Singular reduction of Nambu-Poisson manifolds
Das, Apurba
The version of Marsden-Ratiu Poisson reduction theorem for Nambu-Poisson manifolds by a regular foliation have been studied by Ibáñez et al. In this paper, we show that this reduction procedure can be extended to the singular case. Under a suitable notion of Hamiltonian flow on the reduced space, we show that a set of Hamiltonians on a Nambu-Poisson manifold can also be reduced.
M theory and singularities of exceptional holonomy manifolds
International Nuclear Information System (INIS)
Acharya, Bobby S.; Gukov, Sergei
2004-12-01
M theory compactifications on G 2 holonomy manifolds, whilst supersymmetric, require singularities in order to obtain non-Abelian gauge groups, chiral fermions and other properties necessary for a realistic model of particle physics. We review recent progress in understanding the physics of such singularities. Our main aim is to describe the techniques which have been used to develop our understanding of M theory physics near these singularities. In parallel, we also describe similar sorts of singularities in Spin(7) holonomy manifolds which correspond to the properties of three dimensional field theories. As an application, we review how various aspects of strongly coupled gauge theories, such as confinement, mass gap and non-perturbative phase transitions may be given a simple explanation in M theory. (author)
Multiscale singular value manifold for rotating machinery fault diagnosis
Energy Technology Data Exchange (ETDEWEB)
Feng, Yi; Lu, BaoChun; Zhang, Deng Feng [School of Mechanical Engineering, Nanjing University of Science and Technology,Nanjing (United States)
2017-01-15
Time-frequency distribution of vibration signal can be considered as an image that contains more information than signal in time domain. Manifold learning is a novel theory for image recognition that can be also applied to rotating machinery fault pattern recognition based on time-frequency distributions. However, the vibration signal of rotating machinery in fault condition contains cyclical transient impulses with different phrases which are detrimental to image recognition for time-frequency distribution. To eliminate the effects of phase differences and extract the inherent features of time-frequency distributions, a multiscale singular value manifold method is proposed. The obtained low-dimensional multiscale singular value manifold features can reveal the differences of different fault patterns and they are applicable to classification and diagnosis. Experimental verification proves that the performance of the proposed method is superior in rotating machinery fault diagnosis.
Pseudo-differential operators on manifolds with singularities
Schulze, B-W
1991-01-01
The analysis of differential equations in domains and on manifolds with singularities belongs to the main streams of recent developments in applied and pure mathematics. The applications and concrete models from engineering and physics are often classical but the modern structure calculus was only possible since the achievements of pseudo-differential operators. This led to deep connections with index theory, topology and mathematical physics. The present book is devoted to elliptic partial differential equations in the framework of pseudo-differential operators. The first chapter contains the Mellin pseudo-differential calculus on R+ and the functional analysis of weighted Sobolev spaces with discrete and continuous asymptotics. Chapter 2 is devoted to the analogous theory on manifolds with conical singularities, Chapter 3 to manifolds with edges. Employed are pseudo-differential operators along edges with cone-operator-valued symbols.
The index of Fourier integral operators on manifolds with conical singularities
International Nuclear Information System (INIS)
Nazaikinskii, Vladimir E; Sternin, B Yu; Schulze, B-W
2001-01-01
We describe homogeneous canonical transformations of the cotangent bundle of a manifold with conical singular points and compute the index of an elliptic Fourier integral operator obtained by the quantization of such a transformation. The answer involves the index of an elliptic Fourier integral operator on a smooth manifold and the residues of the conormal symbol
Examples of integrable and non-integrable systems on singular symplectic manifolds
Delshams, Amadeu; Kiesenhofer, Anna; Miranda, Eva
2017-05-01
We present a collection of examples borrowed from celestial mechanics and projective dynamics. In these examples symplectic structures with singularities arise naturally from regularization transformations, Appell's transformation or classical changes like McGehee coordinates, which end up blowing up the symplectic structure or lowering its rank at certain points. The resulting geometrical structures that model these examples are no longer symplectic but symplectic with singularities which are mainly of two types: bm-symplectic and m-folded symplectic structures. These examples comprise the three body problem as non-integrable exponent and some integrable reincarnations such as the two fixed-center problem. Given that the geometrical and dynamical properties of bm-symplectic manifolds and folded symplectic manifolds are well-understood [10-12,9,15,13,14,24,20,22,25,28], we envisage that this new point of view in this collection of examples can shed some light on classical long-standing problems concerning the study of dynamical properties of these systems seen from the Poisson viewpoint.
The Hodge theory of projective manifolds
de Cataldo, Mark Andrea
2007-01-01
This book is a written-up and expanded version of eight lectures on the Hodge theory of projective manifolds. It assumes very little background and aims at describing how the theory becomes progressively richer and more beautiful as one specializes from Riemannian, to Kähler, to complex projective manifolds. Though the proof of the Hodge Theorem is omitted, its consequences - topological, geometrical and algebraic - are discussed at some length. The special properties of complex projective manifolds constitute an important body of knowledge and readers are guided through it with the help of selected exercises. Despite starting with very few prerequisites, the concluding chapter works out, in the meaningful special case of surfaces, the proof of a special property of maps between complex projective manifolds, which was discovered only quite recently.
Project Development Specification for Valve Pit Manifold
International Nuclear Information System (INIS)
MCGREW, D.L.
2000-01-01
Establishes the performance, design development, and test requirements for the valve pit manifolds. The system engineering approach was used to develop this document in accordance with the guidelines laid out in the Systems Engineering Management Plan for Project W-314
International Nuclear Information System (INIS)
Kates, R.E.
1979-01-01
This thesis shows that a small body with possibly strong internal gravity moves through an empty region of a curved, and not necessarily asymptotically flat, external spacetime on an approximate geodesic. By approximate geodesic, the following is meant: Suppose the ratio epsilon = m/L 1 - where m is the body's mass and L is a curvature reference length of the external field - is a small parameter. Then the body's worldline deviates from a geodesic only by distances of at most THETA(epsilon) L over times of order L. The worldline is calculated directly from the Einstein field equation using a singular perturbation technique that has been generalized from the method of matched asymptotic expansions. The need for singular perturbation techniques has long been appreciated in fluid mechanics, where they are now standard procedure in problems in which the straightforward expansion in powers of a small parameter fails to give a correct qualitative picture. In part I of this thesis, singular perturbations on manifolds are formulated in a coordinate-free way suitable for treating problems in general relativity and other field theories. Most importantly for this thesis, the coordinate-free formulation of singular perturbations given in part I is essential for treatment of the problem of motion in part II
Quantization of a symplectic manifold associated to a manifold with projective structure
International Nuclear Information System (INIS)
Biswas, Indranil
2009-01-01
Let X be a complex manifold equipped with a projective structure P. There is a holomorphic principal C*-bundle L P ' over X associated with P. We show that the holomorphic cotangent bundle of the total space of L P ' equipped with the Liouville symplectic form has a canonical deformation quantization. This generalizes the construction in the work of and Ben-Zvi and Biswas [''A quantization on Riemann surfaces with projective structure,'' Lett. Math. Phys. 54, 73 (2000)] done under the assumption that dim C X=1.
Singular p-harmonic functions and related quasilinear equations on manifolds
Directory of Open Access Journals (Sweden)
Laurent Veron
2002-10-01
Full Text Available We give here an overview of some recent developments in the study of the description of singular solutions of $$ -abla.(|abla u|^{p-2}abla u +varepsilon |u|^{q-1}u=0 %label{NLE} $$ in $mathbb{R}^Nsetminus {0}$, where $p>1$, $varepsilon in {0,1,-1}$ and $qgeq p-1$.
A critical view on singular therapeutic projects
Directory of Open Access Journals (Sweden)
Fernando Sfair Kinker
2016-04-01
Full Text Available This article discusses the issue of unique therapeutic projects within the mental health services built in the Brazilian psychiatric reform process. Starting from the concepts that have gained strength in both the psychiatric reform as in the collective health, this study proposes that current notions of the therapeutic project still are influenced by biological, psychological or social paradigms that simplify the complexity of the experience suffered by the subjects. Despite therapeutic projects are an essential achievement for the qualification of mental health care, it is still necessary to produce an epistemological rupture in the relationship with mental suffering so that they can achieve the greatest potential for transformation. Therefore, the article suggests that the practice of therapeutic projects should hold discussions with the reality of users life of and their relationships in the territories of existence, to transform the relations of power and knowledge that reproduce the subjects annulment. Thus, it is possible to dialogue with the complexity of the mental suffering experience, producing changes in the scenes that produce it.
