Hoffman, Kenneth
2007-01-01
Developed for an introductory course in mathematical analysis at MIT, this text focuses on concepts, principles, and methods. Its introductions to real and complex analysis are closely formulated, and they constitute a natural introduction to complex function theory.Starting with an overview of the real number system, the text presents results for subsets and functions related to Euclidean space of n dimensions. It offers a rigorous review of the fundamentals of calculus, emphasizing power series expansions and introducing the theory of complex-analytic functions. Subsequent chapters cover seq
Variational submanifolds of Euclidean spaces
Krupka, D.; Urban, Z.; Volná, J.
2018-03-01
Systems of ordinary differential equations (or dynamical forms in Lagrangian mechanics), induced by embeddings of smooth fibered manifolds over one-dimensional basis, are considered in the class of variational equations. For a given non-variational system, conditions assuring variationality (the Helmholtz conditions) of the induced system with respect to a submanifold of a Euclidean space are studied, and the problem of existence of these "variational submanifolds" is formulated in general and solved for second-order systems. The variational sequence theory on sheaves of differential forms is employed as a main tool for the analysis of local and global aspects (variationality and variational triviality). The theory is illustrated by examples of holonomic constraints (submanifolds of a configuration Euclidean space) which are variational submanifolds in geometry and mechanics.
Random walks in Euclidean space
Varjú, Péter Pál
2012-01-01
Consider a sequence of independent random isometries of Euclidean space with a previously fixed probability law. Apply these isometries successively to the origin and consider the sequence of random points that we obtain this way. We prove a local limit theorem under a suitable moment condition and a necessary non-degeneracy condition. Under stronger hypothesis, we prove a limit theorem on a wide range of scales: between e^(-cl^(1/4)) and l^(1/2), where l is the number of steps.
Noncommutative products of Euclidean spaces
Dubois-Violette, Michel; Landi, Giovanni
2018-05-01
We present natural families of coordinate algebras on noncommutative products of Euclidean spaces R^{N_1} × _R R^{N_2} . These coordinate algebras are quadratic ones associated with an R -matrix which is involutive and satisfies the Yang-Baxter equations. As a consequence, they enjoy a list of nice properties, being regular of finite global dimension. Notably, we have eight-dimensional noncommutative euclidean spaces R4 × _R R4 . Among these, particularly well behaved ones have deformation parameter u \\in S^2 . Quotients include seven spheres S7_u as well as noncommutative quaternionic tori TH_u = S^3 × _u S^3 . There is invariance for an action of {{SU}}(2) × {{SU}}(2) on the torus TH_u in parallel with the action of U(1) × U(1) on a `complex' noncommutative torus T^2_θ which allows one to construct quaternionic toric noncommutative manifolds. Additional classes of solutions are disjoint from the classical case.
Ideas of space. Euclidean, non-Euclidean and relativistic
Energy Technology Data Exchange (ETDEWEB)
Gray, J
1979-01-01
An historical and chronological account of mathematics is presented in which familiarity with simple equations and elements of trigonometry is needed but no specialist knowledge is assumed although difficult problems are discussed. By discussion of the difficulties and confusions it is hoped to understand mathematics as a dynamic activity. Beginning with early Greek mathematics, the Eastern legacy and the transition to deductive and geometric thinking the problem of parallels is then encountered and discussed. The second part of the book takes the story from Wallis, Saccheri and Lambert through to its resolution by Gauss, Lobachevskii, Bolyai, Riemann and Bettrami. The background of the 19th century theory of surfaces is given. The third part gives an account of Einstein's theories based on what has gone before, moving from a Newtonian-Euclidean picture to an Einsteinian-nonEuclidean one. A brief account of gravitation, the nature of space and black holes concludes the book.
Fuzzy Euclidean wormholes in de Sitter space
Energy Technology Data Exchange (ETDEWEB)
Chen, Pisin; Hu, Yao-Chieh; Yeom, Dong-han, E-mail: pisinchen@phys.ntu.edu.tw, E-mail: r04244003@ntu.edu.tw, E-mail: innocent.yeom@gmail.com [Leung Center for Cosmology and Particle Astrophysics, National Taiwan University, Taipei 10617, Taiwan (China)
2017-07-01
We investigate Euclidean wormholes in Einstein gravity with a massless scalar field in de Sitter space. Euclidean wormholes are possible due to the analytic continuation of the time as well as complexification of fields, where we need to impose the classicality after the Wick-rotation to the Lorentzian signatures. For some parameters, wormholes are preferred than Hawking-Moss instantons, and hence wormholes can be more fundamental than Hawking-Moss type instantons. Euclidean wormholes can be interpreted in three ways: (1) classical big bounce, (2) either tunneling from a small to a large universe or a creation of a collapsing and an expanding universe from nothing, and (3) either a transition from a contracting to a bouncing phase or a creation of two expanding universes from nothing. These various interpretations shed some light on challenges of singularities. In addition, these will help to understand tensions between various kinds of quantum gravity theories.
Calculus and analysis in Euclidean space
Shurman, Jerry
2016-01-01
The graceful role of analysis in underpinning calculus is often lost to their separation in the curriculum. This book entwines the two subjects, providing a conceptual approach to multivariable calculus closely supported by the structure and reasoning of analysis. The setting is Euclidean space, with the material on differentiation culminating in the inverse and implicit function theorems, and the material on integration culminating in the general fundamental theorem of integral calculus. More in-depth than most calculus books but less technical than a typical analysis introduction, Calculus and Analysis in Euclidean Space offers a rich blend of content to students outside the traditional mathematics major, while also providing transitional preparation for those who will continue on in the subject. The writing in this book aims to convey the intent of ideas early in discussion. The narrative proceeds through figures, formulas, and text, guiding the reader to do mathematics resourcefully by marshaling the skil...
Bochner-Riesz means on Euclidean spaces
Lu, Shanzhen
2013-01-01
This book mainly deals with the Bochner-Riesz means of multiple Fourier integral and series on Euclidean spaces. It aims to give a systematical introduction to the fundamental theories of the Bochner-Riesz means and important achievements attained in the last 50 years. For the Bochner-Riesz means of multiple Fourier integral, it includes the Fefferman theorem which negates the Disc multiplier conjecture, the famous Carleson-Sjölin theorem, and Carbery-Rubio de Francia-Vega's work on almost everywhere convergence of the Bochner-Riesz means below the critical index. For the Bochner-Riesz means o
Uniform Page Migration Problem in Euclidean Space
Directory of Open Access Journals (Sweden)
Amanj Khorramian
2016-08-01
Full Text Available The page migration problem in Euclidean space is revisited. In this problem, online requests occur at any location to access a single page located at a server. Every request must be served, and the server has the choice to migrate from its current location to a new location in space. Each service costs the Euclidean distance between the server and request. A migration costs the distance between the former and the new server location, multiplied by the page size. We study the problem in the uniform model, in which the page has size D = 1 . All request locations are not known in advance; however, they are sequentially presented in an online fashion. We design a 2.75 -competitive online algorithm that improves the current best upper bound for the problem with the unit page size. We also provide a lower bound of 2.732 for our algorithm. It was already known that 2.5 is a lower bound for this problem.
International Nuclear Information System (INIS)
Saveliev, M.V.
1983-01-01
In the framework of the algebraic approach a construction of exactly integrable two-dimensional Riemannian manifolds embedded into enveloping Euclidean (pseudo-Euclidean) space Rsub(N) of an arbitrary dimension is presented. The construction is based on a reformulation of the Gauss, Peterson-Codazzi and Ricci equations in the form of a Lax-type representation in two-dimensional space. Here the Lax pair operators take the values in algebra SO(N)
Extended supersymmetry in four-dimensional Euclidean space
International Nuclear Information System (INIS)
McKeon, D.G.C.; Sherry, T.N.
2000-01-01
Since the generators of the two SU(2) groups which comprise SO(4) are not Hermitian conjugates of each other, the simplest supersymmetry algebra in four-dimensional Euclidean space more closely resembles the N=2 than the N=1 supersymmetry algebra in four-dimensional Minkowski space. An extended supersymmetry algebra in four-dimensional Euclidean space is considered in this paper; its structure resembles that of N=4 supersymmetry in four-dimensional Minkowski space. The relationship of this algebra to the algebra found by dimensionally reducing the N=1 supersymmetry algebra in ten-dimensional Euclidean space to four-dimensional Euclidean space is examined. The dimensional reduction of N=1 super Yang-Mills theory in ten-dimensional Minkowski space to four-dimensional Euclidean space is also considered
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.
On the invariant theory of Weingarten surfaces in Euclidean space
International Nuclear Information System (INIS)
Ganchev, Georgi; Mihova, Vesselka
2010-01-01
On any Weingarten surface in Euclidean space (strongly regular or rotational), we introduce locally geometric principal parameters and prove that such a surface is determined uniquely up to a motion by a special invariant function, which satisfies a natural nonlinear partial differential equation. This result can be interpreted as a solution to the Lund-Regge reduction problem for Weingarten surfaces in Euclidean space. We apply this theory to fractional-linear Weingarten surfaces and obtain the nonlinear partial differential equations describing them.
What does the Euclidean pseudoparticle do in Minkowski space
International Nuclear Information System (INIS)
Ju, I.
1978-08-01
Self dual pseudoparticle solutions for the classical Yang--Mills field equation with finite action have been constructed in Minkowski space. It is shown that the topological structures apparent in Euclidean space are no longer present in Minkowski space. Topological charges become fractional leading to the unquantized axial charge violation in the process involving fermions. 17 references
Optimal Embeddings of Distance Regular Graphs into Euclidean Spaces
F. Vallentin (Frank)
2008-01-01
htmlabstractIn this paper we give a lower bound for the least distortion embedding of a distance regular graph into Euclidean space. We use the lower bound for finding the least distortion for Hamming graphs, Johnson graphs, and all strongly regular graphs. Our technique involves semidefinite
International Nuclear Information System (INIS)
Catoni, Francesco; Cannata, Roberto; Zampetti, Paolo
2005-08-01
The Riemann and Lorentz constant curvature surfaces are investigated from an Euclidean point of view. The four surfaces (constant positive and constant negative curvatures with definite and non-definite fine elements) are represented as surfaces in a Riemannian or in a particular semi-Riemannian flat space and it is shown that the complex and the hyperbolic numbers allow to obtain the same equations for the corresponding Riemann and Lorentz surfaces, respectively. Moreover it is shown that the geodesics on the Lorentz surfaces states, from a physical point of view, a link between curvature and fields. This result is obtained just as a consequence of the space-time geometrical symmetry, without invoking the famous Einstein general relativity postulate [it
Biharmonic Submanifolds with Parallel Mean Curvature Vector in Pseudo-Euclidean Spaces
Energy Technology Data Exchange (ETDEWEB)
Fu, Yu, E-mail: yufudufe@gmail.com [Dongbei University of Finance and Economics, School of Mathematics and Quantitative Economics (China)
2013-12-15
In this paper, we investigate biharmonic submanifolds in pseudo-Euclidean spaces with arbitrary index and dimension. We give a complete classification of biharmonic spacelike submanifolds with parallel mean curvature vector in pseudo-Euclidean spaces. We also determine all biharmonic Lorentzian surfaces with parallel mean curvature vector field in pseudo-Euclidean spaces.
Biharmonic Submanifolds with Parallel Mean Curvature Vector in Pseudo-Euclidean Spaces
International Nuclear Information System (INIS)
Fu, Yu
2013-01-01
In this paper, we investigate biharmonic submanifolds in pseudo-Euclidean spaces with arbitrary index and dimension. We give a complete classification of biharmonic spacelike submanifolds with parallel mean curvature vector in pseudo-Euclidean spaces. We also determine all biharmonic Lorentzian surfaces with parallel mean curvature vector field in pseudo-Euclidean spaces
Spinors and supersymmetry in four-dimensional Euclidean space
International Nuclear Information System (INIS)
McKeon, D.G.C.; Sherry, T.N.
2001-01-01
Spinors in four-dimensional Euclidean space are treated using the decomposition of the Euclidean space SO(4) symmetry group into SU(2)xSU(2). Both 2- and 4-spinor representations of this SO(4) symmetry group are shown to differ significantly from the corresponding spinor representations of the SO(3, 1) symmetry group in Minkowski space. The simplest self conjugate supersymmetry algebra allowed in four-dimensional Euclidean space is demonstrated to be an N=2 supersymmetry algebra which resembles the N=2 supersymmetry algebra in four-dimensional Minkowski space. The differences between the two supersymmetry algebras gives rise to different representations; in particular an analysis of the Clifford algebra structure shows that the momentum invariant is bounded above by the central charges in 4dE, while in 4dM the central charges bound the momentum invariant from below. Dimensional reduction of the N=1 SUSY algebra in six-dimensional Minkowski space (6dM) to 4dE reproduces our SUSY algebra in 4dE. This dimensional reduction can be used to introduce additional generators into the SUSY algebra in 4dE. Well known interpolating maps are used to relate the N=2 SUSY algebra in 4dE derived in this paper to the N=2 SUSY algebra in 4dM. The nature of the spinors in 4dE allows us to write an axially gauge invariant model which is shown to be both Hermitian and anomaly-free. No equivalent model exists in 4dM. Useful formulae in 4dE are collected together in two appendixes
A Class of Weingarten Surfaces in Euclidean 3-Space
Directory of Open Access Journals (Sweden)
Yu Fu
2013-01-01
Full Text Available The class of biconservative surfaces in Euclidean 3-space 3 are defined in (Caddeo et al., 2012 by the equation A(grad H=-H grad H for the mean curvature function H and the Weingarten operator A. In this paper, we consider the more general case that surfaces in 3 satisfying A(grad H=kH grad H for some constant k are called generalized bi-conservative surfaces. We show that this class of surfaces are linear Weingarten surfaces. We also give a complete classification of generalized bi-conservative surfaces in 3.
Complex networks in the Euclidean space of communicability distances
Estrada, Ernesto
2012-06-01
We study the properties of complex networks embedded in a Euclidean space of communicability distances. The communicability distance between two nodes is defined as the difference between the weighted sum of walks self-returning to the nodes and the weighted sum of walks going from one node to the other. We give some indications that the communicability distance identifies the least crowded routes in networks where simultaneous submission of packages is taking place. We define an index Q based on communicability and shortest path distances, which allows reinterpreting the “small-world” phenomenon as the region of minimum Q in the Watts-Strogatz model. It also allows the classification and analysis of networks with different efficiency of spatial uses. Consequently, the communicability distance displays unique features for the analysis of complex networks in different scenarios.
Characterizations of Space Curves According to Bishop Darboux Vector in Euclidean 3-Space E3
Huseyin KOCAYIGIT; Ali OZDEMIR
2014-01-01
In this paper, we obtained some characterizations of space curves according to Bihop frame in Euclidean 3-space E3 by using Laplacian operator and Levi-Civita connection. Furthermore, we gave the general differential equations which characterize the space curves according to the Bishop Darboux vector and the normal Bishop Darboux vector.
Euclidean and Minkowski space formulations of linearized gravitational potential in various gauges
International Nuclear Information System (INIS)
Lim, S.C.
1979-01-01
We show that there exists a unitary map connecting linearized theories of gravitational potential in vacuum, formulated in various covariant gauges and noncovariant radiation gauge. The free Euclidean gravitational potentials in covariant gauges satisfy the Markov property of Nelson, but are nonreflexive. For the noncovariant radiation gauge, the corresponding Euclidean field is reflexive but it only satisfies the Markov property with respect to special half spaces. The Feynman--Kac--Nelson formula is established for the Euclidean gravitational potential in radiation gauge
Large parallel volumes of finite and compact sets in d-dimensional Euclidean space
DEFF Research Database (Denmark)
Kampf, Jürgen; Kiderlen, Markus
The r-parallel volume V (Cr) of a compact subset C in d-dimensional Euclidean space is the volume of the set Cr of all points of Euclidean distance at most r > 0 from C. According to Steiner’s formula, V (Cr) is a polynomial in r when C is convex. For finite sets C satisfying a certain geometric...
Asymptotic analysis of fundamental solutions of Dirac operators on even dimensional Euclidean spaces
International Nuclear Information System (INIS)
Arai, A.
1985-01-01
We analyze the short distance asymptotic behavior of some quantities formed out of fundamental solutions of Dirac operators on even dimensional Euclidean spaces with finite dimensional matrix-valued potentials. (orig.)
Manton, Jonathan H.
2012-01-01
The Newton iteration is a popular method for minimising a cost function on Euclidean space. Various generalisations to cost functions defined on manifolds appear in the literature. In each case, the convergence rate of the generalised Newton iteration needed establishing from first principles. The present paper presents a framework for generalising iterative methods from Euclidean space to manifolds that ensures local convergence rates are preserved. It applies to any (memoryless) iterative m...
General Rotational Surfaces in Pseudo-Euclidean 4-Space with Neutral Metric
Aleksieva, Yana; Milousheva, Velichka; Turgay, Nurettin Cenk
2016-01-01
We define general rotational surfaces of elliptic and hyperbolic type in the pseudo-Euclidean 4-space with neutral metric which are analogous to the general rotational surfaces of C. Moore in the Euclidean 4-space. We study Lorentz general rotational surfaces with plane meridian curves and give the complete classification of minimal general rotational surfaces of elliptic and hyperbolic type, general rotational surfaces with parallel normalized mean curvature vector field, flat general rotati...
Intrinsic Regularization in a Lorentz invariant non-orthogonal Euclidean Space
Tornow, Carmen
2006-01-01
It is shown that the Lorentz transformations can be derived for a non-orthogonal Euclidean space. In this geometry one finds the same relations of special relativity as the ones known from the orthogonal Minkowski space. In order to illustrate the advantage of a non-orthogonal Euclidean metric the two-point Green’s function at x = 0 for a self-interacting scalar field is calculated. In contrast to the Minkowski space the one loop mass correction derived from this function gives a convergent r...
Scalar Green's functions in an Euclidean space with a conical-type line singularity
International Nuclear Information System (INIS)
Guimaraes, M.E.X.; Linet, B.
1994-01-01
In an Euclidean space with a conical-type line singularity, we determine the Green's function for a charged massive scalar field interacting with a magnetic flux running through the line singularity. We give an integral expression of the Green's function and a local form in the neighbourhood of the point source, where it is the sum of the usual Green's function in Euclidean space and a regular term. As an application, we derive the vacuum energy-momentum tensor in the massless case for an arbitrary magnetic flux. (orig.)
Linear embeddings of finite-dimensional subsets of Banach spaces into Euclidean spaces
International Nuclear Information System (INIS)
Robinson, James C
2009-01-01
This paper treats the embedding of finite-dimensional subsets of a Banach space B into finite-dimensional Euclidean spaces. When the Hausdorff dimension of X − X is finite, d H (X − X) k are injective on X. The proof motivates the definition of the 'dual thickness exponent', which is the key to proving that a prevalent set of such linear maps have Hölder continuous inverse when the box-counting dimension of X is finite and k > 2d B (X). A related argument shows that if the Assouad dimension of X − X is finite and k > d A (X − X), a prevalent set of such maps are bi-Lipschitz with logarithmic corrections. This provides a new result for compact homogeneous metric spaces via the Kuratowksi embedding of (X, d) into L ∞ (X)
Faster exact algorithms for computing Steiner trees in higher dimensional Euclidean spaces
DEFF Research Database (Denmark)
Fonseca, Rasmus; Brazil, Marcus; Winter, Pawel
The Euclidean Steiner tree problem asks for a network of minimum total length interconnecting a finite set of points in d-dimensional space. For d ≥ 3, only one practical algorithmic approach exists for this problem --- proposed by Smith in 1992. A number of refinements of Smith's algorithm have...
Convexity and the Euclidean Metric of Space-Time
Directory of Open Access Journals (Sweden)
Nikolaos Kalogeropoulos
2017-02-01
Full Text Available We address the reasons why the “Wick-rotated”, positive-definite, space-time metric obeys the Pythagorean theorem. An answer is proposed based on the convexity and smoothness properties of the functional spaces purporting to provide the kinematic framework of approaches to quantum gravity. We employ moduli of convexity and smoothness which are eventually extremized by Hilbert spaces. We point out the potential physical significance that functional analytical dualities play in this framework. Following the spirit of the variational principles employed in classical and quantum Physics, such Hilbert spaces dominate in a generalized functional integral approach. The metric of space-time is induced by the inner product of such Hilbert spaces.
de Wit, Bernard; Reys, Valentin
2017-12-01
Supergravity with eight supercharges in a four-dimensional Euclidean space is constructed at the full non-linear level by performing an off-shell time-like reduction of five-dimensional supergravity. The resulting four-dimensional theory is realized off-shell with the Weyl, vector and tensor supermultiplets and a corresponding multiplet calculus. Hypermultiplets are included as well, but they are themselves only realized with on-shell supersymmetry. We also briefly discuss the non-linear supermultiplet. The off-shell reduction leads to a full understanding of the Euclidean theory. A complete multiplet calculus is presented along the lines of the Minkowskian theory. Unlike in Minkowski space, chiral and anti-chiral multiplets are real and supersymmetric actions are generally unbounded from below. Precisely as in the Minkowski case, where one has different formulations of Poincaré supergravity upon introducing different compensating supermultiplets, one can also obtain different versions of Euclidean supergravity.
From Euclidean to Minkowski space with the Cauchy-Riemann equations
International Nuclear Information System (INIS)
Gimeno-Segovia, Mercedes; Llanes-Estrada, Felipe J.
2008-01-01
We present an elementary method to obtain Green's functions in non-perturbative quantum field theory in Minkowski space from Green's functions calculated in Euclidean space. Since in non-perturbative field theory the analytical structure of amplitudes often is unknown, especially in the presence of confined fields, dispersive representations suffer from systematic uncertainties. Therefore, we suggest to use the Cauchy-Riemann equations, which perform the analytical continuation without assuming global information on the function in the entire complex plane, but only in the region through which the equations are solved. We use as example the quark propagator in Landau gauge quantum chromodynamics, which is known from lattice and Dyson-Schwinger studies in Euclidean space. The drawback of the method is the instability of the Cauchy-Riemann equations against high-frequency noise,which makes it difficult to achieve good accuracy. We also point out a few curious details related to the Wick rotation. (orig.)
Green's functions in Bianchi type-I spaces. Relation between Minkowski and Euclidean approaches
International Nuclear Information System (INIS)
Bukhbinder, I.L.; Kirillova, E.N.
1988-01-01
A theory is considered for a free scalar field with a conformal connection in a curved space-time with a Bianchi type-I metric. A representation is obtained for the Green's function G∼ in in in the form of an integral of a Schwinger-DeWitt kernel along a contour in a plane of complex-valued proper time. It is shown how as transition may be accomplished from Green's functions in space with the Euclidean signature to Green's functions in space with Minkowski signature and vice versa
Steiner tree heuristic in the Euclidean d-space using bottleneck distances
DEFF Research Database (Denmark)
Lorenzen, Stephan Sloth; Winter, Pawel
2016-01-01
Some of the most efficient heuristics for the Euclidean Steiner minimal tree problem in the d-dimensional space, d ≥2, use Delaunay tessellations and minimum spanning trees to determine small subsets of geometrically close terminals. Their low-cost Steiner trees are determined and concatenated...... in a greedy fashion to obtain a low cost tree spanning all terminals. The weakness of this approach is that obtained solutions are topologically related to minimum spanning trees. To avoid this and to obtain even better solutions, bottleneck distances are utilized to determine good subsets of terminals...
The stochastic versus the Euclidean approach to quantum fields on a static space-time
International Nuclear Information System (INIS)
De Angelis, G.F.; de Falco, D.
1986-01-01
Equations are presented which modify the definition of the Gaussian field in the Rindler chart in order to make contact with the Wightman state, the Hartle-Hawking state, and the Euclidean field. By taking Ornstein-Uhlenbeck processes the authors have chosen, in the sense of stochastic mechanics, to place precisely the Fulling modes in their harmonic oscillator ground state. In this respect, together with the periodicity of Minkowski space-time, the authors observe that the covariance of the Ornstein-Uhlenbeck process can be obtained by analytical continuation of the Wightman function of the harmonic oscillator at zero temperature
Derivatives, forms and vector fields on the κ-deformed Euclidean space
International Nuclear Information System (INIS)
Dimitrijevic, Marija; Moeller, Lutz; Tsouchnika, Efrossini
2004-01-01
The model of κ-deformed space is an interesting example of a noncommutative space, since it allows a deformed symmetry. In this paper, we present new results concerning different sets of derivatives on the coordinate algebra of κ-deformed Euclidean space. We introduce a differential calculus with two interesting sets of one-forms and higher-order forms. The transformation law of vector fields is constructed in accordance with the transformation behaviour of derivatives. The crucial property of the different derivatives, forms and vector fields is that in an n-dimensional spacetime there are always n of them. This is the key difference with respect to conventional approaches, in which the differential calculus is (n + 1)-dimensional. This work shows that derivative-valued quantities such as derivative-valued vector fields appear in a generic way on noncommutative spaces
A relationship between scalar Green functions on hyperbolic and Euclidean Rindler spaces
International Nuclear Information System (INIS)
Haba, Z
2007-01-01
We derive a formula connecting in any dimension the Green function on the (D + 1)-dimensional Euclidean Rindler space and the one for a minimally coupled scalar field with a mass m in the D-dimensional hyperbolic space. The relation takes a simple form in the momentum space where the Green functions are equal at the momenta (p 0 , p) for Rindler and (m,p-hat) for hyperbolic space with a simple additive relation between the squares of the mass and the momenta. The formula has applications to finite temperature Green functions, Green functions on the cone and on the (compactified) Milne spacetime. Analytic continuations and interacting quantum fields are briefly discussed
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...
Euclidean scalar Green function in a higher dimensional global monopole space-time
International Nuclear Information System (INIS)
Bezerra de Mello, E.R.
2002-01-01
We construct the explicit Euclidean scalar Green function associated with a massless field in a higher dimensional global monopole space-time, i.e., a (1+d)-space-time with d≥3 which presents a solid angle deficit. Our result is expressed in terms of an infinite sum of products of Legendre functions with Gegenbauer polynomials. Although this Green function cannot be expressed in a closed form, for the specific case where the solid angle deficit is very small, it is possible to develop the sum and obtain the Green function in a more workable expression. Having this expression it is possible to calculate the vacuum expectation value of some relevant operators. As an application of this formalism, we calculate the renormalized vacuum expectation value of the square of the scalar field, 2 (x)> Ren , and the energy-momentum tensor, μν (x)> Ren , for the global monopole space-time with spatial dimensions d=4 and d=5
Superintegrability in two-dimensional Euclidean space and associated polynomial solutions
International Nuclear Information System (INIS)
Kalnins, E.G.; Miller, W. Jr; Pogosyan, G.S.
1996-01-01
In this work we examine the basis functions for those classical and quantum mechanical systems in two dimensions which admit separation of variables in at least two coordinate systems. We do this for the corresponding systems defined in Euclidean space and on the two dimensional sphere. We present all of these cases from a unified point of view. In particular, all of the spectral functions that arise via variable separation have their essential features expressed in terms of their zeros. The principal new results are the details of the polynomial base for each of the nonsubgroup base, not just the subgroup cartesian and polar coordinate case, and the details of the structure of the quadratic algebras. We also study the polynomial eigenfunctions in elliptic coordinates of the N-dimensional isotropic quantum oscillator. 28 refs., 1 tab
New results on embeddings of polyhedra and manifolds in Euclidean spaces
International Nuclear Information System (INIS)
Repovs, D; Skopenkov, A B
1999-01-01
The aim of this survey is to present several classical results on embeddings and isotopies of polyhedra and manifolds in R m . We also describe the revival of interest in this beautiful branch of topology and give an account of new results, including an improvement of the Haefliger-Weber theorem on the completeness of the deleted product obstruction to embeddability and isotopy of highly connected manifolds in R m (Skopenkov) as well as the unimprovability of this theorem for polyhedra (Freedman, Krushkal, Teichner, Segal, Skopenkov, and Spiez) and for manifolds without the necessary connectedness assumption (Skopenkov). We show how algebraic obstructions (in terms of cohomology, characteristic classes, and equivariant maps) arise from geometric problems of embeddability in Euclidean spaces. Several classical and modern results on completeness or incompleteness of these obstructions are stated and proved. By these proofs we illustrate classical and modern tools of geometric topology (engulfing, the Whitney trick, van Kampen and Casson finger moves, and their generalizations)
Classical and quantum integrability of 2D dilaton gravities in Euclidean space
International Nuclear Information System (INIS)
Bergamin, L; Grumiller, D; Kummer, W; Vassilevich, D V
2005-01-01
Euclidean dilaton gravity in two dimensions is studied exploiting its representation as a complexified first order gravity model. All local classical solutions are obtained. A global discussion reveals that for a given model only a restricted class of topologies is consistent with the metric and the dilaton. A particular case of string motivated Liouville gravity is studied in detail. Path integral quantization in generic Euclidean dilaton gravity is performed non-perturbatively by analogy to the Minkowskian case
$O(N)$ model in Euclidean de Sitter space: beyond the leading infrared approximation
Nacir, Diana López; Trombetta, Leonardo G
2016-01-01
We consider an $O(N)$ scalar field model with quartic interaction in $d$-dimensional Euclidean de Sitter space. In order to avoid the problems of the standard perturbative calculations for light and massless fields, we generalize to the $O(N)$ theory a systematic method introduced previously for a single field, which treats the zero modes exactly and the nonzero modes perturbatively. We compute the two-point functions taking into account not only the leading infrared contribution, coming from the self-interaction of the zero modes, but also corrections due to the interaction of the ultraviolet modes. For the model defined in the corresponding Lorentzian de Sitter spacetime, we obtain the two-point functions by analytical continuation. We point out that a partial resummation of the leading secular terms (which necessarily involves nonzero modes) is required to obtain a decay at large distances for massless fields. We implement this resummation along with a systematic double expansion in an effective coupling c...
International Nuclear Information System (INIS)
Bezerra de Mello, E.R.
2006-01-01
In this paper we present, in a integral form, the Euclidean Green function associated with a massless scalar field in the five-dimensional Kaluza-Klein magnetic monopole superposed to a global monopole, admitting a nontrivial coupling between the field with the geometry. This Green function is expressed as the sum of two contributions: the first one related with uncharged component of the field, is similar to the Green function associated with a scalar field in a four-dimensional global monopole space-time. The second contains the information of all the other components. Using this Green function it is possible to study the vacuum polarization effects on this space-time. Explicitly we calculate the renormalized vacuum expectation value * (x)Φ(x)> Ren , which by its turn is also expressed as the sum of two contributions
Wang, Yong-Long; Jiang, Hua; Zong, Hong-Shi
2017-08-01
In the spirit of the thin-layer quantization approach, we give the formula of the geometric influences of a particle confined to a curved surface embedded in three-dimensional Euclidean space. The geometric contributions can result from the reduced commutation relation between the acted function depending on normal variable and the normal derivative. According to the formula, we obtain the geometric potential, geometric momentum, geometric orbital angular momentum, geometric linear Rashba, and cubic Dresselhaus spin-orbit couplings. As an example, a truncated cone surface is considered. We find that the geometric orbital angular momentum can provide an azimuthal polarization for spin, and the sign of the geometric Dresselhaus spin-orbit coupling can be flipped through the inclination angle of generatrix.
Biess, Armin
2013-01-01
The study of the kinematic and dynamic features of human arm movements provides insights into the computational strategies underlying human motor control. In this paper a differential geometric approach to movement control is taken by endowing arm configuration space with different non-Euclidean metric structures to study the predictions of the generalized minimum-jerk (MJ) model in the resulting Riemannian manifold for different types of human arm movements. For each metric space the solution of the generalized MJ model is given by reparametrized geodesic paths. This geodesic model is applied to a variety of motor tasks ranging from three-dimensional unconstrained movements of a four degree of freedom arm between pointlike targets to constrained movements where the hand location is confined to a surface (e.g., a sphere) or a curve (e.g., an ellipse). For the latter speed-curvature relations are derived depending on the boundary conditions imposed (periodic or nonperiodic) and the compatibility with the empirical one-third power law is shown. Based on these theoretical studies and recent experimental findings, I argue that geodesics may be an emergent property of the motor system and that the sensorimotor system may shape arm configuration space by learning metric structures through sensorimotor feedback.
Improved Epstein-Glaser Renormalization in Coordinate Space I. Euclidean Framework
International Nuclear Information System (INIS)
Gracia-Bondia, Jose M.
2003-01-01
In a series of papers, we investigate the reformulation of Epstein-Glaser renormalization in coordinate space, both in analytic and (Hopf) algebraic terms. This first article deals with analytical aspects. Some of the (historically good) reasons for the divorces of the Epstein-Glaser method, both from mainstream quantum field theory and the mathematical literature on distributions, are made plain; and overcome
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
Learning Euclidean Embeddings for Indexing and Classification
National Research Council Canada - National Science Library
Athitsos, Vassilis; Alon, Joni; Sclaroff, Stan; Kollios, George
2004-01-01
BoostMap is a recently proposed method for efficient approximate nearest neighbor retrieval in arbitrary non-Euclidean spaces with computationally expensive and possibly non-metric distance measures...
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.
Micrononcasual Euclidean wave functions
International Nuclear Information System (INIS)
Enatsu, H.; Takenaka, A.; Okazaki, M.
1978-01-01
A theory which describes the internal attributes of hadrons in terms of space-time wave functions is presented. In order to develop the theory on the basis of a rather realistic model, covariant wave equations are first derived for the deuteron, in which the co-ordinates of the centre of mass of two nucleons can be defined unambiguously. Then the micro-noncasual behaviour of virtual mesons mediating between the two nucleons is expressed by means of wave functions depending only on the relative Euclidean co-ordinates with respect to the centre of mass of the two nucleons; the wave functions are assumed to obey the 0 4 and SU 2 x SU 2 groups. The properties of the wave functions under space inversion, time reversal and particle-antiparticle conjugation are investigated. It is found that the internal attributes of the mesons, such as spin, isospin, strangeness, intrinsic parity, charge parity and G-parity are explained consistently. The theory is applicable also to the case of baryons
Local algebras in Euclidean quantum field theory
International Nuclear Information System (INIS)
Guerra, Francesco.
1975-06-01
The general structure of the local observable algebras of Euclidean quantum field theory is described, considering the very simple examples of the free scalar field, the vector meson field, and the electromagnetic field. The role of Markov properties, and the relations between Euclidean theory and Hamiltonian theory in Minkowski space-time are especially emphasized. No conflict appears between covariance (in the Euclidean sense) and locality (in the Markov sense) on one hand and positive definiteness of the metric on the other hand [fr
Trudeau, Richard J
1986-01-01
How unique and definitive is Euclidean geometry in describing the "real" space in which we live? Richard Trudeau confronts the fundamental question of truth and its representation through mathematical models in The Non-Euclidean Revolution. First, the author analyzes geometry in its historical and philosophical setting; second, he examines a revolution every bit as significant as the Copernican revolution in astronomy and the Darwinian revolution in biology; third, on the most speculative level, he questions the possibility of absolute knowledge of the world. Trudeau writes in a lively, entertaining, and highly accessible style. His book provides one of the most stimulating and personal presentations of a struggle with the nature of truth in mathematics and the physical world. A portion of the book won the Pólya Prize, a distinguished award from the Mathematical Association of America. "Trudeau meets the challenge of reaching a broad audience in clever ways...(The book) is a good addition to our literature o...
Energy Technology Data Exchange (ETDEWEB)
Oblakov, Konstantin I; Oblakova, Tat' yana A [M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow (Russian Federation)
2012-10-31
The paper is devoted to the characteristic of a graph that is the minimal (over all embeddings of the graph into a space of given dimension) number of points that belong to the same hyperplane. Upper and lower estimates for this number are given that linearly depend on the dimension of the space. For trees a more precise upper estimate is obtained, which asymptotically coincides with the lower one for large dimension of the space. Bibliography: 9 titles.
Phylogenetic trees and Euclidean embeddings.
Layer, Mark; Rhodes, John A
2017-01-01
It was recently observed by de Vienne et al. (Syst Biol 60(6):826-832, 2011) that a simple square root transformation of distances between taxa on a phylogenetic tree allowed for an embedding of the taxa into Euclidean space. While the justification for this was based on a diffusion model of continuous character evolution along the tree, here we give a direct and elementary explanation for it that provides substantial additional insight. We use this embedding to reinterpret the differences between the NJ and BIONJ tree building algorithms, providing one illustration of how this embedding reflects tree structures in data.
On the scaling limits in the Euclidean (quantum) field theory
International Nuclear Information System (INIS)
Gielerak, R.
1983-01-01
The author studies the concept of scaling limits in the context of the constructive field theory. He finds that the domain of attraction of a free massless Euclidean scalar field in the two-dimensional space time contains almost all Euclidean self-interacting models of quantum fields so far constructed. The renormalized scaling limit of the Wick polynomials of several self-interacting Euclidean field theory models are shown to be the same as in the free field theory. (Auth.)
Draisma, J.; Horobet, E.; Ottaviani, G.; Sturmfels, B.; Thomas, R.R.; Zhi, L.; Watt, M.
2014-01-01
The nearest point map of a real algebraic variety with respect to Euclidean distance is an algebraic function. For instance, for varieties of low rank matrices, the Eckart-Young Theorem states that this map is given by the singular value decomposition. This article develops a theory of such nearest
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.
The relation between Euclidean and Lorentzian 2D quantum gravity
Ambjørn, J.; Correia, J.; Kristjansen, C.; Loll, R.
1999-01-01
Starting from 2D Euclidean quantum gravity, we show that one recovers 2D Lorentzian quantum gravity by removing all baby universes. Using a peeling procedure to decompose the discrete, triangulated geometries along a one-dimensional path, we explicitly associate with each Euclidean space-time a
Topological methods in Euclidean spaces
Naber, Gregory L
2000-01-01
Extensive development of a number of topics central to topology, including elementary combinatorial techniques, Sperner's Lemma, the Brouwer Fixed Point Theorem, homotopy theory and the fundamental group, simplicial homology theory, the Hopf Trace Theorem, the Lefschetz Fixed Point Theorem, the Stone-Weierstrass Theorem, and Morse functions. Includes new section of solutions to selected problems.
Spinors in euclidean field theory, complex structures and discrete symmetries
International Nuclear Information System (INIS)
Wetterich, C.
2011-01-01
We discuss fermions for arbitrary dimensions and signature of the metric, with special emphasis on euclidean space. Generalized Majorana spinors are defined for d=2,3,4,8,9mod8, independently of the signature. These objects permit a consistent analytic continuation of Majorana spinors in Minkowski space to euclidean signature. Compatibility of charge conjugation with complex conjugation requires for euclidean signature a new complex structure which involves a reflection in euclidean time. The possible complex structures for Minkowski and euclidean signature can be understood in terms of a modulo two periodicity in the signature. The concepts of a real action and hermitean observables depend on the choice of the complex structure. For a real action the expectation values of all hermitean multi-fermion observables are real. This holds for arbitrary signature, including euclidean space. In particular, a chemical potential is compatible with a real action for the euclidean theory. We also discuss the discrete symmetries of parity, time reversal and charge conjugation for arbitrary dimension and signature.
Non-euclidean simplex optimization
International Nuclear Information System (INIS)
Silver, G.L.
1977-01-01
Geometric optimization techniques useful for studying chemical equilibrium traditionally rely upon principles of euclidean geometry, but such algorithms may also be based upon principles of a non-euclidean geometry. The sequential simplex method is adapted to the hyperbolic plane, and application of optimization to problems such as the potentiometric titration of plutonium is suggested
Broadband invisibility by non-Euclidean cloaking.
Leonhardt, Ulf; Tyc, Tomás
2009-01-02
Invisibility and negative refraction are both applications of transformation optics where the material of a device performs a coordinate transformation for electromagnetic fields. The device creates the illusion that light propagates through empty flat space, whereas in physical space, light is bent around a hidden interior or seems to run backward in space or time. All of the previous proposals for invisibility require materials with extreme properties. Here we show that transformation optics of a curved, non-Euclidean space (such as the surface of a virtual sphere) relax these requirements and can lead to invisibility in a broad band of the spectrum.
Matrices and Graphs in Euclidean Geometry
Czech Academy of Sciences Publication Activity Database
Fiedler, Miroslav
2005-01-01
Roč. 14, - (2005), s. 51-58 E-ISSN 1081-3810 R&D Projects: GA AV ČR IAA1030302 Institutional research plan: CEZ:AV0Z10300504 Keywords : Euclidean space * Gram matrix * biorthogonal bases * simplex * interior angle * Steiner circumscribed ellipsoid * right simplex Subject RIV: BA - General Mathematics http://www.math.technion.ac.il/iic/ ela / ela -articles/14.html
Non-Euclidean Geometry and Gravitation
Directory of Open Access Journals (Sweden)
Stavroulakis N.
2006-04-01
Full Text Available A great deal of misunderstandings and mathematical errors are involved in the currently accepted theory of the gravitational field generated by an isotropic spherical mass. The purpose of the present paper is to provide a short account of the rigorous mathematical theory and exhibit a new formulation of the problem. The solution of the corresponding equations of gravitation points out several new and unusual features of the stationary gravitational field which are related to the non-Euclidean structure of the space. Moreover it precludes the black hole from being a mathematical and physical notion.
Fast Exact Euclidean Distance (FEED) Transformation
Schouten, Theo; Kittler, J.; van den Broek, Egon; Petrou, M.; Nixon, M.
2004-01-01
Fast Exact Euclidean Distance (FEED) transformation is introduced, starting from the inverse of the distance transformation. The prohibitive computational cost of a naive implementation of traditional Euclidean Distance Transformation, is tackled by three operations: restriction of both the number
Growth Modeling of Human Mandibles using Non-Euclidean Metrics
DEFF Research Database (Denmark)
Hilger, Klaus Baggesen; Larsen, Rasmus; Wrobel, Mark
2003-01-01
From a set of 31 three-dimensional CT scans we model the temporal shape and size of the human mandible. Each anatomical structure is represented using 14851 semi-landmarks, and mapped into Procrustes tangent space. Exploratory subspace analyses are performed leading to linear models of mandible...... shape evolution in Procrustes space. The traditional variance analysis results in a one-dimensional growth model. However, working in a non-Euclidean metric results in a multimodal model with uncorrelated modes of biological variation. The applied non-Euclidean metric is governed by the correlation...... structure of the estimated noise in the data. The generative models are compared, and evaluated on the basis of a cross validation study. The new non-Euclidean analysis is completely data driven. It not only gives comparable results w.r.t. to previous studies of the mean modelling error, but in addition...
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
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...
Algebraic Methods for Counting Euclidean Embeddings of Rigid Graphs
I.Z. Emiris; E.P. Tsigaridas; A. Varvitsiotis (Antonios); E.R. Gasner
2009-01-01
textabstract The study of (minimally) rigid graphs is motivated by numerous applications, mostly in robotics and bioinformatics. A major open problem concerns the number of embeddings of such graphs, up to rigid motions, in Euclidean space. We capture embeddability by polynomial systems
Fisher type inequalities for Euclidean t-designs
Delsarte, Ph.; Seidel, J.J.
1989-01-01
The notion of a Euclidean t-design is analyzed in the framework of appropriate inner product spaces of polynomial functions. Some Fisher type inequalities are obtained in a simple manner by this method. The same approach is used to deal with certain analogous combinatorial designs.
Directory of Open Access Journals (Sweden)
Malloy Vanja
2013-09-01
Full Text Available John Keats once wrote that ‘there is no such thing as time and space’ rather, believing that time and space are mental constructs that are subject to a variety of forms and as diverse as the human mind. In the 1920s through the 1930s, modern physics in many ways supported this idea through the various philosophical writings on the Theory of General Relativity to the masses by scientists such as Arthur Eddington and Albert Einstein. These new concepts of modern physics fundamentally changed our understanding of time and space and had substantial philosophical implications, which were absorbed by modern artists resulting in the 1936 Dimensionist Manifesto. Seeking to internalize the developments of modern science within modern art, this manifesto was widely endorsed by the most prominent figures of the avant-garde such as Marcel Duchamp, Jean Arp, Naum Gabo, Joan Miró, László Moholy-Nagy, Wassily Kandinsky and Alexander Calder. Of particular interest to this manifesto was the new concept of the fourth-dimension, which in many ways revolutionized the arts. Importantly, its interpretation varied widely in the artistic community, ranging from a purely physical four-dimensional space, to a kinetic concept of space in which space and time are linked, to a metaphysical interest in a space that exists beyond the material realm. The impact of modern science and astronomy on avant-garde art is currently a bourgeoning area of research with considerable implications to our rethinking of substantial artistic figures of this era. Through a case study of Alexander Calder’s Mobiles and Ben Nicholson’s Reliefs, this paper explores how these artworks were informed by an interest in modern science.
