope of the paper is on how User-generated Content on YouTube initiates a certain kind of audiovisual representation and a particular interpretation of reality that can...... be distinguished within Vlogs. This will be analysed through selected case studies taken from a representative sample of empirically based observations of YouTube videos. The analysis includes a focus on how certain forms of representation can be identified as representations of the self (Turkle 1995, Scannell...... 1996, Walker 2005) and further how these forms must be comprehended within a context of technological constrains, institutional structures and social as well as economical practices on YouTube (Burgess and Green 2009, Van Dijck 2009). It is argued that these different contexts play a vital part...
Semantic Knowledge Representation (SKR) API
U.S. Department of Health & Human Services — The SKR Project was initiated at NLM in order to develop programs to provide usable semantic representation of biomedical free text by building on resources...
Solitons and theory of representations
International Nuclear Information System (INIS)
Kulish, P.P.
1985-01-01
Problems on the theory of group representations finding application in constructing the quantum variant of the inverse scattering problem are discussed. The multicomponent nonlinear Shroedinger equation is considered as a main example of nonlinear evolution equations (NEE)
Computer representation of molecular surfaces
International Nuclear Information System (INIS)
Max, N.L.
1981-01-01
This review article surveys recent work on computer representation of molecular surfaces. Several different algorithms are discussed for producing vector or raster drawings of space-filling models formed as the union of spheres. Other smoother surfaces are also considered
Differential Geometry Based Multiscale Models
Wei, Guo-Wei
2010-01-01
Large chemical and biological systems such as fuel cells, ion channels, molecular motors, and viruses are of great importance to the scientific community and public health. Typically, these complex systems in conjunction with their aquatic environment pose a fabulous challenge to theoretical description, simulation, and prediction. In this work, we propose a differential geometry based multiscale paradigm to model complex macromolecular systems, and to put macroscopic and microscopic descriptions on an equal footing. In our approach, the differential geometry theory of surfaces and geometric measure theory are employed as a natural means to couple the macroscopic continuum mechanical description of the aquatic environment with the microscopic discrete atom-istic description of the macromolecule. Multiscale free energy functionals, or multiscale action functionals are constructed as a unified framework to derive the governing equations for the dynamics of different scales and different descriptions. Two types of aqueous macromolecular complexes, ones that are near equilibrium and others that are far from equilibrium, are considered in our formulations. We show that generalized Navier–Stokes equations for the fluid dynamics, generalized Poisson equations or generalized Poisson–Boltzmann equations for electrostatic interactions, and Newton's equation for the molecular dynamics can be derived by the least action principle. These equations are coupled through the continuum-discrete interface whose dynamics is governed by potential driven geometric flows. Comparison is given to classical descriptions of the fluid and electrostatic interactions without geometric flow based micro-macro interfaces. The detailed balance of forces is emphasized in the present work. We further extend the proposed multiscale paradigm to micro-macro analysis of electrohydrodynamics, electrophoresis, fuel cells, and ion channels. We derive generalized Poisson–Nernst–Planck equations that
Differential geometry based multiscale models.
Wei, Guo-Wei
2010-08-01
Large chemical and biological systems such as fuel cells, ion channels, molecular motors, and viruses are of great importance to the scientific community and public health. Typically, these complex systems in conjunction with their aquatic environment pose a fabulous challenge to theoretical description, simulation, and prediction. In this work, we propose a differential geometry based multiscale paradigm to model complex macromolecular systems, and to put macroscopic and microscopic descriptions on an equal footing. In our approach, the differential geometry theory of surfaces and geometric measure theory are employed as a natural means to couple the macroscopic continuum mechanical description of the aquatic environment with the microscopic discrete atomistic description of the macromolecule. Multiscale free energy functionals, or multiscale action functionals are constructed as a unified framework to derive the governing equations for the dynamics of different scales and different descriptions. Two types of aqueous macromolecular complexes, ones that are near equilibrium and others that are far from equilibrium, are considered in our formulations. We show that generalized Navier-Stokes equations for the fluid dynamics, generalized Poisson equations or generalized Poisson-Boltzmann equations for electrostatic interactions, and Newton's equation for the molecular dynamics can be derived by the least action principle. These equations are coupled through the continuum-discrete interface whose dynamics is governed by potential driven geometric flows. Comparison is given to classical descriptions of the fluid and electrostatic interactions without geometric flow based micro-macro interfaces. The detailed balance of forces is emphasized in the present work. We further extend the proposed multiscale paradigm to micro-macro analysis of electrohydrodynamics, electrophoresis, fuel cells, and ion channels. We derive generalized Poisson-Nernst-Planck equations that are
Paired structures in knowledge representation
DEFF Research Database (Denmark)
Montero, J.; Bustince, H.; Franco de los Ríos, Camilo
2016-01-01
In this position paper we propose a consistent and unifying view to all those basic knowledge representation models that are based on the existence of two somehow opposite fuzzy concepts. A number of these basic models can be found in fuzzy logic and multi-valued logic literature. Here...... of the relationships between several existing knowledge representation formalisms, providing a basis from which more expressive models can be later developed....
Functional representations of integrable hierarchies
International Nuclear Information System (INIS)
Dimakis, Aristophanes; Mueller-Hoissen, Folkert
2006-01-01
We consider a general framework for integrable hierarchies in Lax form and derive certain universal equations from which 'functional representations' of particular hierarchies (such as KP, discrete KP, mKP, AKNS), i.e. formulations in terms of functional equations, are systematically and quite easily obtained. The formalism genuinely applies to hierarchies where the dependent variables live in a noncommutative (typically matrix) algebra. The obtained functional representations can be understood as 'noncommutative' analogues of 'Fay identities' for the KP hierarchy
Crystal structure representations for machine learning models of formation energies
Energy Technology Data Exchange (ETDEWEB)
Faber, Felix [Department of Chemistry, Institute of Physical Chemistry and National Center for Computational Design and Discovery of Novel Materials, University of Basel Switzerland; Lindmaa, Alexander [Department of Physics, Chemistry and Biology, Linköping University, SE-581 83 Linköping Sweden; von Lilienfeld, O. Anatole [Department of Chemistry, Institute of Physical Chemistry and National Center for Computational Design and Discovery of Novel Materials, University of Basel Switzerland; Argonne Leadership Computing Facility, Argonne National Laboratory, 9700 S. Cass Avenue Lemont Illinois 60439; Armiento, Rickard [Department of Physics, Chemistry and Biology, Linköping University, SE-581 83 Linköping Sweden
2015-04-20
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 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 dataset of 3938 crystal structures obtained from the Materials Project. For training sets consisting of 3000 crystals, the generalization error in predicting formation energies of new structures corresponds to (i) 0.49, (ii) 0.64, and (iii) 0.37eV/atom for the respective representations.
A Model of Representational Spaces in Human Cortex.
Guntupalli, J Swaroop; Hanke, Michael; Halchenko, Yaroslav O; Connolly, Andrew C; Ramadge, Peter J; Haxby, James V
2016-06-01
Current models of the functional architecture of human cortex emphasize areas that capture coarse-scale features of cortical topography but provide no account for population responses that encode information in fine-scale patterns of activity. Here, we present a linear model of shared representational spaces in human cortex that captures fine-scale distinctions among population responses with response-tuning basis functions that are common across brains and models cortical patterns of neural responses with individual-specific topographic basis functions. We derive a common model space for the whole cortex using a new algorithm, searchlight hyperalignment, and complex, dynamic stimuli that provide a broad sampling of visual, auditory, and social percepts. The model aligns representations across brains in occipital, temporal, parietal, and prefrontal cortices, as shown by between-subject multivariate pattern classification and intersubject correlation of representational geometry, indicating that structural principles for shared neural representations apply across widely divergent domains of information. The model provides a rigorous account for individual variability of well-known coarse-scale topographies, such as retinotopy and category selectivity, and goes further to account for fine-scale patterns that are multiplexed with coarse-scale topographies and carry finer distinctions. © The Author 2016. Published by Oxford University Press.
