Search

Lyra geometry is a conformai geometry that originated from Weyl geometry. In this article, we derive the exterior field equation under a spherically symmetric gauge function [x.sup.0](r) and metric in Lyra geometry. When we impose a specific form of the gauge function [x.sup.0](r), the radial differential equation of the metric component [g.sub.00] will possess an irregular singular point (ISP) at r = 0. Moreover, we can apply the method of dominant balance to get the asymptotic behavior of the new space-time solution. The significance of this work is that we can use a series of smooth gauge functions [x.sup.0](r) to modulate the degree of divergence of the singularity at r =0, which will become a naked singularity under certain conditions. Furthermore, we investigate the physical meaning of this novel behavior of space-time in Lyra geometry and find out that no spaceship with finite integrated acceleration can arrive at this singularity at r =0. The physical meaning of the gauge function and integrability is also discussed. Key words: Lyra geometry, Weyl geometry, singularity, event horizon, dominant balance. La geometrie de Lyra est une geometrie conforme qui origine de la geometrie de Weyl. Dans ce travail, nous derivons l'equation du champ exterieur sous une fonction de jauge [x.sup.0](r) de symetrie spherique et une metrique en geometrie de Lyra. Quand nous imposons une forme specifique a la fonction de jauge [x.sup.0](r), l'equation differentielle radiale de la composante metrique [g.sub.00] possede alors un point singulier irregulier (PSI/ISP) a r = 0. De plus, nous appliquons la methode du comportement asymptotique dominant pour obtenir la forme asymptotique de notre nouvelle solution espace-temps. La signification de ce travail est que nous pourrions utiliser une serie de fonctions de jauge continues [x.sup.0](r) pour moduler le niveau de divergence de la singularite a r = 0, avec comme resultat que la singularite devient alors une singularite nue sous certaines conditions. De plus, nous analysons la signification physique de l'espace-temps dans la geometrie de Lyra et nous trouvons qu'aucun vaisseau spatial d'acceleration integree finie ne peut parvenir a la singularite a r =0. Nous discutons aussi la signification physique de la fonction de jauge et l'integrabilite. [Traduit par la Redaction] Mots-cles : geometrie de Lyra, singularite, horizon des evenements, comportement asymptotique dominant, geometrie de Weyl., 1. Introduction Weyl [1] created his version of generalized Riemannian geometry, Weyl geometry, to try to unify gravitation and electromagnetism. The structure of Weyl geometry is insightful because it has [...]

Distribution of the electric potential in a very long plate (for example, a long metal ruler) is determined. This is achieved by conformally mapping the plate into a plane, simplifying the geometry of the boundary conditions. Singularities of the potential are discussed as well as their regularization by the final size of electrical contacts. An analogy with renormalization is pointed out. Results are compared with previous studies. PACS Nos.: 01.55.+b, 03.50.De. Nous determinons la distribution du potentiel electrique dans une plaque tres longue (comme une regle metallique). Par transformation conforme, la regle devient un plan, simplifiant la geometrie des conditions limites. Nous analysons les singularites du potentiel, ainsi que leur regularisation suivant la dimension finie des contacts. Nous soulignons une analogie avec la renormalisation. Nous comparons nos resultats avec des etudes anterieures. [Traduit par la Redaction], 1. Introduction This paper is motivated by an intriguing question posed in an excellent collection of physics problems [1], based on an exam problem from the prestigious Moscow Institute of [...]