International Nuclear Information System (INIS)
Corbera, Montserrat; Llibre, Jaume; Perez-Chavela, Ernesto
2006-01-01
In this paper we consider vector fields in R 3 that are invariant under a suitable symmetry and that possess a 'generalized heteroclinic loop' L formed by two singular points (e + and e - ) and their invariant manifolds: one of dimension 2 (a sphere minus the points e + and e - ) and one of dimension 1 (the open diameter of the sphere having endpoints e + and e - ). In particular, we analyse the dynamics of the vector field near the heteroclinic loop L by means of a convenient Poincar? map, and we prove the existence of infinitely many symmetric periodic orbits near L. We also study two families of vector fields satisfying this dynamics. The first one is a class of quadratic polynomial vector fields in R 3 , and the second one is the charged rhomboidal four-body problem
On the K(a)hler-Ricci Flow on Projective Manifolds of General Type
Institute of Scientific and Technical Information of China (English)
Gang TIAN; Zhou ZHANG
2006-01-01
This note concerns the global existence and convergence of the solution for K(a)hler-Ricci flow equation when the canonical class, Kx, is numerically effective and big.We clarify some known results regarding this flow on projective manifolds of general type and also show some new observations and refined results.
Camera-pose estimation via projective Newton optimization on the manifold.
Sarkis, Michel; Diepold, Klaus
2012-04-01
Determining the pose of a moving camera is an important task in computer vision. In this paper, we derive a projective Newton algorithm on the manifold to refine the pose estimate of a camera. The main idea is to benefit from the fact that the 3-D rigid motion is described by the special Euclidean group, which is a Riemannian manifold. The latter is equipped with a tangent space defined by the corresponding Lie algebra. This enables us to compute the optimization direction, i.e., the gradient and the Hessian, at each iteration of the projective Newton scheme on the tangent space of the manifold. Then, the motion is updated by projecting back the variables on the manifold itself. We also derive another version of the algorithm that employs homeomorphic parameterization to the special Euclidean group. We test the algorithm on several simulated and real image data sets. Compared with the standard Newton minimization scheme, we are now able to obtain the full numerical formula of the Hessian with a 60% decrease in computational complexity. Compared with Levenberg-Marquardt, the results obtained are more accurate while having a rather similar complexity.
Directory of Open Access Journals (Sweden)
Xin Xu
2009-03-01
Full Text Available The significant economic contributions of the tourism industry in recent years impose an unprecedented force for data mining and machine learning methods to analyze tourism data. The intrinsic problems of raw data in tourism are largely related to the complexity, noise and nonlinearity in the data that may introduce many challenges for the existing data mining techniques such as rough sets and neural networks. In this paper, a novel method using SVM- based classification with two nonlinear feature projection techniques is proposed for tourism data analysis. The first feature projection method is based on ISOMAP (Isometric Feature Mapping, which is a class of manifold learning approaches for dimension reduction. By making use of ISOMAP, part of the noisy data can be identified and the classification accuracy of SVMs can be improved by appropriately discarding the noisy training data. The second feature projection method is a probabilistic space mapping technique for scale transformation. Experimental results on expenditure data of business travelers show that the proposed method can improve prediction performance both in terms of testing accuracy and statistical coincidence. In addition, both of the feature projection methods are helpful to reduce the training time of SVMs.
Energy Technology Data Exchange (ETDEWEB)
Heras Celemin, M. R.
2008-07-01
The R and D activities for the scientific-technological singular strategic Project on Bio climatic Architecture and Solar Cooling PSE-ARFRISOL are being carried out from November 2005 to December 2010. This project aims to demonstrate that bio climatic architecture and low-temperature solar energy are the appropriate basic elements for climatization of future buildings. (Author) 12 refs.
Energy Technology Data Exchange (ETDEWEB)
Liang, Wei; Zhang, Laibin; Mingda, Wang; Jinqiu, Hu [College of Mechanical and Transportation Engineering, China University of Petroleum, Beijing, (China)
2010-07-01
The negative wave pressure method is one of the processes used to detect leaks on oil pipelines. The development of new leakage recognition processes is difficult because it is practically impossible to collect leakage pressure samples. The method of leakage feature extraction and the selection of the recognition model are also important in pipeline leakage detection. This study investigated a new feature extraction approach Singular Value Projection (SVP). It projects the singular value to a standard basis. A new pipeline recognition model based on the multi-class Support Vector Machines was also developed. It was found that SVP is a clear and concise recognition feature of the negative pressure wave. Field experiments proved that the model provided a high recognition accuracy rate. This approach to pipeline leakage detection based on the SVP and SVM has a high application value.
The geometry of warped product singularities
Stoica, Ovidiu Cristinel
In this article, the degenerate warped products of singular semi-Riemannian manifolds are studied. They were used recently by the author to handle singularities occurring in General Relativity, in black holes and at the big-bang. One main result presented here is that a degenerate warped product of semi-regular semi-Riemannian manifolds with the warping function satisfying a certain condition is a semi-regular semi-Riemannian manifold. The connection and the Riemann curvature of the warped product are expressed in terms of those of the factor manifolds. Examples of singular semi-Riemannian manifolds which are semi-regular are constructed as warped products. Applications include cosmological models and black holes solutions with semi-regular singularities. Such singularities are compatible with a certain reformulation of the Einstein equation, which in addition holds at semi-regular singularities too.
Ling, Eric
The big bang theory is a model of the universe which makes the striking prediction that the universe began a finite amount of time in the past at the so called "Big Bang singularity." We explore the physical and mathematical justification of this surprising result. After laying down the framework of the universe as a spacetime manifold, we combine physical observations with global symmetrical assumptions to deduce the FRW cosmological models which predict a big bang singularity. Next we prove a couple theorems due to Stephen Hawking which show that the big bang singularity exists even if one removes the global symmetrical assumptions. Lastly, we investigate the conditions one needs to impose on a spacetime if one wishes to avoid a singularity. The ideas and concepts used here to study spacetimes are similar to those used to study Riemannian manifolds, therefore we compare and contrast the two geometries throughout.
Optimal image alignment with random projections of manifolds: algorithm and geometric analysis.
Kokiopoulou, Effrosyni; Kressner, Daniel; Frossard, Pascal
2011-06-01
This paper addresses the problem of image alignment based on random measurements. Image alignment consists of estimating the relative transformation between a query image and a reference image. We consider the specific problem where the query image is provided in compressed form in terms of linear measurements captured by a vision sensor. We cast the alignment problem as a manifold distance minimization problem in the linear subspace defined by the measurements. The transformation manifold that represents synthesis of shift, rotation, and isotropic scaling of the reference image can be given in closed form when the reference pattern is sparsely represented over a parametric dictionary. We show that the objective function can then be decomposed as the difference of two convex functions (DC) in the particular case where the dictionary is built on Gaussian functions. Thus, the optimization problem becomes a DC program, which in turn can be solved globally by a cutting plane method. The quality of the solution is typically affected by the number of random measurements and the condition number of the manifold that describes the transformations of the reference image. We show that the curvature, which is closely related to the condition number, remains bounded in our image alignment problem, which means that the relative transformation between two images can be determined optimally in a reduced subspace.
International Nuclear Information System (INIS)
Finkelstein, D.; Finkelstein, S.R.; Holm, C.
1986-01-01
Riemannian manifolds are but one of three ways to extrapolate from fourdimensional Minkowskian manifolds to spaces of higher dimension, and not the most plausible. If we take seriously a certain construction of time space from spinors, and replace the underlying binary spinors by N-ary hyperspinors with new ''internal'' components besides the usual two ''external'' ones, this leads to a second line, the hyperspin manifolds /sub n/ and their tangent spaces d/sub n/, different in structure and symmetry group from the Riemannian line, except that the binary spaces d 2 (Minkowski time space) and 2 (Minkowskian manifold) lie on both. d/sub n/ and /sub n/ have dimension n = N 2 . In hyperspin manifolds the energies of modes of motion multiply instead of adding their squares, and the N-ary chronometric form is not quadratic, but N-ic, with determinantal normal form. For the nine-dimensional ternary hyperspin manifold, we construct the trino, trine-Gordon, and trirac equations and their mass spectra in flat time space. It is possible that our four-dimensional time space sits in a hyperspin manifold rather than in a Kaluza-Klein Riemannian manifold. If so, then gauge quanta with spin-3 exist
Slow Integral Manifolds and Control Problems in Critical and Twice Critical Cases
International Nuclear Information System (INIS)
Sobolev, Vladimir
2016-01-01
We consider singularly perturbed differential systems in cases where the standard theory to establish a slow integral manifold existence does not work. The theory has traditionally dealt only with perturbation problems near normally hyperbolic manifold of singularities and this manifold is supposed to isolated. Applying transformations we reduce the original singularly perturbed problem to a regularized one such that the existence of slow integral manifolds can be established by means of the standard theory. We illustrate our approach by several examples. (paper)
Sinha, Rajnikant
2014-01-01
This book offers an introduction to the theory of smooth manifolds, helping students to familiarize themselves with the tools they will need for mathematical research on smooth manifolds and differential geometry. The book primarily focuses on topics concerning differential manifolds, tangent spaces, multivariable differential calculus, topological properties of smooth manifolds, embedded submanifolds, Sard’s theorem and Whitney embedding theorem. It is clearly structured, amply illustrated and includes solved examples for all concepts discussed. Several difficult theorems have been broken into many lemmas and notes (equivalent to sub-lemmas) to enhance the readability of the book. Further, once a concept has been introduced, it reoccurs throughout the book to ensure comprehension. Rank theorem, a vital aspect of smooth manifolds theory, occurs in many manifestations, including rank theorem for Euclidean space and global rank theorem. Though primarily intended for graduate students of mathematics, the book ...