Valued Graphs and the Representation Theory of Lie Algebras
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Joel Lemay
2012-07-01
Full Text Available Quivers (directed graphs, species (a generalization of quivers and their representations play a key role in many areas of mathematics including combinatorics, geometry, and algebra. Their importance is especially apparent in their applications to the representation theory of associative algebras, Lie algebras, and quantum groups. In this paper, we discuss the most important results in the representation theory of species, such as Dlab and Ringel’s extension of Gabriel’s theorem, which classifies all species of finite and tame representation type. We also explain the link between species and K-species (where K is a field. Namely, we show that the category of K -species can be viewed as a subcategory of the category of species. Furthermore, we prove two results about the structure of the tensor ring of a species containing no oriented cycles. Specifically, we prove that two such species have isomorphic tensor rings if and only if they are isomorphic as “crushed” species, and we show that if K is a perfect field, then the tensor algebra of a K -species tensored with the algebraic closure of K is isomorphic to, or Morita equivalent to, the path algebra of a quiver.
Gravitational and Magnetic Anomaly Inversion Using a Tree-Based Geometry Representation
2009-06-01
find successive mini- ized vectors. Throughout this paper, the term iteration refers to a ingle loop through a stage of the global scheme, not...BOX 12211 RESEARCH TRIANGLE PARK NC 27709-2211 5 NAVAL RESEARCH LAB E R FRANCHI CODE 7100 M H ORR CODE 7120 J A BUCARO CODE 7130
Energy Technology Data Exchange (ETDEWEB)
Yuan, Rui; Singh, Sudhanshu S.; Chawla, Nikhilesh; Oswald, Jay, E-mail: joswald1@asu.edu
2016-08-15
We present a robust method for automating removal of “segregation artifacts” in segmented tomographic images of three-dimensional heterogeneous microstructures. The objective of this method is to accurately identify and separate discrete features in composite materials where limitations in imaging resolution lead to spurious connections near close contacts. The method utilizes betweenness centrality, a measure of the importance of a node in the connectivity of a graph network, to identify voxels that create artificial bridges between otherwise distinct geometric features. To facilitate automation of the algorithm, we develop a relative centrality metric to allow for the selection of a threshold criterion that is not sensitive to inclusion size or shape. As a demonstration of the effectiveness of the algorithm, we report on the segmentation of a 3D reconstruction of a SiC particle reinforced aluminum alloy, imaged by X-ray synchrotron tomography.
Scale space representations locally adapted to the geometry of base and target manifold
Florack, L.M.J.
2010-01-01
We generalize the Gaussian multi-resolution image paradigm for a Euclidean domain to general Riemannian base manifolds and also account for the codomain by considering the extension into a fibre bundle structure. We elaborate on aspects of parametrization and gauge, as these are important in
Many-particle hydrodynamic interactions in parallel-wall geometry: Cartesian-representation method
International Nuclear Information System (INIS)
Blawzdziewicz, J.; Wajnryb, E.; Bhattacharya, S.
2005-01-01
This talk will describe the results of our theoretical and numerical studies of hydrodynamic interactions in a suspension of spherical particles confined between two parallel planar walls, under creeping-flow conditions. We propose an efficient algorithm for evaluating many-particle friction matrix in this system-no Stokesian-dynamics algorithm of this kind has been available so far. Our approach involves expanding the fluid velocity field in the wall-bounded suspension into spherical and Cartesian fundamental sets of Stokes flows. The spherical set is used to describe the interaction of the fluid with the particles and the Cartesian set to describe the interaction with the walls. At the core of our method are transformation relations between the spherical and Cartesian fundamental sets. Using the transformation formulas, we derive a system of linear equations for the force multipoles induced on the particle surfaces; the coefficients in these equations are given in terms of lateral Fourier integrals corresponding to the directions parallel to the walls. The force-multipole equations have been implemented in a numerical algorithm for the evaluation of the multiparticle friction matrix in the wall-bounded system. The algorithm involves subtraction of the particle-wall and particle-particle lubrication contributions to accelerate the convergence of the results with the spherical-harmonics order, and a subtraction of the single-wall contributions to accelerate the convergence of the Fourier integrals. (author)
Hopf algebras in noncommutative geometry
International Nuclear Information System (INIS)
Varilly, Joseph C.
2001-10-01
We give an introductory survey to the use of Hopf algebras in several problems of non- commutative geometry. The main example, the Hopf algebra of rooted trees, is a graded, connected Hopf algebra arising from a universal construction. We show its relation to the algebra of transverse differential operators introduced by Connes and Moscovici in order to compute a local index formula in cyclic cohomology, and to the several Hopf algebras defined by Connes and Kreimer to simplify the combinatorics of perturbative renormalization. We explain how characteristic classes for a Hopf module algebra can be obtained from the cyclic cohomology of the Hopf algebra which acts on it. Finally, we discuss the theory of non- commutative spherical manifolds and show how they arise as homogeneous spaces of certain compact quantum groups. (author)
Integrable systems, geometry, and topology
Terng, Chuu-Lian
2006-01-01
The articles in this volume are based on lectures from a program on integrable systems and differential geometry held at Taiwan's National Center for Theoretical Sciences. As is well-known, for many soliton equations, the solutions have interpretations as differential geometric objects, and thereby techniques of soliton equations have been successfully applied to the study of geometric problems. The article by Burstall gives a beautiful exposition on isothermic surfaces and their relations to integrable systems, and the two articles by Guest give an introduction to quantum cohomology, carry out explicit computations of the quantum cohomology of flag manifolds and Hirzebruch surfaces, and give a survey of Givental's quantum differential equations. The article by Heintze, Liu, and Olmos is on the theory of isoparametric submanifolds in an arbitrary Riemannian manifold, which is related to the n-wave equation when the ambient manifold is Euclidean. Mukai-Hidano and Ohnita present a survey on the moduli space of ...
Tarski Geometry Axioms. Part III
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Coghetto Roland
2017-12-01
Full Text Available In the article, we continue the formalization of the work devoted to Tarski’s geometry - the book “Metamathematische Methoden in der Geometrie” by W. Schwabhäuser, W. Szmielew, and A. Tarski. After we prepared some introductory formal framework in our two previous Mizar articles, we focus on the regular translation of underlying items faithfully following the abovementioned book (our encoding covers first seven chapters. Our development utilizes also other formalization efforts of the same topic, e.g. Isabelle/HOL by Makarios, Metamath or even proof objects obtained directly from Prover9. In addition, using the native Mizar constructions (cluster registrations the propositions (“Satz” are reformulated under weaker conditions, i.e. by using fewer axioms or by proposing an alternative version that uses just another axioms (ex. Satz 2.1 or Satz 2.2.
Applied geometry and discrete mathematics
Sturm; Gritzmann, Peter; Sturmfels, Bernd
1991-01-01
This volume, published jointly with the Association for Computing Machinery, comprises a collection of research articles celebrating the occasion of Victor Klee's sixty-fifth birthday in September 1990. During his long career, Klee has made contributions to a wide variety of areas, such as discrete and computational geometry, convexity, combinatorics, graph theory, functional analysis, mathematical programming and optimization, and theoretical computer science. In addition, Klee made important contributions to mathematics education, mathematical methods in economics and the decision sciences, applications of discrete mathematics in the biological and social sciences, and the transfer of knowledge from applied mathematics to industry. In honor of Klee's achievements, this volume presents more than forty papers on topics related to Klee's research. While the majority of the papers are research articles, a number of survey articles are also included. Mirroring the breadth of Klee's mathematical contributions, th...
Introduction to global variational geometry
Krupka, Demeter
2015-01-01
The book is devoted to recent research in the global variational theory on smooth manifolds. Its main objective is an extension of the classical variational calculus on Euclidean spaces to (topologically nontrivial) finite-dimensional smooth manifolds; to this purpose the methods of global analysis of differential forms are used. Emphasis is placed on the foundations of the theory of variational functionals on fibered manifolds - relevant geometric structures for variational principles in geometry, physical field theory and higher-order fibered mechanics. The book chapters include: - foundations of jet bundles and analysis of differential forms and vector fields on jet bundles, - the theory of higher-order integral variational functionals for sections of a fibred space, the (global) first variational formula in infinitesimal and integral forms- extremal conditions and the discussion of Noether symmetries and generalizations,- the inverse problems of the calculus of variations of Helmholtz type- variational se...