We investigate f(R, T) gravity models (where R is the curvature scalar and T is the trace of the stress-energy tensor of ordinary matter) that are able to reproduce the four known types of future finite-time singularities. We choose a suitable expression for the Hubble parameter to realise the cosmic acceleration and we introduce two parameters, [alpha] and [H.sub.s], which characterise each type of singularity. We address the conformal anomaly and we observe that it cannot remove the sudden singularity or the Big Brake, but, for some values of [alpha], the Big Rip and the Big Freeze may be avoided. We also find that, even without taking into account the conformal anomaly, the Big Rip and the Big Freeze may be removed thanks to the presence of the T contribution of the f(R, T) theory. PACS Nos.: 04.50.Kd, 95.35.+d, 95.36.+X, 98.80.Qc. Nous analysons les modeles de gravite f(R, T), ou R est la courbure scalaire et T la trace du tenseur d'energieimpulsion, qui sont capables de reproduire les quatre types connus de singularites des temps futurs. Nous choisissons une expression raisonnable pour le parametre de Hubble, de facon a realiser l'acceleration cosmique et nous introduisons deux parametres, [alpha] et [H.sub.s] qui caracterisent chaque type de singularite. Nous nous penchons sur l'anomalie conforme et nous observons qu'elle ne peut eliminer la Singularite Brusque ou le Grand Gel, mais pour certaines valeurs de [alpha], on evite la Grande Dechirure et le Grand Gel. Nous trouvons aussi qu'il est possible d'eliminer la Grande Dechirure et le Grand Gel sans tenir compte de l'anomalie conforme, simplement par la contribution de T a la theorie f(R, T). [Traduit par la Redaction], 1. Introduction Observation indicates that the current expansion of the universe is accelerating [1, 2]. There are two large branches of cosmology attempting to explain this phenomenon [3-12] using two [...]

We investigate models of future finite-time singularities in f(T) theory, where T is the torsion scalar. The algebraic function f(T) is the teleparallel term, T, plus an arbitrary function, g(T). A suitable expression for the Hubble parameter is assumed and constraints are imposed to provide an expanding universe. Two parameters, [beta] and [H.sub.s], that appear in the Hubble parameter are relevant in specifying the types of singularities. Differential equations of g(T) are established and solved, leading to algebraic f(T) models for each type of future finite-time singularity. Moreover, we take into account the viscosity in the fluid and discuss three interesting cases: constant viscosity, viscosity proportional to [square root of (-T)], and the general one where the viscosity is proportional to [(-T).sup.n/2], where n is a natural number. We see that for the first and second cases, in general, the singularities are robust against the viscous fluid, while for the general case, the Big Rip and the Big Freeze can be avoided from the effects of the viscosity for some values of n. PACS Nos.: 95.36.+x, 04.50.Kd, 66.20.-d. Nous analysons la theorie des modeles de singularites de temps futur fini, f(T)ou T est le scalaire de torsion. La fonction algebrique est posee comme etant le terme teleparallele de T plus une fonction g(T). Nous supposons une expression adequate pour le parametre de Hubble et nous imposons des contraintes de facon a avoir un univers en expansion. Les deux parametres [beta] et [H.sub.s] qui apparaissent dans l'expression pour le parametre de Hubble sont pertinents pour specifier les types de singularite. Nous etablissons et solutionnons les equations differentielles pour g(T), menant aux modeles algebriques f(T) pour chaque type de singularite de temps futur fini. Nous tenons egalement compte de la viscosite du fluide et discutons trois cas interessants: viscosite constante, viscosite proportionnelle a [square root of (-T)] et un cas general ou la viscosite est proportionnelle a [(-T).sup.n/2], ou n est un entier naturel. Pour les deux premiers cas, generalement les singularites sont robustes devant la viscosite du fluide, alors que pour le cas general, la viscosite correspondant a certaines valeurs de n permet d'eviter la Grande Dechirure et le Grand Gel. [Traduit par la Redaction], 1. Introduction Recent observations of type Ia supernovae (SNIa) and Wilkinson microwave anisotropy probe (WMAP) [1, 2] indicate that our universe is currently undergoing an accelerating expansion, which confronts the [...]

In this paper we study a gravitational theory in which tachyons play the role of a scalar field. Also, nonminimal derivative coupling between tachyons and the Einstein tensor is considered in the model. We show that at the initial time, tachyon field behavior is exponential and its behavior at late times is liner in cosmic time. We investigate the asymptotic behavior of scale factor a(t) = [e.sup.α(t)] and show that in the limit t [right arrow]∞ to it is impossible to have [??] constant a and the model has an initial cosmological singularity (i.e., a [varies] [(t - [t.sub.i]).sup.2/β]) in the limit t - [t.sub.i]. PACS Nos: 95.36.+x, 98.80.-k, 04.50.kd Nous etudions ici une theorie de la gravitation dans laquelle les tachyons jouent le role de champ scalaire. Nous considerons aussi un couplage non minimal entre le tachyon et le tenseur d'Einstein. Nous montrons que le champ de tachyon a un comportement initialement exponentiel, devenant ulterieurement lineaire en temps cosmique. Nous analysons le comportement asymptotique du facteur d'echelle a(t) = [e.sup.α(t)] et montrons que dans la limite t →∞ to, il est impossible d'avoir un [??] constant et le modele a une singularite cosmologique initiale, c.-a-d., a [varia en proporcion con] (t - [t.sub.i])2/β dans la limite t - [t.sub.i]. [Traduit par la Redaction], 1. Introduction Scalar fields are important ingredients of physics, and in the last three decades their role in cosmology has been distinguished in the description of various sides of nature. [...]