Hempel, John
2004-01-01
A careful and systematic development of the theory of the topology of 3-manifolds, focusing on the critical role of the fundamental group in determining the topological structure of a 3-manifold … self-contained … one can learn the subject from it … would be very appropriate as a text for an advanced graduate course or as a basis for a working seminar. -Mathematical Reviews For many years, John Hempel's book has been a standard text on the topology of 3-manifolds. Even though the field has grown tremendously, the book remains one of the best and most popular introductions to the subject. The t
Kosinski, Antoni A
2007-01-01
The concepts of differential topology form the center of many mathematical disciplines such as differential geometry and Lie group theory. Differential Manifolds presents to advanced undergraduates and graduate students the systematic study of the topological structure of smooth manifolds. Author Antoni A. Kosinski, Professor Emeritus of Mathematics at Rutgers University, offers an accessible approach to both the h-cobordism theorem and the classification of differential structures on spheres.""How useful it is,"" noted the Bulletin of the American Mathematical Society, ""to have a single, sho
Influence of the choice of projection manifolds in the CASPT2 implementation
Czech Academy of Sciences Publication Activity Database
Yanai, T.; Kurashige, Y.; Saitow, M.; Chalupský, Jakub; Lindh, R.; Malmqvist, P. A.
2017-01-01
Roč. 115, 17/18 (2017), s. 2077-2085 ISSN 0026-8976 R&D Projects: GA ČR GA15-19143S Institutional support: RVO:61388963 Keywords : multireference theory * CASPT2 * MOLCAS * computer-aided programming Subject RIV: CF - Physical ; Theoretical Chemistry OBOR OECD: Physical chemistry Impact factor: 1.870, year: 2016
International Nuclear Information System (INIS)
Littlejohn, R.G.
1982-01-01
The Hamiltonian structures discovered by Morrison and Greene for various fluid equations were obtained by guessing a Hamiltonian and a suitable Poisson bracket formula, expressed in terms of noncanonical (but physical) coordinates. In general, such a procedure for obtaining a Hamiltonian system does not produce a Hamiltonian phase space in the usual sense (a symplectic manifold), but rather a family of symplectic manifolds. To state the matter in terms of a system with a finite number of degrees of freedom, the family of symplectic manifolds is parametrized by a set of Casimir functions, which are characterized by having vanishing Poisson brackets with all other functions. The number of independent Casimir functions is the corank of the Poisson tensor J/sup ij/, the components of which are the Poisson brackets of the coordinates among themselves. Thus, these Casimir functions exist only when the Poisson tensor is singular
Dobrokhotov, S. Yu.; Nazaikinskii, V. E.
2017-01-01
The following results are obtained for the Cauchy problem with localized initial data for the crystal lattice vibration equations with continuous and discrete time: (i) the asymptotics of the solution is determined by Lagrangian manifolds with singularities ("punctured" Lagrangian manifolds); (ii) Maslov's canonical operator is defined on such manifolds as a modification of a new representation recently obtained for the canonical operator by the present authors together with A. I. Shafarevich (Dokl. Ross. Akad. Nauk 46 (6), 641-644 (2016)); (iii) the projection of the Lagrangian manifold onto the configuration plane specifies a bounded oscillation region, whose boundary (which is naturally referred to as the leading edge front) is determined by the Hamiltonians corresponding to the limit wave equations; (iv) the leading edge front is a special caustic, which possibly contains stronger focal points. These observations, together with earlier results, lead to efficient formulas for the wave field in a neighborhood of the leading edge front.
Morrow, James
2006-01-01
This book, a revision and organization of lectures given by Kodaira at Stanford University in 1965-66, is an excellent, well-written introduction to the study of abstract complex (analytic) manifolds-a subject that began in the late 1940's and early 1950's. It is largely self-contained, except for some standard results about elliptic partial differential equations, for which complete references are given. -D. C. Spencer, MathSciNet The book under review is the faithful reprint of the original edition of one of the most influential textbooks in modern complex analysis and geometry. The classic
Multidimensional singular integrals and integral equations
Mikhlin, Solomon Grigorievich; Stark, M; Ulam, S
1965-01-01
Multidimensional Singular Integrals and Integral Equations presents the results of the theory of multidimensional singular integrals and of equations containing such integrals. Emphasis is on singular integrals taken over Euclidean space or in the closed manifold of Liapounov and equations containing such integrals. This volume is comprised of eight chapters and begins with an overview of some theorems on linear equations in Banach spaces, followed by a discussion on the simplest properties of multidimensional singular integrals. Subsequent chapters deal with compounding of singular integrals
Hirzebruch genera of manifolds with torus action
International Nuclear Information System (INIS)
Panov, T E
2001-01-01
A quasitoric manifold is a smooth 2n-manifold M 2n with an action of the compact torus T n such that the action is locally isomorphic to the standard action of T n on C n and the orbit space is diffeomorphic, as a manifold with corners, to a simple polytope P n . The name refers to the fact that topological and combinatorial properties of quasitoric manifolds are similar to those of non-singular algebraic toric varieties (or toric manifolds). Unlike toric varieties, quasitoric manifolds may fail to be complex. However, they always admit a stably (or weakly almost) complex structure, and their cobordism classes generate the complex cobordism ring. Buchstaber and Ray have recently shown that the stably complex structure on a quasitoric manifold is determined in purely combinatorial terms, namely, by an orientation of the polytope and a function from the set of codimension-one faces of the polytope to primitive vectors of the integer lattice. We calculate the χ y -genus of a quasitoric manifold with a fixed stably complex structure in terms of the corresponding combinatorial data. In particular, this gives explicit formulae for the classical Todd genus and the signature. We also compare our results with well-known facts in the theory of toric varieties
Controllability of non-linear systems: generic singularities and their stability
International Nuclear Information System (INIS)
Davydov, Alexey A; Zakalyukin, Vladimir M
2012-01-01
This paper presents an overview of the state of the art in applications of singularity theory to the analysis of generic singularities of controllability of non-linear systems on manifolds. Bibliography: 40 titles.
The structure of some classes of K-contact manifolds
Indian Academy of Sciences (India)
Abstract. We study projective curvature tensor in K-contact and Sasakian manifolds. We prove that (1) if a K-contact manifold is quasi projectively flat then it is Einstein and (2) a K-contact manifold is ξ-projectively flat if and only if it is Einstein Sasakian. Necessary and sufficient conditions for a K-contact manifold to be quasi ...
Strongly not relatives Kähler manifolds
Directory of Open Access Journals (Sweden)
Zedda Michela
2017-02-01
Full Text Available In this paper we study Kähler manifolds that are strongly not relative to any projective Kähler manifold, i.e. those Kähler manifolds that do not share a Kähler submanifold with any projective Kähler manifold even when their metric is rescaled by the multiplication by a positive constant. We prove two results which highlight some relations between this property and the existence of a full Kähler immersion into the infinite dimensional complex projective space. As application we get that the 1-parameter families of Bergman-Hartogs and Fock-Bargmann-Hartogs domains are strongly not relative to projective Kähler manifolds.
Graded manifolds and supermanifolds
International Nuclear Information System (INIS)
Batchelor, M.
1984-01-01
In this paper, a review is presented on graded manifolds and supermanifolds. Many theorems, propositions, corrollaries, etc. are given with proofs or sketch proofs. Graded manifolds, supereuclidian space, Lie supergroups, etc. are dealt with
Pilca, Mihaela
2016-09-01
Vaisman manifolds are strongly related to Kähler and Sasaki geometry. In this paper we introduce toric Vaisman structures and show that this relationship still holds in the toric context. It is known that the so-called minimal covering of a Vaisman manifold is the Riemannian cone over a Sasaki manifold. We show that if a complete Vaisman manifold is toric, then the associated Sasaki manifold is also toric. Conversely, a toric complete Sasaki manifold, whose Kähler cone is equipped with an appropriate compatible action, gives rise to a toric Vaisman manifold. In the special case of a strongly regular compact Vaisman manifold, we show that it is toric if and only if the corresponding Kähler quotient is toric.
