Internal space decimation for lattice gauge theories
International Nuclear Information System (INIS)
Flyvbjerg, H.
1984-01-01
By a systematic decimation of internal space lattice gauge theories with continuous symmetry groups are mapped into effective lattice gauge theories with finite symmetry groups. The decimation of internal space makes a larger lattice tractable with the same computational resources. In this sense the method is an alternative to Wilson's and Symanzik's programs of improved actions. As an illustrative test of the method U(1) is decimated to Z(N) and the results compared with Monte Carlo data for Z(4)- and Z(5)-invariant lattice gauge theories. The result of decimating SU(3) to its 1080-element crystal-group-like subgroup is given and discussed. (orig.)
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
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
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.
Geometry and quantization of moduli spaces
Andersen, Jørgen; Riera, Ignasi
2016-01-01
This volume is based on four advanced courses held at the Centre de Recerca Matemàtica (CRM), Barcelona. It presents both background information and recent developments on selected topics that are experiencing extraordinary growth within the broad research area of geometry and quantization of moduli spaces. The lectures focus on the geometry of moduli spaces which are mostly associated to compact Riemann surfaces, and are presented from both classical and quantum perspectives.
Geometry of Theory Space and RG Flows
Kar, Sayan
The space of couplings of a given theory is the arena of interest in this article. Equipped with a metric ansatz akin to the Fisher information matrix in the space of parameters in statistics (similar metrics in physics are the Zamolodchikov metric or the O'Connor-Stephens metric) we investigate the geometry of theory space through a study of specific examples. We then look into renormalisation group flows in theory space and make an attempt to characterise such flows via its isotropic expansion, rotation and shear. Consequences arising from the evolution equation for the isotropic expansion are discussed. We conclude by pointing out generalisations and pose some open questions.
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.
Statistical geometry and space-time
International Nuclear Information System (INIS)
Grauert, H.
1976-01-01
In this paper I try to construct a mathematical tool by which the full structure of Lorentz geometry to space time can be given, but beyond that the background - to speak pictorially - the subsoil for electromagnetic and matter waves, too. The tool could be useful to describe the connections between various particles, electromagnetism and gravity and to compute observables which were not theoretically related, up to now. Moreover, the tool is simpler than the Riemann tensor: it consists just of a set S of line segments in space time, briefly speaking. (orig.) [de
Geometry and Hamiltonian mechanics on discrete spaces
International Nuclear Information System (INIS)
Talasila, V; Clemente-Gallardo, J; Schaft, A J van der
2004-01-01
Numerical simulation is often crucial for analysing the behaviour of many complex systems which do not admit analytic solutions. To this end, one either converts a 'smooth' model into a discrete (in space and time) model, or models systems directly at a discrete level. The goal of this paper is to provide a discrete analogue of differential geometry, and to define on these discrete models a formal discrete Hamiltonian structure-in doing so we try to bring together various fundamental concepts from numerical analysis, differential geometry, algebraic geometry, simplicial homology and classical Hamiltonian mechanics. For example, the concept of a twisted derivation is borrowed from algebraic geometry for developing a discrete calculus. The theory is applied to a nonlinear pendulum and we compare the dynamics obtained through a discrete modelling approach with the dynamics obtained via the usual discretization procedures. Also an example of an energy-conserving algorithm on a simple harmonic oscillator is presented, and its effect on the Poisson structure is discussed
5 Indicators of Decimal Understandings
Cramer, Kathleen; Monson, Debra; Ahrendt, Sue; Colum, Karen; Wiley, Bethann; Wyberg, Terry
2015-01-01
The authors of this article collaborated with fourth-grade teachers from two schools to support implementation of a research-based fraction and decimal curriculum (Rational Number Project: Fraction Operations and Initial Decimal Ideas). Through this study, they identified five indicators of rich conceptual understanding of decimals, which are…
A Gyrovector Space Approach to Hyperbolic Geometry
Ungar, Abraham
2009-01-01
The mere mention of hyperbolic geometry is enough to strike fear in the heart of the undergraduate mathematics and physics student. Some regard themselves as excluded from the profound insights of hyperbolic geometry so that this enormous portion of human achievement is a closed door to them. The mission of this book is to open that door by making the hyperbolic geometry of Bolyai and Lobachevsky, as well as the special relativity theory of Einstein that it regulates, accessible to a wider audience in terms of novel analogies that the modern and unknown share with the classical and familiar. T
Decimal Classification Editions
Directory of Open Access Journals (Sweden)
Zenovia Niculescu
2009-01-01
Full Text Available The study approaches the evolution of Dewey Decimal Classification editions from the perspective of updating the terminology, reallocating and expanding the main and auxilary structure of Dewey indexing language. The comparative analysis of DDC editions emphasizes the efficiency of Dewey scheme from the point of view of improving the informational offer, through basic index terms, revised and developed, as well as valuing the auxilary notations.
Decimal Classification Editions
Zenovia Niculescu
2009-01-01
The study approaches the evolution of Dewey Decimal Classification editions from the perspective of updating the terminology, reallocating and expanding the main and auxilary structure of Dewey indexing language. The comparative analysis of DDC editions emphasizes the efficiency of Dewey scheme from the point of view of improving the informational offer, through basic index terms, revised and developed, as well as valuing the auxilary notations.
The homogeneous geometries of real hyperbolic space
DEFF Research Database (Denmark)
Castrillón López, Marco; Gadea, Pedro Martínez; Swann, Andrew Francis
We describe the holonomy algebras of all canonical connections of homogeneous structures on real hyperbolic spaces in all dimensions. The structural results obtained then lead to a determination of the types, in the sense of Tricerri and Vanhecke, of the corresponding homogeneous tensors. We use...... our analysis to show that the moduli space of homogeneous structures on real hyperbolic space has two connected components....
Fiber bundle geometry and space-time structure
International Nuclear Information System (INIS)
Nascimento, J.C.
1977-01-01
Within the framework of the geometric formulation of Gauge theories in fiber bundles, the general relation between the bundle connection (Gauge field) and the geometry of the base space is obtained. A possible Gauge theory for gravitation is presented [pt
The algebraic approach to space-time geometry
International Nuclear Information System (INIS)
Heller, M.; Multarzynski, P.; Sasin, W.
1989-01-01
A differential manifold can be defined in terms of smooth real functions carried by it. By rejecting the postulate, in such a definition, demanding the local diffeomorphism of a manifold to the Euclidean space, one obtains the so-called differential space concept. Every subset of R n turns out to be a differential space. Extensive parts of differential geometry on differential spaces, developed by Sikorski, are reviewed and adapted to relativistic purposes. Differential space as a new model of space-time is proposed. The Lorentz structure and Einstein's field equations on differential spaces are discussed. 20 refs. (author)
Nifty Nines and Repeating Decimals
Brown, Scott A.
2016-01-01
The traditional technique for converting repeating decimals to common fractions can be found in nearly every algebra textbook that has been published, as well as in many precalculus texts. However, students generally encounter repeating decimal numerals earlier than high school when they study rational numbers in prealgebra classes. Therefore, how…
Geometry and Hamiltonian mechanics on discrete spaces
Talasila, V.; Clemente-Gallardo, J.; Schaft, A.J. van der
2004-01-01
Numerical simulation is often crucial for analysing the behaviour of many complex systems which do not admit analytic solutions. To this end, one either converts a ‘smooth’ model into a discrete (in space and time) model, or models systems directly at a discrete level. The goal of this paper is to
Geometry and Hamiltonian mechanics on discrete spaces
Talasila, V.; Clemente Gallardo, J.J.; Clemente-Gallardo, J.; van der Schaft, Arjan
2004-01-01
Numerical simulation is often crucial for analysing the behaviour of many complex systems which do not admit analytic solutions. To this end, one either converts a 'smooth' model into a discrete (in space and time) model, or models systems directly at a discrete level. The goal of this paper is to
Special relativity and space-time geometry.
Molski, M.
An attempt has been made to formulate the special theory of relativity in a space-time that is explicitly absolute and strictly determines the kinematical characteristics of a particle in uniform translational motion. The approach developed is consistent with Einstein's relativity and permits explanation of the inertia phenomenon.
Open problems in the geometry and analysis of Banach spaces
Guirao, Antonio J; Zizler, Václav
2016-01-01
This is a collection of some easily-formulated problems that remain open in the study of the geometry and analysis of Banach spaces. Assuming the reader has a working familiarity with the basic results of Banach space theory, the authors focus on concepts of basic linear geometry, convexity, approximation, optimization, differentiability, renormings, weak compact generating, Schauder bases and biorthogonal systems, fixed points, topology and nonlinear geometry. The main purpose of this work is to help convince young researchers in Functional Analysis that the theory of Banach spaces is a fertile field of research, full of interesting open problems. Inside the Banach space area, the text should help expose young researchers to the depth and breadth of the work that remains, and to provide the perspective necessary to choose a direction for further study. Some of the problems presented herein are longstanding open problems, some are recent, some are more important and some are only "local" problems. Some would ...
Momentum-space cigar geometry in topological phases
Palumbo, Giandomenico
2018-01-01
In this paper, we stress the importance of momentum-space geometry in the understanding of two-dimensional topological phases of matter. We focus, for simplicity, on the gapped boundary of three-dimensional topological insulators in class AII, which are described by a massive Dirac Hamiltonian and characterized by an half-integer Chern number. The gap is induced by introducing a magnetic perturbation, such as an external Zeeman field or a ferromagnet on the surface. The quantum Bures metric acquires a central role in our discussion and identifies a cigar geometry. We first derive the Chern number from the cigar geometry and we then show that the quantum metric can be seen as a solution of two-dimensional non-Abelian BF theory in momentum space. The gauge connection for this model is associated to the Maxwell algebra, which takes into account the Lorentz symmetries related to the Dirac theory and the momentum-space magnetic translations connected to the magnetic perturbation. The Witten black-hole metric is a solution of this gauge theory and coincides with the Bures metric. This allows us to calculate the corresponding momentum-space entanglement entropy that surprisingly carries information about the real-space conformal field theory describing the defect lines that can be created on the gapped boundary.
Space-Time Geometry of Quark and Strange Quark Matter
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
We study quark and strange quark matter in the context of general relativity. For this purpose, we solve Einstein's field equations for quark and strange quark matter in spherical symmetric space-times. We analyze strange quark matter for the different equations of state (EOS) in the spherical symmetric space-times, thus we are able to obtain the space-time geometries of quark and strange quark matter. Also, we discuss die features of the obtained solutions. The obtained solutions are consistent with the results of Brookhaven Laboratory, i.e. the quark-gluon plasma has a vanishing shear (i.e. quark-gluon plasma is perfect).
Topology as fluid geometry two-dimensional spaces, volume 2
Cannon, James W
2017-01-01
This is the second of a three volume collection devoted to the geometry, topology, and curvature of 2-dimensional spaces. The collection provides a guided tour through a wide range of topics by one of the twentieth century's masters of geometric topology. The books are accessible to college and graduate students and provide perspective and insight to mathematicians at all levels who are interested in geometry and topology. The second volume deals with the topology of 2-dimensional spaces. The attempts encountered in Volume 1 to understand length and area in the plane lead to examples most easily described by the methods of topology (fluid geometry): finite curves of infinite length, 1-dimensional curves of positive area, space-filling curves (Peano curves), 0-dimensional subsets of the plane through which no straight path can pass (Cantor sets), etc. Volume 2 describes such sets. All of the standard topological results about 2-dimensional spaces are then proved, such as the Fundamental Theorem of Algebra (two...
The geometry of plane waves in spaces of constant curvature
International Nuclear Information System (INIS)
Tran, H.V.
1988-01-01
We examined the geometry of possible plane wave fronts in spaces of constant curvature for three cases in which the cosmological constant is positive, zero, or negative. The cosmological constant and a second-order invariant determined by a congruence of null rays were used in the investigation. We embedded the spaces under investigation in a flat five-dimensional space, and studied the null hyperplanes passing through the origin of the flat five-dimensional space. The embedded spaces are represented by quadrics in the five-dimensional space. The plane wave fronts are represented by the intersection of the quadric with null hyperplanes passing through the origin of the five-dimensional space. We concluded that in Minkowski spaces (zero cosmological constant), the plane-fronted waves will intersect if and only if the second-order invariant mentioned above is non-zero. For deSitter spaces (positive cosmological constant), plane-fronted waves will always intersect. For anti-deSitter spaces (negative cosmological constant), plane-fronted waves may but need not intersect
Neutron guide geometries for homogeneous phase space volume transformation
International Nuclear Information System (INIS)
Stüßer, N.; Bartkowiak, M.; Hofmann, T.
2014-01-01
We extend geometries for recently developed optical guide systems that perform homogeneous phase space volume transformations on neutron beams. These modules allow rotating beam directions and can simultaneously compress or expand the beam cross-section. Guide systems combining these modules offer the possibility to optimize ballistic guides with and without direct view on the source and beam splitters. All systems are designed for monochromatic beams with a given divergence. The case of multispectral beams with wavelength-dependent divergence distributions is addressed as well. - Highlights: • Form invariant volume transformation in phase space. • Geometrical approach. • Ballistic guide, beam splitter, beam bender
Neutron guide geometries for homogeneous phase space volume transformation
Energy Technology Data Exchange (ETDEWEB)
Stüßer, N., E-mail: stuesser@helmholtz-berlin.de; Bartkowiak, M.; Hofmann, T.
2014-06-01
We extend geometries for recently developed optical guide systems that perform homogeneous phase space volume transformations on neutron beams. These modules allow rotating beam directions and can simultaneously compress or expand the beam cross-section. Guide systems combining these modules offer the possibility to optimize ballistic guides with and without direct view on the source and beam splitters. All systems are designed for monochromatic beams with a given divergence. The case of multispectral beams with wavelength-dependent divergence distributions is addressed as well. - Highlights: • Form invariant volume transformation in phase space. • Geometrical approach. • Ballistic guide, beam splitter, beam bender.
Phase space descriptions for simplicial 4D geometries
International Nuclear Information System (INIS)
Dittrich, Bianca; Ryan, James P
2011-01-01
Starting from the canonical phase space for discretized (4D) BF theory, we implement a canonical version of the simplicity constraints and construct phase spaces for simplicial geometries. Our construction allows us to study the connection between different versions of Regge calculus and approaches using connection variables, such as loop quantum gravity. We find that on a fixed triangulation the (gauge invariant) phase space associated with loop quantum gravity is genuinely larger than the one for length and even area Regge calculus. Rather, it corresponds to the phase space of area-angle Regge calculus, as defined in [1] (prior to the imposition of gluing constraints, which ensure the metricity of the triangulation). Finally, we show that for a subclass of triangulations one can construct first-class Hamiltonian and diffeomorphism constraints leading to flat 4D spacetimes.
Conceptual Knowledge of Decimal Arithmetic
Lortie-Forgues, Hugues; Siegler, Robert S.
2017-01-01
In 2 studies (Ns = 55 and 54), the authors examined a basic form of conceptual understanding of rational number arithmetic, the direction of effect of decimal arithmetic operations, at a level of detail useful for informing instruction. Middle school students were presented tasks examining knowledge of the direction of effects (e.g., "True or…
Dewey Decimal Classification: A Quagmire.
Gamaluddin, Ahmad Fouad
1980-01-01
A survey of 660 Pennsylvania school librarians indicates that, though there is limited professional interest in the Library of Congress Classification system, Dewey Decimal Classification (DDC) appears to be firmly entrenched. This article also discusses the relative merits of DDC, the need for a uniform system, librarianship preparation, and…
Geometry of quantum dynamics in infinite-dimensional Hilbert space
Grabowski, Janusz; Kuś, Marek; Marmo, Giuseppe; Shulman, Tatiana
2018-04-01
We develop a geometric approach to quantum mechanics based on the concept of the Tulczyjew triple. Our approach is genuinely infinite-dimensional, i.e. we do not restrict considerations to finite-dimensional Hilbert spaces, contrary to many other works on the geometry of quantum mechanics, and include a Lagrangian formalism in which self-adjoint (Schrödinger) operators are obtained as Lagrangian submanifolds associated with the Lagrangian. As a byproduct we also obtain results concerning coadjoint orbits of the unitary group in infinite dimensions, embedding of pure states in the unitary group, and self-adjoint extensions of symmetric relations.
Fuzzy Geometry of Commutative Spaces and Quantum Dynamics
International Nuclear Information System (INIS)
Mayburov, S.N.
2016-01-01
Fuzzy topology and geometry considered as the possible mathematical framework for novel quantum-mechanical formalism. In such formalism the states of massive particle m correspond to the elements of fuzzy manifold called fuzzy points. Due to the manifold weak topology, m space coordinate x acquires principal uncertainty σ_x and described by the positive, normalized density w(r-vector , t) in 3-dimensional case. It’s shown that the evolution of m state on such 3-dimensional manifold corresponds to Shroedinger dynamics of massive quantum particle
Geometry and Gâteaux smoothness in separable Banach spaces
Czech Academy of Sciences Publication Activity Database
Hájek, Petr Pavel; Montesinos, V.; Zizler, Václav
2012-01-01
Roč. 6, č. 2 (2012), s. 201-232 ISSN 1846-3886 R&D Projects: GA ČR(CZ) GAP201/11/0345; GA AV ČR IAA100190901 Institutional research plan: CEZ:AV0Z10190503 Keywords : Gâteaux differentiable norms * extreme points * Radon -Nikodým property Subject RIV: BA - General Mathematics Impact factor: 0.529, year: 2012 http://oam.ele-math.com/06-15/Geometry-and-Gateaux-smoothness-in-separable-Banach-spaces
Founding Gravitation in 4D Euclidean Space-Time Geometry
International Nuclear Information System (INIS)
Winkler, Franz-Guenter
2010-01-01
The Euclidean interpretation of special relativity which has been suggested by the author is a formulation of special relativity in ordinary 4D Euclidean space-time geometry. The natural and geometrically intuitive generalization of this view involves variations of the speed of light (depending on location and direction) and a Euclidean principle of general covariance. In this article, a gravitation model by Jan Broekaert, which implements a view of relativity theory in the spirit of Lorentz and Poincare, is reconstructed and shown to fulfill the principles of the Euclidean approach after an appropriate reinterpretation.
Orienteering in knowledge spaces: the hyperbolic geometry of Wikipedia Mathematics.
Directory of Open Access Journals (Sweden)
Gregory Leibon
Full Text Available In this paper we show how the coupling of the notion of a network with directions with the adaptation of the four-point probe from materials testing gives rise to a natural geometry on such networks. This four-point probe geometry shares many of the properties of hyperbolic geometry wherein the network directions take the place of the sphere at infinity, enabling a navigation of the network in terms of pairs of directions: the geodesic through a pair of points is oriented from one direction to another direction, the pair of which are uniquely determined. We illustrate this in the interesting example of the pages of Wikipedia devoted to Mathematics, or "The MathWiki." The applicability of these ideas extends beyond Wikipedia to provide a natural framework for visual search and to prescribe a natural mode of navigation for any kind of "knowledge space" in which higher order concepts aggregate various instances of information. Other examples would include genre or author organization of cultural objects such as books, movies, documents or even merchandise in an online store.
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...
Geometry of the Gene Expression Space of Individual Cells.
Directory of Open Access Journals (Sweden)
Yael Korem
2015-07-01
Full Text Available There is a revolution in the ability to analyze gene expression of single cells in a tissue. To understand this data we must comprehend how cells are distributed in a high-dimensional gene expression space. One open question is whether cell types form discrete clusters or whether gene expression forms a continuum of states. If such a continuum exists, what is its geometry? Recent theory on evolutionary trade-offs suggests that cells that need to perform multiple tasks are arranged in a polygon or polyhedron (line, triangle, tetrahedron and so on, generally called polytopes in gene expression space, whose vertices are the expression profiles optimal for each task. Here, we analyze single-cell data from human and mouse tissues profiled using a variety of single-cell technologies. We fit the data to shapes with different numbers of vertices, compute their statistical significance, and infer their tasks. We find cases in which single cells fill out a continuum of expression states within a polyhedron. This occurs in intestinal progenitor cells, which fill out a tetrahedron in gene expression space. The four vertices of this tetrahedron are each enriched with genes for a specific task related to stemness and early differentiation. A polyhedral continuum of states is also found in spleen dendritic cells, known to perform multiple immune tasks: cells fill out a tetrahedron whose vertices correspond to key tasks related to maturation, pathogen sensing and communication with lymphocytes. A mixture of continuum-like distributions and discrete clusters is found in other cell types, including bone marrow and differentiated intestinal crypt cells. This approach can be used to understand the geometry and biological tasks of a wide range of single-cell datasets. The present results suggest that the concept of cell type may be expanded. In addition to discreet clusters in gene-expression space, we suggest a new possibility: a continuum of states within a
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
Indian Academy of Sciences (India)
. In the previous article we looked at the origins of synthetic and analytic geometry. More practical minded people, the builders and navigators, were studying two other aspects of geometry- trigonometry and integral calculus. These are actually ...
Prasolov, V V
2015-01-01
This book provides a systematic introduction to various geometries, including Euclidean, affine, projective, spherical, and hyperbolic geometries. Also included is a chapter on infinite-dimensional generalizations of Euclidean and affine geometries. A uniform approach to different geometries, based on Klein's Erlangen Program is suggested, and similarities of various phenomena in all geometries are traced. An important notion of duality of geometric objects is highlighted throughout the book. The authors also include a detailed presentation of the theory of conics and quadrics, including the theory of conics for non-Euclidean geometries. The book contains many beautiful geometric facts and has plenty of problems, most of them with solutions, which nicely supplement the main text. With more than 150 figures illustrating the arguments, the book can be recommended as a textbook for undergraduate and graduate-level courses in geometry.
Optimized reversible binary-coded decimal adders
DEFF Research Database (Denmark)
Thomsen, Michael Kirkedal; Glück, Robert
2008-01-01
Abstract Babu and Chowdhury [H.M.H. Babu, A.R. Chowdhury, Design of a compact reversible binary coded decimal adder circuit, Journal of Systems Architecture 52 (5) (2006) 272-282] recently proposed, in this journal, a reversible adder for binary-coded decimals. This paper corrects and optimizes...... their design. The optimized 1-decimal BCD full-adder, a 13 × 13 reversible logic circuit, is faster, and has lower circuit cost and less garbage bits. It can be used to build a fast reversible m-decimal BCD full-adder that has a delay of only m + 17 low-power reversible CMOS gates. For a 32-decimal (128-bit....... Keywords: Reversible logic circuit; Full-adder; Half-adder; Parallel adder; Binary-coded decimal; Application of reversible logic synthesis...
Quantum Riemannian geometry of phase space and nonassociativity
Directory of Open Access Journals (Sweden)
Beggs Edwin J.
2017-04-01
Full Text Available Noncommutative or ‘quantum’ differential geometry has emerged in recent years as a process for quantizing not only a classical space into a noncommutative algebra (as familiar in quantum mechanics but also differential forms, bundles and Riemannian structures at this level. The data for the algebra quantisation is a classical Poisson bracket while the data for quantum differential forms is a Poisson-compatible connection. We give an introduction to our recent result whereby further classical data such as classical bundles, metrics etc. all become quantised in a canonical ‘functorial’ way at least to 1st order in deformation theory. The theory imposes compatibility conditions between the classical Riemannian and Poisson structures as well as new physics such as typical nonassociativity of the differential structure at 2nd order. We develop in detail the case of ℂℙn where the commutation relations have the canonical form [wi, w̄j] = iλδij similar to the proposal of Penrose for quantum twistor space. Our work provides a canonical but ultimately nonassociative differential calculus on this algebra and quantises the metric and Levi-Civita connection at lowest order in λ.
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
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
INEXTENSIBLE FLOWS OF CURVES IN THE EQUIFORM GEOMETRY OF THE PSEUDO-GALILEAN SPACE G13
Directory of Open Access Journals (Sweden)
HANDAN OZTEKIN
2016-12-01
Full Text Available In this paper, we study inextensible ows of curves in 3-dimensional pseudo- Galilean space. We give necessary and sucient conditions for inextensible ows of curves according to equiform geometry in pseudo-Galilean space.
Space, Geometry and the Imagination from Antiquity to the Early Modern Age
Mathematizing Space : The Objects of Geometry from Antiquity to the Early Modern Age
2015-01-01
This book brings together papers of the conference on 'Space, Geometry and the Imagination from Antiquity to the Modern Age' held in Berlin, Germany, 27-29 August 2012. Focusing on the interconnections between the history of geometry and the philosophy of space in the pre-Modern and Early Modern Age, the essays in this volume are particularly directed toward elucidating the complex epistemological revolution that transformed the classical geometry of figures into the modern geometry of space. Contributors: Graciela De Pierris Franco Farinelli Michael Friedman Daniel Garber Jeremy Gray Gary Hatfield Andrew Janiak Douglas Jesseph Alexander Jones Henry Mendell David Rabouin
FPGA Based Acceleration of Decimal Operations
DEFF Research Database (Denmark)
Nannarelli, Alberto
2011-01-01
Field Programmable Gate-Arrays (FPGAs) can efficiently implement application specific processors in nonconventional number systems, such as the decimal (Binary- Coded Decimal, or BCD) number system required for accounting accuracy in financial applications. The main purpose of this work is to show...... an advanced input/output interface, can achieve a speed-up of about 10 over its execution on the CPU of the hosting computer....
Orienteering in Knowledge Spaces: The Hyperbolic Geometry of Wikipedia Mathematics
Leibon, Gregory; Rockmore, Daniel N.
2013-01-01
In this paper we show how the coupling of the notion of a network with directions with the adaptation of the four-point probe from materials testing gives rise to a natural geometry on such networks. This four-point probe geometry shares many of the properties of hyperbolic geometry wherein the network directions take the place of the sphere at infinity, enabling a navigation of the network in terms of pairs of directions: the geodesic through a pair of points is oriented from one direction to another direction, the pair of which are uniquely determined. We illustrate this in the interesting example of the pages of Wikipedia devoted to Mathematics, or “The MathWiki.” The applicability of these ideas extends beyond Wikipedia to provide a natural framework for visual search and to prescribe a natural mode of navigation for any kind of “knowledge space” in which higher order concepts aggregate various instances of information. Other examples would include genre or author organization of cultural objects such as books, movies, documents or even merchandise in an online store. PMID:23844017
Geometry in a dynamical system without space: Hyperbolic Geometry in Kuramoto Oscillator Systems
Engelbrecht, Jan; Chen, Bolun; Mirollo, Renato
Kuramoto oscillator networks have the special property that their time evolution is constrained to lie on 3D orbits of the Möbius group acting on the N-fold torus TN which explains the N - 3 constants of motion discovered by Watanabe and Strogatz. The dynamics for phase models can be further reduced to 2D invariant sets in T N - 1 which have a natural geometry equivalent to the unit disk Δ with hyperbolic metric. We show that the classic Kuramoto model with order parameter Z1 (the first moment of the oscillator configuration) is a gradient flow in this metric with a unique fixed point on each generic 2D invariant set, corresponding to the hyperbolic barycenter of an oscillator configuration. This gradient property makes the dynamics especially easy to analyze. We exhibit several new families of Kuramoto oscillator models which reduce to gradient flows in this metric; some of these have a richer fixed point structure including non-hyperbolic fixed points associated with fixed point bifurcations. Work Supported by NSF DMS 1413020.
Non-commutative geometry on quantum phase-space
International Nuclear Information System (INIS)
Reuter, M.
1995-06-01
A non-commutative analogue of the classical differential forms is constructed on the phase-space of an arbitrary quantum system. The non-commutative forms are universal and are related to the quantum mechanical dynamics in the same way as the classical forms are related to classical dynamics. They are constructed by applying the Weyl-Wigner symbol map to the differential envelope of the linear operators on the quantum mechanical Hilbert space. This leads to a representation of the non-commutative forms considered by A. Connes in terms of multiscalar functions on the classical phase-space. In an appropriate coincidence limit they define a quantum deformation of the classical tensor fields and both commutative and non-commutative forms can be studied in a unified framework. We interprete the quantum differential forms in physical terms and comment on possible applications. (orig.)
Quantum Hamiltonian differential geometry: how does quantization affect space?
International Nuclear Information System (INIS)
Aldrovandi, R.
1993-01-01
Quantum phase space is given a description which entirely parallels the usual presentation of Classical Phase Space. A particular Schwinger unitary operator basis, in which the expansion of each operator is its own Weyl expression, is specially convenient for the purpose. The quantum Hamiltonian structure obtains from the classical structure by the conversion of the classical pointwise product of dynamical quantities into the noncommutative star product of Wigner functions. The main qualitative difference in the general structure is that, in the quantum case, the inverse symplectic matrix is not simply antisymmetric. This difference leads to the presence of braiding in the backstage of Quantum Mechanics. (author)
Spinor Field Nonlinearity and Space-Time Geometry
Saha, Bijan
2018-03-01
Within the scope of Bianchi type VI,VI0,V, III, I, LRSBI and FRW cosmological models we have studied the role of nonlinear spinor field on the evolution of the Universe and the spinor field itself. It was found that due to the presence of non-trivial non-diagonal components of the energy-momentum tensor of the spinor field in the anisotropic space-time, there occur some severe restrictions both on the metric functions and on the components of the spinor field. In this report we have considered a polynomial nonlinearity which is a function of invariants constructed from the bilinear spinor forms. It is found that in case of a Bianchi type-VI space-time, depending of the sign of self-coupling constants, the model allows either late time acceleration or oscillatory mode of evolution. In case of a Bianchi VI 0 type space-time due to the specific behavior of the spinor field we have two different scenarios. In one case the invariants constructed from bilinear spinor forms become trivial, thus giving rise to a massless and linear spinor field Lagrangian. This case is equivalent to the vacuum solution of the Bianchi VI 0 type space-time. The second case allows non-vanishing massive and nonlinear terms and depending on the sign of coupling constants gives rise to accelerating mode of expansion or the one that after obtaining some maximum value contracts and ends in big crunch, consequently generating space-time singularity. In case of a Bianchi type-V model there occur two possibilities. In one case we found that the metric functions are similar to each other. In this case the Universe expands with acceleration if the self-coupling constant is taken to be a positive one, whereas a negative coupling constant gives rise to a cyclic or periodic solution. In the second case the spinor mass and the spinor field nonlinearity vanish and the Universe expands linearly in time. In case of a Bianchi type-III model the space-time remains locally rotationally symmetric all the time
The geometry of the Pareto front in biological phenotype space
Sheftel, Hila; Shoval, Oren; Mayo, Avi; Alon, Uri
2013-01-01
When organisms perform a single task, selection leads to phenotypes that maximize performance at that task. When organisms need to perform multiple tasks, a trade-off arises because no phenotype can optimize all tasks. Recent work addressed this question, and assumed that the performance at each task decays with distance in trait space from the best phenotype at that task. Under this assumption, the best-fitness solutions (termed the Pareto front) lie on simple low-dimensional shapes in trait space: line segments, triangles and other polygons. The vertices of these polygons are specialists at a single task. Here, we generalize this finding, by considering performance functions of general form, not necessarily functions that decay monotonically with distance from their peak. We find that, except for performance functions with highly eccentric contours, simple shapes in phenotype space are still found, but with mildly curving edges instead of straight ones. In a wide range of systems, complex data on multiple quantitative traits, which might be expected to fill a high-dimensional phenotype space, is predicted instead to collapse onto low-dimensional shapes; phenotypes near the vertices of these shapes are predicted to be specialists, and can thus suggest which tasks may be at play. PMID:23789060
International Nuclear Information System (INIS)
Sitaramayya, M.