Power law singularities and critical exponents in n-vector models are considered within a theoretical approach called GFD (grouping of Feynman diagrams) theory. It is discussed how possible values of the critical exponents can be related to specific n-vector models in this approach. A good agreement with the estimates of the perturbative renormalization group (RG) theory can be obtained. Predictions for corrections to scaling of the perturbative RG and GFD approaches are different. A nonperturbative proof is provided, supporting corrections to scaling of the GFD theory. Highly accurate experimental data very close to the l-transition point in liquid helium, as well as the Goldstone mode singularities in n-vector spin models, evaluated from Monte Carlo simulation results, are discussed with an aim to test the theoretical predictions. Our analysis shows that in both cases the data can be well interpreted within GFD theory. PACS Nos: 64.60.Fr, 64.60.Cn, 75.10.Hk, 05.50.+q, 05.10.Ln, 05.10.Cc Nous etudions les singularities en loi de puissance et les exposants critiques dans les modeles a n vecteurs, a l'interieur d'un cadre theorique appele le GDF (regroupement de diagrammes de Feynman). Nous analysons comment les valeurs possibles des exposants critiques peuvent etre reliees a des modeles a n vecteurs specifiques dans cette approche. Nous pouvons obtenir un bon accord avec les resultats de la theorie du groupe de renormalisation (RG) perturbative. Les predictions de correction d'echelle de la RG perturbative sont differentes de celles de l'approche GFD. Nous produisons une preuve non perturbative qui supporte la correction d'echelle de GFD. Afin de tester les predictions theoriques, nous analysons des donnees experimentales precises tres pres du point de transition λ dans l'helium liquide, ainsi les singularites du mode de Goldstone dans les modeles a n spins vectoriels, evaluees a partir de simulations Monte-Carlo. Nos resultats montrent dans les deux cas que les donnees peuvent etre bien interpretees par la theorie GDF. [Traduit par la Redaction], 1. Introduction Critical phenomena in interacting many-particle systems are associated with cooperative fluctuations of a large number of microscopic degrees of freedom. Various physical quantities typically exhibit power law singularities [...]

Toroidal shells are widely used in structural engineering. The governing equations of toroidal shells are very complicated because of its variable coefficients with singularity. To find their analytical solution, traditionally, the complex form governing equations were proposed and some useful solutions were obtained. Unfortunately, no any closed-form solution has even been obtained for either general or slender toroidal shells. This paper focus on a special case of toroidal shells, i.e., slender symmetrical toroidal shells. For the first time, the closed-form solution of this kind of shell has been successfully obtained from displacement form governing equations. The closed-form solution is demonstrated for the example of thermal compensation devices. The correction of well-known Dahl formula for slender toroidal shell has been proposed based on the solution obtained in this paper. DOI: 10.1061/(ASCE)EM.1943-7889.0000175 CE Database subject headings: Shells; Axisymmetry; Bending; Deformation; Elasticity; Closed form solutions. Author keywords: Toroidal shells; Axisymmetry; Revolution shells; Slender shells; Bending; Deformation; Elastic materials.

This paper describes the interval boundary element method treatment of the pointwise discretization error for systems with geometrically generated flux singularities. Worst-case interval bounds are provided for the local discretization error for all elements except for the element with a singular flux solution, for which the flux intensity factor is enclosed. An example is presented showing the behavior of the interval bounds on the local discretization error for systems with geometrically induced singularities. DOI: 10.1061/(ASCE)EM. 1943-7889.0000109 CE Database subject headings: Boundary element method; Errors. Author keywords: Boundary element method; Interval boundary element method; Discretization error; Flux singularity; Flux intensity factor; Discretization error bounds; Flux intensity factor bounds.