Some nonunitary, indecomposable representations of the Euclidean algebra e(3)
International Nuclear Information System (INIS)
Douglas, Andrew; De Guise, Hubert
2010-01-01
The Euclidean group E(3) is the noncompact, semidirect product group E(3)≅R 3 x SO(3). It is the Lie group of orientation-preserving isometries of three-dimensional Euclidean space. The Euclidean algebra e(3) is the complexification of the Lie algebra of E(3). We construct three distinct families of finite-dimensional, nonunitary representations of e(3) and show that each representation is indecomposable. The representations of the first family are explicitly realized as subspaces of the polynomial ring F[X,Y,Z] with the action of e(3) given by differential operators. The other families are constructed via duals and tensor products of the representations within the first family. We describe subrepresentations, quotients and duals of these indecomposable representations.
Euclidean distance degrees of real algebraic groups
Baaijens, J.A.; Draisma, J.
2015-01-01
We study the problem of finding, in a real algebraic matrix group, the matrix closest to a given data matrix. We do so from the algebro-geometric perspective of Euclidean distance degrees. We recover several classical results; and among the new results that we prove is a formula for the Euclidean
Euclidean distance degrees of real algebraic groups
Baaijens, J.A.; Draisma, J.
2014-01-01
We study the problem of finding, in a real algebraic matrix group, the matrix closest to a given data matrix. We do so from the algebro-geometric perspective of Euclidean distance degrees. We recover several classical results; and among the new results that we prove is a formula for the Euclidean
Curves of restricted type in euclidean spaces
Directory of Open Access Journals (Sweden)
Bengü Kılıç Bayram
2014-01-01
Full Text Available Submanifolds of restricted type were introduced in [7]. In the present study we consider restricted type of curves in Em. We give some special examples. We also show that spherical curve in S2(r C E3 is of restricted type if and only if either ƒ(s is constant or a linear function of s of the form ƒ(s = ±s + b and every closed W - curve of rank k and of length 2(r in E2k is of restricted type.
Euclidean to Minkowski Bethe-Salpeter amplitude and observables
International Nuclear Information System (INIS)
Carbonell, J.; Frederico, T.; Karmanov, V.A.
2017-01-01
We propose a method to reconstruct the Bethe-Salpeter amplitude in Minkowski space given the Euclidean Bethe-Salpeter amplitude - or alternatively the light-front wave function - as input. The method is based on the numerical inversion of the Nakanishi integral representation and computing the corresponding weight function. This inversion procedure is, in general, rather unstable, and we propose several ways to considerably reduce the instabilities. In terms of the Nakanishi weight function, one can easily compute the BS amplitude, the LF wave function and the electromagnetic form factor. The latter ones are very stable in spite of residual instabilities in the weight function. This procedure allows both, to continue the Euclidean BS solution in the Minkowski space and to obtain a BS amplitude from a LF wave function. (orig.)
Tunneling in expanding Universe: Euclidean and Hamiltonian approaches
International Nuclear Information System (INIS)
Goncharov, A.S.; Linde, A.D.
1986-01-01
The theory of the false vacuum decay in de Sitter space and in the inflationary Universe, and also the theory of the Universe creation ''from nothing'' are discussed. This explained why tunneling in the inflationary Universe differs from that in de Sitter space and cannot be exactly homogeneous. It is shown that in several important cases the Euclidean approach should be considerably modified or is absolutely inapplicable for the description of tunneling in the expanding Universe and of the process of the quantum creation of the Universe. The Hamiltonian approach to the theory of tunneling in expanding Universe is developed. The results obtained by this method are compared with the results obtained by the Euclidean approach
Euclidean to Minkowski Bethe-Salpeter amplitude and observables
Energy Technology Data Exchange (ETDEWEB)
Carbonell, J. [Universite Paris-Sud, IN2P3-CNRS, Institut de Physique Nucleaire, Orsay Cedex (France); Frederico, T. [Instituto Tecnologico de Aeronautica, DCTA, Sao Jose dos Campos (Brazil); Karmanov, V.A. [Lebedev Physical Institute, Moscow (Russian Federation)
2017-01-15
We propose a method to reconstruct the Bethe-Salpeter amplitude in Minkowski space given the Euclidean Bethe-Salpeter amplitude - or alternatively the light-front wave function - as input. The method is based on the numerical inversion of the Nakanishi integral representation and computing the corresponding weight function. This inversion procedure is, in general, rather unstable, and we propose several ways to considerably reduce the instabilities. In terms of the Nakanishi weight function, one can easily compute the BS amplitude, the LF wave function and the electromagnetic form factor. The latter ones are very stable in spite of residual instabilities in the weight function. This procedure allows both, to continue the Euclidean BS solution in the Minkowski space and to obtain a BS amplitude from a LF wave function. (orig.)
Dynamic hyperbolic geometry: building intuition and understanding mediated by a Euclidean model
Moreno-Armella, Luis; Brady, Corey; Elizondo-Ramirez, Rubén
2018-05-01
This paper explores a deep transformation in mathematical epistemology and its consequences for teaching and learning. With the advent of non-Euclidean geometries, direct, iconic correspondences between physical space and the deductive structures of mathematical inquiry were broken. For non-Euclidean ideas even to become thinkable the mathematical community needed to accumulate over twenty centuries of reflection and effort: a precious instance of distributed intelligence at the cultural level. In geometry education after this crisis, relations between intuitions and geometrical reasoning must be established philosophically, rather than taken for granted. One approach seeks intuitive supports only for Euclidean explorations, viewing non-Euclidean inquiry as fundamentally non-intuitive in nature. We argue for moving beyond such an impoverished approach, using dynamic geometry environments to develop new intuitions even in the extremely challenging setting of hyperbolic geometry. Our efforts reverse the typical direction, using formal structures as a source for a new family of intuitions that emerge from exploring a digital model of hyperbolic geometry. This digital model is elaborated within a Euclidean dynamic geometry environment, enabling a conceptual dance that re-configures Euclidean knowledge as a support for building intuitions in hyperbolic space-intuitions based not directly on physical experience but on analogies extending Euclidean concepts.
Euclidean scalar field theory in the bilocal approximation
Nagy, S.; Polonyi, J.; Steib, I.
2018-04-01
The blocking step of the renormalization group method is usually carried out by restricting it to fluctuations and to local blocked action. The tree-level, bilocal saddle point contribution to the blocking, defined by the infinitesimal decrease of the sharp cutoff in momentum space, is followed within the three dimensional Euclidean ϕ6 model in this work. The phase structure is changed, new phases and relevant operators are found, and certain universality classes are restricted by the bilocal saddle point.
General Nth order integrals of motion in the Euclidean plane
International Nuclear Information System (INIS)
Post, S; Winternitz, P
2015-01-01
The general form of an integral of motion that is a polynomial of order N in the momenta is presented for a Hamiltonian system in two-dimensional Euclidean space. The classical and the quantum cases are treated separately, emphasizing both the similarities and the differences between the two. The main application will be to study Nth order superintegrable systems that allow separation of variables in the Hamilton–Jacobi and Schrödinger equations, respectively. (paper)
Euclidean supersymmetry, twisting and topological sigma models
International Nuclear Information System (INIS)
Hull, C.M.; Lindstroem, U.; Santos, L. Melo dos; Zabzine, M.; Unge, R. von
2008-01-01
We discuss two dimensional N-extended supersymmetry in Euclidean signature and its R-symmetry. For N = 2, the R-symmetry is SO(2) x SO(1, 1), so that only an A-twist is possible. To formulate a B-twist, or to construct Euclidean N = 2 models with H-flux so that the target geometry is generalised Kahler, it is necessary to work with a complexification of the sigma models. These issues are related to the obstructions to the existence of non-trivial twisted chiral superfields in Euclidean superspace.
The elements of non-Euclidean geometry
Sommerville, D MY
2012-01-01
Renowned for its lucid yet meticulous exposition, this classic allows students to follow the development of non-Euclidean geometry from a fundamental analysis of the concept of parallelism to more advanced topics. 1914 edition. Includes 133 figures.
Scaling limits of Euclidean quantum fields
International Nuclear Information System (INIS)
Enss, V.
1981-01-01
The author studies the long-distance and short-distance behaviour of generalized random processes which arise in Euclidean Boson field theories. Among them are Wick-polynomials of free fields and P(PHI) 2 -models. (Auth.)
Axioms for Euclidean Green's functions. Pt. 2
International Nuclear Information System (INIS)
Osterwalder, K.; Schrader, R.
1975-01-01
We give new (necessary and) sufficient conditions for Euclidean Green's functions to have analytic continuations to a relativistic field theory. These results extend and correct a previous paper. (orig.) [de
Constructive curves in non-Euclidean planes
Horváth, Ákos G.
2016-01-01
In this paper we overview the theory of conics and roulettes in four non-Euclidean planes. We collect the literature about these classical concepts, from the eighteenth century to the present, including papers available only on arXiv. The comparison of the four non-Euclidean planes, in terms of the known results on conics and roulettes, reflects only the very subjective view of the author.
Classical geometry Euclidean, transformational, inversive, and projective
Leonard, I E; Liu, A C F; Tokarsky, G W
2014-01-01
Features the classical themes of geometry with plentiful applications in mathematics, education, engineering, and science Accessible and reader-friendly, Classical Geometry: Euclidean, Transformational, Inversive, and Projective introduces readers to a valuable discipline that is crucial to understanding bothspatial relationships and logical reasoning. Focusing on the development of geometric intuitionwhile avoiding the axiomatic method, a problem solving approach is encouraged throughout. The book is strategically divided into three sections: Part One focuses on Euclidean geometry, which p
Euclidean D-branes and higher-dimensional gauge theory
International Nuclear Information System (INIS)
Acharya, B.S.; Figueroa-O'Farrill, J.M.; Spence, B.; O'Loughlin, M.
1997-07-01
We consider euclidean D-branes wrapping around manifolds of exceptional holonomy in dimensions seven and eight. The resulting theory on the D-brane-that is, the dimensional reduction of 10-dimensional supersymmetric Yang-Mills theory-is a cohomological field theory which describes the topology of the moduli space of instantons. The 7-dimensional theory is an N T =2 (or balanced) cohomological theory given by an action potential of Chern-Simons type. As a by-product of this method, we construct a related cohomological field theory which describes the monopole moduli space on a 7-manifold of G 2 holonomy. (author). 22 refs, 3 tabs
Convergent perturbation expansions for Euclidean quantum field theory
International Nuclear Information System (INIS)
Mack, G.; Pordt, A.
1984-09-01
Mayer perturbation theory is designed to provide computable convergent expansions which permit calculation of Greens functions in Euclidean Quantum Field Theory to arbitrary accuracy, including 'nonperturbative' contributions from large field fluctuations. Here we describe the expansions at the example of 3-dimensional lambdaphi 4 -theory (in continuous space). They are not essentially more complicated than standard perturbation theory. The n-th order term is expressed in terms of 0(n)-dimensional integrals, and is of order lambda 4 if 4k-3<=n<=4k. (orig.)
The G_Newton --> 0 Limit of Euclidean Quantum Gravity
Smolin, Lee
1992-01-01
Using the Ashtekar formulation, it is shown that the G_{Newton} --> 0 limit of Euclidean or complexified general relativity is not a free field theory, but is a theory that describes a linearized self-dual connection propagating on an arbitrary anti-self-dual background. This theory is quantized in the loop representation and, as in the full theory, an infinite dimnensional space of exact solutions to the constraint is found. An inner product is also proposed. The path integral is constructed...
A strong coupling simulation of Euclidean quantum gravity
International Nuclear Information System (INIS)
Berg, B.; Hamburg Univ.
1984-12-01
Relying on Regge calculus a systematic numerical investigation of models of 4d Euclidean gravity is proposed. The scale a = 1 0 is set by fixing the expectation value of a length. Possible universality of such models is discussed. The strong coupling limit is defined by taking Planck mass msub(p) -> 0 (in units of 1 0 -1 ). The zero order approximation msub(p) = 0 is called 'fluctuating space' and investigated numerically in two 4d models. Canonical dimensions are realized and both models give a negative expectation value for the scalar curvature density. (orig.)
Epileptic Seizure Detection with Log-Euclidean Gaussian Kernel-Based Sparse Representation.
Yuan, Shasha; Zhou, Weidong; Wu, Qi; Zhang, Yanli
2016-05-01
Epileptic seizure detection plays an important role in the diagnosis of epilepsy and reducing the massive workload of reviewing electroencephalography (EEG) recordings. In this work, a novel algorithm is developed to detect seizures employing log-Euclidean Gaussian kernel-based sparse representation (SR) in long-term EEG recordings. Unlike the traditional SR for vector data in Euclidean space, the log-Euclidean Gaussian kernel-based SR framework is proposed for seizure detection in the space of the symmetric positive definite (SPD) matrices, which form a Riemannian manifold. Since the Riemannian manifold is nonlinear, the log-Euclidean Gaussian kernel function is applied to embed it into a reproducing kernel Hilbert space (RKHS) for performing SR. The EEG signals of all channels are divided into epochs and the SPD matrices representing EEG epochs are generated by covariance descriptors. Then, the testing samples are sparsely coded over the dictionary composed by training samples utilizing log-Euclidean Gaussian kernel-based SR. The classification of testing samples is achieved by computing the minimal reconstructed residuals. The proposed method is evaluated on the Freiburg EEG dataset of 21 patients and shows its notable performance on both epoch-based and event-based assessments. Moreover, this method handles multiple channels of EEG recordings synchronously which is more speedy and efficient than traditional seizure detection methods.
Lorentz violations and Euclidean signature metrics
International Nuclear Information System (INIS)
Barbero G, J. Fernando; Villasenor, Eduardo J.S.
2003-01-01
We show that the families of effective actions considered by Jacobson et al. to study Lorentz invariance violations contain a class of models that represent pure general relativity with a Euclidean signature. We also point out that some members of this family of actions preserve Lorentz invariance in a generalized sense
Majorization in Euclidean Geometry and Beyond
Czech Academy of Sciences Publication Activity Database
Fiedler, Miroslav
2015-01-01
Roč. 466, 1 February (2015), s. 233-240 ISSN 0024-3795 Institutional support: RVO:67985807 Keywords : Majorization * Doubly stochastic matrix * Euclidean simplex * Star * Regular simplex * Volume of a simplex Subject RIV: BA - General Mathematics Impact factor: 0.965, year: 2015
On the Schroedinger representation of the Euclidean quantum field theory
International Nuclear Information System (INIS)
Semmler, U.
1987-04-01
The theme of the present thesis is the Schroedinger representation of the Euclidean quantum field theory: We define the time development of the quantum field states as functional integral in a novel, mathematically precise way. In the following we discuss the consequences which result from this approach to the Euclidean quantum field theory. Chapter 1 introduces the theory of abstract Wiener spaces which is here proved as suitable mathematical tool for the treatment of the physical problems. In chapter 2 the diffusion theory is formulated in the framework of abstract Wiener spaces. In chapter 3 we define the field functional ψ 5 u, t 7 as functional integral, determine the functional differential equation which ψ satisfies (Schroedinger equation), and summarize the consequences resulting from this. Chapter 4 is dedicated to the attempt to determine the kernel of the time-development operator, by the knowledge of which the time development of each initial state is fixed. In chapter 5 the consequences of the theory presented in chapter 3 and 4 are discussed by means of simple examples. In chapter 6 the renormalization which results for the φ 4 potential from the definition of the functional integral in chapter 3 is calculated up to the first-order perturbation theory, and it is shown that the problems in the Symanzik renormalization procedure can be removed. (orig./HSI) [de
A linear-time algorithm for Euclidean feature transform sets
Hesselink, Wim H.
2007-01-01
The Euclidean distance transform of a binary image is the function that assigns to every pixel the Euclidean distance to the background. The Euclidean feature transform is the function that assigns to every pixel the set of background pixels with this distance. We present an algorithm to compute the
Euclidean wormholes with minimally coupled scalar fields
International Nuclear Information System (INIS)
Ruz, Soumendranath; Modak, Bijan; Debnath, Subhra; Sanyal, Abhik Kumar
2013-01-01
A detailed study of quantum and semiclassical Euclidean wormholes for Einstein's theory with a minimally coupled scalar field has been performed for a class of potentials. Massless, constant, massive (quadratic in the scalar field) and inverse (linear) potentials admit the Hawking and Page wormhole boundary condition both in the classically forbidden and allowed regions. An inverse quartic potential has been found to exhibit a semiclassical wormhole configuration. Classical wormholes under a suitable back-reaction leading to a finite radius of the throat, where the strong energy condition is satisfied, have been found for the zero, constant, quadratic and exponential potentials. Treating such classical Euclidean wormholes as an initial condition, a late stage of cosmological evolution has been found to remain unaltered from standard Friedmann cosmology, except for the constant potential which under the back-reaction produces a term like a negative cosmological constant. (paper)
Euclidean fields: vector mesons and photons
International Nuclear Information System (INIS)
Loffelholz, J.
1979-01-01
Free transverse vector fields of mass >= 0 are studied. The model is related to the usual free vector meson and electromagnetic quantum field theories by extension of the field operators from transverse to arbitrary test functions. The one-particle states in transverse gauge and their localization are described. Reflexion positivity is proved and derived are free Feynman-Kac-Nelson formulas. An Euclidean approach to a photon field in a spherical world using dilatation covariance and inversions is given
The positive action conjecture and asymptotically euclidean metrics in quantum gravity
International Nuclear Information System (INIS)
Gibbons, G.W.; Pope, C.N.
1979-01-01
The positive action conjecture requires that the action of any asymptotically Euclidean 4-dimensional Riemannian metric be positive, vanishing if and only if the space is flat. Because any Ricci flat, asymptotically Euclidean metric has zero action and is local extremum of the action which is a local minimum at flat space, the conjecture requires that there are no Ricci flat asymptotically Euclidean metrics other than flat space, which would establish that flat space is the only local minimum. We prove this for metrics on R 4 and a large class of more complicated topologies and for self-dual metrics. We show that if Rsupμsubμ >= 0 there are no bound states of the Dirac equation and discuss the relevance to possible baryon non-conserving processes mediated by gravitational instantons. We conclude that these are forbidden in the lowest stationary phase approximation. We give a detailed discussion of instantons invariant under an SU(2) or SO(3) isometry group. We find all regular solutions, none of which is asymptotically Euclidean and all of which possess a further Killing vector. In an appendix we construct an approximate self-dual metric on K3 - the only simply connected compact manifold which admits a self-dual metric. (orig.) [de
Hubble expansion in a Euclidean framework
International Nuclear Information System (INIS)
Alfven, H.
1979-01-01
There now seems to be strong evidence for a non-cosmological interpretation of the QSO redshift - in any case, so strong that it is of interest to investigate the consequences. The purpose of this paper is to construct a model of the Hubble expansion which is as far as possible from the conventional Big Bang model without coming in conflict with any well-established observational results (while introducing no new laws of physics). This leads to an essentially Euclidean metagalactic model (see Table I) with very little mass outside one-third or half of the Hubble radius. The total kinetic energy of the Hubble expansion need only to be about 5% of the rest mass energy. Present observations support backwards in time extrapolation of the Hubble expansion to a 'minimum size galaxy' Rsub(m), which may have any value in 0 26 cm. Other arguments speak in favor of a size close to the upper value, say Rsub(m) = 10 26 cm (Table II). As this size is probably about 100 times the Schwarzschild limit, an essentially Euclidean description is allowed. The kinetic energy of the Hubble expansion may derive from an intense QSO-like activity in the minimum size metagalaxy, with an energy release corresponding to the annihilation of a few solar masses per galaxy per year. Some of the conclusions based on the Big Bang hypothesis are criticized and in several cases alternative interpretations are suggested. A comparison between the Euclidean and the conventional models is given in Table III. (orig.)
Exploring Concepts of Geometry not Euclidean
Directory of Open Access Journals (Sweden)
Luiz Ambrozi
2016-02-01
Full Text Available With this article we intend to propose different situations of teaching and learning, how they can be applied in schools, mediated by the use of concrete materials and Geogebra software, emphasizing the use of technology in the classroom, that this proposal has the role of assisting in the conceptualization and identification of elements of non-Euclidean geometry. In addition, this short course is designed to be a time of current and continuing education for teachers, with activities to be developed with dynamic geometry and based on the theory of Conceptual Fields of Vergnaud.
Euclidean approach to the inflationary universe
International Nuclear Information System (INIS)
Hawking, S.W.
1983-01-01
The aim of this article is to show how the Euclidean approach can be used to study the inflationary universe. Although this formulation may appear counterintuitive in some respects, it has the advantage that it defines a definite quantum state and provides a framework for calculating quantities of interest such as correlation functions or tunnelling probabilities. By contrast, in the more usual approach in real Lorentzian spacetime, it is not so clear what the quantum state should be or how to evaluate such quantities. (author)
Introduction to non-Euclidean geometry
Wolfe, Harold E
2012-01-01
One of the first college-level texts for elementary courses in non-Euclidean geometry, this concise, readable volume is geared toward students familiar with calculus. A full treatment of the historical background explores the centuries-long efforts to prove Euclid's parallel postulate and their triumphant conclusion. Numerous original exercises form an integral part of the book.Topics include hyperbolic plane geometry and hyperbolic plane trigonometry, applications of calculus to the solutions of some problems in hyperbolic geometry, elliptic plane geometry and trigonometry, and the consistenc
SLE as a Mating of Trees in Euclidean Geometry
Holden, Nina; Sun, Xin
2018-05-01
The mating of trees approach to Schramm-Loewner evolution (SLE) in the random geometry of Liouville quantum gravity (LQG) has been recently developed by Duplantier et al. (Liouville quantum gravity as a mating of trees, 2014. arXiv:1409.7055). In this paper we consider the mating of trees approach to SLE in Euclidean geometry. Let {η} be a whole-plane space-filling SLE with parameter {κ > 4} , parameterized by Lebesgue measure. The main observable in the mating of trees approach is the contour function, a two-dimensional continuous process describing the evolution of the Minkowski content of the left and right frontier of {η} . We prove regularity properties of the contour function and show that (as in the LQG case) it encodes all the information about the curve {η} . We also prove that the uniform spanning tree on {Z^2} converges to SLE8 in the natural topology associated with the mating of trees approach.
Buckling transition and boundary layer in non-Euclidean plates.
Efrati, Efi; Sharon, Eran; Kupferman, Raz
2009-07-01
Non-Euclidean plates are thin elastic bodies having no stress-free configuration, hence exhibiting residual stresses in the absence of external constraints. These bodies are endowed with a three-dimensional reference metric, which may not necessarily be immersible in physical space. Here, based on a recently developed theory for such bodies, we characterize the transition from flat to buckled equilibrium configurations at a critical value of the plate thickness. Depending on the reference metric, the buckling transition may be either continuous or discontinuous. In the infinitely thin plate limit, under the assumption that a limiting configuration exists, we show that the limit is a configuration that minimizes the bending content, among all configurations with zero stretching content (isometric immersions of the midsurface). For small but finite plate thickness, we show the formation of a boundary layer, whose size scales with the square root of the plate thickness and whose shape is determined by a balance between stretching and bending energies.
Statistical mechanics, gravity, and Euclidean theory
International Nuclear Information System (INIS)
Fursaev, Dmitri V.
2002-01-01
A review of computations of free energy for Gibbs states on stationary but not static gravitational and gauge backgrounds is given. On these backgrounds wave equations for free fields are reduced to eigenvalue problems which depend non-linearly on the spectral parameter. We present a method to deal with such problems. In particular, we demonstrate how some results of the spectral theory of second-order elliptic operators, such as heat kernel asymptotics, can be extended to a class of non-linear spectral problems. The method is used to trace down the relation between the canonical definition of the free energy based on summation over the modes and the covariant definition given in Euclidean quantum gravity. As an application, high-temperature asymptotics of the free energy and of the thermal part of the stress-energy tensor in the presence of rotation are derived. We also discuss statistical mechanics in the presence of Killing horizons where canonical and Euclidean theories are related in a non-trivial way
Euclidean supergravity and multi-centered solutions
Directory of Open Access Journals (Sweden)
W.A. Sabra
2017-04-01
Full Text Available In ungauged supergravity theories, the no-force condition for BPS states implies the existence of stable static multi-centered solutions. The first solutions to Einstein–Maxwell theory with a positive cosmological constant describing an arbitrary number of charged black holes were found by Kastor and Traschen. Generalisations to five and higher dimensional theories were obtained by London. Multi-centered solutions in gauged supergravity, even with time-dependence allowed, have yet to be constructed. In this letter we construct supersymmetry-preserving multi-centered solutions for the case of D=5, N=2 Euclidean gauged supergravity coupled to an arbitrary number of vector multiplets. Higher dimensional Einstein–Maxwell multi-centered solutions are also presented.
Euclidean Monte Carlo simulation of nuclear interactions
International Nuclear Information System (INIS)
Montvay, Istvan; Bonn Univ.; Urbach, Carsten
2011-05-01
We present an exploratory study of chiral effective theories of nuclei with methods adopted from lattice quantum chromodynamics (QCD). We show that the simulations in the Euclidean path integral approach are feasible and that we can determine the energy of the two nucleon state. By varying the parameters and the simulated volumes phase shifts can be determined in principle and hopefully tuned to their physical values in the future. The physical cut-off of the theory is realised by blocking of the lattice fields. By keeping this physical cut-off fixed in physical units the lattice cut-off can be changed and in this way the lattice artefacts can be eliminated. (orig.)
Euclidean null controllability of perturbed infinite delay systems with ...
African Journals Online (AJOL)
Euclidean null controllability of perturbed infinite delay systems with limited control. ... Open Access DOWNLOAD FULL TEXT ... The results are established by placing conditions on the perturbation function which guarantee that, if the linear control base system is completely Euclidean controllable, then the perturbed system ...
Euclidean null controllability of nonlinear infinite delay systems with ...
African Journals Online (AJOL)
Sufficient conditions for the Euclidean null controllability of non-linear delay systems with time varying multiple delays in the control and implicit derivative are derived. If the uncontrolled system is uniformly asymptotically stable and if the control system is controllable, then the non-linear infinite delay system is Euclidean null ...
Euclidean null controllability of linear systems with delays in state ...
African Journals Online (AJOL)
Sufficient conditions are developed for the Euclidean controllability of linear systems with delay in state and in control. Namely, if the uncontrolled system is uniformly asymptotically stable and the control equation proper, then the control system is Euclidean null controllable. Journal of the Nigerian Association of ...
Walwyn, Amy L.; Navarro, Daniel J.
2010-01-01
An experiment is reported comparing human performance on two kinds of visually presented traveling salesperson problems (TSPs), those reliant on Euclidean geometry and those reliant on city block geometry. Across multiple array sizes, human performance was near-optimal in both geometries, but was slightly better in the Euclidean format. Even so,…
Statistical 2D and 3D shape analysis using Non-Euclidean Metrics
DEFF Research Database (Denmark)
Larsen, Rasmus; Hilger, Klaus Baggesen; Wrobel, Mark Christoph
2002-01-01
We address the problem of extracting meaningful, uncorrelated biological modes of variation from tangent space shape coordinates in 2D and 3D using non-Euclidean metrics. We adapt the maximum autocorrelation factor analysis and the minimum noise fraction transform to shape decomposition. Furtherm......We address the problem of extracting meaningful, uncorrelated biological modes of variation from tangent space shape coordinates in 2D and 3D using non-Euclidean metrics. We adapt the maximum autocorrelation factor analysis and the minimum noise fraction transform to shape decomposition....... Furthermore, we study metrics based on repated annotations of a training set. We define a way of assessing the correlation between landmarks contrary to landmark coordinates. Finally, we apply the proposed methods to a 2D data set consisting of outlines of lungs and a 3D/(4D) data set consisting of sets...
The Euclidean three-point function in loop and perturbative gravity
International Nuclear Information System (INIS)
Rovelli, Carlo; Zhang Mingyi
2011-01-01
We compute the leading order of the three-point function in loop quantum gravity, using the vertex expansion of the Euclidean version of the new spin foam dynamics, in the region of γ < 1. We find results consistent with Regge calculus in the limit γ → 0, j → ∞. We also compute the tree-level three-point function of perturbative quantum general relativity in position space and discuss the possibility of directly comparing the two results.
Non-Euclidean Geometry, Nontrivial Topology and Quantum Vacuum Effects
Directory of Open Access Journals (Sweden)
Yurii A. Sitenko
2018-01-01
Full Text Available Space out of a topological defect of the Abrikosov–Nielsen–Olesen (ANO vortex type is locally flat but non-Euclidean. If a spinor field is quantized in such a space, then a variety of quantum effects are induced in the vacuum. On the basis of the continuum model for long-wavelength electronic excitations originating in the tight-binding approximation for the nearest-neighbor interaction of atoms in the crystal lattice, we consider quantum ground-state effects in Dirac materials with two-dimensional monolayer structures warped into nanocones by a disclination; the nonzero size of the disclination is taken into account, and a boundary condition at the edge of the disclination is chosen to ensure self-adjointness of the Dirac–Weyl Hamiltonian operator. We show that the quantum ground-state effects are independent of the disclination size, and we find circumstances in which they are independent of parameters of the boundary condition.
Quaternion analyticity and conformally Kaehlerian structure in Euclidean gravity
International Nuclear Information System (INIS)
Guersey, F.; Chia-Hsiung Tze
1984-01-01
Starting from the fact that the d = 4 Euclidean flat spacetime is conformally related to the Kaehler manifold H 2 xS 2 , we show the Euclidean Schwarzschild metric to be conformally related to another Kaehler manifold M 2 xS 2 with M 2 being conformal to H 2 in two dimensions. Both metrics which are conformally Kaehlerian, are form-invariant under the infinite parameter Fueter group, the Euclidean counterpart of Milne's group of clock regraduation. The associated Einstein's equations translate into Fueter's quaternionic analyticity. The latter leads to an infinite number of local continuity equations. (orig.)
Hu, Weiming; Li, Xi; Luo, Wenhan; Zhang, Xiaoqin; Maybank, Stephen; Zhang, Zhongfei
2012-12-01
Object appearance modeling is crucial for tracking objects, especially in videos captured by nonstationary cameras and for reasoning about occlusions between multiple moving objects. Based on the log-euclidean Riemannian metric on symmetric positive definite matrices, we propose an incremental log-euclidean Riemannian subspace learning algorithm in which covariance matrices of image features are mapped into a vector space with the log-euclidean Riemannian metric. Based on the subspace learning algorithm, we develop a log-euclidean block-division appearance model which captures both the global and local spatial layout information about object appearances. Single object tracking and multi-object tracking with occlusion reasoning are then achieved by particle filtering-based Bayesian state inference. During tracking, incremental updating of the log-euclidean block-division appearance model captures changes in object appearance. For multi-object tracking, the appearance models of the objects can be updated even in the presence of occlusions. Experimental results demonstrate that the proposed tracking algorithm obtains more accurate results than six state-of-the-art tracking algorithms.
New solutions of euclidean SU(2) gauge theory
International Nuclear Information System (INIS)
Khan, I.
1983-08-01
New solutions of the Euclidean SU(2) gauge theory having finite field strength everywhere are presented. The solutions are self dual or antidual and constitute a two-parameter family which includes the instantons. (author)
PERBANDINGAN EUCLIDEAN DISTANCE DENGAN CANBERRA DISTANCE PADA FACE RECOGNITION
Directory of Open Access Journals (Sweden)
Sendhy Rachmat Wurdianarto
2014-08-01
Full Text Available Perkembangan ilmu pada dunia komputer sangatlah pesat. Salah satu yang menandai hal ini adalah ilmu komputer telah merambah pada dunia biometrik. Arti biometrik sendiri adalah karakter-karakter manusia yang dapat digunakan untuk membedakan antara orang yang satu dengan yang lainnya. Salah satu pemanfaatan karakter / organ tubuh pada setiap manusia yang digunakan untuk identifikasi (pengenalan adalah dengan memanfaatkan wajah. Dari permasalahan diatas dalam pengenalan lebih tentang aplikasi Matlab pada Face Recognation menggunakan metode Euclidean Distance dan Canberra Distance. Model pengembangan aplikasi yang digunakan adalah model waterfall. Model waterfall beriisi rangkaian aktivitas proses yang disajikan dalam proses analisa kebutuhan, desain menggunakan UML (Unified Modeling Language, inputan objek gambar diproses menggunakan Euclidean Distance dan Canberra Distance. Kesimpulan yang dapat ditarik adalah aplikasi face Recognation menggunakan metode euclidean Distance dan Canverra Distance terdapat kelebihan dan kekurangan masing-masing. Untuk kedepannya aplikasi tersebut dapat dikembangkan dengan menggunakan objek berupa video ataupun objek lainnya. Kata kunci : Euclidean Distance, Face Recognition, Biometrik, Canberra Distance
Singular Minkowski and Euclidean solutions for SU(2) Yang-Mills theory
International Nuclear Information System (INIS)
Singleton, D.
1996-01-01
In this paper it is examined a solution to the SU(2) Yang-Mills-Higgs system, which is a trivial mathematical extension of recently discovered Schwarzschild- like solutions (Singleton D., Phys. Rev. D, 51 (1955) 5911). Physically, however, this new solution has drastically different properties from the Schwarzschild-like solutions. It is also studied a new classical solution for Euclidean SU(2) Yang-Mills theory. Again this new solution is a mathematically trivial extension of the Belavin-Polyakov-Schwartz-Tyupkin (BPST) (Belavin A. A. et al., Phys. Lett. B, 59 (1975) 85) instanton, but is physically very different. Unlike the usual instanton solution, the present solution is singular on a sphere of arbitrary radius in Euclidean space. Both of these solutions are infinite-energy solutions, so their practical value is somewhat unclear. However, they may be useful in exploring some of the mathematical aspects of classical Yang-Mills theory
The non-Euclidean revolution with an introduction by H.S.M. Coxeter
Trudeau, Richard J
2001-01-01
How unique and definitive is Euclidean geometry in describing the "real" space in which we live? Richard Trudeau confronts the fundamental question of truth and its representation through mathematical models in The Non-Euclidean Revolution. First, the author analyzes geometry in its historical and philosophical setting; second, he examines a revolution every bit as significant as the Copernican revolution in astronomy and the Darwinian revolution in biology; third, on the most speculative level, he questions the possibility of absolute knowledge of the world. Trudeau writes in a lively, entertaining, and highly accessible style. His book provides one of the most stimulating and personal presentations of a struggle with the nature of truth in mathematics and the physical world. A portion of the book won the Pólya Prize, a distinguished award from the Mathematical Association of America.
Modelling non-Euclidean movement and landscape connectivity in highly structured ecological networks
Sutherland, Christopher; Fuller, Angela K.; Royle, J. Andrew
2015-01-01
Movement is influenced by landscape structure, configuration and geometry, but measuring distance as perceived by animals poses technical and logistical challenges. Instead, movement is typically measured using Euclidean distance, irrespective of location or landscape structure, or is based on arbitrary cost surfaces. A recently proposed extension of spatial capture-recapture (SCR) models resolves this issue using spatial encounter histories of individuals to calculate least-cost paths (ecological distance: Ecology, 94, 2013, 287) thereby relaxing the Euclidean assumption. We evaluate the consequences of not accounting for movement heterogeneity when estimating abundance in highly structured landscapes, and demonstrate the value of this approach for estimating biologically realistic space-use patterns and landscape connectivity.
Biased discriminant euclidean embedding for content-based image retrieval.
Bian, Wei; Tao, Dacheng
2010-02-01
With many potential multimedia applications, content-based image retrieval (CBIR) has recently gained more attention for image management and web search. A wide variety of relevance feedback (RF) algorithms have been developed in recent years to improve the performance of CBIR systems. These RF algorithms capture user's preferences and bridge the semantic gap. However, there is still a big room to further the RF performance, because the popular RF algorithms ignore the manifold structure of image low-level visual features. In this paper, we propose the biased discriminative Euclidean embedding (BDEE) which parameterises samples in the original high-dimensional ambient space to discover the intrinsic coordinate of image low-level visual features. BDEE precisely models both the intraclass geometry and interclass discrimination and never meets the undersampled problem. To consider unlabelled samples, a manifold regularization-based item is introduced and combined with BDEE to form the semi-supervised BDEE, or semi-BDEE for short. To justify the effectiveness of the proposed BDEE and semi-BDEE, we compare them against the conventional RF algorithms and show a significant improvement in terms of accuracy and stability based on a subset of the Corel image gallery.
Euclidean supersymmetric solutions with the self-dual Weyl tensor
Directory of Open Access Journals (Sweden)
Masato Nozawa
2017-07-01
Full Text Available We explore the Euclidean supersymmetric solutions admitting the self-dual gauge field in the framework of N=2 minimal gauged supergravity in four dimensions. According to the classification scheme utilizing the spinorial geometry or the bilinears of Killing spinors, the general solution preserves one quarter of supersymmetry and is described by the Przanowski–Tod class with the self-dual Weyl tensor. We demonstrate that there exists an additional Killing spinor, provided the Przanowski–Tod metric admits a Killing vector that commutes with the principal one. The proof proceeds by recasting the metric into another Przanowski–Tod form. This formalism enables us to show that the self-dual Reissner–Nordström–Taub–NUT–AdS metric possesses a second Killing spinor, which has been missed over many years. We also address the supersymmetry when the Przanowski–Tod space is conformal to each of the self-dual ambi-toric Kähler metrics. It turns out that three classes of solutions are all reduced to the self-dual Carter family, by virtue of the nondegenerate Killing–Yano tensor.
Efficient gamma index calculation using fast Euclidean distance transform
Energy Technology Data Exchange (ETDEWEB)
Chen Mingli; Lu Weiguo; Chen Quan; Ruchala, Kenneth; Olivera, Gustavo [TomoTherapy Inc., 1240 Deming Way, Madison, WI 53717 (United States)], E-mail: wlu@tomotherapy.com
2009-04-07
The gamma index is a tool for dose distribution comparison. It combines both dose difference (DD) and distance to agreement (DTA) into a single quantity. Though it is an effective measure, making up for the inadequacy of DD or DTA alone, its calculation can be very time-consuming. For a k-D space with N quantization levels in each dimension, the complexity of the exhaustive search is O(N{sup 2k}). In this work, we proposed an efficient method that reduces the complexity from O(N{sup 2k}) to O(N{sup k}M), where M is the number of discretized dose values and is comparable to N. More precisely, by embedding the reference dose distribution in a (k+1)-D spatial-dose space, we can use fast Euclidean distance transform with linear complexity to obtain a table of gamma indices evaluated over a range of the (k+1)-D spatial-dose space. Then, to obtain gamma indices for the test dose distribution, it requires only table lookup with complexity O(N{sup k}). Such a table can also be used for other test dose distributions as long as the reference dose distribution is the same. Simulations demonstrated the efficiency of our proposed method. The speedup for 3D gamma index calculation is expected to be on the order of tens of thousands (from O(N{sup 6}) to O(N{sup 3}M)) if N is a few hundreds, which makes clinical usage of the 3D gamma index feasible. A byproduct of the gamma index table is that the gradient of the gamma index with respect to either the spatial or dose dimension can be easily derived. The gradient can be used to identify the main causes of the discrepancy from the reference distribution at any dose point in the test distribution or incorporated in treatment planning and machine parameter optimization.
Some notes on tetrahedrally closed spherical sets in Euclidean spaces
Indian Academy of Sciences (India)
47
is a relation between these sets. P is called the point set, L the line set and I the incidence relation. A point-line geometry S = (P,L,I) is called a near polygon if every two distinct points are incident with at most one line and if for every point x and every line L, there exists a unique point on L that is nearest to x with respect to ...
The quark Schwinger-Dyson equation in temporal Euclidean space
Czech Academy of Sciences Publication Activity Database
Šauli, Vladimír; Batiz, Z.
2009-01-01
Roč. 36, č. 3 (2009), 035002/1-035002/13 ISSN 0954-3899 Institutional research plan: CEZ:AV0Z10480505 Keywords : ANALYTIC PERTURBATION-THEORY * DYNAMICAL SYMMETRY-BREAKING * BACKGROUND FIELD METHOD Subject RIV: BE - Theoretical Physics Impact factor: 2.124, year: 2009
Mannheim Partner D-Curves in the Euclidean 3-space
Directory of Open Access Journals (Sweden)
Mustafa Kazaz
2015-02-01
Full Text Available In this paper, we consider the idea of Mannheim partner curves for curves lying on surfaces. By considering the Darboux frames of surface curves, we define Mannheim partner D-curves and give the characterizations for these curves. We also find the relations between geodesic curvatures, normal curvatures and geodesic torsions of these associated curves. Furthermore, we show that definition and characterizations of Mannheim partner D-curves include those of Mannheim partner curves in some special cases.
Weyl, Hermann
1922-01-01
Excellent introduction probes deeply into Euclidean space, Riemann's space, Einstein's general relativity, gravitational waves and energy, and laws of conservation. "A classic of physics." - British Journal for Philosophy and Science.
MEDOF - MINIMUM EUCLIDEAN DISTANCE OPTIMAL FILTER
Barton, R. S.
1994-01-01
The Minimum Euclidean Distance Optimal Filter program, MEDOF, generates filters for use in optical correlators. The algorithm implemented in MEDOF follows theory put forth by Richard D. Juday of NASA/JSC. This program analytically optimizes filters on arbitrary spatial light modulators such as coupled, binary, full complex, and fractional 2pi phase. MEDOF optimizes these modulators on a number of metrics including: correlation peak intensity at the origin for the centered appearance of the reference image in the input plane, signal to noise ratio including the correlation detector noise as well as the colored additive input noise, peak to correlation energy defined as the fraction of the signal energy passed by the filter that shows up in the correlation spot, and the peak to total energy which is a generalization of PCE that adds the passed colored input noise to the input image's passed energy. The user of MEDOF supplies the functions that describe the following quantities: 1) the reference signal, 2) the realizable complex encodings of both the input and filter SLM, 3) the noise model, possibly colored, as it adds at the reference image and at the correlation detection plane, and 4) the metric to analyze, here taken to be one of the analytical ones like SNR (signal to noise ratio) or PCE (peak to correlation energy) rather than peak to secondary ratio. MEDOF calculates filters for arbitrary modulators and a wide range of metrics as described above. MEDOF examines the statistics of the encoded input image's noise (if SNR or PCE is selected) and the filter SLM's (Spatial Light Modulator) available values. These statistics are used as the basis of a range for searching for the magnitude and phase of k, a pragmatically based complex constant for computing the filter transmittance from the electric field. The filter is produced for the mesh points in those ranges and the value of the metric that results from these points is computed. When the search is concluded, the
What if? Exploring the multiverse through Euclidean wormholes
Bouhmadi-López, Mariam; Krämer, Manuel; Morais, João; Robles-Pérez, Salvador
2017-10-01
We present Euclidean wormhole solutions describing possible bridges within the multiverse. The study is carried out in the framework of third quantisation. The matter content is modelled through a scalar field which supports the existence of a whole collection of universes. The instanton solutions describe Euclidean solutions that connect baby universes with asymptotically de Sitter universes. We compute the tunnelling probability of these processes. Considering the current bounds on the energy scale of inflation and assuming that all the baby universes are nucleated with the same probability, we draw some conclusions about which universes are more likely to tunnel and therefore undergo a standard inflationary era.
What if? Exploring the multiverse through Euclidean wormholes
International Nuclear Information System (INIS)
Bouhmadi-Lopez, Mariam; Kraemer, Manuel; Morais, Joao; Robles-Perez, Salvador
2017-01-01
We present Euclidean wormhole solutions describing possible bridges within the multiverse. The study is carried out in the framework of third quantisation. The matter content is modelled through a scalar field which supports the existence of a whole collection of universes. The instanton solutions describe Euclidean solutions that connect baby universes with asymptotically de Sitter universes. We compute the tunnelling probability of these processes. Considering the current bounds on the energy scale of inflation and assuming that all the baby universes are nucleated with the same probability, we draw some conclusions about which universes are more likely to tunnel and therefore undergo a standard inflationary era. (orig.)
What if? Exploring the multiverse through Euclidean wormholes
Energy Technology Data Exchange (ETDEWEB)
Bouhmadi-Lopez, Mariam [University of the Basque Country UPV/EHU, Department of Theoretical Physics, Bilbao (Spain); Ikerbasque, Basque Foundation for Science, Bilbao (Spain); Kraemer, Manuel [University of Szczecin, Institute of Physics, Szczecin (Poland); Morais, Joao [University of the Basque Country UPV/EHU, Department of Theoretical Physics, Bilbao (Spain); Robles-Perez, Salvador [Instituto de Fisica Fundamental, CSIC, Madrid (Spain); Estacion Ecologica de Biocosmologia, Medellin (Spain)
2017-10-15
We present Euclidean wormhole solutions describing possible bridges within the multiverse. The study is carried out in the framework of third quantisation. The matter content is modelled through a scalar field which supports the existence of a whole collection of universes. The instanton solutions describe Euclidean solutions that connect baby universes with asymptotically de Sitter universes. We compute the tunnelling probability of these processes. Considering the current bounds on the energy scale of inflation and assuming that all the baby universes are nucleated with the same probability, we draw some conclusions about which universes are more likely to tunnel and therefore undergo a standard inflationary era. (orig.)