1993-11-01
After a brief review of the geometry of Moishezon spaces, their relation with l-convex spaces and a reasonable and up to date understanding of the obstructions for projectivity of Moishezon objects both in singular and non-singular case is given. The geometry of l-convex manifolds and with l-dimensional exceptional set is studied and some problems and conjectures are stated. The tools of cohomology vanishing theorems important for the subject are briefly sketched. Compactifications of C 3 and Stein spaces are finally outlined. given. 111 refs, 2 figs
Quantum-deformed geometry on phase-space
International Nuclear Information System (INIS)
Gozzi, E.; Reuter, M.
1992-12-01
In this paper we extend the standard Moyal formalism to the tangent and cotangent bundle of the phase-space of any hamiltonian mechanical system. In this manner we build the quantum analog of the classical hamiltonian vector-field of time evolution and its associated Lie-derivative. We also use this extended Moyal formalism to develop a quantum analog of the Cartan calculus on symplectic manifolds. (orig.)
The Influence of Hierarchy and Layout Geometry in the Design of Learning Spaces
Smith, Charlie
2017-01-01
For a number of years, higher education has moved away from didactic teaching toward collaborative and self-directed learning. This paper discusses how the configuration and spatial geometry of learning spaces influences engagement and interaction, with a particular focus on hierarchies between people within the space. Layouts, presented as…
An introduction to Lie groups and the geometry of homogeneous spaces
Arvanitoyeorgos, Andreas
2003-01-01
It is remarkable that so much about Lie groups could be packed into this small book. But after reading it, students will be well-prepared to continue with more advanced, graduate-level topics in differential geometry or the theory of Lie groups. The theory of Lie groups involves many areas of mathematics. In this book, Arvanitoyeorgos outlines enough of the prerequisites to get the reader started. He then chooses a path through this rich and diverse theory that aims for an understanding of the geometry of Lie groups and homogeneous spaces. In this way, he avoids the extra detail needed for a thorough discussion of other topics. Lie groups and homogeneous spaces are especially useful to study in geometry, as they provide excellent examples where quantities (such as curvature) are easier to compute. A good understanding of them provides lasting intuition, especially in differential geometry. The book is suitable for advanced undergraduates, graduate students, and research mathematicians interested in differenti...
Primary teachers' subject matter knowledge: decimals
Ubuz, Behiye; Yayan, Betül
2010-09-01
The main objective of this study was to investigate primary teachers' subject matter knowledge in the domain of decimals and more elaborately to investigate their performance and difficulties in reading scale, ordering numbers, finding the nearest decimal and doing operations, such as addition and subtraction. The difficulties in these particular areas are analysed and suggestions are made regarding their causes. Further, factors that influence this knowledge were explored. The sample of the study was 63 primary teachers. A decimal concepts test including 18 tasks was administered and the total scores for the 63 primary teachers ranged from 3 to 18 with a mean and median of 12. Fifty per cent of the teachers were above the mean score. The detailed investigation of the responses revealed that the primary teachers faced similar difficulties that students and pre-service teachers faced. Discrepancy on teachers' knowledge revealed important differences based on educational level attained, but not the number of years of teaching experience and experience in teaching decimals. Some suggestions have been made regarding the implications for pre- and in-service teacher training.
Real numbers as infinite decimals and irrationality of $\\sqrt{2}$
Klazar, Martin
2009-01-01
In order to prove irrationality of \\sqrt{2} by using only decimal expansions (and not fractions), we develop in detail a model of real numbers based on infinite decimals and arithmetic operations with them.
State-Space Geometry, Statistical Fluctuations, and Black Holes in String Theory
Directory of Open Access Journals (Sweden)
Stefano Bellucci
2014-01-01
Full Text Available We study the state-space geometry of various extremal and nonextremal black holes in string theory. From the notion of the intrinsic geometry, we offer a state-space perspective to the black hole vacuum fluctuations. For a given black hole entropy, we explicate the intrinsic geometric meaning of the statistical fluctuations, local and global stability conditions, and long range statistical correlations. We provide a set of physical motivations pertaining to the extremal and nonextremal black holes, namely, the meaning of the chemical geometry and physics of correlation. We illustrate the state-space configurations for general charge extremal black holes. In sequel, we extend our analysis for various possible charge and anticharge nonextremal black holes. From the perspective of statistical fluctuation theory, we offer general remarks, future directions, and open issues towards the intrinsic geometric understanding of the vacuum fluctuations and black holes in string theory.
Non-Euclidean geometry and curvature two-dimensional spaces, volume 3
Cannon, James W
2017-01-01
This is the final volume of a three volume collection devoted to the geometry, topology, and curvature of 2-dimensional spaces. The collection provides a guided tour through a wide range of topics by one of the twentieth century's masters of geometric topology. The books are accessible to college and graduate students and provide perspective and insight to mathematicians at all levels who are interested in geometry and topology. Einstein showed how to interpret gravity as the dynamic response to the curvature of space-time. Bill Thurston showed us that non-Euclidean geometries and curvature are essential to the understanding of low-dimensional spaces. This third and final volume aims to give the reader a firm intuitive understanding of these concepts in dimension 2. The volume first demonstrates a number of the most important properties of non-Euclidean geometry by means of simple infinite graphs that approximate that geometry. This is followed by a long chapter taken from lectures the author gave at MSRI, wh...
Children, algorithm and the decimal numeral system
Directory of Open Access Journals (Sweden)
Clélia Maria Ignatius Nogueira
2010-08-01
Full Text Available A large number of studies in Mathematics Education approach some possible problems in the study of algorithms in the early school years of arithmetic teaching. However, this discussion is not exhausted. In this feature, this article presents the results of a research which proposed to investigate if the arithmetic’s teaching, with emphasis in the fundamental operation’s algorithm, cooperate to build the mathematics knowledge, specifically of the Decimal Numeral System. In order to achieve this purpose, we interviewed, using the Piaget Critique Clinical Method, twenty students from a public school. The result’s analysis indicates that they mechanically reproduce the regular algorithm’s techniques without notice the relations between the techniques and the principle and the Decimal Numeral System’s properties.
Correlation-based decimation in constraint satisfaction problems
International Nuclear Information System (INIS)
Higuchi, Saburo; Mezard, Marc
2010-01-01
We study hard constraint satisfaction problems using some decimation algorithms based on mean-field approximations. The message-passing approach is used to estimate, beside the usual one-variable marginals, the pair correlation functions. The identification of strongly correlated pairs allows to use a new decimation procedure, where the relative orientation of a pair of variables is fixed. We apply this novel decimation to locked occupation problems, a class of hard constraint satisfaction problems where the usual belief-propagation guided decimation performs poorly. The pair-decimation approach provides a significant improvement.
Two-stage nonrecursive filter/decimator
International Nuclear Information System (INIS)
Yoder, J.R.; Richard, B.D.
1980-08-01
A two-stage digital filter/decimator has been designed and implemented to reduce the sampling rate associated with the long-term computer storage of certain digital waveforms. This report describes the design selection and implementation process and serves as documentation for the system actually installed. A filter design with finite-impulse response (nonrecursive) was chosen for implementation via direct convolution. A newly-developed system-test statistic validates the system under different computer-operating environments
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.
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)
The geometry of higher-order Lagrange spaces applications to mechanics and physics
Miron, Radu
1997-01-01
This monograph is devoted to the problem of the geometrizing of Lagrangians which depend on higher-order accelerations It presents a construction of the geometry of the total space of the bundle of the accelerations of order k>=1 A geometrical study of the notion of the higher-order Lagrange space is conducted, and the old problem of prolongation of Riemannian spaces to k-osculator manifolds is solved Also, the geometrical ground for variational calculus on the integral of actions involving higher-order Lagrangians is dealt with Applications to higher-order analytical mechanics and theoretical physics are included as well Audience This volume will be of interest to scientists whose work involves differential geometry, mechanics of particles and systems, calculus of variation and optimal control, optimization, optics, electromagnetic theory, and biology
The identification of van Hiele level students on the topic of space analytic geometry
Yudianto, E.; Sunardi; Sugiarti, T.; Susanto; Suharto; Trapsilasiwi, D.
2018-03-01
Geometry topics are still considered difficult by most students. Therefore, this study focused on the identification of students related to van Hiele levels. The task used from result of the development of questions related to analytical geometry of space. The results of the work involving 78 students who worked on these questions covered 11.54% (nine students) classified on a visual level; 5.13% (four students) on analysis level; 1.28% (one student) on informal deduction level; 2.56% (two students) on deduction and 2.56% (two students) on rigor level, and 76.93% (sixty students) classified on the pre-visualization level.
van den Broek, P.M.
1984-01-01
The aim of this paper is to give a detailed exposition of the relation between the geometry of twistor space and the geometry of Minkowski space. The paper has a didactical purpose; no use has been made of differential geometry and cohomology.
Geometry of lengths, areas, and volumes two-dimensional spaces, volume 1
Cannon, James W
2017-01-01
This is the first of a three volume collection devoted to the geometry, topology, and curvature of 2-dimensional spaces. The collection provides a guided tour through a wide range of topics by one of the twentieth century's masters of geometric topology. The books are accessible to college and graduate students and provide perspective and insight to mathematicians at all levels who are interested in geometry and topology. The first volume begins with length measurement as dominated by the Pythagorean Theorem (three proofs) with application to number theory; areas measured by slicing and scaling, where Archimedes uses the physical weights and balances to calculate spherical volume and is led to the invention of calculus; areas by cut and paste, leading to the Bolyai-Gerwien theorem on squaring polygons; areas by counting, leading to the theory of continued fractions, the efficient rational approximation of real numbers, and Minkowski's theorem on convex bodies; straight-edge and compass constructions, giving c...
Exirifard, Qasem
2013-01-01
We present a phenomenological model for the nature in the Finsler and Randers space-time geometries. We show that the parity-odd light speed anisotropy perpendicular to the gravitational equipotential surfaces encodes the deviation from the Riemann geometry toward the Randers geometry. We utilize an asymmetrical ring resonator and propose a setup in order to directly measure this deviation. We address the constraints that the current technology will impose on the deviation should the anisotro...
A look towards the future in the handling of space science mission geometry
Acton, Charles; Bachman, Nathaniel; Semenov, Boris; Wright, Edward
2018-01-01
The "SPICE" system has been widely used since the days of the Magellan mission to Venus as the method for scientists and engineers to access a variety of space mission geometry such as positions, velocities, directions, orientations, sizes and shapes, and field-of-view projections (Acton, 1996). While originally focused on supporting NASA's planetary missions, the use of SPICE has slowly grown to include most worldwide planetary missions, and it has also been finding application in heliophysics and other space science disciplines. This paper peeks under the covers to see what new capabilities are being developed or planned at SPICE headquarters to better support the future of space science. The SPICE system is implemented and maintained by NASA's Navigation and Ancillary Information Facility (NAIF) located at the Jet Propulsion Laboratory in Pasadena, California (http://naif.jpl.nasa.gov).
Geometry and dynamics in Gromov hyperbolic metric spaces with an emphasis on non-proper settings
Das, Tushar; Urbański, Mariusz
2016-01-01
This book presents the foundations of the theory of groups and semigroups acting isometrically on Gromov hyperbolic metric spaces. Particular emphasis is paid to the geometry of their limit sets and on behavior not found in the proper setting. The authors provide a number of examples of groups which exhibit a wide range of phenomena not to be found in the finite-dimensional theory. The book contains both introductory material to help beginners as well as new research results, and closes with a list of attractive unsolved problems.
Local differential geometry of null curves in conformally flat space-time
International Nuclear Information System (INIS)
Urbantke, H.
1989-01-01
The conformally invariant differential geometry of null curves in conformally flat space-times is given, using the six-vector formalism which has generalizations to higher dimensions. This is then paralleled by a twistor description, with a twofold merit: firstly, sometimes the description is easier in twistor terms, sometimes in six-vector terms, which leads to a mutual enlightenment of both; and secondly, the case of null curves in timelike pseudospheres or 2+1 Minkowski space we were only able to treat twistorially, making use of an invariant differential found by Fubini and Cech. The result is the expected one: apart from stated exceptional cases there is a conformally invariant parameter and two conformally invariant curvatures which, when specified in terms of this parameter, serve to characterize the curve up to conformal transformations. 12 refs. (Author)
Three dimensional range geometry and texture data compression with space-filling curves.
Chen, Xia; Zhang, Song
2017-10-16
This paper presents a novel method to effectively store three-dimensional (3D) data and 2D texture data into a regular 24-bit image. The proposed method uses the Hilbert space-filling curve to map the normalized unwrapped phase map to two 8-bit color channels, and saves the third color channel for 2D texture storage. By further leveraging existing 2D image and video compression techniques, the proposed method can achieve high compression ratios while effectively preserving data quality. Since the encoding and decoding processes can be applied to most of the current 2D media platforms, this proposed compression method can make 3D data storage and transmission available for many electrical devices without requiring special hardware changes. Experiments demonstrate that if a lossless 2D image/video format is used, both original 3D geometry and 2D color texture can be accurately recovered; if lossy image/video compression is used, only black-and-white or grayscale texture can be properly recovered, but much higher compression ratios (e.g., 1543:1 against the ASCII OBJ format) are achieved with slight loss of 3D geometry quality.
Algebrodynamics over complex space and phase extension of the Minkowski geometry
International Nuclear Information System (INIS)
Kassandrov, V. V.
2009-01-01
First principles should predetermine physical geometry and dynamics both together. In the 'algebrodynamics' they follow solely from the properties of biquaternion algebra B and the analysis over B. We briefly present the algebrodynamics over Minkowski background based on a nonlinear generalization to B of the Cauchi-Riemann analyticity conditions. Further, we consider the effective real geometry uniquely resulting from the structure of B multiplication and found it to be of the Minkowski type, with an additional phase invariant. Then we pass to study the primordial dynamics that takes place in the complex B space and brings into consideration a number of remarkable structures: an ensemble of identical correlated matter pre-elements ('duplicons'), caustic-like signals (interaction carriers), a concept of random complex time resulting in irreversibility of physical time at macrolevel, etc. In partucular, the concept of 'dimerous electron' naturally arises in the framework of complex algebrodynamics and, together with the above-mentioned phase invariant, allows for a novel approach to explanation of quantum interference phenomena alternative to recently accepted wave-particle dualism paradigm.
Space-charge-limited currents for cathodes with electric field enhanced geometry
Energy Technology Data Exchange (ETDEWEB)
Lai, Dingguo, E-mail: laidingguo@nint.ac.cn; Qiu, Mengtong; Xu, Qifu [State Key Laboratory of Intense Pulsed Radiation Simulation and Effect, Northwest Institute of Nuclear Technology, Xi' an 701124 (China); Huang, Zhongliang [Department of Engineering Physics, Tsinghua University, Beijing 100084 (China)
2016-08-15
This paper presents the approximate analytic solutions of current density for annulus and circle cathodes. The current densities of annulus and circle cathodes are derived approximately from first principles, which are in agreement with simulation results. The large scaling laws can predict current densities of high current vacuum diodes including annulus and circle cathodes in practical applications. In order to discuss the relationship between current density and electric field on cathode surface, the existing analytical solutions of currents for concentric cylinder and sphere diodes are fitted from existing solutions relating with electric field enhancement factors. It is found that the space-charge-limited current density for the cathode with electric-field enhanced geometry can be written in a general form of J = g(β{sub E}){sup 2}J{sub 0}, where J{sub 0} is the classical (1D) Child-Langmuir current density, β{sub E} is the electric field enhancement factor, and g is the geometrical correction factor depending on the cathode geometry.
Characteristics of eye-position gain field populations determine geometry of visual space
Directory of Open Access Journals (Sweden)
Sidney R Lehky
2016-01-01
Full Text Available We have previously demonstrated differences in eye-position spatial maps for anterior inferotemporal cortex (AIT in the ventral stream and lateral intraparietal cortex (LIP in the dorsal stream, based on population decoding of gaze angle modulations of neural visual responses (i.e., eye-position gain fields. Here we explore the basis of such spatial encoding differences through modeling of gain field characteristics. We created a population of model neurons, each having a different eye-position gain field. This population was used to reconstruct eye-position visual space using multidimensional scaling. As gain field shapes have never been well established experimentally, we examined different functions, including planar, sigmoidal, elliptical, hyperbolic, and mixtures of those functions. All functions successfully recovered positions, indicating weak constraints on allowable gain field shapes. We then used a genetic algorithm to modify the characteristics of model gain field populations until the recovered spatial maps closely matched those derived from monkey neurophysiological data in AIT and LIP. The primary differences found between model AIT and LIP gain fields were that AIT gain fields were more foveally dominated. That is, gain fields in AIT operated on smaller spatial scales and smaller dispersions than in LIP. Thus we show that the geometry of eye-position visual space depends on the population characteristics of gain fields, and that differences in gain field characteristics for different cortical areas may underlie differences in the representation of space.
Digital atom interferometer with single particle control on a discretized space-time geometry.
Steffen, Andreas; Alberti, Andrea; Alt, Wolfgang; Belmechri, Noomen; Hild, Sebastian; Karski, Michał; Widera, Artur; Meschede, Dieter
2012-06-19
Engineering quantum particle systems, such as quantum simulators and quantum cellular automata, relies on full coherent control of quantum paths at the single particle level. Here we present an atom interferometer operating with single trapped atoms, where single particle wave packets are controlled through spin-dependent potentials. The interferometer is constructed from a sequence of discrete operations based on a set of elementary building blocks, which permit composing arbitrary interferometer geometries in a digital manner. We use this modularity to devise a space-time analogue of the well-known spin echo technique, yielding insight into decoherence mechanisms. We also demonstrate mesoscopic delocalization of single atoms with a separation-to-localization ratio exceeding 500; this result suggests their utilization beyond quantum logic applications as nano-resolution quantum probes in precision measurements, being able to measure potential gradients with precision 5 x 10(-4) in units of gravitational acceleration g.
The Mass-Longevity Triangle: Pareto Optimality and the Geometry of Life-History Trait Space
Szekely, Pablo; Korem, Yael; Moran, Uri; Mayo, Avi; Alon, Uri
2015-01-01
When organisms need to perform multiple tasks they face a fundamental tradeoff: no phenotype can be optimal at all tasks. This situation was recently analyzed using Pareto optimality, showing that tradeoffs between tasks lead to phenotypes distributed on low dimensional polygons in trait space. The vertices of these polygons are archetypes—phenotypes optimal at a single task. This theory was applied to examples from animal morphology and gene expression. Here we ask whether Pareto optimality theory can apply to life history traits, which include longevity, fecundity and mass. To comprehensively explore the geometry of life history trait space, we analyze a dataset of life history traits of 2105 endothermic species. We find that, to a first approximation, life history traits fall on a triangle in log-mass log-longevity space. The vertices of the triangle suggest three archetypal strategies, exemplified by bats, shrews and whales, with specialists near the vertices and generalists in the middle of the triangle. To a second approximation, the data lies in a tetrahedron, whose extra vertex above the mass-longevity triangle suggests a fourth strategy related to carnivory. Each animal species can thus be placed in a coordinate system according to its distance from the archetypes, which may be useful for genome-scale comparative studies of mammalian aging and other biological aspects. We further demonstrate that Pareto optimality can explain a range of previous studies which found animal and plant phenotypes which lie in triangles in trait space. This study demonstrates the applicability of multi-objective optimization principles to understand life history traits and to infer archetypal strategies that suggest why some mammalian species live much longer than others of similar mass. PMID:26465336
The Mass-Longevity Triangle: Pareto Optimality and the Geometry of Life-History Trait Space.
Szekely, Pablo; Korem, Yael; Moran, Uri; Mayo, Avi; Alon, Uri
2015-10-01
When organisms need to perform multiple tasks they face a fundamental tradeoff: no phenotype can be optimal at all tasks. This situation was recently analyzed using Pareto optimality, showing that tradeoffs between tasks lead to phenotypes distributed on low dimensional polygons in trait space. The vertices of these polygons are archetypes--phenotypes optimal at a single task. This theory was applied to examples from animal morphology and gene expression. Here we ask whether Pareto optimality theory can apply to life history traits, which include longevity, fecundity and mass. To comprehensively explore the geometry of life history trait space, we analyze a dataset of life history traits of 2105 endothermic species. We find that, to a first approximation, life history traits fall on a triangle in log-mass log-longevity space. The vertices of the triangle suggest three archetypal strategies, exemplified by bats, shrews and whales, with specialists near the vertices and generalists in the middle of the triangle. To a second approximation, the data lies in a tetrahedron, whose extra vertex above the mass-longevity triangle suggests a fourth strategy related to carnivory. Each animal species can thus be placed in a coordinate system according to its distance from the archetypes, which may be useful for genome-scale comparative studies of mammalian aging and other biological aspects. We further demonstrate that Pareto optimality can explain a range of previous studies which found animal and plant phenotypes which lie in triangles in trait space. This study demonstrates the applicability of multi-objective optimization principles to understand life history traits and to infer archetypal strategies that suggest why some mammalian species live much longer than others of similar mass.
The Mass-Longevity Triangle: Pareto Optimality and the Geometry of Life-History Trait Space.
Directory of Open Access Journals (Sweden)
Pablo Szekely
2015-10-01
Full Text Available When organisms need to perform multiple tasks they face a fundamental tradeoff: no phenotype can be optimal at all tasks. This situation was recently analyzed using Pareto optimality, showing that tradeoffs between tasks lead to phenotypes distributed on low dimensional polygons in trait space. The vertices of these polygons are archetypes--phenotypes optimal at a single task. This theory was applied to examples from animal morphology and gene expression. Here we ask whether Pareto optimality theory can apply to life history traits, which include longevity, fecundity and mass. To comprehensively explore the geometry of life history trait space, we analyze a dataset of life history traits of 2105 endothermic species. We find that, to a first approximation, life history traits fall on a triangle in log-mass log-longevity space. The vertices of the triangle suggest three archetypal strategies, exemplified by bats, shrews and whales, with specialists near the vertices and generalists in the middle of the triangle. To a second approximation, the data lies in a tetrahedron, whose extra vertex above the mass-longevity triangle suggests a fourth strategy related to carnivory. Each animal species can thus be placed in a coordinate system according to its distance from the archetypes, which may be useful for genome-scale comparative studies of mammalian aging and other biological aspects. We further demonstrate that Pareto optimality can explain a range of previous studies which found animal and plant phenotypes which lie in triangles in trait space. This study demonstrates the applicability of multi-objective optimization principles to understand life history traits and to infer archetypal strategies that suggest why some mammalian species live much longer than others of similar mass.
Jumarie, Guy
2013-04-01
By using fractional differences, one recently proposed an alternative to the formulation of fractional differential calculus, of which the main characteristics is a new fractional Taylor series and its companion Rolle's formula which apply to non-differentiable functions. The key is that now we have at hand a differential increment of fractional order which can be manipulated exactly like in the standard Leibniz differential calculus. Briefly the fractional derivative is the quotient of fractional increments. It has been proposed that this calculus can be used to construct a differential geometry on manifold of fractional order. The present paper, on the one hand, refines the framework, and on the other hand, contributes some new results related to arc length of fractional curves, area on fractional differentiable manifold, covariant fractal derivative, Riemann-Christoffel tensor of fractional order, fractional differential equations of fractional geodesic, strip modeling of fractal space time and its relation with Lorentz transformation. The relation with Nottale's fractal space-time theory then appears in quite a natural way.
Hock, Tan Tong; Tarmizi, Rohani Ahmad; Yunus, Aida Suraya Md.; Ayub, Ahmad Fauzi
2015-01-01
This study was conducted using a new hybrid method of research which combined qualitative and quantitative designs to investigate the viewpoints of primary school students' conceptual understanding in learning geometry from the aspect of shapes and spaces according to van Hiele theory. Q-methodology is used in this research to find out what…
Relative-locality distant observers and the phenomenology of momentum-space geometry
International Nuclear Information System (INIS)
Amelino-Camelia, Giovanni; Rosati, Giacomo; Trevisan, Gabriele; Arzano, Michele; Kowalski-Glikman, Jerzy
2012-01-01
We study the translational invariance of the relative-locality framework proposed in Amelino-Camelia et al (2011 Phys. Rev. D 84 084010), which had been previously established only for the case of a single interaction. We provide an explicit example of boundary conditions at endpoints of worldlines, which indeed ensures the desired translational invariance for processes involving several interactions, even when some of the interactions are causally connected (particle exchange). We illustrate the properties of the associated relativistic description of distant observers within the example of a κ-Poincare-inspired momentum-space geometry, with de Sitter metric and parallel transport governed by a non-metric and torsionful connection. We find that in such a theory, simultaneously emitted massless particles do not reach simultaneously a distant detector, as expected in light of the findings of Freidel and Smolin (2011 arXiv:1103.5626) on the implications of non-metric connections. We also show that the theory admits a free-particle limit, where the relative-locality results of Amelino-Camelia et al (2011 Phys. Lett. B 700 150) are reproduced. We establish that the torsion of the κ-Poincare connection introduces a small (but observably large) dependence of the time of detection, for simultaneously emitted particles, on some properties of the interactions producing the particles at the source. (paper)
Relative-locality distant observers and the phenomenology of momentum-space geometry
Amelino-Camelia, Giovanni; Arzano, Michele; Kowalski-Glikman, Jerzy; Rosati, Giacomo; Trevisan, Gabriele
2012-04-01
We study the translational invariance of the relative-locality framework proposed in Amelino-Camelia et al (2011 Phys. Rev. D 84 084010), which had been previously established only for the case of a single interaction. We provide an explicit example of boundary conditions at endpoints of worldlines, which indeed ensures the desired translational invariance for processes involving several interactions, even when some of the interactions are causally connected (particle exchange). We illustrate the properties of the associated relativistic description of distant observers within the example of a κ-Poincaré-inspired momentum-space geometry, with de Sitter metric and parallel transport governed by a non-metric and torsionful connection. We find that in such a theory, simultaneously emitted massless particles do not reach simultaneously a distant detector, as expected in light of the findings of Freidel and Smolin (2011 arXiv:1103.5626) on the implications of non-metric connections. We also show that the theory admits a free-particle limit, where the relative-locality results of Amelino-Camelia et al (2011 Phys. Lett. B 700 150) are reproduced. We establish that the torsion of the κ-Poincaré connection introduces a small (but observably large) dependence of the time of detection, for simultaneously emitted particles, on some properties of the interactions producing the particles at the source.
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
Word-serial Architectures for Filtering and Variable Rate Decimation
Directory of Open Access Journals (Sweden)
Eugene Grayver
2002-01-01
Full Text Available A new flexible architecture is proposed for word-serial filtering and variable rate decimation/interpolation. The architecture is targeted for low power applications requiring medium to low data rate and is ideally suited for implementation on either an ASIC or an FPGA. It combines the small size and low power of an ASIC with the programmability and flexibility of a DSP. An efficient memory addressing scheme eliminates the need for power hungry shift registers and allows full reconfiguration. The decimation ratio, filter length and filter coefficients can all be changed in real time. The architecture takes advantage of coefficient symmetries in linear phase filters and in polyphase components.
The theory and practice of the Dewey Decimal Classification system
Satija, M P
2013-01-01
The Dewey Decimal Classification system (DDC) is the world's most popular library classification system. The 23rd edition of the DDC was published in 2011. This second edition of The Theory and Practice of the Dewey Decimal Classification System examines the history, management and technical aspects of the DDC up to its latest edition. The book places emphasis on explaining the structure and number building techniques in the DDC and reviews all aspects of subject analysis and number building by the most recent version of the DDC. A history of, and introduction to, the DDC is followed by subjec
IMPLEMENTATION AND COMPARISON OF DIFFERENT CIC FILTER STRUCTURE FOR DECIMATION
Directory of Open Access Journals (Sweden)
M. Madheswaran
2013-06-01
Full Text Available This paper briefs an implementation of different CIC filter architectures for decimation. The different decimation filter structures are implemented using cascaded integrator-comb filter to work for the down sampling ratio of 8. The prototype is designed with MATLAB Simulink model and it is converted to VHDL code using Xilinx system generator. Prototype is implemented in Virtex V- XC5VLX110T-3ff1136 FPGA kit and simulation results and device utilization reports are generated and tabulated. Finally different architectures are compared using number of used LUTs, Registers, Power consumption etc.
Use of Geometry for Spatial Reorientation in Children Applies Only to Symmetric Spaces
Lew, Adina R.; Gibbons, Bryony; Murphy, Caroline; Bremner, J. Gavin
2010-01-01
Proponents of the geometric module hypothesis argue that following disorientation, many species reorient by use of macro-environment geometry. It is suggested that attention to the surface layout geometry of natural terrain features may have been selected for over evolutionary time due to the enduring and unambiguous location information it…
Why Is Learning Fraction and Decimal Arithmetic so Difficult?
Lortie-Forgues, Hugues; Tian, Jing; Siegler, Robert S.
2015-01-01
Fraction and decimal arithmetic are crucial for later mathematics achievement and for ability to succeed in many professions. Unfortunately, these capabilities pose large difficulties for many children and adults, and students' proficiency in them has shown little sign of improvement over the past three decades. To summarize what is known about…
Decimal Engine for Energy-Efficient Multicore Processors
DEFF Research Database (Denmark)
Nannarelli, Alberto
2014-01-01
propose a hybrid BFP/DFP engine to perform BFP division and DFP addition, multiplication and division. The main purpose of this engine is to offload the binary floating-point units for this type of operations and reduce the latency for decimal operations, and power and temperature for the whole die....
Renormalization group decimation technique for disordered binary harmonic chains
International Nuclear Information System (INIS)
Wiecko, C.; Roman, E.
1983-10-01
The density of states of disordered binary harmonic chains is calculated using the Renormalization Group Decimation technique on the displacements of the masses from their equilibrium positions. The results are compared with numerical simulation data and with those obtained with the current method of Goncalves da Silva and Koiller. The advantage of our procedure over other methods is discussed. (author)
Decimal Fraction Arithmetic: Logical Error Analysis and Its Validation.
Standiford, Sally N.; And Others
This report illustrates procedures of item construction for addition and subtraction examples involving decimal fractions. Using a procedural network of skills required to solve such examples, an item characteristic matrix of skills analysis was developed to describe the characteristics of the content domain by projected student difficulties. Then…
FPGA Implementation of Decimal Processors for Hardware Acceleration
DEFF Research Database (Denmark)
Borup, Nicolas; Dindorp, Jonas; Nannarelli, Alberto
2011-01-01
Applications in non-conventional number systems can benefit from accelerators implemented on reconfigurable platforms, such as Field Programmable Gate-Arrays (FPGAs). In this paper, we show that applications requiring decimal operations, such as the ones necessary in accounting or financial trans...... execution on the CPU of the hosting computer....