The dynamical behavior of learning is known to be very slow for the multilayer perceptron, being often trapped in the 'plateau.' It has been recently understood that this is due to the singularity in the parameter space of perceptrons, in which trajectories of learning are drawn. The space is Riemannian from the point of view of information geometry and contains singular regions where the Riemannian metric or the Fisher information matrix degenerates. This paper analyzes the dynamics of learning in a neighborhood of the singular regions when the true teacher machine ties at the singularity. We give explicit asymptotic analytical solutions (trajectories) both for the standard gradient (SGD) and natural gradient (NGD) methods. It is clearly shown, in the case of the SGD method, that the plateau phenomenon appears in a neighborhood of the critical regions, where the dynamical behavior is extremely slow. The analysis of the NGD method is much more difficult, because the inverse of the Fisher information matrix diverges. We conquer the difficulty by introducing the 'blow-down' technique used in algebraic geometry. The NGD method works efficiently, and the state converges directly to the true parameters very quickly while it staggers in the case of the SGD method. The analytical results are compared with computer simulations, showing good agreement. The effects of singularities on learning are thus qualitatively clarified for both standard and NGD methods. Index Terms--Dynamics of learning, multilayer perceptrous, natural gradient (NGD) learning, singularity, standard gradient (SGD) learning.

1. Introduction Today a wide variety of crystal structures are solved using x-ray or neutron powder diffraction data in conjunction with Rietveld refinement techniques. The sequence of steps in the […]

This paper is a handyman's manual for learning how to resolve the singularities of algebraic varieties defined over a field of characteristic zero by sequences of blowups.

This paper presents the first motion planning methodology applicable to articulated, nonpoint nonholonomic robots with guaranteed collision avoidance and convergence properties. It is based on a new class of nonsmooth Lyapunov functions and a novel extension of the navigation function method to account for nonpoint articulated robots. The dipolar inverse Lyapunov functions introduced are appropriate for nonholonomic control and offer superior performance characteristics compared to existing tools. The new potential field technique uses diffeomorphic transformations and exploits the resulting point-world topology. The combined approach is applied to the problem of handling deformable material by multiple nonholonomic mobile manipulators in an obstacle environment to yield a centralized coordinating control law. Simulation results verify asymptotic convergence of the robots, obstacle avoidance, boundedness of object deformations, and singularity avoidance for the manipulators. Index Terms--Cooperative mobile manipulators, inverse Lyapunov functions, nonholonomic motion planning, potential fields.

It is known that any scattered wave field carrying energy into infinity must have source singularity centers within a bounded space. Otherwise, the scattered field should be identically equal to zero everywhere [1]. In this paper, attention is paid to localization of these singularities under the assumption that every scattered wave is determined uniquely by its own singularities. Investigations have shown that these singularities are distributed as 'bright centers' and the distance between them depends on frequency. To determine the position (localization) of the scattered wave field singularities, the functions describing converging and diverging waves are used. Based on these concepts and the method of auxiliary sources, an efficient numerical method to reconstruct a field up to its singularities is suggested. The localization of singularities is used for partial representation of the scattered fields, which reduces significantly the number of unknowns in describing the scattering process and leading into optimized inverse scattering problem solutions. Index Terms--Auxiliary absorbers, auxiliary sources, scattered field singularities.

Research is presented concerning the development of a novel derivation for doubly connected domains within the Schwarz-Christofell transformation. The construction of the pre-Schwarzian by reflection of the singularities is discussed.

When analyzing field problems with the finite element method, the numerical solution will converge against the physical solution. This paper deals with the influence of singularities on the convergence behaviour. Index terms - Convergence of numerical methods, finite element methods, electrostatic analysis, magnetostatics

The extended Jacobian method is a popular approach for controlling a kinematically redundant arm which allows one to resolve redundancy by locally optimizing an objective function and to gain repeatability for a cyclic end effector trajectory. It is a special case of a family of methods called constraint function methods. It has been found that the occurrence of algorithmic singularities can cause severe difficulties and the advantages of the methods such as repeatability might no longer exist. The purpose of this paper is to study the characteristics of algorithmic singularities, especially those of corank 1. A result of the authors on kinematic singularities is used to obtain a sufficient condition for the existence of solution paths at algorithmic singularities of the constrained function method. The phenomenon of branch repeatability is shown to occur at an algorithmic singularity. We also show that the extended Jacobian method cannot successfully optimize the objective function beyond the singularity without loss of continuity of the joint derivative. Examples are given to demonstrate the use of our theoretical results. Index Terms - Algorithmic singularity, extended Jacobian method, redundancy resolution.