Obstruction theory on 8-manifolds
Czech Academy of Sciences Publication Activity Database
Čadek, M.; Crabb, M.; Vanžura, Jiří
2008-01-01
Roč. 127, č. 2 (2008), s. 167-186 ISSN 0025-2611 R&D Projects: GA ČR GA201/05/2117 Institutional research plan: CEZ:AV0Z10190503 Keywords : 8-manifolds * obstruction theory Subject RIV: BA - General Mathematics Impact factor: 0.509, year: 2008
Renteln, Paul
2013-11-01
Preface; 1. Linear algebra; 2. Multilinear algebra; 3. Differentiation on manifolds; 4. Homotopy and de Rham cohomology; 5. Elementary homology theory; 6. Integration on manifolds; 7. Vector bundles; 8. Geometric manifolds; 9. The degree of a smooth map; Appendixes; References; Index.
Slow Invariant Manifolds in Chemically Reactive Systems
Paolucci, Samuel; Powers, Joseph M.
2006-11-01
The scientific design of practical gas phase combustion devices has come to rely on the use of mathematical models which include detailed chemical kinetics. Such models intrinsically admit a wide range of scales which renders their accurate numerical approximation difficult. Over the past decade, rational strategies, such as Intrinsic Low Dimensional Manifolds (ILDM) or Computational Singular Perturbations (CSP), for equilibrating fast time scale events have been successfully developed, though their computation can be challenging and their accuracy in most cases uncertain. Both are approximations to the preferable slow invariant manifold which best describes how the system evolves in the long time limit. Strategies for computing the slow invariant manifold are examined, and results are presented for practical combustion systems.
One Critical Case in Singularly Perturbed Control Problems
Sobolev, Vladimir
2017-02-01
The aim of the paper is to describe the special critical case in the theory of singularly perturbed optimal control problems. We reduce the original singularly perturbed problem to a regularized one such that the existence of slow integral manifolds can be established by means of the standard theory. We illustrate our approach by an example of control problem.
Heterotic model building: 16 special manifolds
International Nuclear Information System (INIS)
He, Yang-Hui; Lee, Seung-Joo; Lukas, Andre; Sun, Chuang
2014-01-01
We study heterotic model building on 16 specific Calabi-Yau manifolds constructed as hypersurfaces in toric four-folds. These 16 manifolds are the only ones among the more than half a billion manifolds in the Kreuzer-Skarke list with a non-trivial first fundamental group. We classify the line bundle models on these manifolds, both for SU(5) and SO(10) GUTs, which lead to consistent supersymmetric string vacua and have three chiral families. A total of about 29000 models is found, most of them corresponding to SO(10) GUTs. These models constitute a starting point for detailed heterotic model building on Calabi-Yau manifolds in the Kreuzer-Skarke list. The data for these models can be downloaded http://www-thphys.physics.ox.ac.uk/projects/CalabiYau/toricdata/index.html.
Towards generalized mirror symmetry for twisted connected sum G 2 manifolds
Braun, Andreas P.; Del Zotto, Michele
2018-03-01
We revisit our construction of mirror symmetries for compactifications of Type II superstrings on twisted connected sum G 2 manifolds. For a given G 2 manifold, we discuss evidence for the existence of mirror symmetries of two kinds: one is an autoequivalence for a given Type II superstring on a mirror pair of G 2 manifolds, the other is a duality between Type II strings with different chiralities for another pair of mirror manifolds. We clarify the role of the B-field in the construction, and check that the corresponding massless spectra are respected by the generalized mirror maps. We discuss hints towards a homological version based on BPS spectroscopy. We provide several novel examples of smooth, as well as singular, mirror G 2 backgrounds via pairs of dual projecting tops. We test our conjectures against a Joyce orbifold example, where we reproduce, using our geometrical methods, the known mirror maps that arise from the SCFT worldsheet perspective. Along the way, we discuss non-Abelian gauge symmetries, and argue for the generation of the Affleck-Harvey-Witten superpotential in the pure SYM case.
Symmetries and singularities in Hamiltonian systems
International Nuclear Information System (INIS)
Miranda, Eva
2009-01-01
This paper contains several results concerning the role of symmetries and singularities in the mathematical formulation of many physical systems. We concentrate in systems which find their mathematical model on a symplectic or Poisson manifold and we present old and new results from a global perspective.
Singular interactions supported by embedded curves
International Nuclear Information System (INIS)
Kaynak, Burak Tevfik; Turgut, O Teoman
2012-01-01
In this work, singular interactions supported by embedded curves on Riemannian manifolds are discussed from a more direct and physical perspective, via the heat kernel approach. We show that the renormalized problem is well defined, the ground state is finite and the corresponding wavefunction is positive. The renormalization group invariance of the model is also discussed. (paper)
Introduction to differentiable manifolds
Auslander, Louis
2009-01-01
The first book to treat manifold theory at an introductory level, this text surveys basic concepts in the modern approach to differential geometry. The first six chapters define and illustrate differentiable manifolds, and the final four chapters investigate the roles of differential structures in a variety of situations.Starting with an introduction to differentiable manifolds and their tangent spaces, the text examines Euclidean spaces, their submanifolds, and abstract manifolds. Succeeding chapters explore the tangent bundle and vector fields and discuss their association with ordinary diff
Global embeddings for branes at toric singularities
Balasubramanian, Vijay; Braun, Volker; García-Etxebarria, Iñaki
2012-01-01
We describe how local toric singularities, including the Toric Lego construction, can be embedded in compact Calabi-Yau manifolds. We study in detail the addition of D-branes, including non-compact flavor branes as typically used in semi-realistic model building. The global geometry provides constraints on allowable local models. As an illustration of our discussion we focus on D3 and D7-branes on (the partially resolved) (dP0)^3 singularity, its embedding in a specific Calabi-Yau manifold as a hypersurface in a toric variety, the related type IIB orientifold compactification, as well as the corresponding F-theory uplift. Our techniques generalize naturally to complete intersections, and to a large class of F-theory backgrounds with singularities.
International Nuclear Information System (INIS)
HAMMERS, J.S.
1999-01-01
The purpose of the test was to verify that the AN Tank Farm Manifold Valves can be manually manipulated to the required operating position and that the electrical and visual indications accurately reflect that position. Physical locking devices were also verified to function. The Acceptance Test Procedure HNF-4642, 241-AN-A Valve Pit Manifold Valves and Position Indication was conducted between 23 June and 10 August 1999 at the 200E AN Tank Farm. The test has no open test exceptions. The test was conducted prior to final engineering ''as built'' activities being completed, this had an impact on the procedure and test results, ECN 653752 was written to correct the mismatch between the procedure and actual field conditions. P and ID H-14-100941 was changed via ECN-W-314-4C-120. All components, identified in the procedure, were not found to be labeled and identified as written in the procedure, temporary tags were used for operational identification. A retest of valve ANA-WT-V 318 was required because it was removed from its installed position and modified after testing was completed
Kalka, Morris; Patrizio, Giorgio
2014-01-01
We study the geometric properties of complex manifolds possessing a pair of plurisubharmonic functions satisfying Monge-Amp\\`ere type of condition. The results are applied to characterize complex manifolds biholomorphic to $\\C^{N}$ viewed as a product of lower dimensional complex euclidean spaces.
Yoshidome, Takashi; Oroguchi, Tomotaka; Nakasako, Masayoshi; Ikeguchi, Mitsunori
2015-09-01
Coherent x-ray diffraction imaging (CXDI) enables us to visualize noncrystalline sample particles with micrometer to submicrometer dimensions. Using x-ray free-electron laser (XFEL) sources, two-dimensional diffraction patterns are collected from fresh samples supplied to the irradiation area in the "diffraction-before-destruction" scheme. A recent significant increase in the intensity of the XFEL pulse is promising and will allow us to visualize the three-dimensional structures of proteins using XFEL-CXDI in the future. For the protocol proposed for molecular structure determination using future XFEL-CXDI [T. Oroguchi and M. Nakasako, Phys. Rev. E 87, 022712 (2013), 10.1103/PhysRevE.87.022712], we require an algorithm that can classify the data in accordance with the structural polymorphism of proteins arising from their conformational dynamics. However, most of the algorithms proposed primarily require the numbers of conformational classes, and then the results are biased by the numbers. To improve this point, here we examine whether a method based on the manifold concept can classify simulated XFEL-CXDI data with respect to the structural polymorphism of a protein that predominantly adopts two states. After random sampling of the conformations of the two states and in-between states from the trajectories of molecular dynamics simulations, a diffraction pattern is calculated from each conformation. Classification was performed by using our custom-made program suite named enma, in which the diffusion map (DM) method developed based on the manifold concept was implemented. We successfully classify most of the projection electron density maps phase retrieved from diffraction patterns into each of the two states and in-between conformations without the knowledge of the number of conformational classes. We also examined the classification of the projection electron density maps of each of the three states with respect to the Euler angle. The present results suggest
On local invariants of singular symplectic forms
Domitrz, Wojciech
2017-04-01
We find a complete set of local invariants of singular symplectic forms with the structurally stable Martinet hypersurface on a 2 n-dimensional manifold. In the C-analytic category this set consists of the Martinet hypersurface Σ2, the restriction of the singular symplectic form ω to TΣ2 and the kernel of ω n - 1 at the point p ∈Σ2. In the R-analytic and smooth categories this set contains one more invariant: the canonical orientation of Σ2. We find the conditions to determine the kernel of ω n - 1 at p by the other invariants. In dimension 4 we find sufficient conditions to determine the equivalence class of a singular symplectic form-germ with the structurally smooth Martinet hypersurface by the Martinet hypersurface and the restriction of the singular symplectic form to it. We also study the singular symplectic forms with singular Martinet hypersurfaces. We prove that the equivalence class of such singular symplectic form-germ is determined by the Martinet hypersurface, the canonical orientation of its regular part and the restriction of the singular symplectic form to its regular part if the Martinet hypersurface is a quasi-homogeneous hypersurface with an isolated singularity.