Dewey Decimal Classification for U. S. Conn: An Advantage?
Marek, Kate
This paper examines the use of the Dewey Decimal Classification (DDC) system at the U. S. Conn Library at Wayne State College (WSC) in Nebraska. Several developments in the last 20 years which have eliminated the trend toward reclassification of academic library collections from DDC to the Library of Congress (LC) classification scheme are…
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)
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
Landi, Giovanni
1997-01-01
These lecture notes are an introduction to several ideas and applications of noncommutative geometry. It starts with a not necessarily commutative but associative algebra which is thought of as the algebra of functions on some 'virtual noncommutative space'. Attention is switched from spaces, which in general do not even exist, to algebras of functions. In these notes, particular emphasis is put on seeing noncommutative spaces as concrete spaces, namely as a collection of points with a topology. The necessary mathematical tools are presented in a systematic and accessible way and include among other things, C'*-algebras, module theory and K-theory, spectral calculus, forms and connection theory. Application to Yang--Mills, fermionic, and gravity models are described. Also the spectral action and the related invariance under automorphism of the algebra is illustrated. Some recent work on noncommutative lattices is presented. These lattices arose as topologically nontrivial approximations to 'contuinuum' topolo...
Interpolation of final geometry and result fields in process parameter space
Misiun, Grzegorz Stefan; Wang, Chao; Geijselaers, Hubertus J.M.; van den Boogaard, Antonius H.; Saanouni, K.
2016-01-01
Different routes to produce a product in a bulk forming process can be described by a limited set of process parameters. The parameters determine the final geometry as well as the distribution of state variables in the final shape. Ring rolling has been simulated using different parameter settings.
International Nuclear Information System (INIS)
Kelokaski, M.; Siitari-Kauppi, M.; Kauppi, I.; Hellmuth, K.-H.; Moeri, A.; Inderbitzin, L.; Biggin, C.; Kickmaier, W.; Martin, A.
2010-04-01
In Finland high-level radioactive waste is planned to be disposed of in a deep geological repository within a crystalline host rock. The potential role of the geosphere as a safety barrier in repository performance assessment is well established. However, uncertainties in both transport pathway definition and pore space characterisation of crystalline rock still exist and the repository safety evaluation today requires going from laboratory and surface-based field work to the underground repository level. Little is known about the changes to rock transport properties during sampling and decompression. Recent investigations using resin impregnation of the rock matrix at the Grimsel Test Site imply that non-conservative errors in calculated transport properties derived from laboratory data may reach factors of two to three. Due to the potentially great significance of pore space characterisation to safety analysis calculations, it was decided to study the rock matrix characteristics in situ using methylmethacrylate (MMA) resin labelled with 14 C. During the last decade, the poly-methylmethacrylate (PMMA) method has been developed for characterising the porosity of low permeable granitic rocks in the laboratory. Impregnation with 14 C-labelled methylmethacrylate ( 14 C-MMA) and autoradiography allows investigation of the spatial distribution of accessible porosity at the centimetre scale. Quantitative measurements of total or mineral-specific local porosities have been obtained using image analysis tools. Electron microscopy examinations and mercury porosimetry measurements have provided detailed information on pore and fissure apertures. The objective of this work was to develop an in situ application of the PMMA impregnation technique. The changes in rock porosity due to stress relaxation when overcoring the samples from the bedrock for the laboratory studies were examined. The concept behind the work was to inject 14 C-MMA from a central borehole at a depth of
Straight flavor of Binary Number in Decimal Number System
MD. Abdul Awal Ansary; Sushanta Acharjee
2012-01-01
Different number systems are available on the basis of their base numbers. For instance, decimal number system is of base 10, hexadecimal number system which base is 16 and, Binary number system which base is 2 etc. Some numbers systems are easy to understand by the human being and some are easy to understand by electronics machine for instance digital computers. Computers only can understand data and instructions that are stored in binary form, though we input the data and instruction in dec...
Modeling discrete and continuous entities with fractions and decimals.
Rapp, Monica; Bassok, Miriam; DeWolf, Melissa; Holyoak, Keith J
2015-03-01
When people use mathematics to model real-life situations, their use of mathematical expressions is often mediated by semantic alignment (Bassok, Chase, & Martin, 1998): The entities in a problem situation evoke semantic relations (e.g., tulips and vases evoke the functionally asymmetric "contain" relation), which people align with analogous mathematical relations (e.g., the noncommutative division operation, tulips/vases). Here we investigate the possibility that semantic alignment is also involved in the comprehension and use of rational numbers (fractions and decimals). A textbook analysis and results from two experiments revealed that both mathematic educators and college students tend to align the discreteness versus continuity of the entities in word problems (e.g., marbles vs. distance) with distinct symbolic representations of rational numbers--fractions versus decimals, respectively. In addition, fractions and decimals tend to be used with nonmetric units and metric units, respectively. We discuss the importance of the ontological distinction between continuous and discrete entities to mathematical cognition, the role of symbolic notations, and possible implications of our findings for the teaching of rational numbers. PsycINFO Database Record (c) 2015 APA, all rights reserved.
Pitts, J. Brian
2016-02-01
What if gravity satisfied the Klein-Gordon equation? Both particle physics from the 1920-30s and the 1890s Neumann-Seeliger modification of Newtonian gravity with exponential decay suggest considering a "graviton mass term" for gravity, which is algebraic in the potential. Unlike Nordström's "massless" theory, massive scalar gravity is strictly special relativistic in the sense of being invariant under the Poincaré group but not the 15-parameter Bateman-Cunningham conformal group. It therefore exhibits the whole of Minkowski space-time structure, albeit only indirectly concerning volumes. Massive scalar gravity is plausible in terms of relativistic field theory, while violating most interesting versions of Einstein's principles of general covariance, general relativity, equivalence, and Mach. Geometry is a poor guide to understanding massive scalar gravity(s): matter sees a conformally flat metric due to universal coupling, but gravity also sees the rest of the flat metric (barely or on long distances) in the mass term. What is the 'true' geometry, one might wonder, in line with Poincaré's modal conventionality argument? Infinitely many theories exhibit this bimetric 'geometry,' all with the total stress-energy's trace as source; thus geometry does not explain the field equations. The irrelevance of the Ehlers-Pirani-Schild construction to a critique of conventionalism becomes evident when multi-geometry theories are contemplated. Much as Seeliger envisaged, the smooth massless limit indicates underdetermination of theories by data between massless and massive scalar gravities-indeed an unconceived alternative. At least one version easily could have been developed before General Relativity; it then would have motivated thinking of Einstein's equations along the lines of Einstein's newly re-appreciated "physical strategy" and particle physics and would have suggested a rivalry from massive spin 2 variants of General Relativity (massless spin 2, Pauli and Fierz
The geometry of empty space is the key to arresting dynamics
Energy Technology Data Exchange (ETDEWEB)
Lawlor, Aonghus; De Gregorio, Paolo; Dawson, K A [Department of Chemistry, University College Dublin, Irish Centre for Colloid Science and Biomaterials, Belfield, Dublin 4 (Ireland)
2004-10-27
We present the concept of dynamically available volume as a suitable order parameter for dynamical arrest. We show that dynamical arrest can be understood as a de-percolation transition of a vacancy network or available space. Beyond the arrest transition we find that droplets of available space are disconnected and the dynamics is frozen. This connection of the dynamics to the underlying geometrical structure of empty space provides us with a rich framework for studying the arrest transition.
Gigli, Nicola
2018-01-01
The author discusses in which sense general metric measure spaces possess a first order differential structure. Building on this, spaces with Ricci curvature bounded from below a second order calculus can be developed, permitting the author to define Hessian, covariant/exterior derivatives and Ricci curvature.
Geometry on the parameter space of the belief propagation algorithm on Bayesian networks
Energy Technology Data Exchange (ETDEWEB)
Watanabe, Yodai [National Institute of Informatics, Research Organization of Information and Systems, 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo 101-8430 (Japan); Laboratory for Mathematical Neuroscience, RIKEN Brain Science Institute, 2-1 Hirosawa, Wako-shi, Saitama 351-0198 (Japan)
2006-01-30
This Letter considers a geometrical structure on the parameter space of the belief propagation algorithm on Bayesian networks. The statistical manifold of posterior distributions is introduced, and the expression for the information metric on the manifold is derived. The expression is used to construct a cost function which can be regarded as a measure of the distance in the parameter space.
Soni, Rahul Kumar; De, Ashoke
2018-05-01
The present study primarily focuses on the effect of the jet spacing and strut geometry on the evolution and structure of the large-scale vortices which play a key role in mixing characteristics in turbulent supersonic flows. Numerically simulated results corresponding to varying parameters such as strut geometry and jet spacing (Xn = nDj such that n = 2, 3, and 5) for a square jet of height Dj = 0.6 mm are presented in the current study, while the work also investigates the presence of the local quasi-two-dimensionality for the X2(2Dj) jet spacing; however, the same is not true for higher jet spacing. Further, the tapered strut (TS) section is modified into the straight strut (SS) for investigation, where the remarkable difference in flow physics is unfolded between the two configurations for similar jet spacing (X2: 2Dj). The instantaneous density and vorticity contours reveal the structures of varying scales undergoing different evolution for the different configurations. The effect of local spanwise rollers is clearly manifested in the mixing efficiency and the jet spreading rate. The SS configuration exhibits excellent near field mixing behavior amongst all the arrangements. However, in the case of TS cases, only the X2(2Dj) configuration performs better due to the presence of local spanwise rollers. The qualitative and quantitative analysis reveals that near-field mixing is strongly affected by the two-dimensional rollers, while the early onset of the wake mode is another crucial parameter to have improved mixing. Modal decomposition performed for the SS arrangement sheds light onto the spatial and temporal coherence of the structures, where the most dominant structures are found to be the von Kármán street vortices in the wake region.
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...
Symplectic geometry on moduli spaces of holomorphic bundles over complex surfaces
Khesin, Boris; Rosly, Alexei
2000-01-01
We give a comparative description of the Poisson structures on the moduli spaces of flat connections on real surfaces and holomorphic Poisson structures on the moduli spaces of holomorphic bundles on complex surfaces. The symplectic leaves of the latter are classified by restrictions of the bundles to certain divisors. This can be regarded as fixing a "complex analogue of the holonomy" of a connection along a "complex analogue of the boundary" in analogy with the real case.
International Nuclear Information System (INIS)
McMillan, B.F.; Jolliet, S.; Tran, T.M.; Villard, L.; Bottino, A.; Angelino, P.
2010-01-01
Fluctuating quantities in magnetic confinement geometries often inherit a strong anisotropy along the field lines. One technique for describing these structures is the use of a certain set of Fourier components on the tori of nested flux surfaces. We describe an implementation of this approach for solving partial differential equations, like Poisson's equation, where a different set of Fourier components may be chosen on each surface according to the changing safety factor profile. Allowing the resolved components to change to follow the anisotropy significantly reduces the total number of degrees of freedom in the description. This can permit large gains in computational performance. We describe, in particular, how this approach can be applied to rapidly solve the gyrokinetic Poisson equation in a particle code, ORB5 (Jolliet et al. (2007) [5]), with a regular (non-field-aligned) mesh. (authors)
U(N) instantons on N=(1/2) superspace: Exact solution and geometry of moduli space
International Nuclear Information System (INIS)
Britto, Ruth; Feng Bo; Lunin, Oleg; Rey, Soo-Jong
2004-01-01
We construct the exact solution of one (anti-)instanton in N=(1/2) super Yang-Mills theory defined on non(anti-)commutative superspace. We first identify N=(1/2) superconformal invariance as maximal spacetime symmetry. For the gauge group U(2), the SU(2) part of the solution is given by the standard (anti-)instanton, but the U(1) field strength also turns out to be nonzero. The solution is SO(4) rotationally symmetric. For the gauge group U(N), in contrast with the U(2) case, we show that the entire U(N) part of the solution is deformed by non(anti-)commutativity and fermion zero modes. The solution is no longer rotationally symmetric; it is polarized into an axially symmetric configuration because of the underlying non(anti-)commutativity. We compute the 'information metric' of one (anti-)instanton. We find that the moduli space geometry is deformed from the hyperbolic space H 5 (Euclidean anti-de Sitter space) in a way anticipated from reduced spacetime symmetry. Remarkably, the volume measure of the moduli space turns out to be independent of the non(anti-)commutativity. Implications for D branes in the Ramond-Ramond flux background and the gauge-gravity correspondence are discussed
Space Versus Time: Unimodular Versus Non-Unimodular Projective Ring Geometries?
Czech Academy of Sciences Publication Activity Database
Saniga, M.; Pracna, Petr
2010-01-01
Roč. 4, - (2010), s. 719-735 ISSN 2159-063X Institutional research plan: CEZ:AV0Z40400503 Keywords : projective ring lines * smallest ring of ternions * Germas: of space-time Subject RIV: CF - Physical ; Theoretical Chemistry http://journalofcosmology.com/Multiverse4.html
Kinematic algebras, groups for elementary particles, and the geometry of momentum space
International Nuclear Information System (INIS)
Izmest'ev, A.A.
1986-01-01
It is shown that to each n-dimensional (n≥2) homogeneous isotropic Riemannian momentum (coordinate) space there corresponds a definite kinematic local algebra of operators N/sub a/, M/sub a//sub b/, P/sub a//sub ,/ ω(a,b = 1,2,...,n). In the three-dimensional case this gives the possibility of classifying particles in accordance with the algebras of the types of momentum space. The approach developed also makes it possible to obtain generalized equations describing particles of the different types. The operators under consideration satisfy not only the relevant algebra but also relations independent of the algebra that coincide in form with the Maxwell equations
Decimal multiplication using compressor based-BCD to binary converter
Directory of Open Access Journals (Sweden)
Sasidhar Mukkamala
2018-02-01
Full Text Available The objective of this work is to implement a scalable decimal to binary converter from 8 to 64 bits (i.e 2-digit to 16-digit using parallel architecture. The proposed converters, along with binary coded decimal (BCD adder and binary to BCD converters, are used in parallel implementation of Urdhva Triyakbhyam (UT-based 32-bit BCD multiplier. To increase the performance, compressor circuits were used in converters and multiplier. The designed hardware circuits were verified by behavioural and post layout simulations. The implementation was carried out using Virtex-6 Field Programmable Gate Array (FPGA and Application Specific Integrated Circuit (ASIC with 90-nm technology library platforms. The results on FPGA shows that compressor based converters and multipliers produced less amount of propagation delay with a slight increase of hardware resources. In case of ASIC implementation, a compressor based converter delay is equivalent to conventional converter with a slight increase of gate count. However, the reduction of delay is evident in case of compressor based multiplier.
Formation of concept of decimal system in Mexican school children
Directory of Open Access Journals (Sweden)
L. Quintanar Rojas
2013-04-01
Full Text Available The present study deals with initial formation of concept of decimal system in second year of education at primary school in Mexico (City of Puebla. Our research is based on Activity Theory conception of teaching-learning process and of gradual introduction of scientific concepts in school age. The method has been designed and worked out with the help of actions in which logic, symbolic, spatial and mathematical aspects were implemented. All actions were introduced within divided activity of children in group guided by adult. A pretest-posttest design was used with an experimental group of Mexican school children. The results showed that children have developed the significant skills necessary for understanding the concept of decimal number system. They were also able to apply this concept for new kind if activity al the end of school year. Such new activity was solving of mathematic problems, which was not included in official school program. We consider that proposed method can be an approximation for solution of common difficulties which arise at primary school concerning teaching of mathematics.
Czech Academy of Sciences Publication Activity Database
Polák, M.; Němec, Lubomír
2010-01-01
Roč. 54, č. 3 (2010), s. 212-218 ISSN 0862-5468 R&D Projects: GA MPO 2A-1TP1/063 Institutional research plan: CEZ:AV0Z40320502 Keywords : space utilization, * sand dissolution * bubble removal * space geometry Subject RIV: JH - Ceramics, Fire-Resistant Materials and Glass Impact factor: 0.297, year: 2010
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
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.
Directory of Open Access Journals (Sweden)
Nowak Aleksander
2015-12-01
Full Text Available Nowadays, we can observe an increase in research on the use of small unmanned autonomous vessel (SUAV to patrol and guiding critical areas including harbours. The proposal to “snapshot” RAIM (Receiver Autonomous Integrity Monitoring method for GNSS receivers mounted on SUAV operating in poor space segment geometry is presented in the paper. Existing “snapshot” RAIM methods and algorithms which are used in practical applications have been developed for airborne receivers, thus two main assumptions have been made. The first one is that the geometry of visible satellites is strong. It means that the exclusion of any satellite from the positioning solution don’t cause significant deterioration of Dilution of Precision (DOP coefficients. The second one is that only one outlier could appear in pseudorange measurements. In case of SUAV operating in harbour these two assumptions cannot be accepted. Because of their small dimensions, GNSS antenna is only a few decimetres above sea level and regular ships, buildings and harbour facilities block and reflect satellite signals. Thus, different approach to “snapshot” RAIM is necessary. The proposal to method based on analyses of allowable maximal separation of positioning sub-solutions with using some information from EGNOS messages is described in the paper. Theoretical assumptions and results of numerical experiments are presented.
International Nuclear Information System (INIS)
Stoeger, W.R.; Whitman, A.P.; Knill, R.J.
1985-01-01
After showing that Rosen's bimetric theory of gravity is a harmonic map, the geometry of the ten-dimensional harmonic mapping space (HMS), and of its nine-dimensional symmetric submanifolds, which are the leaves of the codimension one foliation of the HMS, is detailed. Both structures are global affinely symmetric spaces. For each, the metric, connections, and Riemann, Ricci, and scalar curvatures are given. The Killing vectors in each case are also worked out and related to the ''conserved quantities'' naturally associated with the harmonic mapping character of the theory. The structure of the Rosen HMS is very much like that determined by the DeWitt metric on the six-dimensional Wheeler superspace of all positive definite three-dimensional metrics. It is clear that a slight modification of the Rosen HMS metric will yield the corresponding metric on the space of all four-dimensional metrics of Lorentz signature. Finally, interesting avenues of further research are indicated, particularly with respect to the structure and comparison of Lagrangian-based gravitational theories which are similar to Einstein's general relativity
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.
Cusimano, N.; Gerardo-Giorda, L.
2018-06-01
Classical models of electrophysiology do not typically account for the effects of high structural heterogeneity in the spatio-temporal description of excitation waves propagation. We consider a modification of the Monodomain model obtained by replacing the diffusive term of the classical formulation with a fractional power of the operator, defined in the spectral sense. The resulting nonlocal model describes different levels of tissue heterogeneity as the fractional exponent is varied. The numerical method for the solution of the fractional Monodomain relies on an integral representation of the nonlocal operator combined with a finite element discretisation in space, allowing to handle in a natural way bounded domains in more than one spatial dimension. Numerical tests in two spatial dimensions illustrate the features of the model. Activation times, action potential duration and its dispersion throughout the domain are studied as a function of the fractional parameter: the expected peculiar behaviour driven by tissue heterogeneities is recovered.
More on the rainbow chain: entanglement, space-time geometry and thermal states
International Nuclear Information System (INIS)
Rodríguez-Laguna, Javier; Dubail, Jérôme; Ramírez, Giovanni; Calabrese, Pasquale; Sierra, Germán
2017-01-01
The rainbow chain is an inhomogenous exactly solvable local spin model that, in its ground state, displays a half-chain entanglement entropy growing linearly with the system size. Although many exact results about the rainbow chain are known, the structure of the underlying quantum field theory has not yet been unraveled. Here we show that the universal scaling features of this model are captured by a massless Dirac fermion in a curved space-time with constant negative curvature R = − h "2 ( h is the amplitude of the inhomogeneity). This identification allows us to use recently developed techniques to study inhomogeneous conformal systems and to analytically characterise the entanglement entropies of more general bipartitions. These results are carefully tested against exact numerical calculations. Finally, we study the entanglement entropies of the rainbow chain in thermal states, and find that there is a non-trivial interplay between the rainbow effective temperature T_R and the physical temperature T . (paper)
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...
Directory of Open Access Journals (Sweden)
Luigi Giuliani
2013-05-01
Full Text Available Review of Henry S. Turner, The English Renaissance Stage. Geometry, Poetics, and the Practical Spatial Arts 1580-1630, Oxford University Press, Oxford, 2006, reimpr. 2010, 326 pp. ISBN: 978-0-19-959545-7 y Tim Fitzpatrick, Playwright, Space and Place in Early Modern Performance, Ashgate, Franham, 2011, 314 pp. ISBN: 978-1-4094-2827-5.
van den Heuvel, C.
2014-01-01
In 1983 Boyd Rayward described the early diffusion abroad of the Dewey Decimal Classification (and indirectly of the Universal Decimal Classification) in Australia, Great Britain, Belgium, France, Switzerland, and Russia. Here, I discuss the enormous interest in the decimal system in the Netherlands
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.
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.
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.)
Fabanich, William A., Jr.
2014-01-01
SpaceClaim/TD Direct has been used extensively in the development of the Advanced Stirling Radioisotope Generator (ASRG) thermal model. This paper outlines the workflow for that aspect of the task and includes proposed best practices and lessons learned. The ASRG thermal model was developed to predict component temperatures and power output and to provide insight into the prime contractor's thermal modeling efforts. The insulation blocks, heat collectors, and cold side adapter flanges (CSAFs) were modeled with this approach. The model was constructed using mostly TD finite difference (FD) surfaces/solids. However, some complex geometry could not be reproduced with TD primitives while maintaining the desired degree of geometric fidelity. Using SpaceClaim permitted the import of original CAD files and enabled the defeaturing/repair of those geometries. TD Direct (a SpaceClaim add-on from CRTech) adds features that allowed the "mark-up" of that geometry. These so-called "mark-ups" control how finite element (FE) meshes are to be generated through the "tagging" of features (e.g. edges, solids, surfaces). These tags represent parameters that include: submodels, material properties, material orienters, optical properties, and radiation analysis groups. TD aliases were used for most tags to allow analysis to be performed with a variety of parameter values. "Domain-tags" were also attached to individual and groups of surfaces and solids to allow them to be used later within TD to populate objects like, for example, heaters and contactors. These tools allow the user to make changes to the geometry in SpaceClaim and then easily synchronize the mesh in TD without having to redefine the objects each time as one would if using TDMesher. The use of SpaceClaim/TD Direct helps simplify the process for importing existing geometries and in the creation of high fidelity FE meshes to represent complex parts. It also saves time and effort in the subsequent analysis.
Fabanich, William
2014-01-01
SpaceClaim/TD Direct has been used extensively in the development of the Advanced Stirling Radioisotope Generator (ASRG) thermal model. This paper outlines the workflow for that aspect of the task and includes proposed best practices and lessons learned. The ASRG thermal model was developed to predict component temperatures and power output and to provide insight into the prime contractors thermal modeling efforts. The insulation blocks, heat collectors, and cold side adapter flanges (CSAFs) were modeled with this approach. The model was constructed using mostly TD finite difference (FD) surfaces solids. However, some complex geometry could not be reproduced with TD primitives while maintaining the desired degree of geometric fidelity. Using SpaceClaim permitted the import of original CAD files and enabled the defeaturing repair of those geometries. TD Direct (a SpaceClaim add-on from CRTech) adds features that allowed the mark-up of that geometry. These so-called mark-ups control how finite element (FE) meshes were generated and allowed the tagging of features (e.g. edges, solids, surfaces). These tags represent parameters that include: submodels, material properties, material orienters, optical properties, and radiation analysis groups. TD aliases were used for most tags to allow analysis to be performed with a variety of parameter values. Domain-tags were also attached to individual and groups of surfaces and solids to allow them to be used later within TD to populate objects like, for example, heaters and contactors. These tools allow the user to make changes to the geometry in SpaceClaim and then easily synchronize the mesh in TD without having to redefine these objects each time as one would if using TD Mesher.The use of SpaceClaim/TD Direct has helped simplify the process for importing existing geometries and in the creation of high fidelity FE meshes to represent complex parts. It has also saved time and effort in the subsequent analysis.
Geometry of multihadron production
Energy Technology Data Exchange (ETDEWEB)
Bjorken, J.D.
1994-10-01
This summary talk only reviews a small sample of topics featured at this symposium: Introduction; The Geometry and Geography of Phase space; Space-Time Geometry and HBT; Multiplicities, Intermittency, Correlations; Disoriented Chiral Condensate; Deep Inelastic Scattering at HERA; and Other Contributions.
Geometry of multihadron production
International Nuclear Information System (INIS)
Bjorken, J.D.
1994-10-01
This summary talk only reviews a small sample of topics featured at this symposium: Introduction; The Geometry and Geography of Phase space; Space-Time Geometry and HBT; Multiplicities, Intermittency, Correlations; Disoriented Chiral Condensate; Deep Inelastic Scattering at HERA; and Other Contributions
Multiple-scale stochastic processes: Decimation, averaging and beyond
Energy Technology Data Exchange (ETDEWEB)
Bo, Stefano, E-mail: stefano.bo@nordita.org [Nordita, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, SE-106 91 Stockholm (Sweden); Celani, Antonio [Quantitative Life Sciences, The Abdus Salam International Centre for Theoretical Physics (ICTP), Strada Costiera 11, I-34151 - Trieste (Italy)
2017-02-07
The recent experimental progresses in handling microscopic systems have allowed to probe them at levels where fluctuations are prominent, calling for stochastic modeling in a large number of physical, chemical and biological phenomena. This has provided fruitful applications for established stochastic methods and motivated further developments. These systems often involve processes taking place on widely separated time scales. For an efficient modeling one usually focuses on the slower degrees of freedom and it is of great importance to accurately eliminate the fast variables in a controlled fashion, carefully accounting for their net effect on the slower dynamics. This procedure in general requires to perform two different operations: decimation and coarse-graining. We introduce the asymptotic methods that form the basis of this procedure and discuss their application to a series of physical, biological and chemical examples. We then turn our attention to functionals of the stochastic trajectories such as residence times, counting statistics, fluxes, entropy production, etc. which have been increasingly studied in recent years. For such functionals, the elimination of the fast degrees of freedom can present additional difficulties and naive procedures can lead to blatantly inconsistent results. Homogenization techniques for functionals are less covered in the literature and we will pedagogically present them here, as natural extensions of the ones employed for the trajectories. We will also discuss recent applications of these techniques to the thermodynamics of small systems and their interpretation in terms of information-theoretic concepts.
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.
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.
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...
EXTINCTION AND DUST GEOMETRY IN M83 H II REGIONS: AN HUBBLE SPACE TELESCOPE/WFC3 STUDY
Energy Technology Data Exchange (ETDEWEB)
Liu, Guilin; Calzetti, Daniela; Hong, Sungryong [Astronomy Department, University of Massachusetts, Amherst, MA 01003 (United States); Whitmore, Bradley [Space Telescope Science Institute, Baltimore, MD 21218 (United States); Chandar, Rupali [Department of Physics and Astronomy, University of Toledo, Toledo, OH 43606 (United States); O' Connell, Robert W. [Astronomy Department, University of Virginia, P.O. Box 3818, Charlottesville, VA 22903 (United States); Blair, William P. [Center for Astrophysical Sciences, Johns Hopkins University, Baltimore, MD 21218 (United States); Cohen, Seth H.; Kim, Hwihyun [School of Earth and Space Exploration, Arizona State University, Tempe, AZ 85287 (United States); Frogel, Jay A., E-mail: liu@pha.jhu.edu [Galaxies Unlimited, Lutherville, MD 21093 (United States)
2013-12-01
We present Hubble Space Telescope/WFC3 narrow-band imaging of the starburst galaxy M83 targeting the hydrogen recombination lines (Hβ, Hα, and Paβ), which we use to investigate the dust extinction in the H II regions. We derive extinction maps with 6 pc spatial resolution from two combinations of hydrogen lines (Hα/Hβ and Hα/Paβ), and show that the longer wavelengths probe larger optical depths, with A{sub V} values larger by ≳1 mag than those derived from the shorter wavelengths. This difference leads to a factor ≳2 discrepancy in the extinction-corrected Hα luminosity, a significant effect when studying extragalactic H II regions. By comparing these observations to a series of simple models, we conclude that a large diversity of absorber/emitter geometric configurations can account for the data, implying a more complex physical structure than the classical foreground ''dust screen'' assumption. However, most data points are bracketed by the foreground screen and a model where dust and emitters are uniformly mixed. When averaged over large (≳100-200 pc) scales, the extinction becomes consistent with a ''dust screen'', suggesting that other geometries tend to be restricted to more local scales. Moreover, the extinction in any region can be described by a combination of the foreground screen and the uniform mixture model with weights of 1/3 and 2/3 in the center (≲2 kpc), respectively, and 2/3 and 1/3 for the rest of the disk. This simple prescription significantly improves the accuracy of the dust extinction corrections and can be especially useful for pixel-based analyses of galaxies similar to M83.
Lay-Ekuakille, Aimé; Fabbiano, Laura; Vacca, Gaetano; Kitoko, Joël Kidiamboko; Kulapa, Patrice Bibala; Telesca, Vito
2018-06-04
Pipelines conveying fluids are considered strategic infrastructures to be protected and maintained. They generally serve for transportation of important fluids such as drinkable water, waste water, oil, gas, chemicals, etc. Monitoring and continuous testing, especially on-line, are necessary to assess the condition of pipelines. The paper presents findings related to a comparison between two spectral response algorithms based on the decimated signal diagonalization (DSD) and decimated Padé approximant (DPA) techniques that allow to one to process signals delivered by pressure sensors mounted on an experimental pipeline.
Directory of Open Access Journals (Sweden)
Aimé Lay-Ekuakille
2018-06-01
Full Text Available Pipelines conveying fluids are considered strategic infrastructures to be protected and maintained. They generally serve for transportation of important fluids such as drinkable water, waste water, oil, gas, chemicals, etc. Monitoring and continuous testing, especially on-line, are necessary to assess the condition of pipelines. The paper presents findings related to a comparison between two spectral response algorithms based on the decimated signal diagonalization (DSD and decimated Padé approximant (DPA techniques that allow to one to process signals delivered by pressure sensors mounted on an experimental pipeline.