Supersymmetry on a euclidean spacetime lattice 1. A target theory with four supercharges
International Nuclear Information System (INIS)
Cohen, Andrew G.; Kaplan, David B.; Katz, Emanuel; Uensal, Mithat
2003-01-01
We formulate a euclidean spacetime lattice whose continuum limit is (2,2) supersymmetric Yang-Mills theory in two dimensions, a theory which possesses four supercharges and an anomalous global chiral symmetry. The lattice action respects one exact supersymmetry, which allows the target theory to emerge in the continuum limit without fine-tuning. Our method exploits an orbifold construction described previously for spatial lattices in Minkowski space, and can be generalized to more complicated theories with additional supersymmetry and more spacetime dimensions. (author)
Constant curvature black holes in Einstein AdS gravity: Euclidean action and thermodynamics
Guilleminot, Pablo; Olea, Rodrigo; Petrov, Alexander N.
2018-03-01
We compute the Euclidean action for constant curvature black holes (CCBHs), as an attempt to associate thermodynamic quantities to these solutions of Einstein anti-de Sitter (AdS) gravity. CCBHs are gravitational configurations obtained by identifications along isometries of a D -dimensional globally AdS space, such that the Riemann tensor remains constant. Here, these solutions are interpreted as extended objects, which contain a (D -2 )-dimensional de-Sitter brane as a subspace. Nevertheless, the computation of the free energy for these solutions shows that they do not obey standard thermodynamic relations.
Ultraviolet stability in euclidean scalar field theories
Energy Technology Data Exchange (ETDEWEB)
Benfatto, G; Cassandro, M; Gallavotti, G; Nicolo, F; Olivieri, E; Presutti, E; Scacciatelli, E [Rome Univ. (Italy). Istituto di Matematica; Rome Univ. (Italy). Istituto di Fisica)
1980-01-01
We develop a technique for reducing the problem of the ultraviolet divergences and their removal to a free field problem. This work is an example of a problem to which a rather general method can be applied. It can be thought as an attempt towards a rigorous version (in 2 or 3 space-time dimensions) of the analysis of the structure of the functional integrals, the underlying mechanism being essentially the same as in Glimms approach.
Euclidean self-dual Yang-Mills field configurations
International Nuclear Information System (INIS)
Sartori, G.
1980-01-01
The determination of a large class of regular and singular Euclidean self-dual Yang-Mills field configurations is reduced to the solution of a set of linear algebraic equations. The matrix of the coefficients is a polynomial functions of x and the rules for its construction are elementary. (author)
The toroidal Hausdorff dimension of 2d Euclidean quantum gravity
DEFF Research Database (Denmark)
Ambjorn, Jan; Budd, Timothy George
2013-01-01
The lengths of shortest non-contractible loops are studied numerically in 2d Euclidean quantum gravity on a torus coupled to conformal field theories with central charge less than one. We find that the distribution of these geodesic lengths displays a scaling in agreement with a Hausdorff dimension...
Timed Fast Exact Euclidean Distance (tFEED) maps
Kehtarnavaz, Nasser; Schouten, Theo E.; Laplante, Philip A.; Kuppens, Harco; van den Broek, Egon
2005-01-01
In image and video analysis, distance maps are frequently used. They provide the (Euclidean) distance (ED) of background pixels to the nearest object pixel. In a naive implementation, each object pixel feeds its (exact) ED to each background pixel; then the minimum of these values denotes the ED to
The Euclidean distance degree of an algebraic variety
Draisma, J.; Horobet, E.; Ottaviani, G.; Sturmfels, B.; Thomas, R.R.
2013-01-01
The nearest point map of a real algebraic variety with respect to Euclidean distance is an algebraic function. For instance, for varieties of low rank matrices, the Eckart-Young Theorem states that this map is given by the singular value decomposition. This article develops a theory of such nearest
The Euclidean distance degree of an algebraic variety
Draisma, J.; Horobet, E.; Ottaviani, G.; Sturmfels, B.; Thomas, R.R.
The nearest point map of a real algebraic variety with respect to Euclidean distance is an algebraic function. For instance, for varieties of low-rank matrices, the Eckart–Young Theorem states that this map is given by the singular value decomposition. This article develops a theory of such nearest
Superconvergent perturbation theory for euclidean scalar field theories
International Nuclear Information System (INIS)
Ushveridze, A.G.
1984-01-01
It is shown that the bare (unrenormalized) correlation functions in the euclidean scalar field theories can be expanded in a series whose terms, being computable in a relatively simple way, are free from ultraviolet and infrared divergencies. This series is convergent (divergent) for finite (infinite) values of the correlation functions. (orig.)
Improvement in quality testing of Braille printer output with Euclidean ...
African Journals Online (AJOL)
This paper focuses on quality testing of Braille printed paper using calibrated camera by detecting dots and measuring the Euclidean distances between them with equal gap, vertically and horizontally. For higher accuracy, camera calibration is essential to observe a planar checker board pattern from different distances and ...
The Role of Structure in Learning Non-Euclidean Geometry
Asmuth, Jennifer A.
2009-01-01
How do people learn novel mathematical information that contradicts prior knowledge? The focus of this thesis is the role of structure in the acquisition of knowledge about hyperbolic geometry, a non-Euclidean geometry. In a series of three experiments, I contrast a more holistic structure--training based on closed figures--with a mathematically…
Euclidean Primes Have the Minimum Number of Primitive Roots
Czech Academy of Sciences Publication Activity Database
Křížek, Michal; Somer, L.
2008-01-01
Roč. 12, č. 1 (2008), s. 121-127 ISSN 0972-5555 R&D Projects: GA AV ČR(CZ) IAA100190803 Institutional research plan: CEZ:AV0Z10190503 Keywords : Euclidean primes * Fermat primes * Sophie Germain primes Subject RIV: BA - General Mathematics
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.
Optimal recovery of linear operators in non-Euclidean metrics
Energy Technology Data Exchange (ETDEWEB)
Osipenko, K Yu [Moscow State Aviation Technological University, Moscow (Russian Federation)
2014-10-31
The paper looks at problems concerning the recovery of operators from noisy information in non-Euclidean metrics. A number of general theorems are proved and applied to recovery problems for functions and their derivatives from the noisy Fourier transform. In some cases, a family of optimal methods is found, from which the methods requiring the least amount of original information are singled out. Bibliography: 25 titles.
Change of Measure between Light Travel Time and Euclidean Distances
Directory of Open Access Journals (Sweden)
Heymann Y.
2013-04-01
Full Text Available The problem of cosmological distances is approached using a method based on the propagation of light in an expanding Universe. From the chan ge of measure between Light Travel Time and Euclidean Distances, a formula is deri ved to compute distances as a function of redshift. This formula is identical to Matti g’s formula (with q 0 = 1 / 2 which is based on Friedmann’s equations of general relativi ty.
Jégat , Alain
2014-01-01
The usual framework for Einstein’s special theory of relativity is the pseudo-euclidean spacetime proposed by Hermann Minkowski. This article aims at proposing a different model.The framework is an euclidean four-dimensional space in which all the objects move regularly (it means that, between two observations, whatever their trajectories, they cover the same distance), but where the events are seen in projection according to a privileged direction, as we are going to explain. The remark, rat...
Constraint algebra in Smolin's G →0 limit of 4D Euclidean gravity
Varadarajan, Madhavan
2018-05-01
Smolin's generally covariant GNewton→0 limit of 4d Euclidean gravity is a useful toy model for the study of the constraint algebra in loop quantum gravity (LQG). In particular, the commutator between its Hamiltonian constraints has a metric dependent structure function. While a prior LQG-like construction of nontrivial anomaly free constraint commutators for the model exists, that work suffers from two defects. First, Smolin's remarks on the inability of the quantum dynamics to generate propagation effects apply. Second, the construction only yields the action of a single Hamiltonian constraint together with the action of its commutator through a continuum limit of corresponding discrete approximants; the continuum limit of a product of two or more constraints does not exist. Here, we incorporate changes in the quantum dynamics through structural modifications in the choice of discrete approximants to the quantum Hamiltonian constraint. The new structure is motivated by that responsible for propagation in an LQG-like quantization of paramatrized field theory and significantly alters the space of physical states. We study the off shell constraint algebra of the model in the context of these structural changes and show that the continuum limit action of multiple products of Hamiltonian constraints is (a) supported on an appropriate domain of states, (b) yields anomaly free commutators between pairs of Hamiltonian constraints, and (c) is diffeomorphism covariant. Many of our considerations seem robust enough to be applied to the setting of 4d Euclidean gravity.
Directory of Open Access Journals (Sweden)
Atamurat Kuchkarov
2016-01-01
Full Text Available We consider pursuit and evasion differential games of a group of m pursuers and one evader on manifolds with Euclidean metric. The motions of all players are simple, and maximal speeds of all players are equal. If the state of a pursuer coincides with that of the evader at some time, we say that pursuit is completed. We establish that each of the differential games (pursuit or evasion is equivalent to a differential game of m groups of countably many pursuers and one group of countably many evaders in Euclidean space. All the players in any of these groups are controlled by one controlled parameter. We find a condition under which pursuit can be completed, and if this condition is not satisfied, then evasion is possible. We construct strategies for the pursuers in pursuit game which ensure completion the game for a finite time and give a formula for this time. In the case of evasion game, we construct a strategy for the evader.
Multi-stability in folded shells: non-Euclidean origami
Evans, Arthur
2015-03-01
Both natural and man-made structures benefit from having multiple mechanically stable states, from the quick snapping motion of hummingbird beaks to micro-textured surfaces with tunable roughness. Rather than discuss special fabrication techniques for creating bi-stability through material anisotropy, in this talk I will present several examples of how folding a structure can modify the energy landscape and thus lead to multiple stable states. Using ideas from origami and differential geometry, I will discuss how deforming a non-Euclidean surface can be done either continuously or discontinuously, and explore the effects that global constraints have on the ultimate stability of the surface.
ILUCG algorithm which minimizes in the Euclidean norm
International Nuclear Information System (INIS)
Petravic, M.; Kuo-Petravic, G.
1978-07-01
An algroithm is presented which solves sparse systems of linear equations of the form Ax = Y, where A is non-symmetric, by the Incomplete LU Decomposition-Conjugate Gradient (ILUCG) method. The algorithm minimizes the error in the Euclidean norm vertical bar x/sub i/ - x vertical bar 2 , where x/sub i/ is the solution vector after the i/sup th/ iteration and x the exact solution vector. The results of a test on one real problem indicate that the algorithm is likely to be competitive with the best existing algorithms of its type
Non-perturbative BRST quantization of Euclidean Yang-Mills theories in Curci-Ferrari gauges
Pereira, A. D.; Sobreiro, R. F.; Sorella, S. P.
2016-10-01
In this paper we address the issue of the non-perturbative quantization of Euclidean Yang-Mills theories in the Curci-Ferrari gauge. In particular, we construct a refined Gribov-Zwanziger action for this gauge, which takes into account the presence of gauge copies as well as the dynamical formation of dimension-two condensates. This action enjoys a non-perturbative BRST symmetry recently proposed in Capri et al. (Phys. Rev. D 92(4), 045039. doi: 10.1103/PhysRevD.92.045039 arXiv:1506.06995 [hep-th], 2015). Finally, we pay attention to the gluon propagator in different space-time dimensions.
Non-perturbative BRST quantization of Euclidean Yang-Mills theories in Curci-Ferrari gauges
International Nuclear Information System (INIS)
Pereira, A.D.; Sobreiro, R.F.; Sorella, S.P.
2016-01-01
In this paper we address the issue of the non-perturbative quantization of Euclidean Yang-Mills theories in the Curci-Ferrari gauge. In particular, we construct a refined Gribov-Zwanziger action for this gauge, which takes into account the presence of gauge copies as well as the dynamical formation of dimension-two condensates. This action enjoys a non-perturbative BRST symmetry recently proposed in Capri et al. (Phys. Rev. D 92(4), 045039. doi:10.1103/PhysRevD.92.045039. arXiv:1506.06995 [hepth], 2015). Finally, we pay attention to the gluon propagator in different space-time dimensions. (orig.)
Non-perturbative BRST quantization of Euclidean Yang-Mills theories in Curci-Ferrari gauges
Energy Technology Data Exchange (ETDEWEB)
Pereira, A.D. [UFF, Universidade Federal Fluminense, Instituto de Fisica, Campus da Praia Vermelha, Niteroi, RJ (Brazil); Max Planck Institute for Gravitational Physics, Albert Einstein Institute, Potsdam (Germany); UERJ, Universidade do Estado do Rio de Janeiro, Departamento de Fisica Teorica, Rio de Janeiro (Brazil); Sobreiro, R.F. [UFF, Universidade Federal Fluminense, Instituto de Fisica, Campus da Praia Vermelha, Niteroi, RJ (Brazil); Sorella, S.P. [UERJ, Universidade do Estado do Rio de Janeiro, Departamento de Fisica Teorica, Rio de Janeiro (Brazil)
2016-10-15
In this paper we address the issue of the non-perturbative quantization of Euclidean Yang-Mills theories in the Curci-Ferrari gauge. In particular, we construct a refined Gribov-Zwanziger action for this gauge, which takes into account the presence of gauge copies as well as the dynamical formation of dimension-two condensates. This action enjoys a non-perturbative BRST symmetry recently proposed in Capri et al. (Phys. Rev. D 92(4), 045039. doi:10.1103/PhysRevD.92.045039. arXiv:1506.06995 [hepth], 2015). Finally, we pay attention to the gluon propagator in different space-time dimensions. (orig.)
Euclidean scalar Green's functions near the black hole and black brane horizons
International Nuclear Information System (INIS)
Haba, Z
2009-01-01
We discuss approximations of the Riemannian geometry near the horizon. If a (D + 1)-dimensional manifold N has a bifurcate Killing horizon then we approximate N by a product of the two-dimensional Rindler space R 2 and a (D - 1)-dimensional Riemannian manifold M. We obtain approximate formulae for scalar Green's functions. We study the behavior of the Green's functions near the horizon and their dimensional reduction. We show that if M is compact then the Green's function near the horizon can be approximated by the Green's function of the two-dimensional quantum field theory. The correction term is exponentially small away from the horizon. We extend the results to black brane solutions of supergravity in 10 and 11 dimensions. The near-horizon geometry can be approximated by N=AdS p xS q . We discuss the Euclidean Green's functions on N and their behavior near the horizon.
Texture classification using non-Euclidean Minkowski dilation
Florindo, Joao B.; Bruno, Odemir M.
2018-03-01
This study presents a new method to extract meaningful descriptors of gray-scale texture images using Minkowski morphological dilation based on the Lp metric. The proposed approach is motivated by the success previously achieved by Bouligand-Minkowski fractal descriptors on texture classification. In essence, such descriptors are directly derived from the morphological dilation of a three-dimensional representation of the gray-level pixels using the classical Euclidean metric. In this way, we generalize the dilation for different values of p in the Lp metric (Euclidean is a particular case when p = 2) and obtain the descriptors from the cumulated distribution of the distance transform computed over the texture image. The proposed method is compared to other state-of-the-art approaches (such as local binary patterns and textons for example) in the classification of two benchmark data sets (UIUC and Outex). The proposed descriptors outperformed all the other approaches in terms of rate of images correctly classified. The interesting results suggest the potential of these descriptors in this type of task, with a wide range of possible applications to real-world problems.
Speckle Suppression by Weighted Euclidean Distance Anisotropic Diffusion
Directory of Open Access Journals (Sweden)
Fengcheng Guo
2018-05-01
Full Text Available To better reduce image speckle noise while also maintaining edge information in synthetic aperture radar (SAR images, we propose a novel anisotropic diffusion algorithm using weighted Euclidean distance (WEDAD. Presented here is a modified speckle reducing anisotropic diffusion (SRAD method, which constructs a new edge detection operator using weighted Euclidean distances. The new edge detection operator can adaptively distinguish between homogenous and heterogeneous image regions, effectively generate anisotropic diffusion coefficients for each image pixel, and filter each pixel at different scales. Additionally, the effects of two different weighting methods (Gaussian weighting and non-linear weighting of de-noising were analyzed. The effect of different adjustment coefficient settings on speckle suppression was also explored. A series of experiments were conducted using an added noise image, GF-3 SAR image, and YG-29 SAR image. The experimental results demonstrate that the proposed method can not only significantly suppress speckle, thus improving the visual effects, but also better preserve the edge information of images.
Isometric immersions and embeddings of locally Euclidean metrics in R2
International Nuclear Information System (INIS)
Sabitov, I Kh
1999-01-01
This paper deals with the problem of isometric immersions and embeddings of two-dimensional locally Euclidean metrics in the Euclidean plane. We find explicit formulae for the immersions of metrics defined on a simply connected domain and a number of sufficient conditions for the existence of isometric embeddings. In the case when the domain is multiply connected we find necessary conditions for the existence of isometric immersions and classify the cases when the metric admits no isometric immersion in the Euclidean plane
The manifold model for space-time
International Nuclear Information System (INIS)
Heller, M.
1981-01-01
Physical processes happen on a space-time arena. It turns out that all contemporary macroscopic physical theories presuppose a common mathematical model for this arena, the so-called manifold model of space-time. The first part of study is an heuristic introduction to the concept of a smooth manifold, starting with the intuitively more clear concepts of a curve and a surface in the Euclidean space. In the second part the definitions of the Csub(infinity) manifold and of certain structures, which arise in a natural way from the manifold concept, are given. The role of the enveloping Euclidean space (i.e. of the Euclidean space appearing in the manifold definition) in these definitions is stressed. The Euclidean character of the enveloping space induces to the manifold local Euclidean (topological and differential) properties. A suggestion is made that replacing the enveloping Euclidean space by a discrete non-Euclidean space would be a correct way towards the quantization of space-time. (author)
Anisotropic, Mixed-Norm Lizorkin-Triebel Spaces and Diffeomorphic Maps
DEFF Research Database (Denmark)
Johnsen, Jon; Hansen, Sabrina Munch; Sickel, Winfried
2014-01-01
This paper gives general results on invariance of anisotropic Lizorkin-Triebel spaces with mixed norms under coordinate transformations on Euclidean space, open sets, and cylindrical domains.......This paper gives general results on invariance of anisotropic Lizorkin-Triebel spaces with mixed norms under coordinate transformations on Euclidean space, open sets, and cylindrical domains....
Reduction of product platform complexity by vectorial Euclidean algorithm
International Nuclear Information System (INIS)
Navarrete, Israel Aguilera; Guzman, Alejandro A. Lozano
2013-01-01
In traditional machine, equipment and devices design, technical solutions are practically independent, thus increasing designs cost and complexity. Overcoming this situation has been tackled just using designer's experience. In this work, a product platform complexity reduction is presented based on a matrix representation of technical solutions versus product properties. This matrix represents the product platform. From this matrix, the Euclidean distances among technical solutions are obtained. Thus, the vectorial distances among technical solutions are identified in a new matrix of order of the number of technical solutions identified. This new matrix can be reorganized in groups with a hierarchical structure, in such a way that modular design of products is now more tractable. As a result of this procedure, the minimum vector distances are found thus being possible to identify the best technical solutions for the design problem raised. Application of these concepts is shown with two examples.
Curvature-driven morphing of non-Euclidean shells
Pezzulla, Matteo; Stoop, Norbert; Jiang, Xin; Holmes, D. P.
2017-05-01
We investigate how thin structures change their shape in response to non-mechanical stimuli that can be interpreted as variations in the structure's natural curvature. Starting from the theory of non-Euclidean plates and shells, we derive an effective model that reduces a three-dimensional stimulus to the natural fundamental forms of the mid-surface of the structure, incorporating expansion, or growth, in the thickness. Then, we apply the model to a variety of thin bodies, from flat plates to spherical shells, obtaining excellent agreement between theory and numerics. We show how cylinders and cones can either bend more or unroll, and eventually snap and rotate. We also study the nearly isometric deformations of a spherical shell and describe how this shape change is ruled by the geometry of a spindle. As the derived results stem from a purely geometrical model, they are general and scalable.
Defects and boundary layers in non-Euclidean plates
International Nuclear Information System (INIS)
Gemmer, J A; Venkataramani, S C
2012-01-01
We investigate the behaviour of non-Euclidean plates with constant negative Gaussian curvature using the Föppl–von Kármán reduced theory of elasticity. Motivated by recent experimental results, we focus on annuli with a periodic profile. We prove rigorous upper and lower bounds for the elastic energy that scales like the thickness squared. In particular we show that are only two types of global minimizers—deformations that remain flat and saddle shaped deformations with isolated regions of stretching near the edge of the annulus. We also show that there exist local minimizers with a periodic profile that have additional boundary layers near their lines of inflection. These additional boundary layers are a new phenomenon in thin elastic sheets and are necessary to regularize jump discontinuities in the azimuthal curvature across lines of inflection. We rigorously derive scaling laws for the width of these boundary layers as a function of the thickness of the sheet. (paper)
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...
Euclidean mirrors: enhanced vacuum decay from reflected instantons
Akal, Ibrahim; Moortgat-Pick, Gudrid
2018-05-01
We study the tunnelling of virtual matter–antimatter pairs from the quantum vacuum in the presence of a spatially uniform, time-dependent electric background composed of a strong, slow field superimposed with a weak, rapid field. After analytic continuation to Euclidean spacetime, we obtain from the instanton equations two critical points. While one of them is the closing point of the instanton path, the other serves as an Euclidean mirror which reflects and squeezes the instanton. It is this reflection and shrinking which is responsible for an enormous enhancement of the vacuum pair production rate. We discuss how important features of two different mechanisms can be analysed and understood via such a rotation in the complex plane. (a) Consistent with previous studies, we first discuss the standard assisted mechanism with a static strong field and certain weak fields with a distinct pole structure in order to show that the reflection takes place exactly at the poles. We also discuss the effect of possible sub-cycle structures. We extend this reflection picture then to weak fields which have no poles present and illustrate the effective reflections with explicit examples. An additional field strength dependence for the rate occurs in such cases. We analytically compute the characteristic threshold for the assisted mechanism given by the critical combined Keldysh parameter. We discuss significant differences between these two types of fields. For various backgrounds, we present the contributing instantons and perform analytical computations for the corresponding rates treating both fields nonperturbatively. (b) In addition, we also study the case with a nonstatic strong field which gives rise to the assisted dynamical mechanism. For different strong field profiles we investigate the impact on the critical combined Keldysh parameter. As an explicit example, we analytically compute the rate by employing the exact reflection points. The validity of the predictions
Euclidean mirrors. Enhanced vacuum decay from reflected instantons
Energy Technology Data Exchange (ETDEWEB)
Akal, Ibrahim [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany). Theory Group; Moortgat-Pick, Gudrid [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik
2017-06-15
We study the tunneling of virtual matter-antimatter pairs from the quantum vacuum in the presence of a spatially uniform temporal electric background composed of of a strong slow field superimposed with a weak rapid field. After analytic continuation to Euclidean spacetime we obtain from the instanton equations two critical points. While one of them is the closing point of the instanton path, the other serves as an Euclidean mirror which reflects and squeezes the instanton. It is this reflection and shrinking which is responsible for an enormous enhancement of the vacuum pair production rate. We discuss how important features of this mechanism can be analysed and understood via such a rotation in the complex plane. Consistent with previous studies, we consider certain examples where we apply weak fields with a distinct pole structure in order to show that the reflection takes place exactly at the poles. We also discuss the effect of possible sub-cycle structures. We extend this reflection picture to fields which have no poles present and illustrate the effective reflections with explicit examples. An additional field strength dependence for the rate occurs in such cases. We analytically compute the characteristic threshold for this mechanism given by the critical combined Keldysh parameter. We discuss significant differences between these two types of fields. For various backgrounds, we present the contributing instantons and perform analytical computations for the corresponding rates treating both fields nonperturbatively. The validity of the results is confirmed by numerical computations. Considering different profiles for the strong field, we also discuss its impact on the critical combined Keldysh parameter.
Three Dimensional Fast Exact Euclidean Distance (3D-FEED) Maps
Latecki, L.J.; Schouten, Theo E.; Mount, D.M.; Kuppens, Harco C.; Wu, A.Y.; van den Broek, Egon
2006-01-01
In image and video analysis, distance maps are frequently used. They provide the (Euclidean) distance (ED) of background pixels to the nearest object pixel. Recently, the Fast Exact Euclidean Distance (FEED) transformation was launched. In this paper, we present the three dimensional (3D) version of
Uniqueness of Gibbs states and global Markov property for Euclidean fields
International Nuclear Information System (INIS)
Albeverio, S.; Hoeegh-Krohn, R.
1981-01-01
The authors briefly discuss the proof of the uniqueness of solutions of the DLR equations (uniqueness of Gibbs states) in the class of regular generalized random fields (in the sense of having second moments bounded by those of some Euclidean field), for the Euclidean fields with trigonometric interaction. (Auth.)
Non-euclidean simplex optimization. [Application to potentiometric titration of Pu
Energy Technology Data Exchange (ETDEWEB)
Silver, G.L.
1977-08-15
Geometric optimization techniques useful for studying chemical equilibrium traditionally rely upon principles of euclidean geometry, but such algorithms may also be based upon principles of a non-euclidean geometry. The sequential simplex method is adapted to the hyperbolic plane, and application of optimization to problems such as the potentiometric titration of plutonium is suggested.
Squared Euclidean distance: a statistical test to evaluate plant community change
Raymond D. Ratliff; Sylvia R. Mori
1993-01-01
The concepts and a procedure for evaluating plant community change using the squared Euclidean distance (SED) resemblance function are described. Analyses are based on the concept that Euclidean distances constitute a sample from a population of distances between sampling units (SUs) for a specific number of times and SUs. With different times, the distances will be...
International Nuclear Information System (INIS)
Loran, Farhang
2004-01-01
We solve Klein-Gordon equation for massless scalars on (d+1)-dimensional Minkowski (Euclidean) space in terms of the Cauchy data on the hypersurface t=0. By inserting the solution into the action of massless scalars in Minkowski (Euclidean) space we obtain the action of dual theory on the boundary t=0 which is exactly the holographic dual of conformally coupled scalars on (d+1)-dimensional (Euclidean anti) de Sitter space obtained in (A)dS/CFT correspondence. The observed equivalence of dual theories is explained using the one-to-one map between conformally coupled scalar fields on Minkowski (Euclidean) space and (Euclidean anti) de Sitter space which is an isomorphism between the hypersurface t=0 of Minkowski (Euclidean) space and the boundary of (A)dS space
The Dirac equation in the Lobachevsky space-time
International Nuclear Information System (INIS)
Paramonov, D.V.; Paramonova, N.N.; Shavokhina, N.S.
2000-01-01
The product of the Lobachevsky space and the time axis is termed the Lobachevsky space-time. The Lobachevsky space is considered as a hyperboloid's sheet in the four-dimensional pseudo-Euclidean space. The Dirac-Fock-Ivanenko equation is reduced to the Dirac equation in two special forms by passing from Lame basis in the Lobachevsky space to the Cartesian basis in the enveloping pseudo-Euclidean space
A general Euclidean connection for so(n,m) lie algebra and the algebraic approach to scattering
International Nuclear Information System (INIS)
Ionescu, R.A.
1994-11-01
We obtain a general Euclidean connection for so(n,m). This Euclidean connection allows an algebraic derivation of the S matrix and it reduces to the known one in suitable circumstances. (author). 8 refs
On the space dimensionality based on metrics
International Nuclear Information System (INIS)
Gorelik, G.E.
1978-01-01
A new approach to space time dimensionality is suggested, which permits to take into account the possibility of altering dimensionality depending on the phenomenon scale. An attempt is made to give the definition of dimensionality, equivalent to a conventional definition for the Euclidean space and variety. The conventional definition of variety dimensionality is connected with the possibility of homeomorphic reflection of the Euclidean space on some region of each variety point
Maximally-localized position, Euclidean path-integral, and thermodynamics in GUP quantum mechanics
Bernardo, Reginald Christian S.; Esguerra, Jose Perico H.
2018-04-01
In dealing with quantum mechanics at very high energies, it is essential to adapt to a quasiposition representation using the maximally-localized states because of the generalized uncertainty principle. In this paper, we look at maximally-localized states as eigenstates of the operator ξ = X + iβP that we refer to as the maximally-localized position. We calculate the overlap between maximally-localized states and show that the identity operator can be expressed in terms of the maximally-localized states. Furthermore, we show that the maximally-localized position is diagonal in momentum-space and that the maximally-localized position and its adjoint satisfy commutation and anti-commutation relations reminiscent of the harmonic oscillator commutation and anti-commutation relations. As application, we use the maximally-localized position in developing the Euclidean path-integral and introduce the compact form of the propagator for maximal localization. The free particle momentum-space propagator and the propagator for maximal localization are analytically evaluated up to quadratic-order in β. Finally, we obtain a path-integral expression for the partition function of a thermodynamic system using the maximally-localized states. The partition function of a gas of noninteracting particles is evaluated. At temperatures exceeding the Planck energy, we obtain the gas' maximum internal energy N / 2 β and recover the zero heat capacity of an ideal gas.
Entropy, extremality, euclidean variations, and the equations of motion
Dong, Xi; Lewkowycz, Aitor
2018-01-01
We study the Euclidean gravitational path integral computing the Rényi entropy and analyze its behavior under small variations. We argue that, in Einstein gravity, the extremality condition can be understood from the variational principle at the level of the action, without having to solve explicitly the equations of motion. This set-up is then generalized to arbitrary theories of gravity, where we show that the respective entanglement entropy functional needs to be extremized. We also extend this result to all orders in Newton's constant G N , providing a derivation of quantum extremality. Understanding quantum extremality for mixtures of states provides a generalization of the dual of the boundary modular Hamiltonian which is given by the bulk modular Hamiltonian plus the area operator, evaluated on the so-called modular extremal surface. This gives a bulk prescription for computing the relative entropies to all orders in G N . We also comment on how these ideas can be used to derive an integrated version of the equations of motion, linearized around arbitrary states.
Euclidean quantum field theory and the Hawking effect
International Nuclear Information System (INIS)
Lapedes, A.S.
1978-01-01
Complex analytic continuation in a time variable in order to define a Feynman propagator is investigated in a general relativistic context. When external electric fields are present a complex analytic continuation in the electric charge is also introduced. The new Euclidean formalism is checked by reproducing Schwinger's special relativistic result for pair creation by an external, homogenous, electric field, and then applied to the Robinson-Bertotti universe. The Robinson-Bertotti universe, although unphysical, provides an interesting theoretical laboratory in which to investigate quantum effects, much as the unphysical Taub-NUT (Newman-Unti-Tamburino) universe does for purely classical general relativity. A conformally related problem of pair creation by a supercritically charged nucleus is also considered, and a sensible resolution is obtained to this classic problem. The essential mathematical point throughout is the use of the Feynman path-integral form of the propagator to motivate replacing hyperbolic equations by elliptic equations. The unique, bounded solution for the elliptic Green's function is then analytically continued back to physical values to define the Feynman Green's function
Numerical evaluation of tensor Feynman integrals in Euclidean kinematics
Energy Technology Data Exchange (ETDEWEB)
Gluza, J.; Kajda [Silesia Univ., Katowice (Poland). Inst. of Physics; Riemann, T.; Yundin, V. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)
2010-10-15
For the investigation of higher order Feynman integrals, potentially with tensor structure, it is highly desirable to have numerical methods and automated tools for dedicated, but sufficiently 'simple' numerical approaches. We elaborate two algorithms for this purpose which may be applied in the Euclidean kinematical region and in d=4-2{epsilon} dimensions. One method uses Mellin-Barnes representations for the Feynman parameter representation of multi-loop Feynman integrals with arbitrary tensor rank. Our Mathematica package AMBRE has been extended for that purpose, and together with the packages MB (M. Czakon) or MBresolve (A. V. Smirnov and V. A. Smirnov) one may perform automatically a numerical evaluation of planar tensor Feynman integrals. Alternatively, one may apply sector decomposition to planar and non-planar multi-loop {epsilon}-expanded Feynman integrals with arbitrary tensor rank. We automatized the preparations of Feynman integrals for an immediate application of the package sectordecomposition (C. Bogner and S. Weinzierl) so that one has to give only a proper definition of propagators and numerators. The efficiency of the two implementations, based on Mellin-Barnes representations and sector decompositions, is compared. The computational packages are publicly available. (orig.)
Variational estimates for the mass gap of SU(2) Euclidean lattice gauge theory
International Nuclear Information System (INIS)
Hari Dass, N.D.
1984-10-01
The purpose of this letter is to report on the progress made in our understanding of series expansions for the masses in lattice gauge theories by the application of variational techniques to the Euclidean SU(2) lattice gauge theory. (Auth.)
Euclidean action for vacuum decay in a de Sitter universe
International Nuclear Information System (INIS)
Balek, V.; Demetrian, M.
2005-01-01
The behavior of the action of the instantons describing vacuum decay in a de Sitter is investigated. For a near-to-limit instanton (a Coleman-de Luccia instanton close to some Hawking-Moss instanton) we find approximate formulas for the Euclidean action by expanding the scalar field and the metric of the instanton in the powers of the scalar field amplitude. The order of the magnitude of the correction to the Hawking-Moss action depends on the order of the instanton (the number of crossings of the barrier by the scalar field): for instantons of odd and even orders the correction is of the fourth and third order in the scalar field amplitude, respectively. If a near-to-limit instanton of the first order exists in a potential with the curvature at the top of the barrier greater than 4x(Hubble constant) 2 , which is the case if the fourth derivative of the potential at the top of the barrier is greater than some negative limit value, the action of the instanton is less than the Hawking-Moss action and, consequently, the instanton determines the outcome of the vacuum decay if no other Coleman-de Luccia instanton is admitted by the potential. A numerical study shows that for the quartic potential the physical mode of the vacuum decay is given by the Coleman-de Luccia instanton of the first order also in the region of parameters in which the potential admits two instantons of the second order
Directory of Open Access Journals (Sweden)
Yuxian Zhang
2015-01-01
Full Text Available The quality index model in slashing process is difficult to build by reason of the outliers and noise data from original data. To the above problem, a fuzzy neural network based on non-Euclidean distance clustering is proposed in which the input space is partitioned into many local regions by the fuzzy clustering based on non-Euclidean distance so that the computation complexity is decreased, and fuzzy rule number is determined by validity function based on both the separation and the compactness among clusterings. Then, the premise parameters and consequent parameters are trained by hybrid learning algorithm. The parameters identification is realized; meanwhile the convergence condition of consequent parameters is obtained by Lyapunov function. Finally, the proposed method is applied to build the quality index model in slashing process in which the experimental data come from the actual slashing process. The experiment results show that the proposed fuzzy neural network for quality index model has lower computation complexity and faster convergence time, comparing with GP-FNN, BPNN, and RBFNN.
Euclidean Geometry Codes, minimum weight words and decodable error-patterns using bit-flipping
DEFF Research Database (Denmark)
Høholdt, Tom; Justesen, Jørn; Jonsson, Bergtor
2005-01-01
We determine the number of minimum wigth words in a class of Euclidean Geometry codes and link the performance of the bit-flipping decoding algorithm to the geometry of the error patterns.......We determine the number of minimum wigth words in a class of Euclidean Geometry codes and link the performance of the bit-flipping decoding algorithm to the geometry of the error patterns....
Linearization of Euclidean Norm Dependent Inequalities Applied to Multibeam Satellites Design
Camino , Jean-Thomas; Artigues , Christian; Houssin , Laurent; Mourgues , Stéphane
2016-01-01
Euclidean norm computations over continuous variables appear naturally in the constraints or in the objective of many problems in the optimization literature, possibly defining non-convex feasible regions or cost functions. When some other variables have discrete domains, it positions the problem in the challenging Mixed Integer Nonlinear Programming (MINLP) class. For any MINLP where the nonlinearity is only present in the form of inequality constraints involving the Euclidean norm, we propo...
Non-Hermitian systems of Euclidean Lie algebraic type with real energy spectra
Dey, Sanjib; Fring, Andreas; Mathanaranjan, Thilagarajah
2014-07-01
We study several classes of non-Hermitian Hamiltonian systems, which can be expressed in terms of bilinear combinations of Euclidean-Lie algebraic generators. The classes are distinguished by different versions of antilinear (PT)-symmetries exhibiting various types of qualitative behaviour. On the basis of explicitly computed non-perturbative Dyson maps we construct metric operators, isospectral Hermitian counterparts for which we solve the corresponding time-independent Schrödinger equation for specific choices of the coupling constants. In these cases general analytical expressions for the solutions are obtained in the form of Mathieu functions, which we analyze numerically to obtain the corresponding energy spectra. We identify regions in the parameter space for which the corresponding spectra are entirely real and also domains where the PT symmetry is spontaneously broken and sometimes also regained at exceptional points. In some cases it is shown explicitly how the threshold region from real to complex spectra is characterized by the breakdown of the Dyson maps or the metric operator. We establish the explicit relationship to models currently under investigation in the context of beam dynamics in optical lattices.
Directory of Open Access Journals (Sweden)
Q. Zhou
2017-07-01
Full Text Available Visual Odometry (VO is a critical component for planetary robot navigation and safety. It estimates the ego-motion using stereo images frame by frame. Feature points extraction and matching is one of the key steps for robotic motion estimation which largely influences the precision and robustness. In this work, we choose the Oriented FAST and Rotated BRIEF (ORB features by considering both accuracy and speed issues. For more robustness in challenging environment e.g., rough terrain or planetary surface, this paper presents a robust outliers elimination method based on Euclidean Distance Constraint (EDC and Random Sample Consensus (RANSAC algorithm. In the matching process, a set of ORB feature points are extracted from the current left and right synchronous images and the Brute Force (BF matcher is used to find the correspondences between the two images for the Space Intersection. Then the EDC and RANSAC algorithms are carried out to eliminate mismatches whose distances are beyond a predefined threshold. Similarly, when the left image of the next time matches the feature points with the current left images, the EDC and RANSAC are iteratively performed. After the above mentioned, there are exceptional remaining mismatched points in some cases, for which the third time RANSAC is applied to eliminate the effects of those outliers in the estimation of the ego-motion parameters (Interior Orientation and Exterior Orientation. The proposed approach has been tested on a real-world vehicle dataset and the result benefits from its high robustness.
DEFF Research Database (Denmark)
Gravesen, Jens
2015-01-01
and found the MacAdam ellipses which are often interpreted as defining the metric tensor at their centres. An important question is whether it is possible to define colour coordinates such that the Euclidean distance in these coordinates correspond to human perception. Using cubic splines to represent......The space of colours is a fascinating space. It is a real vector space, but no matter what inner product you put on the space the resulting Euclidean distance does not correspond to human perception of difference between colours. In 1942 MacAdam performed the first experiments on colour matching...
Assessment of the Log-Euclidean Metric Performance in Diffusion Tensor Image Segmentation
Directory of Open Access Journals (Sweden)
Mostafa Charmi
2010-06-01
Full Text Available Introduction: Appropriate definition of the distance measure between diffusion tensors has a deep impact on Diffusion Tensor Image (DTI segmentation results. The geodesic metric is the best distance measure since it yields high-quality segmentation results. However, the important problem with the geodesic metric is a high computational cost of the algorithms based on it. The main goal of this paper is to assess the possible substitution of the geodesic metric with the Log-Euclidean one to reduce the computational cost of a statistical surface evolution algorithm. Materials and Methods: We incorporated the Log-Euclidean metric in the statistical surface evolution algorithm framework. To achieve this goal, the statistics and gradients of diffusion tensor images were defined using the Log-Euclidean metric. Numerical implementation of the segmentation algorithm was performed in the MATLAB software using the finite difference techniques. Results: In the statistical surface evolution framework, the Log-Euclidean metric was able to discriminate the torus and helix patterns in synthesis datasets and rat spinal cords in biological phantom datasets from the background better than the Euclidean and J-divergence metrics. In addition, similar results were obtained with the geodesic metric. However, the main advantage of the Log-Euclidean metric over the geodesic metric was the dramatic reduction of computational cost of the segmentation algorithm, at least by 70 times. Discussion and Conclusion: The qualitative and quantitative results have shown that the Log-Euclidean metric is a good substitute for the geodesic metric when using a statistical surface evolution algorithm in DTIs segmentation.
Renormalized G-convolution of n-point functions in quantum field theory. I. The Euclidean case
International Nuclear Information System (INIS)
Bros, Jacques; Manolessou-Grammaticou, Marietta.
1977-01-01
The notion of Feynman amplitude associated with a graph G in perturbative quantum field theory admits a generalized version in which each vertex v of G is associated with a general (non-perturbative) nsub(v)-point function Hsup(nsub(v)), nsub(v) denoting the number of lines which are incident to v in G. In the case where no ultraviolet divergence occurs, this has been performed directly in complex momentum space through Bros-Lassalle's G-convolution procedure. The authors propose a generalization of G-convolution which includes the case when the functions Hsup(nsub(v)) are not integrable at infinity but belong to a suitable class of slowly increasing functions. A finite part of the G-convolution integral is then defined through an algorithm which closely follows Zimmermann's renormalization scheme. The case of Euclidean four-momentum configurations is only treated
Directory of Open Access Journals (Sweden)
Hajime Matsui
2017-12-01
Full Text Available In this study, we consider codes over Euclidean domains modulo their ideals. In the first half of the study, we deal with arbitrary Euclidean domains. We show that the product of generator matrices of codes over the rings mod a and mod b produces generator matrices of all codes over the ring mod a b , i.e., this correspondence is onto. Moreover, we show that if a and b are coprime, then this correspondence is one-to-one, i.e., there exist unique codes over the rings mod a and mod b that produce any given code over the ring mod a b through the product of their generator matrices. In the second half of the study, we focus on the typical Euclidean domains such as the rational integer ring, one-variable polynomial rings, rings of Gaussian and Eisenstein integers, p-adic integer rings and rings of one-variable formal power series. We define the reduced generator matrices of codes over Euclidean domains modulo their ideals and show their uniqueness. Finally, we apply our theory of reduced generator matrices to the Hecke rings of matrices over these Euclidean domains.
On the Convergence and Law of Large Numbers for the Non-Euclidean Lp -Means
Directory of Open Access Journals (Sweden)
George Livadiotis
2017-05-01
Full Text Available This paper describes and proves two important theorems that compose the Law of Large Numbers for the non-Euclidean L p -means, known to be true for the Euclidean L 2 -means: Let the L p -mean estimator, which constitutes the specific functional that estimates the L p -mean of N independent and identically distributed random variables; then, (i the expectation value of the L p -mean estimator equals the mean of the distributions of the random variables; and (ii the limit N → ∞ of the L p -mean estimator also equals the mean of the distributions.
Products of Snowflaked Euclidean Lines Are Not Minimal for Looking Down
Directory of Open Access Journals (Sweden)
Joseph Matthieu
2017-11-01
Full Text Available We show that products of snowflaked Euclidean lines are not minimal for looking down. This question was raised in Fractured fractals and broken dreams, Problem 11.17, by David and Semmes. The proof uses arguments developed by Le Donne, Li and Rajala to prove that the Heisenberg group is not minimal for looking down. By a method of shortcuts, we define a new distance d such that the product of snowflaked Euclidean lines looks down on (RN , d, but not vice versa.
On Euclidean connections for su(1,1), suq(1,1) and the algebraic approach to scattering
International Nuclear Information System (INIS)
Ionescu, R.A.
1994-11-01
We obtain a general Euclidean connection for su(1,1) and suq(1,1) algebras. Our Euclidean connection allows an algebraic derivation for the S matrix. These algebraic S matrices reduce to the known ones in suitable circumstances. Also, we obtain a map between su(1,1) and su q (1,1) representations. (author). 8 refs
Usability Evaluation of an Augmented Reality System for Teaching Euclidean Vectors
Martin-Gonzalez, Anabel; Chi-Poot, Angel; Uc-Cetina, Victor
2016-01-01
Augmented reality (AR) is one of the emerging technologies that has demonstrated to be an efficient technological tool to enhance learning techniques. In this paper, we describe the development and evaluation of an AR system for teaching Euclidean vectors in physics and mathematics. The goal of this pedagogical tool is to facilitate user's…
Rooij, van I.; Stege, U.; Schactman, A.
2003-01-01
Recently there has been growing interest among psychologists in human performance on the Euclidean traveling salesperson problem (E-TSP). A debate has been initiated on what strategy people use in solving visually presented E-TSP instances. The most prominent hypothesis is the convex-hull
International Nuclear Information System (INIS)
Pordt, A.
1985-10-01
The author describes the Mayer expansion in Euclidean lattice field theory by comparing it with the statistical mechanics of polymer systems. In this connection he discusses the Borel summability and the analyticity of the activities on the lattice. Furthermore the relations between renormalization and the Mayer expansion are considered. (HSI)
Fast Exact Euclidean Distance (FEED): A new class of adaptable distance transforms
Schouten, Theo E.; van den Broek, Egon
2014-01-01
A new unique class of foldable distance transforms of digital images (DT) is introduced, baptized: Fast Exact Euclidean Distance (FEED) transforms. FEED class algorithms calculate the DT starting directly from the definition or rather its inverse. The principle of FEED class algorithms is
Fast Exact Euclidean Distance (FEED) : A new class of adaptable distance transforms
Schouten, Theo E.; van den Broek, Egon L.