Some Progress in Conformal Geometry
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Sun-Yung A. Chang
2007-12-01
Full Text Available This is a survey paper of our current research on the theory of partial differential equations in conformal geometry. Our intention is to describe some of our current works in a rather brief and expository fashion. We are not giving a comprehensive survey on the subject and references cited here are not intended to be complete. We introduce a bubble tree structure to study the degeneration of a class of Yamabe metrics on Bach flat manifolds satisfying some global conformal bounds on compact manifolds of dimension 4. As applications, we establish a gap theorem, a finiteness theorem for diffeomorphism type for this class, and diameter bound of the $sigma_2$-metrics in a class of conformal 4-manifolds. For conformally compact Einstein metrics we introduce an eigenfunction compactification. As a consequence we obtain some topological constraints in terms of renormalized volumes.
Seesaw mechanism in warped geometry
International Nuclear Information System (INIS)
Huber, S.J.; Shafi, Q.
2003-09-01
We show how the seesaw mechanism for neutrino masses can be realized within a five dimensional (5D) warped geometry framework. Intermediate scale standard model (SM) singlet neutrino masses, needed to explain the atmospheric and solar neutrino oscillations, are shown to be proportional to M P1 .exp((2c-1)πkR), where c denotes the coefficient of the 5D Dirac mass term for the singlet neutrino which also has a Planck scale Majorana mass localized on the Planck-brane, and kR∼11 in order to resolve the gauge hierarchy problem. The case with a bulk 5D Majorana mass term for the singlet neutrino is briefly discussed. (orig.)
Seesaw mechanism in warped geometry
International Nuclear Information System (INIS)
Huber, Stephan J.; Shafi, Qaisar
2004-01-01
We show how the seesaw mechanism for neutrino masses can be realized within a five-dimensional (5D) warped geometry framework. Intermediate scale standard model (SM) singlet neutrino masses, needed to explain the atmospheric and solar neutrino oscillations, are shown to be proportional to M Pl exp((2c-1)πkR), where c denotes the coefficient of the 5D Dirac mass term for the singlet neutrino which also has a Planck scale Majorana mass localized on the Planck-brane, and kR∼11 in order to resolve the gauge hierarchy problem. The case with a bulk 5D Majorana mass term for the singlet neutrino is briefly discussed
Conformal geometry and quasiregular mappings
Vuorinen, Matti
1988-01-01
This book is an introduction to the theory of spatial quasiregular mappings intended for the uninitiated reader. At the same time the book also addresses specialists in classical analysis and, in particular, geometric function theory. The text leads the reader to the frontier of current research and covers some most recent developments in the subject, previously scatterd through the literature. A major role in this monograph is played by certain conformal invariants which are solutions of extremal problems related to extremal lengths of curve families. These invariants are then applied to prove sharp distortion theorems for quasiregular mappings. One of these extremal problems of conformal geometry generalizes a classical two-dimensional problem of O. Teichmüller. The novel feature of the exposition is the way in which conformal invariants are applied and the sharp results obtained should be of considerable interest even in the two-dimensional particular case. This book combines the features of a textbook an...
Quantization of the Schwarzschild geometry
International Nuclear Information System (INIS)
Melas, Evangelos
2013-01-01
The conditional symmetries of the reduced Einstein-Hilbert action emerging from a static, spherically symmetric geometry are used as supplementary conditions on the wave function. Based on their integrability conditions, only one of the three existing symmetries can be consistently imposed, while the unique Casimir invariant, being the product of the remaining two symmetries, is calculated as the only possible second condition on the wave function. This quadratic integral of motion is identified with the reparametrization generator, as an implication of the uniqueness of the dynamical evolution, by fixing a suitable parametrization of the r-lapse function. In this parametrization, the determinant of the supermetric plays the role of the mesure. The combined Wheeler – DeWitt and linear conditional symmetry equations are analytically solved. The solutions obtained depend on the product of the two ''scale factors''.
Geometry and project: the example of Piazza della Vittoria in Genoa
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Luisa Cogorno
2012-06-01
Full Text Available The study on the Genoese architectures in the thirties of Piazza della Vittoria highlights the paramount role of geometry for the project. The square, created by architect Marcello Piacentini between 1927 and 1930, stands opposite the railway station Genoa Brignole, pursuing a very logical representation: a new, very wide square surrounded by arcades ... the new civic-wordly heart of the city (M. Piacentini. The methodological tool applied for the critical reading was the integrated relief: perceptual and historical analysis, relief and graphic representation of the whole and of the details, reconstruction of the compositional logic, study of materials used; the different phases showed the trasversality of the role of geometry –verified by the metric survey and by the compositive reading of the proportions- and the presence of dimensional canons unusual for the city.
An integral equation-based numerical solver for Taylor states in toroidal geometries
O'Neil, Michael; Cerfon, Antoine J.
2018-04-01
We present an algorithm for the numerical calculation of Taylor states in toroidal and toroidal-shell geometries using an analytical framework developed for the solution to the time-harmonic Maxwell equations. Taylor states are a special case of what are known as Beltrami fields, or linear force-free fields. The scheme of this work relies on the generalized Debye source representation of Maxwell fields and an integral representation of Beltrami fields which immediately yields a well-conditioned second-kind integral equation. This integral equation has a unique solution whenever the Beltrami parameter λ is not a member of a discrete, countable set of resonances which physically correspond to spontaneous symmetry breaking. Several numerical examples relevant to magnetohydrodynamic equilibria calculations are provided. Lastly, our approach easily generalizes to arbitrary geometries, both bounded and unbounded, and of varying genus.
Eliashberg, Yakov; Maeda, Yoshiaki; Symplectic, Poisson, and Noncommutative geometry
2014-01-01
Symplectic geometry originated in physics, but it has flourished as an independent subject in mathematics, together with its offspring, symplectic topology. Symplectic methods have even been applied back to mathematical physics. Noncommutative geometry has developed an alternative mathematical quantization scheme based on a geometric approach to operator algebras. Deformation quantization, a blend of symplectic methods and noncommutative geometry, approaches quantum mechanics from a more algebraic viewpoint, as it addresses quantization as a deformation of Poisson structures. This volume contains seven chapters based on lectures given by invited speakers at two May 2010 workshops held at the Mathematical Sciences Research Institute: Symplectic and Poisson Geometry in Interaction with Analysis, Algebra and Topology (honoring Alan Weinstein, one of the key figures in the field) and Symplectic Geometry, Noncommutative Geometry and Physics. The chapters include presentations of previously unpublished results and ...
Semantic representation of reported measurements in radiology.
Oberkampf, Heiner; Zillner, Sonja; Overton, James A; Bauer, Bernhard; Cavallaro, Alexander; Uder, Michael; Hammon, Matthias
2016-01-22
In radiology, a vast amount of diverse data is generated, and unstructured reporting is standard. Hence, much useful information is trapped in free-text form, and often lost in translation and transmission. One relevant source of free-text data consists of reports covering the assessment of changes in tumor burden, which are needed for the evaluation of cancer treatment success. Any change of lesion size is a critical factor in follow-up examinations. It is difficult to retrieve specific information from unstructured reports and to compare them over time. Therefore, a prototype was implemented that demonstrates the structured representation of findings, allowing selective review in consecutive examinations and thus more efficient comparison over time. We developed a semantic Model for Clinical Information (MCI) based on existing ontologies from the Open Biological and Biomedical Ontologies (OBO) library. MCI is used for the integrated representation of measured image findings and medical knowledge about the normal size of anatomical entities. An integrated view of the radiology findings is realized by a prototype implementation of a ReportViewer. Further, RECIST (Response Evaluation Criteria In Solid Tumors) guidelines are implemented by SPARQL queries on MCI. The evaluation is based on two data sets of German radiology reports: An oncologic data set consisting of 2584 reports on 377 lymphoma patients and a mixed data set consisting of 6007 reports on diverse medical and surgical patients. All measurement findings were automatically classified as abnormal/normal using formalized medical background knowledge, i.e., knowledge that has been encoded into an ontology. A radiologist evaluated 813 classifications as correct or incorrect. All unclassified findings were evaluated as incorrect. The proposed approach allows the automatic classification of findings with an accuracy of 96.4 % for oncologic reports and 92.9 % for mixed reports. The ReportViewer permits
Convection in Slab and Spheroidal Geometries
Porter, David H.; Woodward, Paul R.; Jacobs, Michael L.