Deformations of Lagrangian subvarieties of holomorphic symplectic manifolds
Lehn, Christian
2011-01-01
We generalize Voisin's theorem on deformations of pairs of a symplectic manifold and a Lagrangian submanifold to the case of Lagrangian normal crossing subvarieties. Partial results are obtained for arbitrary Lagrangian subvarieties. We apply our results to the study of singular fibers of Lagrangian fibrations.
Ensemble manifold regularization.
Geng, Bo; Tao, Dacheng; Xu, Chao; Yang, Linjun; Hua, Xian-Sheng
2012-06-01
We propose an automatic approximation of the intrinsic manifold for general semi-supervised learning (SSL) problems. Unfortunately, it is not trivial to define an optimization function to obtain optimal hyperparameters. Usually, cross validation is applied, but it does not necessarily scale up. Other problems derive from the suboptimality incurred by discrete grid search and the overfitting. Therefore, we develop an ensemble manifold regularization (EMR) framework to approximate the intrinsic manifold by combining several initial guesses. Algorithmically, we designed EMR carefully so it 1) learns both the composite manifold and the semi-supervised learner jointly, 2) is fully automatic for learning the intrinsic manifold hyperparameters implicitly, 3) is conditionally optimal for intrinsic manifold approximation under a mild and reasonable assumption, and 4) is scalable for a large number of candidate manifold hyperparameters, from both time and space perspectives. Furthermore, we prove the convergence property of EMR to the deterministic matrix at rate root-n. Extensive experiments over both synthetic and real data sets demonstrate the effectiveness of the proposed framework.
Energy conditions and spacetime singularities
International Nuclear Information System (INIS)
Tipler, F.J.
1978-01-01
In this paper, a number of theorems are proven which collectively show that singularities will occur in spacetime under weaker energy conditions than the strong energy condition. In particular, the Penrose theorem, which uses only the weak energy condition but which applies only to open universes, is extended to all closed universes which have a Cauchy surface whose universal covering manifold is not a three-sphere. Furthermore, it is shown that the strong energy condition in the Hawking-Penrose theorem can be replaced by the weak energy condition and the assumption that the strong energy condition holds only on the average. In addition, it is demonstrated that if the Universe is closed, then the existence of singularities follows from the averaged strong energy condition alone. It is argued that any globally hyperbolic spacetime which satisfies the weak energy condition and which contains a black hole must be null geodesically incomplete
International Nuclear Information System (INIS)
Aspinwall, P.S.; Luetken, C.A.
1991-01-01
We analyze the mirror manifold hypothesis in one and three dimensions using the simplest available representations of the N = 2 superconformal algebra. The symmetries of these tensor models can be divided out to give an explicit representation of the mirror, and we give a simple group theoretical algorithm for determining which symmetries should be used. We show that the mirror of a superconformal field theory does not always have a geometrical interpretation, but when it does, deformations of complex structure of one manifold are reflected in deformations of the Kaehler form of the mirror manifold, and we show how the large radius limit of a manifold corresponds to a large complex structure limit in the mirror manifold. The mirror of the Tian-Yau three generation model is constructed both as a conformal field theory and as an algebraic variety with Euler number six. The Hodge numbers of this manifolds are fixed, but the intersection numbes are highly ambiguous, presumably reflected a rich structure of multicritical points in the moduli space of the field theory. (orig.)
M Theory, G2-manifolds and four dimensional physics
International Nuclear Information System (INIS)
Acharya, B.S.
2003-01-01
M theory on a manifold of G 2 -holonomy is a natural framework for obtaining vacua with four large spacetime dimensions and N = 1 supersymmetry. In order to obtain, within this framework, the standard features of particle physics, namely non-Abelian gauge groups and chiral fermions, we consider G 2 -manifolds with certain kinds of singularities at which these features reside. The aim of these lectures is to describe in detail how the above picture emerges. Along the way we will see how interesting aspects of strongly coupled gauge theories, such as confinement, receive relatively simple explanations within the context of M theory. (author)
Adams, Scot
2001-01-01
Within the general framework of the dynamics of "large" groups on geometric spaces, the focus is on the types of groups that can act in complicated ways on Lorentz manifolds, and on the structure of the resulting manifolds and actions. This particular area of dynamics is an active one, and not all the results are in their final form. However, at this point, a great deal can be said about the particular Lie groups that come up in this context. It is impressive that, even assuming very weak recurrence of the action, the list of possible groups is quite restricted. For the most complicated of the
Manifold Regularized Reinforcement Learning.
Li, Hongliang; Liu, Derong; Wang, Ding
2018-04-01
This paper introduces a novel manifold regularized reinforcement learning scheme for continuous Markov decision processes. Smooth feature representations for value function approximation can be automatically learned using the unsupervised manifold regularization method. The learned features are data-driven, and can be adapted to the geometry of the state space. Furthermore, the scheme provides a direct basis representation extension for novel samples during policy learning and control. The performance of the proposed scheme is evaluated on two benchmark control tasks, i.e., the inverted pendulum and the energy storage problem. Simulation results illustrate the concepts of the proposed scheme and show that it can obtain excellent performance.
Computation at a coordinate singularity
Prusa, Joseph M.
2018-05-01
Coordinate singularities are sometimes encountered in computational problems. An important example involves global atmospheric models used for climate and weather prediction. Classical spherical coordinates can be used to parameterize the manifold - that is, generate a grid for the computational spherical shell domain. This particular parameterization offers significant benefits such as orthogonality and exact representation of curvature and connection (Christoffel) coefficients. But it also exhibits two polar singularities and at or near these points typical continuity/integral constraints on dependent fields and their derivatives are generally inadequate and lead to poor model performance and erroneous results. Other parameterizations have been developed that eliminate polar singularities, but problems of weaker singularities and enhanced grid noise compared to spherical coordinates (away from the poles) persist. In this study reparameterization invariance of geometric objects (scalars, vectors and the forms generated by their covariant derivatives) is utilized to generate asymptotic forms for dependent fields of interest valid in the neighborhood of a pole. The central concept is that such objects cannot be altered by the metric structure of a parameterization. The new boundary conditions enforce symmetries that are required for transformations of geometric objects. They are implemented in an implicit polar filter of a structured grid, nonhydrostatic global atmospheric model that is simulating idealized Held-Suarez flows. A series of test simulations using different configurations of the asymptotic boundary conditions are made, along with control simulations that use the default model numerics with no absorber, at three different grid sizes. Typically the test simulations are ∼ 20% faster in wall clock time than the control-resulting from a decrease in noise at the poles in all cases. In the control simulations adverse numerical effects from the polar
Maps between Grassmann manifolds
Indian Academy of Sciences (India)
Parameswaran Sankaran Institute of Mathematical Sciences Chennai, India sankaran@imsc.res.in Indian Academy of Sciences Platinum Jubilee Meeting Hyderabad
2009-07-02
Jul 2, 2009 ... Classification of all manifolds (or maps between them) is an impossible task. The coarser, homotopical classification, is relatively easier–but only relatively! Homotopy is, roughly speaking, the study of properties of spaces and maps invariant under continuous deformations. Denote by [X, Y ] the set of all ...
International Nuclear Information System (INIS)
Lisboa, P.; Michael, C.
1982-01-01
We address the question of designing optimum discrete sets of points to represent numerically a continuous group manifold. We consider subsets which are extensions of the regular discrete subgroups. Applications to Monte Carlo simulation of SU(2) and SU(3) gauge theory are discussed. (orig.)