LEARNING ONE-DIGIT DECIMAL NUMBERS BY MEASUREMENT AND GAME PREDICTING LENGTH
Directory of Open Access Journals (Sweden)
Puji Astuti
2014-01-01
Full Text Available This paper aims to describe how students develop understanding of one-digit decimals. To achieve the aim, Local Instruction Theory (LIT about the process of learning decimals and the means designed to support that learning are developed. Along with this idea, the framework of Realistic Mathematics Education (RME is proposed. Based on the aim, design research methodology is used. This paper discusses learning activities of three meetings from teaching experiment of the focus group students of the fourth grade elementary school in Surabaya: SDIT Al Ghilmani. The data indicated that the learning activities promoted the students’ understanding of one-digit decimal numbers.Keyword: measurement, decimal numbers, number line DOI: http://dx.doi.org/10.22342/jme.5.1.1447.35-46
An ERP Study of the Processing of Common and Decimal Fractions: How Different They Are
Zhang, Li; Wang, Qi; Lin, Chongde; Ding, Cody; Zhou, Xinlin
2013-01-01
This study explored event-related potential (ERP) correlates of common fractions (1/5) and decimal fractions (0.2). Thirteen subjects performed a numerical magnitude matching task under two conditions. In the common fraction condition, a nonsymbolic fraction was asked to be judged whether its magnitude matched the magnitude of a common fraction; in the decimal fraction condition, a nonsymbolic fraction was asked to be matched with a decimal fraction. Behavioral results showed significant main effects of condition and numerical distance, but no significant interaction of condition and numerical distance. Electrophysiological data showed that when nonsymbolic fractions were compared to common fractions, they displayed larger N1 and P3 amplitudes than when they were compared to decimal fractions. This finding suggested that the visual identification for nonsymbolic fractions was different under the two conditions, which was not due to perceptual differences but to task demands. For symbolic fractions, the condition effect was observed in the N1 and P3 components, revealing stimulus-specific visual identification processing. The effect of numerical distance as an index of numerical magnitude representation was observed in the P2, N3 and P3 components under the two conditions. However, the topography of the distance effect was different under the two conditions, suggesting stimulus specific semantic processing of common fractions and decimal fractions. PMID:23894491
An ERP study of the processing of common and decimal fractions: how different they are.
Directory of Open Access Journals (Sweden)
Li Zhang
Full Text Available This study explored event-related potential (ERP correlates of common fractions (1/5 and decimal fractions (0.2. Thirteen subjects performed a numerical magnitude matching task under two conditions. In the common fraction condition, a nonsymbolic fraction was asked to be judged whether its magnitude matched the magnitude of a common fraction; in the decimal fraction condition, a nonsymbolic fraction was asked to be matched with a decimal fraction. Behavioral results showed significant main effects of condition and numerical distance, but no significant interaction of condition and numerical distance. Electrophysiological data showed that when nonsymbolic fractions were compared to common fractions, they displayed larger N1 and P3 amplitudes than when they were compared to decimal fractions. This finding suggested that the visual identification for nonsymbolic fractions was different under the two conditions, which was not due to perceptual differences but to task demands. For symbolic fractions, the condition effect was observed in the N1 and P3 components, revealing stimulus-specific visual identification processing. The effect of numerical distance as an index of numerical magnitude representation was observed in the P2, N3 and P3 components under the two conditions. However, the topography of the distance effect was different under the two conditions, suggesting stimulus specific semantic processing of common fractions and decimal fractions.
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...
Habash, Jarjis; Boggon, Titus J; Raftery, James; Chayen, Naomi E; Zagalsky, Peter F; Helliwell, John R
2003-07-01
Models of apocrustacyanin C(1) were refined against X-ray data recorded on Bending Magnet 14 at the ESRF to resolutions of 1.85 and 2 A from a space-grown and an earth-grown crystal, respectively, both using vapour-diffusion crystal-growth geometry. The space crystals were grown in the APCF on the NASA Space Shuttle. The microgravity crystal growth showed a cyclic nature attributed to Marangoni convection, thus reducing the benefits of the microgravity environment, as reported previously [Chayen et al. (1996), Q. Rev. Biophys. 29, 227-278]. A subsequent mosaicity evaluation, also reported previously, showed only a partial improvement in the space-grown crystals over the earth-grown crystals [Snell et al. (1997), Acta Cryst. D53, 231-239], contrary to the case for lysozyme crystals grown in space with liquid-liquid diffusion, i.e. without any major motion during growth [Snell et al. (1995), Acta Cryst. D52, 1099-1102]. In this paper, apocrustacyanin C(1) electron-density maps from the two refined models are now compared. It is concluded that the electron-density maps of the protein and the bound waters are found to be better overall for the structures of apocrustacyanin C(1) studied from the space-grown crystal compared with those from the earth-grown crystal, even though both crystals were grown using vapour-diffusion crystal-growth geometry. The improved residues are on the surface of the protein, with two involved in or nearby crystal lattice-forming interactions, thus linking an improved crystal-growth mechanism to the molecular level. The structural comparison procedures developed should themselves be valuable for evaluating crystal-growth procedures in the future.
The analysis of decimation and interpolation in the linear canonical transform domain.
Xu, Shuiqing; Chai, Yi; Hu, Youqiang; Huang, Lei; Feng, Li
2016-01-01
Decimation and interpolation are the two basic building blocks in the multirate digital signal processing systems. As the linear canonical transform (LCT) has been shown to be a powerful tool for optics and signal processing, it is worthwhile and interesting to analyze the decimation and interpolation in the LCT domain. In this paper, the definition of equivalent filter in the LCT domain have been given at first. Then, by applying the definition, the direct implementation structure and polyphase networks for decimator and interpolator in the LCT domain have been proposed. Finally, the perfect reconstruction expressions for differential filters in the LCT domain have been presented as an application. The proposed theorems in this study are the bases for generalizations of the multirate signal processing in the LCT domain, which can advance the filter banks theorems in the LCT domain.
Properties of the Tent map for decimal fractions with fixed precision
Chetverikov, V. M.
2018-01-01
The one-dimensional discrete Tent map is a well-known example of a map whose fixed points are all unstable on the segment [0,1]. This map leads to the positivity of the Lyapunov exponent for the corresponding recurrent sequence. Therefore in a situation of general position, this sequence must demonstrate the properties of deterministic chaos. However if the first term of the recurrence sequence is taken as a decimal fraction with a fixed number “k” of digits after the decimal point and all calculations are carried out accurately, then the situation turns out to be completely different. In this case, first, the Tent map does not lead to an increase in significant digits in the terms of the sequence, and secondly, demonstrates the existence of a finite number of eventually periodic orbits, which are attractors for all other decimal numbers with the number of significant digits not exceeding “k”.
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
Mitchell, Joan S
2013-01-01
Can the Dewey Decimal System meet the needs of the rapidly changing information environment?Moving Beyond the Presentation Layer explores the Dewey Decimal System from a variety of perspectives, each of which peels away a bit of the ?presentation layer??the familiar linear notational sequence-to reveal the content and context offered by the DDS. Library professionals from around the word examine how the content and context offered by the DDS can evolve to meet the needs of the changing information environment, with a special focus on the impact of the Internet on current and future
Special geometry on the moduli space for the two-moduli non-Fermat Calabi–Yau
Directory of Open Access Journals (Sweden)
Konstantin Aleshkin
2018-01-01
Full Text Available We clarify the recently proposed method for computing a special Kähler metric on a Calabi–Yau complex structure moduli space using the fact that the moduli space is a subspace of a particular Frobenius manifold. We use this method to compute a previously unknown special Kähler metric in a two-moduli non-Fermat model.
Special geometry on the moduli space for the two-moduli non-Fermat Calabi-Yau
Aleshkin, Konstantin; Belavin, Alexander
2018-01-01
We clarify the recently proposed method for computing a special Kähler metric on a Calabi-Yau complex structure moduli space using the fact that the moduli space is a subspace of a particular Frobenius manifold. We use this method to compute a previously unknown special Kähler metric in a two-moduli non-Fermat model.
Landry, C. J.; Prodanovic, M.; Eichhubl, P.
2015-12-01
Mudrocks and shales are currently a significant source of natural gas and understanding the basic transport properties of these formations is critical to predicting long-term production, however, the nanoporous nature of mudrocks presents a unique challenge. Mudrock pores are predominantly in the range of 1-100 nm, and within this size range the flow of gas at reservoir conditions will fall within the slip-flow and early transition-flow regime (0.001 clays). Here we present a local effective viscosity lattice Boltzmann model (LEV-LBM) constructed for flow simulation in the slip- and early-transition flow regimes, adapted here for complex geometries. At the macroscopic scale the LEV-LBM is parameterized with local effective viscosities at each node to capture the variance of the mean free path of gas molecules in a bounded system. The LEV-LBM is first validated in simple tube geometries, where excellent agreement with linearized Boltzmann solutions is found for Knudsen numbers up to 1.0. The LEV-LBM is then employed to quantify the length effect on the apparent permeability of tubes, which suggests pore network modeling of flow in the slip and early-transition regime will result in overestimation unless the length effect is considered. Furthermore, the LEV-LBM is used to evaluate the predictive value of commonly measured pore geometry characteristics such as porosity, pore size distribution, and specific solid surface area for the calculation of permeability. We show that bundle of tubes models grossly overestimate apparent permeability, as well as underestimate the increase in apparent permeability with decreasing pressure as a result of excluding topology and pore shape from calculations.
International Nuclear Information System (INIS)
Fueloep, L.
1987-10-01
The forceless mechanics of Hertz is a reformulation of the classical mechanics in a curved configuration space. The relationship between the forceless mechanics and the general relativity theory which uses curved Riemann spaces as well is investigated on the simple example of the harmonic oscillator. The mathematical similarities and differences and the different interpretations of similar formulas are discussed. Some formal constants of the Hertz mechanics have got concrete physical meanings in the general relativity. (D.Gy.)
Directory of Open Access Journals (Sweden)
N.S. Khalifa
2013-12-01
Full Text Available In light of using laser power in space applications, the motivation of this paper is to use a space based solar pumped laser to produce a torque on LEO satellites of various shapes. It is assumed that there is a space station that fires laser beam toward the satellite so the beam spreading due to diffraction is considered to be the dominant effect on the laser beam propagation. The laser torque is calculated at the point of closest approach between the space station and some sun synchronous low Earth orbit cubesats. The numerical application shows that space based laser torque has a significant contribution on the LEO cubesats. It has a maximum value in the order of 10−8 Nm which is comparable with the residual magnetic moment. However, it has a minimum value in the order 10−11 Nm which is comparable with the aerodynamic and gravity gradient torque. Consequently, space based laser torque can be used as an active attitude control system.
Varma, Sashank; Karl, Stacy R.
2013-01-01
Much of the research on mathematical cognition has focused on the numbers 1, 2, 3, 4, 5, 6, 7, 8, and 9, with considerably less attention paid to more abstract number classes. The current research investigated how people understand decimal proportions--rational numbers between 0 and 1 expressed in the place-value symbol system. The results…
Durkin, Kelley; Shafto, Patrick
2016-01-01
The epistemic trust literature emphasizes that children's evaluations of informants' trustworthiness affects learning, but there is no evidence that epistemic trust affects learning in academic domains. The current study investigated how reliability affects decimal learning. Fourth and fifth graders (N = 122; M[subscript age] = 10.1 years)…
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
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
International Nuclear Information System (INIS)
Constantin, Magdalena; Perl, Joseph; LoSasso, Tom; Salop, Arthur; Whittum, David; Narula, Anisha; Svatos, Michelle; Keall, Paul J.
2011-01-01
Purpose: To create an accurate 6 MV Monte Carlo simulation phase space for the Varian TrueBeam treatment head geometry imported from cad (computer aided design) without adjusting the input electron phase space parameters. Methods: geant4 v4.9.2.p01 was employed to simulate the 6 MV beam treatment head geometry of the Varian TrueBeam linac. The electron tracks in the linear accelerator were simulated with Parmela, and the obtained electron phase space was used as an input to the Monte Carlo beam transport and dose calculations. The geometry components are tessellated solids included in geant4 as gdml (generalized dynamic markup language) files obtained via STEP (standard for the exchange of product) export from Pro/Engineering, followed by STEP import in Fastrad, a STEP-gdml converter. The linac has a compact treatment head and the small space between the shielding collimator and the divergent arc of the upper jaws forbids the implementation of a plane for storing the phase space. Instead, an IAEA (International Atomic Energy Agency) compliant phase space writer was implemented on a cylindrical surface. The simulation was run in parallel on a 1200 node Linux cluster. The 6 MV dose calculations were performed for field sizes varying from 4 x 4 to 40 x 40 cm 2 . The voxel size for the 60x60x40 cm 3 water phantom was 4x4x4 mm 3 . For the 10x10 cm 2 field, surface buildup calculations were performed using 4x4x2 mm 3 voxels within 20 mm of the surface. Results: For the depth dose curves, 98% of the calculated data points agree within 2% with the experimental measurements for depths between 2 and 40 cm. For depths between 5 and 30 cm, agreement within 1% is obtained for 99% (4x4), 95% (10x10), 94% (20x20 and 30x30), and 89% (40x40) of the data points, respectively. In the buildup region, the agreement is within 2%, except at 1 mm depth where the deviation is 5% for the 10x10 cm 2 open field. For the lateral dose profiles, within the field size for fields up to 30x30 cm 2
Energy Technology Data Exchange (ETDEWEB)
Constantin, Magdalena; Perl, Joseph; LoSasso, Tom; Salop, Arthur; Whittum, David; Narula, Anisha; Svatos, Michelle; Keall, Paul J. [Department of Radiation Oncology, Radiation Physics Division, Stanford University, Stanford, California 94304 (United States); SLAC National Accelerator Laboratory, Menlo Park, California 94025 (United States); Memorial Sloan-Kettering Cancer Center, New York 10021 (United States); Varian Medical Systems, Inc., Palo Alto, California 94304 (United States); Department of Radiation Oncology, Radiation Physics Division, Stanford University, Stanford, California 94304 (United States)
2011-07-15
Purpose: To create an accurate 6 MV Monte Carlo simulation phase space for the Varian TrueBeam treatment head geometry imported from cad (computer aided design) without adjusting the input electron phase space parameters. Methods: geant4 v4.9.2.p01 was employed to simulate the 6 MV beam treatment head geometry of the Varian TrueBeam linac. The electron tracks in the linear accelerator were simulated with Parmela, and the obtained electron phase space was used as an input to the Monte Carlo beam transport and dose calculations. The geometry components are tessellated solids included in geant4 as gdml (generalized dynamic markup language) files obtained via STEP (standard for the exchange of product) export from Pro/Engineering, followed by STEP import in Fastrad, a STEP-gdml converter. The linac has a compact treatment head and the small space between the shielding collimator and the divergent arc of the upper jaws forbids the implementation of a plane for storing the phase space. Instead, an IAEA (International Atomic Energy Agency) compliant phase space writer was implemented on a cylindrical surface. The simulation was run in parallel on a 1200 node Linux cluster. The 6 MV dose calculations were performed for field sizes varying from 4 x 4 to 40 x 40 cm{sup 2}. The voxel size for the 60x60x40 cm{sup 3} water phantom was 4x4x4 mm{sup 3}. For the 10x10 cm{sup 2} field, surface buildup calculations were performed using 4x4x2 mm{sup 3} voxels within 20 mm of the surface. Results: For the depth dose curves, 98% of the calculated data points agree within 2% with the experimental measurements for depths between 2 and 40 cm. For depths between 5 and 30 cm, agreement within 1% is obtained for 99% (4x4), 95% (10x10), 94% (20x20 and 30x30), and 89% (40x40) of the data points, respectively. In the buildup region, the agreement is within 2%, except at 1 mm depth where the deviation is 5% for the 10x10 cm{sup 2} open field. For the lateral dose profiles, within the field size
DeWolf, Melissa; Bassok, Miriam; Holyoak, Keith J
2015-02-01
The standard number system includes several distinct types of notations, which differ conceptually and afford different procedures. Among notations for rational numbers, the bipartite format of fractions (a/b) enables them to represent 2-dimensional relations between sets of discrete (i.e., countable) elements (e.g., red marbles/all marbles). In contrast, the format of decimals is inherently 1-dimensional, expressing a continuous-valued magnitude (i.e., proportion) but not a 2-dimensional relation between sets of countable elements. Experiment 1 showed that college students indeed view these 2-number notations as conceptually distinct. In a task that did not involve mathematical calculations, participants showed a strong preference to represent partitioned displays of discrete objects with fractions and partitioned displays of continuous masses with decimals. Experiment 2 provided evidence that people are better able to identify and evaluate ratio relationships using fractions than decimals, especially for discrete (or discretized) quantities. Experiments 3 and 4 found a similar pattern of performance for a more complex analogical reasoning task. When solving relational reasoning problems based on discrete or discretized quantities, fractions yielded greater accuracy than decimals; in contrast, when quantities were continuous, accuracy was lower for both symbolic notations. Whereas previous research has established that decimals are more effective than fractions in supporting magnitude comparisons, the present study reveals that fractions are relatively advantageous in supporting relational reasoning with discrete (or discretized) concepts. These findings provide an explanation for the effectiveness of natural frequency formats in supporting some types of reasoning, and have implications for teaching of rational numbers.
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
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
Effects of the mean-field dynamics and the phase-space geometry on the cluster formation
International Nuclear Information System (INIS)
Basrak, Z.; Eudes, P.; Abgrall, P.; Haddad, F.; Sebille, F.
1997-01-01
A model allowing to simulate the production of clusters is developed and applied to heavy-ion reactions at intermediate energies. The model investigates the geometrical properties of the dynamically generated one-body phase space. The collision process is entirely governed by the Landau-Vlasov model, which provides the time evolution of the one-body phase-space distribution. Particles emitted during successive time intervals of the dynamics are gathered together into subensembles to which a clusterization procedure is applied. Comparison with the experimental data for the Ar(65 MeV/nucleon) + Al reaction shows that the average behaviour of particle-dependent global observables is correctly reproduced within this framework. These results point out that the studied global properties of heavy-ion collisions greatly rely on the dynamical effects of the primary non-steady stage of the nuclear reaction. (orig.)
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
Punjabi, Alkesh; Ali, Halima
2008-12-01
A new approach to integration of magnetic field lines in divertor tokamaks is proposed. In this approach, an analytic equilibrium generating function (EGF) is constructed in natural canonical coordinates (ψ,θ) from experimental data from a Grad-Shafranov equilibrium solver for a tokamak. ψ is the toroidal magnetic flux and θ is the poloidal angle. Natural canonical coordinates (ψ,θ,φ) can be transformed to physical position (R,Z,φ) using a canonical transformation. (R,Z,φ) are cylindrical coordinates. Another canonical transformation is used to construct a symplectic map for integration of magnetic field lines. Trajectories of field lines calculated from this symplectic map in natural canonical coordinates can be transformed to trajectories in real physical space. Unlike in magnetic coordinates [O. Kerwin, A. Punjabi, and H. Ali, Phys. Plasmas 15, 072504 (2008)], the symplectic map in natural canonical coordinates can integrate trajectories across the separatrix surface, and at the same time, give trajectories in physical space. Unlike symplectic maps in physical coordinates (x,y) or (R,Z), the continuous analog of a symplectic map in natural canonical coordinates does not distort trajectories in toroidal planes intervening the discrete map. This approach is applied to the DIII-D tokamak [J. L. Luxon and L. E. Davis, Fusion Technol. 8, 441 (1985)]. The EGF for the DIII-D gives quite an accurate representation of equilibrium magnetic surfaces close to the separatrix surface. This new approach is applied to demonstrate the sensitivity of stochastic broadening using a set of perturbations that generically approximate the size of the field errors and statistical topological noise expected in a poloidally diverted tokamak. Plans for future application of this approach are discussed.
International Nuclear Information System (INIS)
Punjabi, Alkesh; Ali, Halima
2008-01-01
A new approach to integration of magnetic field lines in divertor tokamaks is proposed. In this approach, an analytic equilibrium generating function (EGF) is constructed in natural canonical coordinates (ψ,θ) from experimental data from a Grad-Shafranov equilibrium solver for a tokamak. ψ is the toroidal magnetic flux and θ is the poloidal angle. Natural canonical coordinates (ψ,θ,φ) can be transformed to physical position (R,Z,φ) using a canonical transformation. (R,Z,φ) are cylindrical coordinates. Another canonical transformation is used to construct a symplectic map for integration of magnetic field lines. Trajectories of field lines calculated from this symplectic map in natural canonical coordinates can be transformed to trajectories in real physical space. Unlike in magnetic coordinates [O. Kerwin, A. Punjabi, and H. Ali, Phys. Plasmas 15, 072504 (2008)], the symplectic map in natural canonical coordinates can integrate trajectories across the separatrix surface, and at the same time, give trajectories in physical space. Unlike symplectic maps in physical coordinates (x,y) or (R,Z), the continuous analog of a symplectic map in natural canonical coordinates does not distort trajectories in toroidal planes intervening the discrete map. This approach is applied to the DIII-D tokamak [J. L. Luxon and L. E. Davis, Fusion Technol. 8, 441 (1985)]. The EGF for the DIII-D gives quite an accurate representation of equilibrium magnetic surfaces close to the separatrix surface. This new approach is applied to demonstrate the sensitivity of stochastic broadening using a set of perturbations that generically approximate the size of the field errors and statistical topological noise expected in a poloidally diverted tokamak. Plans for future application of this approach are discussed.
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...
Liu, Xiaoyong; Lu, Pei; Shao, Jianxin; Cao, Haibin; Zhu, Zhenmin
2017-10-01
In this paper, an information hiding method using decimal expansion of irrational numbers to generate random phase mask is proposed. Firstly, the decimal expansion parts of irrational numbers generate pseudo-random sequences using a new coding schemed, the irrational number and start and end bit numbers were used as keys in image information hiding. Secondly, we apply the coding schemed to the double phase encoding system, the pseudo-random sequences are taken to generate random phase masks. The mean square error is used to calculate the quality of the recovered image information. Finally, two tests had been carried out to verify the security of our method; the experimental results demonstrate that the cipher image has such features, strong robustness, key sensitivity, and resistance to brute force attack.
Amazing 7-day, super-simple, scripted guide to teaching or learning decimals
Kolby, Jeff
2014-01-01
Welcome to The Amazing 7-Day Super-Simple, Scripted Guide to Teaching or Learning Decimals. I have attempted to do just what the title says: make learning decimals super simple. I have also attempted to make it fun and even ear-catching. The reason for this is not that I am a frustrated stand-up comic, but because in my fourteen years of teaching the subject, I have come to realize that my jokes, even the bad ones, have a crazy way of sticking in my students' heads. And should I use a joke (even a bad one) repetitively, the associations become embedded in their brains, many times to their chag
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.
, N. Lajçi; , X. Lajçi; , B. Baruti
2016-01-01
Disinfection operation is of great importance within the beer processing industry for beer safety reasons. Microbiological risk management is essential in the production of high-quality beer since quality defects may lead to substantial economic losses. The objective of this research was to investigate the effect of commercial peracetic acid (PAA) concentration for disinfection and the resistance of microorganisms in beer based on the decimal reduction time (D-value), and reduction 6-log10 of...
Significant decimal digits for energy representation on short-word computers
International Nuclear Information System (INIS)
Sartori, E.
1989-01-01
The general belief that single precision floating point numbers have always at least seven significant decimal digits on short word computers such as IBM is erroneous. Seven significant digits are required however for representing the energy variable in nuclear cross-section data sets containing sharp p-wave resonances at 0 Kelvin. It is suggested that either the energy variable is stored in double precision or that cross-section resonances are reconstructed to room temperature or higher on short word computers
Renormalization-group decimation technique for spectra, wave-functions and density of states
International Nuclear Information System (INIS)
Wiecko, C.; Roman, E.
1983-09-01
The Renormalization Group decimation technique is very useful for problems described by 1-d nearest neighbour tight-binding model with or without translational invariance. We show how spectra, wave-functions and density of states can be calculated with little numerical work from the renormalized coefficients upon iteration. The results of this new procedure are verified using the model of Soukoulis and Economou. (author)
Cenek, Martin; Dahl, Spencer K.
2016-11-01
Systems with non-linear dynamics frequently exhibit emergent system behavior, which is important to find and specify rigorously to understand the nature of the modeled phenomena. Through this analysis, it is possible to characterize phenomena such as how systems assemble or dissipate and what behaviors lead to specific final system configurations. Agent Based Modeling (ABM) is one of the modeling techniques used to study the interaction dynamics between a system's agents and its environment. Although the methodology of ABM construction is well understood and practiced, there are no computational, statistically rigorous, comprehensive tools to evaluate an ABM's execution. Often, a human has to observe an ABM's execution in order to analyze how the ABM functions, identify the emergent processes in the agent's behavior, or study a parameter's effect on the system-wide behavior. This paper introduces a new statistically based framework to automatically analyze agents' behavior, identify common system-wide patterns, and record the probability of agents changing their behavior from one pattern of behavior to another. We use network based techniques to analyze the landscape of common behaviors in an ABM's execution. Finally, we test the proposed framework with a series of experiments featuring increasingly emergent behavior. The proposed framework will allow computational comparison of ABM executions, exploration of a model's parameter configuration space, and identification of the behavioral building blocks in a model's dynamics.
DeWolf, Melissa; Bassok, Miriam; Holyoak, Keith J
2015-05-01
To understand the development of mathematical cognition and to improve instructional practices, it is critical to identify early predictors of difficulty in learning complex mathematical topics such as algebra. Recent work has shown that performance with fractions on a number line estimation task predicts algebra performance, whereas performance with whole numbers on similar estimation tasks does not. We sought to distinguish more specific precursors to algebra by measuring multiple aspects of knowledge about rational numbers. Because fractions are the first numbers that are relational expressions to which students are exposed, we investigated how understanding the relational bipartite format (a/b) of fractions might connect to later algebra performance. We presented middle school students with a battery of tests designed to measure relational understanding of fractions, procedural knowledge of fractions, and placement of fractions, decimals, and whole numbers onto number lines as well as algebra performance. Multiple regression analyses revealed that the best predictors of algebra performance were measures of relational fraction knowledge and ability to place decimals (not fractions or whole numbers) onto number lines. These findings suggest that at least two specific components of knowledge about rational numbers--relational understanding (best captured by fractions) and grasp of unidimensional magnitude (best captured by decimals)--can be linked to early success with algebraic expressions. Copyright © 2015 Elsevier Inc. All rights reserved.
Rational-number comparison across notation: Fractions, decimals, and whole numbers.
Hurst, Michelle; Cordes, Sara
2016-02-01
Although fractions, decimals, and whole numbers can be used to represent the same rational-number values, it is unclear whether adults conceive of these rational-number magnitudes as lying along the same ordered mental continuum. In the current study, we investigated whether adults' processing of rational-number magnitudes in fraction, decimal, and whole-number notation show systematic ratio-dependent responding characteristic of an integrated mental continuum. Both reaction time (RT) and eye-tracking data from a number-magnitude comparison task revealed ratio-dependent performance when adults compared the relative magnitudes of rational numbers, both within the same notation (e.g., fractions vs. fractions) and across different notations (e.g., fractions vs. decimals), pointing to an integrated mental continuum for rational numbers across notation types. In addition, eye-tracking analyses provided evidence of an implicit whole-number bias when we compared values in fraction notation, and individual differences in this whole-number bias were related to the individual's performance on a fraction arithmetic task. Implications of our results for both cognitive development research and math education are discussed. (PsycINFO Database Record (c) 2016 APA, all rights reserved).
Design and Implementation of Decimation Filter for 13-bit Sigma-Delta ADC Based on FPGA
Directory of Open Access Journals (Sweden)
Khalid Khaleel Mohammed
2016-10-01
Full Text Available A 13 bit Sigma-Delta ADC for a signal band of 40K Hz is designed in MATLAB Simulink and then implemented using Xilinx system generator tool. The first order Sigma-Delta modulator is designed to work at a signal band of 40 KHz at an oversampling ratio (OSR of 256 with a sampling frequency of 20.48 MHz. The proposed decimation filter design is consists of a second order Cascaded Integrator Comb filter (CIC followed by two finite impulse response (FIR filters. This architecture reduces the need for multiplication which is need very large area. This architecture implements a decimation ratio of 256 and allows a maximum resolution of 13 bits in the output of the filter. The decimation filter was designed and tested in Xilinx system generator tool which reduces the design cycle by directly generating efficient VHDL code. The results obtained show that the overall Sigma-Delta ADC is able to achieve an ENOB (Effective Number Of Bit of 13.71 bits and SNR of 84.3 dB
Varma, Sashank; Karl, Stacy R
2013-05-01
Much of the research on mathematical cognition has focused on the numbers 1, 2, 3, 4, 5, 6, 7, 8, and 9, with considerably less attention paid to more abstract number classes. The current research investigated how people understand decimal proportions--rational numbers between 0 and 1 expressed in the place-value symbol system. The results demonstrate that proportions are represented as discrete structures and processed in parallel. There was a semantic interference effect: When understanding a proportion expression (e.g., "0.29"), both the correct proportion referent (e.g., 0.29) and the incorrect natural number referent (e.g., 29) corresponding to the visually similar natural number expression (e.g., "29") are accessed in parallel, and when these referents lead to conflicting judgments, performance slows. There was also a syntactic interference effect, generalizing the unit-decade compatibility effect for natural numbers: When comparing two proportions, their tenths and hundredths components are processed in parallel, and when the different components lead to conflicting judgments, performance slows. The results also reveal that zero decimals--proportions ending in zero--serve multiple cognitive functions, including eliminating semantic interference and speeding processing. The current research also extends the distance, semantic congruence, and SNARC effects from natural numbers to decimal proportions. These findings inform how people understand the place-value symbol system, and the mental implementation of mathematical symbol systems more generally. Copyright © 2013 Elsevier Inc. All rights reserved.
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...
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…
Principios filosóficos en el desarrollo y funcionamiento de la Clasificación Decimal Dewey
Moyano-Grimaldo, Wilmer Arturo
2017-01-01
Objective. The philosophical foundations that support the use and development of the Dewey Decimal Classification (DDC) were explored. Design/Methodology/Approach. Different primary and secondary sources were reviewed to analyze the theories and ideas that founded the DDC. Results/Discussion. The DDC is a system that bases its scheme on the ideas put forward by Bacon and Hegel. However, its operation is due to what has been called “Decimal theory”. Conclusions. The DDC is a system of library ...
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)
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,
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.
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
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...
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...
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...
Hurst, Michelle A; Cordes, Sara
2018-04-01
Fraction and decimal concepts are notoriously difficult for children to learn yet are a major component of elementary and middle school math curriculum and an important prerequisite for higher order mathematics (i.e., algebra). Thus, recently there has been a push to understand how children think about rational number magnitudes in order to understand how to promote rational number understanding. However, prior work investigating these questions has focused almost exclusively on fraction notation, overlooking the open questions of how children integrate rational number magnitudes presented in distinct notations (i.e., fractions, decimals, and whole numbers) and whether understanding of these distinct notations may independently contribute to pre-algebra ability. In the current study, we investigated rational number magnitude and arithmetic performance in both fraction and decimal notation in fourth- to seventh-grade children. We then explored how these measures of rational number ability predicted pre-algebra ability. Results reveal that children do represent the magnitudes of fractions and decimals as falling within a single numerical continuum and that, despite greater experience with fraction notation, children are more accurate when processing decimal notation than when processing fraction notation. Regression analyses revealed that both magnitude and arithmetic performance predicted pre-algebra ability, but magnitude understanding may be particularly unique and depend on notation. The educational implications of differences between children in the current study and previous work with adults are discussed. Copyright © 2017 Elsevier Inc. All rights reserved.
Area efficient decimation filter based on merged delay transformation for wireless applications
International Nuclear Information System (INIS)
Rashid, U.; Siddiq, F.; Muhammad, T.; Jamal, H.