2000-01-01
Three-dimensional numerical simulations of compressible turbulent thermally driven convection, in both slab and spheroidal geometries, are reviewed and analyzed in terms of velocity spectra and mixing-length theory. The same ideal gas model is used in both geometries, and resulting flows are compared. The piecewise-parabolic method (PPM), with either thermal conductivity or photospheric boundary conditions, is used to solve the fluid equations of motion. Fluid motions in both geometries exhibit a Kolmogorov-like k(sup -5/3) range in their velocity spectra. The longest wavelength modes are energetically dominant in both geometries, typically leading to one convection cell dominating the flow. In spheroidal geometry, a dipolar flow dominates the largest scale convective motions. Downflows are intensely turbulent and up drafts are relatively laminar in both geometries. In slab geometry, correlations between temperature and velocity fluctuations, which lead to the enthalpy flux, are fairly independent of depth. In spheroidal geometry this same correlation increases linearly with radius over the inner 70 percent by radius, in which the local pressure scale heights are a sizable fraction of the radius. The effects from the impenetrable boundary conditions in the slab geometry models are confused with the effects from non-local convection. In spheroidal geometry nonlocal effects, due to coherent plumes, are seen as far as several pressure scale heights from the lower boundary and are clearly distinguishable from boundary effects.
Mathematical Modeling of Resonant Processes in Confined Geometry of Atomic and Atom-Ion Traps
Melezhik, Vladimir S.
2018-02-01
We discuss computational aspects of the developed mathematical models for resonant processes in confined geometry of atomic and atom-ion traps. The main attention is paid to formulation in the nondirect product discrete-variable representation (npDVR) of the multichannel scattering problem with nonseparable angular part in confining traps as the boundary-value problem. Computational efficiency of this approach is demonstrated in application to atomic and atom-ion confinement-induced resonances we predicted recently.
Analysis of Paralleling Limited Capacity Voltage Sources by Projective Geometry Method
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Alexandr Penin
2014-01-01
Full Text Available The droop current-sharing method for voltage sources of a limited capacity is considered. Influence of equalizing resistors and load resistor is investigated on uniform distribution of relative values of currents when the actual loading corresponds to the capacity of a concrete source. Novel concepts for quantitative representation of operating regimes of sources are entered with use of projective geometry method.
Creating New VLS Silicon Nanowire Contact Geometries by Controlling Catalyst Migration
DEFF Research Database (Denmark)
Alam, Sardar Bilal; Panciera, Federico; Hansen, Ole
2015-01-01
The formation of self-assembled contacts between vapor-liquid-solid grown silicon nanowires and flat silicon surfaces was imaged in situ using electron microscopy. By measuring the structural evolution of the contact formation process, we demonstrate how different contact geometries are created b...
Directory of Open Access Journals (Sweden)
Okky Riswandha Imawan
2015-12-01
Abstract This research aims to describe the effectiveness and effectiveness differences of the Guided Discovery Learning (GDL Model and the Project Based Learning (PjBL Model in terms of achievement, self-confidence, and critical thinking skills of students on the Solid Geometry subjects. This research was quasi experimental. The research subjects were two undergraduate classes of Mathematics Education Program, Ahmad Dahlan University, in their second semester, established at random. The data analysis to test the effectiveness of the GDL and PjBL Models in terms of each of the dependent variables used the t-test. The data analysis to test differences between effectiveness of the GDL and that of the PjBL Model used the MANOVA test. The results of this research show that viewed from achievement, self confidence, and critical thinking skills of the students are the application of the GDL Model on Solid Geometry subject is effective, the application of the PjBL Model on Solid Geometry subject is effective, and there is no difference in the effectiveness of GDL and PjBL Models on Solid Geometry subject in terms of achievement, self confidence, and critical thinking skills of the students. Keywords: guided discovery learning model, project-based learning model, achievement, self-confidence, critical thinking skills
Weyl geometry and the nonlinear mechanics of distributed point defects
Yavari, A.
2012-09-05
The residual stress field of a nonlinear elastic solid with a spherically symmetric distribution of point defects is obtained explicitly using methods from differential geometry. The material manifold of a solid with distributed point defects-where the body is stress-free-is a flat Weyl manifold, i.e. a manifold with an affine connection that has non-metricity with vanishing traceless part, but both its torsion and curvature tensors vanish. Given a spherically symmetric point defect distribution, we construct its Weyl material manifold using the method of Cartan\\'s moving frames. Having the material manifold, the anelasticity problem is transformed to a nonlinear elasticity problem and reduces the problem of computing the residual stresses to finding an embedding into the Euclidean ambient space. In the case of incompressible neo-Hookean solids, we calculate explicitly this residual stress field. We consider the example of a finite ball and a point defect distribution uniform in a smaller ball and vanishing elsewhere. We show that the residual stress field inside the smaller ball is uniform and hydrostatic. We also prove a nonlinear analogue of Eshelby\\'s celebrated inclusion problem for a spherical inclusion in an isotropic incompressible nonlinear solid. © 2012 The Royal Society.
Topological vertex, string amplitudes and spectral functions of hyperbolic geometry
Energy Technology Data Exchange (ETDEWEB)
Guimaraes, M.E.X.; Rosa, T.O. [Universidade Federal Fluminense, Instituto de Fisica, Av. Gal. Milton Tavares de Souza, s/n, CEP 24210-346, Niteroi, RJ (Brazil); Luna, R.M. [Universidade Estadual de Londrina, Departamento de Fisica, Caixa Postal 6001, Londrina, Parana (Brazil)
2014-05-15
We discuss the homological aspects of the connection between quantum string generating function and the formal power series associated to the dimensions of chains and homologies of suitable Lie algebras. Our analysis can be considered as a new straightforward application of the machinery of modular forms and spectral functions (with values in the congruence subgroup of SL(2,Z)) to the partition functions of Lagrangian branes, refined vertex and open string partition functions, represented by means of formal power series that encode Lie algebra properties. The common feature in our examples lies in the modular properties of the characters of certain representations of the pertinent affine Lie algebras and in the role of Selberg-type spectral functions of a hyperbolic three-geometry associated with q-series in the computation of the string amplitudes. (orig.)