Upon solving the inverse kinematics problem of robot manipulators, the inherent singularity problem should always be considered. When a manipulator is approaching a singular configuration, a certain degree of freedom will be lost such that there are no feasible solutions of the manipulator to move into this singular direction. In this paper, the singularities of a 6-DOF PUMA manipulator are analyzed in detail and all the corresponding singular directions in task space are clearly identified. In order to resolve this singularity problem, an approach denoted Singularity Isolation Plus Compact QP (SICQP) method is proposed. The SICQP method decomposes the work space into achievable and unachievable (i.e., singular) directions. Then, the exactness in the singular directions are released such that extra redundancy is provided to the achievable directions. Finally, the Compact QP method is applied to maintain the exactness in the achievable directions, and to minimize the tracking errors in the singular directions under the condition that feasible joint solutions must be obtained. In the end, some simulation results for PUMA manipulator are given to demonstrate the effectiveness of the SICQP method.

Using known techniques of desingularization for singular plane projective curves over finite fields [F.sub.q], q = [2.sup.m], we found several new binary plane projective curves of genus 3, 4, and 5 with the maximal number of [F.sub.q]-rational points (q = [2.sup.m], m = 3, 4, 5, 6, 7, 8, and 9) on their smooth projective models, which are close to or meet Serre's upper bound.

The still-unsolved Opaque Square Problem has been extended to various shapes, polygons and plane regions. An analysis illustrates three possible solutions to the Opaque Cube Problem, with the best one achieving an optimal surface area of 4.2324. The Opaque Sphere Problem, on the other hand, is shown to possibly have no solution because the surface or object that blocks sight may have to be widened, thus complicating what defines opaqueness. Topics for future research are also recommended.

A fractional slope on the log-log Bode plot has been observed in characterizing a certain type of physical phenomena and has been called the fractal system or the fractional power pole. In order to represent and study its dynamical behavior, a method of singularity function is presented which consists of cascaded branches of a number of pole-zero (negative real) pairs or simple RC section. The distribution spectrum of the system can also be easily calculated and its accuracy depends on a prescribed error specified in the beginning. The method is then extended to a multiple-fractal system which consists of a number of fractional power poles and the result can be simulated by a combination of singularity functions, each representing a single-fractal system.

Correct association of equivalent current and magnetic charge sheets in adjacent elements over the surface of non-magnetic conducting media removes the logarithmic singularities which otherwise occur at the edges and corners. This not only improves the accuracy of computed fields near corners but is also shown to allow magnetic flux to enter the medium naturally, and to remove the need to modify the surface impedance near corners in eddy-current problems.

This paper introduces a novel extension to a scalar two-dimensional polynomial finite-element basis to better cope with wedge singularities in waveguide problems. An error estimate for the computed cutoff frequencies of the waveguide shows that the relative [H.sup.1] error of the modal solution is critical. We demonstrate that the present extension significantly improves the approximation properties of a polynomial basis, especially in the [H.sup.1] norm. Numerical examples show that the present extension compares well with other recent techniques. Combining variable order elements with singular basis extension provides further significant reduction of the computational burden. Index Terms--High-order FEM methods, wedge singularities.

This paper presents two kinds of robust controllers for stabilizing singularly perturbed discrete bilinear systems. The first one is an [Epsilon]-dependent controller that stabilizes the closed-loop system for all [Epsilon] [element of] ([MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]) where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is the prespecified upper bound of the singular perturbation parameter. The second one is an [Epsilon]-independent controller, which is able to stabilize the system in the entire state space for all [Epsilon] [element] (0, [Epsilon]*, where [Epsilon]*] is the exact upper [Epsilon]-bound. The [Epsilon]* can be calculated by the critical stability criterion once the robust controller is determined. An example is presented to illustrate the proposed schemes. Index Terms--Lyapunov equation, robust controller, singularly perturbed discrete bilinear systems, singular perturbation parameter.