Singular perturbation in the physical sciences
Neu, John C
2015-01-01
This book is the testimony of a physical scientist whose language is singular perturbation analysis. Classical mathematical notions, such as matched asymptotic expansions, projections of large dynamical systems onto small center manifolds, and modulation theory of oscillations based either on multiple scales or on averaging/transformation theory, are included. The narratives of these topics are carried by physical examples: Let's say that the moment when we "see" how a mathematical pattern fits a physical problem is like "hitting the ball." Yes, we want to hit the ball. But a powerful stroke includes the follow-through. One intention of this book is to discern in the structure and/or solutions of the equations their geometric and physical content. Through analysis, we come to sense directly the shape and feel of phenomena. The book is structured into a main text of fundamental ideas and a subtext of problems with detailed solutions. Roughly speaking, the former is the initial contact between mathematics and p...
Dual manifold heat pipe evaporator
Adkins, D.R.; Rawlinson, K.S.
1994-01-04
An improved evaporator section is described for a dual manifold heat pipe. Both the upper and lower manifolds can have surfaces exposed to the heat source which evaporate the working fluid. The tubes in the tube bank between the manifolds have openings in their lower extensions into the lower manifold to provide for the transport of evaporated working fluid from the lower manifold into the tubes and from there on into the upper manifold and on to the condenser portion of the heat pipe. A wick structure lining the inner walls of the evaporator tubes extends into both the upper and lower manifolds. At least some of the tubes also have overflow tubes contained within them to carry condensed working fluid from the upper manifold to pass to the lower without spilling down the inside walls of the tubes. 1 figure.
Analytic manifolds in uniform algebras
International Nuclear Information System (INIS)
Tonev, T.V.
1988-12-01
Here we extend Bear-Hile's result concerning the version of famous Bishop's theorem for one-dimensional analytic structures in two directions: for n-dimensional complex analytic manifolds, n>1, and for generalized analytic manifolds. 14 refs
Building Reproducible Science with Singularity Containers
CERN. Geneva
2018-01-01
Michael Bauer first began working with containers at GSI national lab in Darmstadt, Germany, in 2017 while taking a semester off of school at the University of Michigan. Michael met Greg Kurtzer, project lead of Singularity, during his time at GSI and he began contributing heavily to the Singularity project. At the start of summer 2017, Greg hired Michael to work at the ...
Holonomy of Einstein Lorentzian manifolds
International Nuclear Information System (INIS)
Galaev, Anton S
2010-01-01
The classification of all possible holonomy algebras of Einstein and vacuum Einstein Lorentzian manifolds is obtained. It is shown that each such algebra appears as the holonomy algebra of an Einstein (resp. vacuum Einstein) Lorentzian manifold; the direct constructions are given. Also the holonomy algebras of totally Ricci-isotropic Lorentzian manifolds are classified. The classification of the holonomy algebras of Lorentzian manifolds is reviewed and a complete description of the spaces of curvature tensors for these holonomies is given.
Eigenvalue pinching on spinc manifolds
Roos, Saskia
2017-02-01
We derive various pinching results for small Dirac eigenvalues using the classification of spinc and spin manifolds admitting nontrivial Killing spinors. For this, we introduce a notion of convergence for spinc manifolds which involves a general study on convergence of Riemannian manifolds with a principal S1-bundle. We also analyze the relation between the regularity of the Riemannian metric and the regularity of the curvature of the associated principal S1-bundle on spinc manifolds with Killing spinors.
A generalized construction of mirror manifolds
International Nuclear Information System (INIS)
Berglund, P.; Huebsch, T.
1993-01-01
We generalize the known method for explicit construction of mirror pairs of (2,2)-superconformal field theories, using the formalism of Landau-Ginzburg orbifolds. Geometrically, these theories are realized as Calabi-Yau hypersurfaces in weighted projective spaces. This generalization makes it possible to construct the mirror partners of many manifolds for which the mirror was not previously known. (orig.)
Unimodularity criteria for Poisson structures on foliated manifolds
Pedroza, Andrés; Velasco-Barreras, Eduardo; Vorobiev, Yury
2018-03-01
We study the behavior of the modular class of an orientable Poisson manifold and formulate some unimodularity criteria in the semilocal context, around a (singular) symplectic leaf. Our results generalize some known unimodularity criteria for regular Poisson manifolds related to the notion of the Reeb class. In particular, we show that the unimodularity of the transverse Poisson structure of the leaf is a necessary condition for the semilocal unimodular property. Our main tool is an explicit formula for a bigraded decomposition of modular vector fields of a coupling Poisson structure on a foliated manifold. Moreover, we also exploit the notion of the modular class of a Poisson foliation and its relationship with the Reeb class.
Travelling wave solutions for a singularly perturbed Burgers–KdV ...
Indian Academy of Sciences (India)
This paper concerns with the existence problem of travelling wave solutions to a singularly perturbed Burgers–KdV equation. For this, we use the dynamical systems approach, specifically, the geometric singular perturbation theory and centre manifold theory. We also numerically show approximations, in particular, for ...
The construction of combinatorial manifolds with prescribed sets of links of vertices
International Nuclear Information System (INIS)
Gaifullin, A A
2008-01-01
To every oriented closed combinatorial manifold we assign the set (with repetitions) of isomorphism classes of links of its vertices. The resulting transformation L is the main object of study in this paper. We pose an inversion problem for L and show that this problem is closely related to Steenrod's problem on the realization of cycles and to the Rokhlin-Schwartz-Thom construction of combinatorial Pontryagin classes. We obtain a necessary condition for a set of isomorphism classes of combinatorial spheres to belong to the image of L. (Sets satisfying this condition are said to be balanced.) We give an explicit construction showing that every balanced set of isomorphism classes of combinatorial spheres falls into the image of L after passing to a multiple set and adding several pairs of the form (Z,-Z), where -Z is the sphere Z with the orientation reversed. Given any singular simplicial cycle ξ of a space X, this construction enables us to find explicitly a combinatorial manifold M and a map φ:M→X such that φ * [M]=r[ξ] for some positive integer r. The construction is based on resolving singularities of ξ. We give applications of the main construction to cobordisms of manifolds with singularities and cobordisms of simple cells. In particular, we prove that every rational additive invariant of cobordisms of manifolds with singularities admits a local formula. Another application is the construction of explicit (though inefficient) local combinatorial formulae for polynomials in the rational Pontryagin classes of combinatorial manifolds
Distribution of flux vacua around singular points in Calabi-Yau moduli space
International Nuclear Information System (INIS)
Eguchi, Tohru; Tachikawa, Yuji
2006-01-01
We study the distribution of type-IIB flux vacua in the moduli space near various singular loci, e.g. conifolds, ADE singularities on P 1 , Argyres-Douglas point etc, using the Ashok-Douglas density det (R+ω). We find that the vacuum density is integrable around each of them, irrespective of the type of the singularities. We study in detail an explicit example of an Argyres-Douglas point embedded in a compact Calabi-Yau manifold
LIFE CYCLE DESIGN OF AIR INTAKE MANIFOLDS; PHASE I: 2.0 L FORD CONTOUR AIR INTAKE MANIFOLD
The project team applied the life cycle design methodology to the design analysis of three alternative air intake manifolds: a sand cast aluminum, brazed aluminum tubular, and nylon composite. The design analysis included a life cycle inventory analysis, environmental regulatory...
Huang, Anpeng; Xu, Wenyao; Li, Zhinan; Xie, Linzhen; Sarrafzadeh, Majid; Li, Xiaoming; Cong, Jason
2014-09-01
Cardiovascular disease (CVD) is a major issue to public health. It contributes 41% to the Chinese death rate each year. This huge loss encouraged us to develop a Wearable Efficient teleCARdiology systEm (WE-CARE) for early warning and prevention of CVD risks in real time. WE-CARE is expected to work 24/7 online for mobile health (mHealth) applications. Unfortunately, this purpose is often disrupted in system experiments and clinical trials, even if related enabling technologies work properly. This phenomenon is rooted in the overload issue of complex Electrocardiogram (ECG) data in terms of system integration. In this study, our main objective is to get a system light-loading technology to enable mHealth with a benchmarked ECG anomaly recognition rate. To achieve this objective, we propose an approach to purify clinical features from ECG raw data based on manifold learning, called the Manifold-based ECG-feature Purification algorithm. Our clinical trials verify that our proposal can detect anomalies with a recognition rate of up to 94% which is highly valuable in daily public health-risk alert applications based on clinical criteria. Most importantly, the experiment results demonstrate that the WE-CARE system enabled by our proposal can enhance system reliability by at least two times and reduce false negative rates to 0.76%, and extend the battery life by 40.54%, in the system integration level.