Evolved Representation and Computational Creativity
Directory of Open Access Journals (Sweden)
Ashraf Fouad Hafez Ismail
2001-01-01
Full Text Available Advances in science and technology have influenced designing activity in architecture throughout its history. Observing the fundamental changes to architectural designing due to the substantial influences of the advent of the computing era, we now witness our design environment gradually changing from conventional pencil and paper to digital multi-media. Although designing is considered to be a unique human activity, there has always been a great dependency on design aid tools. One of the greatest aids to architectural design, amongst the many conventional and widely accepted computational tools, is the computer-aided object modeling and rendering tool, commonly known as a CAD package. But even though conventional modeling tools have provided designers with fast and precise object handling capabilities that were not available in the pencil-and-paper age, they normally show weaknesses and limitations in covering the whole design process.In any kind of design activity, the design worked on has to be represented in some way. For a human designer, designs are for example represented using models, drawings, or verbal descriptions. If a computer is used for design work, designs are usually represented by groups of pixels (paintbrush programs, lines and shapes (general-purpose CAD programs or higher-level objects like ‘walls’ and ‘rooms’ (purpose-specific CAD programs.A human designer usually has a large number of representations available, and can use the representation most suitable for what he or she is working on. Humans can also introduce new representations and thereby represent objects that are not part of the world they experience with their sensory organs, for example vector representations of four and five dimensional objects. In design computing on the other hand, the representation or representations used have to be explicitly defined. Many different representations have been suggested, often optimized for specific design domains
Connections between algebra, combinatorics, and geometry
Sather-Wagstaff, Sean
2014-01-01
Commutative algebra, combinatorics, and algebraic geometry are thriving areas of mathematical research with a rich history of interaction. Connections Between Algebra, Combinatorics, and Geometry contains lecture notes, along with exercises and solutions, from the Workshop on Connections Between Algebra and Geometry held at the University of Regina from May 29-June 1, 2012. It also contains research and survey papers from academics invited to participate in the companion Special Session on Interactions Between Algebraic Geometry and Commutative Algebra, which was part of the CMS Summer Meeting at the University of Regina held June 2–3, 2012, and the meeting Further Connections Between Algebra and Geometry, which was held at the North Dakota State University, February 23, 2013. This volume highlights three mini-courses in the areas of commutative algebra and algebraic geometry: differential graded commutative algebra, secant varieties, and fat points and symbolic powers. It will serve as a useful resou...
Second International workshop Geometry and Symbolic Computation
Walczak, Paweł; Geometry and its Applications
2014-01-01
This volume has been divided into two parts: Geometry and Applications. The geometry portion of the book relates primarily to geometric flows, laminations, integral formulae, geometry of vector fields on Lie groups, and osculation; the articles in the applications portion concern some particular problems of the theory of dynamical systems, including mathematical problems of liquid flows and a study of cycles for non-dynamical systems. This Work is based on the second international workshop entitled "Geometry and Symbolic Computations," held on May 15-18, 2013 at the University of Haifa and is dedicated to modeling (using symbolic calculations) in differential geometry and its applications in fields such as computer science, tomography, and mechanics. It is intended to create a forum for students and researchers in pure and applied geometry to promote discussion of modern state-of-the-art in geometric modeling using symbolic programs such as Maple™ and Mathematica®, as well as presentation of new results. ...
On Behavioral Equivalence of Rational Representations
Trentelman, Harry L.; Willems, JC; Hara, S; Ohta, Y; Fujioka, H
2010-01-01
This article deals with the equivalence of representations of behaviors of linear differential systems In general. the behavior of a given linear differential system has many different representations. In this paper we restrict ourselves to kernel representations and image representations Two kernel
A vector space approach to geometry
Hausner, Melvin
2010-01-01
The effects of geometry and linear algebra on each other receive close attention in this examination of geometry's correlation with other branches of math and science. In-depth discussions include a review of systematic geometric motivations in vector space theory and matrix theory; the use of the center of mass in geometry, with an introduction to barycentric coordinates; axiomatic development of determinants in a chapter dealing with area and volume; and a careful consideration of the particle problem. 1965 edition.
Classical geometry Euclidean, transformational, inversive, and projective
Leonard, I E; Liu, A C F; Tokarsky, G W
2014-01-01
Features the classical themes of geometry with plentiful applications in mathematics, education, engineering, and science Accessible and reader-friendly, Classical Geometry: Euclidean, Transformational, Inversive, and Projective introduces readers to a valuable discipline that is crucial to understanding bothspatial relationships and logical reasoning. Focusing on the development of geometric intuitionwhile avoiding the axiomatic method, a problem solving approach is encouraged throughout. The book is strategically divided into three sections: Part One focuses on Euclidean geometry, which p
On Representation in Information Theory
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Joseph E. Brenner
2011-09-01
Full Text Available Semiotics is widely applied in theories of information. Following the original triadic characterization of reality by Peirce, the linguistic processes involved in information—production, transmission, reception, and understanding—would all appear to be interpretable in terms of signs and their relations to their objects. Perhaps the most important of these relations is that of the representation-one, entity, standing for or representing some other. For example, an index—one of the three major kinds of signs—is said to represent something by being directly related to its object. My position, however, is that the concept of symbolic representations having such roles in information, as intermediaries, is fraught with the same difficulties as in representational theories of mind. I have proposed an extension of logic to complex real phenomena, including mind and information (Logic in Reality; LIR, most recently at the 4th International Conference on the Foundations of Information Science (Beijing, August, 2010. LIR provides explanations for the evolution of complex processes, including information, that do not require any entities other than the processes themselves. In this paper, I discuss the limitations of the standard relation of representation. I argue that more realistic pictures of informational systems can be provided by reference to information as an energetic process, following the categorial ontology of LIR. This approach enables naïve, anti-realist conceptions of anti-representationalism to be avoided, and enables an approach to both information and meaning in the same novel logical framework.
Introduction to non-Euclidean geometry
Wolfe, Harold E
2012-01-01
One of the first college-level texts for elementary courses in non-Euclidean geometry, this concise, readable volume is geared toward students familiar with calculus. A full treatment of the historical background explores the centuries-long efforts to prove Euclid's parallel postulate and their triumphant conclusion. Numerous original exercises form an integral part of the book.Topics include hyperbolic plane geometry and hyperbolic plane trigonometry, applications of calculus to the solutions of some problems in hyperbolic geometry, elliptic plane geometry and trigonometry, and the consistenc
Disformal transformation in Newton-Cartan geometry
Energy Technology Data Exchange (ETDEWEB)
Huang, Peng [Zhejiang Chinese Medical University, Department of Information, Hangzhou (China); Sun Yat-Sen University, School of Physics and Astronomy, Guangzhou (China); Yuan, Fang-Fang [Nankai University, School of Physics, Tianjin (China)
2016-08-15
Newton-Cartan geometry has played a central role in recent discussions of the non-relativistic holography and condensed matter systems. Although the conformal transformation in non-relativistic holography can easily be rephrased in terms of Newton-Cartan geometry, we show that it requires a nontrivial procedure to arrive at the consistent form of anisotropic disformal transformation in this geometry. Furthermore, as an application of the newly obtained transformation, we use it to induce a geometric structure which may be seen as a particular non-relativistic version of the Weyl integrable geometry. (orig.)
Applications of Affine and Weyl geometry
García-Río, Eduardo; Nikcevic, Stana
2013-01-01
Pseudo-Riemannian geometry is, to a large extent, the study of the Levi-Civita connection, which is the unique torsion-free connection compatible with the metric structure. There are, however, other affine connections which arise in different contexts, such as conformal geometry, contact structures, Weyl structures, and almost Hermitian geometry. In this book, we reverse this point of view and instead associate an auxiliary pseudo-Riemannian structure of neutral signature to certain affine connections and use this correspondence to study both geometries. We examine Walker structures, Riemannia
Special Geometry and Automorphic Forms
Berglund, P; Wyllard, N; Berglund, Per; Henningson, Mans; Wyllard, Niclas
1997-01-01
We consider special geometry of the vector multiplet moduli space in compactifications of the heterotic string on $K3 \\times T^2$ or the type IIA string on $K3$-fibered Calabi-Yau threefolds. In particular, we construct a modified dilaton that is invariant under $SO(2, n; Z)$ T-duality transformations at the non-perturbative level and regular everywhere on the moduli space. The invariant dilaton, together with a set of other coordinates that transform covariantly under $SO(2, n; Z)$, parameterize the moduli space. The construction involves a meromorphic automorphic function of $SO(2, n; Z)$, that also depends on the invariant dilaton. In the weak coupling limit, the divisor of this automorphic form is an integer linear combination of the rational quadratic divisors where the gauge symmetry is enhanced classically. We also show how the non-perturbative prepotential can be expressed in terms of meromorphic automorphic forms, by expanding a T-duality invariant quantity both in terms of the standard special coord...
Differential geometry in string models
International Nuclear Information System (INIS)
Alvarez, O.