2014-01-01
A new unique class of foldable distance transforms of digital images (DT) is introduced, baptized: Fast Exact Euclidean Distance (FEED) transforms. FEED class algorithms calculate the DT startingdirectly from the definition or rather its inverse. The principle of FEED class algorithms is introduced,
Loci of points in the Euclidean plane are deter- mined from ...
Indian Academy of Sciences (India)
Loci of points in the Euclidean plane are deter- mined from prescribed relations of the points with given points, and/or, lines. The depen- dence of these relations on parameters lead to the differential equations representing the fam- ily of loci under concern. Incidentally most of the differential equations thus obtained are non ...
Non-Euclidean spacetime structure and the two-slit experiment
International Nuclear Information System (INIS)
El Naschie, M.S.
2005-01-01
A simple mathematical model for the two-slit experiment is given to account for the wave-particle duality. Subsequently, the various solutions are interpreted via the experimental evidence as a property of the underlying non-Euclidean spacetime topology and geometry at the quantum level
Nonrenormalizable quantum field models in four-dimensional space-time
International Nuclear Information System (INIS)
Raczka, R.
1978-01-01
The construction of no-cutoff Euclidean Green's functions for nonrenormalizable interactions L/sub I/(phi) = lambda∫ddelta (epsilon): expepsilonphi: in four-dimensional space-time is carried out. It is shown that all axioms for the generating functional of the Euclidean Green's function are satisfied except perhaps SO(4) invariance
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
Finite Metric Spaces of Strictly negative Type
DEFF Research Database (Denmark)
Hjorth, Poul G.
If a finite metric space is of strictly negative type then its transfinite diameter is uniquely realized by an infinite extent (“load vector''). Finite metric spaces that have this property include all trees, and all finite subspaces of Euclidean and Hyperbolic spaces. We prove that if the distance...
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...
3D-Ising model as a string theory in three-dimensional euclidean space
International Nuclear Information System (INIS)
Sedrakyan, A.
1992-11-01
A three-dimensional string model is analyzed in the strong coupling regime. The contribution of surfaces with different topology to the partition function is essential. A set of corresponding models is discovered. Their critical indices, which depend on two integers (m,n) are calculated analytically. The critical indices of the three-dimensional Ising model should belong to this set. A possible connection with the chain of three dimensional lattice Pott's models is pointed out. (author) 22 refs.; 2 figs
On the areas of various bodies in the Euclidean space: The case of irregular convex polygons
International Nuclear Information System (INIS)
Ozoemena, P.C.
1988-11-01
A theorem is proposed for the areas of n-sided irregular convex polygons, of given length of sides. The theorem is illustrated as a simple but powerful one in estimating the areas of irregular polygons, being dependent only on the number of sides n (and not on any of the explicit angles) of the irregular polygon. Finally, because of the global symmetry shown by equilateral triangles, squares and circles under group (gauge) theory, the relationships governing their areas, when they are inscribed or escribed in one another are discussed as riders, and some areas of their applications in graph theory, ratios and maxima and minima problems of differential calculus briefly mentioned. (author). 11 refs, 6 figs, 1 tab
Lorentz-force equations as Heisenberg equations for a quantum system in the euclidean space
International Nuclear Information System (INIS)
Rodriguez D, R.
2007-01-01
In an earlier work, the dynamic equations for a relativistic charged particle under the action of electromagnetic fields were formulated by R. Yamaleev in terms of external, as well as internal momenta. Evolution equations for external momenta, the Lorentz-force equations, were derived from the evolution equations for internal momenta. The mapping between the observables of external and internal momenta are related by Viete formulae for a quadratic polynomial, the characteristic polynomial of the relativistic dynamics. In this paper we show that the system of dynamic equations, can be cast into the Heisenberg scheme for a four-dimensional quantum system. Within this scheme the equations in terms of internal momenta play the role of evolution equations for a state vector, whereas the external momenta obey the Heisenberg equation for an operator evolution. The solutions of the Lorentz-force equation for the motion inside constant electromagnetic fields are presented via pentagonometric functions. (Author)
Self-dual solutions to Euclidean Yang-Mills equations
International Nuclear Information System (INIS)
Corrigan, E.
1979-01-01
The paper provides an introduction to two approaches towards understanding the classical Yang-Mills field equations. On the one hand, the work of Atiyah and Ward showed that the self-dual equations, which are non-linear, could be regarded as a set of linear equations which turned out to be related to each other by Baecklund transformations. Fundamental to their procedure was the observation that the information carried by the vector potential could be coded into the structure of certain analytic vector bundles over a three dimensional projective space. The classification of these bundles and the subsequent recovery of the gauge field led to the infinite set of ansaetze, corresponding to the sets of linear equation mentioned already. On the other hand, Atiyah, Hitchin, Drinfeld and Manin have recently constructed, completely algebraically, the bundles of interest and indicated how the Yang-Mills potential may be obtained. Remarkably, their construction differs very little as the gauge group is changed (to any of the classical compact groups) and, uses only the elementary operations of linear algebra to yield potentials as rational functions of the spatial coordinates. (Auth.)
An excursion through elementary mathematics, volume ii euclidean geometry
Caminha Muniz Neto, Antonio
2018-01-01
This book provides a comprehensive, in-depth overview of elementary mathematics as explored in Mathematical Olympiads around the world. It expands on topics usually encountered in high school and could even be used as preparation for a first-semester undergraduate course. This second volume covers Plane Geometry, Trigonometry, Space Geometry, Vectors in the Plane, Solids and much more. As part of a collection, the book differs from other publications in this field by not being a mere selection of questions or a set of tips and tricks that applies to specific problems. It starts from the most basic theoretical principles, without being either too general or too axiomatic. Examples and problems are discussed only if they are helpful as applications of the theory. Propositions are proved in detail and subsequently applied to Olympic problems or to other problems at the Olympic level. The book also explores some of the hardest problems presented at National and International Mathematics Olympiads, as well as many...
Membrane paradigm and entropy of black holes in the Euclidean action approach
International Nuclear Information System (INIS)
Lemos, Jose P. S.; Zaslavskii, Oleg B.
2011-01-01
The membrane paradigm approach to black holes fixes in the vicinity of the event horizon a fictitious surface, the stretched horizon, so that the spacetime outside remains unchanged and the spacetime inside is vacuum. Using this powerful method, several black hole properties have been found and settled, such as the horizon's viscosity, electrical conductivity, resistivity, as well as other properties. On the other hand, the Euclidean action approach to black hole spacetimes has been very fruitful in understanding black hole entropy. Combining both the Euclidean action and membrane paradigm approaches, a direct derivation of the black hole entropy is given. In the derivation, it is considered that the only fields present are the gravitational and matter fields, with no electric field.
A Low-Complexity Euclidean Orthogonal LDPC Architecture for Low Power Applications
Directory of Open Access Journals (Sweden)
M. Revathy
2015-01-01
Full Text Available Low-density parity-check (LDPC codes have been implemented in latest digital video broadcasting, broadband wireless access (WiMax, and fourth generation of wireless standards. In this paper, we have proposed a high efficient low-density parity-check code (LDPC decoder architecture for low power applications. This study also considers the design and analysis of check node and variable node units and Euclidean orthogonal generator in LDPC decoder architecture. The Euclidean orthogonal generator is used to reduce the error rate of the proposed LDPC architecture, which can be incorporated between check and variable node architecture. This proposed decoder design is synthesized on Xilinx 9.2i platform and simulated using Modelsim, which is targeted to 45 nm devices. Synthesis report proves that the proposed architecture greatly reduces the power consumption and hardware utilizations on comparing with different conventional architectures.
A Low-Complexity Euclidean Orthogonal LDPC Architecture for Low Power Applications.
Revathy, M; Saravanan, R
2015-01-01
Low-density parity-check (LDPC) codes have been implemented in latest digital video broadcasting, broadband wireless access (WiMax), and fourth generation of wireless standards. In this paper, we have proposed a high efficient low-density parity-check code (LDPC) decoder architecture for low power applications. This study also considers the design and analysis of check node and variable node units and Euclidean orthogonal generator in LDPC decoder architecture. The Euclidean orthogonal generator is used to reduce the error rate of the proposed LDPC architecture, which can be incorporated between check and variable node architecture. This proposed decoder design is synthesized on Xilinx 9.2i platform and simulated using Modelsim, which is targeted to 45 nm devices. Synthesis report proves that the proposed architecture greatly reduces the power consumption and hardware utilizations on comparing with different conventional architectures.
Structure functions at small xBj in a Euclidean field theory approach
International Nuclear Information System (INIS)
Hebecker, A.; Meggiolaro, E.; Nachtmann, O.
2000-01-01
The small-x Bj limit of deep inelastic scattering is related to the high-energy limit of the forward Compton amplitude in a familiar way. We show that the analytic continuation of this amplitude in the energy variable is calculable from a matrix element in Euclidean field theory. This matrix element can be written as a Euclidean functional integral in an effective field theory. Its effective Lagrangian has a simple expression in terms of the original Lagrangian. The functional integral expression obtained can, at least in principle, be evaluated using genuinely non-perturbative methods, e.g., on the lattice. Thus, a fundamentally new approach to the long-standing problem of structure functions at very small x Bj seems possible. We give arguments that the limit x Bj →0 corresponds to a critical point of the effective field theory where the correlation length becomes infinite in one direction
International Nuclear Information System (INIS)
Dasgupta, I.
1998-01-01
We discuss new bounce-like (but non-time-reversal-invariant) solutions to Euclidean equations of motion, which we dub boomerons. In the Euclidean path integral approach to quantum theories, boomerons make an imaginary contribution to the vacuum energy. The fake vacuum instability can be removed by cancelling boomeron contributions against contributions from time reversed boomerons (anti-boomerons). The cancellation rests on a sign choice whose significance is not completely understood in the path integral method. (orig.)
Finite Topological Spaces as a Pedagogical Tool
Helmstutler, Randall D.; Higginbottom, Ryan S.
2012-01-01
We propose the use of finite topological spaces as examples in a point-set topology class especially suited to help students transition into abstract mathematics. We describe how carefully chosen examples involving finite spaces may be used to reinforce concepts, highlight pathologies, and develop students' non-Euclidean intuition. We end with a…
Triebel, Hans
1983-01-01
The book deals with the two scales Bsp,q and Fsp,q of spaces of distributions, where -8spaces, such as Hölder spaces, Zygmund classes, Sobolev spaces, Besov spaces, Bessel-potential spaces, Hardy spaces and spaces of BMO-type. It is the main aim of this book to give a unified treatment of the corresponding spaces on the Euclidean n-space Rn in the framework of Fourier analysis, which is based on the technique of maximal functions, Fourier multipliers and interpolation assertions. These topics are treated in Chapter 2, which is the heart
Absence of even-integer ζ-function values in Euclidean physical quantities in QCD
Jamin, Matthias; Miravitllas, Ramon
2018-04-01
At order αs4 in perturbative quantum chromodynamics, even-integer ζ-function values are present in Euclidean physical correlation functions like the scalar quark correlation function or the scalar gluonium correlator. We demonstrate that these contributions cancel when the perturbative expansion is expressed in terms of the so-called C-scheme coupling αˆs which has recently been introduced in Ref. [1]. It is furthermore conjectured that a ζ4 term should arise in the Adler function at order αs5 in the MS ‾-scheme, and that this term is expected to disappear in the C-scheme as well.
DEFF Research Database (Denmark)
Meng, Weizhi; Li, Wenjuan; Wang, Yu
2017-01-01
and healthcare personnel. The underlying network architecture to support such devices is also referred to as medical smartphone networks (MSNs). Similar to other networks, MSNs also suffer from various attacks like insider attacks (e.g., leakage of sensitive patient information by a malicious insider......). In this work, we focus on MSNs and design a trust-based intrusion detection approach through Euclidean distance-based behavioral profiling to detect malicious devices (or called nodes). In the evaluation, we collaborate with healthcare organizations and implement our approach in a real simulated MSN...
Exact Boson-Fermion Duality on a 3D Euclidean Lattice
Chen, Jing-Yuan; Son, Jun Ho; Wang, Chao; Raghu, S.
2018-01-01
The idea of statistical transmutation plays a crucial role in descriptions of the fractional quantum Hall effect. However, a recently conjectured duality between a critical boson and a massless two-component Dirac fermion extends this notion to gapless systems. This duality sheds light on highly nontrivial problems such as the half-filled Landau level, the superconductor-insulator transition, and surface states of strongly coupled topological insulators. Although this boson-fermion duality has undergone many consistency checks, it has remained unproven. We describe the duality in a nonperturbative fashion using an exact UV mapping of partition functions on a 3D Euclidean lattice.
Two-stage sparse coding of region covariance via Log-Euclidean kernels to detect saliency.
Zhang, Ying-Ying; Yang, Cai; Zhang, Ping
2017-05-01
In this paper, we present a novel bottom-up saliency detection algorithm from the perspective of covariance matrices on a Riemannian manifold. Each superpixel is described by a region covariance matrix on Riemannian Manifolds. We carry out a two-stage sparse coding scheme via Log-Euclidean kernels to extract salient objects efficiently. In the first stage, given background dictionary on image borders, sparse coding of each region covariance via Log-Euclidean kernels is performed. The reconstruction error on the background dictionary is regarded as the initial saliency of each superpixel. In the second stage, an improvement of the initial result is achieved by calculating reconstruction errors of the superpixels on foreground dictionary, which is extracted from the first stage saliency map. The sparse coding in the second stage is similar to the first stage, but is able to effectively highlight the salient objects uniformly from the background. Finally, three post-processing methods-highlight-inhibition function, context-based saliency weighting, and the graph cut-are adopted to further refine the saliency map. Experiments on four public benchmark datasets show that the proposed algorithm outperforms the state-of-the-art methods in terms of precision, recall and mean absolute error, and demonstrate the robustness and efficiency of the proposed method. Copyright © 2017 Elsevier Ltd. All rights reserved.
International Nuclear Information System (INIS)
Gray, J.
1979-01-01
An historical and chronological account of mathematics Familiarity with simple equations and elements of trigonometry is needed but no specialist knowledge is assumed although difficult problems are discussed. By discussion of the difficulties and confusions it is hoped to understand mathematics as a dynamic activity. Beginning with early Greek mathematics, the Eastern legacy and the transition to deductive and geometric thinking the problem of parallels is then encountered and discussed. The second part of the book takes the story from Wallis, Saccheri and Lambert through to its resolution by Gauss, Lobachevskii, Bolyai, Riemann and Bettrami. The background of the 19th century theory of surfaces is given. The third part gives an account of Einstein's theories based on what has gone before, moving from a Newtonian-Euclidean picture to an Einsteinian-nonEuclidean one. A brief account of gravitation, the nature of space and black holes concludes the book. (UK)
Directory of Open Access Journals (Sweden)
Lambert Marie-Ève
2012-06-01
Full Text Available Abstract Background Porcine reproductive and respiratory syndrome (PRRS is a viral disease that has a major economic impact for the swine industry. Its control is mostly directed towards preventing its spread which requires a better understanding of the mechanisms of transmission of the virus between herds. The objectives of this study were to describe the genetic diversity and to assess the correlation among genetic, Euclidean and temporal distances and ownership to better understand pathways of transmission. Results A cross-sectional study was conducted on sites located in a high density area of swine production in Quebec. Geographical coordinates (longitude/latitude, date of submission and ownership were obtained for each site. ORF5 sequencing was attempted on PRRSV positive sites. Proportion of pairwise combinations of strains having ≥98% genetic homology were analysed according to Euclidean distances and ownership. Correlations between genetic, Euclidean and temporal distances and ownership were assessed using Mantel tests on continuous and binary matrices. Sensitivity of the correlations between genetic and Euclidean as well as temporal distances was evaluated for different Euclidean and temporal distance thresholds. An ORF5 sequence was identified for 132 of the 176 (75% PRRSV positive sites; 122 were wild-type strains. The mean (min-max genetic, Euclidean and temporal pairwise distances were 11.6% (0–18.7, 15.0 km (0.04-45.7 and 218 days (0–852, respectively. Significant positive correlations were observed between genetic and ownership, genetic and Euclidean and between genetic and temporal binary distances. The relationship between genetic and ownership suggests either common sources of animals or semen, employees, technical services or vehicles, whereas that between genetic and Euclidean binary distances is compatible with area spread of the virus. The latter correlation was observed only up to 5 km. Conclusions This study
Clear evidence of a continuum theory of 4D Euclidean simplicial quantum gravity
International Nuclear Information System (INIS)
Egawa, H.S.; Horata, S.; Yukawa, T.
2002-01-01
Four-dimensional (4D) simplicial quantum gravity coupled to both scalar fields (N X ) and gauge fields (N A ) has been studied using Monte-Carlo simulations. The matter dependence of the string susceptibility exponent γ (4) is estimated. Furthermore, we compare our numerical results with Background-Metric-Independent (BMI) formulation conjectured to describe the quantum field theory of gravity in 4D. The numerical results suggest that the 4D simplicial quantum gravity is related to the conformal gravity in 4D. Therefore, we propose a phase structure in detail with adding both scalar and gauge fields and discuss the possibility and the property of a continuum theory of 4D Euclidean simplicial quantum gravity
Bayesian Approach to Spectral Function Reconstruction for Euclidean Quantum Field Theories
Burnier, Yannis; Rothkopf, Alexander
2013-11-01
We present a novel approach to the inference of spectral functions from Euclidean time correlator data that makes close contact with modern Bayesian concepts. Our method differs significantly from the maximum entropy method (MEM). A new set of axioms is postulated for the prior probability, leading to an improved expression, which is devoid of the asymptotically flat directions present in the Shanon-Jaynes entropy. Hyperparameters are integrated out explicitly, liberating us from the Gaussian approximations underlying the evidence approach of the maximum entropy method. We present a realistic test of our method in the context of the nonperturbative extraction of the heavy quark potential. Based on hard-thermal-loop correlator mock data, we establish firm requirements in the number of data points and their accuracy for a successful extraction of the potential from lattice QCD. Finally we reinvestigate quenched lattice QCD correlators from a previous study and provide an improved potential estimation at T=2.33TC.
Hadronic vacuum polarization in QCD and its evaluation in Euclidean spacetime
de Rafael, Eduardo
2017-07-01
We discuss a new technique to evaluate integrals of QCD Green's functions in the Euclidean based on their Mellin-Barnes representation. We present as a first application the evaluation of the lowest order hadronic vacuum polarization (HVP) contribution to the anomalous magnetic moment of the muon 1/2 (gμ-2 )HVP≡aμHVP . It is shown that with a precise determination of the slope and curvature of the HVP function at the origin from lattice QCD (LQCD), one can already obtain a result for aμHVP which may serve as a test of the determinations based on experimental measurements of the e+e- annihilation cross section into hadrons.
Euler numbers of four-dimensional rotating black holes with the Euclidean signature
International Nuclear Information System (INIS)
Ma Zhengze
2003-01-01
For a black hole's spacetime manifold in the Euclidean signature, its metric is positive definite and therefore a Riemannian manifold. It can be regarded as a gravitational instanton and a topological characteristic which is the Euler number to which it is associated. In this paper we derive a formula for the Euler numbers of four-dimensional rotating black holes by the integral of the Euler density on the spacetime manifolds of black holes. Using this formula, we obtain that the Euler numbers of Kerr and Kerr-Newman black holes are 2. We also obtain that the Euler number of the Kerr-Sen metric in the heterotic string theory with one boost angle nonzero is 2, which is in accordance with its topology
Solution for a bipartite Euclidean traveling-salesman problem in one dimension
Caracciolo, Sergio; Di Gioacchino, Andrea; Gherardi, Marco; Malatesta, Enrico M.
2018-05-01
The traveling-salesman problem is one of the most studied combinatorial optimization problems, because of the simplicity in its statement and the difficulty in its solution. We characterize the optimal cycle for every convex and increasing cost function when the points are thrown independently and with an identical probability distribution in a compact interval. We compute the average optimal cost for every number of points when the distance function is the square of the Euclidean distance. We also show that the average optimal cost is not a self-averaging quantity by explicitly computing the variance of its distribution in the thermodynamic limit. Moreover, we prove that the cost of the optimal cycle is not smaller than twice the cost of the optimal assignment of the same set of points. Interestingly, this bound is saturated in the thermodynamic limit.
Unstable spiral waves and local Euclidean symmetry in a model of cardiac tissue
International Nuclear Information System (INIS)
Marcotte, Christopher D.; Grigoriev, Roman O.
2015-01-01
This paper investigates the properties of unstable single-spiral wave solutions arising in the Karma model of two-dimensional cardiac tissue. In particular, we discuss how such solutions can be computed numerically on domains of arbitrary shape and study how their stability, rotational frequency, and spatial drift depend on the size of the domain as well as the position of the spiral core with respect to the boundaries. We also discuss how the breaking of local Euclidean symmetry due to finite size effects as well as the spatial discretization of the model is reflected in the structure and dynamics of spiral waves. This analysis allows identification of a self-sustaining process responsible for maintaining the state of spiral chaos featuring multiple interacting spirals
Unstable spiral waves and local Euclidean symmetry in a model of cardiac tissue.
Marcotte, Christopher D; Grigoriev, Roman O
2015-06-01
This paper investigates the properties of unstable single-spiral wave solutions arising in the Karma model of two-dimensional cardiac tissue. In particular, we discuss how such solutions can be computed numerically on domains of arbitrary shape and study how their stability, rotational frequency, and spatial drift depend on the size of the domain as well as the position of the spiral core with respect to the boundaries. We also discuss how the breaking of local Euclidean symmetry due to finite size effects as well as the spatial discretization of the model is reflected in the structure and dynamics of spiral waves. This analysis allows identification of a self-sustaining process responsible for maintaining the state of spiral chaos featuring multiple interacting spirals.
Finite Metric Spaces of Strictly Negative Type
DEFF Research Database (Denmark)
Hjorth, Poul; Lisonek, P.; Markvorsen, Steen
1998-01-01
of Euclidean spaces. We prove that, if the distance matrix is both hypermetric and regular, then it is of strictly negative type. We show that the strictly negative type finite subspaces of spheres are precisely those which do not contain two pairs of antipodal points. In connection with an open problem raised...
Directory of Open Access Journals (Sweden)
Septa Cahyani
2018-04-01
Full Text Available The human ability to recognize a variety of objects, however complex the object, is the special ability that humans possess. Any normal human will have no difficulty in recognizing handwriting objects between an author and another author. With the rapid development of digital technology, the human ability to recognize handwriting objects has been applied in a program known as Computer Vision. This study aims to create identification system different types of handwriting capital letters that have different sizes, thickness, shape, and tilt (distinctive features in handwriting using Linear Discriminant Analysis (LDA and Euclidean Distance methods. LDA is used to obtain characteristic characteristics of the image and provide the distance between the classes becomes larger, while the distance between training data in one class becomes smaller, so that the introduction time of digital image of handwritten capital letter using Euclidean Distance becomes faster computation time (by searching closest distance between training data and data testing. The results of testing the sample data showed that the image resolution of 50x50 pixels is the exact image resolution used for data as much as 1560 handwritten capital letter data compared to image resolution 25x25 pixels and 40x40 pixels. While the test data and training data testing using the method of 10-fold cross validation where 1404 for training data and 156 for data testing showed identification of digital image handwriting capital letter has an average effectiveness of the accuracy rate of 75.39% with the average time computing of 0.4199 seconds.
Ait-Haddou, Rachid
2015-01-01
We show that the best degree reduction of a given polynomial P from degree n to m with respect to the discrete (Formula presented.)-norm is equivalent to the best Euclidean distance of the vector of h-Bézier coefficients of P from the vector
Directory of Open Access Journals (Sweden)
Robert M. Yamaleev
2013-01-01
Full Text Available The hyperbolic cosines and sines theorems for the curvilinear triangle bounded by circular arcs of three intersecting circles are formulated and proved by using the general complex calculus. The method is based on a key formula establishing a relationship between exponential function and the cross-ratio. The proofs are carried out on Euclidean plane.
International Nuclear Information System (INIS)
Haba, Z.
1981-01-01
In the usual models of Euclidean field theory the Schwinger functions are moments of a positive measure. In this paper the author discusses the basic properties of the measure μ, i.e. properties of the sample paths of the random field. (Auth.)
q-deformed phase-space and its lattice structure
International Nuclear Information System (INIS)
Wess, J.
1998-01-01
Quantum groups lead to an algebraic structure that can be realized on quantum spaces. These are non-commutative spaces that inherit a well-defined mathematical structure from the quantum group symmetry. In turn, such quantum spaces can be interpreted as non-commutative configuration spaces for physical systems. We study the non-commutative Euclidean space that is based on the quantum group SO q (3)
On spaces of functions of smoothness zero
International Nuclear Information System (INIS)
Besov, Oleg V
2012-01-01
The paper is concerned with the new spaces B-bar p,q 0 of functions of smoothness zero defined on the n-dimensional Euclidean space R n or on a subdomain G of R n . These spaces are compared with the spaces B p,q 0 (R n ) and bmo(R n ). The embedding theorems for Sobolev spaces are refined in terms of the space B-bar p,q 0 with the limiting exponent. Bibliography: 8 titles.
Anthropology in the post-Euclidean State, or from textual to oral anthropology
Directory of Open Access Journals (Sweden)
Antonio Luigi Palmisano
2011-12-01
Full Text Available The actual crisis of anthropology is examined in relation to its wide public success. Anthropology has prospered and the anthropologists have proliferated becoming more specific. But the theoretical debate has come to a halt over the last decades. The article suggests that both the methodology and the form of expression of the ethnographic report have developed and then become crystallized around actual protocols. A critique of the dichotomy Subject/Object, namely the key discussion about the notion of Otherness, is here reexamined as the testimony for an immanent “non-protocolar” character of anthropology. This critique together with the end of anthropology as tekhne, i.e. as protocolar activity, will allow anthropology to go on enhancing many other social and non social sciences. The article discusses the re-definition of anthropology in the context of Daseinanalysis and, therefore the changing relation between man and power, that is between the social actor and the post-Euclidean State in the era of the tekhne.
Chaos of discrete dynamical systems in complete metric spaces
International Nuclear Information System (INIS)
Shi Yuming; Chen Guanrong
2004-01-01
This paper is concerned with chaos of discrete dynamical systems in complete metric spaces. Discrete dynamical systems governed by continuous maps in general complete metric spaces are first discussed, and two criteria of chaos are then established. As a special case, two corresponding criteria of chaos for discrete dynamical systems in compact subsets of metric spaces are obtained. These results have extended and improved the existing relevant results of chaos in finite-dimensional Euclidean spaces
Durato, M. V.; Albano, A. M.; Rapp, P. E.; Nawang, S. A.
2015-06-01
The validity of ERPs as indices of stable neurophysiological traits is partially dependent on their stability over time. Previous studies on ERP stability, however, have reported diverse stability estimates despite using the same component scoring methods. This present study explores a novel approach in investigating the longitudinal stability of average ERPs—that is, by treating the ERP waveform as a time series and then applying Euclidean Distance and Kolmogorov-Smirnov analyses to evaluate the similarity or dissimilarity between the ERP time series of different sessions or run pairs. Nonlinear dynamical analysis show that in the absence of a change in medical condition, the average ERPs of healthy human adults are highly longitudinally stable—as evaluated by both the Euclidean distance and the Kolmogorov-Smirnov test.
International Nuclear Information System (INIS)
Durato, M V; Nawang, S A; Albano, A M; Rapp, P E
2015-01-01
The validity of ERPs as indices of stable neurophysiological traits is partially dependent on their stability over time. Previous studies on ERP stability, however, have reported diverse stability estimates despite using the same component scoring methods. This present study explores a novel approach in investigating the longitudinal stability of average ERPs—that is, by treating the ERP waveform as a time series and then applying Euclidean Distance and Kolmogorov-Smirnov analyses to evaluate the similarity or dissimilarity between the ERP time series of different sessions or run pairs. Nonlinear dynamical analysis show that in the absence of a change in medical condition, the average ERPs of healthy human adults are highly longitudinally stable—as evaluated by both the Euclidean distance and the Kolmogorov-Smirnov test. (paper)
The philosophy of space and time
Reichenbach, Hans
1958-01-01
With unusual depth and clarity, the author covers the problem of the foundations of geometry, the theory of time, the theory and consequences of Einstein's relativity including: relations between theory and observations, coordinate definitions, relations between topological and metrical properties of space, the psychological problem of the possibility of a visual intuition of non-Euclidean structures, and many other important topics in modern science and philosophy. While some of the book utilizes mathematics of a somewhat advanced nature, the exposition is so careful and complete that most people familiar with the philosophy of science or some intermediate mathematics will understand the majority of the ideas and problems discussed. Partial contents: I. The Problem of Physical Geometry. Universal and Differential Forces. Visualization of Geometries. Spaces with non-Euclidean Topological Properties. Geometry as a Theory of Relations. II. The Difference between Space and Time. Simultaneity. Time Order. Unreal ...
A 4D spacetime embedded in a 5D pseudo-Euclidean space describing interior of compact stars
Energy Technology Data Exchange (ETDEWEB)
Singh, K.N. [National Defence Academy, Department of Physics, Khadakwasla (India); Murad, Mohammad Hassan [BRAC University, Department of Mathematics and Natural Sciences, Dhaka (Bangladesh); Pant, Neeraj [National Defence Academy, Department of Mathematics, Khadakwasla (India)
2017-02-15
The present paper provides a new model of compact stars satisfying the Karmarkar condition. The model is obtained by assuming a new type of metric potential for g{sub rr} from the condition of embedding class I. The model parameters are obtained accordingly by employing the metric potentials to Einstein's field equations. Our model is free from geometric singularity and satisfies all the physical conditions. The obtained mass and radius of the compact stars Cen X-3, EXO 1785-248 and SAX 1808.4-3658 obtained from the model are consistent with the observational data of T. Gangopadhyay et al. Detailed analyses of these neutron stars (Cen X-3, EXO 1785-248 and SAX 1808.4-3658) are also given with the help of graphical representations. (orig.)
Metrics of a 'mole hole' against the Lobachevsky space background
International Nuclear Information System (INIS)
Tentyukov, M.N.
1994-01-01
'Classical' mole hole are the Euclidean metrics consisting of two large space regions connected by a throat. They are the instanton solutions of the Einstein equations. It is shown that for existence of mole holes in the general relativity theory it is required the energy-momentum tensor breaking energetic conditions. 9 refs., 7 figs
From free fields to AdS space: Thermal case
International Nuclear Information System (INIS)
Furuuchi, Kazuyuki
2005-01-01
We analyze the reorganization of free field theory correlators to closed string amplitudes investigated in previous papers in the case of Euclidean thermal field theory and study how the dual bulk geometry is encoded on them. The expectation value of Polyakov loop, which is an order parameter for confinement-deconfinement transition, is directly reflected on the dual bulk geometry. The dual geometry of the confined phase is found to be AdS space periodically identified in Euclidean time direction. The gluing of Schwinger parameters, which is a key step for the reorganization of field theory correlators, works in the same way as in the nonthermal case. In the deconfined phase the gluing is made possible only by taking the dual geometry correctly. The dual geometry for the deconfined phase does not have a noncontractable circle in the Euclidean time direction
Euclidean Dynamical Triangulation revisited: is the phase transition really 1st order?
International Nuclear Information System (INIS)
Rindlisbacher, Tobias; Forcrand, Philippe de
2015-01-01
The transition between the two phases of 4D Euclidean Dynamical Triangulation (http://dx.doi.org/10.1016/0370-2693(92)90709-D) was long believed to be of second order until in 1996 first order behavior was found for sufficiently large systems (http://dx.doi.org/10.1016/0550-3213(96)00214-3, http://dx.doi.org/10.1016/S0370-2693(96)01277-4). However, one may wonder if this finding was affected by the numerical methods used: to control volume fluctuations, in both studies (http://dx.doi.org/10.1016/0550-3213(96)00214-3, http://dx.doi.org/10.1016/S0370-2693(96)01277-4) an artificial harmonic potential was added to the action and in (http://dx.doi.org/10.1016/S0370-2693(96)01277-4) measurements were taken after a fixed number of accepted instead of attempted moves which introduces an additional error. Finally the simulations suffer from strong critical slowing down which may have been underestimated. In the present work, we address the above weaknesses: we allow the volume to fluctuate freely within a fixed interval; we take measurements after a fixed number of attempted moves; and we overcome critical slowing down by using an optimized parallel tempering algorithm (http://dx.doi.org/10.1088/1742-5468/2010/01/P01020). With these improved methods, on systems of size up to N_4=64k 4-simplices, we confirm that the phase transition is 1"s"t order. In addition, we discuss a local criterion to decide whether parts of a triangulation are in the elongated or crumpled state and describe a new correspondence between EDT and the balls in boxes model. The latter gives rise to a modified partition function with an additional, third coupling. Finally, we propose and motivate a class of modified path-integral measures that might remove the metastability of the Markov chain and turn the phase transition into 2"n"d order.
Zhang, Dongwen; Zhu, Qingsong; Xiong, Jing; Wang, Lei
2014-04-27
In a deforming anatomic environment, the motion of an instrument suffers from complex geometrical and dynamic constraints, robot assisted minimally invasive surgery therefore requires more sophisticated skills for surgeons. This paper proposes a novel dynamic virtual fixture (DVF) to enhance the surgical operation accuracy of admittance-type medical robotics in the deforming environment. A framework for DVF on the Euclidean Group SE(3) is presented, which unites rotation and translation in a compact form. First, we constructed the holonomic/non-holonomic constraints, and then searched for the corresponded reference to make a distinction between preferred and non-preferred directions. Second, different control strategies are employed to deal with the tasks along the distinguished directions. The desired spatial compliance matrix is synthesized from an allowable motion screw set to filter out the task unrelated components from manual input, the operator has complete control over the preferred directions; while the relative motion between the surgical instrument and the anatomy structures is actively tracked and cancelled, the deviation relative to the reference is compensated jointly by the operator and DVF controllers. The operator, haptic device, admittance-type proxy and virtual deforming environment are involved in a hardware-in-the-loop experiment, human-robot cooperation with the assistance of DVF controller is carried out on a deforming sphere to simulate beating heart surgery, performance of the proposed DVF on admittance-type proxy is evaluated, and both human factors and control parameters are analyzed. The DVF can improve the dynamic properties of human-robot cooperation in a low-frequency (0 ~ 40 rad/sec) deforming environment, and maintain synergy of orientation and translation during the operation. Statistical analysis reveals that the operator has intuitive control over the preferred directions, human and the DVF controller jointly control the
Gravity mediated Dark Matter models in the de Sitter space
Vancea, Ion V.
2018-01-01
In this paper, we generalize the simplified Dark Matter models with graviton mediator to the curved space-time, in particular to the de Sitter space. We obtain the generating functional of the Green's functions in the Euclidean de Sitter space for the covariant free gravitons. We determine the generating functional of the interacting theory between Dark Matter particles and the covariant gravitons. Also, we calculate explicitly the 2-point and 3-point interacting Green's functions for the sym...
The Perspective Structure of Visual Space
2015-01-01
Luneburg’s model has been the reference for experimental studies of visual space for almost seventy years. His claim for a curved visual space has been a source of inspiration for visual scientists as well as philosophers. The conclusion of many experimental studies has been that Luneburg’s model does not describe visual space in various tasks and conditions. Remarkably, no alternative model has been suggested. The current study explores perspective transformations of Euclidean space as a model for visual space. Computations show that the geometry of perspective spaces is considerably different from that of Euclidean space. Collinearity but not parallelism is preserved in perspective space and angles are not invariant under translation and rotation. Similar relationships have shown to be properties of visual space. Alley experiments performed early in the nineteenth century have been instrumental in hypothesizing curved visual spaces. Alleys were computed in perspective space and compared with reconstructed alleys of Blumenfeld. Parallel alleys were accurately described by perspective geometry. Accurate distance alleys were derived from parallel alleys by adjusting the interstimulus distances according to the size-distance invariance hypothesis. Agreement between computed and experimental alleys and accommodation of experimental results that rejected Luneburg’s model show that perspective space is an appropriate model for how we perceive orientations and angles. The model is also appropriate for perceived distance ratios between stimuli but fails to predict perceived distances. PMID:27648222
Gómez, Daviel; Hernández, L Ázaro; Yabor, Lourdes; Beemster, Gerrit T S; Tebbe, Christoph C; Papenbrock, Jutta; Lorenzo, José Carlos
2018-03-15
Plant scientists usually record several indicators in their abiotic factor experiments. The common statistical management involves univariate analyses. Such analyses generally create a split picture of the effects of experimental treatments since each indicator is addressed independently. The Euclidean distance combined with the information of the control treatment could have potential as an integrating indicator. The Euclidean distance has demonstrated its usefulness in many scientific fields but, as far as we know, it has not yet been employed for plant experimental analyses. To exemplify the use of the Euclidean distance in this field, we performed an experiment focused on the effects of mannitol on sugarcane micropropagation in temporary immersion bioreactors. Five mannitol concentrations were compared: 0, 50, 100, 150 and 200 mM. As dependent variables we recorded shoot multiplication rate, fresh weight, and levels of aldehydes, chlorophylls, carotenoids and phenolics. The statistical protocol which we then carried out integrated all dependent variables to easily identify the mannitol concentration that produced the most remarkable integral effect. Results provided by the Euclidean distance demonstrate a gradually increasing distance from the control in function of increasing mannitol concentrations. 200 mM mannitol caused the most significant alteration of sugarcane biochemistry and physiology under the experimental conditions described here. This treatment showed the longest statistically significant Euclidean distance to the control treatment (2.38). In contrast, 50 and 100 mM mannitol showed the lowest Euclidean distances (0.61 and 0.84, respectively) and thus poor integrated effects of mannitol. The analysis shown here indicates that the use of the Euclidean distance can contribute to establishing a more integrated evaluation of the contrasting mannitol treatments.
Ait-Haddou, Rachid
2015-06-04
We show that the best degree reduction of a given polynomial P from degree n to m with respect to the discrete (Formula presented.)-norm is equivalent to the best Euclidean distance of the vector of h-Bézier coefficients of P from the vector of degree raised h-Bézier coefficients of polynomials of degree m. Moreover, we demonstrate the adequacy of h-Bézier curves for approaching the problem of weighted discrete least squares approximation. Applications to discrete orthogonal polynomials are also presented. © 2015 Springer Science+Business Media Dordrecht
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)
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.
Teichmuller Space Resolution of the EPR Paradox
Winterberg, Friedwardt
2013-04-01
The mystery of Newton's action-at-a-distance law of gravity was resolved by Einstein with Riemann's non-Euclidean geometry, which permitted the explanation of the departure from Newton's law for the motion of Mercury. It is here proposed that the similarly mysterious non-local EPR-type quantum correlations may be explained by a Teichmuller space geometry below the Planck length, for which an experiment for its verification is proposed.
Zhang, Ying-Ying; Yang, Cai; Zhang, Ping
2017-08-01
In this paper, we present a novel bottom-up saliency detection algorithm from the perspective of covariance matrices on a Riemannian manifold. Each superpixel is described by a region covariance matrix on Riemannian Manifolds. We carry out a two-stage sparse coding scheme via Log-Euclidean kernels to extract salient objects efficiently. In the first stage, given background dictionary on image borders, sparse coding of each region covariance via Log-Euclidean kernels is performed. The reconstruction error on the background dictionary is regarded as the initial saliency of each superpixel. In the second stage, an improvement of the initial result is achieved by calculating reconstruction errors of the superpixels on foreground dictionary, which is extracted from the first stage saliency map. The sparse coding in the second stage is similar to the first stage, but is able to effectively highlight the salient objects uniformly from the background. Finally, three post-processing methods-highlight-inhibition function, context-based saliency weighting, and the graph cut-are adopted to further refine the saliency map. Experiments on four public benchmark datasets show that the proposed algorithm outperforms the state-of-the-art methods in terms of precision, recall and mean absolute error, and demonstrate the robustness and efficiency of the proposed method. Copyright © 2017 Elsevier Ltd. All rights reserved.
Chiral symmetry breaking and confinement in Minkowski space QED2+1
International Nuclear Information System (INIS)
Sauli, V.; Batiz, Z.
2010-01-01
Without any analytical assumption we solve the ladder QED2+1 in Minkowski space. Obtained complex fermion propagator exhibits confinement in the sense that it has no pole. Further, we transform Greens functions to the Temporal Euclidean space, wherein we show that in the special case of ladder QED2+1 the solution is fully equivalent to the Minkowski one. Obvious invalidity of Wick rotation is briefly discussed. The infrared value of the dynamical mass is compared with other known approaches, e. g. with the standard Euclidean calculation. We have presented for the first analysis of the electron gap equation in Minkowski and Temporal Euclidean space. The dynamical generation of imaginary part of the fermion mass leads to the absence of Khallen-Lehmann representation, providing thus confining solution for all value of m. Apart very small κ the real pole in the propagator is absent as well. Similarly to Euclidean QED3 Minkowski QED2+1 exhibits spontaneous chiral symmetry breaking the mass function has nontrivial solution in the limit m = 0, however the mass is complex function. Furthermore, we compare with QED solved in similar approximation in spacelike Euclidean and Temporal Euclidean space. As a interesting results, although based on the simple ladder approximation, is the proof of the exact equivalence between the theories defined in Minkowski 2+1 and 3D Temporal Euclidean space. We expect large quantitative changes when the polarization effect is taken account, especially the existence of critical number of flavors can be different when compared to the known Euclidean space estimates. Opposite to naive belief we showed and explained that the Wick rotation -the well known calculational trick in quantum theory- provides continuation of Schwinger function of the Euclidean theory which do not correspond with the Greens function calculated directly in the original Minkowski space. We can note our finding has a little to do with the know usefulness of various
Uniform color space is not homogeneous
Kuehni, Rolf G.
2002-06-01
Historical data of chroma scaling and hue scaling are compared and evidence is shown that we do not have a reliable basis in either case. Several data sets indicate explicitly or implicitly that the number of constant sized hue differences between unique hues as well as in the quadrants of the a*, b* diagram differs making what is commonly regarded as uniform color space inhomogeneous. This problem is also shown to affect the OSA-UCS space. A Euclidean uniform psychological or psychophysical color space appears to be impossible.
Green functions in Bianci-type spaces
International Nuclear Information System (INIS)
Bukhbinder, I.L.; Kirillova, E.N.
1988-01-01
The theory of free scalar field with conformal connection in distorted space - time with Bianci 1 type metrics is considered. The presentation of the Green functions G-tilde approximately in in in the form of integral from the Schwinger - De Witt kernel over the contour in the plane of complex values of eigentime is obtained. The way, in which the transfer from the Green function in space with Euclidean signature to the Green functions in space with Minkowski signature and vice versa is realized, has been shown
International Nuclear Information System (INIS)
Villasenor, R.F.; Bonilla, J.L.L.; Zuniga, G.O.; Matos, T.
1989-01-01
The authors study space-times embedded in E 5 (that means, pseudo-euclidean five-dimensional spaces) in the intrinsic rigidity case, i.e., when the second fundamental form b if can be determined by the internal geometry of the four-dimensional Riemannian space R 4 . They write down the Gauss and Codazzi equations determining the local isometric embedding of R 4 in E 5 and give some consequences of it. They prove that when there exists intrinsic rigidity, then b if is a linear combination of the metric and Ricci tensor; it is given some applications for the de Sitter and Einstein models
Are the field and space variables on an equal footing
International Nuclear Information System (INIS)
Schwarz, A.S.
1980-01-01
The problem of formulation of the quantum field theory is investigated in the case when the field and space variables are not distinguished a priori. For this aim some mathematical results concerning additive functionals defined on n dimensional surfaces in the r dimensional Euclidean space are obtained. The considered problem is solved in a positive way. Applications to the supergravity are given. The action functional of the supergravity is constructed
DEFF Research Database (Denmark)
Brander, David; Rossman, Wayne; Schmitt, Nicholas
2010-01-01
We give an infinite dimensional generalized Weierstrass representation for spacelike constant mean curvature (CMC) surfaces in Minkowski 3-space $\\R^{2,1}$. The formulation is analogous to that given by Dorfmeister, Pedit and Wu for CMC surfaces in Euclidean space, replacing the group $SU_2$ with...
International Nuclear Information System (INIS)
Carinena, Jose F; Ranada, Manuel F; Santander, Mariano
2007-01-01
The equation of the orbits (in the configuration space) and of the hodographs (in the 'momentum' plane) for the 'curved' Kepler and harmonic oscillator systems, living in a configuration space of any constant curvature and either signature type, are derived by purely algebraic means. This result extends to the 'curved' Kepler or harmonic oscillator for the classical Hamilton derivation of the orbits of the Euclidean Kepler problem through its hodographs. In both cases, the fundamental property allowing these derivations to work is the superintegrability of the 'curved' Kepler and harmonic oscillator, no matter whether the constant curvature of the configuration space is zero or not, or whether the configuration space metric is Riemannian or Lorentzian. In the 'curved' case the basic result does not refer to the 'velocity hodograph' but to the 'momentum hodograph'; both coincide in a Euclidean configuration space, but only the latter is unambiguously defined in all curved spaces
A measure of variable planar locations anchored on the centroid of the vowel space
DEFF Research Database (Denmark)
Watt, Dominic; Fabricius, Anne
2011-01-01
as an anchor point or vertex for calculation of planar locations on formant plots, permitting quantification of the distribution of vowel tokens within the space. This information, along with details such as Euclidean distances, can then be used to precisely pinpoint the trajectories of diachronic change...