Analysis, manifolds and physics
Choquet-Bruhat, Y
2000-01-01
Twelve problems have been added to the first edition; four of them are supplements to problems in the first edition. The others deal with issues that have become important, since the first edition of Volume II, in recent developments of various areas of physics. All the problems have their foundations in volume 1 of the 2-Volume set Analysis, Manifolds and Physics. It would have been prohibitively expensive to insert the new problems at their respective places. They are grouped together at the end of this volume, their logical place is indicated by a number of parenthesis following the title.
Daverman, Robert J
2007-01-01
Decomposition theory studies decompositions, or partitions, of manifolds into simple pieces, usually cell-like sets. Since its inception in 1929, the subject has become an important tool in geometric topology. The main goal of the book is to help students interested in geometric topology to bridge the gap between entry-level graduate courses and research at the frontier as well as to demonstrate interrelations of decomposition theory with other parts of geometric topology. With numerous exercises and problems, many of them quite challenging, the book continues to be strongly recommended to eve
Manifold Regularized Correlation Object Tracking
Hu, Hongwei; Ma, Bo; Shen, Jianbing; Shao, Ling
2017-01-01
In this paper, we propose a manifold regularized correlation tracking method with augmented samples. To make better use of the unlabeled data and the manifold structure of the sample space, a manifold regularization-based correlation filter is introduced, which aims to assign similar labels to neighbor samples. Meanwhile, the regression model is learned by exploiting the block-circulant structure of matrices resulting from the augmented translated samples over multiple base samples cropped fr...
Smooth Maps of a Foliated Manifold in a Symplectic Manifold
Indian Academy of Sciences (India)
Let be a smooth manifold with a regular foliation F and a 2-form which induces closed forms on the leaves of F in the leaf topology. A smooth map f : ( M , F ) ⟶ ( N , ) in a symplectic manifold ( N , ) is called a foliated symplectic immersion if restricts to an immersion on each leaf of the foliation and further, the ...
A study of Para-Sasakian manifold
International Nuclear Information System (INIS)
Rahman, M.S.
1995-08-01
A Para-Sasakian manifold M is viewed in the light of an almost paracontact manifold. The fundamental concepts of M in spirit to Recurrent, Ricci-recurrent, 2-Recurrent and 2-Ricci-recurrent manifolds are presented. An η-Einstein manifold modelled on P-Sasakian manifold is then treated with simplified proofs of some results. (author). 7 refs
Moment-angle manifolds, intersection of quadrics and higher dimensional contact manifolds
Barreto, Yadira; Verjovsky, Alberto
2013-01-01
We construct new examples of contact manifolds in arbitrarily large dimensions. These manifolds which we call quasi moment-angle manifolds, are closely related to the classical moment-angle manifolds.
Yuan, Rui; Lv, Yong; Song, Gangbing
2018-04-16
Rolling bearings are important components in rotary machinery systems. In the field of multi-fault diagnosis of rolling bearings, the vibration signal collected from single channels tends to miss some fault characteristic information. Using multiple sensors to collect signals at different locations on the machine to obtain multivariate signal can remedy this problem. The adverse effect of a power imbalance between the various channels is inevitable, and unfavorable for multivariate signal processing. As a useful, multivariate signal processing method, Adaptive-projection has intrinsically transformed multivariate empirical mode decomposition (APIT-MEMD), and exhibits better performance than MEMD by adopting adaptive projection strategy in order to alleviate power imbalances. The filter bank properties of APIT-MEMD are also adopted to enable more accurate and stable intrinsic mode functions (IMFs), and to ease mode mixing problems in multi-fault frequency extractions. By aligning IMF sets into a third order tensor, high order singular value decomposition (HOSVD) can be employed to estimate the fault number. The fault correlation factor (FCF) analysis is used to conduct correlation analysis, in order to determine effective IMFs; the characteristic frequencies of multi-faults can then be extracted. Numerical simulations and the application of multi-fault situation can demonstrate that the proposed method is promising in multi-fault diagnoses of multivariate rolling bearing signal.
Diffeomorphisms of elliptic 3-manifolds
Hong, Sungbok; McCullough, Darryl; Rubinstein, J Hyam
2012-01-01
This work concerns the diffeomorphism groups of 3-manifolds, in particular of elliptic 3-manifolds. These are the closed 3-manifolds that admit a Riemannian metric of constant positive curvature, now known to be exactly the closed 3-manifolds that have a finite fundamental group. The (Generalized) Smale Conjecture asserts that for any elliptic 3-manifold M, the inclusion from the isometry group of M to its diffeomorphism group is a homotopy equivalence. The original Smale Conjecture, for the 3-sphere, was proven by J. Cerf and A. Hatcher, and N. Ivanov proved the generalized conjecture for many of the elliptic 3-manifolds that contain a geometrically incompressible Klein bottle. The main results establish the Smale Conjecture for all elliptic 3-manifolds containing geometrically incompressible Klein bottles, and for all lens spaces L(m,q) with m at least 3. Additional results imply that for a Haken Seifert-fibered 3 manifold V, the space of Seifert fiberings has contractible components, and apart from a small...
Manifolds of positive scalar curvature
Energy Technology Data Exchange (ETDEWEB)
Stolz, S [Department of Mathematics, University of Notre Dame, Notre Dame (United States)
2002-08-15
This lecture gives an survey on the problem of finding a positive scalar curvature metric on a closed manifold. The Gromov-Lawson-Rosenberg conjecture and its relation to the Baum-Connes conjecture are discussed and the problem of finding a positive Ricci curvature metric on a closed manifold is explained.
Energy Technology Data Exchange (ETDEWEB)
Manzano, E.; Maleta, E. J.; Carrasco, J. E.
2008-07-01
The Singular Strategic Project (PSE) On Cultivos, Development, demonstration and evaluation of the viability of energy crop biomass-based energy production in Spain, has been under way since 2005. This article describes the project objectives and general data indicating the current project status and the most relevant preliminary results obtained since it began. The On Cultivos PSE is proving to be an effective tool to channel the R and D efforts required to achieve the integral commercial implementation of energy crops in Spain. (Author) 4 refs.
Complex manifolds in relativity
International Nuclear Information System (INIS)
Flaherty, E.J. Jr.
1975-01-01
Complex manifold theory is applied to the study of certain problems in general relativity. The first half of the work is devoted to the mathematical theory of complex manifold. Then a brief review of general relativity is given. It is shown that any spacetime admits locally an almost Hermitian structure, suitably modified to be compatible with the indefinite metric of spacetime. This structure is integrable if and only if the spacetime admits two geodesic and shearfree null congruences, thus in particular if the spacetime is type D vacuum or electrified. The structure is ''half-integrable'' in a suitable sense if and only if the spacetime admits one geodesic and shearfree null congruence, thus in particular for all algebraically special vacuum spacetimes. Conditions for the modified Hermitian spacetime to be Kahlerian are presented. The most general metric for such a modified Kahlerian spacetime is found. It is shown that the type D vacuum and electrified spacetimes are conformally related to modified Kahlerian spacetimes by a generally complex conformal factor. These latter are shown to possess a very rich structure, including the existence of Killing tensors and Killing vectors. A new ''explanation'' of Newman's complex coordinate transformations is given. It is felt to be superior to previous ''explanations'' on several counts. For example, a physical interpretation in terms of a symmetry group is given. The existence of new complex coordinate transformations is established: Nt is shown that any type D vacuum spacetime is obtainable from either Schwarzschild spacetime or ''C'' spacetime by a complex coordinate transformation. Finally, some related topics are discussed and areas for future work are outlined. (Diss. Abstr. Int., B)
Singular points in moduli spaces of Yang-Mills fields
International Nuclear Information System (INIS)
Ticciati, R.
1984-01-01
This thesis investigates the metric dependence of the moduli spaces of Yang-Mills fields of an SU(2) principal bundle P with chern number -1 over a four-dimensional, simply-connected, oriented, compact smooth manifold M with positive definite intersection form. The purpose of this investigation is to suggest that the surgery class of the moduli space of irreducible connections is, for a generic metric, a Z 2 topological invariant of the smooth structure on M. There are three main parts. The first two parts are local analysis of singular points in the moduli spaces. The last part is global. The first part shows that the set of metrics for which the moduli space of irreducible connections has only non-degenerate singularities has codimension at least one in the space of all metrics. The second part shows that, for a one-parameter family of moduli spaces in a direction transverse to the set of metrics for which the moduli spaces have singularities, passing through a non-degenerate singularity of the simplest type changes the moduli space by a cobordism. The third part shows that generic one-parameter families of metrics give rise to six-dimensional manifolds, the corresponding family of moduli spaces of irreducible connections. It is shown that when M is homeomorphic to S 4 the six-dimensional manifold is a proper cobordism, thus establishing the independence of the surgery class of the moduli space on the metric on M
Dirac operator on spaces with conical singularities
International Nuclear Information System (INIS)
Chou, A.W.