1986-01-01
In this article the author reviews the differential geometric approach to the quantization of strings. A seminal paper demonstrates the connection between the trace anomaly and the critical dimension. The role played by the Faddeev-Popov ghosts has been instrumental in much of the subsequent work on the quantization of strings. This paper discusses the differential geometry of two dimensional surfaces and its importance in the quantization of strings. The path integral quantization approach to strings will be carefully analyzed to determine the correct effective measure for string theories. The choice of measure for the path integral is determined by differential geometric considerations. Once the measure is determined, the manifest diffeomorphism invariance of the theory will have to be broken by using the Faddeev-Popov ansatz. The gauge fixed theory is studied in detail with emphasis on the role of conformal and gravitational anomalies. In the analysis, the path integral formulation of the gauge fixed theory requires summing over all the distinct complex structures on the manifold
Geometry of lattice field theory
International Nuclear Information System (INIS)
Honan, T.J.
1986-01-01
Using some tools of algebraic topology, a general formalism for lattice field theory is presented. The lattice is taken to be a simplicial complex that is also a manifold and is referred to as a simplicial manifold. The fields on this lattice are cochains, that are called lattice forms to emphasize the connections with differential forms in the continuum. This connection provides a new bridge between lattice and continuum field theory. A metric can be put onto this simplicial manifold by assigning lengths to every link or I-simplex of the lattice. Regge calculus is a way of defining general relativity on this lattice. A geometric discussion of Regge calculus is presented. The Regge action, which is a discrete form of the Hilbert action, is derived from the Hilbert action using distribution valued forms. This is a new derivation that emphasizes the underlying geometry. Kramers-Wannier duality in statistical mechanics is discussed in this general setting. Nonlinear field theories, which include gauge theories and nonlinear sigma models are discussed in the continuum and then are put onto a lattice. The main new result here is the generalization to curved spacetime, which consists of making the theory compatible with Regge calculus
Latent geometry of bipartite networks
Kitsak, Maksim; Papadopoulos, Fragkiskos; Krioukov, Dmitri
2017-03-01
Despite the abundance of bipartite networked systems, their organizing principles are less studied compared to unipartite networks. Bipartite networks are often analyzed after projecting them onto one of the two sets of nodes. As a result of the projection, nodes of the same set are linked together if they have at least one neighbor in common in the bipartite network. Even though these projections allow one to study bipartite networks using tools developed for unipartite networks, one-mode projections lead to significant loss of information and artificial inflation of the projected network with fully connected subgraphs. Here we pursue a different approach for analyzing bipartite systems that is based on the observation that such systems have a latent metric structure: network nodes are points in a latent metric space, while connections are more likely to form between nodes separated by shorter distances. This approach has been developed for unipartite networks, and relatively little is known about its applicability to bipartite systems. Here, we fully analyze a simple latent-geometric model of bipartite networks and show that this model explains the peculiar structural properties of many real bipartite systems, including the distributions of common neighbors and bipartite clustering. We also analyze the geometric information loss in one-mode projections in this model and propose an efficient method to infer the latent pairwise distances between nodes. Uncovering the latent geometry underlying real bipartite networks can find applications in diverse domains, ranging from constructing efficient recommender systems to understanding cell metabolism.
Fractal Geometry and Stochastics V
Falconer, Kenneth; Zähle, Martina
2015-01-01
This book brings together leading contributions from the fifth conference on Fractal Geometry and Stochastics held in Tabarz, Germany, in March 2014. The book is divided into five sections covering different facets of this fast developing area: geometric measure theory, self-similar fractals and recurrent structures, analysis and algebra on fractals, multifractal theory, and random constructions. There are state-of-the-art surveys as well as papers highlighting more specific recent advances. The authors are world-experts who present their topics comprehensibly and attractively. The book provides an accessible gateway to the subject for newcomers as well as a reference for recent developments for specialists. Authors include: Krzysztof Barański, Julien Barral, Kenneth Falconer, De-Jun Feng, Peter J. Grabner, Rostislav Grigorchuk, Michael Hinz, Stéphane Jaffard, Maarit Järvenpää, Antti Käenmäki, Marc Kesseböhmer, Michel Lapidus, Klaus Mecke, Mark Pollicott, Michał Rams, Pablo Shmerkin, and András Te...
Stochastic geometry in PRIZMA code
International Nuclear Information System (INIS)
Malyshkin, G. N.; Kashaeva, E. A.; Mukhamadiev, R. F.
2007-01-01
The paper describes a method used to simulate radiation transport through random media - randomly placed grains in a matrix material. The method models the medium consequently from one grain crossed by particle trajectory to another. Like in the Limited Chord Length Sampling (LCLS) method, particles in grains are tracked in the actual grain geometry, but unlike LCLS, the medium is modeled using only Matrix Chord Length Sampling (MCLS) from the exponential distribution and it is not necessary to know the grain chord length distribution. This helped us extend the method to media with randomly oriented arbitrarily shaped convex grains. Other extensions include multicomponent media - grains of several sorts, and polydisperse media - grains of different sizes. Sort and size distributions of crossed grains were obtained and an algorithm was developed for sampling grain orientations and positions. Special consideration was given to medium modeling at the boundary of the stochastic region. The method was implemented in the universal 3D Monte Carlo code PRIZMA. The paper provides calculated results for a model problem where we determine volume fractions of modeled components crossed by particle trajectories. It also demonstrates the use of biased sampling techniques implemented in PRIZMA for solving a problem of deep penetration in model random media. Described are calculations for the spectral response of a capacitor dose detector whose anode was modeled with account for its stochastic structure. (authors)
The geometry of population genetics
Akin, Ethan
1979-01-01
The differential equations which model the action of selection and recombination are nonlinear equations which are impossible to It is even difficult to describe in general the solve explicitly. Recently, Shahshahani began using qualitative behavior of solutions. differential geometry to study these equations [28]. with this mono graph I hope to show that his ideas illuminate many aspects of pop ulation genetics. Among these are his proof and clarification of Fisher's Fundamental Theorem of Natural Selection and Kimura's Maximum Principle and also the effect of recombination on entropy. We also discover the relationship between two classic measures of 2 genetic distance: the x measure and the arc-cosine measure. There are two large applications. The first is a precise definition of the biological concept of degree of epistasis which applies to general (i.e. frequency dependent) forms of selection. The second is the unexpected appearance of cycling. We show that cycles can occur in the two-locus-two-allele...
A CAD based geometry model for simulation and analysis of particle detector data
Energy Technology Data Exchange (ETDEWEB)
Milde, Michael; Losekamm, Martin; Poeschl, Thomas; Greenwald, Daniel; Paul, Stephan [Technische Universitaet Muenchen, 85748 Garching (Germany)
2016-07-01
The development of a new particle detector requires a good understanding of its setup. A detailed model of the detector's geometry is not only needed during construction, but also for simulation and data analysis. To arrive at a consistent description of the detector geometry a representation is needed that can be easily implemented in different software tools used during data analysis. We developed a geometry representation based on CAD files that can be easily used within the Geant4 simulation framework and analysis tools based on the ROOT framework. This talk presents the structure of the geometry model and show its implementation using the example of the event reconstruction developed for the Multi-purpose Active-target Particle Telescope (MAPT). The detector consists of scintillating plastic fibers and can be used as a tracking detector and calorimeter with omnidirectional acceptance. To optimize the angular resolution and the energy reconstruction of measured particles, a detailed detector model is needed at all stages of the reconstruction.
A study in derived algebraic geometry volume I : correspondences and duality
Gaitsgory, Dennis
2017-01-01
Derived algebraic geometry is a far-reaching generalization of algebraic geometry. It has found numerous applications in various parts of mathematics, most prominently in representation theory. This volume develops the theory of ind-coherent sheaves in the context of derived algebraic geometry. Ind-coherent sheaves are a "renormalization" of quasi-coherent sheaves and provide a natural setting for Grothendieck-Serre duality as well as geometric incarnations of numerous categories of interest in representation theory. This volume consists of three parts and an appendix. The first part is a survey of homotopical algebra in the setting of \\infty-categories and the basics of derived algebraic geometry. The second part builds the theory of ind-coherent sheaves as a functor out of the category of correspondences and studies the relationship between ind-coherent and quasi-coherent sheaves. The third part sets up the general machinery of the \\mathrm{(}\\infty, 2\\mathrm{)}-category of correspondences needed for the sec...