Static, self-dual, finite action SU(3) gauge fields in the de Sitter space
International Nuclear Information System (INIS)
Chakrabarti, A.; Comtet, A.; Viswanathan, K.S.; Simon Fraser Univ., Burnaby, British Columbia
1980-01-01
Static, self-dual, finite action SU(3) gauge fields are constructed on the euclidean section of the positive curvature de Sitter metric with periodic time. Their relation to known time dependent flat space solutions is pointed out. Their significances and possible applications are indicated. (orig.)
Schwinger functions for the Yukawa model in two dimensions with space-time cutoff
International Nuclear Information System (INIS)
Seiler, E.
1975-01-01
It is shown that a Euclidean version of the formulae of Matthews and Salam for the Green's functions of a two-dimensional Yukawa model with interaction in a finite space-time volume makes sense, if renormalized correctly. (orig.) [de
Conformal maps between pseudo-Finsler spaces
Voicu, Nicoleta
The paper aims to initiate a systematic study of conformal mappings between Finsler spacetimes and, more generally, between pseudo-Finsler spaces. This is done by extending several results in pseudo-Riemannian geometry which are necessary for field-theoretical applications and by proposing a technique that reduces some problems involving pseudo-Finslerian conformal vector fields to their pseudo-Riemannian counterparts. Also, we point out, by constructing classes of examples, that conformal groups of flat (locally Minkowskian) pseudo-Finsler spaces can be much richer than both flat Finslerian and pseudo-Euclidean conformal groups.
The separating topology for the space-times of general relativity
International Nuclear Information System (INIS)
Lindstroem, U.
1977-08-01
The separating topology, first suggested by Zeeman, is defined for the space-times of general relativity. It is defined by a basis. A number of properties are derived. The topology induces the ordinary Euclidean topology on space-like hypersurfaces as well as on timelike curves and the discrete topology on null-cones. The group of auto-homeomorphisms is found to be the group of smooth conformal diffeomorphisms if the space-time is strongly causal. (author)
Non-Hermitian systems of Euclidean Lie algebraic type with real energy spectra
International Nuclear Information System (INIS)
Dey, Sanjib; Fring, Andreas; Mathanaranjan, Thilagarajah
2014-01-01
We study several classes of non-Hermitian Hamiltonian systems, which can be expressed in terms of bilinear combinations of Euclidean–Lie algebraic generators. The classes are distinguished by different versions of antilinear (PT)-symmetries exhibiting various types of qualitative behaviour. On the basis of explicitly computed non-perturbative Dyson maps we construct metric operators, isospectral Hermitian counterparts for which we solve the corresponding time-independent Schrödinger equation for specific choices of the coupling constants. In these cases general analytical expressions for the solutions are obtained in the form of Mathieu functions, which we analyze numerically to obtain the corresponding energy spectra. We identify regions in the parameter space for which the corresponding spectra are entirely real and also domains where the PT symmetry is spontaneously broken and sometimes also regained at exceptional points. In some cases it is shown explicitly how the threshold region from real to complex spectra is characterized by the breakdown of the Dyson maps or the metric operator. We establish the explicit relationship to models currently under investigation in the context of beam dynamics in optical lattices. -- Highlights: •Different PT-symmetries lead to qualitatively different systems. •Construction of non-perturbative Dyson maps and isospectral Hermitian counterparts. •Numerical discussion of the eigenvalue spectra for one of the E(2)-systems. •Established link to systems studied in the context of optical lattices. •Setup for the E(3)-algebra is provided
International Nuclear Information System (INIS)
Volovikov, A Yu
2000-01-01
With a G-space, where G is a compact Lie group, one can associate an ideal in the cohomology ring of the classifying space for G. It is called the ideal-valued index of the G-space. A filtration of the ideal-valued index that arises in a natural way from the Leray spectral sequence is considered. Properties of the index with filtration are studied and numerical indices are introduced. These indices are convenient for estimates of the G-category and the study of the set of critical points of a G-invariant functional defined on a manifold. A generalization of the Bourgin-Yang theorem for the index with filtration is proved. This result is used for estimates of the index of the space of partial coincidences for a map of a space with p-torus action in a Euclidean space
Instantons from geodesics in AdS moduli spaces
Ruggeri, Daniele; Trigiante, Mario; Van Riet, Thomas
2018-03-01
We investigate supergravity instantons in Euclidean AdS5 × S5/ℤk. These solutions are expected to be dual to instantons of N = 2 quiver gauge theories. On the supergravity side the (extremal) instanton solutions are neatly described by the (lightlike) geodesics on the AdS moduli space for which we find the explicit expression and compute the on-shell actions in terms of the quantised charges. The lightlike geodesics fall into two categories depending on the degree of nilpotency of the Noether charge matrix carried by the geodesic: for degree 2 the instantons preserve 8 supercharges and for degree 3 they are non-SUSY. We expect that these findings should apply to more general situations in the sense that there is a map between geodesics on moduli-spaces of Euclidean AdS vacua and instantons with holographic counterparts.
Kim, Won Hwa; Chung, Moo K; Singh, Vikas
2013-01-01
The analysis of 3-D shape meshes is a fundamental problem in computer vision, graphics, and medical imaging. Frequently, the needs of the application require that our analysis take a multi-resolution view of the shape's local and global topology, and that the solution is consistent across multiple scales. Unfortunately, the preferred mathematical construct which offers this behavior in classical image/signal processing, Wavelets, is no longer applicable in this general setting (data with non-uniform topology). In particular, the traditional definition does not allow writing out an expansion for graphs that do not correspond to the uniformly sampled lattice (e.g., images). In this paper, we adapt recent results in harmonic analysis, to derive Non-Euclidean Wavelets based algorithms for a range of shape analysis problems in vision and medical imaging. We show how descriptors derived from the dual domain representation offer native multi-resolution behavior for characterizing local/global topology around vertices. With only minor modifications, the framework yields a method for extracting interest/key points from shapes, a surprisingly simple algorithm for 3-D shape segmentation (competitive with state of the art), and a method for surface alignment (without landmarks). We give an extensive set of comparison results on a large shape segmentation benchmark and derive a uniqueness theorem for the surface alignment problem.
International Nuclear Information System (INIS)
Abd El-Monsef, M.M.; Kozae, A.M.; Seddeek, M.K.; Medhat, T.; Sharshar, T.; Badran, H.M.
2004-01-01
Form the geological point of view, the origin and transport of black and normal sands is particularly important. Black and normal sands came to their places along the Mediterranean-sea coast after transport by some natural process. Both types of sands have different radiological properties. This study is, therefore, attempts to use mathematical methods to classify Egyptian sand samples collected from 42 locations in an area of 40 x 19 km 2 based on their radioactivity contents. The use of all information resulted from the experimental measurements of radioactivity contents as well as some other parameters can be a time and effort consuming task. So that the process of eliminating unnecessary attributes is of prime importance. This elimination process of the superfluous attributes that cannot affect the decision was carried out. Some topological techniques to classify the information systems resulting from the radioactivity measurements were then carried out. These techniques were applied in Euclidean and quasi-discrete topological cases. While there are some applications in environmental radioactivity of the former case, the use of the quasi-discrete in the so-called rough set information analysis is new in such a study. The mathematical methods are summarized and the results and their radiological implications are discussed. Generally, the results indicate no radiological anomaly and it supports the hypothesis previously suggested about the presence of two types of sand in the studied area
International Nuclear Information System (INIS)
Bubelev, E.G.; Kuchin, I.A.
1998-01-01
The necessity of creating mesophysics is motivated on the basis of a general likeness of the description of many phenomena and processes in micro- and macroworld. For a general and detailed investigation of the former in modern high energy physics (HEP), the Absolute (arising from Minkovsky and irrespective of any reference system) universal approach is used. Its two conceptually new branches are non-linear system-dynamic and non-Euclidean evolutionary ones. They are complementary ones and completely adequate to an extreme complexity of directly unobservable HEP objects. Some primary problems of them are briefly made clear on the basis of synergetics principles and HEP's internal Lobachevsky-Euclidean geometry. They are noted as the primary content of the Lobachevsky-Poincare Programme (LPP) the idea of which has been proposed recently for their successive solution
Meyer, Harvey B.
2017-09-01
We present a Lorentz-covariant, Euclidean coordinate-space expression for the hadronic vacuum polarisation, the Adler function and the leading hadronic contribution to the anomalous magnetic moment of the muon. The representation offers a high degree of flexibility for an implementation in lattice QCD. We expect it to be particularly helpful for the quark-line disconnected contributions.
Energy Technology Data Exchange (ETDEWEB)
Meyer, Harvey B. [Mainz Univ., PRISMA Cluster of Excellence, Inst. fuer Kernphysik und Helmholtz Institut Mainz (Germany)
2017-09-15
We present a Lorentz-covariant, Euclidean coordinate-space expression for the hadronic vacuum polarisation, the Adler function and the leading hadronic contribution to the anomalous magnetic moment of the muon. The representation offers a high degree of flexibility for an implementation in lattice QCD. We expect it to be particularly helpful for the quark-line disconnected contributions. (orig.)
Metrics in Keplerian orbits quotient spaces
Milanov, Danila V.
2018-03-01
Quotient spaces of Keplerian orbits are important instruments for the modelling of orbit samples of celestial bodies on a large time span. We suppose that variations of the orbital eccentricities, inclinations and semi-major axes remain sufficiently small, while arbitrary perturbations are allowed for the arguments of pericentres or longitudes of the nodes, or both. The distance between orbits or their images in quotient spaces serves as a numerical criterion for such problems of Celestial Mechanics as search for common origin of meteoroid streams, comets, and asteroids, asteroid families identification, and others. In this paper, we consider quotient sets of the non-rectilinear Keplerian orbits space H. Their elements are identified irrespective of the values of pericentre arguments or node longitudes. We prove that distance functions on the quotient sets, introduced in Kholshevnikov et al. (Mon Not R Astron Soc 462:2275-2283, 2016), satisfy metric space axioms and discuss theoretical and practical importance of this result. Isometric embeddings of the quotient spaces into R^n, and a space of compact subsets of H with Hausdorff metric are constructed. The Euclidean representations of the orbits spaces find its applications in a problem of orbit averaging and computational algorithms specific to Euclidean space. We also explore completions of H and its quotient spaces with respect to corresponding metrics and establish a relation between elements of the extended spaces and rectilinear trajectories. Distance between an orbit and subsets of elliptic and hyperbolic orbits is calculated. This quantity provides an upper bound for the metric value in a problem of close orbits identification. Finally the invariance of the equivalence relations in H under coordinates change is discussed.
Dual transformations of the non-abelian fields in Minkowsky, Euclid, and Galilei-Newton spaces
International Nuclear Information System (INIS)
Tolkaehev, E.A.; Kurochkin, Y.A.; Trequbovich, A.Y.
1991-01-01
In this paper it is shown that the generalization of the Yang-Mills equations in Minkowsky space to the case of the biquaternions over dual and double numbers enables one to define the corresponding representations of the Galilei and SO(4) groups in a rather natural way. it makes construction of the non-Abelian field equations in Euclidean and Galilei-Newton spaces possible and proves their invariance under generalized dual transformations by use of the analogy with the Abelian gauge
International Nuclear Information System (INIS)
Carow-Watamura, U.; Schlieker, M.; Watamura, S.
1991-01-01
We construct a differential calculus on the N-dimensional non-commutative Euclidean space, i.e., the space on which the quantum group SO q (N) is acting. The differential calculus is required to be manifestly covariant under SO q (N) transformations. Using this calculus, we consider the Schroedinger equation corresponding to the harmonic oscillator in the limit of q→1. The solution of it is given by q-deformed functions. (orig.)
Interactions for winding strings in Misner space
International Nuclear Information System (INIS)
Hikida, Y.
2006-06-01
We compute correlation functions of closed strings in Misner space, a big crunch big bang universe. We develop a general method for correlators with twist fields, which are relevant for the investigation on the condensation of winding tachyon. We propose to compute the correlation functions by performing an analytic continuation of the results in C/Z N Euclidean orbifold. In particular, we obtain a finite result for a general four point function of twist fields, which might be important for the interpretation as the quartic term of the tachyon potential. Three point functions are read off through the factorization, which are consistent with the known results. (Orig.)
Special relativity induced by granular space
International Nuclear Information System (INIS)
Jizba, Petr; Scardigli, Fabio
2013-01-01
We show that the special relativistic dynamics, when combined with quantum mechanics and the concept of superstatistics, can be interpreted as arising from two interlocked non-relativistic stochastic processes that operate at different energy scales. This framework leads to Feynman amplitudes that are, in the Euclidean regime, identical to the transition probability of a Brownian particle propagating through a granular space. For illustration we consider the dynamics and the propagator of a Klein-Gordon particle. Implications for deformed special relativity, quantum field theory, quantum gravity and cosmology are also discussed. (orig.)
Principal component analysis and the locus of the Fréchet mean in the space of phylogenetic trees.
Nye, Tom M W; Tang, Xiaoxian; Weyenberg, Grady; Yoshida, Ruriko
2017-12-01
Evolutionary relationships are represented by phylogenetic trees, and a phylogenetic analysis of gene sequences typically produces a collection of these trees, one for each gene in the analysis. Analysis of samples of trees is difficult due to the multi-dimensionality of the space of possible trees. In Euclidean spaces, principal component analysis is a popular method of reducing high-dimensional data to a low-dimensional representation that preserves much of the sample's structure. However, the space of all phylogenetic trees on a fixed set of species does not form a Euclidean vector space, and methods adapted to tree space are needed. Previous work introduced the notion of a principal geodesic in this space, analogous to the first principal component. Here we propose a geometric object for tree space similar to the [Formula: see text]th principal component in Euclidean space: the locus of the weighted Fréchet mean of [Formula: see text] vertex trees when the weights vary over the [Formula: see text]-simplex. We establish some basic properties of these objects, in particular showing that they have dimension [Formula: see text], and propose algorithms for projection onto these surfaces and for finding the principal locus associated with a sample of trees. Simulation studies demonstrate that these algorithms perform well, and analyses of two datasets, containing Apicomplexa and African coelacanth genomes respectively, reveal important structure from the second principal components.
2011-06-01
centered at OPi with radius β. Let δ ∗ be the coverage level of the entire polygon P , AP be the area of polygon P , APi be the area of sub-polygon...30 1104 512 1120 992 512 297 1.72 40 600 512 480 544 480 167 2.87 80 158 128 120 136 120 42 2.86 120 70 32 70 62 32 19 1.68 160 38 32 30 34 30 11
Clifford Space as a Generalization of Spacetime: Prospects for QFT of Point Particles and Strings
Pavsic, Matej
2005-01-01
The idea that spacetime has to be replaced by Clifford space (C-space) is explored. Quantum field theory (QFT) and string theory are generalized to C-space. It is shown how one can solve the cosmological constant problem and formulate string theory without central terms in the Virasoro algebra by exploiting the peculiar pseudo-Euclidean signature of C-space and the Jackiw definition of the vacuum state. As an introduction into the subject, a toy model of the harmonic oscillator in pseudo-Eucl...
Bhattacharya, Abhishek; Dunson, David B
2012-08-01
This article considers a broad class of kernel mixture density models on compact metric spaces and manifolds. Following a Bayesian approach with a nonparametric prior on the location mixing distribution, sufficient conditions are obtained on the kernel, prior and the underlying space for strong posterior consistency at any continuous density. The prior is also allowed to depend on the sample size n and sufficient conditions are obtained for weak and strong consistency. These conditions are verified on compact Euclidean spaces using multivariate Gaussian kernels, on the hypersphere using a von Mises-Fisher kernel and on the planar shape space using complex Watson kernels.
Representation of SO(4,1) group and Hawking effect in the de-Sitter space
International Nuclear Information System (INIS)
Bogush, A.A.; Otchik, V.S.
1983-01-01
Expression relating the solution of the equation for particles with spin 1/2 to matrix elements of group SO(4, 1), is obtained. When using the relation of the Dirac equation solutions in the de Sitter space with matrix elements of representations of group SO(4, 1) the presence of the Hawking effect in the space is established. The de Sitter space is considered as 4-dimensional hyperboloid, inserted into 5-dimensional pseudo-Euclidean space. It is established, that the average number of emitted spinor particles obeys the Fermi-Dirac distribution
Quantitative Hahn-Banach Theorems and Isometric Extensions forWavelet and Other Banach Spaces
Directory of Open Access Journals (Sweden)
Sergey Ajiev
2013-05-01
Full Text Available We introduce and study Clarkson, Dol’nikov-Pichugov, Jacobi and mutual diameter constants reflecting the geometry of a Banach space and Clarkson, Jacobi and Pichugov classes of Banach spaces and their relations with James, self-Jung, Kottman and Schäffer constants in order to establish quantitative versions of Hahn-Banach separability theorem and to characterise the isometric extendability of Hölder-Lipschitz mappings. Abstract results are further applied to the spaces and pairs from the wide classes IG and IG+ and non-commutative Lp-spaces. The intimate relation between the subspaces and quotients of the IG-spaces on one side and various types of anisotropic Besov, Lizorkin-Triebel and Sobolev spaces of functions on open subsets of an Euclidean space defined in terms of differences, local polynomial approximations, wavelet decompositions and other means (as well as the duals and the lp-sums of all these spaces on the other side, allows us to present the algorithm of extending the main results of the article to the latter spaces and pairs. Special attention is paid to the matter of sharpness. Our approach is quasi-Euclidean in its nature because it relies on the extrapolation of properties of Hilbert spaces and the study of 1-complemented subspaces of the spaces under consideration.
Coherent states for FLRW space-times in loop quantum gravity
International Nuclear Information System (INIS)
Magliaro, Elena; Perini, Claudio; Marciano, Antonino
2011-01-01
We construct a class of coherent spin-network states that capture properties of curved space-times of the Friedmann-Lamaitre-Robertson-Walker type on which they are peaked. The data coded by a coherent state are associated to a cellular decomposition of a spatial (t=const) section with a dual graph given by the complete five-vertex graph, though the construction can be easily generalized to other graphs. The labels of coherent states are complex SL(2,C) variables, one for each link of the graph, and are computed through a smearing process starting from a continuum extrinsic and intrinsic geometry of the canonical surface. The construction covers both Euclidean and Lorentzian signatures; in the Euclidean case and in the limit of flat space we reproduce the simplicial 4-simplex semiclassical states used in spin foams.
Path integration in conical space
International Nuclear Information System (INIS)
Inomata, Akira; Junker, Georg
2012-01-01
Quantum mechanics in conical space is studied by the path integral method. It is shown that the curvature effect gives rise to an effective potential in the radial path integral. It is further shown that the radial path integral in conical space can be reduced to a form identical with that in flat space when the discrete angular momentum of each partial wave is replaced by a specific non-integral angular momentum. The effective potential is found proportional to the squared mean curvature of the conical surface embedded in Euclidean space. The path integral calculation is compatible with the Schrödinger equation modified with the Gaussian and the mean curvature. -- Highlights: ► We study quantum mechanics on a cone by the path integral approach. ► The path integral depends only on the metric and the curvature effect is built in. ► The approach is consistent with the Schrödinger equation modified by an effective potential. ► The effective potential is found to be of the “Jensen–Koppe” and “da Costa” type.
International Nuclear Information System (INIS)
Raczka, R.
1979-01-01
Construction of non-cutoff Euclidean Green's functions for nonrenormalizable interactions Lsub(I)(phi)=lambda∫dσ(epsilon):expepsilonphi: in four-dimensional space-time is presented. It is shown that all axioms for the generating functional of E.G.F. are satisfied except perhaps the SO(4) invariance. It is shown that the singularities of E.G.F. for coinciding points are not worse than those of the free theory. (author)
Fractals and spectra related to fourier analysis and function spaces
Triebel, Hans
1997-01-01
Fractals and Spectra Hans Triebel This book deals with the symbiotic relationship between the theory of function spaces, fractal geometry, and spectral theory of (fractal) pseudodifferential operators as it has emerged quite recently. Atomic and quarkonial (subatomic) decompositions in scalar and vector valued function spaces on the euclidean n-space pave the way to study properties (compact embeddings, entropy numbers) of function spaces on and of fractals. On this basis, distributions of eigenvalues of fractal (pseudo)differential operators are investigated. Diverse versions of fractal drums are played. The book is directed to mathematicians interested in functional analysis, the theory of function spaces, fractal geometry, partial and pseudodifferential operators, and, in particular, in how these domains are interrelated. ------ It is worth mentioning that there is virtually no literature on this topic and hence the most of the presented material is published here the first time. - Zentralblatt MATH (…) ...
Resonances for Obstacles in Hyperbolic Space
Hintz, Peter; Zworski, Maciej
2017-12-01
We consider scattering by star-shaped obstacles in hyperbolic space and show that resonances satisfy a universal bound { Im λ ≤ - 1/2 } , which is optimal in dimension 2. In odd dimensions we also show that { Im λ ≤ - μ/ρ } for a universal constant {μ} , where { ρ } is the radius of a ball containing the obstacle; this gives an improvement for small obstacles. In dimensions 3 and higher the proofs follow the classical vector field approach of Morawetz, while in dimension 2 we obtain our bound by working with spaces coming from general relativity. We also show that in odd dimensions resonances of small obstacles are close, in a suitable sense, to Euclidean resonances.
International Nuclear Information System (INIS)
Capri, M.A.L.; Lemes, V.E.R.; Sobreiro, R.F.; Sorella, S.P.; Dudal, D.; Verschelde, H.; Gracey, J.A.
2006-01-01
The ghost condensate abc c b c c > is considered together with the gluon condensate μ 2 > in SU(2) Euclidean Yang-Mills theories quantized in the Landau gauge. The vacuum polarization ceases to be transverse due to the nonvanishing condensate abc c b c c >. The gluon propagator itself remains transverse. By polarization effects, this ghost condensate induces then a splitting in the gluon mass parameter, which is dynamically generated through μ 2 >. The obtained effective masses are real when μ 2 > is included in the analysis. In the absence of μ 2 >, the already known result that the ghost condensate induces effective tachyonic masses is recovered. At the one-loop level, we find that the effective diagonal mass becomes smaller than the off-diagonal one. This might serve as an indication for some kind of Abelian dominance in the Landau gauge, similar to what happens in the maximal Abelian gauge
International Nuclear Information System (INIS)
Kovarik, M.D.; Barnes, T.; Tennessee Univ., Knoxville, TN
1993-01-01
We describe a Monte Carlo simulation of a dynamical fermion problem in two spatial dimensions on an Intel iPSC/860 hypercube. The problem studied is the determination of the dispersion relation of a dynamical hole in the t-J model of the high temperature superconductors. Since this problem involves the motion of many fermions in more than one spatial dimensions, it is representative of the class of systems that suffer from the ''minus sign problem'' of dynamical fermions which has made Monte Carlo simulation very difficult. We demonstrate that for small values of the hole hopping parameter one can extract the entire hole dispersion relation using the GRW Monte Carlo algorithm, which is a simulation of the Euclidean time Schroedinger equation, and present results on 4 x 4 and 6 x 6 lattices. Generalization to physical hopping parameter values wig only require use of an improved trial wavefunction for importance sampling
Cosmological space-times with resolved Big Bang in Yang-Mills matrix models
Steinacker, Harold C.
2018-02-01
We present simple solutions of IKKT-type matrix models that can be viewed as quantized homogeneous and isotropic cosmological space-times, with finite density of microstates and a regular Big Bang (BB). The BB arises from a signature change of the effective metric on a fuzzy brane embedded in Lorentzian target space, in the presence of a quantized 4-volume form. The Hubble parameter is singular at the BB, and becomes small at late times. There is no singularity from the target space point of view, and the brane is Euclidean "before" the BB. Both recollapsing and expanding universe solutions are obtained, depending on the mass parameters.
Method of a covering space in quantum field theory
International Nuclear Information System (INIS)
Serebryanyj, E.M.
1982-01-01
To construct the Green function of the Laplace operator in the domain M bounded by conducting surfaces the generalized method of images is used. It is based on replacement of the domain M by its discrete bundle and that is why the term ''method of covering space'' is used. Continuing one of the coordinates to imaginary values the euclidean Green function is transformed into the causal one. This allows one to compute vacuum stress-energy tensor of the scalar massless field if the vacuum is stable [ru
QCD calculation of π0γγ vertex at equal Euclidean q2 of both photons
International Nuclear Information System (INIS)
Voloshin, M.B.
1982-01-01
The form factor of the π 6 γγ vertex at equal space-like four- momentum q 2 of the photons (q 1 2 =q 2 2 =-Q 2 ) and a small four- momentum p 2 of the pion is calculated within QCD. Explicit expressions for leading perturbative and non perturbative preasymptotic corrections are derived. To find the latter correction matrix elements of operators of dimension d=5 between the pion and vacuum are calculated. The result for the form factor smoothly matches at Q 2 approximately 0.5 GeV 2 the estimate based on the vector mesom dominance model [ru
Surface-knots in 4-space an introduction
Kamada, Seiichi
2017-01-01
This introductory volume provides the basics of surface-knots and related topics, not only for researchers in these areas but also for graduate students and researchers who are not familiar with the field. Knot theory is one of the most active research fields in modern mathematics. Knots and links are closed curves (one-dimensional manifolds) in Euclidean 3-space, and they are related to braids and 3-manifolds. These notions are generalized into higher dimensions. Surface-knots or surface-links are closed surfaces (two-dimensional manifolds) in Euclidean 4-space, which are related to two-dimensional braids and 4-manifolds. Surface-knot theory treats not only closed surfaces but also surfaces with boundaries in 4-manifolds. For example, knot concordance and knot cobordism, which are also important objects in knot theory, are surfaces in the product space of the 3-sphere and the interval. Included in this book are basics of surface-knots and the related topics of classical knots, the motion picture method, surf...
Metrics for measuring distances in configuration spaces
International Nuclear Information System (INIS)
Sadeghi, Ali; Ghasemi, S. Alireza; Schaefer, Bastian; Mohr, Stephan; Goedecker, Stefan; Lill, Markus A.
2013-01-01
In order to characterize molecular structures we introduce configurational fingerprint vectors which are counterparts of quantities used experimentally to identify structures. The Euclidean distance between the configurational fingerprint vectors satisfies the properties of a metric and can therefore safely be used to measure dissimilarities between configurations in the high dimensional configuration space. In particular we show that these metrics are a perfect and computationally cheap replacement for the root-mean-square distance (RMSD) when one has to decide whether two noise contaminated configurations are identical or not. We introduce a Monte Carlo approach to obtain the global minimum of the RMSD between configurations, which is obtained from a global minimization over all translations, rotations, and permutations of atomic indices
International Nuclear Information System (INIS)
Capri, M. A. L.; Lemes, V. E. R.; Sobreiro, R. F.; Sorella, S. P.; Thibes, R.
2006-01-01
We pursue the study of SU(2) Euclidean Yang-Mills theory in the maximal Abelian gauge by taking into account the effects of the Gribov horizon. The Gribov approximation, previously introduced in [M. A. L. Capri, V. E. R. Lemes, R. F. Sobreiro, S. P. Sorella, and R. Thibes, Phys. Rev. D 72, 085021 (2005).], is improved through the introduction of the horizon function, which is constructed under the requirements of localizability and renormalizability. By following Zwanziger's treatment of the horizon function in the Landau gauge, we prove that, when cast in local form, the horizon term of the maximal Abelian gauge leads to a quantized theory which enjoys multiplicative renormalizability, a feature which is established to all orders by means of the algebraic renormalization. Furthermore, it turns out that the horizon term is compatible with the local residual U(1) Ward identity, typical of the maximal Abelian gauge, which is easily derived. As a consequence, the nonrenormalization theorem, Z g Z A 1/2 =1, relating the renormalization factors of the gauge coupling constant Z g and of the diagonal gluon field Z A , still holds in the presence of the Gribov horizon. Finally, we notice that a generalized dimension two gluon operator can be also introduced. It is BRST invariant on-shell, a property which ensures its multiplicative renormalizability. Its anomalous dimension is not an independent parameter of the theory, being obtained from the renormalization factors of the gauge coupling constant and of the diagonal antighost field
Osseiran, Sam; Roider, Elisabeth M.; Wang, Hequn; Suita, Yusuke; Murphy, Michael; Fisher, David E.; Evans, Conor L.
2017-12-01
Chemical sun filters are commonly used as active ingredients in sunscreens due to their efficient absorption of ultraviolet (UV) radiation. Yet, it is known that these compounds can photochemically react with UV light and generate reactive oxygen species and oxidative stress in vitro, though this has yet to be validated in vivo. One label-free approach to probe oxidative stress is to measure and compare the relative endogenous fluorescence generated by cellular coenzymes nicotinamide adenine dinucleotides and flavin adenine dinucleotides. However, chemical sun filters are fluorescent, with emissive properties that contaminate endogenous fluorescent signals. To accurately distinguish the source of fluorescence in ex vivo skin samples treated with chemical sun filters, fluorescence lifetime imaging microscopy data were processed on a pixel-by-pixel basis using a non-Euclidean separation algorithm based on Mahalanobis distance and validated on simulated data. Applying this method, ex vivo samples exhibited a small oxidative shift when exposed to sun filters alone, though this shift was much smaller than that imparted by UV irradiation. Given the need for investigative tools to further study the clinical impact of chemical sun filters in patients, the reported methodology may be applied to visualize chemical sun filters and measure oxidative stress in patients' skin.
Eigenmodes of three-dimensional spherical spaces and their application to cosmology
International Nuclear Information System (INIS)
Lehoucq, Roland; Weeks, Jeffrey; Uzan, Jean-Philippe; Gausmann, Evelise; Luminet, Jean-Pierre
2002-01-01
This paper investigates the computation of the eigenmodes of the Laplacian operator in multi-connected three-dimensional spherical spaces. General mathematical results and analytical solutions for lens and prism spaces are presented. Three complementary numerical methods are developed and compared with our analytic results and previous investigations. The cosmological applications of these results are discussed, focusing on the cosmic microwave background (CMB) anisotropies. In particular, whereas in the Euclidean case too-small universes are excluded by present CMB data, in the spherical case, candidate topologies will always exist even if the total energy density parameter of the universe is very close to unity
Eigenmodes of three-dimensional spherical spaces and their application to cosmology
Energy Technology Data Exchange (ETDEWEB)
Lehoucq, Roland [CE-Saclay, DSM/DAPNIA/Service d' Astrophysique, F-91191 Gif sur Yvette (France); Weeks, Jeffrey [15 Farmer St, Canton, NY 13617-1120 (United States); Uzan, Jean-Philippe [Institut d' Astrophysique de Paris, GReCO, CNRS-FRE 2435, 98 bis, Bd Arago, 75014 Paris (France); Gausmann, Evelise [Instituto de Fisica Teorica, Rua Pamplona, 145 Bela Vista - Sao Paulo - SP, CEP 01405-900 (Brazil); Luminet, Jean-Pierre [Laboratoire Univers et Theories, CNRS-FRE 2462, Observatoire de Paris, F-92195 Meudon (France)
2002-09-21
This paper investigates the computation of the eigenmodes of the Laplacian operator in multi-connected three-dimensional spherical spaces. General mathematical results and analytical solutions for lens and prism spaces are presented. Three complementary numerical methods are developed and compared with our analytic results and previous investigations. The cosmological applications of these results are discussed, focusing on the cosmic microwave background (CMB) anisotropies. In particular, whereas in the Euclidean case too-small universes are excluded by present CMB data, in the spherical case, candidate topologies will always exist even if the total energy density parameter of the universe is very close to unity.
Chiral-symmetry breaking and confinement in Minkowski space
Energy Technology Data Exchange (ETDEWEB)
Biernat, Elmer P. [Unibersidade de Lisboa, 104-001, Lisboa, Portugal; Pena, M. T. [Universidade de Lisboa, 1049-001, Lisboa, Portugal; Ribiero, J. E. [Universidade de Lisboa, 1049-001 Lisboa, Portugal; Stadler, Alfred [Universidade de Ãvora, 7000-671 Ãvora, Portugal; Universidade de Lisboa, 1049-001 Lisboa, Portugal; Gross, Franz [Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
2016-01-01
We present a model for the quark-antiquark interaction formulated in Minkowski space using the Covariant Spectator Theory. The quark propagators are dressed with the same kernel that describes the interaction between different quarks. By applying the axial-vector Ward-Takahashi identity we show that our model satisfies the Adler-zero constraint imposed by chiral symmetry. For this model, our Minkowski-space results of the dressed quark mass function are compared to lattice QCD data obtained in Euclidean space. The mass function is then used in the calculation of the electromagnetic pion form factor in relativistic impulse approximation, and the results are presented and compared with the experimental data from JLab.
Chiral-symmetry breaking and confinement in Minkowski space
International Nuclear Information System (INIS)
Biernat, Elmar P.; Peña, M. T.; Ribeiro, J. E.; Stadler, Alfred; Gross, Franz
2016-01-01
We present a model for the quark-antiquark interaction formulated in Minkowski space using the Covariant Spectator Theory. The quark propagators are dressed with the same kernel that describes the interaction between different quarks. By applying the axial-vector Ward-Takahashi identity we show that our model satisfies the Adler-zero constraint imposed by chiral symmetry. For this model, our Minkowski-space results of the dressed quark mass function are compared to lattice QCD data obtained in Euclidean space. The mass function is then used in the calculation of the electromagnetic pion form factor in relativistic impulse approximation, and the results are presented and compared with the experimental data from JLab
Chiral-symmetry breaking and confinement in Minkowski space
Energy Technology Data Exchange (ETDEWEB)
Biernat, Elmar P. [Centro de Física Teórica de Partículas (CFTP), Instituto Superior Técnico (IST), Universidade de Lisboa, 1049-001 Lisboa (Portugal); Peña, M. T. [Centro de Física Teórica de Partículas (CFTP), Instituto Superior Técnico (IST), Universidade de Lisboa, 1049-001 Lisboa (Portugal); Departamento de Física, Instituto Superior Técnico (IST), Universidadede Lisboa, 1049-001 Lisboa (Portugal); Ribeiro, J. E. [Centro de Física das Interações Fundamentais (CFIF), Instituto Superior Técnico (IST), Universidade de Lisboa, 1049-001 Lisboa (Portugal); Stadler, Alfred [Departamento de Física, Universidade de Évora, 7000-671 Évora (Portugal); Centro de Física Teórica de Partículas (CFTP), Instituto Superior Técnico (IST), Universidade de Lisboa, 1049-001 Lisboa (Portugal); Gross, Franz [Thomas Jefferson National Accelerator Facility (JLab), Newport News, Virginia 23606 (United States)
2016-01-22
We present a model for the quark-antiquark interaction formulated in Minkowski space using the Covariant Spectator Theory. The quark propagators are dressed with the same kernel that describes the interaction between different quarks. By applying the axial-vector Ward-Takahashi identity we show that our model satisfies the Adler-zero constraint imposed by chiral symmetry. For this model, our Minkowski-space results of the dressed quark mass function are compared to lattice QCD data obtained in Euclidean space. The mass function is then used in the calculation of the electromagnetic pion form factor in relativistic impulse approximation, and the results are presented and compared with the experimental data from JLab.
Lie-Hamilton systems on curved spaces: a geometrical approach
Herranz, Francisco J.; de Lucas, Javier; Tobolski, Mariusz
2017-12-01
A Lie-Hamilton system is a nonautonomous system of first-order ordinary differential equations describing the integral curves of a t-dependent vector field taking values in a finite-dimensional Lie algebra, a Vessiot-Guldberg Lie algebra, of Hamiltonian vector fields relative to a Poisson structure. Its general solution can be written as an autonomous function, the superposition rule, of a generic finite family of particular solutions and a set of constants. We pioneer the study of Lie-Hamilton systems on Riemannian spaces (sphere, Euclidean and hyperbolic plane), pseudo-Riemannian spaces (anti-de Sitter, de Sitter, and Minkowski spacetimes) as well as on semi-Riemannian spaces (Newtonian spacetimes). Their corresponding constants of motion and superposition rules are obtained explicitly in a geometric way. This work extends the (graded) contraction of Lie algebras to a contraction procedure for Lie algebras of vector fields, Hamiltonian functions, and related symplectic structures, invariants, and superposition rules.
Kalanov, Temur Z.
2003-04-01
, calculates) the parameters of the subsystem researched physical object (for example, the coordinates of the object M); the parameters characterize the system of reference (for example, the system of coordinates S). (3) Each parameter of the object is its measure. Total number of the mutually independent parameters of the object is called dimension of the space of the object. (4) The set of numerical values (i.e. the range, the spectrum) of each parameter is the subspace of the object. (The coordinate space, the momentum space and the energy space are examples of the subspaces of the object). (5) The set of the parameters of the object is divided into two non intersecting (opposite) classes: the class of the internal parameters and the class of the non internal (i.e. external) parameters. The class of the external parameters is divided into two non intersecting (opposite) subclasses: the subclass of the absolute parameters (characterizing the form, the sizes of the object) and the subclass of the non absolute (relative) parameters (characterizing the position, the coordinates of the object). (6) Set of the external parameters forms the external space of object. It is called geometrical space of object. (7) Since a macroscopic object has three mutually independent sizes, the dimension of its external absolute space is equal to three. Consequently, the dimension of its external relative space is also equal to three. Thus, the total dimension of the external space of the macroscopic object is equal to six. (8) In general case, the external absolute space (i.e. the form, the sizes) and the external relative space (i.e. the position, the coordinates) of any object are mutually dependent because of influence of a medium. The geometrical space of such object is called non Euclidean space. If the external absolute space and the external relative space of some object are mutually independent, then the external relative space of such object is the homogeneous and isotropic geometrical
All ASD complex and real 4-dimensional Einstein spaces with Λ≠0 admitting a nonnull Killing vector
Chudecki, Adam
2016-12-01
Anti-self-dual (ASD) 4-dimensional complex Einstein spaces with nonzero cosmological constant Λ equipped with a nonnull Killing vector are considered. It is shown that any conformally nonflat metric of such spaces can be always brought to a special form and the Einstein field equations can be reduced to the Boyer-Finley-Plebański equation (Toda field equation). Some alternative forms of the metric are discussed. All possible real slices (neutral, Euclidean and Lorentzian) of ASD complex Einstein spaces with Λ≠0 admitting a nonnull Killing vector are found.
Emergent gravity in spaces of constant curvature
Energy Technology Data Exchange (ETDEWEB)
Alvarez, Orlando; Haddad, Matthew [Department of Physics, University of Miami,1320 Campo Sano Ave, Coral Gables, FL 33146 (United States)
2017-03-07
In physical theories where the energy (action) is localized near a submanifold of a constant curvature space, there is a universal expression for the energy (or the action). We derive a multipole expansion for the energy that has a finite number of terms, and depends on intrinsic geometric invariants of the submanifold and extrinsic invariants of the embedding of the submanifold. This is the second of a pair of articles in which we try to develop a theory of emergent gravity arising from the embedding of a submanifold into an ambient space equipped with a quantum field theory. Our theoretical method requires a generalization of a formula due to by Hermann Weyl. While the first paper discussed the framework in Euclidean (Minkowski) space, here we discuss how this framework generalizes to spaces of constant sectional curvature. We focus primarily on anti de Sitter space. We then discuss how such a theory can give rise to a cosmological constant and Planck mass that are within reasonable bounds of the experimental values.
Instability of flat space at finite temperature
International Nuclear Information System (INIS)
Gross, D.J.; Perry, M.J.; Yaffe, L.G.
1982-01-01
The instabilities of quantum gravity are investigated using the path-integral formulation of Einstein's theory. A brief review is given of the classical gravitational instabilities, as well as the stability of flat space. The Euclidean path-integral representation of the partition function is employed to discuss the instability of flat space at finite temperature. Semiclassical, or saddle-point, approximations are utilized. We show how the Jeans instability arises as a tachyon in the graviton propagator when small perturbations about hot flat space are considered. The effect due to the Schwarzschild instanton is studied. The small fluctuations about this instanton are analyzed and a negative mode is discovered. This produces, in the semiclassical approximation, an imaginary part of the free energy. This is interpreted as being due to the metastability of hot flat space to nucleate black holes. These then evolve by evaporation or by accretion of thermal gravitons, leading to the instability of hot flat space. The nucleation rate of black holes is calculated as a function of temperature
Jat, Prahlad; Serre, Marc L
2016-12-01
Widespread contamination of surface water chloride is an emerging environmental concern. Consequently accurate and cost-effective methods are needed to estimate chloride along all river miles of potentially contaminated watersheds. Here we introduce a Bayesian Maximum Entropy (BME) space/time geostatistical estimation framework that uses river distances, and we compare it with Euclidean BME to estimate surface water chloride from 2005 to 2014 in the Gunpowder-Patapsco, Severn, and Patuxent subbasins in Maryland. River BME improves the cross-validation R 2 by 23.67% over Euclidean BME, and river BME maps are significantly different than Euclidean BME maps, indicating that it is important to use river BME maps to assess water quality impairment. The river BME maps of chloride concentration show wide contamination throughout Baltimore and Columbia-Ellicott cities, the disappearance of a clean buffer separating these two large urban areas, and the emergence of multiple localized pockets of contamination in surrounding areas. The number of impaired river miles increased by 0.55% per year in 2005-2009 and by 1.23% per year in 2011-2014, corresponding to a marked acceleration of the rate of impairment. Our results support the need for control measures and increased monitoring of unassessed river miles. Copyright © 2016. Published by Elsevier Ltd.
Directory of Open Access Journals (Sweden)
Rodríguez Velásquez, Javier Oswaldo
2014-01-01
Full Text Available Background: Pathological interpretation of cellular form in cervical cytology is very important for preven- tion of cervical cancer. The methods most frequently used for assessment of this test have reproducibility and inter-observer variability problems. Objective: To make fractal and Euclidean measure- ments to mathematically diagnose normal and pre- malignant cells of cervical squamous epithelium. Methodology: 21 cells with normal, ASCUS or LSIL diagnosis according to the Bethesda system were assessed. Fractal and Euclidean geometric measures of three mathematical objects were calculated: cyto- plasm, nucleus and whole cell. Mathematical propor- tions between these measurements were calculated in order to compare them with conventional classification methods. Results: It was found that the nuclear border measures calculated with the 2-pixel grill and the surface measures could mathematically and objectively differentiate normal cells from the pre-malignant ones (ASCUS and LSIL. Conclusions: An objective and reproducible diagnos- tic method was developed; it allows to identify the evolution towards malignant cellular states based on simultaneous fractal and Euclidean measures, estab- lishing the severity level of ASCUS and LSIL cells.
Topological Structures on DMC Spaces †
Directory of Open Access Journals (Sweden)
Rajai Nasser
2018-05-01
Full Text Available Two channels are said to be equivalent if they are degraded from each other. The space of equivalent channels with input alphabet X and output alphabet Y can be naturally endowed with the quotient of the Euclidean topology by the equivalence relation. A topology on the space of equivalent channels with fixed input alphabet X and arbitrary but finite output alphabet is said to be natural if and only if it induces the quotient topology on the subspaces of equivalent channels sharing the same output alphabet. We show that every natural topology is σ -compact, separable and path-connected. The finest natural topology, which we call the strong topology, is shown to be compactly generated, sequential and T 4 . On the other hand, the strong topology is not first-countable anywhere, hence it is not metrizable. We introduce a metric distance on the space of equivalent channels which compares the noise levels between channels. The induced metric topology, which we call the noisiness topology, is shown to be natural. We also study topologies that are inherited from the space of meta-probability measures by identifying channels with their Blackwell measures.
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.
Non-Euclidean visibility problems
Indian Academy of Sciences (India)
FERNANDO CHAMIZO. Departamento de Matemáticas, Facultad de Ciencias, Universidad Autónoma de Madrid, 28049 Madrid, Spain. MS received 14 November 2005. Abstract. We consider the analog of visibility problems in hyperbolic plane (repre- sented by Poincaré half-plane model H), replacing the standard lattice Z ...
Spinors, superalgebras and the signature of space-time
Ferrara, S.
2001-01-01
Superconformal algebras embedding space-time in any dimension and signature are considered. Different real forms of the $R$-symmetries arise both for usual space-time signature (one time) and for Euclidean or exotic signatures (more than one times). Application of these superalgebras are found in the context of supergravities with 32 supersymmetries, in any dimension $D \\leq 11$. These theories are related to $D = 11, M, M^*$ and $M^\\prime$ theories or $D = 10$, IIB, IIB$^*$ theories when compactified on Lorentzian tori. All dimensionally reduced theories fall in three distinct phases specified by the number of (128 bosonic) positive and negative norm states: $(n^+,n^-) = (128,0), (64,64), (72,56)$.