2013-01-01
Expected by 2014 is the 4G standard for cellular wireless communications, which will improve bandwidth, connectivity and roaming for mobile and stationary devices, 4G and other wireless systems are currently hot topics of research and development in the communication field. In wireless technologies like Global System for Mobile (GSM), Digital Enhanced Cordless Telecommunications (DECT) and Wi-Fi, decimation filters are essential part of transceivers being used. This paper describes a decimation filter which is efficient in terms of both the power consumption and the area used. The architecture is based upon Merged Delay Transformation (MDT). The existing Merged Delay Transformed Infinite Impulse Response (IIR) architecture is power efficient but requires larger area. The proposed and existing filters were implemented on Field-Programmable Gate Array (FPGA). The computational cost of the proposed filter is reduced to (3N/2 + 1) and M-1 times reduction in the number of multipliers in comparison to the existing FIR filter is achieved. The power consumption and speed remain nearly the same. (author)
Directory of Open Access Journals (Sweden)
Stefan eHuber
2014-04-01
Full Text Available Decimal fractions comply with the base-10 notational system of natural Arabic numbers. Nevertheless, recent research suggested that decimal fractions may be represented differently than natural numbers because two number processing effects (i.e., semantic interference and compatibility effects differed in their size between decimal fractions and natural numbers. In the present study, we examined whether these differences indeed indicate that decimal fractions are represented differently from natural numbers. Therefore, we provided an alternative explanation for the semantic congruity effect, namely a string length congruity effect. Moreover, we suggest that the smaller compatibility effect for decimal fractions compared to natural numbers was driven by differences in processing strategy (sequential vs. parallel.To evaluate this claim, we manipulated the tenth and hundredth digits in a magnitude comparison task with participants' eye movements recorded, while the unit digits remained identical. In addition, we evaluated whether our empirical findings could be simulated by an extended version of our computational model originally developed to simulate magnitude comparisons of two-digit natural numbers. In the eye-tracking study, we found evidence that participants processed decimal fractions more sequentially than natural numbers because of the identical leading digit. Importantly, our model was able to account for the smaller compatibility effect found for decimal fractions. Moreover, string length congruity was an alternative account for the prolonged reaction times for incongruent decimal pairs. Consequently, we suggest that representations of natural numbers and decimal fractions do not differ.
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
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.)
Lyusternik, L A
1965-01-01
Ten-Decimal Tables of the Logarithms of Complex Numbers and for the Transformation from Cartesian to Polar Coordinates contains Tables of mathematical functions up to ten-decimal value. These tables are compiled in the Department for Approximate Computations of the Institute of Exact Mechanics and Computational Methods of the U.S.S.R. Academy of Sciences. The computations are carried out by this department in conjunction with the Computational-Experimental Laboratory of the Institute.This book will be of value to mathematicians and researchers.
An evaluation of different delivery methods for teaching binary, hex and decimal conversion
Directory of Open Access Journals (Sweden)
Daniel Kempthorne
Full Text Available The ability to convert between binary, hexadecimal, and decimal numbering systems is a fundamental skill commonly taught to tertiary-level computing and ICT students. This paper presents the results of a multiple year investigation into the application of differing approaches for the teaching and learning of these skills. Specifically, the study compares traditional lectures, games, and group activities with student levels of academic achievement. Student prior experience with numbering system conversion is also analysed. The study reveals that, overall, the game-based approach resulted in the highest average test scores; however, when students were divided into groups with and without prior experience, the students with prior experience performed better with a traditional lecture approach.
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...
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...
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
Rimbey, Kimberly
2007-01-01
Created by teachers for teachers, the Math Academy tools and activities included in this booklet were designed to create hands-on activities and a fun learning environment for the teaching of mathematics to the students. This booklet contains the "Math Academy--Dining Out! Explorations in Fractions, Decimals, and Percents," which teachers can use…
Markey, Karen; Demeyer, Anh N.
This research project focuses on the implementation and testing of the Dewey Decimal Classification (DDC) system as an online searcher's tool for subject access, browsing, and display in an online catalog. The research project comprises 12 activities. The three interim reports in this document cover the first seven of these activities: (1) obtain…
Argyres, Philip C.; Lotito, Matteo; Lü, Yongchao; Martone, Mario
2018-02-01
This is the second in a series of three papers on systematic analysis of rank 1 Coulomb branch geometries of four dimensional N = 2 SCFTs. In [1] we developed a strategy for classifying physical rank-1 CB geometries of N = 2 SCFTs. Here we show how to carry out this strategy computationally to construct the Seiberg-Witten curves and one-forms for all the rank-1 SCFTs. Explicit expressions are given for all 28 cases, with the exception of the N f =4 su(2) gauge theory and the E n SCFTs which were constructed in [2, 3] and [4, 5].
Walsh, Edward T
2014-01-01
This introductory text is designed to help undergraduate students develop a solid foundation in geometry. Early chapters progress slowly, cultivating the necessary understanding and self-confidence for the more rapid development that follows. The extensive treatment can be easily adapted to accommodate shorter courses. Starting with the language of mathematics as expressed in the algebra of logic and sets, the text covers geometric sets of points, separation and angles, triangles, parallel lines, similarity, polygons and area, circles, space geometry, and coordinate geometry. Each chapter incl
Differential geometry 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.
International Nuclear Information System (INIS)
Hook, D W
2008-01-01
A geometric framework for quantum mechanics arose during the mid 1970s when authors such as Cantoni explored the notion of generalized transition probabilities, and Kibble promoted the idea that the space of pure quantum states provides a natural quantum mechanical analogue for classical phase space. This central idea can be seen easily since the projection of Schroedinger's equation from a Hilbert space into the space of pure spaces is a set of Hamilton's equations. Over the intervening years considerable work has been carried out by a variety of authors and a mature description of quantum mechanics in geometric terms has emerged with many applications. This current offering would seem ideally placed to review the last thirty years of progress and relate this to the most recent work in quantum entanglement. Bengtsson and Zyczkowski's beautifully illustrated volume, Geometry of Quantum States (referred to as GQS from now on) attempts to cover considerable ground in its 466 pages. Its topics range from colour theory in Chapter 1 to quantum entanglement in Chapter 15-to say that this is a whirlwind tour is, perhaps, no understatement. The use of the work 'introduction' in the subtitle of GQS, might suggest to the reader that this work be viewed as a textbook and I think that this interpretation would be incorrect. The authors have chosen to present a survey of different topics with the specific aim to introduce entanglement in geometric terms-the book is not intended as a pedagogical introduction to the geometric approach to quantum mechanics. Each of the fifteen chapters is a short, and mostly self-contained, essay on a particular aspect or application of geometry in the context of quantum mechanics with entanglement being addressed specifically in the final chapter. The chapters fall into three classifications: those concerned with the mathematical background, those which discuss quantum theory and the foundational aspects of the geometric framework, and
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...
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.
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...
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
Analogy and Dynamic Geometry System Used to Introduce Three-Dimensional Geometry
Mammana, M. F.; Micale, B.; Pennisi, M.
2012-01-01
We present a sequence of classroom activities on Euclidean geometry, both plane and space geometry, used to make three dimensional geometry more catchy and simple. The activity consists of a guided research activity that leads the students to discover unexpected properties of two apparently distant geometrical entities, quadrilaterals and…
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.
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)
Choice of sterilizing/disinfecting agent: determination of the Decimal ReductionTime (D-Value
Directory of Open Access Journals (Sweden)
Priscila Gava Mazzola
2009-12-01
Full Text Available Efforts to diminish the transmission of infections include programs in which disinfectants play a crucial role. Hospital surfaces and medical devices are potential sources of cross contamination, and each instrument, surface or area in a health care unit can be responsible for spread of infection. The decimal reduction time was used to study and compare the behavior of selected strains of microorganisms. The highest D-values for various bacteria were obtained for the following solutions: (i 0.1% sodium dichloroisocyanurate (pH 7.0 - E. coli and A. calcoaceticus (D = 5.9 min; (ii sodium hypochlorite (pH 7.0 at 0.025% for B. stearothermophilus (D = 24 min, E. coli and E. cloacae (D = 7.5 min; at 0.05% for B. stearothermophilus (D = 9.4 min and E. coli (D = 6.1 min. The suspension studies were an indication of the disinfectant efficacy on a surface. The data in this study reflect the formulations used and may vary from product to product. The expected effectiveness from the studied formulations shows that the tested agents can be recommended for surface disinfection as stated in present guidelines and emphasize the importance and need to develop routine and novel programs to evaluate product utility.Esforços para diminuir o risco de transmissões de infecções incluem programas nos quais os desinfetantes desempenham papel crucial. As superfícies de materiais médico-hospitalares, se não estiverem diretamente ligados à transmissão de doenças, podem contribuir, potencialmente, para uma contaminação cruzada secundária. Cada instrumento ou superfície do estabelecimento do ambiente de saúde que entra em contato com um paciente é um disseminador potencial de infecção. Para estudar e comparar o comportamento dos microrganismos selecionados foram realizados ensaios de determinação do tempo de redução decimal. Os maiores valores D determinados, foram: (i 0,1% dicloroisocianurato de sódio (NaDCC (pH 7.0 - E. coli e A. calcoaceticus (D = 5
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)
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
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
Curvature tensor copies in affine geometry
International Nuclear Information System (INIS)
Srivastava, P.P.
1981-01-01
The sets of space-time and spin-connections which give rise to the same curvature tensor are constructed. The corresponding geometries are compared. Results are illustrated by an explicit calculation and comment on the copies in Einstein-Cartan and Weyl-Cartan geometries. (Author) [pt
Quantification of variability in bedform geometry
van der Mark, C.F.; Blom, Astrid; Hulscher, Suzanne J.M.H.
2008-01-01
We analyze the variability in bedform geometry in laboratory and field studies. Even under controlled steady flow conditions in laboratory flumes, bedforms are irregular in size, shape, and spacing, also in case of well-sorted sediment. Our purpose is to quantify the variability in bedform geometry.
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)
Crowe, Benjamin J. III
2009-01-01
Nucleon-deuteron (Nd) breakup is an important tool for obtaining a better understanding of three-nucleon (3N) dynamics and for developing meson exchange descriptions of nuclear systems. The kinematics of the nd breakup reaction enable observables to be studied in a variety of exit-channel configurations that show sensitivity to realistic nucleon-nucleon (NN) potential models and three-nucleon force (3NF) models. Rigorous 3N calculations give very good descriptions of most 3N reaction data. However, there are still some serious discrepancies between data and theory. The largest discrepancy observed between theory and data for nd breakup is for the cross section for the space-star configuration. This discrepancy is known as the 'Space Star Anomaly'. Several experimental groups have obtained results consistent with the 'Space Star Anomaly', but it is important to note that they all used essentially the same experimental setup and so their experimental results are subject to the same systematic errors. We propose to measure the space-star cross-section at the Triangle Universities Nuclear Laboratory (TUNL) using an experimental technique that is significantly different from the one used in previous breakup experiments. This technique has been used by a research group from the University of Bonn to measure the neutron-neutron scattering length. There are three possible scenarios for the outcome of this work: (1) the new data are consistent with previous measurements; (2) the new data are not in agreement with previous measurements, but are in agreement with theory; and (3) the new data are not in agreement with either theory or previous measurements. Any one of the three scenarios will provide valuable insight on the Space Star Anomaly.
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.
Directory of Open Access Journals (Sweden)
Mohammad Hossein Moazzeni
2016-07-01
Full Text Available Daylight can be considered as one of the most important principles of sustainable architecture. It is unfortunate that this is neglected by designers in Tehran, a city that benefits from a significant amount of daylight and many clear sunny days during the year. Using a daylight controller system increases space natural light quality and decreases building lighting consumption by 60%. It also affects building thermal behavior, because most of them operate as shading. The light shelf is one of the passive systems for controlling daylight, mostly used with shading and installed in the upper half of the windows above eye level. The influence of light shelf parameters, such as its dimensions, shelf rotation angle and orientation on daylight efficiency and visual comfort in educational spaces is investigated in this article. Daylight simulation software and annual analysis based on climate information during space occupation hours were used. The results show that light shelf dimensions, as well as different orientations, especially in southern part, are influential in the distribution of natural light and visual comfort. At the southern orientation, increased light shelf dimensions result in an increase of the area of the work plane with suitable daylight levels by 2%–40% and a significant decrease in disturbing and intolerable glare hours.
Mazzola, Priscila Gava; Penna, Thereza Christina Vessoni; da S Martins, Alzira M
2003-01-01
Background Prior to the selection of disinfectants for low, intermediate and high (sterilizing) levels, the decimal reduction time, D-value, for the most common and persistent bacteria identified at a health care facility should be determined. Methods The D-value was determined by inoculating 100 mL of disinfecting solution with 1 mL of a bacterial suspension (104 – 105 CFU/mL for vegetative and spore forms). At regular intervals, 1 mL aliquots of this mixture were transferred to 8 mL of growth media containing a neutralizing agent, and incubated at optimal conditions for the microorganism. Results The highest D-values for various bacteria were determined for the following solutions: (i) 0.1% sodium dichloroisocyanurate (pH 7.0) – E. coli and A. calcoaceticus (D = 5.9 min); (ii) sodium hypochlorite (pH 7.0) at 0.025% for B. stearothermophilus (D = 24 min), E. coli and E. cloacae (D = 7.5 min); at 0.05% for B. stearothermophilus (D = 9.4 min) and E. coli (D = 6.1 min) and 0.1% for B. stearothermophilus (D = 3.5 min) and B. subtilis (D = 3.2 min); (iii) 2.0% glutaraldehyde (pH 7.4) – B. stearothermophilus, B. subtilis (D = 25 min) and E. coli (D = 7.1 min); (iv) 0.5% formaldehyde (pH 6.5) – B. subtilis (D = 11.8 min), B. stearothermophilus (D = 10.9 min) and A. calcoaceticus (D = 5.2 min); (v) 2.0% chlorhexidine (pH 6.2) – B. stearothermophilus (D = 9.1 min), and at 0.4% for E. cloacae (D = 8.3 min); (vi) 1.0% Minncare® (peracetic acid and hydrogen peroxide, pH 2.3) – B. stearothermophilus (D = 9.1 min) and E. coli (D = 6.7 min). Conclusions The suspension studies were an indication of the disinfectant efficacy on a surface. The data in this study reflect the formulations used and may vary from product to product. The expected effectiveness from the studied formulations showed that the tested agents can be recommended for surface disinfection as stated in present guidelines and emphasizes the importance and need to develop routine and novel programs to
Directory of Open Access Journals (Sweden)
da S Martins Alzira M
2003-10-01
Full Text Available Abstract Background Prior to the selection of disinfectants for low, intermediate and high (sterilizing levels, the decimal reduction time, D-value, for the most common and persistent bacteria identified at a health care facility should be determined. Methods The D-value was determined by inoculating 100 mL of disinfecting solution with 1 mL of a bacterial suspension (104 – 105 CFU/mL for vegetative and spore forms. At regular intervals, 1 mL aliquots of this mixture were transferred to 8 mL of growth media containing a neutralizing agent, and incubated at optimal conditions for the microorganism. Results The highest D-values for various bacteria were determined for the following solutions: (i 0.1% sodium dichloroisocyanurate (pH 7.0 – E. coli and A. calcoaceticus (D = 5.9 min; (ii sodium hypochlorite (pH 7.0 at 0.025% for B. stearothermophilus (D = 24 min, E. coli and E. cloacae (D = 7.5 min; at 0.05% for B. stearothermophilus (D = 9.4 min and E. coli (D = 6.1 min and 0.1% for B. stearothermophilus (D = 3.5 min and B. subtilis (D = 3.2 min; (iii 2.0% glutaraldehyde (pH 7.4 – B. stearothermophilus, B. subtilis (D = 25 min and E. coli (D = 7.1 min; (iv 0.5% formaldehyde (pH 6.5 – B. subtilis (D = 11.8 min, B. stearothermophilus (D = 10.9 min and A. calcoaceticus (D = 5.2 min; (v 2.0% chlorhexidine (pH 6.2 – B. stearothermophilus (D = 9.1 min, and at 0.4% for E. cloacae (D = 8.3 min; (vi 1.0% Minncare® (peracetic acid and hydrogen peroxide, pH 2.3 – B. stearothermophilus (D = 9.1 min and E. coli (D = 6.7 min. Conclusions The suspension studies were an indication of the disinfectant efficacy on a surface. The data in this study reflect the formulations used and may vary from product to product. The expected effectiveness from the studied formulations showed that the tested agents can be recommended for surface disinfection as stated in present guidelines and emphasizes the importance and need to develop routine and novel programs to
Noncommutative Geometry, Quantum Fields and Motives
Connes, Alain
2007-01-01
The unifying theme of this book is the interplay among noncommutative geometry, physics, and number theory. The two main objects of investigation are spaces where both the noncommutative and the motivic aspects come to play a role: space-time, where the guiding principle is the problem of developing a quantum theory of gravity, and the space of primes, where one can regard the Riemann Hypothesis as a long-standing problem motivating the development of new geometric tools. The book stresses the relevance of noncommutative geometry in dealing with these two spaces. The first part of the book dea
Special metrics and group actions in geometry
Fino, Anna; Musso, Emilio; Podestà, Fabio; Vezzoni, Luigi
2017-01-01
The volume is a follow-up to the INdAM meeting “Special metrics and quaternionic geometry” held in Rome in November 2015. It offers a panoramic view of a selection of cutting-edge topics in differential geometry, including 4-manifolds, quaternionic and octonionic geometry, twistor spaces, harmonic maps, spinors, complex and conformal geometry, homogeneous spaces and nilmanifolds, special geometries in dimensions 5–8, gauge theory, symplectic and toric manifolds, exceptional holonomy and integrable systems. The workshop was held in honor of Simon Salamon, a leading international scholar at the forefront of academic research who has made significant contributions to all these subjects. The articles published here represent a compelling testimony to Salamon’s profound and longstanding impact on the mathematical community. Target readership includes graduate students and researchers working in Riemannian and complex geometry, Lie theory and mathematical physics.
Information geometry near randomness and near independence
Arwini, Khadiga A
2008-01-01
This volume will be useful to practising scientists and students working in the application of statistical models to real materials or to processes with perturbations of a Poisson process, a uniform process, or a state of independence for a bivariate process. We use information geometry to provide a common differential geometric framework for a wide range of illustrative applications including amino acid sequence spacings in protein chains, cryptology studies, clustering of communications and galaxies, cosmological voids, coupled spatial statistics in stochastic fibre networks and stochastic porous media, quantum chaology. Introduction sections are provided to mathematical statistics, differential geometry and the information geometry of spaces of probability density functions.
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...
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 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
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
Directory of Open Access Journals (Sweden)
Koh Jinseok
2006-01-01
Full Text Available We present a discrete-time second-order multibit sigma-delta ADC that filters and decimates by two the input data samples. At the same time it provides gain control function in its input sampling stage. A 4-tap FIR switched capacitor (SC architecture was chosen for antialiasing filtering. The decimation-by-two function is realized using divided-by-two clock signals in the antialiasing filter. Antialiasing, gain control, and sampling functions are merged in the sampling network using SC techniques. This compact architecture allows operating the preceding blocks at twice the ADC's clock frequency, thus improving the noise performance of the wireless receiver channel and relaxing settling requirements of the analog building blocks. The presented approach has been validated and incorporated in a commercial single-chip Bluetooth radio realized in a 1.5 V 130 nm digital CMOS process. The measured antialiasing filtering shows better than 75 dB suppression at the folding frequency band edge. A 67 dB dynamic range was measured with a sampling frequency of 37.5MHz.
On relational nature of geometry of microphysics
International Nuclear Information System (INIS)
Chylinski, Z.
1985-11-01
A relativity principle and a curiosity of Galilei space-time is described. An internal space-time of R 4 relation is presented. Lorentz limit of R 4 geometry and a field theory is given. The sources of the effects of R 4 hypothesis are characterized. The completeness of quantum description is discussed. 32 refs. (A.S.)
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.
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.)
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.
Physical meaning of the optical reference geometry
International Nuclear Information System (INIS)
Abramowicz, M.A.
1990-09-01
I show that contrary to a popular misconception the optical reference geometry, introduced a few years ago as a formally possible metric of a 3-space corresponding to a static spacetime, is quite satisfactory also from the physical point of view. The optical reference geometry has a clear physical meaning, as it may be constructed experimentally by measuring light round travel time between static observers. Distances and directions in the optical reference geometry are more strongly connected to experiment than distances and directions in the widely used directly projected metric (discussed e.g. in Landau and Lifshitz textbook. In addition, the optical reference geometry is more natural and convenient than the directly projected one in application to dynamics. In the optical geometry dynamical behaviour of matter is described by concepts and formulae identical to those well known in Newtonian dynamics on a given two dimensional (curved) surface. (author). 22 refs
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.
Blasjo, Viktor|info:eu-repo/dai/nl/338038108
2013-01-01
We discuss how a creature accustomed to Euclidean space would fare in a world of hyperbolic or spherical geometry, and conversely. Various optical illusions and counterintuitive experiences arise, which can be explicated mathematically using plane models of these geometries.
Minimal length uncertainty and generalized non-commutative geometry
International Nuclear Information System (INIS)
Farmany, A.; Abbasi, S.; Darvishi, M.T.; Khani, F.; Naghipour, A.
2009-01-01
A generalized formulation of non-commutative geometry for the Bargmann-Fock space of quantum field theory is presented. The analysis is related to the symmetry of the simplistic space and a minimal length uncertainty.
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
Geometry and topology of wild translation surfaces
Randecker, Anja
2016-01-01
A translation surface is a two-dimensional manifold, equipped with a translation structure. It can be obtained by considering Euclidean polygons and identifying their edges via translations. The vertices of the polygons form singularities if the translation structure can not be extended to them. We study translation surfaces with wild singularities, regarding the topology (genus and space of ends), the geometry (behavior of the singularities), and how the topology and the geometry are related.
Differential geometry and topology of curves
Animov, Yu
2001-01-01
Differential geometry is an actively developing area of modern mathematics. This volume presents a classical approach to the general topics of the geometry of curves, including the theory of curves in n-dimensional Euclidean space. The author investigates problems for special classes of curves and gives the working method used to obtain the conditions for closed polygonal curves. The proof of the Bakel-Werner theorem in conditions of boundedness for curves with periodic curvature and torsion is also presented. This volume also highlights the contributions made by great geometers. past and present, to differential geometry and the topology of curves.
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.
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'…
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...
Selman, Delon; And Others
1976-01-01
The relationships among measures of quantitative thinking in first through fifth grade children assigned either to an experimental math program emphasizing tactile, manipulative, or individual activity in learning metric and decimal concepts, or to a control group, were examined. Tables are presented and conclusions discussed. (Author/JKS)
Atherton, Pauline; And Others
A single issue of Nuclear Science Abstracts, containing about 2,300 abstracts, was indexed by Universal Decimal Classification (UDC) using the Special Subject Edition of UDC for Nuclear Science and Technology. The descriptive cataloging and UDC-indexing records formed a computer-stored data base. A systematic random sample of 500 additional…
Markey, Karen; Demeyer, Anh N.
In this research project, subject terms from the Dewey Decimal Classification (DDC) Schedules and Relative Index were incorporated into an online catalog as searcher's tools for subject access, browsing, and display. Four features of the DDC were employed to help searchers browse for and match their own subject terms with the online catalog's…
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.
Projective geometry and projective metrics
Busemann, Herbert
2005-01-01
The basic results and methods of projective and non-Euclidean geometry are indispensable for the geometer, and this book--different in content, methods, and point of view from traditional texts--attempts to emphasize that fact. Results of special theorems are discussed in detail only when they are needed to develop a feeling for the subject or when they illustrate a general method. On the other hand, an unusual amount of space is devoted to the discussion of the fundamental concepts of distance, motion, area, and perpendicularity.Topics include the projective plane, polarities and conic sectio
Geometry of supersymmetric gauge theories
International Nuclear Information System (INIS)
Gieres, F.
1988-01-01
This monograph gives a detailed and pedagogical account of the geometry of rigid superspace and supersymmetric Yang-Mills theories. While the core of the text is concerned with the classical theory, the quantization and anomaly problem are briefly discussed following a comprehensive introduction to BRS differential algebras and their field theoretical applications. Among the treated topics are invariant forms and vector fields on superspace, the matrix-representation of the super-Poincare group, invariant connections on reductive homogeneous spaces and the supermetric approach. Various aspects of the subject are discussed for the first time in textbook and are consistently presented in a unified geometric formalism
Freudenthal duality and generalized special geometry
Energy Technology Data Exchange (ETDEWEB)
Ferrara, Sergio, E-mail: sergio.ferrara@cern.ch [Physics Department, Theory Unit, CERN, CH-1211, Geneva 23 (Switzerland); INFN - Laboratori Nazionali di Frascati, Via Enrico Fermi 40, I-00044 Frascati (Italy); Marrani, Alessio, E-mail: Alessio.Marrani@cern.ch [Physics Department, Theory Unit, CERN, CH-1211, Geneva 23 (Switzerland); Yeranyan, Armen, E-mail: ayeran@lnf.infn.it [INFN - Laboratori Nazionali di Frascati, Via Enrico Fermi 40, I-00044 Frascati (Italy); Department of Physics, Yerevan State University, Alex Manoogian St. 1, Yerevan, 0025 (Armenia)
2011-07-27
Freudenthal duality, introduced in Borsten et al. (2009) and defined as an anti-involution on the dyonic charge vector in d=4 space-time dimensions for those dualities admitting a quartic invariant, is proved to be a symmetry not only of the classical Bekenstein-Hawking entropy but also of the critical points of the black hole potential. Furthermore, Freudenthal duality is extended to any generalized special geometry, thus encompassing all N>2 supergravities, as well as N=2 generic special geometry, not necessarily having a coset space structure.
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.
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.
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...
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.
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...
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 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
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.
Cari Merkley
2011-01-01
Objective – To determine the extent to which knowledge is currently addressed by the Library of Congress (LCC), Dewey Decimal (DDC), and Universal Decimal (UDC) classification systems.Design – Comparative analysis of the LCC, DDC, and UDC systems using Zin’s 10 Pillars of Knowledge.Setting – The Faculty of Philosophy and Science at a Brazilian university.Subjects – Forty one subject-related classes and 386 subclasses from the first two levels of the LCC, DDC, and UDC systems.Methods – To eval...
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
Non-Perturbative Quantum Geometry III
Krefl, Daniel
2016-08-02
The Nekrasov-Shatashvili limit of the refined topological string on toric Calabi-Yau manifolds and the resulting quantum geometry is studied from a non-perturbative perspective. The quantum differential and thus the quantum periods exhibit Stockes phenomena over the combined string coupling and quantized Kaehler moduli space. We outline that the underlying formalism of exact quantization is generally applicable to points in moduli space featuring massless hypermultiplets, leading to non-perturbative band splitting. Our prime example is local P1xP1 near a conifold point in moduli space. In particular, we will present numerical evidence that in a Stockes chamber of interest the string based quantum geometry reproduces the non-perturbative corrections for the Nekrasov-Shatashvili limit of 4d supersymmetric SU(2) gauge theory at strong coupling found in the previous part of this series. A preliminary discussion of local P2 near the conifold point in moduli space is also provided.
International conference on Algebraic and Complex Geometry
Kloosterman, Remke; Schütt, Matthias
2014-01-01
Several important aspects of moduli spaces and irreducible holomorphic symplectic manifolds were highlighted at the conference “Algebraic and Complex Geometry” held September 2012 in Hannover, Germany. These two subjects of recent ongoing progress belong to the most spectacular developments in Algebraic and Complex Geometry. Irreducible symplectic manifolds are of interest to algebraic and differential geometers alike, behaving similar to K3 surfaces and abelian varieties in certain ways, but being by far less well-understood. Moduli spaces, on the other hand, have been a rich source of open questions and discoveries for decades and still continue to be a hot topic in itself as well as with its interplay with neighbouring fields such as arithmetic geometry and string theory. Beyond the above focal topics this volume reflects the broad diversity of lectures at the conference and comprises 11 papers on current research from different areas of algebraic and complex geometry sorted in alphabetic order by the ...
Discrete quantum geometries and their effective dimension
International Nuclear Information System (INIS)
Thuerigen, Johannes
2015-01-01
In several approaches towards a quantum theory of gravity, such as group field theory and loop quantum gravity, quantum states and histories of the geometric degrees of freedom turn out to be based on discrete spacetime. The most pressing issue is then how the smooth geometries of general relativity, expressed in terms of suitable geometric observables, arise from such discrete quantum geometries in some semiclassical and continuum limit. In this thesis I tackle the question of suitable observables focusing on the effective dimension of discrete quantum geometries. For this purpose I give a purely combinatorial description of the discrete structures which these geometries have support on. As a side topic, this allows to present an extension of group field theory to cover the combinatorially larger kinematical state space of loop quantum gravity. Moreover, I introduce a discrete calculus for fields on such fundamentally discrete geometries with a particular focus on the Laplacian. This permits to define the effective-dimension observables for quantum geometries. Analysing various classes of quantum geometries, I find as a general result that the spectral dimension is more sensitive to the underlying combinatorial structure than to the details of the additional geometric data thereon. Semiclassical states in loop quantum gravity approximate the classical geometries they are peaking on rather well and there are no indications for stronger quantum effects. On the other hand, in the context of a more general model of states which are superposition over a large number of complexes, based on analytic solutions, there is a flow of the spectral dimension from the topological dimension d on low energy scales to a real number between 0 and d on high energy scales. In the particular case of 1 these results allow to understand the quantum geometry as effectively fractal.
An improved injector bunching geometry for ATLAS
Indian Academy of Sciences (India)
This geometry improves the handling of space charge for high-current beams, signiﬁcantly increases the capture fraction into the primary rf bucket and reduces the capture fraction of the unwanted parasitic rf bucket. Total capture and transport through the PII has been demonstrated as high as 80% of the injected dc beam ...
On the geometry of fracture and frustration
Koning, Vinzenz
2014-01-01
Geometric frustration occurs when local order cannot propagate through space. A common example is the surface of a soccer ball, which cannot be tiled with hexaganons only. Geometric frustration can also be present in materials. In fact, geometry can act as an instrument to design the mechanical,
Non-commutative geometry and supersymmetry 2
International Nuclear Information System (INIS)
Hussain, F.; Thompson, G.
1991-05-01
Following the general construction of supersymmetric models, the model based on the idea of non-commutative geometry is formulated as a Yang-Mills theory of the graded Lie algebra U(2/1) over a graded space-time manifold. 4 refs
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...
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
Fútbol, música y narcisismo: algunas conjeturas sobre “Brasil, decime qué se siente”
Directory of Open Access Journals (Sweden)
Pablo Alabarces
2015-02-01
Full Text Available Durante la Copa del Mundo 2014 en Brasil, los hinchas argentinos viajaron en gran cantidad e inundaron las calles (incluso más que los estadios cantando de modo unánime una canción de aliento, reconocida por su primer verso: “Brasil, decime qué se siente”. La canción, basada en una vieja melodía del grupo de rock norteamericano Creedence Clearwater Revival, fue rápidamente adoptada por centenares de miles de hinchas en Brasil y otros millones en la Argentina, viralizándose asimismo por las redes sociales. A partir de este fenómeno, el trabajo analiza la canción, las tradiciones musicales y políticas sobre las que trabaja, así como la relación entre música y nacionalidad que puede desprenderse de ese análisis; en el mismo sentido, discute esa relación en la historia de las Copas del Mundo. La actuación de los hinchas argentinos se convierte, entonces, en una actuación centralmente musical, en la que es posible leer la cultura futbolística argentina, organizada por el narcisismo y las lógicas del aguante.