Social representations of female orgasm.
Lavie-Ajayi, Maya; Joffe, Hélène
2009-01-01
This study examines women's social representations of female orgasm. Fifty semi-structured interviews were conducted with British women. The data were thematically analysed and compared with the content of female orgasm-related writing in two women's magazines over a 30-year period. The results indicate that orgasm is deemed the goal of sex with emphasis on its physiological dimension. However, the women and the magazines graft onto this scientifically driven representation the importance of relational and emotive aspects of orgasm. For the women, particularly those who experience themselves as having problems with orgasm, the scientifically driven representations induce feelings of failure, but are also resisted. The findings highlight the role played by the social context in women's subjective experience of their sexual health.
An introduction to quiver representations
Derksen, Harm
2017-01-01
This book is an introduction to the representation theory of quivers and finite dimensional algebras. It gives a thorough and modern treatment of the algebraic approach based on Auslander-Reiten theory as well as the approach based on geometric invariant theory. The material in the opening chapters is developed starting slowly with topics such as homological algebra, Morita equivalence, and Gabriel's theorem. Next, the book presents Auslander-Reiten theory, including almost split sequences and the Auslander-Reiten transform, and gives a proof of Kac's generalization of Gabriel's theorem. Once this basic material is established, the book goes on with developing the geometric invariant theory of quiver representations. The book features the exposition of the saturation theorem for semi-invariants of quiver representations and its application to Littlewood-Richardson coefficients. In the final chapters, the book exposes tilting modules, exceptional sequences and a connection to cluster categories. The book is su...
Preon representations and composite models
International Nuclear Information System (INIS)
Kang, Kyungsik
1982-01-01
This is a brief report on the preon models which are investigated by In-Gyu Koh, A. N. Schellekens and myself and based on complex, anomaly-free and asymptotically free representations of SU(3) to SU(8), SO(4N+2) and E 6 with no more than two different preons. Complete list of the representations that are complex anomaly-free and asymptotically free has been given by E. Eichten, I.-G. Koh and myself. The assumptions made about the ground state composites and the role of Fermi statistics to determine the metaflavor wave functions are discussed in some detail. We explain the method of decompositions of tensor products with definite permutation properties which has been developed for this purpose by I.-G. Koh, A.N. Schellekens and myself. An example based on an anomaly-free representation of the confining metacolor group SU(5) is discussed
Representational constraints on children's suggestibility.
Ceci, Stephen J; Papierno, Paul B; Kulkofsky, Sarah
2007-06-01
In a multistage experiment, twelve 4- and 9-year-old children participated in a triad rating task. Their ratings were mapped with multidimensional scaling, from which euclidean distances were computed to operationalize semantic distance between items in target pairs. These children and age-mates then participated in an experiment that employed these target pairs in a story, which was followed by a misinformation manipulation. Analyses linked individual and developmental differences in suggestibility to children's representations of the target items. Semantic proximity was a strong predictor of differences in suggestibility: The closer a suggested distractor was to the original item's representation, the greater was the distractor's suggestive influence. The triad participants' semantic proximity subsequently served as the basis for correctly predicting memory performance in the larger group. Semantic proximity enabled a priori counterintuitive predictions of reverse age-related trends to be confirmed whenever the distance between representations of items in a target pair was greater for younger than for older children.
Digital models for architectonical representation
Directory of Open Access Journals (Sweden)
Stefano Brusaporci
2011-12-01
Full Text Available Digital instruments and technologies enrich architectonical representation and communication opportunities. Computer graphics is organized according the two phases of visualization and construction, that is modeling and rendering, structuring dichotomy of software technologies. Visualization modalities give different kinds of representations of the same 3D model and instruments produce a separation between drawing and image’s creation. Reverse modeling can be related to a synthesis process, ‘direct modeling’ follows an analytic procedure. The difference between interactive and not interactive applications is connected to the possibilities offered by informatics instruments, and relates to modeling and rendering. At the same time the word ‘model’ describes different phenomenon (i.e. files: mathematical model of the building and of the scene; raster representation and post-processing model. All these correlated different models constitute the architectonical interpretative model, that is a simulation of reality made by the model for improving the knowledge.
Asymptotical representation of discrete groups
International Nuclear Information System (INIS)
Mishchenko, A.S.; Mohammad, N.
1995-08-01
If one has a unitary representation ρ: π → U(H) of the fundamental group π 1 (M) of the manifold M then one can do may useful things: 1. To construct a natural vector bundle over M; 2. To construct the cohomology groups with respect to the local system of coefficients; 3. To construct the signature of manifold M with respect to the local system of coefficients; and others. In particular, one can write the Hirzebruch formula which compares the signature with the characteristic classes of the manifold M, further based on this, find the homotopy invariant characteristic classes (i.e. the Novikov conjecture). Taking into account that the family of known representations is not sufficiently large, it would be interesting to extend this family to some larger one. Using the ideas of A.Connes, M.Gromov and H.Moscovici a proper notion of asymptotical representation is defined. (author). 7 refs
Vivid Representations and Their Effects
Directory of Open Access Journals (Sweden)
Kengo Miyazono
2018-04-01
Full Text Available Sinhababu’s Humean Nature contains many interesting and important ideas, but in this short commentary I focus on the idea of vivid representations. Sinhababu inherits his idea of vivid representations from Hume’s discussions, in particular his discussion of calm and violent passions. I am sympathetic to the idea of developing Hume’s insight that has been largely neglected by philosophers. I believe that Sinhababu and Hume are on the right track. What I do in this short commentary is to raise some questions about the details. The aim of asking these questions is not to challenge Sinhababu’s proposal (at least his main ideas, but rather to point at some interesting issues arising out of his proposal. The questions are about (1 the nature of vividness, (2 the effects of vivid representations, and (3 Sinhababu’s account of alief cases.
A Framework for Parallel Numerical Simulations on Multi-Scale Geometries
Varduhn, Vasco
2012-06-01
In this paper, an approach on performing numerical multi-scale simulations on fine detailed geometries is presented. In particular, the focus lies on the generation of sufficient fine mesh representations, whereas a resolution of dozens of millions of voxels is inevitable in order to sufficiently represent the geometry. Furthermore, the propagation of boundary conditions is investigated by using simulation results on the coarser simulation scale as input boundary conditions on the next finer scale. Finally, the applicability of our approach is shown on a two-phase simulation for flooding scenarios in urban structures running from a city wide scale to a fine detailed in-door scale on feature rich building geometries. © 2012 IEEE.
Contribution to study of interfaces instabilities in plane, cylindrical and spherical geometry
Toque, Nathalie
1996-12-01
This thesis proposes several experiments of hydrodynamical instabilities which are studied, numerically and theoretically. The experiments are in plane and cylindrical geometry. Their X-ray radiographies show the evolution of an interface between two solid media crossed by a detonation wave. These materials are initially solid. They become liquide under shock wave or stay between two phases, solid and liquid. The numerical study aims at simulating with the codes EAD and Ouranos, the interfaces instabilities which appear in the experiments. The experimental radiographies and the numerical pictures are in quite good agreement. The theoretical study suggests to modelise a spatio-temporal part of the experiments to obtain the quantitative development of perturbations at the interfaces and in the flows. The models are linear and in plane, cylindrical and spherical geometry. They preceed the inoming study of transition between linear and non linear development of instabilities in multifluids flows crossed by shock waves.
(Self)-representations on youtube
Simonsen, Thomas Mosebo
2011-01-01
This paper examines forms of self-representation on YouTube with specific focus on Vlogs (Video blogs). The analytical scope of the paper is on how User-generated Content on YouTube initiates a certain kind of audiovisual representation and a particular interpretation of reality that can be distinguished within Vlogs. This will be analysed through selected case studies taken from a representative sample of empirically based observations of YouTube videos. The analysis includes a focus on how ...