Intertwined Hamiltonians in two-dimensional curved spaces
International Nuclear Information System (INIS)
Aghababaei Samani, Keivan; Zarei, Mina
2005-01-01
The problem of intertwined Hamiltonians in two-dimensional curved spaces is investigated. Explicit results are obtained for Euclidean plane, Minkowski plane, Poincare half plane (AdS 2 ), de Sitter plane (dS 2 ), sphere, and torus. It is shown that the intertwining operator is related to the Killing vector fields and the isometry group of corresponding space. It is shown that the intertwined potentials are closely connected to the integral curves of the Killing vector fields. Two problems are considered as applications of the formalism presented in the paper. The first one is the problem of Hamiltonians with equispaced energy levels and the second one is the problem of Hamiltonians whose spectrum is like the spectrum of a free particle
Popov, M.
Erwin Schrodinger suggested that " Scientific knowledge forms part of the idealistic background of human life", which exalted man from a nude and savage state to true humanity [Science and Humanism, Cambridge, 1961, p9]. Modern space sciences an space exploration are a brilliant demonstration of the validity of Schrodinger's thesis on Idealism. Moreover, Schrodingers thesis could be considered also as a basic principle for the New Educational Space Philosophical Project "TIMAEUS"."TIMAEUS" is not only an attempt to to start a new dialogue between Science, the Humanities and Religion; but also it is an origin of the cultural innovations of our so strange of globilisation. TIMAEUS, thus, can reveal Idealism as something more fundamental , more refined, more developed than is now accepted by the scientific community and the piblic. TIMAEUS has a significant cultural agenda, connected with the high orbital performance of the synthetic arts, combining a knowledge of the truly spiritual as well as the universal. In particular, classical ballet as a synthetic art can be a new and powerful perfector and re-creator of the real human, real idealistic, real complex culture in orbit. As is well known, Carlo Blasis, the most important dance theorist of the 19t h .century, made probably the first attempts to use the scientific ideas of Leonardo da Vinci and Isaac Newton for the understanding of the gravitational nature of balance and allegro in ballet. In particular Blasis's idea of the limited use of the legs in classical dance realised by the gifted pupils of Enrico Cecchetti - M.Fokine, A.Pavlova and V.Nijinsky, with thinkable purity and elegance of style. V.Nijinsky in his remarkable animation of the dance of two dimensional creatures of a Euclidean flat world (L'Apres Midi d'un Faune,1912) discovered that true classical dance has some gravitational limits. For example, Nijinsky's Faunes and Nymphs mut use running on the heels (In accordance with "Partitura" 1916); they
D. C. Kent; Won Keun Min
2002-01-01
Neighborhood spaces, pretopological spaces, and closure spaces are topological space generalizations which can be characterized by means of their associated interior (or closure) operators. The category NBD of neighborhood spaces and continuous maps contains PRTOP as a bicoreflective subcategory and CLS as a bireflective subcategory, whereas TOP is bireflectively embedded in PRTOP and bicoreflectively embedded in CLS. Initial and final structures are described in these categories, and it is s...
Infinite-parametric extension of the conformal algebra in D>2 space-time dimension
International Nuclear Information System (INIS)
Fradkin, E.S.; Linetsky, V.Ya.
1990-09-01
On the basis of the analytic continuations of semisimple Lie algebras discovered recently by us we construct manifestly quasiconformal infinite-dimensional algebras AC(so(4,1)) and PAC(so(3,2)) extending the conformal algebras in three-dimensional Euclidean and Minkowski space-time like the Virasoro algebra extends so(2,1). Their higher spin generalizations are also constructed. A counterpart of the central extension for D>2 and possible applications in exactly solvable conformal quantum field models in D>2 are discussed. (author). 31 refs, 2 figs
Oversampling the Minority Class in the Feature Space.
Perez-Ortiz, Maria; Gutierrez, Pedro Antonio; Tino, Peter; Hervas-Martinez, Cesar
2016-09-01
The imbalanced nature of some real-world data is one of the current challenges for machine learning researchers. One common approach oversamples the minority class through convex combination of its patterns. We explore the general idea of synthetic oversampling in the feature space induced by a kernel function (as opposed to input space). If the kernel function matches the underlying problem, the classes will be linearly separable and synthetically generated patterns will lie on the minority class region. Since the feature space is not directly accessible, we use the empirical feature space (EFS) (a Euclidean space isomorphic to the feature space) for oversampling purposes. The proposed method is framed in the context of support vector machines, where the imbalanced data sets can pose a serious hindrance. The idea is investigated in three scenarios: 1) oversampling in the full and reduced-rank EFSs; 2) a kernel learning technique maximizing the data class separation to study the influence of the feature space structure (implicitly defined by the kernel function); and 3) a unified framework for preferential oversampling that spans some of the previous approaches in the literature. We support our investigation with extensive experiments over 50 imbalanced data sets.
Mutational analysis a joint framework for Cauchy problems in and beyond vector spaces
Lorenz, Thomas
2010-01-01
Ordinary differential equations play a central role in science and have been extended to evolution equations in Banach spaces. For many applications, however, it is difficult to specify a suitable normed vector space. Shapes without a priori restrictions, for example, do not have an obvious linear structure. This book generalizes ordinary differential equations beyond the borders of vector spaces with a focus on the well-posed Cauchy problem in finite time intervals. Here are some of the examples: - Feedback evolutions of compact subsets of the Euclidean space - Birth-and-growth processes of random sets (not necessarily convex) - Semilinear evolution equations - Nonlocal parabolic differential equations - Nonlinear transport equations for Radon measures - A structured population model - Stochastic differential equations with nonlocal sample dependence and how they can be coupled in systems immediately - due to the joint framework of Mutational Analysis. Finally, the book offers new tools for modelling.
Frames and other bases in abstract and function spaces novel methods in harmonic analysis
Gia, Quoc; Mayeli, Azita; Mhaskar, Hrushikesh; Zhou, Ding-Xuan
2017-01-01
The first of a two volume set on novel methods in harmonic analysis, this book draws on a number of original research and survey papers from well-known specialists detailing the latest innovations and recently discovered links between various fields. Along with many deep theoretical results, these volumes contain numerous applications to problems in signal processing, medical imaging, geodesy, statistics, and data science. The chapters within cover an impressive range of ideas from both traditional and modern harmonic analysis, such as: the Fourier transform, Shannon sampling, frames, wavelets, functions on Euclidean spaces, analysis on function spaces of Riemannian and sub-Riemannian manifolds, Fourier analysis on manifolds and Lie groups, analysis on combinatorial graphs, sheaves, co-sheaves, and persistent homologies on topological spaces. Volume I is organized around the theme of frames and other bases in abstract and function spaces, covering topics such as: The advanced development of frames, including ...
Adelstein, Pamela
2018-01-01
A space can be sacred, providing those who inhabit a particular space with sense of transcendence-being connected to something greater than oneself. The sacredness may be inherent in the space, as for a religious institution or a serene place outdoors. Alternatively, a space may be made sacred by the people within it and events that occur there. As medical providers, we have the opportunity to create sacred space in our examination rooms and with our patient interactions. This sacred space can be healing to our patients and can bring us providers opportunities for increased connection, joy, and gratitude in our daily work.
Adams, Robert A
2003-01-01
Sobolev Spaces presents an introduction to the theory of Sobolev Spaces and other related spaces of function, also to the imbedding characteristics of these spaces. This theory is widely used in pure and Applied Mathematics and in the Physical Sciences.This second edition of Adam''s ''classic'' reference text contains many additions and much modernizing and refining of material. The basic premise of the book remains unchanged: Sobolev Spaces is intended to provide a solid foundation in these spaces for graduate students and researchers alike.* Self-contained and accessible for readers in other disciplines.* Written at elementary level making it accessible to graduate students.
Cosmic microwave background anisotropies in multiconnected flat spaces
International Nuclear Information System (INIS)
Riazuelo, Alain; Weeks, Jeffrey; Uzan, Jean-Philippe; Lehoucq, Roland; Luminet, Jean-Pierre
2004-01-01
This article investigates the signature of the seventeen multiconnected flat spaces in cosmic microwave background (CMB) maps. For each such space it recalls a fundamental domain and a set of generating matrices, and then goes on to find an orthonormal basis for the set of eigenmodes of the Laplace operator on that space. The basis eigenmodes are expressed as linear combinations of eigenmodes of the simply connected Euclidean space. A preceding work, which provides a general method for implementing multiconnected topologies in standard CMB codes, is then applied to simulate CMB maps and angular power spectra for each space. Unlike in the 3-torus, the results in most multiconnected flat spaces depend on the location of the observer. This effect is discussed in detail. In particular, it is shown that the correlated circles on a CMB map are generically not back to back, so that negative search of back-to-back circles in the Wilkinson Microwave Anisotropy Probe data does not exclude a vast majority of flat or nearly flat topologies
On asphericity of convex bodies in linear normed spaces.
Faried, Nashat; Morsy, Ahmed; Hussein, Aya M
2018-01-01
In 1960, Dvoretzky proved that in any infinite dimensional Banach space X and for any [Formula: see text] there exists a subspace L of X of arbitrary large dimension ϵ -iometric to Euclidean space. A main tool in proving this deep result was some results concerning asphericity of convex bodies. In this work, we introduce a simple technique and rigorous formulas to facilitate calculating the asphericity for each set that has a nonempty boundary set with respect to the flat space generated by it. We also give a formula to determine the center and the radius of the smallest ball containing a nonempty nonsingleton set K in a linear normed space, and the center and the radius of the largest ball contained in it provided that K has a nonempty boundary set with respect to the flat space generated by it. As an application we give lower and upper estimations for the asphericity of infinite and finite cross products of these sets in certain spaces, respectively.
Mass, entropy, and holography in asymptotically de Sitter spaces
International Nuclear Information System (INIS)
Balasubramanian, Vijay; Boer, Jan de; Minic, Djordje
2002-01-01
We propose a novel prescription for computing the boundary stress tensor and charges of asymptotically de Sitter (dS) spacetimes from data at early or late time infinity. If there is a holographic dual to dS spaces, defined analogously to the AdS/conformal field theory correspondence, our methods compute the (Euclidean) stress tensor of the dual. We compute the masses of Schwarzschild-de Sitter black holes in four and five dimensions, and the masses and angular momenta of Kerr-de Sitter spaces in three dimensions. All these spaces are less massive than de Sitter space, a fact which we use to qualitatively and quantitatively relate de Sitter entropy to the degeneracy of possible dual field theories. Our results in general dimensions lead to a conjecture: Any asymptotically de Sitter spacetime with mass greater than de Sitter space has a cosmological singularity. Finally, if a dual to de Sitter space exists, the trace of our stress tensor computes the renormalized group (RG) equation of the dual field theory. Cosmological time evolution corresponds to RG evolution in the dual. The RG evolution of the c function is then related to changes in accessible degrees of freedom in an expanding universe
DEFF Research Database (Denmark)
2005-01-01
Digital technologies and media are becoming increasingly embodied and entangled in the spaces and places at work and at home. However, our material environment is more than a geometric abstractions of space: it contains familiar places, social arenas for human action. For designers, the integration...... of digital technology with space poses new challenges that call for new approaches. Creative alternatives to traditional systems methodologies are called for when designers use digital media to create new possibilities for action in space. Design Spaces explores how design and media art can provide creative...... alternatives for integrating digital technology with space. Connecting practical design work with conceptual development and theorizing, art with technology, and usesr-centered methods with social sciences, Design Spaces provides a useful research paradigm for designing ubiquitous computing. This book...
Vozmishcheva, Tatiana
2016-09-01
The connection between the problems of celestial mechanics: the Kepler problem, the two-center problem and the two body problem in spaces of constant curvature with the generalized Kepler and Hooke potentials is investigated. The limit passage in the two-center and two body problems in the Lobachevsky space and on a sphere is carried out as λto0 (λ is the curvature of the corresponding space) for the two potentials. The potentials and metrics in spaces under study are written in the gnomonic coordinates. It is shown that as the curvature radius tends to infinity, the generalized gravitational and elastic potentials transform to the Kepler and Hooke forms in the Euclidean space.
Algorithms for Planar Graphs and Graphs in Metric Spaces
DEFF Research Database (Denmark)
Wulff-Nilsen, Christian
structural properties that can be exploited. For instance, a road network or a wire layout on a microchip is typically (near-)planar and distances in the network are often defined w.r.t. the Euclidean or the rectilinear metric. Specialized algorithms that take advantage of such properties are often orders...... of magnitude faster than the corresponding algorithms for general graphs. The first and main part of this thesis focuses on the development of efficient planar graph algorithms. The most important contributions include a faster single-source shortest path algorithm, a distance oracle with subquadratic...... for geometric graphs and graphs embedded in metric spaces. Roughly speaking, the stretch factor is a real value expressing how well a (geo-)metric graph approximates the underlying complete graph w.r.t. distances. We give improved algorithms for computing the stretch factor of a given graph and for augmenting...
Martin, Gary L.
2011-01-01
A robust and competitive commercial space sector is vital to continued progress in space. The United States is committed to encouraging and facilitating the growth of a U.S. commercial space sector that supports U.S. needs, is globally competitive, and advances U.S. leadership in the generation of new markets and innovation-driven entrepreneurship. Energize competitive domestic industries to participate in global markets and advance the development of: satellite manufacturing; satellite-based services; space launch; terrestrial applications; and increased entrepreneurship. Purchase and use commercial space capabilities and services to the maximum practical extent Actively explore the use of inventive, nontraditional arrangements for acquiring commercial space goods and services to meet United States Government requirements, including measures such as public-private partnerships, . Refrain from conducting United States Government space activities that preclude, discourage, or compete with U.S. commercial space activities. Pursue potential opportunities for transferring routine, operational space functions to the commercial space sector where beneficial and cost-effective.
Noncommutative spaces and matrix embeddings on flat ℝ{sup 2n+1}
Energy Technology Data Exchange (ETDEWEB)
Karczmarek, Joanna L.; Yeh, Ken Huai-Che [Department of Physics and Astronomy, University of British Columbia,6224 Agricultural Road, Vancouver (Canada)
2015-11-23
We conjecture an embedding operator which assigns, to any 2n+1 hermitian matrices, a 2n-dimensional hypersurface in flat (2n+1)-dimensional Euclidean space. This corresponds to precisely defining a fuzzy D(2n)-brane corresponding to N D0-branes. Points on the emergent hypersurface correspond to zero eigenstates of the embedding operator, which have an interpretation as coherent states underlying the emergent noncommutative geometry. Using this correspondence, all physical properties of the emergent D(2n)-brane can be computed. We apply our conjecture to noncommutative flat and spherical spaces. As a by-product, we obtain a construction of a rotationally symmetric flat noncommutative space in 4 dimensions.
Particles and Dirac-type operators on curved spaces
International Nuclear Information System (INIS)
Visinescu, Mihai
2003-01-01
We review the geodesic motion of pseudo-classical particles in curved spaces. Investigating the generalized Killing equations for spinning spaces, we express the constants of motion in terms of Killing-Yano tensors. Passing from the spinning spaces to the Dirac equation in curved backgrounds we point out the role of the Killing-Yano tensors in the construction of the Dirac-type operators. The general results are applied to the case of the four-dimensional Euclidean Taub-Newman-Unti-Tamburino space. From the covariantly constant Killing-Yano tensors of this space we construct three new Dirac-type operators which are equivalent with the standard Dirac operator. Finally the Runge-Lenz operator for the Dirac equation in this background is expressed in terms of the fourth Killing-Yano tensor which is not covariantly constant. As a rule the covariantly constant Killing-Yano tensors realize certain square roots of the metric tensor. Such a Killing-Yano tensor produces simultaneously a Dirac-type operator and the generator of a one-parameter Lie group connecting this operator with the standard Dirac one. On the other hand, the not covariantly constant Killing-Yano tensors are important in generating hidden symmetries. The presence of not covariantly constant Killing-Yano tensors implies the existence of non-standard supersymmetries in point particle theories on curved background. (author)
Falmagne, Jean-Claude
2011-01-01
Learning spaces offer a rigorous mathematical foundation for practical systems of educational technology. Learning spaces generalize partially ordered sets and are special cases of knowledge spaces. The various structures are investigated from the standpoints of combinatorial properties and stochastic processes. Leaning spaces have become the essential structures to be used in assessing students' competence of various topics. A practical example is offered by ALEKS, a Web-based, artificially intelligent assessment and learning system in mathematics and other scholarly fields. At the heart of A
Closed-String Tachyons and the Hagedorn Transition in AdS Space
Barbón, José L F
2002-01-01
We discuss some aspects of the behaviour of a string gas at the Hagedorn temperature from a Euclidean point of view. Using AdS space as an infrared regulator, the Hagedorn tachyon can be effectively quasi-localized and its dynamics controled by a finite energetic balance. We propose that the off-shell RG flow matches to an Euclidean AdS black hole geometry in a generalization of the string/black-hole correspondence principle. The final stage of the RG flow can be interpreted semiclassically as the growth of a cool black hole in a hotter radiation bath. The end-point of the condensation is the large Euclidan AdS black hole, and the part of spacetime behind the horizon has been removed. In the flat-space limit, holography is manifest by the system creating its own transverse screen at infinity. This leads to an argument, based on the energetics of the system, explaining why the non-supersymmetric type 0A string theory decays into the supersymmetric type IIB vacuum. We also suggest a notion of `boundary entropy'...
Maximal superintegrability of the generalized Kepler-Coulomb system on N-dimensional curved spaces
International Nuclear Information System (INIS)
Ballesteros, Angel; Herranz, Francisco J
2009-01-01
The superposition of the Kepler-Coulomb potential on the 3D Euclidean space with three centrifugal terms has recently been shown to be maximally superintegrable (Verrier and Evans 2008 J. Math. Phys. 49 022902) by finding an additional (hidden) integral of motion which is quartic in the momenta. In this paper, we present the generalization of this result to the N-dimensional spherical, hyperbolic and Euclidean spaces by making use of a unified symmetry approach that makes use of the curvature parameter. The resulting Hamiltonian, formed by the (curved) Kepler-Coulomb potential together with N centrifugal terms, is shown to be endowed with 2N - 1 functionally independent integrals of the motion: one of them is quartic and the remaining ones are quadratic. The transition from the proper Kepler-Coulomb potential, with its associated quadratic Laplace-Runge-Lenz N-vector, to the generalized system is fully described. The role of spherical, nonlinear (cubic) and coalgebra symmetries in all these systems is highlighted
Visualizing the inner product space ℝm×n in a MATLAB-assisted linear algebra classroom
Caglayan, Günhan
2018-05-01
This linear algebra note offers teaching and learning ideas in the treatment of the inner product space ? in a technology-supported learning environment. Classroom activities proposed in this note demonstrate creative ways of integrating MATLAB technology into various properties of Frobenius inner product as visualization tools that complement the algebraic approach. As implemented in linear algebra lessons in a university in the Unites States, the article also incorporates algebraic and visual work of students who experienced these activities with MATLAB software. The connection between the Frobenius norm and the Euclidean norm is also emphasized.
Horneck, Gerda; Klaus, David M.; Mancinelli, Rocco L.
2010-01-01
Summary: The responses of microorganisms (viruses, bacterial cells, bacterial and fungal spores, and lichens) to selected factors of space (microgravity, galactic cosmic radiation, solar UV radiation, and space vacuum) were determined in space and laboratory simulation experiments. In general, microorganisms tend to thrive in the space flight environment in terms of enhanced growth parameters and a demonstrated ability to proliferate in the presence of normally inhibitory levels of antibiotics. The mechanisms responsible for the observed biological responses, however, are not yet fully understood. A hypothesized interaction of microgravity with radiation-induced DNA repair processes was experimentally refuted. The survival of microorganisms in outer space was investigated to tackle questions on the upper boundary of the biosphere and on the likelihood of interplanetary transport of microorganisms. It was found that extraterrestrial solar UV radiation was the most deleterious factor of space. Among all organisms tested, only lichens (Rhizocarpon geographicum and Xanthoria elegans) maintained full viability after 2 weeks in outer space, whereas all other test systems were inactivated by orders of magnitude. Using optical filters and spores of Bacillus subtilis as a biological UV dosimeter, it was found that the current ozone layer reduces the biological effectiveness of solar UV by 3 orders of magnitude. If shielded against solar UV, spores of B. subtilis were capable of surviving in space for up to 6 years, especially if embedded in clay or meteorite powder (artificial meteorites). The data support the likelihood of interplanetary transfer of microorganisms within meteorites, the so-called lithopanspermia hypothesis. PMID:20197502
Parin, V. V.; Gorbov, F. D.; Kosmolinskiy, F. P.
1974-01-01
Psychological selection of astronauts considers mental responses and adaptation to the following space flight stress factors: (1) confinement in a small space; (2) changes in three dimensional orientation; (3) effects of altered gravity and weightlessness; (4) decrease in afferent nerve pulses; (5) a sensation of novelty and danger; and (6) a sense of separation from earth.
Berberian, S K
2002-01-01
A detailed exposition of G.W. Mackey's theory of Borel spaces (standard, substandard, analytic), based on results in Chapter 9 of Bourbaki's General Topology. Appended are five informal lectures on the subject (given at the CIMPA/ICPAM Summer School, Nice, 1986), sketching the connection between Borel spaces and representations of operator algebras.
Alexander, Harold L.
1991-01-01
Human productivity was studied for extravehicular tasks performed in microgravity, particularly including in-space assembly of truss structures and other large objects. Human factors research probed the anthropometric constraints imposed on microgravity task performance and the associated workstation design requirements. Anthropometric experiments included reach envelope tests conducted using the 3-D Acoustic Positioning System (3DAPS), which permitted measuring the range of reach possible for persons using foot restraints in neutral buoyancy, both with and without space suits. Much neutral buoyancy research was conducted using the support of water to simulate the weightlessness environment of space. It became clear over time that the anticipated EVA requirement associated with the Space Station and with in-space construction of interplanetary probes would heavily burden astronauts, and remotely operated robots (teleoperators) were increasingly considered to absorb the workload. Experience in human EVA productivity led naturally to teleoperation research into the remote performance of tasks through human controlled robots.
Gia, Quoc; Mayeli, Azita; Mhaskar, Hrushikesh; Zhou, Ding-Xuan
2017-01-01
The second of a two volume set on novel methods in harmonic analysis, this book draws on a number of original research and survey papers from well-known specialists detailing the latest innovations and recently discovered links between various fields. Along with many deep theoretical results, these volumes contain numerous applications to problems in signal processing, medical imaging, geodesy, statistics, and data science. The chapters within cover an impressive range of ideas from both traditional and modern harmonic analysis, such as: the Fourier transform, Shannon sampling, frames, wavelets, functions on Euclidean spaces, analysis on function spaces of Riemannian and sub-Riemannian manifolds, Fourier analysis on manifolds and Lie groups, analysis on combinatorial graphs, sheaves, co-sheaves, and persistent homologies on topological spaces. Volume II is organized around the theme of recent applications of harmonic analysis to function spaces, differential equations, and data science, covering topics such a...
Kellett, B. J.; Griffin, D. K.; Bingham, R.; Campbell, R. N.; Forbes, A.; Michaelis, M. M.
2008-05-01
Hybrid space propulsion has been a feature of most space missions. Only the very early rocket propulsion experiments like the V2, employed a single form of propulsion. By the late fifties multi-staging was routine and the Space Shuttle employs three different kinds of fuel and rocket engines. During the development of chemical rockets, other forms of propulsion were being slowly tested, both theoretically and, relatively slowly, in practice. Rail and gas guns, ion engines, "slingshot" gravity assist, nuclear and solar power, tethers, solar sails have all seen some real applications. Yet the earliest type of non-chemical space propulsion to be thought of has never been attempted in space: laser and photon propulsion. The ideas of Eugen Saenger, Georgii Marx, Arthur Kantrowitz, Leik Myrabo, Claude Phipps and Robert Forward remain Earth-bound. In this paper we summarize the various forms of nonchemical propulsion and their results. We point out that missions beyond Saturn would benefit from a change of attitude to laser-propulsion as well as consideration of hybrid "polypropulsion" - which is to say using all the rocket "tools" available rather than possibly not the most appropriate. We conclude with three practical examples, two for the next decades and one for the next century; disposal of nuclear waste in space; a grand tour of the Jovian and Saturnian moons - with Huygens or Lunoxod type, landers; and eventually mankind's greatest space dream: robotic exploration of neighbouring planetary systems.
Doignon, Jean-Paul
1999-01-01
Knowledge spaces offer a rigorous mathematical foundation for various practical systems of knowledge assessment. An example is offered by the ALEKS system (Assessment and LEarning in Knowledge Spaces), a software for the assessment of mathematical knowledge. From a mathematical standpoint, knowledge spaces generalize partially ordered sets. They are investigated both from a combinatorial and a stochastic viewpoint. The results are applied to real and simulated data. The book gives a systematic presentation of research and extends the results to new situations. It is of interest to mathematically oriented readers in education, computer science and combinatorics at research and graduate levels. The text contains numerous examples and exercises and an extensive bibliography.
DEFF Research Database (Denmark)
Birke, Alexander; Schoenau-Fog, Henrik; Reng, Lars
2012-01-01
This paper presents Space Bugz! - a novel crowd game for large venues or cinemas that utilises the audience's smartphones as controllers for the game. This paper explains what crowd gaming is and describes how the approach used in Space Bugz! enables more advanced gameplay concepts and individual...... player control than current technologies allow. The gameplay of Space Bugz! is then explained along with the technical architecture of the game. After this, the iterative design process used to create the game is described together with future perspectives. The article concludes with links to a video...
Supersymmetries and constants of motion in spinning spaces
International Nuclear Information System (INIS)
Visinescu, Mihai
1999-01-01
The models of relativistic particles with spin have been proposed for a long time. The first published work concerning the Lagrangian description of the relativistic particle with spin was the paper by Frenkel which appeared in 1926. After that the literature on the particle with spin grew vast. The models involving only conventional coordinates are called the classical models while the models involving anticommuting (Grassmann) coordinates are generally called pseudo-classical. We shall confine ourselves to discuss the relativistic spin one half particle models involving anticommuting vectorial degrees of freedom which are usually called spinning particles. Spinning particles are in some sense the classical limit of the Dirac particles. After the first quantization these new anticommuting variables are mapped into the Dirac matrices and they disappear from the theory. We investigate the motion of pseudo-classical spinning point particles in curved spaces. The generalized Killing equations for the configuration space of spinning particles (spinning space) are analyzed and the solutions are expressed in terms of Killing-Yano tensors. The general results are applied to the case of the four-dimensional Euclidean Taub-NUT spinning space. (author)
International Nuclear Information System (INIS)
Corno, S.E.
1995-01-01
Analytical methods for Space Dynamics of fission reactors, are presented. It is shown how a few sample problems in space dynamics can be solved, within the one and two group diffusion model, by purely analytical tools, essentially based on Laplace transform and complex Green function techniques. A quite suggestive generalization of this approach, applicable to the fluid core reactors, whose fuel is undergoing a violent mixing, is reported and briefly discussed. (author)
Kundu, Prasun K.
2017-11-01
In a comment published several years ago in this journal, Mitra [J. Math. Phys. 50, 042502 (2009)] has claimed to prove that a neutral point particle in general relativity as described by the Schwarzschild metric must have zero gravitational mass, i.e., the mass parameter M0 of a Schwarzschild black hole necessarily vanishes. It is shown that the purported proof is incorrect. The error stems from a basic misunderstanding of the mathematical description of coordinate volume element in a differentiable manifold.
Directory of Open Access Journals (Sweden)
Elena Grigoryeva
2013-01-01
Full Text Available The topic of this issue is PUBLIC SPACES. It is familiar and clear to every citizen. The streets and courtyards as childhood experiences remain with us forever. And these are the places where we come with our parents at weekends, where we meet friends, where we have dates and where we already come for a walk with our children.The history of public spaces is long and captivating. It was the main city squares where the most important events took place in history. The Agoras of Ancient Greece and the Roman Forums, the squares of Vatican, Paris and London, Moscow and Saint Petersburg… Greve, Trafalgar, Senate, Palace, Red, Bolotnaya – behind every name there is life of capitals, countries and nations.Public spaces, their shapes, image and development greatly influence the perception of the city as a whole. Both visitors and inhabitants can see in public spaces not only the visage but the heart, the soul and the mind of the city.Unfortunately, sometimes we have to prove the value of public spaces and defend them from those who consider them nothing but a blank space, nobody’s land destined for barbarous development.What should happen to make citizens perceive public spaces as their own and to make authorities consider development and maintenance of squares and parks their priority task against the background of increasing competition between cities and the fight for human capital? Lately they more often say about “a high-quality human capital”. And now, when they say “the city should be liveable” they add “for all groups of citizens, including the creative class”.
Muratore, John F.
2007-01-01
Space Rescue has been a topic of speculation for a wide community of people for decades. Astronauts, aerospace engineers, diplomats, medical and rescue professionals, inventors and science fiction writers have all speculated on this problem. Martin Caidin's 1964 novel Marooned dealt with the problems of rescuing a crew stranded in low earth orbit. Legend at the Johnson Space Center says that Caidin's portrayal of a Russian attempt to save the American crew played a pivotal role in convincing the Russians to join the real joint Apollo-Soyuz mission. Space Rescue has been a staple in science fiction television and movies portrayed in programs such as Star Trek, Stargate-SG1 and Space 1999 and movies such as Mission To Mars and Red Planet. As dramatic and as difficult as rescue appears in fictional accounts, in the real world it has even greater drama and greater difficulty. Space rescue is still in its infancy as a discipline and the purpose of this chapter is to describe the issues associated with space rescue and the work done so far in this field. For the purposes of this chapter, the term space rescue will refer to any system which allows for rescue or escape of personnel from situations which endanger human life in a spaceflight operation. This will span the period from crew ingress prior to flight through crew egress postlanding. For the purposes of this chapter, the term primary system will refer to the spacecraft system that a crew is either attempting to escape from or from which an attempt is being made to rescue the crew.
Underground spaces/cybernetic spaces
Directory of Open Access Journals (Sweden)
Tomaž Novljan
2000-01-01
Full Text Available A modern city space is a space where in the vertical and horizontal direction dynamic, non-linear processes exist, similar as in nature. Alongside the “common” city surface, cities have underground spaces as well that are increasingly affecting the functioning of the former. It is the space of material and cybernetic communication/transport. The psychophysical specifics of using underground places have an important role in their conceptualisation. The most evident facts being their limited volume and often limited connections to the surface and increased level of potential dangers of all kinds. An efficient mode for alleviating the effects of these specific features are artistic interventions, such as: shape, colour, lighting, all applications of the basic principles of fractal theory.
The physical boundary Hilbert space and volume operator in the Lorentzian new spin-foam theory
International Nuclear Information System (INIS)
Ding You; Rovelli, Carlo
2010-01-01
A covariant spin-foam formulation of quantum gravity has been recently developed, characterized by a kinematics which appears to match well the one of canonical loop quantum gravity. In this paper we reconsider the implementation of the constraints that defines the model. We define in a simple way the boundary Hilbert space of the theory, introducing a slight modification of the embedding of the SU(2) representations into the SL(2,C) ones. We then show directly that all constraints vanish on this space in a weak sense. The vanishing is exact (and not just in the large quantum number limit). We also generalize the definition of the volume operator in the spin-foam model to the Lorentzian signature and show that it matches the one of loop quantum gravity, as in the Euclidean case.
Three-dimensionality of space and the quantum bit: an information-theoretic approach
International Nuclear Information System (INIS)
Müller, Markus P; Masanes, Lluís
2013-01-01
It is sometimes pointed out as a curiosity that the state space of quantum two-level systems, i.e. the qubit, and actual physical space are both three-dimensional and Euclidean. In this paper, we suggest an information-theoretic analysis of this relationship, by proving a particular mathematical result: suppose that physics takes place in d spatial dimensions, and that some events happen probabilistically (not assuming quantum theory in any way). Furthermore, suppose there are systems that carry ‘minimal amounts of direction information’, interacting via some continuous reversible time evolution. We prove that this uniquely determines spatial dimension d = 3 and quantum theory on two qubits (including entanglement and unitary time evolution), and that it allows observers to infer local spatial geometry from probability measurements. (paper)
Realization of bicovariant differential calculus on the Lie algebra type noncommutative spaces
Meljanac, Stjepan; Krešić–Jurić, Saša; Martinić, Tea
2017-07-01
This paper investigates bicovariant differential calculus on noncommutative spaces of the Lie algebra type. For a given Lie algebra g0, we construct a Lie superalgebra g =g0⊕g1 containing noncommutative coordinates and one-forms. We show that g can be extended by a set of generators TAB whose action on the enveloping algebra U (g ) gives the commutation relations between monomials in U (g0 ) and one-forms. Realizations of noncommutative coordinates, one-forms, and the generators TAB as formal power series in a semicompleted Weyl superalgebra are found. In the special case dim(g0 ) =dim(g1 ) , we also find a realization of the exterior derivative on U (g0 ) . The realizations of these geometric objects yield a bicovariant differential calculus on U (g0 ) as a deformation of the standard calculus on the Euclidean space.
Sector models—A toolkit for teaching general relativity: I. Curved spaces and spacetimes
International Nuclear Information System (INIS)
Zahn, C; Kraus, U
2014-01-01
Teaching the general theory of relativity to high school or undergraduate students must be based on an approach that is conceptual rather than mathematical. In this paper we present such an approach that requires no more than elementary mathematics. The central idea of this introduction to general relativity is the use of so-called sector models. Sector models describe curved spaces the Regge calculus way by subdivision into blocks with euclidean geometry. This procedure is similar to the approximation of a curved surface by flat triangles. We outline a workshop for high school and undergraduate students that introduces the notion of curved space by means of sector models of black holes. We further describe the extension to sector models of curved spacetimes. The spacetime models are suitable for learners with a basic knowledge of special relativity. The teaching materials presented in this paper are available online for teaching purposes at www.spacetimetravel.org. (paper)
Global embedding of the Kerr black hole event horizon into hyperbolic 3-space
International Nuclear Information System (INIS)
Gibbons, G. W.; Herdeiro, C. A. R.; Rebelo, C.
2009-01-01
An explicit global and unique isometric embedding into hyperbolic 3-space, H 3 , of an axi-symmetric 2-surface with Gaussian curvature bounded below is given. In particular, this allows the embedding into H 3 of surfaces of revolution having negative, but finite, Gaussian curvature at smooth fixed points of the U(1) isometry. As an example, we exhibit the global embedding of the Kerr-Newman event horizon into H 3 , for arbitrary values of the angular momentum. For this example, considering a quotient of H 3 by the Picard group, we show that the hyperbolic embedding fits in a fundamental domain of the group up to a slightly larger value of the angular momentum than the limit for which a global embedding into Euclidean 3-space is possible. An embedding of the double-Kerr event horizon is also presented, as an example of an embedding that cannot be made global.
Minkowski space pion model inspired by lattice QCD running quark mass
Energy Technology Data Exchange (ETDEWEB)
Mello, Clayton S. [Instituto Tecnológico de Aeronáutica, DCTA, 12.228-900 São José dos Campos, SP (Brazil); Melo, J.P.B.C. de [Laboratório de Física Teórica e Computacional – LFTC, Universidade Cruzeiro do Sul, 01506-000 São Paulo, SP (Brazil); Frederico, T., E-mail: tobias@ita.br [Instituto Tecnológico de Aeronáutica, DCTA, 12.228-900 São José dos Campos, SP (Brazil)
2017-03-10
The pion structure in Minkowski space is described in terms of an analytic model of the Bethe–Salpeter amplitude combined with Euclidean Lattice QCD results. The model is physically motivated to take into account the running quark mass, which is fitted to Lattice QCD data. The pion pseudoscalar vertex is associated to the quark mass function, as dictated by dynamical chiral symmetry breaking requirements in the limit of vanishing current quark mass. The quark propagator is analyzed in terms of a spectral representation, and it shows a violation of the positivity constraints. The integral representation of the pion Bethe–Salpeter amplitude is also built. The pion space-like electromagnetic form factor is calculated with a quark electromagnetic current, which satisfies the Ward–Takahashi identity to ensure current conservation. The results for the form factor and weak decay constant are found to be consistent with the experimental data.
Minkowski space pion model inspired by lattice QCD running quark mass
Directory of Open Access Journals (Sweden)
Clayton S. Mello
2017-03-01
Full Text Available The pion structure in Minkowski space is described in terms of an analytic model of the Bethe–Salpeter amplitude combined with Euclidean Lattice QCD results. The model is physically motivated to take into account the running quark mass, which is fitted to Lattice QCD data. The pion pseudoscalar vertex is associated to the quark mass function, as dictated by dynamical chiral symmetry breaking requirements in the limit of vanishing current quark mass. The quark propagator is analyzed in terms of a spectral representation, and it shows a violation of the positivity constraints. The integral representation of the pion Bethe–Salpeter amplitude is also built. The pion space-like electromagnetic form factor is calculated with a quark electromagnetic current, which satisfies the Ward–Takahashi identity to ensure current conservation. The results for the form factor and weak decay constant are found to be consistent with the experimental data.
Three-dimensionality of space in the structure of the periodic table of chemical elements
International Nuclear Information System (INIS)
Veremeichik, T. F.
2006-01-01
The effect of the dimension of the 3D homogeneous and isotropic Euclidean space, and the electron spin on the self-organization of the electron systems of atoms of chemical elements is considered. It is shown that the finite dimension of space creates the possibility of periodicity in the structure of an electron cloud, while the value of the dimension determines the number of stable systems of electrons at different levels of the periodic table of chemical elements and some characteristics of the systems. The conditions for the stability of systems of electrons and the electron system of an atom as a whole are considered. On the basis of the results obtained, comparison with other hierarchical systems (nanostructures and biological structures) is performed
Vacuum polarization and topological self-interaction of a charge in multiconic space
International Nuclear Information System (INIS)
Gal'tsov, D.V.; Grats, Y.V.; Lavrent'ev, A.B.
1995-01-01
The behavior of classical and quantized massless scalar fields in n-dimensional multiconic space-time is considered. An expression for the Euclidean Green's function is obtained using the methods of perturbation theory. It is shown that a nontrivial topology of the space distorts the electrostatic field of a pointlike charge; as a result, the self-energy of the particle assumes a nonzero value, and a force of topological self-interaction arises. Similarly, a change in the spectrum of vacuum fluctuations of a quantized scalar field leads to nonzero vacuum expectation values left-angle φ 2 right-angle vac and left-angle T μv right-angle va and gives rise to vacuum attraction between parallel cosmic strings. 28 refs
Temperature and entropy of Schwarzschild-de Sitter space-time
International Nuclear Information System (INIS)
Shankaranarayanan, S.
2003-01-01
In the light of recent interest in quantum gravity in de Sitter space, we investigate semiclassical aspects of four-dimensional Schwarzschild-de Sitter space-time using the method of complex paths. The standard semiclassical techniques (such as Bogoliubov coefficients and Euclidean field theory) have been useful to study quantum effects in space-times with single horizons; however, none of these approaches seem to work for Schwarzschild-de Sitter space-time or, in general, for space-times with multiple horizons. We extend the method of complex paths to space-times with multiple horizons and obtain the spectrum of particles produced in these space-times. We show that the temperature of radiation in these space-times is proportional to the effective surface gravity--the inverse harmonic sum of surface gravity of each horizon. For the Schwarzschild-de Sitter space-time, we apply the method of complex paths to three different coordinate systems--spherically symmetric, Painleve, and Lemaitre. We show that the equilibrium temperature in Schwarzschild-de Sitter space-time is the harmonic mean of cosmological and event horizon temperatures. We obtain Bogoliubov coefficients for space-times with multiple horizons by analyzing the mode functions of the quantum fields near the horizons. We propose a new definition of entropy for space-times with multiple horizons, analogous to the entropic definition for space-times with a single horizon. We define entropy for these space-times to be inversely proportional to the square of the effective surface gravity. We show that this definition of entropy for Schwarzschild-de Sitter space-time satisfies the D-bound conjecture
A Cantorian potential theory for describing dynamical systems on El Naschie's space-time
International Nuclear Information System (INIS)
Iovane, G.; Gargiulo, G.; Zappale, E.
2006-01-01
In this paper we analyze classical systems, in which motion is not on a classical continuous path, but rather on a Cantorian one. Starting from El Naschie's space-time we introduce a mathematical approach based on a potential to describe the interaction system-support. We study some relevant force fields on Cantorian space and analyze the differences with respect to the analogous case on a continuum in the context of Lagrangian formulation. Here we confirm the idea proposed by the first author in dynamical systems on El Naschie's o (∞) Cantorian space-time that a Cantorian space could explain some relevant stochastic and quantum processes, if the space acts as an harmonic oscillating support, such as that found in Nature. This means that a quantum process could sometimes be explained as a classical one, but on a nondifferential and discontinuous support. We consider the validity of this point of view, that in principle could be more realistic, because it describes the real nature of matter and space. These do not exist in Euclidean space or curved Riemanian space-time, but in a Cantorian one. The consequence of this point of view could be extended in many fields such as biomathematics, structural engineering, physics, astronomy, biology and so on
DEFF Research Database (Denmark)
Larsen, Henrik Gutzon
Using the development of intergovernmental environmental cooperation in the Baltic Sea area as a concrete example, the aim of this study is to explore how the 'environment' in situations of environmental interdependence is identified and institutionalised as political-geographical objects....... 'Environmental interdependence' is to this end conceptualised as a tension between 'political spaces' of discrete state territories and 'environmental spaces' of spatially nested ecosystems. This tension between geographies of political separateness and environmental wholeness is the implicit or explicit basis...... for a large and varied literature. But in both its critical and problemsolving manifestations, this literature tends to naturalise the spatiality of environmental concerns: environmental spaces are generally taken for granted. On the suggestion that there is a subtle politics to the specification...
Casazza, Peter G
1989-01-01
This monograph provides a structure theory for the increasingly important Banach space discovered by B.S. Tsirelson. The basic construction should be accessible to graduate students of functional analysis with a knowledge of the theory of Schauder bases, while topics of a more advanced nature are presented for the specialist. Bounded linear operators are studied through the use of finite-dimensional decompositions, and complemented subspaces are studied at length. A myriad of variant constructions are presented and explored, while open questions are broached in almost every chapter. Two appendices are attached: one dealing with a computer program which computes norms of finitely-supported vectors, while the other surveys recent work on weak Hilbert spaces (where a Tsirelson-type space provides an example).
Directory of Open Access Journals (Sweden)
YU Wenhao
2015-01-01
Full Text Available The distribution pattern and the distribution density of urban facility POIs are of great significance in the fields of infrastructure planning and urban spatial analysis. The kernel density estimation, which has been usually utilized for expressing these spatial characteristics, is superior to other density estimation methods (such as Quadrat analysis, Voronoi-based method, for that the Kernel density estimation considers the regional impact based on the first law of geography. However, the traditional kernel density estimation is mainly based on the Euclidean space, ignoring the fact that the service function and interrelation of urban feasibilities is carried out on the network path distance, neither than conventional Euclidean distance. Hence, this research proposed a computational model of network kernel density estimation, and the extension type of model in the case of adding constraints. This work also discussed the impacts of distance attenuation threshold and height extreme to the representation of kernel density. The large-scale actual data experiment for analyzing the different POIs' distribution patterns (random type, sparse type, regional-intensive type, linear-intensive type discusses the POI infrastructure in the city on the spatial distribution of characteristics, influence factors, and service functions.
Rega, Joseph Mark
2003-01-01
Dissertação (mestrado) - Universidade Federal de Santa Catarina, Centro de Comunicação e Expressão. Programa de Pós-Graduação em Inglês e Literatura Correspondente. The recent surge in cyberspace science fiction follows previous trends within the genre, i.e. those connected with future city-space and outer space, and is an inevitable result of economic forces. There has always been a close relationship between capitalism and spatial expansion, compelled by technological innovations that ha...
DEFF Research Database (Denmark)
Raahauge, Kirsten Marie
2008-01-01
This article deals with representations of one specific city, Århus, Denmark, especially its central district. The analysis is based on anthropological fieldwork conducted in Skåde Bakker and Fedet, two well-off neighborhoods. The overall purpose of the project is to study perceptions of space...... and the interaction of cultural, social, and spatial organizations, as seen from the point of view of people living in Skåde Bakker and Fedet. The focus is on the city dwellers’ representations of the central district of Århus with specific reference to the concept of transit space. When applied to various Århusian...
Managing the resilience space of the German energy system - A vector analysis.