Directory of Open Access Journals (Sweden)
M.T. Hoffman
1993-09-01
Full Text Available Between June 1919 and August 1920, the largest population of elephants in South Africa at the time was reduced from about 130 to 16 individuals by one man. Major P. J. Pretorius. Conflict between farmers and the elephants over dwindling water resources, coupled with the threat that the elephants posed to the future agricultural development of the region, precipitated the Provincial Administration's extermination order. Major Pretorius' figure of "120-odd" elephants killed during the year is reasonably accurate and the fate of the animal products is traced. Most of the skins were processed, by Pretorius himself, to make whips. A few specimens can be traced to local and overseas museums. Because records of the sex and age of animals killed by Major Pretorius have either been lost or were never detailed, reconstruction of the Addo elephant herd before the decimation, is difficult. Finally, details of the alleged public debate are discussed. It is concluded that it was probably a handful of individuals that convinced the Provincial Administration to spare 16 animals. The Rev J.R.L. Kingon as well as Major Pretorius himself are two key figures in the debate. There is little evidence to confirm the view that a public outcry, in the modem sense of the word, stopped the killing. Six photographs are included as an appendix. They show Major Pretorius at work in the Addo Bush.
Arbitrariness of geometry and the aether
International Nuclear Information System (INIS)
Browne, P.F.
1976-01-01
As emphasized by Milne, an observer ultimately depends on the transmission and reception of light signals for the measurement of natural lengths and periods remote from his world point. The laws of geometry which are obeyed when these lengths and periods are plotted on a space--time depend, inevitably, on assumptions concerning the dependence of light velocity on the spatial and temporal coordinates. A convention regarding light velocity fixes the geometry, and conversely. However, the convention of flat space--time implies nonintegrable ''radar distances'' unless the concept of coordinate-dependent units of measure is employed. Einstein's space--time has the advantage of admitting a special reference system R with respect to which the aether fluid is at rest and the total gravitational field vanishes. A holonomic transformation from R to another reference system R belonging to the same space--time introduces a nonpermanent gravitational field and holonomic aether motion. A nonholonomic transformation from R to a reference system R* which belongs to a different space--time introduces a permanent gravitational field and nonholonomic aether motion. The arbitrariness of geometry is expressed by extending covariance to include the latter transformation. By means of a nonholonomic (or units) transformation it is possible, with the aid of the principle of equivalence, to obtain the Schwarzschild and de Sitter metrics from the Newtonian fields that would arise in a flat space--time description. Some light is thrown on the interpretation of cosmological models
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.
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...
Sulistyo-Basuki, L.
2007-01-01
Although Indonesian libraries have been using Dewey Decimal Classification for more than half century, since 1952 until present times, from 15th through 22nd editions still many Indonesian librarians and users complained on certain DDC notation which they thought didn’t reflect the true condition of Indonesia as well as the real needs of the users. This paper proposed some modification and corrections for DDC notations especially those notations on languages in Indonesia including Bahasa Indo...
Directory of Open Access Journals (Sweden)
Cari Merkley
2011-01-01
Full Text Available Objective – To determine the extent to which knowledge is currently addressed by the Library of Congress (LCC, Dewey Decimal (DDC, and Universal Decimal (UDC classification systems.Design – Comparative analysis of the LCC, DDC, and UDC systems using Zin’s 10 Pillars of Knowledge.Setting – The Faculty of Philosophy and Science at a Brazilian university.Subjects – Forty one subject-related classes and 386 subclasses from the first two levels of the LCC, DDC, and UDC systems.Methods – To evaluate the LCC, DDC, and UDC systems, the researchers employed the 10 Pillars of Knowledge, a “hierarchical knowledge tree” developed by the lead author of this study (p. 878. According to the authors, the 10 Pillars of Knowledge seek to illustrate relationships between fields of knowledge while capturing their breadth. The first level of the Pillars consists of the following categories: Knowledge, Supernatural, Matter and Energy, Space and Earth, Nonhuman Organizations, Body and Mind, Society, Thought and Art, Technology, and History. Each of the 10 Pillars is further subdivided, resulting in a four level hierarchical structure of 76 categories. Of the 76 categories, 55 are unique subject areas. A selection of subject-based classes and subclasses from the first two levels of the LCC, DDC, and UDC systems were then mapped to the relevant subclasses within the Pillars. Analysis was limited to the first two levels of LCC, DDC, and UDC, except for the LCC categories of BF and BL where further subclasses were analyzed. Classes or subclasses in LCC, DDC, or UDC that were not subject based (for example, those based on publication type were excluded from the study. In total, 41 main classes and 386 subclasses from LLC, DDC, and UDC were categorized using the 10 Pillars.Main Results – The LLC, DDC, and UDC systems were deemed to be complete and systematic in their coverage of only three of the 10 Pillars: Matter and Energy, Thought and Art, and History
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.)
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.
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…
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 ...
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
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...
Riemannian geometry in an orthogonal frame
Cartan, Elie Joseph
2001-01-01
Foreword by S S Chern. In 1926-27, Cartan gave a series of lectures in which he introduced exterior forms at the very beginning and used extensively orthogonal frames throughout to investigate the geometry of Riemannian manifolds. In this course he solved a series of problems in Euclidean and non-Euclidean spaces, as well as a series of variational problems on geodesics. In 1960, Sergei P Finikov translated from French into Russian his notes of these Cartan's lectures and published them as a book entitled Riemannian Geometry in an Orthogonal Frame. This book has many innovations, such as the n
Quasi-crystalline geometry for architectural structures
DEFF Research Database (Denmark)
Wester, Ture; Weinzieri, Barbara
The quasi-crystal (QC) type of material was discovered in 1983 by Dan Schechtman from Technion, Haifa. This new crystalline structure of material broke totally with the traditional conception of crystals and geometry introducing non-periodic close packing of cells with fivefold symmetry in 3D space....... The quasi-crystal geometry can be constructed from two different cubic cells with identical rhombic facets, where the relation between the diagonals is the golden section. All cells have identical rhombic faces, identical edges and identical icosahedral/dodecahedral nodes....
Geometry of the local equivalence of states
Energy Technology Data Exchange (ETDEWEB)
Sawicki, A; Kus, M, E-mail: assawi@cft.edu.pl, E-mail: marek.kus@cft.edu.pl [Center for Theoretical Physics, Polish Academy of Sciences, Al Lotnikow 32/46, 02-668 Warszawa (Poland)
2011-12-09
We present a description of locally equivalent states in terms of symplectic geometry. Using the moment map between local orbits in the space of states and coadjoint orbits of the local unitary group, we reduce the problem of local unitary equivalence to an easy part consisting of identifying the proper coadjoint orbit and a harder problem of the geometry of fibers of the moment map. We give a detailed analysis of the properties of orbits of 'equally entangled states'. In particular, we show connections between certain symplectic properties of orbits such as their isotropy and coisotropy with effective criteria of local unitary equivalence. (paper)
The role of geometry in 4-vertex origami mechanics
Waitukaitis, Scott; Dieleman, Peter; van Hecke, Martin
Origami offers an interesting design platform metamaterials because it strongly couples mechanics with geometry. Even so, most research carried out so far has been limited to one or two particular patterns. I will discuss the full geometrical space of the most common origami building block, the 4-vertex, and show how exotic geometries can have dramatic effects on the mechanics.
The interplay between differential geometry and differential equations
Lychagin, V V
1995-01-01
This work applies symplectic methods and discusses quantization problems to emphasize the advantage of an algebraic geometry approach to nonlinear differential equations. One common feature in most of the presentations in this book is the systematic use of the geometry of jet spaces.
Using 3D Geometric Models to Teach Spatial Geometry Concepts.
Bertoline, Gary R.
1991-01-01
An explanation of 3-D Computer Aided Design (CAD) usage to teach spatial geometry concepts using nontraditional techniques is presented. The software packages CADKEY and AutoCAD are described as well as their usefulness in solving space geometry problems. (KR)
A Geometry in which all Triangles are Isosceles
Indian Academy of Sciences (India)
The real number line has a geometry which is Euclidean. Imagine a small pygmy tortoise trying to travel along a very long path; assume that its destination is at a very ..... are: geometry of space-time at small distances; classi- cal and quantum ...
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...
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 ...
Directory of Open Access Journals (Sweden)
Julián Monge-Nájera
2000-06-01
Full Text Available The controversy about a Cambrian "explosion" of morphological disparity (followed by decimation, cladogenesis and fossilization is of central importance for the history of life. This paper revisits the controversy (with emphasis in onychophorans, which include emblematic organisms such as Hallucigenia, presents new data about the Chengjiang (Cambrian of China faunal community and compares it and the Burgess Shale (Cambrian of Canada with an ecologically similar but modern tropical marine site where onychophorans are absent, and with a modern neotropical terrestrial onychophoran community. Biovolume was estimated from material collected in Costa Rica and morphometric measurements were made on enlarged images of fossils. Cambrian tropical mudflats were characterized by the adaptive radiation of two contrasting groups: the vagile arthropods and the sessile poriferans. Arthropods were later replaced as the dominant benthic taxon by polychaetes. Vagility and the exoskeleton may explain the success of arthropods from the Cambrian to the modern marine and terrestrial communities, both in population and biovolume. Food ecological displacement was apparent in the B. Shale, but not in Chengjiang or the terrestrial community. When only hard parts were preserved, marine and terrestrial fossil deposits of tropical origin are even less representative than deposits produced by temperate taxa, Chengjiang being an exception. Nutrient limitations might explain why deposit feeding is less important in terrestrial onychophoran communities, where carnivory, scavenging and omnivory (associated with high motility and life over the substrate became more important. Fossil morphometry supports the interpretation of "lobopod animals" as onychophorans, whose abundance in Chengjiang was equal to their abundance in modern communities. The extinction of marine onychophorans may reflect domination of the infaunal habitat by polychaetes. We conclude that (1 a mature ecological
Multivariate calculus and geometry
Dineen, Seán
2014-01-01
Multivariate calculus can be understood best by combining geometric insight, intuitive arguments, detailed explanations and mathematical reasoning. This textbook has successfully followed this programme. It additionally provides a solid description of the basic concepts, via familiar examples, which are then tested in technically demanding situations. In this new edition the introductory chapter and two of the chapters on the geometry of surfaces have been revised. Some exercises have been replaced and others provided with expanded solutions. Familiarity with partial derivatives and a course in linear algebra are essential prerequisites for readers of this book. Multivariate Calculus and Geometry is aimed primarily at higher level undergraduates in the mathematical sciences. The inclusion of many practical examples involving problems of several variables will appeal to mathematics, science and engineering students.
Transformational plane geometry
Umble, Ronald N
2014-01-01
Axioms of Euclidean Plane Geometry The Existence and Incidence Postulates The Distance and Ruler Postulates The Plane Separation Postulate The Protractor Postulate The Side-Angle-Side Postulate and the Euclidean Parallel Postulate Theorems of Euclidean Plane Geometry The Exterior Angle Theorem Triangle Congruence Theorems The Alternate Interior Angles Theorem and the Angle Sum Theorem Similar Triangles Introduction to Transformations, Isometries, and Similarities Transformations Isometries and SimilaritiesAppendix: Proof of Surjectivity Translations, Rotations, and Reflections Translations Rotations Reflections Appendix: Geometer's Sketchpad Commands Required by Exploratory Activities Compositions of Translations, Rotations, and Reflections The Three Points Theorem Rotations as Compositions of Two Reflections Translations as Compositions of Two Halfturns or Two Reflections The Angle Addition Theorem Glide Reflections Classification of Isometries The Fundamental Theorem and Congruence Classification of Isometr...
Multilevel geometry optimization
Rodgers, Jocelyn M.; Fast, Patton L.; Truhlar, Donald G.
2000-02-01
Geometry optimization has been carried out for three test molecules using six multilevel electronic structure methods, in particular Gaussian-2, Gaussian-3, multicoefficient G2, multicoefficient G3, and two multicoefficient correlation methods based on correlation-consistent basis sets. In the Gaussian-2 and Gaussian-3 methods, various levels are added and subtracted with unit coefficients, whereas the multicoefficient Gaussian-x methods involve noninteger parameters as coefficients. The multilevel optimizations drop the average error in the geometry (averaged over the 18 cases) by a factor of about two when compared to the single most expensive component of a given multilevel calculation, and in all 18 cases the accuracy of the atomization energy for the three test molecules improves; with an average improvement of 16.7 kcal/mol.
Multilevel geometry optimization
Energy Technology Data Exchange (ETDEWEB)
Rodgers, Jocelyn M. [Department of Chemistry and Supercomputer Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431 (United States); Fast, Patton L. [Department of Chemistry and Supercomputer Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431 (United States); Truhlar, Donald G. [Department of Chemistry and Supercomputer Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431 (United States)
2000-02-15
Geometry optimization has been carried out for three test molecules using six multilevel electronic structure methods, in particular Gaussian-2, Gaussian-3, multicoefficient G2, multicoefficient G3, and two multicoefficient correlation methods based on correlation-consistent basis sets. In the Gaussian-2 and Gaussian-3 methods, various levels are added and subtracted with unit coefficients, whereas the multicoefficient Gaussian-x methods involve noninteger parameters as coefficients. The multilevel optimizations drop the average error in the geometry (averaged over the 18 cases) by a factor of about two when compared to the single most expensive component of a given multilevel calculation, and in all 18 cases the accuracy of the atomization energy for the three test molecules improves; with an average improvement of 16.7 kcal/mol. (c) 2000 American Institute of Physics.
Quasi-crystalline geometry for architectural structures
DEFF Research Database (Denmark)
Weizierl, Barbara; Wester, Ture
2001-01-01
Artikel på CD-Rom 8 sider. The quasi-crystal (QC) type of material was discovered in 1983 by Dan Schechtman from Technion, Haifa. This new crystalline structure of material broke totally with the traditional conception of crystals and geometry introducing non-periodic close packing of cells...... with fivefold symmetry in 3D space. The quasi-crystal geometry can be constructed from two different cubic cells with identical rhombic facets, where the relation between the diagonals is the golden section. All cells have identical rhombic faces, identical edges and identical icosahedral/dedecahedral nodes....... The purpose of the paper is to investigate some possibilities for the application of Quasi-Crystal geometry for structures in architecture. The basis for the investigations is A: to use the Golden Cubes (the two different hexahedra consisting of rhombic facets where the length of the diagonals has the Golden...
Geometric Monte Carlo and black Janus geometries
Energy Technology Data Exchange (ETDEWEB)
Bak, Dongsu, E-mail: dsbak@uos.ac.kr [Physics Department, University of Seoul, Seoul 02504 (Korea, Republic of); B.W. Lee Center for Fields, Gravity & Strings, Institute for Basic Sciences, Daejeon 34047 (Korea, Republic of); Kim, Chanju, E-mail: cjkim@ewha.ac.kr [Department of Physics, Ewha Womans University, Seoul 03760 (Korea, Republic of); Kim, Kyung Kiu, E-mail: kimkyungkiu@gmail.com [Department of Physics, Sejong University, Seoul 05006 (Korea, Republic of); Department of Physics, College of Science, Yonsei University, Seoul 03722 (Korea, Republic of); Min, Hyunsoo, E-mail: hsmin@uos.ac.kr [Physics Department, University of Seoul, Seoul 02504 (Korea, Republic of); Song, Jeong-Pil, E-mail: jeong_pil_song@brown.edu [Department of Chemistry, Brown University, Providence, RI 02912 (United States)
2017-04-10
We describe an application of the Monte Carlo method to the Janus deformation of the black brane background. We present numerical results for three and five dimensional black Janus geometries with planar and spherical interfaces. In particular, we argue that the 5D geometry with a spherical interface has an application in understanding the finite temperature bag-like QCD model via the AdS/CFT correspondence. The accuracy and convergence of the algorithm are evaluated with respect to the grid spacing. The systematic errors of the method are determined using an exact solution of 3D black Janus. This numerical approach for solving linear problems is unaffected initial guess of a trial solution and can handle an arbitrary geometry under various boundary conditions in the presence of source fields.
Index theory for locally compact noncommutative geometries
Carey, A L; Rennie, A; Sukochev, F A
2014-01-01
Spectral triples for nonunital algebras model locally compact spaces in noncommutative geometry. In the present text, the authors prove the local index formula for spectral triples over nonunital algebras, without the assumption of local units in our algebra. This formula has been successfully used to calculate index pairings in numerous noncommutative examples. The absence of any other effective method of investigating index problems in geometries that are genuinely noncommutative, particularly in the nonunital situation, was a primary motivation for this study and the authors illustrate this point with two examples in the text. In order to understand what is new in their approach in the commutative setting the authors prove an analogue of the Gromov-Lawson relative index formula (for Dirac type operators) for even dimensional manifolds with bounded geometry, without invoking compact supports. For odd dimensional manifolds their index formula appears to be completely new.
From groups to geometry and back
Climenhaga, Vaughn
2017-01-01
Groups arise naturally as symmetries of geometric objects, and so groups can be used to understand geometry and topology. Conversely, one can study abstract groups by using geometric techniques and ultimately by treating groups themselves as geometric objects. This book explores these connections between group theory and geometry, introducing some of the main ideas of transformation groups, algebraic topology, and geometric group theory. The first half of the book introduces basic notions of group theory and studies symmetry groups in various geometries, including Euclidean, projective, and hyperbolic. The classification of Euclidean isometries leads to results on regular polyhedra and polytopes; the study of symmetry groups using matrices leads to Lie groups and Lie algebras. The second half of the book explores ideas from algebraic topology and geometric group theory. The fundamental group appears as yet another group associated to a geometric object and turns out to be a symmetry group using covering space...
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)
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.
Remarks on Hamiltonian structures in G2-geometry
International Nuclear Information System (INIS)
Cho, Hyunjoo; Salur, Sema; Todd, A. J.
2013-01-01
In this article, we treat G 2 -geometry as a special case of multisymplectic geometry and make a number of remarks regarding Hamiltonian multivector fields and Hamiltonian differential forms on manifolds with an integrable G 2 -structure; in particular, we discuss existence and make a number of identifications of the spaces of Hamiltonian structures associated to the two multisymplectic structures associated to an integrable G 2 -structure. Along the way, we prove some results in multisymplectic geometry that are generalizations of results from symplectic geometry
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.
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
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)
International Nuclear Information System (INIS)
Marmo, G.; Morandi, G.
1995-01-01
In this lecture some mathematical problems that arise when one deals with low-dimensional field theories, such as homotopy and topological invariants, differential calculus on Lie groups and coset spaces, fiber spaces and parallel transport, differential calculus on fiber bundles, sequences on principal bundles and Chern-Simons terms are discussed
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
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
2015-01-01
This stimulating volume offers a broad collection of the principles of geometry and trigonometry and contains colorful diagrams to bring mathematical principles to life. Subjects are enriched by references to famous mathematicians and their ideas, and the stories are presented in a very comprehensible way. Readers investigate the relationships of points, lines, surfaces, and solids. They study construction methods for drawing figures, a wealth of facts about these figures, and above all, methods to prove the facts. They learn about triangle measure for circular motion, sine and cosine, tangent
REA, The Editors of
2012-01-01
REA's Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Geometry I includes methods of proof, points, lines, planes, angles, congruent angles and line segments, triangles, parallelism, quadrilaterals, geometric inequalities, and geometric
Graded geometry and Poisson reduction
Cattaneo, A S; Zambon, M
2009-01-01
The main result of [2] extends the Marsden-Ratiu reduction theorem [4] in Poisson geometry, and is proven by means of graded geometry. In this note we provide the background material about graded geometry necessary for the proof in [2]. Further, we provide an alternative algebraic proof for the main result. ©2009 American Institute of Physics
Doubly special relativity and Finsler geometry
International Nuclear Information System (INIS)
Mignemi, S.
2007-01-01
We discuss the recent proposal of implementing doubly special relativity in configuration space by means of Finsler geometry. Although this formalism leads to a consistent description of the dynamics of a particle, it does not seem to give a complete description of the physics. In particular, the Finsler line element is not invariant under the deformed Lorentz transformations of doubly special relativity. We study in detail some simple applications of the formalism
Extraction electrode geometry for a calutron
International Nuclear Information System (INIS)
Veach, A.M.; Bell, W.A. Jr.
1975-01-01
This patent relates to an improved geometry for the extraction electrode and the ground electrode utilized in the operation of a calutron. The improved electrodes are constructed in a partial-picture-frame fashion with the slits of both electrodes formed by two tungsten elongated rods. Additional parallel spaced-apart rods in each electrode are used to establish equipotential surfaces over the rest of the front of the ion source
Algorithms and file structures for computational geometry
International Nuclear Information System (INIS)
Hinrichs, K.; Nievergelt, J.
1983-01-01
Algorithms for solving geometric problems and file structures for storing large amounts of geometric data are of increasing importance in computer graphics and computer-aided design. As examples of recent progress in computational geometry, we explain plane-sweep algorithms, which solve various topological and geometric problems efficiently; and we present the grid file, an adaptable, symmetric multi-key file structure that provides efficient access to multi-dimensional data along any space dimension. (orig.)
On ''conformal spinor geometry'': An attempt to ''understand'' internal symmetry
International Nuclear Information System (INIS)
Budinich, P.
1982-01-01
The natural homomorphism of pure spinors corresponding to a given Clifford algebra Csub(2n) to polarized isotropic n-planes of complex Euclidean space Esub(2n)sup(c) is taken as a starting point for the construction of a geometry called spinor geometry where pure spinors are the only elements out of which all tensors have to be constructed (analytically as bilinear polynomials of the components of a pure spinor). C 4 and C 6 spinor geometry are analyzed, but it seems that C 8 spinor geometry is necessary to construct Minkowski space Msup(3,1). C 6 spinor field equations give rise in Minkowski space to a pair of Dirac equations (for conformal semispinors) presenting an su(2) internal symmetry algebra. Mass is generated by breaking spontaneously the original O(4,2) symmetry of the spinor equation. (author)
On ''conformal spinor geometry'': An attempt to ''understand'' internal symmetry
International Nuclear Information System (INIS)
Budinich, P.
1981-09-01
The natural homomorphism of pure spinors corresponding to a given Clifford algebra Csub(2n) to polarized isotropic n-planes of complex Euclidean space Esub(2n)sup(c) is taken as a starting point for the construction of a geometry called spinor geometry where pure spinors are the only elements out of which all tensors have to be constructed (analytically as bilinear polynomia of the components of a pure spinor). C 4 and C 6 spinor geometry are analyzed but it seems that C 8 spinor geometry is necessary to construct Minkowski space Msup(3,1). C 6 spinor field equations give rise in Minkowski space to a pair of Dirac equations (for conformal semispinors) presenting an SU(2) internal symmetry algebra. Mass is generated by spontaneously breaking the original O(4,2) symmetry of the spinor equation. (author)
Amir-Moez, A R; Sneddon, I N
1962-01-01
Elements of Linear Space is a detailed treatment of the elements of linear spaces, including real spaces with no more than three dimensions and complex n-dimensional spaces. The geometry of conic sections and quadric surfaces is considered, along with algebraic structures, especially vector spaces and transformations. Problems drawn from various branches of geometry are given.Comprised of 12 chapters, this volume begins with an introduction to real Euclidean space, followed by a discussion on linear transformations and matrices. The addition and multiplication of transformations and matrices a
La introducción del sistema métrico decimal y los libros de texto en España
Picado, Miguel; Rico, Luis
2012-01-01
El artículo resalta la relevancia de los libros de texto en la difusión de determinados conocimientos matemáticos. Este alcance se ejemplifica con resultados de un estudio histórico realizado sobre funcionalidad y características de los textos de matemáticas en la introducción y difusión del sistema métrico decimal en España en el período 1849-1892.
Geometry of hyperbolic monopoles
International Nuclear Information System (INIS)
Nash, C.
1986-01-01
The hyperbolic monopoles of Atiyah [M. F. Atiyah, Commun. Math. Phys. 93, 471 (1984); ''Magnetic monopoles in hyperbolic space,'' in Proceedings of the International Colloquium on Vector Bundles (Tata Institute, Bombay, 1984)] and Chakrabarti [A. Chakrabarti, J. Math. Phys. 27, 340 (1986)] are introduced and their geometric properties and relations to instantons and ordinary monopoles clarified. A key tool is the use of the ball model of hyperbolic space to construct and examine solutions
Real space renormalization group for spectra and density of states
International Nuclear Information System (INIS)
Wiecko, C.; Roman, E.
1984-09-01
We discuss the implementation of the Real Space Renormalization Group Decimation Technique for 1-d tight-binding models with long range interactions with or without disorder and for the 2-d regular square lattice. The procedure follows the ideas developed by Southern et al. Some new explicit formulae are included. The purpose of this study is to calculate spectra and densities of states following the procedure developed in our previous work. (author)
Trembach, Vera
2014-01-01
Space is an introduction to the mysteries of the Universe. Included are Task Cards for independent learning, Journal Word Cards for creative writing, and Hands-On Activities for reinforcing skills in Math and Language Arts. Space is a perfect introduction to further research of the Solar System.
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.
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...
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
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.
Resonance and Fractal Geometry
Broer, Henk W.
The phenomenon of resonance will be dealt with from the viewpoint of dynamical systems depending on parameters and their bifurcations. Resonance phenomena are associated to open subsets in the parameter space, while their complement corresponds to quasi-periodicity and chaos. The latter phenomena
Indian Academy of Sciences (India)
2. Vector bundles and moduli. In response to a question of Serre, as to whether every vector bundle on the affine space is trivial. (equivalently, whether every projective module over a polynomial ring over a field is free),. C S Seshadri proved in 1958 that vector bundles on the affine plane are trivial. The general case was.
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
Geometric control theory and sub-Riemannian geometry
Boscain, Ugo; Gauthier, Jean-Paul; Sarychev, Andrey; Sigalotti, Mario
2014-01-01
This volume presents recent advances in the interaction between Geometric Control Theory and sub-Riemannian geometry. On the one hand, Geometric Control Theory used the differential geometric and Lie algebraic language for studying controllability, motion planning, stabilizability and optimality for control systems. The geometric approach turned out to be fruitful in applications to robotics, vision modeling, mathematical physics etc. On the other hand, Riemannian geometry and its generalizations, such as sub-Riemannian, Finslerian geometry etc., have been actively adopting methods developed in the scope of geometric control. Application of these methods has led to important results regarding geometry of sub-Riemannian spaces, regularity of sub-Riemannian distances, properties of the group of diffeomorphisms of sub-Riemannian manifolds, local geometry and equivalence of distributions and sub-Riemannian structures, regularity of the Hausdorff volume.
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.
Instabilities of microstate geometries with antibranes
International Nuclear Information System (INIS)
Bena, Iosif; Pasini, Giulio
2016-01-01
One can obtain very large classes of horizonless microstate geometries corresponding to near-extremal black holes by placing probe supertubes whose action has metastable minima inside certain supersymmetric bubbling solutions http://dx.doi.org/10.1007/JHEP12(2012)014. We show that these minima can lower their energy when the bubbles move in certain directions in the moduli space, which implies that these near-extremal microstates are in fact unstable once one considers the dynamics of all their degrees of freedom. The decay of these solutions corresponds to Hawking radiation, and we compare the emission rate and frequency to those of the corresponding black hole. Our analysis supports the expectation that generic non-extremal black holes microstate geometries should be unstable. It also establishes the existence of a new type of instabilities for antibranes in highly-warped regions with charge dissolved in fluxes.
Testing R-parity with geometry
Energy Technology Data Exchange (ETDEWEB)
He, Yang-Hui [Department of Mathematics, City University, London,Northampton Square, London EC1V 0HB (United Kingdom); School of Physics, NanKai University,94 Weijin Road, Tianjin, 300071 (China); Merton College, University of Oxford,Merton Street, OX1 4JD (United Kingdom); Jejjala, Vishnu [Mandelstam Institute for Theoretical Physics, NITheP, and School of Physics,University of the Witwatersrand,1 Jan Smuts Avenue, Johannesburg, WITS 2050 (South Africa); Matti, Cyril [Department of Mathematics, City University, London,Northampton Square, London EC1V 0HB (United Kingdom); Mandelstam Institute for Theoretical Physics, NITheP, and School of Physics,University of the Witwatersrand,1 Jan Smuts Avenue, Johannesburg, WITS 2050 (South Africa); Nelson, Brent D. [Department of Physics, Northeastern University,360 Huntington Avenue, Boston, MA 02115 (United States)
2016-03-14
We present a complete classification of the vacuum geometries of all renormalizable superpotentials built from the fields of the electroweak sector of the MSSM. In addition to the Severi and affine Calabi-Yau varieties previously found, new vacuum manifolds are identified; we thereby investigate the geometrical implication of theories which display a manifest matter parity (or R-parity) via the distinction between leptonic and Higgs doublets, and of the lepton number assignment of the right-handed neutrino fields. We find that the traditional R-parity assignments of the MSSM more readily accommodate the neutrino see-saw mechanism with non-trivial geometry than those superpotentials that violate R-parity. However there appears to be no geometrical preference for a fundamental Higgs bilinear in the superpotential, with operators that violate lepton number, such as νHH̄, generating vacuum moduli spaces equivalent to those with a fundamental bilinear.
Laplacians on discrete and quantum geometries
International Nuclear Information System (INIS)
Calcagni, Gianluca; Oriti, Daniele; Thürigen, Johannes
2013-01-01
We extend discrete calculus for arbitrary (p-form) fields on embedded lattices to abstract discrete geometries based on combinatorial complexes. We then provide a general definition of discrete Laplacian using both the primal cellular complex and its combinatorial dual. The precise implementation of geometric volume factors is not unique and, comparing the definition with a circumcentric and a barycentric dual, we argue that the latter is, in general, more appropriate because it induces a Laplacian with more desirable properties. We give the expression of the discrete Laplacian in several different sets of geometric variables, suitable for computations in different quantum gravity formalisms. Furthermore, we investigate the possibility of transforming from position to momentum space for scalar fields, thus setting the stage for the calculation of heat kernel and spectral dimension in discrete quantum geometries. (paper)
Instabilities of microstate geometries with antibranes
Energy Technology Data Exchange (ETDEWEB)
Bena, Iosif; Pasini, Giulio [Institut de physique théorique, Université Paris Saclay, CEA, CNRS,F-91191 Gif-sur-Yvette (France)
2016-04-29
One can obtain very large classes of horizonless microstate geometries corresponding to near-extremal black holes by placing probe supertubes whose action has metastable minima inside certain supersymmetric bubbling solutions http://dx.doi.org/10.1007/JHEP12(2012)014. We show that these minima can lower their energy when the bubbles move in certain directions in the moduli space, which implies that these near-extremal microstates are in fact unstable once one considers the dynamics of all their degrees of freedom. The decay of these solutions corresponds to Hawking radiation, and we compare the emission rate and frequency to those of the corresponding black hole. Our analysis supports the expectation that generic non-extremal black holes microstate geometries should be unstable. It also establishes the existence of a new type of instabilities for antibranes in highly-warped regions with charge dissolved in fluxes.