Concepts, ontologies, and knowledge representation
Jakus, Grega; Omerovic, Sanida; Tomažic, Sašo
2013-01-01
Recording knowledge in a common framework that would make it possible to seamlessly share global knowledge remains an important challenge for researchers. This brief examines several ideas about the representation of knowledge addressing this challenge. A widespread general agreement is followed that states uniform knowledge representation should be achievable by using ontologies populated with concepts. A separate chapter is dedicated to each of the three introduced topics, following a uniform outline: definition, organization, and use. This brief is intended for those who want to get to know
Thinking together with material representations
DEFF Research Database (Denmark)
Stege Bjørndahl, Johanne; Fusaroli, Riccardo; Østergaard, Svend
2014-01-01
of an experiment. Qualitative micro-analyses of the group interactions motivate a taxonomy of different roles that the material representations play in the joint epistemic processes: illustration, elaboration and exploration. Firstly, the LEGO blocks were used to illustrate already well-formed ideas in support......-down and bottom-up cognitive processes and division of cognitive labor.......How do material representations such as models, diagrams and drawings come to shape and aid collective, epistemic processes? This study investigated how groups of participants spontaneously recruited material objects (in this case LEGO blocks) to support collective creative processes in the context...
Movable geometry and eigenvalue search capability in the MC21 Monte Carlo code
International Nuclear Information System (INIS)
Gill, D. F.; Nease, B. R.; Griesheimer, D. P.
2013-01-01
A description of a robust and flexible movable geometry implementation in the Monte Carlo code MC21 is described along with a search algorithm that can be used in conjunction with the movable geometry capability to perform eigenvalue searches based on the position of some geometric component. The natural use of the combined movement and search capability is searching to critical through variation of control rod (or control drum) position. The movable geometry discussion provides the mathematical framework for moving surfaces in the MC21 combinatorial solid geometry description. A discussion of the interface between the movable geometry system and the user is also described, particularly the ability to create a hierarchy of movable groups. Combined with the hierarchical geometry description in MC21 the movable group framework provides a very powerful system for inline geometry modification. The eigenvalue search algorithm implemented in MC21 is also described. The foundations of this algorithm are a regula falsi search though several considerations are made in an effort to increase the efficiency of the algorithm for use with Monte Carlo. Specifically, criteria are developed to determine after each batch whether the Monte Carlo calculation should be continued, the search iteration can be rejected, or the search iteration has converged. These criteria seek to minimize the amount of time spent per iteration. Results for the regula falsi method are shown, illustrating that the method as implemented is indeed convergent and that the optimizations made ultimately reduce the total computational expense. (authors)
Movable geometry and eigenvalue search capability in the MC21 Monte Carlo code
Energy Technology Data Exchange (ETDEWEB)
Gill, D. F.; Nease, B. R.; Griesheimer, D. P. [Bettis Atomic Power Laboratory, PO Box 79, West Mifflin, PA 15122 (United States)
2013-07-01
A description of a robust and flexible movable geometry implementation in the Monte Carlo code MC21 is described along with a search algorithm that can be used in conjunction with the movable geometry capability to perform eigenvalue searches based on the position of some geometric component. The natural use of the combined movement and search capability is searching to critical through variation of control rod (or control drum) position. The movable geometry discussion provides the mathematical framework for moving surfaces in the MC21 combinatorial solid geometry description. A discussion of the interface between the movable geometry system and the user is also described, particularly the ability to create a hierarchy of movable groups. Combined with the hierarchical geometry description in MC21 the movable group framework provides a very powerful system for inline geometry modification. The eigenvalue search algorithm implemented in MC21 is also described. The foundations of this algorithm are a regula falsi search though several considerations are made in an effort to increase the efficiency of the algorithm for use with Monte Carlo. Specifically, criteria are developed to determine after each batch whether the Monte Carlo calculation should be continued, the search iteration can be rejected, or the search iteration has converged. These criteria seek to minimize the amount of time spent per iteration. Results for the regula falsi method are shown, illustrating that the method as implemented is indeed convergent and that the optimizations made ultimately reduce the total computational expense. (authors)
The Koslowski–Sahlmann representation: gauge and diffeomorphism invariance
International Nuclear Information System (INIS)
Campiglia, Miguel; Varadarajan, Madhavan
2014-01-01
The discrete spatial geometry underlying loop quantum gravity (LQG) is degenerate almost everywhere. This is at apparent odds with the non-degeneracy of asymptotically flat metrics near spatial infinity. Koslowski generalized the LQG representation so as to describe states labeled by smooth non-degenerate triad fields. His representation was further studied by Sahlmann with a view to imposing gauge and spatial diffeomorphism invariance through group averaging methods. Motivated by the desire to model asymptotically flat quantum geometry by states with triad labels which are non-degenerate at infinity but not necessarily so in the interior, we initiate a generalization of Sahlmann’s considerations to triads of varying degeneracy. In doing so, we include delicate phase contributions to the averaging procedure which are crucial for the correct implementation of the gauge and diffeomorphism constraints, and whose existence can be traced to the background exponential functions recently constructed by one of us. Our treatment emphasizes the role of symmetries of quantum states in the averaging procedure. Semianalyticity, influential in the proofs of the beautiful uniqueness results for LQG, plays a key role in our considerations. As a by product, we re-derive the group averaging map for standard LQG, highlighting the role of state symmetries and explicitly exhibiting the essential uniqueness of its specification. (paper)
Quantum groups: Geometry and applications
International Nuclear Information System (INIS)
Chu, C.S.
1996-01-01
The main theme of this thesis is a study of the geometry of quantum groups and quantum spaces, with the hope that they will be useful for the construction of quantum field theory with quantum group symmetry. The main tool used is the Faddeev-Reshetikhin-Takhtajan description of quantum groups. A few content-rich examples of quantum complex spaces with quantum group symmetry are treated in details. In chapter 1, the author reviews some of the basic concepts and notions for Hopf algebras and other background materials. In chapter 2, he studies the vector fields of quantum groups. A compact realization of these vector fields as pseudodifferential operators acting on the linear quantum spaces is given. In chapter 3, he describes the quantum sphere as a complex quantum manifold by means of a quantum stereographic projection. A covariant calculus is introduced. An interesting property of this calculus is the existence of a one-form realization of the exterior differential operator. The concept of a braided comodule is introduced and a braided algebra of quantum spheres is constructed. In chapter 4, the author considers the more general higher dimensional quantum complex projective spaces and the quantum Grassman manifolds. Differential calculus, integration and braiding can be introduced as in the one dimensional case. Finally, in chapter 5, he studies the framework of quantum principal bundle and construct the q-deformed Dirac monopole as a quantum principal bundle with a quantum sphere as the base and a U(1) with non-commutative calculus as the fiber. The first Chern class can be introduced and integrated to give the monopole charge
The geometry of elementary particles
International Nuclear Information System (INIS)
Lov, T.R.
1987-01-01
A new model of elementary particles based on the geometry of Quantum deSitter space QdS = SU (3,2)/(SU(3,1) x U(1)) is introduced and studied. QdS is a complexification of quantization of anti-de Sitter space, AdS = SO(3,2)/SO(3,1), which in recent years had played a pivotal role in supergravity. The nontrival principle fiber bundle has total space SU(3,2), fiber SU(3,1) x U(1) and base QdS. In this setting, the standard recipes for Yang-Mills fields don't work. These require connections and the associated covariant derivatives. Here it is shown that the Lie derivatives, not the covariant derivatives are important in quantization. In this setting, the no-go theorems are not valid. This new quantum mechanics leads to a model of elementary particles as vertical vector fields in the bundle with interaction via the Lie bracket. There are five physical interactions modelled by the bracket interaction. The quantum numbers are identified as the roots of su(3,2) and are preserved under the bracket interaction. The model explains conservation of charge, baryon number, lepton number, parity and the heirarchy problem. Since the bracket is the curvature of a homogeneous space, particles are then the curvature of QdS. This model for particles is consistent with the requirements of General Relativity. Furthermore, since the curvature tensor is built from the quantized wave functions, the curvature tensor is quantized and this is quantum theory of gravity