Schlör, Holger; Venghaus, Sandra; Märker, Carolin; Hake, Jürgen-Friedrich
2018-07-15
The UN Sustainable Development Goals formulated in 2016 confirmed the sustainability concept of the Earth Summit of 1992 and supported UNEP's green economy transition concept. The transformation of the energy system (Energiewende) is the keystone of Germany's sustainability strategy and of the German green economy concept. We use ten updated energy-related indicators of the German sustainability strategy to analyse the German energy system. The development of the sustainable indicators is examined in the monitoring process by a vector analysis performed in two-dimensional Euclidean space (Euclidean plane). The aim of the novel vector analysis is to measure the current status of the Energiewende in Germany and thereby provide decision makers with information about the strains for the specific remaining pathway of the single indicators and of the total system in order to meet the sustainability targets of the Energiewende. Within this vector model, three vectors (the normative sustainable development vector, the real development vector, and the green economy vector) define the resilience space of our analysis. The resilience space encloses a number of vectors representing different pathways with different technological and socio-economic strains to achieve a sustainable development of the green economy. In this space, the decision will be made as to whether the government measures will lead to a resilient energy system or whether a readjustment of indicator targets or political measures is necessary. The vector analysis enables us to analyse both the government's ambitiousness, which is expressed in the sustainability target for the indicators at the start of the sustainability strategy representing the starting preference order of the German government (SPO) and, secondly, the current preference order of German society in order to bridge the remaining distance to reach the specific sustainability goals of the strategy summarized in the current preference order (CPO
Institute of Scientific and Technical Information of China (English)
YIN PUMIN
2010-01-01
@@ China plans to launch an unmanned space module,Tiangong 1,in 2011,said Qi Faren,the chief designer of China's Shenzhou spacecraft,at the sidelines of the annual plenary session of the National Committee of the Chinese People's Political Consultative Conference(CPPCC),the country's top political advisory body,on March 3.
Weinstein, Margery
2010-01-01
Creating a balanced learning space for employees is about more than trying different types of seating. It is a challenge that an affect how well employees absorb the lessons and whether they will be able to product better results for the company. The possible solutions are as diverse as the learners. This article describes how three companies…
Miquel, J. (Editor); Economos, A. C. (Editor)
1982-01-01
Presentations are given which address the effects of space flght on the older person, the parallels between the physiological responses to weightlessness and the aging process, and experimental possibilities afforded by the weightless environment to fundamental research in gerontology and geriatrics.
Cort, Cliff
2006-01-01
Education administrators face the dual dilemma of crowded, aging facilities and tightening capital budgets. The challenge is to build the necessary classroom, laboratory and activity space while minimizing the length and expense of the construction process. One solution that offers an affordable alternative is modular construction, a method that…
International Nuclear Information System (INIS)
Tempelmayer, A.
2000-01-01
Space research in Austria began since 1969 and has its roots in Graz. An overview of the projects performed by Austrian organizations such as local network interconnection via satellites systems, MIGMAS (Microanalysis station), ALP-SAT (Autonomous Libration Point-Satellite), MIDAS (Micro-imaging dust analysis system), among others are described. (nevyjel)
2005-01-01
An old water tank from the time of the ISR is being converted into a temporary store for ATLAS muon chambers. This is the last chapter in the big programme by the PH Department to make better use of space at CERN.
WORKSHOP: Inner space - outer space
International Nuclear Information System (INIS)
Anon.
1984-01-01
During the first week of May, the Fermilab theoretical astrophysics group hosted an international conference on science at the interface of particle physics and cosmology/astrophysics. The conference (Inner Space-Outer Space) was attended by a very diverse group of more than 200 physical scientists, including astronomers, astrophysicists, cosmologists, low-temperature physicists, and elementary particle theorists and experimentalists. The common interest which brought this diverse group to gether is the connection between physics on the smallest scale probed by man - the realm of elementary particle physics - and physics on the largest scale imaginable (the entire Universe) - the realm of cosmology
WORKSHOP: Inner space - outer space
Energy Technology Data Exchange (ETDEWEB)
Anon.
1984-09-15
During the first week of May, the Fermilab theoretical astrophysics group hosted an international conference on science at the interface of particle physics and cosmology/astrophysics. The conference (Inner Space-Outer Space) was attended by a very diverse group of more than 200 physical scientists, including astronomers, astrophysicists, cosmologists, low-temperature physicists, and elementary particle theorists and experimentalists. The common interest which brought this diverse group to gether is the connection between physics on the smallest scale probed by man - the realm of elementary particle physics - and physics on the largest scale imaginable (the entire Universe) - the realm of cosmology.
James, John T.
2011-01-01
Safe breathing air for space faring crews is essential whether they are inside an Extravehicular Mobility Suit (EMU), a small capsule such as Soyuz, or the expansive International Space Station (ISS). Sources of air pollution can include entry of propellants, excess offgassing from polymeric materials, leakage of systems compounds, escape of payload compounds, over-use of utility compounds, microbial metabolism, and human metabolism. The toxicological risk posed by a compound is comprised of the probability of escaping to cause air pollution and the magnitude of adverse effects on human health if escape occurs. The risk from highly toxic compounds is controlled by requiring multiple levels of containment to greatly reduce the probability of escape; whereas compounds that are virtually non-toxic may require little or no containment. The potential for toxicity is determined by the inherent toxicity of the compound and the amount that could potentially escape into the breathing air.
DEFF Research Database (Denmark)
Stang Våland, Marianne; Georg, Susse
2018-01-01
In this paper, we analyze how architectural design, and the spatial and material changes this involves, contributes to the continuous shaping of identities in an organization. Based upon a case study of organizational and architectural change in a municipal administration at a time of major public...... sector reforms, we examine how design interventions were used to (re)form work and professional relationships. The paper examines how engagements with spatial arrangements and material artifacts affected people’s sense of both occupational and organizational identity. Taking a relational approach...... to sociomateriality, the paper contributes to the further theorizing of space in organization studies by proposing the concept of spacing identity to capture the fluidity of identity performance....
Coiera, Enrico
2014-01-01
Annotations to physical workspaces such as signs and notes are ubiquitous. When densely annotated, work areas become communication spaces. This study aims to characterize the types and purpose of such annotations. A qualitative observational study was undertaken in two wards and the radiology department of a 440-bed metropolitan teaching hospital. Images were purposefully sampled; 39 were analyzed after excluding inferior images. Annotation functions included signaling identity, location, capability, status, availability, and operation. They encoded data, rules or procedural descriptions. Most aggregated into groups that either created a workflow by referencing each other, supported a common workflow without reference to each other, or were heterogeneous, referring to many workflows. Higher-level assemblies of such groupings were also observed. Annotations make visible the gap between work done and the capability of a space to support work. Annotations are repairs of an environment, improving fitness for purpose, fixing inadequacy in design, or meeting emergent needs. Annotations thus record the missing information needed to undertake tasks, typically added post-implemented. Measuring annotation levels post-implementation could help assess the fit of technology to task. Physical and digital spaces could meet broader user needs by formally supporting user customization, 'programming through annotation'. Augmented reality systems could also directly support annotation, addressing existing information gaps, and enhancing work with context sensitive annotation. Communication spaces offer a model of how work unfolds. Annotations make visible local adaptation that makes technology fit for purpose post-implementation and suggest an important role for annotatable information systems and digital augmentation of the physical environment.
Energy Technology Data Exchange (ETDEWEB)
Corliss, William R.
1968-01-01
This booklet discusses three kinds of space radiation, cosmic rays, Van Allen Belts, and solar plasma. Cosmic rays are penetrating particles that we cannot see, hear or feel, which come from distant stars. Van Allen Belts, named after their discoverer are great belts of protons and electrons that the earth has captured in its magnetic trap. Solar plasma is a gaseous, electrically neutral mixture of positive and negative ions that the sun spews out from convulsed regions on its surface.
1985-01-01
thle early life * of" the system. Figure 4-2 shows the variation in power output for polonium - 210 (Po- 210 ) with a 138-day half-life, curium-242 (Cm...miles above the earth’s surface. Above this altitude they must take everything they need with them. The environment will supply them with neither food ...can move large payloads through space. The radioisotope heat cycle engines use high-energy particle sources such as plutonium and polonium . The walls
Smith, Scott M.
2009-01-01
Optimal nutrition will be critical for crew members who embark on space exploration missions. Nutritional assessment provides an opportunity to ensure that crewmembers begin their missions in optimal nutritional status, to document changes during a mission and, if necessary, to provide intervention to maintain that status throughout the mission, and to assesses changes after landing in order to facilitate the return to their normal status as soon as possible after landing. We report here the findings from our nutritional assessment of astronauts who participated in the International Space Station (ISS) missions, along with flight and ground-based research findings. We also present ongoing and planned nutrition research activities. These studies provide evidence that bone loss, compromised vitamin status, and oxidative damage are the critical nutritional concerns for space travelers. Other nutrient issues exist, including concerns about the stability of nutrients in the food system, which are exposed to longterm storage and radiation during flight. Defining nutrient requirements, and being able to provide and maintain those nutrients on exploration missions, will be critical for maintaining crew member health.
DEFF Research Database (Denmark)
Kristiansen, Erik
2015-01-01
, called “pervasive games.” These are games that are based on computer technology, but use a physical space as the game space as opposed to video games. Coupling spatial configuration with performance theory of rituals as liminal phenomena, I put forward a model and a new understanding of the magic circle......When we play games of any kind, from tennis to board games, it is easy to notice that games seem to be configured in space, often using stripes or a kind of map on a board. Some games are clearly performed within this marked border, while it may be difficult to pinpoint such a border in games like...... hide-and-seek, but even these games are still spatially configured. The border (visible or not) both seem to separate and uphold the game that it is meant for. This chapter sets out to analyse the possible border that separates a game from the surrounding world. Johan Huizinga noted this “separateness...
Tyszka, Steph; Saraiva, Jose; Doran, Rosa
2017-04-01
NUCLIO is a Portuguese non-profit organization with a strong record of investing in science education and outreach. We have developed and implemented many activities mostly directed to a young audience, in a bid to awaken and reinforce the interest that young people devote to Astronomy and all things spatial. In this framework, we have created a week-long program called Space Detectives, supported by the Municipality of Cascais, based on a story-line that provided a number of challenges and opportunities for learning matters as diverse as the electro-magnetic spectrum, means of communication, space travel, the martian environment, coding and robotics. We report on the first session that took place in December 2016. We had as participants several kids aged 9 to 12, with a mixed background in terms of interest in the sciences. Their response varied from enthusiastic to somewhat less interested, depending on the nature of the subject and the way it was presented - a reaction not necessarily related to its complexity. This week was taken as something of a trial run, in preparation for the European Commission- funded project "Stories of Tomorrow", to be implemented in schools. The individual activities and the way they were related to the story-line, as well as the smooth transition from one to the next, were subject to an analysis that will allow for improvements in the next installments of this program. We believe this is an excellent approach to the goals of using Space and Astronomy as an anchor for generating and keeping interest in the scientific areas, and of finding new and richer ways of learning.
CSIR Research Space (South Africa)
Kellett, BJ
2008-04-01
Full Text Available understandably, fallen by the wayside. NASAs putative atom bomb propelled mission, coincidently also baptized ORION, was also curtailed. And last of all, the use of lasers for propulsion remains firmly “stuck in the doldrums.” This mode of access to space...) Except for LOX, very polluting. V. high ζ Launch costs: $20,000/kg. Gas guns. 1 1-4 km/s Most of the system mass stays on the ground. Recoil problems. Large NASA gas gun project abandoned. (too many “g’s”) E-M guns: rail/coil. 1.5 1-10 km...
Vidmachenko, A. P.; Steklov, A. F.; Primak, N. V.
2000-01-01
Two main tendencies of making the Solar System habitable are regarding nowadays: (1) making objects of the Solar System habitable; and (2) making the space of the Solar System habitable. We think that it's better to combine them. We should dezine and build settlements ('technospheres') on such objects as asteroids and comets, using their resources. That is, it is necessary to create 'space technospheres' - a long-termed human settlements in the space. To save energy resources it is necessary to use Near-Earth asteroids enriched with water ice (i. e. extinguished comets) with Near-Earth orbits. To realize listed conceptions it is necessary to decrease (up to 100 times) the cost price of the long-termed settlements. That's why even average UN country will be able to create it's own space house - artificial planet ('technosphere') and maintain life activities there. About 50-100 such artificial planets will represent the future civilization of our Solar System. At the same time Earth will stay basic, maternal planet. There is an interesting problem of correcting orbits of that objects. Orbits can be changed into circular or elongated to make them comfortable for living activities of 5000-10000 settlers, and to maintain connection with maternal planet. Technospheres with the elongated orbits are more advantageous to assimilate the Solar System. While technospheres with circular orbits suit to the industrial cycle with certain specialization. The specialization of the technosphere will depend on mine-workings and/or chosen high-technology industrial process. Because it is profitable to convert raw materials at the technosphere and then to transport finished products to the maternal planet. It worth to be mentioned that because of the low gravitation and changed life cycle technosphere settlers, new 'Columb' of the Solar System will transform into new mankind. It will happen though it is difficult to imaging this. Because long ago, when fish left the ocean, they didn
2009-01-01
Space Exploration, is one book in the Britannica Illustrated Science Library Series that is correlated to the science curriculum in grades 5-8. The Britannica Illustrated Science Library is a visually compelling set that covers earth science, life science, and physical science in 16 volumes. Created for ages 10 and up, each volume provides an overview on a subject and thoroughly explains it through detailed and powerful graphics-more than 1,000 per volume-that turn complex subjects into information that students can grasp. Each volume contains a glossary with full definitions for vocabulary help and an index.
Wotring, Virginia E
2012-01-01
“Space Pharmacology” is a review of the current knowledge regarding the use of pharmaceuticals during spaceflights. It is a comprehensive review of the literature, addressing each area of pharmacokinetics and each major physiological system in turn. Every section begins with a topic overview, and is followed by a discussion of published data from spaceflight, and from ground experiments meant to model the spaceflight situation. Includes a discussion looking forward to the new medical challenges we are likely to face on longer duration exploration missions. This book is a snapshot of our current knowledge that also highlights areas of unknown.
Superintegrability on Three-Dimensional Riemannian and Relativistic Spaces of Constant Curvature
Directory of Open Access Journals (Sweden)
Francisco José Herranz
2006-01-01
Full Text Available A family of classical superintegrable Hamiltonians, depending on an arbitrary radial function, which are defined on the 3D spherical, Euclidean and hyperbolic spaces as well as on the (2+1D anti-de Sitter, Minkowskian and de Sitter spacetimes is constructed. Such systems admit three integrals of the motion (besides the Hamiltonian which are explicitly given in terms of ambient and geodesic polar coordinates. The resulting expressions cover the six spaces in a unified way as these are parametrized by two contraction parameters that govern the curvature and the signature of the metric on each space. Next two maximally superintegrable Hamiltonians are identified within the initial superintegrable family by finding the remaining constant of the motion. The former potential is the superposition of a (curved central harmonic oscillator with other three oscillators or centrifugal barriers (depending on each specific space, so that this generalizes the Smorodinsky-Winternitz system. The latter one is a superposition of the Kepler-Coulomb potential with another two oscillators or centrifugal barriers. As a byproduct, the Laplace-Runge-Lenz vector for these spaces is deduced. Furthermore both potentials are analysed in detail for each particular space. Some comments on their generalization to arbitrary dimension are also presented.
Supersymmetries and constants of motion in Taub-NUT spinning space
International Nuclear Information System (INIS)
Vaman, D.; Visinescu, M.
1998-01-01
Models of relativistic particles with spin have been proposed for a long time. The models involving only conventional coordinates are called classical, while the models involving anticommuting coordinates are generally called pseudo-classical. In this paper, the relativistic spin one half particle models involving anticommuting vectorial degrees of freedom, which are usually called the spinning particles, are considered. Spinning particles are in some sense the classical limit of the Dirac particles. After the first quantization these new anticommuting variables are mapped into the Dirac matrices and they disappear from the theory. In the present paper, the motion of pseudo-classical spinning particles in curved spaces is investigated and the relevant equations of motion are investigated. The generalized Killing equations for the configuration space of spinning particles (spinning spaces) are discussed and the constants of motion are derived in terms of the solutions of these equations. We also analysed the motion of pseudo-classical spinning particles in the Euclidean Taub-NUT space. The generalized Killing equations for this spinning space are examined and derivation of the constants of motion in terms of the Killing-Yano tensors is described. The equations obtained for the special case of motion on cone are solved. This case represents an extension of the scalar particle motions in the usual Taub-NUT space in which the orbits are conic sections. An explicit exact solution is given. In spite of its simplicity, this solution occurs to be far from trivial. (authors)
Quantum universe on extremely small space-time scales
International Nuclear Information System (INIS)
Kuzmichev, V.E.; Kuzmichev, V.V.
2010-01-01
The semiclassical approach to the quantum geometrodynamical model is used for the description of the properties of the Universe on extremely small space-time scales. Under this approach, the matter in the Universe has two components of the quantum nature which behave as antigravitating fluids. The first component does not vanish in the limit h → 0 and can be associated with dark energy. The second component is described by an extremely rigid equation of state and goes to zero after the transition to large spacetime scales. On small space-time scales, this quantum correction turns out to be significant. It determines the geometry of the Universe near the initial cosmological singularity point. This geometry is conformal to a unit four-sphere embedded in a five-dimensional Euclidean flat space. During the consequent expansion of the Universe, when reaching the post-Planck era, the geometry of the Universe changes into that conformal to a unit four-hyperboloid in a five-dimensional Lorentzsignatured flat space. This agrees with the hypothesis about the possible change of geometry after the origin of the expanding Universe from the region near the initial singularity point. The origin of the Universe can be interpreted as a quantum transition of the system from a region in the phase space forbidden for the classical motion, but where a trajectory in imaginary time exists, into a region, where the equations of motion have the solution which describes the evolution of the Universe in real time. Near the boundary between two regions, from the side of real time, the Universe undergoes almost an exponential expansion which passes smoothly into the expansion under the action of radiation dominating over matter which is described by the standard cosmological model.
DEFF Research Database (Denmark)
Fajstrup, Lisbeth; Goubault, Eric; Haucourt, Emmanuel
2012-01-01
in the interleaving semantics of a concurrent program, but rather some equivalence classes. The purpose of this paper is to describe a new algorithm to compute such equivalence classes, and a representative per class, which is based on ideas originating in algebraic topology. We introduce a geometric semantics...... of concurrent languages, where programs are interpreted as directed topological spaces, and study its properties in order to devise an algorithm for computing dihomotopy classes of execution paths. In particular, our algorithm is able to compute a control-flow graph for concurrent programs, possibly containing...... loops, which is “as reduced as possible” in the sense that it generates traces modulo equivalence. A preliminary implementation was achieved, showing promising results towards efficient methods to analyze concurrent programs, with very promising results compared to partial-order reduction techniques....
International Nuclear Information System (INIS)
Verdoolaege, G; Karagounis, G; Oost, G Van; Tendler, M
2012-01-01
Pattern recognition is becoming an increasingly important tool for making inferences from the massive amounts of data produced in fusion experiments. The purpose is to contribute to physics studies and plasma control. In this work, we address the visualization of plasma confinement data, the (real-time) identification of confinement regimes and the establishment of a scaling law for the energy confinement time. We take an intrinsically probabilistic approach, modeling data from the International Global H-mode Confinement Database with Gaussian distributions. We show that pattern recognition operations working in the associated probability space are considerably more powerful than their counterparts in a Euclidean data space. This opens up new possibilities for analyzing confinement data and for fusion data processing in general. We hence advocate the essential role played by measurement uncertainty for data interpretation in fusion experiments. (paper)
Space weather and space anomalies
Directory of Open Access Journals (Sweden)
L. I. Dorman
2005-11-01
Full Text Available A large database of anomalies, registered by 220 satellites in different orbits over the period 1971-1994 has been compiled. For the first time, data from 49 Russian Kosmos satellites have been included in a statistical analysis. The database also contains a large set of daily and hourly space weather parameters. A series of statistical analyses made it possible to quantify, for different satellite orbits, space weather conditions on the days characterized by anomaly occurrences. In particular, very intense fluxes (>1000 pfu at energy >10 MeV of solar protons are linked to anomalies registered by satellites in high-altitude (>15000 km, near-polar (inclination >55° orbits typical for navigation satellites, such as those used in the GPS network, NAVSTAR, etc. (the rate of anomalies increases by a factor ~20, and to a much smaller extent to anomalies in geostationary orbits, (they increase by a factor ~4. Direct and indirect connections between anomaly occurrence and geomagnetic perturbations are also discussed.
Internal space-time symmetries of massive and massless particles and their unification
International Nuclear Information System (INIS)
Kim, Y.S.
2001-01-01
It is noted that the internal space-time symmetries of relativistic particles are dictated by Wigner's little groups. The symmetry of massive particles is like the three-dimensional rotation group, while the symmetry of massless particles is locally isomorphic to the two-dimensional Euclidean group. It is noted also that, while the rotational degree of freedom for a massless particle leads to its helicity, the two translational degrees of freedom correspond to its gauge degrees of freedom. It is shown that the E(2)-like symmetry of of massless particles can be obtained as an infinite-momentum and/or zero-mass limit of the O(3)-like symmetry of massive particles. This mechanism is illustrated in terms of a sphere elongating into a cylinder. In this way, the helicity degree of freedom remains invariant under the Lorentz boost, but the transverse rotational degrees of freedom become contracted into the gauge degree of freedom
Space-Time Trellis Coded 8PSK Schemes for Rapid Rayleigh Fading Channels
Directory of Open Access Journals (Sweden)
Salam A. Zummo
2002-05-01
Full Text Available This paper presents the design of 8PSK space-time (ST trellis codes suitable for rapid fading channels. The proposed codes utilize the design criteria of ST codes over rapid fading channels. Two different approaches have been used. The first approach maximizes the symbol-wise Hamming distance (HD between signals leaving from or entering to the same encoderÃ¢Â€Â²s state. In the second approach, set partitioning based on maximizing the sum of squared Euclidean distances (SSED between the ST signals is performed; then, the branch-wise HD is maximized. The proposed codes were simulated over independent and correlated Rayleigh fading channels. Coding gains up to 4 dB have been observed over other ST trellis codes of the same complexity.
Gallagher, Dennis
2017-01-01
New range Passage Tomb may be the first structure with known astronomical significance. It was built around 3,200 B.C. in Ireland. It's central passage allows light end-to-end for about 2 weeks around winter solstice. The Sun, Moon, Planets, and Stars held significance in early times due to the seasons, significance for food crops, and mythology. Citation: Corel Photography and Windows to the Universe The Greek may be among the first to pursue analytical interpretations of what they saw in the sky. In about 280 B.C. Aristarchus suggested Earth revolves around the Sun and estimated the distance between. Around 130 B.C. Hipparchus developed the first accurate star map. Today still seek to understand how the universe formed and how we came to be and are we alone. Understanding the causes and consequences of climate change using advanced space missions with major Earth science and applications research. center dotFire the public imagination and inspire students to pursue STEM fields. Train college and graduate students to create a U.S. technical workforce with employees that embody the values of competence, innovation, and service. center dotDrive the technical innovations that enable exploration and become the engine of National economic growth. center dotPartner domestically and internationally to leverage resources to extend the reach of research.
Energy Technology Data Exchange (ETDEWEB)
Cichy, Krzysztof [DESY, Zeuthen (Germany). NIC; Adam Mickiewicz Univ., Poznan (Poland). Faculty of Physics; Jansen, Karl [DESY, Zeuthen (Germany). NIC; Korcyl, Piotr [DESY, Zeuthen (Germany). NIC; Jagiellonian Univ., Krakow (Poland). M. Smoluchowski Inst. of Physics
2012-07-15
We present results of a lattice QCD application of a coordinate space renormalization scheme for the extraction of renormalization constants for flavour non-singlet bilinear quark operators. The method consists in the analysis of the small-distance behaviour of correlation functions in Euclidean space and has several theoretical and practical advantages, in particular: it is gauge invariant, easy to implement and has relatively low computational cost. The values of renormalization constants in the X-space scheme can be converted to the MS scheme via 4-loop continuum perturbative formulae. Our results for N{sub f}=2 maximally twisted mass fermions with tree-level Symanzik improved gauge action are compared to the ones from the RI-MOM scheme and show full agreement with this method. (orig.)
International Nuclear Information System (INIS)
Cichy, Krzysztof; Adam Mickiewicz Univ., Poznan; Jansen, Karl; Korcyl, Piotr; Jagiellonian Univ., Krakow
2012-07-01
We present results of a lattice QCD application of a coordinate space renormalization scheme for the extraction of renormalization constants for flavour non-singlet bilinear quark operators. The method consists in the analysis of the small-distance behaviour of correlation functions in Euclidean space and has several theoretical and practical advantages, in particular: it is gauge invariant, easy to implement and has relatively low computational cost. The values of renormalization constants in the X-space scheme can be converted to the MS scheme via 4-loop continuum perturbative formulae. Our results for N f =2 maximally twisted mass fermions with tree-level Symanzik improved gauge action are compared to the ones from the RI-MOM scheme and show full agreement with this method. (orig.)
Spinorial charges and their role in the fusion of internal and space-time symmetries
International Nuclear Information System (INIS)
Daniel, M.; Ktorides, C.N.
1976-01-01
The advent of supersymmetry immediately led to speculations that a non-trivial mixing of internal and space-time symmetries could be achieved within its framework. In fact, the well-known no-go theorems do not apply to the supersymmetry algebra due to the presence, in the latter, of (anticommuting) spinorial charges. However, not until the recent work of Haag, Lopuszanski and Sohnius did a clearcut picture emerge as to how the aforementioned nontrivial mixing can take place. Most notably, the presence of the conformal algebra within the supersymmetry algebra turns out to be vital. The findings of Haag et al. are solidified through an explicit construction which uses as underlying space the pseudo-Euclidean space E(4, 2), i.e. the space for which the conformal group is the group of rotations, and which employs as main tools the spinors associated with the space E(4, 2). The algebro-geometric approach of Cartan is followed in order to understand both the introduction and the properties of these spinors. In this manner, many insights are gained regarding the mathematical foundations of supersymmetry. Thus, the emergence of the anticommutator, rather than the commutator, among spinor charges is fully understood as a natural algebraic consequence and not as an a priori given fact. In addition, it is clearly seen how an (internal) unitary symmetry group can make its appearance within the supersymmetry scheme and verify, via this explicit construction, the results of Haag et al. (Auth.)
Instanton tunneling for de Sitter space with real projective spatial sections
Energy Technology Data Exchange (ETDEWEB)
Ong, Yen Chin [Center for Astronomy and Astrophysics, Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240 (China); Yeom, Dong-han, E-mail: ongyenchin@sjtu.edu.cn, E-mail: innocent.yeom@gmail.com [Leung Center for Cosmology and Particle Astrophysics, National Taiwan University, Taipei 10617, Taiwan (China)
2017-04-01
The physics of tunneling from one spacetime to another is often understood in terms of instantons. For some instantons, it was recently shown in the literature that there are two complementary ''interpretations'' for their analytic continuations. Dubbed ''something-to-something'' and ''nothing-to-something'' interpretations, respectively, the former involves situation in which the initial and final hypersurfaces are connected by a Euclidean manifold, whereas the initial and final hypersurfaces in the latter case are not connected in such a way. We consider a de Sitter space with real projective space RP{sup 3} spatial sections, as was originally understood by de Sitter himself. This original version of de Sitter space has several advantages over the usual de Sitter space with S{sup 3} spatial sections. In particular, the interpretation of the de Sitter entropy as entanglement entropy is much more natural. We discuss the subtleties involved in the tunneling of such a de Sitter space.
Sequence spaces [Formula: see text] and [Formula: see text] with application in clustering.
Khan, Mohd Shoaib; Alamri, Badriah As; Mursaleen, M; Lohani, Qm Danish
2017-01-01
Distance measures play a central role in evolving the clustering technique. Due to the rich mathematical background and natural implementation of [Formula: see text] distance measures, researchers were motivated to use them in almost every clustering process. Beside [Formula: see text] distance measures, there exist several distance measures. Sargent introduced a special type of distance measures [Formula: see text] and [Formula: see text] which is closely related to [Formula: see text]. In this paper, we generalized the Sargent sequence spaces through introduction of [Formula: see text] and [Formula: see text] sequence spaces. Moreover, it is shown that both spaces are BK -spaces, and one is a dual of another. Further, we have clustered the two-moon dataset by using an induced [Formula: see text]-distance measure (induced by the Sargent sequence space [Formula: see text]) in the k-means clustering algorithm. The clustering result established the efficacy of replacing the Euclidean distance measure by the [Formula: see text]-distance measure in the k-means algorithm.
Relationship between five-dimensional black holes and de Sitter spaces
International Nuclear Information System (INIS)
Myung, Y S
2004-01-01
We study a close relationship between the topological anti-de Sitter (TAdS) black holes and topological de Sitter (TdS) spaces including the Schwarzschild-de Sitter (SdS) black hole in five dimensions. We show that all thermal properties of the TdS spaces can be found from those of the TAdS black holes by replacing k by -k. Also we find that all thermal information for the cosmological horizon of the SdS black hole is obtained from either the hyperbolic-AdS black hole or the Schwarzschild-TdS space by substituting m with -m. For this purpose we calculate thermal quantities of bulk (Euclidean) conformal field theory (ECFT) and moving domain wall by using the A(dS)/(E)CFT correspondences. Further, we compute logarithmic corrections to the Bekenstein-Hawking entropy, Cardy-Verlinde formula and Friedmann equation due to thermal fluctuations. It implies that in the thermal relation between the TdS spaces and TAdS black holes, the cosmological horizon plays the same role as the horizon of TAdS black holes. Finally we note that the dS/ECFT correspondence is valid for the TdS spaces in conjunction with the AdS/CFT correspondence for the TAdS black holes
Protein space: a natural method for realizing the nature of protein universe.
Yu, Chenglong; Deng, Mo; Cheng, Shiu-Yuen; Yau, Shek-Chung; He, Rong L; Yau, Stephen S-T
2013-02-07
Current methods cannot tell us what the nature of the protein universe is concretely. They are based on different models of amino acid substitution and multiple sequence alignment which is an NP-hard problem and requires manual intervention. Protein structural analysis also gives a direction for mapping the protein universe. Unfortunately, now only a minuscule fraction of proteins' 3-dimensional structures are known. Furthermore, the phylogenetic tree representations are not unique for any existing tree construction methods. Here we develop a novel method to realize the nature of protein universe. We show the protein universe can be realized as a protein space in 60-dimensional Euclidean space using a distance based on a normalized distribution of amino acids. Every protein is in one-to-one correspondence with a point in protein space, where proteins with similar properties stay close together. Thus the distance between two points in protein space represents the biological distance of the corresponding two proteins. We also propose a natural graphical representation for inferring phylogenies. The representation is natural and unique based on the biological distances of proteins in protein space. This will solve the fundamental question of how proteins are distributed in the protein universe. Copyright © 2012 Elsevier Ltd. All rights reserved.
Space Science in Action: Space Exploration [Videotape].
1999
In this videotape recording, students learn about the human quest to discover what is out in space. Students see the challenges and benefits of space exploration including the development of rocket science, a look back at the space race, and a history of manned space travel. A special section on the Saturn V rocket gives students insight into the…
Large size space construction for space exploitation
Kondyurin, Alexey
2016-07-01
Space exploitation is impossible without large space structures. We need to make sufficient large volume of pressurized protecting frames for crew, passengers, space processing equipment, & etc. We have to be unlimited in space. Now the size and mass of space constructions are limited by possibility of a launch vehicle. It limits our future in exploitation of space by humans and in development of space industry. Large-size space construction can be made with using of the curing technology of the fibers-filled composites and a reactionable matrix applied directly in free space. For curing the fabric impregnated with a liquid matrix (prepreg) is prepared in terrestrial conditions and shipped in a container to orbit. In due time the prepreg is unfolded by inflating. After polymerization reaction, the durable construction can be fitted out with air, apparatus and life support systems. Our experimental studies of the curing processes in the simulated free space environment showed that the curing of composite in free space is possible. The large-size space construction can be developed. A project of space station, Moon base, Mars base, mining station, interplanet space ship, telecommunication station, space observatory, space factory, antenna dish, radiation shield, solar sail is proposed and overviewed. The study was supported by Humboldt Foundation, ESA (contract 17083/03/NL/SFe), NASA program of the stratospheric balloons and RFBR grants (05-08-18277, 12-08-00970 and 14-08-96011).
Realizing spaces as path-component spaces
Banakh, Taras; Brazas, Jeremy
2018-01-01
The path component space of a topological space $X$ is the quotient space $\\pi_0(X)$ whose points are the path components of $X$. We show that every Tychonoff space $X$ is the path-component space of a Tychonoff space $Y$ of weight $w(Y)=w(X)$ such that the natural quotient map $Y\\to \\pi_0(Y)=X$ is a perfect map. Hence, many topological properties of $X$ transfer to $Y$. We apply this result to construct a compact space $X\\subset \\mathbb{R}^3$ for which the fundamental group $\\pi_1(X,x_0)$ is...
Euclidean shortest paths exact or approximate algorithms
Li, Fajie
2014-01-01
This book reviews algorithms for the exact or approximate solution of shortest-path problems, with a specific focus on a class of algorithms called rubberband algorithms. The coverage includes mathematical proofs for many of the given statements.
Folding of non-Euclidean curved shells
Bende, Nakul; Evans, Arthur; Innes-Gold, Sarah; Marin, Luis; Cohen, Itai; Santangelo, Christian; Hayward, Ryan
2015-03-01
Origami-based folding of 2D sheets has been of recent interest for a variety of applications ranging from deployable structures to self-folding robots. Though folding of planar sheets follows well-established principles, folding of curved shells involves an added level of complexity due to the inherent influence of curvature on mechanics. In this study, we use principles from differential geometry and thin shell mechanics to establish fundamental rules that govern folding of prototypical creased shells. In particular, we show how the normal curvature of a crease line controls whether the deformation is smooth or discontinuous, and investigate the influence of shell thickness and boundary conditions. We show that snap-folding of shells provides a route to rapid actuation on time-scales dictated by the speed of sound. The simple geometric design principles developed can be applied at any length-scale, offering potential for bio-inspired soft actuators for tunable optics, microfluidics, and robotics. This work was funded by the National Science Foundation through EFRI ODISSEI-1240441 with additional support to S.I.-G. through the UMass MRSEC DMR-0820506 REU program.
Curved twistor spaces and H-space
International Nuclear Information System (INIS)
Tod, K.P.
1980-01-01
The curved twistor space construction of Penrose for anti-self-dual solutions to the Einstein vacuum equations is described. Curved twistor spaces are defined and it is shown with the aid of an example how to obtain them by deforming the complex structure of regions of flat twistor space. The connection of this procedure with Newman's H-space construction via asymptotic twistor space is outlined. (Auth.)
Preparing future space leaders - International Space University
Stone, Barbara A.; Van Reeth, George P.
1992-01-01
The International Space University (ISU) concept of developing a cadre of space professionals that will lead the universities and industries into space is discussed. ISU is an innovative, permanent worldwide organization for training and academic instruction in all aspects of space studies. ISU's major goal is to provide the young professional academic instruction in technical and nontechnical areas of modern space exploration and research, and a forum to exchange ideas and develop both personal and professional ties at an international level.
Bielas, Wojciech; Plewik, Szymon
2018-01-01
Following Frink's characterization of completely regular spaces, we say that a regular T_1-space is an RC-space whenever the family of all regular open sets constitutes a regular normal base. Normal spaces are RC-spaces and there exist completely regular spaces which are not RC-spaces. So the question arises, which of the known examples of completely regular and not normal spaces are RC-spaces. We show that the Niemytzki plane and the Sorgenfrey plane are RC-spaces.
Constant-work-space algorithms for geometric problems
Directory of Open Access Journals (Sweden)
Tetsuo Asano
2011-07-01
Full Text Available Constant-work-space algorithms may use only constantly many cells of storage in addition to their input, which is provided as a read-only array. We show how to construct several geometric structures efficiently in the constant-work-space model. Traditional algorithms process the input into a suitable data structure (like a doubly-connected edge list that allows efficient traversal of the structure at hand. In the constant-work-space setting, however, we cannot afford to do this. Instead, we provide operations that compute the desired features on the fly by accessing the input with no extra space. The whole geometric structure can be obtained by using these operations to enumerate all the features. Of course, we must pay for the space savings by slower running times. While the standard data structure allows us to implement traversal operations in constant time, our schemes typically take linear time to read the input data in each step.We begin with two simple problems: triangulating a planar point set and finding the trapezoidal decomposition of a simple polygon. In both cases adjacent features can be enumerated in linear time per step, resulting in total quadratic running time to output the whole structure. Actually, we show that the former result carries over to the Delaunay triangulation, and hence the Voronoi diagram. This also means that we can compute the largest empty circle of a planar point set in quadratic time and constant work-space. As another application, we demonstrate how to enumerate the features of an Euclidean minimum spanning tree (EMST in quadratic time per step, so that the whole EMST can be found in cubic time using constant work-space.Finally, we describe how to compute a shortest geodesic path between two points in a simple polygon. Although the shortest path problem in general graphs is NL-complete (Jakoby and Tantau 2003, this constrained problem can be solved in quadratic time using only constant work-space.
Flat tori in three-dimensional space and convex integration.
Borrelli, Vincent; Jabrane, Saïd; Lazarus, Francis; Thibert, Boris
2012-05-08
It is well-known that the curvature tensor is an isometric invariant of C(2) Riemannian manifolds. This invariant is at the origin of the rigidity observed in Riemannian geometry. In the mid 1950s, Nash amazed the world mathematical community by showing that this rigidity breaks down in regularity C(1). This unexpected flexibility has many paradoxical consequences, one of them is the existence of C(1) isometric embeddings of flat tori into Euclidean three-dimensional space. In the 1970s and 1980s, M. Gromov, revisiting Nash's results introduced convex integration theory offering a general framework to solve this type of geometric problems. In this research, we convert convex integration theory into an algorithm that produces isometric maps of flat tori. We provide an implementation of a convex integration process leading to images of an embedding of a flat torus. The resulting surface reveals a C(1) fractal structure: Although the tangent plane is defined everywhere, the normal vector exhibits a fractal behavior. Isometric embeddings of flat tori may thus appear as a geometric occurrence of a structure that is simultaneously C(1) and fractal. Beyond these results, our implementation demonstrates that convex integration, a theory still confined to specialists, can produce computationally tractable solutions of partial differential relations.
International Nuclear Information System (INIS)
Sartori, G; Valente, G
2003-01-01
Functions which are equivariant or invariant under the transformations of a compact linear group G acting in a Euclidean space R n , can profitably be studied as functions defined in the orbit space of the group. The orbit space is the union of a finite set of strata, which are semialgebraic manifolds formed by the G-orbits with the same orbit-type. In this paper, we provide a simple recipe to obtain rational parametrizations of the strata. Our results can be easily exploited, in many physical contexts where the study of equivariant or invariant functions is important, for instance in the determination of patterns of spontaneous symmetry breaking, in the analysis of phase spaces and structural phase transitions (Landau theory), in equivariant bifurcation theory, in crystal field theory and in most areas where use is made of symmetry-adapted functions. A physically significant example of utilization of the recipe is given, related to spontaneous polarization in chiral biaxial liquid crystals, where the advantages with respect to previous heuristic approaches are shown
Energy Technology Data Exchange (ETDEWEB)
Sartori, G; Valente, G [Dipartimento di Fisica, Universita di Padova and INFN, Sezione di Padova, I-35131 Padova (Italy)
2003-02-21
Functions which are equivariant or invariant under the transformations of a compact linear group G acting in a Euclidean space R{sup n}, can profitably be studied as functions defined in the orbit space of the group. The orbit space is the union of a finite set of strata, which are semialgebraic manifolds formed by the G-orbits with the same orbit-type. In this paper, we provide a simple recipe to obtain rational parametrizations of the strata. Our results can be easily exploited, in many physical contexts where the study of equivariant or invariant functions is important, for instance in the determination of patterns of spontaneous symmetry breaking, in the analysis of phase spaces and structural phase transitions (Landau theory), in equivariant bifurcation theory, in crystal field theory and in most areas where use is made of symmetry-adapted functions. A physically significant example of utilization of the recipe is given, related to spontaneous polarization in chiral biaxial liquid crystals, where the advantages with respect to previous heuristic approaches are shown.
DEFF Research Database (Denmark)
Schmidt, Ulrik
Atmosphere and Ambient Space This paper explores the relation between atmosphere and ambient space. Atmosphere and ambient space share many salient properties. They are both ontologically indeterminate, constantly varying and formally diffuse and they are both experienced as a subtle, non......-signifying property of a given space. But from a certain point of view, the two concepts also designate quite dissimilar experiences of space. To be ’ambient’ means to surround. Accordingly, ambient space is that space, which surrounds something or somebody. (Gibson 1987: 65) Since space is essentially...... of a surrounding character, all space can thus be described as having a fundamentally ambient character. So what precisely is an ambient space, then? As I will argue in my presentation, ambient space is a sensory effect of spatiality when a space is experienced as being particularly surrounding: a ‘space effect...
Chirikjian, G; Sajjadi, S; Toptygin, D; Yan, Y
2015-03-01
The main goal of molecular replacement in macromolecular crystallography is to find the appropriate rigid-body transformations that situate identical copies of model proteins in the crystallographic unit cell. The search for such transformations can be thought of as taking place in the coset space Γ\\G where Γ is the Sohncke group of the macromolecular crystal and G is the continuous group of rigid-body motions in Euclidean space. This paper, the third in a series, is concerned with viewing nonsymmorphic Γ in a new way. These space groups, rather than symmorphic ones, are the most common ones for protein crystals. Moreover, their properties impact the structure of the space Γ\\G. In particular, nonsymmorphic space groups contain both Bieberbach subgroups and symmorphic subgroups. A number of new theorems focusing on these subgroups are proven, and it is shown that these concepts are related to the preferences that proteins have for crystallizing in different space groups, as observed in the Protein Data Bank.
International Nuclear Information System (INIS)
Triebel, Hans
2005-01-01
This paper deals with spaces B s pq and F s pq of positive smoothness s>0, based on L p -spaces with 0< p≤∞ and reproducing formulae for smooth functions. These spaces are compared with other B-spaces and F-spaces obtained by different means
Molecular basis sets - a general similarity-based approach for representing chemical spaces.
Raghavendra, Akshay S; Maggiora, Gerald M
2007-01-01
A new method, based on generalized Fourier analysis, is described that utilizes the concept of "molecular basis sets" to represent chemical space within an abstract vector space. The basis vectors in this space are abstract molecular vectors. Inner products among the basis vectors are determined using an ansatz that associates molecular similarities between pairs of molecules with their corresponding inner products. Moreover, the fact that similarities between pairs of molecules are, in essentially all cases, nonzero implies that the abstract molecular basis vectors are nonorthogonal, but since the similarity of a molecule with itself is unity, the molecular vectors are normalized to unity. A symmetric orthogonalization procedure, which optimally preserves the character of the original set of molecular basis vectors, is used to construct appropriate orthonormal basis sets. Molecules can then be represented, in general, by sets of orthonormal "molecule-like" basis vectors within a proper Euclidean vector space. However, the dimension of the space can become quite large. Thus, the work presented here assesses the effect of basis set size on a number of properties including the average squared error and average norm of molecular vectors represented in the space-the results clearly show the expected reduction in average squared error and increase in average norm as the basis set size is increased. Several distance-based statistics are also considered. These include the distribution of distances and their differences with respect to basis sets of differing size and several comparative distance measures such as Spearman rank correlation and Kruscal stress. All of the measures show that, even though the dimension can be high, the chemical spaces they represent, nonetheless, behave in a well-controlled and reasonable manner. Other abstract vector spaces analogous to that described here can also be constructed providing that the appropriate inner products can be directly
International Nuclear Information System (INIS)
Wijland, Frederic van
1997-01-01
The Nature of Space and Time is a seven and a half hour long video that comes in a three tape set. Professors Hawking and Penrose are shown giving a series of one hour lectures at the Isaac Newton Institute. The topics of their talks range from the structure of space-time to the quantum theory of gravitation. They are organized along three main lines. Both speakers first discuss the singularities of space and time within the framework of classical general relativity, that is, as deduced from Einstein's equations. After giving arguments in favour of the existence of closed trapped surfaces (collapsing stars, black holes), Hawking draws a parallel between thermodynamic irreversibility and the loss of information coming from gravity trapped surfaces. Instead, Penrose insists on the mathematical structure of the singularities, using in particular the Weyl curvature to characterize them. From his analysis two classes of singularities emerge: those from which matter comes out (big bang) and those in which matter comes in (big crunch, black holes). The classical setting being recalled, the speakers turn to quantum theory. Hawking's second talk is concerned with the quantum theory of black holes. In order to account for quantum effects, he introduces a path-integral formulation over Euclideanized metrics, Armed with this tool, the validity of which he merely assumes, he proves that black holes actually radiate so that he renders fully consistent the thermodynamic analogy, entropy being replaced by the area event horizon, and statistical fluctuations by quantum fluctuations. Basing his analysis upon an interpretation in terms of information theory, there exists, Hawking asserts, a new level of unpredictability. Penrose prefers not to expand on Hawking's interpretations and starts building upon quantum mechanics (analysis of the EPR experiment) and the density matrix formalism to stress the problems caused by the nonlocality of energy. In his last lecture Hawking comes back
Energy Technology Data Exchange (ETDEWEB)
Wijland, Frederic van
1997-09-01
The Nature of Space and Time is a seven and a half hour long video that comes in a three tape set. Professors Hawking and Penrose are shown giving a series of one hour lectures at the Isaac Newton Institute. The topics of their talks range from the structure of space-time to the quantum theory of gravitation. They are organized along three main lines. Both speakers first discuss the singularities of space and time within the framework of classical general relativity, that is, as deduced from Einstein's equations. After giving arguments in favour of the existence of closed trapped surfaces (collapsing stars, black holes), Hawking draws a parallel between thermodynamic irreversibility and the loss of information coming from gravity trapped surfaces. Instead, Penrose insists on the mathematical structure of the singularities, using in particular the Weyl curvature to characterize them. From his analysis two classes of singularities emerge: those from which matter comes out (big bang) and those in which matter comes in (big crunch, black holes). The classical setting being recalled, the speakers turn to quantum theory. Hawking's second talk is concerned with the quantum theory of black holes. In order to account for quantum effects, he introduces a path-integral formulation over Euclideanized metrics, Armed with this tool, the validity of which he merely assumes, he proves that black holes actually radiate so that he renders fully consistent the thermodynamic analogy, entropy being replaced by the area event horizon, and statistical fluctuations by quantum fluctuations. Basing his analysis upon an interpretation in terms of information theory, there exists, Hawking asserts, a new level of unpredictability. Penrose prefers not to expand on Hawking's interpretations and starts building upon quantum mechanics (analysis of the EPR experiment) and the density matrix formalism to stress the problems caused by the nonlocality of energy. In his last lecture
Fawkes, S.