International Nuclear Information System (INIS)
Heckman, Jonathan J.; Morrison, David R.; Rudelius, Tom; Vafa, Cumrun
2015-01-01
We study renormalization group flows between six-dimensional superconformal field theories (SCFTs) using their geometric realizations as singular limits of F-theory compactified on elliptically fibered Calabi-Yau threefolds. There are two general types of flows: one corresponds to giving expectation values to scalars in the tensor multiplets (tensor branch flow) realized as resolving the base of the geometry. The other corresponds to giving expectation values to hypermultiplets (Higgs branch flow) realized as complex structure deformations of the geometry. To corroborate this physical picture we calculate the change in the anomaly polynomial for these theories, finding strong evidence for a flow from a UV fixed point to an IR fixed point. Moreover, we find evidence against non-trivial dualities for 6D SCFTs. In addition we find non-trivial RG flows for theories realizing small E 8 instantons on ALE spaces.
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.
c-Extremization from toric geometry
Amariti, Antonio; Cassia, Luca; Penati, Silvia
2018-04-01
We derive a geometric formulation of the 2d central charge cr from infinite families of 4d N = 1 superconformal field theories topologically twisted on constant curvature Riemann surfaces. They correspond to toric quiver gauge theories and are associated to D3 branes probing five dimensional Sasaki-Einstein geometries in the AdS/CFT correspondence. We show that cr can be expressed in terms of the areas of the toric diagram describing the moduli space of the 4d theory, both for toric geometries with smooth and singular horizons. We also study the relation between a-maximization in 4d and c-extremization in 2d, giving further evidences of the mixing of the baryonic symmetries with the exact R-current in two dimensions.
Geometry of wave electromagnetics
Energy Technology Data Exchange (ETDEWEB)
Sudarshan, E. C.G.
1980-10-27
A challenge to the commonly held view of light as a wave phenomenon is presented. An exact realization of light as generalized pencils or rays is constructed, with stress placed on using pencils of rays rather than single rays. Exact equations of motion are presented for the rays in the pencil, and these rays tend to travel in straight lines in empty space (not too near the edge of the beam). (GHT)
Geometry as an aspect of dynamics
International Nuclear Information System (INIS)
Videira, A.L.L.; Barros, A.L.R.; Fernandes, N.C.
1982-07-01
Contrary to the predominant way of doing physics, it is shown that the geometric structure of a general differentiable space-time manifold can be determined by means of the introduction in that manifold of a minimal set of fundamental dynamical quantities associated to a free particle endowed with the fundamental property of momentum. Thus, general relativistic physics implies a general pseudo-Riemannian geometry, whereas the physics of the special theory of relativity is tied up with Minkowski space-time, and Newtonian dynamics is bound to Newtonian space-time. While in the relativistic instance, the Riemannian character of the manifold is basically fixed by means only of the Hamiltonian state function of the free particle (its kynetic energy), in the latter case, it has to resort, perhaps not unexpectedly, to the two dynamical entities mass and energy, separately. (Author) [pt
Geometry as an aspect of dynamics
International Nuclear Information System (INIS)
Videira, A.L.L.; Barros, A.L.R.; Fernandes, N.C.
1983-12-01
Contrary to the predominant way of doing physics, it is shown that the geometric structure of a general differentiable space-time manifold can be determined by means of the introduction in that manifold of a minimal set of fundamental dynamical quantities associated to a particle endowed with the fundamental property of covariant momentum. Thus, general relativistic physics implies a general pseudo-Riemannian geometry, whereas the physics of the special theory of relativity is tied up with Minkowski space-time, and Newtonian dynamics is bound to Newtonian space-time. While in the relativistic instance, the Riemannian character of the manifold is basically fixed by means only of the Hamiltonian state function of the particle (its energy), in the latter case, one have to resort, perhaps not unexpectedly, to the two dynamical entities mass energy, separately. (Author) [pt
Flexible intuitions of Euclidean geometry in an Amazonian indigene group
Izard, Véronique; Pica, Pierre; Spelke, Elizabeth S.; Dehaene, Stanislas
2011-01-01
Kant argued that Euclidean geometry is synthesized on the basis of an a priori intuition of space. This proposal inspired much behavioral research probing whether spatial navigation in humans and animals conforms to the predictions of Euclidean geometry. However, Euclidean geometry also includes concepts that transcend the perceptible, such as objects that are infinitely small or infinitely large, or statements of necessity and impossibility. We tested the hypothesis that certain aspects of nonperceptible Euclidian geometry map onto intuitions of space that are present in all humans, even in the absence of formal mathematical education. Our tests probed intuitions of points, lines, and surfaces in participants from an indigene group in the Amazon, the Mundurucu, as well as adults and age-matched children controls from the United States and France and younger US children without education in geometry. The responses of Mundurucu adults and children converged with that of mathematically educated adults and children and revealed an intuitive understanding of essential properties of Euclidean geometry. For instance, on a surface described to them as perfectly planar, the Mundurucu's estimations of the internal angles of triangles added up to ∼180 degrees, and when asked explicitly, they stated that there exists one single parallel line to any given line through a given point. These intuitions were also partially in place in the group of younger US participants. We conclude that, during childhood, humans develop geometrical intuitions that spontaneously accord with the principles of Euclidean geometry, even in the absence of training in mathematics. PMID:21606377
More on microstate geometries of 4d black holes
International Nuclear Information System (INIS)
Bianchi, M.; Morales, J.F.; Pieri, L.; Zinnato, N.
2017-01-01
We construct explicit examples of microstate geometries of four-dimensional black holes that lift to smooth horizon-free geometries in five dimensions. Solutions consist of half-BPS D-brane atoms distributed in ℝ 3 . Charges and positions of the D-brane centers are constrained by the bubble equations and boundary conditions ensuring the regularity of the metric and the match with the black hole geometry. In the case of three centers, we find that the moduli spaces of solutions includes disjoint one-dimensional components of (generically) finite volume.
Graph-drawing algorithms geometries versus molecular mechanics in fullereness
Kaufman, M.; Pisanski, T.; Lukman, D.; Borštnik, B.; Graovac, A.
1996-09-01
The algorithms of Kamada-Kawai (KK) and Fruchterman-Reingold (FR) have been recently generalized (Pisanski et al., Croat. Chem. Acta 68 (1995) 283) in order to draw molecular graphs in three-dimensional space. The quality of KK and FR geometries is studied here by comparing them with the molecular mechanics (MM) and the adjacency matrix eigenvectors (AME) algorithm geometries. In order to compare different layouts of the same molecule, an appropriate method has been developed. Its application to a series of experimentally detected fullerenes indicates that the KK, FR and AME algorithms are able to reproduce plausible molecular geometries.
CIME-CIRM course Rationality Problems in Algebraic Geometry
Pirola, Gian
2016-01-01
Providing an overview of the state of the art on rationality questions in algebraic geometry, this volume gives an update on the most recent developments. It offers a comprehensive introduction to this fascinating topic, and will certainly become an essential reference for anybody working in the field. Rationality problems are of fundamental importance both in algebra and algebraic geometry. Historically, rationality problems motivated significant developments in the theory of abelian integrals, Riemann surfaces and the Abel–Jacobi map, among other areas, and they have strong links with modern notions such as moduli spaces, Hodge theory, algebraic cycles and derived categories. This text is aimed at researchers and graduate students in algebraic geometry.
More on microstate geometries of 4d black holes
Energy Technology Data Exchange (ETDEWEB)
Bianchi, M. [Università di Roma Tor Vergata and I.N.F.N, Dipartimento di Fisica,Via della Ricerca Scientifica, I-00133 Rome (Italy); Morales, J.F. [I.N.F.N. - Sezione di Roma 2 and Università di Roma Tor Vergata, Dipartimento di Fisica,Via della Ricerca Scientifica, I-00133 Roma (Italy); Pieri, L. [Università di Roma Tor Vergata and I.N.F.N, Dipartimento di Fisica,Via della Ricerca Scientifica, I-00133 Rome (Italy); Center for Research in String Theory, School of Physics and Astronomy,Queen Mary University of London, Mile End Road, London, E1 4NS (United Kingdom); Zinnato, N. [Università di Roma Tor Vergata and I.N.F.N, Dipartimento di Fisica,Via della Ricerca Scientifica, I-00133 Rome (Italy)
2017-05-29
We construct explicit examples of microstate geometries of four-dimensional black holes that lift to smooth horizon-free geometries in five dimensions. Solutions consist of half-BPS D-brane atoms distributed in ℝ{sup 3}. Charges and positions of the D-brane centers are constrained by the bubble equations and boundary conditions ensuring the regularity of the metric and the match with the black hole geometry. In the case of three centers, we find that the moduli spaces of solutions includes disjoint one-dimensional components of (generically) finite volume.
The causal structure of spacetime is a parameterized Randers geometry
Energy Technology Data Exchange (ETDEWEB)
Skakala, Jozef; Visser, Matt, E-mail: jozef.skakala@msor.vuw.ac.nz, E-mail: matt.visser@msor.vuw.ac.nz [School of Mathematics, Statistics and Operations Research, Victoria University of Wellington, PO Box 600, Wellington (New Zealand)
2011-03-21
There is a well-established isomorphism between stationary four-dimensional spacetimes and three-dimensional purely spatial Randers geometries-these Randers geometries being a particular case of the more general class of three-dimensional Finsler geometries. We point out that in stably causal spacetimes, by using the (time-dependent) ADM decomposition, this result can be extended to general non-stationary spacetimes-the causal structure (conformal structure) of the full spacetime is completely encoded in a parameterized (t-dependent) class of Randers spaces, which can then be used to define a Fermat principle, and also to reconstruct the null cones and causal structure.
The causal structure of spacetime is a parameterized Randers geometry
International Nuclear Information System (INIS)
Skakala, Jozef; Visser, Matt
2011-01-01
There is a well-established isomorphism between stationary four-dimensional spacetimes and three-dimensional purely spatial Randers geometries-these Randers geometries being a particular case of the more general class of three-dimensional Finsler geometries. We point out that in stably causal spacetimes, by using the (time-dependent) ADM decomposition, this result can be extended to general non-stationary spacetimes-the causal structure (conformal structure) of the full spacetime is completely encoded in a parameterized (t-dependent) class of Randers spaces, which can then be used to define a Fermat principle, and also to reconstruct the null cones and causal structure.
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....
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 ...
A proposal of an open PET geometry
Energy Technology Data Exchange (ETDEWEB)
Yamaya, Taiga [Molecular Imaging Center, National Institute of Radiological Sciences, 4-9-1 Anagawa, Inage-ku, Chiba, 263-8555 (Japan); Inaniwa, Taku [Research Center for Charged Particle Therapy, National Institute of Radiological Sciences, 4-9-1 Anagawa, Inage-ku, Chiba 263-8555 (Japan); Minohara, Shinichi [Research Center for Charged Particle Therapy, National Institute of Radiological Sciences, 4-9-1 Anagawa, Inage-ku, Chiba 263-8555 (Japan); Yoshida, Eiji [Molecular Imaging Center, National Institute of Radiological Sciences, 4-9-1 Anagawa, Inage-ku, Chiba, 263-8555 (Japan); Inadama, Naoko [Molecular Imaging Center, National Institute of Radiological Sciences, 4-9-1 Anagawa, Inage-ku, Chiba, 263-8555 (Japan); Nishikido, Fumihiko [Molecular Imaging Center, National Institute of Radiological Sciences, 4-9-1 Anagawa, Inage-ku, Chiba, 263-8555 (Japan); Shibuya, Kengo [Molecular Imaging Center, National Institute of Radiological Sciences, 4-9-1 Anagawa, Inage-ku, Chiba, 263-8555 (Japan); Lam, Chih Fung [Molecular Imaging Center, National Institute of Radiological Sciences, 4-9-1 Anagawa, Inage-ku, Chiba, 263-8555 (Japan); Murayama, Hideo [Molecular Imaging Center, National Institute of Radiological Sciences, 4-9-1 Anagawa, Inage-ku, Chiba, 263-8555 (Japan)
2008-02-07
The long patient port of a PET scanner tends to put stress on patients, especially patients with claustrophobia. It also prevents doctors and technicians from taking care of patients during scanning. In this paper, we proposed an 'open PET' geometry, which consists of two axially separated detector rings. A long and continuous field-of-view (FOV) including a 360 deg. opened gap between two detector rings can be imaged enabling a fully 3D image reconstruction of all the possible lines-of-response. The open PET will become practical if iterative image reconstruction methods are applied even though image reconstruction of the open PET is analytically an incomplete problem. First we implemented a 'masked' 3D ordered subset expectation maximization (OS-EM) in which the system matrix was obtained from a long 'gapless' scanner by applying a mask to detectors corresponding to the open space. Next, in order to evaluate imaging performance of the proposed open PET geometry, we simulated a dual HR+ scanner (ring diameter of D = 827 mm, axial length of W = 154 mm x 2) separated by a variable gap. The gap W was the maximum limit to have axially continuous FOV of 3W though the maximum diameter of FOV at the central slice was limited to D/2. Artifacts, observed on both sides of the open space when the gap exceeded W, were effectively reduced by inserting detectors partially into unnecessary open spaces. We also tested the open PET geometry using experimental data obtained by the jPET-D4. The jPET-D4 is a prototype brain scanner, which has 5 rings of 24 detector blocks. We simulated the open jPET-D4 with a gap of 66 mm by eliminating 1 block-ring from experimental data. Although some artifacts were seen at both ends of the opened gap, very similar images were obtained with and without the gap. The proposed open PET geometry is expected to lead to realization of in-beam PET, which is a method for an in situ monitoring of charged particle therapy, by
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
Pedagogia Etnomatemática: do “par de cinco” às concepções do sistema de numeração decimal
Directory of Open Access Journals (Sweden)
Francisco de Assis Bandeira
2011-01-01
Full Text Available O objetivo do presente artigo é mostrar possibilidades de se ensinar matemática no nível fundamental levando o aluno a compreender os princípios do sistema de numeração decimal, essenciais a compreensão dos procedimentos utilizados nas operações fundamentais, utilizando, para isto, o conhecimento tradicional de sua comunidade. As observações e reflexões aqui veiculadas tiveram por base os alunos do 5° ano do ensino fundamental da escola de uma comunidade de horticultores e as concepções d’ambrosianas de Etnomatemática, principalmente, a educacional, que procura compreender a realidade sócio-cultural e chegar à ação pedagógica de maneira natural mediante um enfoque cognitivo com forte fundamentação cultural.
Moyano-Grimaldo, Wilmer Arturo
2017-01-01
Resumen Desde el año 1876, cuando Melvil Dewey publicó la primera edición de su sistema de clasificación bibliográfico, este ha ido evolucionando como un sistema de clasificación muy firme y adaptable que permite organizar de manera práctica el conocimiento, incluso en la Internet. El presente artículo, es derivado de una investigación doctoral desarrollada durante 5 años acerca de diferentes aspectos semánticos, epistemológicos, históricos y tecnológicos de la Clasificación Decimal Dewey, in...
Choi, Hwan Bin; Lee, Ji-Woo
2017-09-01
We study quantum phase transitions of a XXZ spin model with spin S = 1/2 and 1 in one dimension. The XXZ spin chain is one of basic models in understanding various one-dimensional magnetic materials. To study this model, we construct infinite-lattice matrix product state (iMPS), which is a tensor product form for a one-dimensional many-body quantum wave function. By using timeevolution- block-decimation method (TEBD) on iMPS, we obtain the ground states of the XXZ model at zero temperature. This method is very delicate in calculating ground states so that we developed a reliable method of finding the ground state with the dimension of entanglement coefficients up to 300, which is beyond the previous works. By analyzing ground-state energies, half-chain entanglement entropies, and entanglement spectrum, we found the signatures of quantum phase transitions between ferromagnetic phase, XY phase, Haldane phase, and antiferromagnetic phase.
Information theory, spectral geometry, and quantum gravity.
Kempf, Achim; Martin, Robert
2008-01-18
We show that there exists a deep link between the two disciplines of information theory and spectral geometry. This allows us to obtain new results on a well-known quantum gravity motivated natural ultraviolet cutoff which describes an upper bound on the spatial density of information. Concretely, we show that, together with an infrared cutoff, this natural ultraviolet cutoff beautifully reduces the path integral of quantum field theory on curved space to a finite number of ordinary integrations. We then show, in particular, that the subsequent removal of the infrared cutoff is safe.
Hyperbolic geometry of Kuramoto oscillator networks
Chen, Bolun; Engelbrecht, Jan R.; Mirollo, Renato
2017-09-01
Kuramoto oscillator networks have the special property that their trajectories are constrained to lie on the (at most) 3D orbits of the Möbius group acting on the state space T N (the N-fold torus). This result has been used to explain the existence of the N-3 constants of motion discovered by Watanabe and Strogatz for Kuramoto oscillator networks. In this work we investigate geometric consequences of this Möbius group action. The dynamics of Kuramoto phase models can be further reduced to 2D reduced group orbits, which have a natural geometry equivalent to the unit disk \
Non-holonomic dynamics and Poisson geometry
International Nuclear Information System (INIS)
Borisov, A V; Mamaev, I S; Tsiganov, A V
2014-01-01
This is a survey of basic facts presently known about non-linear Poisson structures in the analysis of integrable systems in non-holonomic mechanics. It is shown that by using the theory of Poisson deformations it is possible to reduce various non-holonomic systems to dynamical systems on well-understood phase spaces equipped with linear Lie-Poisson brackets. As a result, not only can different non-holonomic systems be compared, but also fairly advanced methods of Poisson geometry and topology can be used for investigating them. Bibliography: 95 titles
Geometry and light the science of invisibility
Leonhardt, Ulf
2010-01-01
The science of invisibility combines two of physics' greatest concepts: Einstein's general relativity and Maxwell's principles of electromagnetism. Recent years have witnessed major breakthroughs in the area, and the authors of this volume - Ulf Leonhardt and Thomas Philbin of Scotland's University of St. Andrews - have been active in the transformation of invisibility from fiction into science. Their work on designing invisibility devices is based on modern metamaterials, inspired by Fermat's principle, analogies between mechanics and optics, and the geometry of curved space. Suitable for gra
Projective geometry for polarization in geometric quantization
International Nuclear Information System (INIS)
Campbell, P.; Dodson, C.T.J.
1976-12-01
It is important to know the extent to which the procedure of geometric quantization depends on a choice of polarization of the symplectic manifold that is the classical phase space. Published results have so far been restricted to real and transversal polarizations. Here we also consider these cases by presenting a formulation in terms of projective geometry. It turns out that there is a natural characterization of real transversal polarizations and maps among them using projective concepts. We give explicit constructions for Rsup(2n)
Primes, Geometry and Condensed Matter
Directory of Open Access Journals (Sweden)
Al Rabeh R. H.
2009-07-01
Full Text Available Fascination with primes dates back to the Greeks and before. Primes are named by some "the elementary particles of arithmetic" as every nonprime integer is made of a unique set of primes. In this article we point to new connections between primes, geometry and physics which show that primes could be called "the elementary particles of physics" too. This study considers the problem of closely packing similar circles/spheres in 2D/3D space. This is in effect a discretization process of space and the allowable number in a pack is found to lead to some unexpected cases of prime configurations which is independent of the size of the constituents. We next suggest that a non-prime can be considered geometrically as a symmetric collection that is separable (factorable into similar parts- six is two threes or three twos for example. A collection that has no such symmetry is a prime. As a result, a physical prime aggregate is more difficult to split symmetrically resulting in an inherent stability. This "number/physical" stability idea applies to bigger collections made from smaller (prime units leading to larger stable prime structures in a limitless scaling up process. The distribution of primes among numbers can be understood better using the packing ideas described here and we further suggest that differing numbers (and values of distinct prime factors making a nonprime collection is an important factor in determining the probability and method of possible and subsequent disintegration. Disintegration is bound by energy conservation and is closely related to symmetry by Noether theorems. Thinking of condensed matter as the packing of identical elements, we examine plots of the masses of chemical elements of the periodic table, and also those of the elementary particles of physics, and show that prime packing rules seem to play a role in the make up of matter. The plots show convincingly that the growth of prime numbers and that of the masses of
Primes, Geometry and Condensed Matter
Directory of Open Access Journals (Sweden)
Al Rabeh R. H.
2009-07-01
Full Text Available Fascination with primes dates back to the Greeks and before. Primes are named by some “the elementary particles of arithmetic” as every nonprime integer is made of a unique set of primes. In this article we point to new connections between primes, geometry and physics which show that primes could be called “the elementary particles of physics” too. This study considers the problem of closely packing similar circles / spheres in 2D / 3D space. This is in effect a discretization process of space and the allowable num- ber in a pack is found to lead to some unexpected cases of prime configurations which is independent of the size of the constituents. We next suggest that a non-prime can be considered geometrically as a symmetric collection that is separable (factorable into similar parts- six is two threes or three twos for example. A collection that has no such symmetry is a prime. As a result, a physical prime aggregate is more difficult to split symmetrically resulting in an inherent stability. This “number / physical” stability idea applies to bigger collections made from smaller (prime units leading to larger sta- ble prime structures in a limitless scaling up process. The distribution of primes among numbers can be understood better using the packing ideas described here and we further suggest that differing numbers (and values of distinct prime factors making a nonprime collection is an important factor in determining the probability and method of possible and subsequent disintegration. Disintegration is bound by energy conservation and is closely related to symmetry by Noether theorems. Thinking of condensed matter as the packing of identical elements, we examine plots of the masses of chemical elements of the periodic table, and also those of the elementary particles of physics, and show that prime packing rules seem to play a role in the make up of matter. The plots show con- vincingly that the growth of prime numbers and that
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
CIMPA Summer School on Arithmetic and Geometry Around Hypergeometric Functions
Uludağ, A; Yoshida, Masaaki; Arithmetic and Geometry Around Hypergeometric Functions
2007-01-01
This volume comprises the Lecture Notes of the CIMPA Summer School "Arithmetic and Geometry around Hypergeometric Functions" held at Galatasaray University, Istanbul in 2005. It contains lecture notes, a survey article, research articles, and the results of a problem session. Key topics are moduli spaces of points on P1 and Picard-Terada-Deligne-Mostow theory, moduli spaces of K3 surfaces, complex hyperbolic geometry, ball quotients, GKZ hypergeometric structures, Hilbert and Picard modular surfaces, uniformizations of complex orbifolds, algebraicity of values of Schwartz triangle functions, and Thakur's hypergeometric function. The book provides a background, gives detailed expositions and indicates new research directions. It is directed to postgraduate students and researchers.
Virial theorem and hypervirial theorem in a spherical geometry
International Nuclear Information System (INIS)
Li Yan; Chen Jingling; Zhang Fulin
2011-01-01
The virial theorem in the one- and two-dimensional spherical geometry are presented in both classical and quantum mechanics. Choosing a special class of hypervirial operators, the quantum hypervirial relations in the spherical spaces are obtained. With the aid of the Hellmann-Feynman theorem, these relations can be used to formulate a perturbation theorem without wavefunctions, corresponding to the hypervirial-Hellmann-Feynman theorem perturbation theorem of Euclidean geometry. The one-dimensional harmonic oscillator and two-dimensional Coulomb system in the spherical spaces are given as two sample examples to illustrate the perturbation method. (paper)
Pengembangan Perangkat Pembelajaran Geometri Ruang dengan Model Proving Theorem
Directory of Open Access Journals (Sweden)
Bambang Eko Susilo
2016-03-01
Full Text Available Kemampuan berpikir kritis dan kreatif mahasiswa masih lemah. Hal ini ditemukan pada mahasiswa yang mengambil mata kuliah Geometri Ruang yaitu dalam membuktikan soal-soal pembuktian (problem to proof. Mahasiswa masih menyelesaikan secara algoritmik atau prosedural sehingga diperlukan pengembangan perangkat pembelajaran Geometri Ruang berbasis kompetensi dan konservasi dengan model Proving Theorem. Dalam penelitian ini perangkat perkuliahan yang dikembangkan yaitu Silabus, Satuan Acara Perkuliahan (SAP, Kontrak Perkuliahan, Media Pembelajaran, Bahan Ajar, Tes UTS dan UAS serta Angket Karakter Konservasi telah dilaksanakan dengan baik dengan kriteria (1 validasi perangkat pembelajaran mata kuliah Geometri ruang berbasis kompetensi dan konservasi dengan model proving theorem berkategori baik dan layak digunakan dan (2 keterlaksanaan RPP pada pembelajaran yang dikembangkan secara keseluruhan berkategori baik.Critical and creative thinking abilities of students still weak. It is found in students who take Space Geometry subjects that is in solving problems to to prove. Students still finish in algorithmic or procedural so that the required the development of Space Geometry learning tools based on competency and conservation with Proving Theorem models. This is a research development which refers to the 4-D models that have been modified for the Space Geometry learning tools, second semester academic year 2014/2015. Instruments used include validation sheet, learning tools and character assessment questionnaire. In this research, the learning tools are developed, namely Syllabus, Lesson Plan, Lecture Contract, Learning Media, Teaching Material, Tests, and Character Conservation Questionnaire had been properly implemented with the criteria (1 validation of Space Geometry learning tools based on competency and conservation with Proving Theorem models categorized good and feasible to use, and (2 the implementation of Lesson Plan on learning categorized
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
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.)
Bonotto, C.
1993-01-01
Examined fifth-grade students' survey responses to investigate incorrect rules that derive from children's efforts to interpret decimals as integers or as fractions. Regarding fractions, difficulties arise because only the whole-part approach to fractions is presented in elementary school. (Author/MDH)
The Use of Geometry Learning Media Based on Augmented Reality for Junior High School Students
Rohendi, D.; Septian, S.; Sutarno, H.
2018-02-01
Understanding the geometry especially of three-dimensional space is still considered difficult by some students. Therefore, a learning innovation is required to overcome students’ difficulties in learning geometry. In this research, we developed geometry learning media based on augmented reality in android flatform’s then it was implemented in teaching three-dimensional objects for some junior high school students to find out: how is the students response in using this new media in geometry and is this media can solve the student’s difficulties in understanding geometry concept. The results showed that the use of geometry learning media based on augmented reality in android flatform is able to get positive responses from the students in learning geometry concepts especially three-dimensional objects and students more easy to understand concept of diagonal in geometry than before using this media.
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.)
Advances in discrete differential geometry
2016-01-01
This is one of the first books on a newly emerging field of discrete differential geometry and an excellent way to access this exciting area. It surveys the fascinating connections between discrete models in differential geometry and complex analysis, integrable systems and applications in computer graphics. The authors take a closer look at discrete models in differential geometry and dynamical systems. Their curves are polygonal, surfaces are made from triangles and quadrilaterals, and time is discrete. Nevertheless, the difference between the corresponding smooth curves, surfaces and classical dynamical systems with continuous time can hardly be seen. This is the paradigm of structure-preserving discretizations. Current advances in this field are stimulated to a large extent by its relevance for computer graphics and mathematical physics. This book is written by specialists working together on a common research project. It is about differential geometry and dynamical systems, smooth and discrete theories, ...
Hyperbolic Metamaterials with Complex Geometry
DEFF Research Database (Denmark)
Lavrinenko, Andrei; Andryieuski, Andrei; Zhukovsky, Sergei
2016-01-01
We investigate new geometries of hyperbolic metamaterialssuch as highly corrugated structures, nanoparticle monolayer assemblies, super-structured or vertically arranged multilayersand nanopillars. All structures retain basic propertiesof hyperbolic metamaterials, but have functionality improved...
An introduction to differential geometry
Willmore, T J
2012-01-01
This text employs vector methods to explore the classical theory of curves and surfaces. Topics include basic theory of tensor algebra, tensor calculus, calculus of differential forms, and elements of Riemannian geometry. 1959 edition.
Symplectic geometry and Fourier analysis
Wallach, Nolan R
2018-01-01
Suitable for graduate students in mathematics, this monograph covers differential and symplectic geometry, homogeneous symplectic manifolds, Fourier analysis, metaplectic representation, quantization, Kirillov theory. Includes Appendix on Quantum Mechanics by Robert Hermann. 1977 edition.
Topology and geometry for physicists
Nash, Charles
1983-01-01
Differential geometry and topology are essential tools for many theoretical physicists, particularly in the study of condensed matter physics, gravity, and particle physics. Written by physicists for physics students, this text introduces geometrical and topological methods in theoretical physics and applied mathematics. It assumes no detailed background in topology or geometry, and it emphasizes physical motivations, enabling students to apply the techniques to their physics formulas and research. ""Thoroughly recommended"" by The Physics Bulletin, this volume's physics applications range fr
Instanton strings and hyper-Kaehler geometry
International Nuclear Information System (INIS)
Dijkgraaf, Robbert
1999-01-01
We discuss two-dimensional sigma models on moduli spaces of instantons on K3 surfaces. These N = (4, 4) superconformal field theories describe the near-horizon dynamics of the D1-D5-brane system and are dual to string theory on AdS 3 . We derive a precise map relating the moduli of the K3 type 1113 string compactification to the moduli of these conformal field theories and the corresponding classical hyper-Kahler geometry. We conclude that in the absence of background gauge fields, the metric on the instanton moduli spaces degenerates exactly to the orbifold symmetric product of K3. Turning on a self-dual NS B-field deforms this symmetric product to a manifold that is diffeomorphic to the Hilbert scheme. We also comment on the mathematical applications of string duality to the global issues of deformations of hyper-Kaehler manifolds
Low-dimensional geometry from euclidean surfaces to hyperbolic knots
Bonahon, Francis
2009-01-01
The study of 3-dimensional spaces brings together elements from several areas of mathematics. The most notable are topology and geometry, but elements of number theory and analysis also make appearances. In the past 30 years, there have been striking developments in the mathematics of 3-dimensional manifolds. This book aims to introduce undergraduate students to some of these important developments. Low-Dimensional Geometry starts at a relatively elementary level, and its early chapters can be used as a brief introduction to hyperbolic geometry. However, the ultimate goal is to describe the very recently completed geometrization program for 3-dimensional manifolds. The journey to reach this goal emphasizes examples and concrete constructions as an introduction to more general statements. This includes the tessellations associated to the process of gluing together the sides of a polygon. Bending some of these tessellations provides a natural introduction to 3-dimensional hyperbolic geometry and to the theory o...