This paper compares and contrasts the characteristics of the first space race, which ran from the late 1950s to the late 1990s, and the second space race that began with the successful space flight of SpaceShipOne in 2004. The first space race was between superpowers seeking to establish geo-political dominance in the Cold War. The second space race will be between competing companies seeking to establish low cost access to space for ordinary people. The first space race achieved its geo- political objectives but did not open up low cost access to space but rather restricted access to a select few, highly trained astronauts and cosmonauts. The second space race, driven by the size and growth of the travel and tourism industry, promises to open up access to space to millions of space tourists.
International Nuclear Information System (INIS)
Li Shiqing; Yan Heping
1995-01-01
The authors briefly discusses the radiation environment in near-earth space and it's influences on material, and electronic devices using in space airship, also, the research developments in space radiation effects are introduced
Directory of Open Access Journals (Sweden)
Coghetto Roland
2016-09-01
Full Text Available In this article, using mostly Pervin [9], Kunzi [6], [8], [7], Williams [11] and Bourbaki [3] works, we formalize in Mizar [2] the notions of quasiuniform space, semi-uniform space and locally uniform space.
Coghetto Roland
2016-01-01
In this article, using mostly Pervin [9], Kunzi [6], [8], [7], Williams [11] and Bourbaki [3] works, we formalize in Mizar [2] the notions of quasiuniform space, semi-uniform space and locally uniform space.
National Aeronautics and Space Administration — The “Space Weather in Operations” effort will provide on-demand and near-real time space weather event information to the Data Access Toolkit (DAT), which is the...
International Nuclear Information System (INIS)
Rahman, M.S.
1991-10-01
A birecurrent space is defined with its classification and studied with involvement of Einstein, conformally flat, conformally symmetric and conformally recurrent spaces. A necessary and sufficient condition that a birecurrent space be recurrent is found. (author). 6 refs
International Nuclear Information System (INIS)
Kozameh, C.N.; Newman, E.T.; Tod, K.P.
1985-01-01
Conformal transformations in four-dimensional. In particular, a new set of two necessary and sufficient conditions for a space to be conformal to an Einstein space is presented. The first condition defines the class of spaces conformal to C spaces, whereas the last one (the vanishing of the Bach tensor) gives the particular subclass of C spaces which are conformally related to Einstein spaces. (author)
National Aeronautics and Space Administration — OBJECTIVES The proposed research will combine the areas of compliant mechanisms and space technology. Compliant mechanisms perform their function through the elastic...
Chistyakov, Vyacheslav
2015-01-01
Aimed toward researchers and graduate students familiar with elements of functional analysis, linear algebra, and general topology; this book contains a general study of modulars, modular spaces, and metric modular spaces. Modulars may be thought of as generalized velocity fields and serve two important purposes: generate metric spaces in a unified manner and provide a weaker convergence, the modular convergence, whose topology is non-metrizable in general. Metric modular spaces are extensions of metric spaces, metric linear spaces, and classical modular linear spaces. The topics covered include the classification of modulars, metrizability of modular spaces, modular transforms and duality between modular spaces, metric and modular topologies. Applications illustrated in this book include: the description of superposition operators acting in modular spaces, the existence of regular selections of set-valued mappings, new interpretations of spaces of Lipschitzian and absolutely continuous mappings, the existe...
Perturbative S-matrix for massive scalar fields in global de Sitter space
International Nuclear Information System (INIS)
Marolf, Donald; Srednicki, Mark; Morrison, Ian A
2013-01-01
We construct a perturbative S-matrix for interacting massive scalar fields in global de Sitter space. Our S-matrix is formulated in terms of asymptotic particle states in the far past and future, taking appropriate care for light fields whose wavefunctions decay only very slowly near the de Sitter conformal boundaries. An alternative formulation expresses this S-matrix in terms of residues of poles in analytically-continued Euclidean correlators (computed in perturbation theory), making it clear that the standard Minkowski-space result is obtained in the flat-space limit. Our S-matrix transforms properly under CPT, is invariant under the de Sitter isometries and perturbative field redefinitions, and is unitary. This unitarity implies a de Sitter version of the optical theorem. We explicitly verify these properties to second order in the coupling for a general cubic interaction, including both tree- and loop-level contributions. Contrary to other statements in the literature, we find that a particle of any positive mass may decay at tree level to any number of particles, each of arbitrary positive masses. In particular, even very light fields (in the complementary series of de Sitter representations) are not protected from tree-level decays. (paper)
Space Toxicology: Human Health during Space Operations
Khan-Mayberry, Noreen; James, John T.; Tyl, ROchelle; Lam, Chiu-Wing
2010-01-01
Space Toxicology is a unique and targeted discipline for spaceflight, space habitation and occupation of celestial bodies including planets, moons and asteroids. Astronaut explorers face distinctive health challenges and limited resources for rescue and medical care during space operation. A central goal of space toxicology is to protect the health of the astronaut by assessing potential chemical exposures during spaceflight and setting safe limits that will protect the astronaut against chemical exposures, in a physiologically altered state. In order to maintain sustained occupation in space on the International Space Station (ISS), toxicological risks must be assessed and managed within the context of isolation continuous exposures, reuse of air and water, limited rescue options, and the need to use highly toxic compounds for propulsion. As we begin to explore other celestial bodies in situ toxicological risks, such as inhalation of reactive mineral dusts, must also be managed.
Sequence spaces M ( ϕ $M(\\phi$ and N ( ϕ $N(\\phi$ with application in clustering
Directory of Open Access Journals (Sweden)
Mohd Shoaib Khan
2017-03-01
Full Text Available Abstract Distance measures play a central role in evolving the clustering technique. Due to the rich mathematical background and natural implementation of l p $l_{p}$ distance measures, researchers were motivated to use them in almost every clustering process. Beside l p $l_{p}$ distance measures, there exist several distance measures. Sargent introduced a special type of distance measures m ( ϕ $m(\\phi$ and n ( ϕ $n(\\phi$ which is closely related to l p $l_{p}$ . In this paper, we generalized the Sargent sequence spaces through introduction of M ( ϕ $M(\\phi$ and N ( ϕ $N(\\phi$ sequence spaces. Moreover, it is shown that both spaces are BK-spaces, and one is a dual of another. Further, we have clustered the two-moon dataset by using an induced M ( ϕ $M(\\phi$ -distance measure (induced by the Sargent sequence space M ( ϕ $M(\\phi$ in the k-means clustering algorithm. The clustering result established the efficacy of replacing the Euclidean distance measure by the M ( ϕ $M(\\phi$ -distance measure in the k-means algorithm.
Johnson, R. D.
1977-01-01
Organic cosmochemistry, organic materials in space exploration, and biochemistry of man in space are briefly surveyed. A model of Jupiter's atmosphere is considered, and the search for organic molecules in the solar system and in interstellar space is discussed. Materials and analytical techniques relevant to space exploration are indicated, and the blood and urine analyses performed on Skylab are described.
Harris, Watson
2011-01-01
There are many articles about space management, including those that discuss space calculations, metrics, and categories. Fewer articles discuss the space budgeting processes used by administrators to allocate space. The author attempts to fill this void by discussing her administrative experiences with Middle Tennessee State University's (MTSU)…
Space Guidelines for Libraries.
Wisconsin Coordinating Committee for Higher Education, Madison.
The following guidelines are recommended: stack space--for each 10 volumes, one square foot of space; reading room--25 square feet per station x 20% of the total undergraduate population; carrel space--25% of the graduate enrollment x 45 square feet; office and auxilliary space--135 square feet x full time equivalent staff. (NI)
Space Physiology and Operational Space Medicine
Scheuring, Richard A.
2009-01-01
The objectives of this slide presentation are to teach a level of familiarity with: the effects of short and long duration space flight on the human body, the major medical concerns regarding future long duration missions, the environmental issues that have potential medical impact on the crew, the role and capabilities of the Space Medicine Flight Surgeon and the environmental impacts experienced by the Apollo crews. The main physiological effects of space flight on the human body reviewed in this presentation are: space motion sickness (SMS), neurovestibular, cardiovascular, musculoskeletal, immune/hematopoietic system and behavioral/psycho-social. Some countermeasures are discussed to these effects.
National Space Agencies vs. Commercial Space: Towards Improved Space Safety
Pelton, J.
2013-09-01
Traditional space policies as developed at the national level includes many elements but they are most typically driven by economic and political objectives. Legislatively administered programs apportion limited public funds to achieve "gains" that can involve employment, stimulus to the economy, national defense or other advancements. Yet political advantage is seldom far from the picture.Within the context of traditional space policies, safety issues cannot truly be described as "afterthoughts", but they are usually, at best, a secondary or even tertiary consideration. "Space safety" is often simply assumed to be "in there" somewhere. The current key question is can "safety and risk minimization", within new commercial space programs actually be elevated in importance and effectively be "designed in" at the outset. This has long been the case with commercial aviation and there is at least reasonable hope that this could also be the case for the commercial space industry in coming years. The cooperative role that the insurance industry has now played for centuries in the shipping industry and for decades in aviation can perhaps now play a constructive role in risk minimization in the commercial space domain as well. This paper begins by examining two historical case studies in the context of traditional national space policy development to see how major space policy decisions involving "manned space programs" have given undue primacy to "political considerations" over "safety" and other factors. The specific case histories examined here include first the decision to undertake the Space Shuttle Program (i.e. 1970-1972) and the second is the International Space Station. In both cases the key and overarching decisions were driven by political, schedule and cost considerations, and safety seems absence as a prime consideration. In publicly funded space programs—whether in the United States, Europe, Russia, Japan, China, India or elsewhere—it seems realistic to
Energy Technology Data Exchange (ETDEWEB)
Reeves, Geoffrey D. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2017-08-10
To advance our understanding of the space environment (from the Sun to the Earth and beyond) and to advance our ability to operate systems in space that protect life and society. Space Science is distinct from other field, such as astrophysics or cosmology, in that Space Science utilizes in-situ measurements from high altitude rockets, balloons and spacecraft or ground-based measurements of objects and conditions in space.
Pseiner, K.; Balogh, W.
2002-01-01
After several years of preparation and discussion among the involved players, the Austrian Space Plan was approved for implementation in November 2001. Based on careful benchmarking and analysis of the capabilities of the Austrian space sector it aims to create excellent conditions for the sector's further development. The new space strategy embraces Austria's participation in the mandatory and optional programmes of the European Space Agency and establishes a National Space Programme supported by separate funding opportunities. A set of clearly-defined indicators ensures that the progress in implementing the Space Plan can be objectively judged through independent, annual reviews. The National Space Programme promotes international cooperation in space research and space activities with the aim to strengthen the role of space science and to better prepare Austrian space industry for the commercial space market. In the framework of the Space Plan the Austrian Space Agency has been tasked with integrating the industry's growing involvement in aeronautics activities to better utilize synergies with the space sector. This paper reviews the various steps leading to the approval of the new space strategy and discusses the hurdles mastered in this process. It reports on the Space Plan's first results, specifically taking into account projects involving international cooperation. For the first the Austria aerospace-sector can rely on an integrated strategy for aeronautics- and space activities which is firmly rooted in the efforts to enhance the country's R&D activities. It may also act as a useful example for other small space- using countries planning to enhance their involvement in space activities.
Esrange Space Center, a Gate to Space
Widell, Ola
Swedish Space Corporation (SSC) is operating the Esrange Space Center in northern Sweden. Space operations have been performed for more than 40 years. We have a unique combination of maintaining balloon and rocket launch operations, and building payloads, providing space vehicles and service systems. Sub-orbital rocket flights with land recovery and short to long duration balloon flights up to weeks are offered. The geographical location, land recovery area and the long term experience makes Swedish Space Corporation and Esrange to an ideal gate for space activities. Stratospheric balloons are primarily used in supporting atmospheric research, validation of satellites and testing of space systems. Balloon operations have been carried out at Esrange since 1974. A large number of balloon flights are yearly launched in cooperation with CNES, France. Since 2005 NASA/CSBF and Esrange provide long duration balloon flights to North America. Flight durations up to 5 days with giant balloons (1.2 Million cubic metres) carrying heavy payload (up to 2500kg) with astronomical instruments has been performed. Balloons are also used as a crane for lifting space vehicles or parachute systems to be dropped and tested from high altitude. Many scientific groups both in US, Europe and Japan have indicated a great need of long duration balloon flights. Esrange will perform a technical polar circum balloon flight during the summer 2008 testing balloon systems and flight technique. We are also working on a permission giving us the opportunity on a circular stratospheric balloon flight around the North Pole.
Unification of Quantum and Gravity by Non Classical Information Entropy Space
Directory of Open Access Journals (Sweden)
Davide Fiscaletti
2013-09-01
Full Text Available A quantum entropy space is suggested as the fundamental arena describing the quantum effects. In the quantum regime the entropy is expressed as the superposition of many different Boltzmann entropies that span the space of the entropies before any measure. When a measure is performed the quantum entropy collapses to one component. A suggestive reading of the relational interpretation of quantum mechanics and of Bohm’s quantum potential in terms of the quantum entropy are provided. The space associated with the quantum entropy determines a distortion in the classical space of position, which appears as a Weyl-like gauge potential connected with Fisher information. This Weyl-like gauge potential produces a deformation of the moments which changes the classical action in such a way that Bohm’s quantum potential emerges as consequence of the non classical definition of entropy, in a non-Euclidean information space under the constraint of a minimum condition of Fisher information (Fisher Bohm- entropy. Finally, the possible quantum relativistic extensions of the theory and the connections with the problem of quantum gravity are investigated. The non classical thermodynamic approach to quantum phenomena changes the geometry of the particle phase space. In the light of the representation of gravity in ordinary phase space by torsion in the flat space (Teleparallel gravity, the change of geometry in the phase space introduces quantum phenomena in a natural way. This gives a new force to F. Shojai’s and A. Shojai’s theory where the geometry of space-time is highly coupled with a quantum potential whose origin is not the Schrödinger equation but the non classical entropy of a system of many particles that together change the geometry of the phase space of the positions (entanglement. In this way the non classical thermodynamic changes the classical geodetic as a consequence of the quantum phenomena and quantum and gravity are unified. Quantum
SpaceTech—Postgraduate space education
de Bruijn, Ferdi J.; Ashford, Edward W.; Larson, Wiley J.
2008-07-01
SpaceTech is a postgraduate program geared primarily for mid-career space professionals seeking to gain or improve their expertise in space systems engineering and in business engineering. SpaceTech provides a lifelong impact on its participants by broadening their capabilities, encouraging systematic "end-to-end" thinking and preparing them for any technical or business-related engineering challenges they may encounter. This flexible 1-year program offers high competency gain and increased business skills. It is held in attractive locations in a flexible, multi-cultural environment. SpaceTech is a highly effective master's program certified by the esteemed Technical University of Delft (TUD), Netherlands. SpaceTech provides expert instructors who place no barriers between themselves and participants. The program combines innovative and flexible new approaches with time-tested methods to give participants the skills required for future missions and new business, while allowing participants to meet their work commitments at the same time as they study for their master's degree. The SpaceTech program is conducted in separate sessions, generally each of 2-week duration, separated by periods of some 6-8 weeks, during which time participants may return to their normal jobs. It also includes introductory online course material that the participants can study at their leisure. The first session is held at the TUD, with subsequent sessions held at strategic space agency locations. By participating at two or more of these sessions, attendees can earn certificates of satisfactory completion from TU Delft. By participating in all of the sessions, as well as taking part in the companion Central Case Project (CCP), participants earn an accredited and highly respected master's degree in Space Systems Engineering from the TUD. Seven distinct SpaceTech modules are provided during these sessions: Space Mission Analysis and Design, Systems Engineering, Business Engineering
Institute of Scientific and Technical Information of China (English)
YAO BIN
2011-01-01
With the successful launch of Tiangong-I (Heavenly Palace -I)unmanned module on September 29,China took a significant step forward in realizing its ambitions in space.China's manned space program consists of three steps.The first step,to send an astronaut into space,was achieved in 2003.The second step,to realize multi-person space flight for extended periods of time,has been fulfilled twice.During China's third manned space flight in 2008,Chinese astronauts walked in space.
Free topological vector spaces
Gabriyelyan, Saak S.; Morris, Sidney A.
2016-01-01
We define and study the free topological vector space $\\mathbb{V}(X)$ over a Tychonoff space $X$. We prove that $\\mathbb{V}(X)$ is a $k_\\omega$-space if and only if $X$ is a $k_\\omega$-space. If $X$ is infinite, then $\\mathbb{V}(X)$ contains a closed vector subspace which is topologically isomorphic to $\\mathbb{V}(\\mathbb{N})$. It is proved that if $X$ is a $k$-space, then $\\mathbb{V}(X)$ is locally convex if and only if $X$ is discrete and countable. If $X$ is a metrizable space it is shown ...
Isometries on Banach spaces function spaces
Fleming, Richard J
2002-01-01
Fundamental to the study of any mathematical structure is an understanding of its symmetries. In the class of Banach spaces, this leads naturally to a study of isometries-the linear transformations that preserve distances. In his foundational treatise, Banach showed that every linear isometry on the space of continuous functions on a compact metric space must transform a continuous function x into a continuous function y satisfying y(t) = h(t)x(p(t)), where p is a homeomorphism and |h| is identically one.Isometries on Banach Spaces: Function Spaces is the first of two planned volumes that survey investigations of Banach-space isometries. This volume emphasizes the characterization of isometries and focuses on establishing the type of explicit, canonical form given above in a variety of settings. After an introductory discussion of isometries in general, four chapters are devoted to describing the isometries on classical function spaces. The final chapter explores isometries on Banach algebras.This treatment p...
Directory of Open Access Journals (Sweden)
Andrei Khrennikov
2016-07-01
Full Text Available We present a new conceptual approach for modeling of fluid flows in random porous media based on explicit exploration of the treelike geometry of complex capillary networks. Such patterns can be represented mathematically as ultrametric spaces and the dynamics of fluids by ultrametric diffusion. The images of p-adic fields, extracted from the real multiscale rock samples and from some reference images, are depicted. In this model the porous background is treated as the environment contributing to the coefficients of evolutionary equations. For the simplest trees, these equations are essentially less complicated than those with fractional differential operators which are commonly applied in geological studies looking for some fractional analogs to conventional Euclidean space but with anomalous scaling and diffusion properties. It is possible to solve the former equation analytically and, in particular, to find stationary solutions. The main aim of this paper is to attract the attention of researchers working on modeling of geological processes to the novel utrametric approach and to show some examples from the petroleum reservoir static and dynamic characterization, able to integrate the p-adic approach with multifractals, thermodynamics and scaling. We also present a non-mathematician friendly review of trees and ultrametric spaces and pseudo-differential operators on such spaces.
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
International Nuclear Information System (INIS)
Red'kov, V.M.; Ovsiyuk, E.M.; Ishkhanyan, A.M.
2013-01-01
The Schrodinger particle on the background of the 2D space of the constant positive curvature S 2 , a sphere in the 3D Euclidean space, is considered in the external magnetic field. By analogy with the case of the hyperbolic Lobachevsky plane H 2 , where quasi-Cartesian coordinates exist with the realization of H 2 as the Poincare half-plane, a specific system of quasi-Cartesian coordinates (x, y) in S 2 is introduced. It turns out that it is possible only if the two coordinates are complex and obey an additional restriction in order to present a real 2D space. The Schrodinger equation is solved using the method of separation of the variables in the both coordinate systems, cylindrical and quasi-Cartesian, the energy spectrum is the same. For parametrization of the space S 2 , one can use the coordinates (x, x*) or (y, y*), however, in this case the separability of the variables in the wave functions is lost. Constructed solutions may be of interest for describing charged particles in magnetic fields in the context of cosmological models, and for simulating the behavior of the particles in a specific field-configuration in the nano-physics. (authors)
Centrioles in Symmetric Spaces
Quast, Peter
2011-01-01
We describe all centrioles in irreducible simply connected pointed symmetric spaces of compact type in terms of the root system of the ambient space, and we study some geometric properties of centrioles.
Olafsson, Gestur; Helgason, Sigurdur
1996-01-01
This book is intended to introduce researchers and graduate students to the concepts of causal symmetric spaces. To date, results of recent studies considered standard by specialists have not been widely published. This book seeks to bring this information to students and researchers in geometry and analysis on causal symmetric spaces.Includes the newest results in harmonic analysis including Spherical functions on ordered symmetric space and the holmorphic discrete series and Hardy spaces on compactly casual symmetric spacesDeals with the infinitesimal situation, coverings of symmetric spaces, classification of causal symmetric pairs and invariant cone fieldsPresents basic geometric properties of semi-simple symmetric spacesIncludes appendices on Lie algebras and Lie groups, Bounded symmetric domains (Cayley transforms), Antiholomorphic Involutions on Bounded Domains and Para-Hermitian Symmetric Spaces
National Aeronautics and Space Administration — The Deep Space Habitat was closed out at the end of Fiscal Year 2013 (September 30, 2013). Results and select content have been incorporated into the new Exploration...
Schweizer, B
2005-01-01
Topics include special classes of probabilistic metric spaces, topologies, and several related structures, such as probabilistic normed and inner-product spaces. 1983 edition, updated with 3 new appendixes. Includes 17 illustrations.
DEFF Research Database (Denmark)
Bjerrum, Peter; Olsen, Kasper Nefer
2001-01-01
Inform@ed space Sensorial Perception And Computer Enchancement - bidrag til Nordisk Arkitekturforskningsforenings IT-konference, AAA april 2001.......Inform@ed space Sensorial Perception And Computer Enchancement - bidrag til Nordisk Arkitekturforskningsforenings IT-konference, AAA april 2001....
National Aeronautics and Space Administration — The Space Robotics Challenge seeks to infuse robot autonomy from the best and brightest research groups in the robotics community into NASA robots for future...
Tarver, William J.
2012-01-01
Learning Objectives are: (1) Understand the unique work environment of astronauts. (2) Understand the effect microgravity has on human physiology (3) Understand how NASA Space Medicine Division is mitigating the health risks of space missions.
Stereotype locally convex spaces
International Nuclear Information System (INIS)
Akbarov, S S
2000-01-01
We give complete proofs of some previously announced results in the theory of stereotype (that is, reflexive in the sense of Pontryagin duality) locally convex spaces. These spaces have important applications in topological algebra and functional analysis
Stereotype locally convex spaces
Energy Technology Data Exchange (ETDEWEB)
Akbarov, S S
2000-08-31
We give complete proofs of some previously announced results in the theory of stereotype (that is, reflexive in the sense of Pontryagin duality) locally convex spaces. These spaces have important applications in topological algebra and functional analysis.
Stereotype locally convex spaces
Akbarov, S. S.
2000-08-01
We give complete proofs of some previously announced results in the theory of stereotype (that is, reflexive in the sense of Pontryagin duality) locally convex spaces. These spaces have important applications in topological algebra and functional analysis.
National Aeronautics and Space Administration — Payload mass reduction and packaging efficiency in launch vehicles are essential for deep space exploration. Inflatable softgoods have been identified as attractive...
Space Radiation Risk Assessment
National Aeronautics and Space Administration — Project A: Integration and Review: A review of current knowledge from space radiation physics was accepted for publication in Reviews of Modern Physics (Durante and...
Federal Laboratory Consortium — The Space Power Facility (SPF) houses the world's largest space environment simulation chamber, measuring 100 ft. in diameter by 122 ft. high. In this chamber, large...
National Oceanic and Atmospheric Administration, Department of Commerce — Collection includes presentation materials and outputs from operational space environment models produced by the NOAA Space Weather Prediction Center (SWPC) and...
National Aeronautics and Space Administration — NASA has released a series of space sounds via sound cloud. We have abstracted away some of the hassle in accessing these sounds, so that developers can play with...
DEFF Research Database (Denmark)
Nilsson, Jørgen Fischer
1999-01-01
Conceptual spaces have been proposed as topological or geometric means for establishing conceptual structures and models. This paper, after briey reviewing conceptual spaces, focusses on the relationship between conceptual spaces and logical concept languages with operations for combining concepts...... to form concepts. Speci cally is introduced an algebraic concept logic, for which conceptual spaces are installed as semantic domain as replacement for, or enrichment of, the traditional....
Space Shuttle Endeavour launch
1992-01-01
A smooth countdown culminated in a picture-perfect launch as the Space Shuttle Endeavour (STS-47) climbed skyward atop a ladder of billowing smoke. Primary payload for the plarned seven-day flight was Spacelab-J science laboratory. The second flight of Endeavour marks a number of historic firsts: the first space flight of an African-American woman, the first Japanese citizen to fly on a Space Shuttle, and the first married couple to fly in space.
On Space Warfare: A Space Power Doctrine
National Research Council Canada - National Science Library
Lupton, David
1998-01-01
.... Nevertheless, the speech was promptly dubbed "Star Wars" because the space environment seems to be the most likely place to deploy a ballistic missile defense system, and several administration...
Space tourism risks: A space insurance perspective
Bensoussan, Denis
2010-06-01
Space transportation is inherently risky to humans, whether they are trained astronauts or paying tourists, given that spaceflight is still in its relative infancy. However, this is easy to forget when subjected to the hype often associated with space tourism and the ventures seeking to enter that market. The development of commercial spaceflight constitutes a challenge as much as a great opportunity to the insurance industry as new risks emerge and standards, policies and procedures to minimise/mitigate and cover them still to be engineered. Therefore the creation of a viable and affordable insurance regime for future space tourists is a critical step in the development of a real space tourism market to address burning risk management issues that may otherwise ultimately hamper this nascent industry before it has a chance to prove itself.
Pick, Luboš; John, Oldrich; Fucík, Svatopluk
2012-01-01
This is the first part of the second revised and extended edition of a well established monograph. It is an introduction to function spaces defined in terms of differentiability and integrability classes. It provides a catalogue of various spaces and benefits as a handbook for those who use function spaces to study other topics such as partial differential equations. Volum
Institute of Scientific and Technical Information of China (English)
无
2011-01-01
With the successful launch of Tiangong-1 (Heavenly Palace-1) unmanned module on September 29,China took a significant step forward in realizing its ambitions in space.China’s manned space program consists of three steps.The first step,to send an astronaut into space,was achieved in 2003.The
Institute of Scientific and Technical Information of China (English)
无
2011-01-01
China launches a prototype space module as a precursor to a manned space station China’s first unmanned space module Tiangong-1,or Heavenly Palace-1,successfully lifted off from the Jiuquan Satellite Launch Center in northwest China’s Gansu Province on September 29. "The successful launch of the 8.5-ton
DEFF Research Database (Denmark)
Bank, Mads; Nissen, Morten
2017-01-01
The article articulates experiments with spatial constructions in two Danish social work agencies, basing on (a) a sketchy genealogical reconstruction of conceptualisations and uses of space in social work and counselling, (b) a search for theoretical resources to articulate new spaces, and (c...... spaces are forms of spatialisations which might be taken as prototypical in attempts to develop social work and counselling...
Kuiper, T. B. H.; Resch, G. M.
2000-01-01
The increasing load on NASA's deep Space Network, the new capabilities for deep space missions inherent in a next-generation radio telescope, and the potential of new telescope technology for reducing construction and operation costs suggest a natural marriage between radio astronomy and deep space telecommunications in developing advanced radio telescope concepts.
Anton TenWolde; Samuel V. Glass
2013-01-01
Crawl space foundations can be designed and built to avoid moisture problems. In this article we provide a brief overview of crawl spaces with emphasis on the physics of moisture. We review trends that have been observed in the research literature and summarize cur-rent recommendations for moisture control in crawl spaces.
Koenderink, Jan J.; van Doorn, Andrea J.; Kappers, Astrid M L; Todd, James T.
Optical space differs from physical space. The structure of optical space has generally been assumed to be metrical. In contradistinction, we do not assume any metric, but only incidence relations (i.e., we assume that optical points and lines exist and that two points define a unique line, and two
Koenderink, J.J.; Doorn, A.J. van; Kappers, A.M.L.; Todd, J.T.
2002-01-01
Optical space differs from physical space. The structure of optical space has generallybeen assumed to be metrical. In contradistinction,we do not assume anymetric, but only incidence relations (i.e., we assume that optical points and lines exist and that two points define a unique line, and two
International Nuclear Information System (INIS)
Fry, R.J.M.
1987-07-01
As more people spend more time in space, and the return to the moon and exploratory missions are considered, the risks require continuing examination. The effects of microgravity and radiation are two potential risks in space. These risks increase with increasing mission duration. This document considers the risk of radiation effects in space workers and explorers. 17 refs., 1 fig., 4 tabs
Felix, Elliot
2011-01-01
Much progress has been made in creating informal learning spaces that incorporate technology and flexibly support a variety of activities. This progress has been principally in designing the right combination of furniture, technology, and space. However, colleges and universities do not design services within learning spaces with nearly the same…
Directory of Open Access Journals (Sweden)
Saleh LAshkari
2016-06-01
Full Text Available Selecting optimal features based on nature of the phenomenon and high discriminant ability is very important in the data classification problems. Since it doesn't require any assumption about stationary condition and size of the signal and the noise in Recurrent Quantification Analysis (RQA, it may be useful for epileptic seizure Detection. In this study, RQA was used to discriminate ictal EEG from the normal EEG where optimal features selected by combination of algorithm genetic and Bayesian Classifier. Recurrence plots of hundred samples in each two categories were obtained with five distance norms in this study: Euclidean, Maximum, Minimum, Normalized and Fixed Norm. In order to choose optimal threshold for each norm, ten threshold of ε was generated and then the best feature space was selected by genetic algorithm in combination with a bayesian classifier. The results shown that proposed method is capable of discriminating the ictal EEG from the normal EEG where for Minimum norm and 0.1˂ε˂1, accuracy was 100%. In addition, the sensitivity of proposed framework to the ε and the distance norm parameters was low. The optimal feature presented in this study is Trans which it was selected in most feature spaces with high accuracy.
Tavana, Madjid
2005-01-01
"To understand and protect our home planet, to explore the universe and search for life, and to inspire the next generation of explorers" is NASA's mission. The Systems Management Office at Johnson Space Center (JSC) is searching for methods to effectively manage the Center's resources to meet NASA's mission. D-Side is a group multi-criteria decision support system (GMDSS) developed to support facility decisions at JSC. D-Side uses a series of sequential and structured processes to plot facilities in a three-dimensional (3-D) graph on the basis of each facility alignment with NASA's mission and goals, the extent to which other facilities are dependent on the facility, and the dollar value of capital investments that have been postponed at the facility relative to the facility replacement value. A similarity factor rank orders facilities based on their Euclidean distance from Ideal and Nadir points. These similarity factors are then used to allocate capital improvement resources across facilities. We also present a parallel model that can be used to support decisions concerning allocation of human resources investments across workforce units. Finally, we present results from a pilot study where 12 experienced facility managers from NASA used D-Side and the organization's current approach to rank order and allocate funds for capital improvement across 20 facilities. Users evaluated D-Side favorably in terms of ease of use, the quality of the decision-making process, decision quality, and overall value-added. Their evaluations of D-Side were significantly more favorable than their evaluations of the current approach. Keywords: NASA, Multi-Criteria Decision Making, Decision Support System, AHP, Euclidean Distance, 3-D Modeling, Facility Planning, Workforce Planning.
Planning of Green Space Ecological Network in Urban Areas: An Example of Nanchang, China.
Li, Haifeng; Chen, Wenbo; He, Wei
2015-10-15
Green space plays an important role in sustainable urban development and ecology by virtue of multiple environmental, recreational, and economic benefits. Constructing an effective and harmonious urban ecological network and maintaining a sustainable living environment in response to rapid urbanization are the key issues required to be resolved by landscape planners. In this paper, Nanchang City, China was selected as a study area. Based on a series of landscape metrics, the landscape pattern analysis of the current (in 2005) and planned (in 2020) green space system were, respectively, conducted by using FRAGSTATS 3.3 software. Considering the actual situation of the Nanchang urban area, a "one river and two banks, north and south twin cities" ecological network was constructed by using network analysis. Moreover, the ecological network was assessed by using corridor structure analysis, and the improvement of an ecological network on the urban landscape was quantitatively assessed through a comparison between the ecological network and green space system planning. The results indicated that: (1) compared to the green space system in 2005, the planned green space system in 2020 of the Nanchang urban area will decline in both districts (Changnan and Changbei districts). Meanwhile, an increase in patch density and a decrease in mean patch size of green space patches at the landscape level implies the fragmentation of the urban green space landscape. In other words, the planned green space system does not necessarily improve the present green space system; (2) the ecological network of two districts has high corridor density, while Changnan's ecological network has higher connectivity, but Changbei's ecological network is more viable from an economic point of view, since it has relatively higher cost efficiency; (3) decrease in patch density, Euclidean nearest neighbor distance, and an increase in mean patch size and connectivity implied that the ecological network
Institute of Scientific and Technical Information of China (English)
YIN PUMIN
2011-01-01
China's first unmanNed space module Tiangong-Ⅰ,or Heavenly Palace-Ⅰ,successfully lifted off from the Jiuquan Satellite Launch Center in northwest China's Gansu Province on September 29."The successful launch of the 8.5-ton prototype space laboratory has opened the gates for China's deep space exploration program," said Qi Faren,former chief designer of China's Shenzhou spacecraft.“It is a decisive leap forward for the Chinese space industry and will bring about the rapid development of space science and related techologies."
Institute of Scientific and Technical Information of China (English)
Yin Pumin
2011-01-01
CHINA'S first unmanned space module Tiangong-1,or Heavenly Palace-1,successfully lifted off from the Jiuquan Satellite Launch Center in northwest China's Gansu Province on September 29."The successfullaunch of the 8.5-ton prototype space laboratory has opened the gates for China's deep space exploration program," said Qi Faren,former chief designer of China's Shenzhou spacecraft."It is a decisive leap forward for the Chinese space industry and will bring about the rapid development of space science and related technologies."
Space Station Habitability Research
Clearwater, Yvonne A.
1988-01-01
The purpose and scope of the Habitability Research Group within the Space Human Factors Office at the NASA/Ames Research Center is described. Both near-term and long-term research objectives in the space human factors program pertaining to the U.S. manned Space Station are introduced. The concept of habitability and its relevancy to the U.S. space program is defined within a historical context. The relationship of habitability research to the optimization of environmental and operational determinants of productivity is discussed. Ongoing habitability research efforts pertaining to living and working on the Space Station are described.
International Nuclear Information System (INIS)
Willis, W.L.; Ahrendt, M.R.
2009-01-01
Since this report was originally issued in 2001, several options proposed for increasing double-shell tank (DST) storage space were implemented or are in the process of implementation. Changes to the single-shell tank (SST) waste retrieval schedule, completion of DST space saving options, and the DST space saving options in progress have delayed the projected shortfall of DST storage space from the 2007-2011 to the 2018-2025 timeframe (ORP-11242, River Protection Project System Plan). This report reevaluates options from Rev. 0 and includes evaluations of new options for alleviating projected restrictions on SST waste retrieval beginning in 2018 because of the lack of DST storage space.
Judd, Stephen; Dallmann, Nicholas; Seitz, Daniel; Martinez, John; Storms, Steven; Kestell, Gayle
2017-07-18
A modular space vehicle chassis may facilitate convenient access to internal components of the space vehicle. Each module may be removable from the others such that each module may be worked on individually. Multiple panels of at least one of the modules may swing open or otherwise be removable, exposing large portions of the internal components of the space vehicle. Such chassis architectures may reduce the time required for and difficulty of performing maintenance or modifications, may allow multiple space vehicles to take advantage of a common chassis design, and may further allow for highly customizable space vehicles.
International Nuclear Information System (INIS)
Kowalski-Glikman, J.
2009-01-01
In this paper we construct, and investigate some thermal properties of, the noncommutative counterpart of Rindler space, which we call κ-Rindler space. This space is obtained by changing variables in the defining commutators of κ-Minkowski space. We then rederive the commutator structure of κ-Rindler space with the help of an appropriate star product, obtained from the κ-Minkowski one. Using this star product, following the idea of Padmanabhan, we find the leading order, 1/κ correction to the Hawking thermal spectrum.
DEFF Research Database (Denmark)
Unterrainer, Walter
2014-01-01
art and architectural space museums and other exhibition spaces or how artists learn to love architects Over the last two decades, innumerable new museums, art galleries and other exhibition spaces have been built and opened all over the globe. The most extreme growth happened in China, where...... purpose of ´uniqueness´ often fail to be a ´home´, a large scale ´picture frame´ or a productive space for communicating art and even do not fulfil basic technical aspects in terms of a consistent indoor climate, optimized lighting or safety. The lecture will focus on inspiring examples of spaces for art...
INFORMATION SPACE– EDUCATIONAL SPACE
Directory of Open Access Journals (Sweden)
Monica LIA
2015-11-01
Full Text Available This paper has set the objective of researching how education is influenced by the information society. The first step was to define more precisely the information space. The second step was to identify how information space intersects with the family space and institutional space educational levels represented by pre-school / school and pre-university (kindergarten, at elementary / middle school / high school. Interrelationship between the above mentioned areas was another objective of the research. All these elements have been investigated through the original intention to identify how the information space can become an educational tool to support the family space, education and institutional space. Also, the aim of this research is to offer some solutions in this regard. Often the educational efforts appear to be blocked by the existence of this space. But this paper demonstrates that Informational space can be an enemy of the educational system or can support systems if we knew the internal structure and mechanisms. We can make the Informational Space to work in order to accomplish the educational scope.
Energy Technology Data Exchange (ETDEWEB)
Zhang, Jian-dong [TianQin Research Center for Gravitational Physics, Sun Yat-sen University, Zhuhai 519082, Guangdong (China); Chen, Bin [Department of Physics and State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing 100871 (China); Collaborative Innovation Center of Quantum Matter, 5 Yiheyuan Rd, Beijing 100871 (China); Center for High Energy Physics, Peking University, 5 Yiheyuan Rd, Beijing 100871 (China)
2017-01-23
The kinematic space could play a key role in constructing the bulk geometry from dual CFT. In this paper, we study the kinematic space from geometric points of view, without resorting to differential entropy. We find that the kinematic space could be intrinsically defined in the embedding space. For each oriented geodesic in the Poincaré disk, there is a corresponding point in the kinematic space. This point is the tip of the causal diamond of the disk whose intersection with the Poincaré disk determines the geodesic. In this geometric construction, the causal structure in the kinematic space can be seen clearly. Moreover, we find that every transformation in the SL(2,ℝ) leads to a geodesic in the kinematic space. In particular, for a hyperbolic transformation defining a BTZ black hole, it is a timelike geodesic in the kinematic space. We show that the horizon length of the static BTZ black hole could be computed by the geodesic length of corresponding points in the kinematic space. Furthermore, we discuss the fundamental regions in the kinematic space for the BTZ blackhole and multi-boundary wormholes.
Dual spaces of local Morrey-type spaces
Gogatishvili, A. (Amiran); Mustafayev, R. (Rza)
2011-01-01
In this paper we show that associated spaces and dual spaces of the local Morrey-type spaces are so called complementary local Morrey-type spaces. Our method is based on an application of multidimensional reverse Hardy inequalities.
Space Power Theory: Controlling the Medium Without Weapons in Space
National Research Council Canada - National Science Library
Wilkerson, Don L
2008-01-01
.... strategic space assets and the ability to negate enemy space systems is essential to U.S. space strategy in controlling the geographical environment of space, predominately in the Lower Earth Orbit (LEO...
Johnson, Christopher Daniel
2018-01-01
Negotiated at the United Nations and in force since 1967, the Outer Space Treaty has been ratified by over 100 countries and is the most important and foundational source of space law. The treaty, whose full title is "Treaty on Principles Governing the Activities of States in the Exploration and Use of Outer Space, Including the Moon and Other Celestial Bodies," governs all of humankind's activities in outer space, including activities on other celestial bodies and many activities on Earth related to outer space. All space exploration and human spaceflight, planetary sciences, and commercial uses of space—such as the global telecommunications industry and the use of space technologies such as position, navigation, and timing (PNT), take place against the backdrop of the general regulatory framework established in the Outer Space Treaty. A treaty is an international legal instrument which balances rights and obligations between states, and exists as a kind of mutual contract of shared understandings, rights, and responsibilities between them. Negotiated and drafted during the Cold War era of heightened political tensions, the Outer Space Treaty is largely the product of efforts by the United States and the USSR to agree on certain minimum standards and obligations to govern their competition in "conquering" space. Additionally, the Outer Space Treaty is similar to other treaties, including treaties governing the high seas, international airspace, and the Antarctic, all of which govern the behavior of states outside of their national borders. The treaty is brief in nature and only contains 17 articles, and is not comprehensive in addressing and regulating every possible scenario. The negotiating states knew that the Outer Space Treaty could only establish certain foundational concepts such as freedom of access, state responsibility and liability, non-weaponization of space, the treatment of astronauts in distress, and the prohibition of non-appropriation of
Ignatiev, A.
2000-01-01
Contents include following: Developing Technologies for Space Resource Utilization - Concept for a Planetary Engineering Research Institute. Results of a Conceptual Systems Analysis of Systems for 200 m Deep Sampling of the Martian Subsurface. The Role of Near-Earth Asteroids in Long-Term Platinum Supply. Core Drilling for Extra-Terrestrial Mining. Recommendations by the "LSP and Manufacturing" Group to the NSF-NASA Workshop on Autonomous Construction and Manufacturing for Space Electrical Power Systems. Plasma Processing of Lunar and Planetary Materials. Percussive Force Magnitude in Permafrost. Summary of the Issues Regarding the Martian Subsurface Explorer. A Costing Strategy for Manufacturing in Orbit Using Extraterrestrial Resources. Mine Planning for Asteroid Orebodies. Organic-based Dissolution of Silicates: A New Approach to Element Extraction from LunarRegohth. Historic Frontier Processes Active in Future Space-based Mineral Extraction. The Near-Earth Space Surveillance (NIESS) Mission: Discovery, Tracking, and Characterization of Asteroids, Comets, and Artificial Satellites with a microsatellite. Privatized Space Resource Property Ownership. The Fabrication of Silicon Solar Cells on the Moon Using In-Situ Resources. A New Strategy for Exploration Technology Development: The Human Exploration and Development of Space (HEDS) Exploratiori/Commercialization Technology Initiative. Space Resources for Space Tourism. Recovery of Volatiles from the Moon and Associated Issues. Preliminary Analysis of a Small Robot for Martian Regolith Excavation. The Registration of Space-based Property. Continuous Processing with Mars Gases. Drilling and Logging in Space; An Oil-Well Perspective. LORPEX for Power Surges: Drilling, Rock Crushing. An End-To-End Near-Earth Asteroid Resource Exploitation Plan. An Engineering and Cost Model for Human Space Settlement Architectures: Focus on Space Hotels and Moon/Mars Exploration. The Development and Realization of a Silicon-60-based
Directory of Open Access Journals (Sweden)
Lisa Lynch
2017-01-01
Full Text Available This article examines how the preschool child is enabled to withdraw from the peer group and create a private, individual space within the institutional collective. The question under consideration is, “What factors are necessary to enable a child to create and maintain a withdrawal space in the preschool?” Data were collected through ethnographic fieldwork at two Montessori schools in the south of Sweden. Analysis of the results reveals that a child is enabled through a combination of two elements: a level of opportunity to create a space and a level of defense of a created space. These two factors are dependent on the teachers’ ability to correctly identify space creation, alongside their desire for the child’s space creation effort to be successful.