Rapkin, James; Jensen, Kim; Archer, C Ruth; House, Clarissa M; Sakaluk, Scott K; Castillo, Enrique Del; Hunt, John
2018-04-01
Life-history theory assumes that traits compete for limited resources, resulting in trade-offs. The most commonly manipulated resource in empirical studies is the quantity or quality of diet. Recent studies using the geometric framework for nutrition, however, suggest that trade-offs are often regulated by the intake of specific nutrients, but a formal approach to identify and quantify the strength of such trade-offs is lacking. We posit that trade-offs occur whenever life-history traits are maximized in different regions of nutrient space, as evidenced by nonoverlapping 95% confidence regions of the global maximum for each trait and large angles (θ) between linear nutritional vectors and Euclidean distances (d) between global maxima. We then examined the effects of protein and carbohydrate intake on the trade-off between reproduction and aspects of immune function in male and female Gryllodes sigillatus. Female encapsulation ability and egg production increased with the intake of both nutrients, whereas male encapsulation ability increased with protein intake but calling effort increased with carbohydrate intake. The trade-offs between traits was therefore larger in males than in females, as demonstrated by significant negative correlations between the traits in males, nonoverlapping 95% confidence regions, and larger estimates of θ and d. Under dietary choice, the sexes had similar regulated intakes, but neither optimally regulated nutrient intake for maximal trait expression. We highlight the fact that greater consideration of specific nutrient intake is needed when examining nutrient space-based trade-offs.
Complex geometry and quantum string theory
International Nuclear Information System (INIS)
Belavin, A.A.; Knizhnik, V.G.
1986-01-01
Summation over closed oriented surfaces of genus p ≥ 2 (p - loop vacuum amplitudes in boson string theory) in a critical dimensions D=26 is reduced to integration over M p space of complex structures of Riemann surfaces of genus p. The analytic properties of the integration measure as a function of the complex coordinates on M p are studied. It is shown that the measure multiplied by (det Im τ-circumflex) 13 (τ-circumflex is the surface period matrix) is the square of the modulus of a function which is holomorphic on M p and does not vanish anywhere. The function has a second order pole at infinity of compactified space of moduli M p . These properties define the measure uniquely up to a constant multiple and this permits one to set up explicitformulae for p=2,3 in terms of the theta-constants. Power and logarithmic divergences connected with renormalization of the tachyon wave function and of the slope respectively are involved in the theory. Quantum geometry of critical strings turns out to be a complex geometry
Hierarchical Cantor set in the large scale structure with torus geometry
Energy Technology Data Exchange (ETDEWEB)
Murdzek, R. [Physics Department, ' Al. I. Cuza' University, Blvd. Carol I, Nr. 11, Iassy 700506 (Romania)], E-mail: rmurdzek@yahoo.com
2008-12-15
The formation of large scale structures is considered within a model with string on toroidal space-time. Firstly, the space-time geometry is presented. In this geometry, the Universe is represented by a string describing a torus surface. Thereafter, the large scale structure of the Universe is derived from the string oscillations. The results are in agreement with the cellular structure of the large scale distribution and with the theory of a Cantorian space-time.
Matter fields in curved space-time
International Nuclear Information System (INIS)
Viet, Nguyen Ai; Wali, Kameshwar C.
2000-01-01
We study the geometry of a two-sheeted space-time within the framework of non-commutative geometry. As a prelude to the Standard Model in curved space-time, we present a model of a left- and a right- chiral field living on the two sheeted-space time and construct the action functionals that describe their interactions
Geometry and physics of branes
International Nuclear Information System (INIS)
Gal'tsov, D V
2003-01-01
deformation theory of holomorphic structures on vector bundles, which is a direct analogue of Kodaira and Spencer's study of the deformation of the complex structure of the complex manifold itself. Then it is explained how the homological algebra of A ∞ or L ∞ algebras can be applied to the problem of moduli, and the theorem is sketched stating that the gauge equivalence class of solutions of the Maurer-Cartan equation is invariant with respect to the homotopy types of these algebras. This discussion is then applied to the homological mirror symmetry, introducing the universal Novikov ring and Floer homology. The last series of lectures is devoted to the so-called geometric conifold transition related to the Gopakumar-Vafa conjecture that the SU(N) Chern-Simons theory on S 3 is dual to IIA string theory (with fluxes) compactified on a certain Calabi-Yau manifold. The geometry of the conifold transition involved in this discussion is described in detail, including physical applications. Some background endcolumn on Chern-Simons theory is presented and spaces with G 2 holonomies are discussed. M-theory treatment of the above correspondence is also given. Useful mathematical definitions are collected in five appendices. The book is certainly very useful both as an introduction to the modern topics of superstring theory and as a rather deep exposition of some advanced mathematical tools involved in it. (book review. Edited by U Bruzzo, V Gorini and U Moschella ISBN: 0-750-30863-X )
Torsional Newton-Cartan geometry and the Schrodinger algebra
Bergshoeff, Eric A.; Hartong, Jelle; Rosseel, Jan
2015-01-01
We show that by gauging the Schrodinger algebra with critical exponent z and imposing suitable curvature constraints, that make diffeomorphisms equivalent to time and space translations, one obtains a geometric structure known as (twistless) torsional Newton-Cartan geometry (TTNC). This is a version
Some questions of differential geometry in the large
Shikin, E V
1996-01-01
This collection contains articles that present recent results by geometers in Russia and the Ukraine. Papers in the collection deal with various questions related to the structure, symmetries, and embeddings of submanifolds in Euclidean and pseudo-Euclidian spaces. This collection offers a review of the challenges facing specialists in geometry in the large and features current research in the field.
Higher dimensional uniformisation and W-geometry
International Nuclear Information System (INIS)
Govindarajan, S.
1995-01-01
We formulate the uniformisation problem underlying the geometry of W n -gravity using the differential equation approach to W-algebras. We construct W n -space (analogous to superspace in supersymmetry) as an (n-1)-dimensional complex manifold using isomonodromic deformations of linear differential equations. The W n -manifold is obtained by the quotient of a Fuchsian subgroup of PSL(n,R) which acts properly discontinuously on a simply connected domain in bfCP n-1 . The requirement that a deformation be isomonodromic furnishes relations which enable one to convert non-linear W-diffeomorphisms to (linear) diffeomorphisms on the W n -manifold. We discuss how the Teichmueller spaces introduced by Hitchin can then be interpreted as the space of complex structures or the space of projective structures with real holonomy on the W n -manifold. The projective structures are characterised by Halphen invariants which are appropriate generalisations of the Schwarzian. This construction will work for all ''generic'' W-algebras. (orig.)
Rahn, A C; Köpke, S; Backhus, I; Kasper, J; Anger, K; Untiedt, B; Alegiani, A; Kleiter, I; Mühlhauser, I; Heesen, C
2018-02-01
Treatment decision-making is complex for people with multiple sclerosis. Profound information on available options is virtually not possible in regular neurologist encounters. The "nurse decision coach model" was developed to redistribute health professionals' tasks in supporting immunotreatment decision-making following the principles of informed shared decision-making. To test the feasibility of a decision coaching programme and recruitment strategies to inform the main trial. Feasibility testing and parallel pilot randomised controlled trial, accompanied by a mixed methods process evaluation. Two German multiple sclerosis university centres. People with suspected or relapsing-remitting multiple sclerosis facing immunotreatment decisions on first line drugs were recruited. Randomisation to the intervention (n = 38) or control group (n = 35) was performed on a daily basis. Quantitative and qualitative process data were collected from people with multiple sclerosis, nurses and physicians. We report on the development and piloting of the decision coaching programme. It comprises a training course for multiple sclerosis nurses and the coaching intervention. The intervention consists of up to three structured nurse-led decision coaching sessions, access to an evidence-based online information platform (DECIMS-Wiki) and a final physician consultation. After feasibility testing, a pilot randomised controlled trial was performed. People with multiple sclerosis were randomised to the intervention or control group. The latter had also access to the DECIMS-Wiki, but received otherwise care as usual. Nurses were not blinded to group assignment, while people with multiple sclerosis and physicians were. The primary outcome was 'informed choice' after six months including the sub-dimensions' risk knowledge (after 14 days), attitude concerning immunotreatment (after physician consultation), and treatment uptake (after six months). Quantitative process evaluation data
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.
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
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
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
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
Homogeneous Spaces and Equivariant Embeddings
Timashev, DA
2011-01-01
Homogeneous spaces of linear algebraic groups lie at the crossroads of algebraic geometry, theory of algebraic groups, classical projective and enumerative geometry, harmonic analysis, and representation theory. By standard reasons of algebraic geometry, in order to solve various problems on a homogeneous space it is natural and helpful to compactify it keeping track of the group action, i.e. to consider equivariant completions or, more generally, open embeddings of a given homogeneous space. Such equivariant embeddings are the subject of this book. We focus on classification of equivariant em
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...
Directory of Open Access Journals (Sweden)
Wilmer Arturo Moyano-Grimaldo
2017-01-01
Full Text Available Desde el año 1876, cuando Melvil Dewey publicó la primera edición de su sistema de clasificación bibliográfico, este ha ido evolucionando como un sistema de clasificación muy firme y adaptable que permite organizar de manera práctica el conocimiento, incluso en la Internet. El presente artículo, es derivado de una investigación doctoral desarrollada durante 5 años acerca de diferentes aspectos semánticos, epistemológicos, históricos y tecnológicos de la Clasificación Decimal Dewey, intentará mostrar la vigencia de este Sistema, a raíz de las nuevas tendencias en organización del conocimiento, mostrando esto desde la perspectiva de la evolución y su forma de adaptarse debido a los cambios tecnológicos y las tendencias actuales de la organización de contenidos.
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.
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 ...
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
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...
Deng, Shaoqiang
2012-01-01
"Homogeneous Finsler Spaces" is the first book to emphasize the relationship between Lie groups and Finsler geometry, and the first to show the validity in using Lie theory for the study of Finsler geometry problems. This book contains a series of new results obtained by the author and collaborators during the last decade. The topic of Finsler geometry has developed rapidly in recent years. One of the main reasons for its surge in development is its use in many scientific fields, such as general relativity, mathematical biology, and phycology (study of algae). This monograph introduc
Computational modeling of geometry dependent phonon transport in silicon nanostructures
Cheney, Drew A.
Recent experiments have demonstrated that thermal properties of semiconductor nanostructures depend on nanostructure boundary geometry. Phonons are quantized mechanical vibrations that are the dominant carrier of heat in semiconductor materials and their aggregate behavior determine a nanostructure's thermal performance. Phonon-geometry scattering processes as well as waveguiding effects which result from coherent phonon interference are responsible for the shape dependence of thermal transport in these systems. Nanoscale phonon-geometry interactions provide a mechanism by which nanostructure geometry may be used to create materials with targeted thermal properties. However, the ability to manipulate material thermal properties via controlling nanostructure geometry is contingent upon first obtaining increased theoretical understanding of fundamental geometry induced phonon scattering processes and having robust analytical and computational models capable of exploring the nanostructure design space, simulating the phonon scattering events, and linking the behavior of individual phonon modes to overall thermal behavior. The overall goal of this research is to predict and analyze the effect of nanostructure geometry on thermal transport. To this end, a harmonic lattice-dynamics based atomistic computational modeling tool was created to calculate phonon spectra and modal phonon transmission coefficients in geometrically irregular nanostructures. The computational tool is used to evaluate the accuracy and regimes of applicability of alternative computational techniques based upon continuum elastic wave theory. The model is also used to investigate phonon transmission and thermal conductance in diameter modulated silicon nanowires. Motivated by the complexity of the transmission results, a simplified model based upon long wavelength beam theory was derived and helps explain geometry induced phonon scattering of low frequency nanowire phonon modes.
A systematic construction of microstate geometries with low angular momentum
Bena, Iosif; Heidmann, Pierre; Ramírez, Pedro F.
2017-10-01
We outline a systematic procedure to obtain horizonless microstate geometries that have the same charges as three-charge five-dimensional black holes with a macroscopically-large horizon area and an arbitrarily-small angular momentum. There are two routes through which such solutions can be constructed: using multi-center Gibbons-Hawking (GH) spaces or using superstratum technology. So far the only solutions corre-sponding to microstate geometries for black holes with no angular momentum have been obtained via superstrata [1], and multi-center Gibbons-Hawking spaces have been believed to give rise only to microstate geometries of BMPV black holes with a large angular mo-mentum [2]. We perform a thorough search throughout the parameter space of smooth horizonless solutions with four GH centers and find that these have an angular momentum that is generally larger than 80% of the cosmic censorship bound. However, we find that solutions with three GH centers and one supertube (which are smooth in six-dimensional supergravity) can have an arbitrarily-low angular momentum. Our construction thus gives a recipe to build large classes of microstate geometries for zero-angular-momentum black holes without resorting to superstratum technology.
Advanced geometries for ballistic neutron guides
International Nuclear Information System (INIS)
Schanzer, Christian; Boeni, Peter; Filges, Uwe; Hils, Thomas
2004-01-01
Sophisticated neutron guide systems take advantage of supermirrors being used to increase the neutron flux. However, the finite reflectivity of supermirrors becomes a major loss mechanism when many reflections occur, e.g. in long neutron guides and for long wavelengths. In order to reduce the number of reflections, ballistic neutron guides have been proposed. Usually linear tapered sections are used to enlarge the cross-section and finally, focus the beam to the sample. The disadvantages of linear tapering are (i) an inhomogeneous phase space at the sample position and (ii) a decreasing flux with increasing distance from the exit of the guide. We investigate the properties of parabolic and elliptic tapering for ballistic neutron guides, using the Monte Carlo program McStas with a new guide component dedicated for such geometries. We show that the maximum flux can indeed be shifted away from the exit of the guide. In addition we explore the possibilities of parabolic and elliptic geometries to create point like sources for dedicated experimental demands
New geometries for black hole horizons
Energy Technology Data Exchange (ETDEWEB)
Armas, Jay [Physique Théorique et Mathématique,Université Libre de Bruxelles and International Solvay Institutes, ULB-Campus Plaine CP231, B-1050 Brussels (Belgium); Blau, Matthias [Albert Einstein Center for Fundamental Physics, University of Bern,Sidlerstrasse 5, 3012 Bern (Switzerland)
2015-07-10
We construct several classes of worldvolume effective actions for black holes by integrating out spatial sections of the worldvolume geometry of asymptotically flat black branes. This provides a generalisation of the blackfold approach for higher-dimensional black holes and yields a map between different effective theories, which we exploit by obtaining new hydrodynamic and elastic transport coefficients via simple integrations. Using Euclidean minimal surfaces in order to decouple the fluid dynamics on different sections of the worldvolume, we obtain local effective theories for ultraspinning Myers-Perry branes and helicoidal black branes, described in terms of a stress-energy tensor, particle currents and non-trivial boost vectors. We then study in detail and present novel compact and non-compact geometries for black hole horizons in higher-dimensional asymptotically flat space-time. These include doubly-spinning black rings, black helicoids and helicoidal p-branes as well as helicoidal black rings and helicoidal black tori in D≥6.
Generalized geometry and partial supersymmetry breaking
Energy Technology Data Exchange (ETDEWEB)
Triendl, Hagen Mathias
2010-08-15
This thesis consists of two parts. In the first part we use the formalism of (exceptional) generalized geometry to derive the scalar field space of SU(2) x SU(2)-structure compactifications. We show that in contrast to SU(3) x SU(3) structures, there is no dynamical SU(2) x SU(2) structure interpolating between an SU(2) structure and an identity structure. Furthermore, we derive the scalar manifold of the low-energy effective action for consistent Kaluza-Klein truncations as expected from N = 4 supergravity. In the second part we then determine the general conditions for the existence of stable Minkowski and AdS N = 1 vacua in spontaneously broken gauged N = 2 supergravities and construct the general solution under the assumption that two appropriate commuting isometries exist in the hypermultiplet sector. Furthermore, we derive the low-energy effective action below the scale of partial supersymmetry breaking and show that it satisfies the constraints of N = 1 supergravity. We then apply the discussion to special quaternionic-Kaehler geometries which appear in the low-energy limit of SU(3) x SU(3)-structure compactifications and construct Killing vectors with the right properties. Finally we discuss the string theory realizations for these solutions. (orig.)
Generalized geometry and partial supersymmetry breaking
International Nuclear Information System (INIS)
Triendl, Hagen Mathias
2010-08-01
This thesis consists of two parts. In the first part we use the formalism of (exceptional) generalized geometry to derive the scalar field space of SU(2) x SU(2)-structure compactifications. We show that in contrast to SU(3) x SU(3) structures, there is no dynamical SU(2) x SU(2) structure interpolating between an SU(2) structure and an identity structure. Furthermore, we derive the scalar manifold of the low-energy effective action for consistent Kaluza-Klein truncations as expected from N = 4 supergravity. In the second part we then determine the general conditions for the existence of stable Minkowski and AdS N = 1 vacua in spontaneously broken gauged N = 2 supergravities and construct the general solution under the assumption that two appropriate commuting isometries exist in the hypermultiplet sector. Furthermore, we derive the low-energy effective action below the scale of partial supersymmetry breaking and show that it satisfies the constraints of N = 1 supergravity. We then apply the discussion to special quaternionic-Kaehler geometries which appear in the low-energy limit of SU(3) x SU(3)-structure compactifications and construct Killing vectors with the right properties. Finally we discuss the string theory realizations for these solutions. (orig.)
Finite quantum physics and noncommutative geometry
International Nuclear Information System (INIS)
Balachandran, A.P.; Ercolessi, E.; Landi, G.; Teotonio-Sobrinho, P.; Lizzi, F.; Sparano, G.
1994-04-01
Conventional discrete approximations of a manifold do not preserve its nontrivial topological features. In this article we describe an approximation scheme due to Sorkin which reproduces physically important aspects of manifold topology with striking fidelity. The approximating topological spaces in this scheme are partially ordered sets (posets). Now, in ordinary quantum physics on a manifold M, continuous probability densities generate the commutative C * -algebra C(M) of continuous functions on M. It has a fundamental physical significance, containing the information to reconstruct the topology of M, and serving to specify the domains of observables like the Hamiltonian. For a poset, the role of this algebra is assumed by a noncommutative C * -algebra A. As noncommutative geometries are based on noncommutative C * -algebra, we therefore have a remarkable connection between finite approximations to quantum physics and noncommutative geometries. Varies methods for doing quantum physics using A are explored. Particular attention is paid to developing numerically viable approximation schemes which at the same time preserve important topological features of continuum physics. (author). 21 refs, 13 figs
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
Global Differential Geometry and Global Analysis
Pinkall, Ulrich; Simon, Udo; Wegner, Berd
1991-01-01
All papers appearing in this volume are original research articles and have not been published elsewhere. They meet the requirements that are necessary for publication in a good quality primary journal. E.Belchev, S.Hineva: On the minimal hypersurfaces of a locally symmetric manifold. -N.Blasic, N.Bokan, P.Gilkey: The spectral geometry of the Laplacian and the conformal Laplacian for manifolds with boundary. -J.Bolton, W.M.Oxbury, L.Vrancken, L.M. Woodward: Minimal immersions of RP2 into CPn. -W.Cieslak, A. Miernowski, W.Mozgawa: Isoptics of a strictly convex curve. -F.Dillen, L.Vrancken: Generalized Cayley surfaces. -A.Ferrandez, O.J.Garay, P.Lucas: On a certain class of conformally flat Euclidean hypersurfaces. -P.Gauduchon: Self-dual manifolds with non-negative Ricci operator. -B.Hajduk: On the obstruction group toexistence of Riemannian metrics of positive scalar curvature. -U.Hammenstaedt: Compact manifolds with 1/4-pinched negative curvature. -J.Jost, Xiaowei Peng: The geometry of moduli spaces of stabl...
Differential geometry on Hopf algebras and quantum groups
International Nuclear Information System (INIS)
Watts, P.
1994-01-01
The differential geometry on a Hopf algebra is constructed, by using the basic axioms of Hopf algebras and noncommutative differential geometry. The space of generalized derivations on a Hopf algebra of functions is presented via the smash product, and used to define and discuss quantum Lie algebras and their properties. The Cartan calculus of the exterior derivative, Lie derivative, and inner derivation is found for both the universal and general differential calculi of an arbitrary Hopf algebra, and, by restricting to the quasitriangular case and using the numerical R-matrix formalism, the aforementioned structures for quantum groups are determined
Combinatorial algebraic geometry selected papers from the 2016 apprenticeship program
Sturmfels, Bernd
2017-01-01
This volume consolidates selected articles from the 2016 Apprenticeship Program at the Fields Institute, part of the larger program on Combinatorial Algebraic Geometry that ran from July through December of 2016. Written primarily by junior mathematicians, the articles cover a range of topics in combinatorial algebraic geometry including curves, surfaces, Grassmannians, convexity, abelian varieties, and moduli spaces. This book bridges the gap between graduate courses and cutting-edge research by connecting historical sources, computation, explicit examples, and new results.
Geometry, algebra and applications from mechanics to cryptography
Encinas, Luis; Gadea, Pedro; María, Mª
2016-01-01
This volume collects contributions written by different experts in honor of Prof. Jaime Muñoz Masqué. It covers a wide variety of research topics, from differential geometry to algebra, but particularly focuses on the geometric formulation of variational calculus; geometric mechanics and field theories; symmetries and conservation laws of differential equations, and pseudo-Riemannian geometry of homogeneous spaces. It also discusses algebraic applications to cryptography and number theory. It offers state-of-the-art contributions in the context of current research trends. The final result is a challenging panoramic view of connecting problems that initially appear distant.
Discrete differential geometry. Consistency as integrability
Bobenko, Alexander I.; Suris, Yuri B.
2005-01-01
A new field of discrete differential geometry is presently emerging on the border between differential and discrete geometry. Whereas classical differential geometry investigates smooth geometric shapes (such as surfaces), and discrete geometry studies geometric shapes with finite number of elements (such as polyhedra), the discrete differential geometry aims at the development of discrete equivalents of notions and methods of smooth surface theory. Current interest in this field derives not ...
Numerically robust geometry engine for compound solid geometries
International Nuclear Information System (INIS)
Vlachoudis, V.; Sinuela-Pastor, D.
2013-01-01
Monte Carlo programs heavily rely on a fast and numerically robust solid geometry engines. However the success of solid modeling, depends on facilities for specifying and editing parameterized models through a user-friendly graphical front-end. Such a user interface has to be fast enough in order to be interactive for 2D and/or 3D displays, but at the same time numerically robust in order to display possible modeling errors at real time that could be critical for the simulation. The graphical user interface Flair for FLUKA currently employs such an engine where special emphasis has been given on being fast and numerically robust. The numerically robustness is achieved by a novel method of estimating the floating precision of the operations, which dynamically adapts all the decision operations accordingly. Moreover a predictive caching mechanism is ensuring that logical errors in the geometry description are found online, without compromising the processing time by checking all regions. (authors)
Differential geometry of curves and surfaces
Banchoff, Thomas F
2010-01-01
Students and professors of an undergraduate course in differential geometry will appreciate the clear exposition and comprehensive exercises in this book that focuses on the geometric properties of curves and surfaces, one- and two-dimensional objects in Euclidean space. The problems generally relate to questions of local properties (the properties observed at a point on the curve or surface) or global properties (the properties of the object as a whole). Some of the more interesting theorems explore relationships between local and global properties. A special feature is the availability of accompanying online interactive java applets coordinated with each section. The applets allow students to investigate and manipulate curves and surfaces to develop intuition and to help analyze geometric phenomena.
Introduction to differential geometry for engineers
Doolin, Brian F
2013-01-01
This outstanding guide supplies important mathematical tools for diverse engineering applications, offering engineers the basic concepts and terminology of modern global differential geometry. Suitable for independent study as well as a supplementary text for advanced undergraduate and graduate courses, this volume also constitutes a valuable reference for control, systems, aeronautical, electrical, and mechanical engineers.The treatment's ideas are applied mainly as an introduction to the Lie theory of differential equations and to examine the role of Grassmannians in control systems analysis. Additional topics include the fundamental notions of manifolds, tangent spaces, vector fields, exterior algebra, and Lie algebras. An appendix reviews concepts related to vector calculus, including open and closed sets, compactness, continuity, and derivative.
Leibniz algebroids, twistings and exceptional generalized geometry
Baraglia, D.
2012-05-01
We investigate a class of Leibniz algebroids which are invariant under diffeomorphisms and symmetries involving collections of closed forms. Under appropriate assumptions we arrive at a classification which in particular gives a construction starting from graded Lie algebras. In this case the Leibniz bracket is a derived bracket and there are higher derived brackets resulting in an L∞-structure. The algebroids can be twisted by a non-abelian cohomology class and we prove that the twisting class is described by a Maurer-Cartan equation. For compact manifolds we construct a Kuranishi moduli space of this equation which is shown to be affine algebraic. We explain how these results are related to exceptional generalized geometry.
Prospects of inflation with perturbed throat geometry
International Nuclear Information System (INIS)
Ali, Amna; Chingangbam, R.; Panda, Sudhakar; Sami, M.
2009-01-01
We study brane inflation in a warped deformed conifold background that includes general possible corrections to the throat geometry sourced by coupling to the bulk of a compact Calabi-Yau space. We focus specifically, on the perturbation by chiral operator of dimension 3/2 in the CFT. We find that the effective potential in this case can give rise to required number of e-foldings and the spectral index n S consistent with observation. The tensor to scalar ratio of perturbations is generally very low in this scenario. The COBE normalization, however, poses certain difficulties which can be circumvented provided model parameters are properly fine tuned. We find the numerical values of parameters which can give rise to enough inflation, observationally consistent values of density perturbations, scalar to tensor ratio of perturbations and the spectral index n S .
Didactical Design Enrichment of Angle in Geometry
Setiadi, D. R.; Suryadi, D.; Mulyana, E.
2017-09-01
The underlying problem of this research is the lack of student’s competencies in understanding the concept of angle in geometry as the results of the teaching and learning pattern that only to receive the topic rather than to construct the topic and has not paid attention to the learning trajectory. The purpose of this research is to develop the didactical design of angle in space learning activity. The used research method is a method of qualitative research in the form of a didactical design research through three phases of analysis i.e. didactical situation analysis, metapedadidactical analysis, and retrospective analysis, which conducted in students from 10th grade at one of private schools in Bandung. Based on the results of research and discussion, the didactical design that has been made, is capable to change student’s learning habit and quite capable to develop student’s competencies although not optimal.
Critical geometry of a thermal big bang
Afshordi, Niayesh; Magueijo, João
2016-11-01
We explore the space of scalar-tensor theories containing two nonconformal metrics, and find a discontinuity pointing to a "critical" cosmological solution. Due to the different maximal speeds of propagation for matter and gravity, the cosmological fluctuations start off inside the horizon even without inflation, and will more naturally have a thermal origin (since there is never vacuum domination). The critical model makes an unambiguous, nontuned prediction for the spectral index of the scalar fluctuations: nS=0.96478 (64 ) . Considering also that no gravitational waves are produced, we have unveiled the most predictive model on offer. The model has a simple geometrical interpretation as a probe 3-brane embedded in an E AdS2×E3 geometry.
Mapping spaces and automorphism groups of toric noncommutative spaces
Barnes, Gwendolyn E.; Schenkel, Alexander; Szabo, Richard J.
2017-09-01
We develop a sheaf theory approach to toric noncommutative geometry which allows us to formalize the concept of mapping spaces between two toric noncommutative spaces. As an application, we study the `internalized' automorphism group of a toric noncommutative space and show that its Lie algebra has an elementary description in terms of braided derivations.
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...
The geometry of celestial mechanics
Geiges, Hansjörg
2016-01-01
Celestial mechanics is the branch of mathematical astronomy devoted to studying the motions of celestial bodies subject to the Newtonian law of gravitation. This mathematical introductory textbook reveals that even the most basic question in celestial mechanics, the Kepler problem, leads to a cornucopia of geometric concepts: conformal and projective transformations, spherical and hyperbolic geometry, notions of curvature, and the topology of geodesic flows. For advanced undergraduate and beginning graduate students, this book explores the geometric concepts underlying celestial mechanics and is an ideal companion for introductory courses. The focus on the history of geometric ideas makes it perfect supplementary reading for students in elementary geometry and topology. Numerous exercises, historical notes and an extensive bibliography provide all the contextual information required to gain a solid grounding in celestial mechanics.
Differential geometry and mathematical physics
Rudolph, Gerd
Starting from an undergraduate level, this book systematically develops the basics of • Calculus on manifolds, vector bundles, vector fields and differential forms, • Lie groups and Lie group actions, • Linear symplectic algebra and symplectic geometry, • Hamiltonian systems, symmetries and reduction, integrable systems and Hamilton-Jacobi theory. The topics listed under the first item are relevant for virtually all areas of mathematical physics. The second and third items constitute the link between abstract calculus and the theory of Hamiltonian systems. The last item provides an introduction to various aspects of this theory, including Morse families, the Maslov class and caustics. The book guides the reader from elementary differential geometry to advanced topics in the theory of Hamiltonian systems with the aim of making current research literature accessible. The style is that of a mathematical textbook,with full proofs given in the text or as exercises. The material is illustrated by numerous d...
Grassmannian geometry of scattering amplitudes
Arkani-Hamed, Nima; Cachazo, Freddy; Goncharov, Alexander; Postnikov, Alexander; Trnka, Jaroslav
2016-01-01
Outlining a revolutionary reformulation of the foundations of perturbative quantum field theory, this book is a self-contained and authoritative analysis of the application of this new formulation to the case of planar, maximally supersymmetric Yang–Mills theory. The book begins by deriving connections between scattering amplitudes and Grassmannian geometry from first principles before introducing novel physical and mathematical ideas in a systematic manner accessible to both physicists and mathematicians. The principle players in this process are on-shell functions which are closely related to certain sub-strata of Grassmannian manifolds called positroids - in terms of which the classification of on-shell functions and their relations becomes combinatorially manifest. This is an essential introduction to the geometry and combinatorics of the positroid stratification of the Grassmannian and an ideal text for advanced students and researchers working in the areas of field theory, high energy physics, and the...
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...
Riemannian geometry during the second half of the twentieth century
Berger, Marcel
1999-01-01
In the last fifty years of the twentieth century Riemannian geometry has exploded with activity. Berger marks the start of this period with Rauch's pioneering paper of 1951, which contains the first real pinching theorem and an amazing leap in the depth of the connection between geometry and topology. Since then, the field has become so rich that it is almost impossible for the uninitiated to find their way through it. Textbooks on the subject invariably must choose a particular approach, thus narrowing the path. In this book, Berger provides a truly remarkable survey of the main developments in Riemannian geometry in the last fifty years, focusing his main attention on the following five areas: Curvature and topology; the construction of and the classification of space forms; distinguished metrics, especially Einstein metrics; eigenvalues and eigenfunctions of the Laplacian; the study of periodic geodesics and the geodesic flow. Other topics are treated in less detail in a separate section. Berger's survey p...
Non commutative geometry and super Yang-Mills theory
International Nuclear Information System (INIS)
Bigatti, D.
1999-01-01
We aim to connect the non commutative geometry 'quotient space' viewpoint with the standard super Yang Mills theory approach in the spirit of Connes-Douglas-Schwartz and Douglas-Hull description of application of noncommutative geometry to matrix theory. This will result in a relation between the parameters of a rational foliation of the torus and the dimension of the group U(N). Namely, we will be provided with a prescription which allows to study a noncommutative geometry with rational parameter p/N by means of a U(N) gauge theory on a torus of size Σ/N with the boundary conditions given by a system with p units of magnetic flux. The transition to irrational parameter can be obtained by letting N and p tend to infinity with fixed ratio. The precise meaning of the limiting process will presumably allow better clarification. (Copyright (c) 1999 Elsevier Science B.V., Amsterdam. All rights reserved.)
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.