1982-01-01
The Dirac operator on compact spaces with conical singularities is studied via the separation of variables formula and the functional calculus of the Dirac Laplacian on the cone. A Bochner type vanishing theorem which gives topological obstructions to the existence of non-negative scalar curvature k greater than or equal to 0 in the singular case is proved. An index formula relating the index of the Dirac operator to the A-genus and Eta-invariant similar to that of Atiyah-Patodi-Singer is obtained. In an appendix, manifolds with boundary with non-negative scalar curvature k greater than or equal to 0 are studied, and several new results on constructing complete metrics with k greater than or equal to on them are obtained
Echocardiogram enhancement using supervised manifold denoising.
Wu, Hui; Huynh, Toan T; Souvenir, Richard
2015-08-01
This paper presents data-driven methods for echocardiogram enhancement. Existing denoising algorithms typically rely on a single noise model, and do not generalize to the composite noise sources typically found in real-world echocardiograms. Our methods leverage the low-dimensional intrinsic structure of echocardiogram videos. We assume that echocardiogram images are noisy samples from an underlying manifold parametrized by cardiac motion and denoise images via back-projection onto a learned (non-linear) manifold. Our methods incorporate synchronized side information (e.g., electrocardiography), which is often collected alongside the visual data. We evaluate the proposed methods on a synthetic data set and real-world echocardiograms. Quantitative results show improved performance of our methods over recent image despeckling methods and video denoising methods, and a visual analysis of real-world data shows noticeable image enhancement, even in the challenging case of noise due to dropout artifacts. Copyright © 2015 Elsevier B.V. All rights reserved.
Pluripotential theory on quaternionic manifolds
Alesker, Semyon
2012-05-01
On any quaternionic manifold of dimension greater than 4 a class of plurisubharmonic functions (or, rather, sections of an appropriate line bundle) is introduced. Then a Monge-Ampère operator is defined. It is shown that it satisfies a version of the theorems of A. D. Alexandrov and Chern-Levine-Nirenberg. For more special classes of manifolds analogous results were previously obtained in Alesker (2003) [1] for the flat quaternionic space Hn and in Alesker and Verbitsky (2006) [5] for hypercomplex manifolds. One of the new technical aspects of the present paper is the systematic use of the Baston differential operators, for which we also prove a new multiplicativity property.
Smooth maps of a foliated manifold in a symplectic manifold
Indian Academy of Sciences (India)
Abstract. Let M be a smooth manifold with a regular foliation F and a 2-form ω which induces closed forms on the leaves of F in the leaf topology. A smooth map f : (M, F) −→ (N,σ) in a symplectic manifold (N,σ) is called a foliated symplectic immersion if f restricts to an immersion on each leaf of the foliation and further, the.
An introduction to differential manifolds
Lafontaine, Jacques
2015-01-01
This book is an introduction to differential manifolds. It gives solid preliminaries for more advanced topics: Riemannian manifolds, differential topology, Lie theory. It presupposes little background: the reader is only expected to master basic differential calculus, and a little point-set topology. The book covers the main topics of differential geometry: manifolds, tangent space, vector fields, differential forms, Lie groups, and a few more sophisticated topics such as de Rham cohomology, degree theory and the Gauss-Bonnet theorem for surfaces. Its ambition is to give solid foundations. In particular, the introduction of “abstract” notions such as manifolds or differential forms is motivated via questions and examples from mathematics or theoretical physics. More than 150 exercises, some of them easy and classical, some others more sophisticated, will help the beginner as well as the more expert reader. Solutions are provided for most of them. The book should be of interest to various readers: undergra...
Manifold Regularized Correlation Object Tracking.
Hu, Hongwei; Ma, Bo; Shen, Jianbing; Shao, Ling
2018-05-01
In this paper, we propose a manifold regularized correlation tracking method with augmented samples. To make better use of the unlabeled data and the manifold structure of the sample space, a manifold regularization-based correlation filter is introduced, which aims to assign similar labels to neighbor samples. Meanwhile, the regression model is learned by exploiting the block-circulant structure of matrices resulting from the augmented translated samples over multiple base samples cropped from both target and nontarget regions. Thus, the final classifier in our method is trained with positive, negative, and unlabeled base samples, which is a semisupervised learning framework. A block optimization strategy is further introduced to learn a manifold regularization-based correlation filter for efficient online tracking. Experiments on two public tracking data sets demonstrate the superior performance of our tracker compared with the state-of-the-art tracking approaches.
Singular stochastic differential equations
Cherny, Alexander S
2005-01-01
The authors introduce, in this research monograph on stochastic differential equations, a class of points termed isolated singular points. Stochastic differential equations possessing such points (called singular stochastic differential equations here) arise often in theory and in applications. However, known conditions for the existence and uniqueness of a solution typically fail for such equations. The book concentrates on the study of the existence, the uniqueness, and, what is most important, on the qualitative behaviour of solutions of singular stochastic differential equations. This is done by providing a qualitative classification of isolated singular points, into 48 possible types.
Non-Kaehler attracting manifolds
International Nuclear Information System (INIS)
Dall'Agata, Gianguido
2006-01-01
We observe that the new attractor mechanism describing IIB flux vacua for Calabi-Yau compactifications has a possible extension to the landscape of non-Kaehler vacua that emerge in heterotic compactifications with fluxes. We focus on the effective theories coming from compactifications on generalized half-flat manifolds, showing that the Minkowski 'attractor points' for 3-form fluxes are special-hermitian manifolds
Vector Fields on Product Manifolds
Kurz, Stefan
2011-01-01
This short report establishes some basic properties of smooth vector fields on product manifolds. The main results are: (i) On a product manifold there always exists a direct sum decomposition into horizontal and vertical vector fields. (ii) Horizontal and vertical vector fields are naturally isomorphic to smooth families of vector fields defined on the factors. Vector fields are regarded as derivations of the algebra of smooth functions.
Characteristic manifolds in relativistic hypoelasticity
Energy Technology Data Exchange (ETDEWEB)
Giambo, S [Messina Univ. (Italy). Istituto di Matematica
1978-10-02
The relativistic hypoelasticity is considered and the characteristic manifolds are determined by using the Cauchy-Kovalevski theorem for the Cauchy problem with analytic initial conditions. Taking into account that the characteristic manifold represents the image of the front-wave in the space-time, it is possible to determine the velocities of propagation. Three wave-species are obtained: material waves, longitudinal waves and transverse waves.
Moduli space of torsional manifolds
International Nuclear Information System (INIS)
Becker, Melanie; Tseng, L.-S.; Yau, S.-T.
2007-01-01
We characterize the geometric moduli of non-Kaehler manifolds with torsion. Heterotic supersymmetric flux compactifications require that the six-dimensional internal manifold be balanced, the gauge bundle be Hermitian Yang-Mills, and also the anomaly cancellation be satisfied. We perform the linearized variation of these constraints to derive the defining equations for the local moduli. We explicitly determine the metric deformations of the smooth flux solution corresponding to a torus bundle over K3
Hazy spaces, tangent spaces, manifolds and groups
International Nuclear Information System (INIS)
Dodson, C.T.J.
1977-03-01
The results on hazy spaces and the developments leading to hazy manifolds and groups are summarized. Proofs have appeared elsewhere so here examples are considered and some motivation for definitions and constructions in the theorems is analyzed. It is shown that quite simple ideas, intuitively acceptable, lead to remarkable similarity with the theory of differentiable manifolds. Hazy n manifolds have tangent bundles that are hazy 2n manifolds and there are hazy manifold structures for groups. Products and submanifolds are easily constructed and in particular the hazy n-sphere manifolds as submanifolds of the standard hazy manifold Zsup(n+1)
The topology of toric origami manifolds
Holm, Tara; Pires, Ana Rita
2012-01-01
A folded symplectic form on a manifold is a closed 2-form with the mildest possible degeneracy along a hypersurface. A special class of folded symplectic manifolds are the origami symplectic manifolds, studied by Cannas da Silva, Guillemin and Pires, who classified toric origami manifolds by combinatorial origami templates. In this paper, we examine the topology of toric origami manifolds that have acyclic origami template and co-orientable folding hypersurface. We prove that the cohomology i...
Quantum evolution across singularities
International Nuclear Information System (INIS)
Craps, Ben; Evnin, Oleg
2008-01-01
Attempts to consider evolution across space-time singularities often lead to quantum systems with time-dependent Hamiltonians developing an isolated singularity as a function of time. Examples include matrix theory in certain singular time-dependent backgounds and free quantum fields on the two-dimensional compactified Milne universe. Due to the presence of the singularities in the time dependence, the conventional quantum-mechanical evolution is not well-defined for such systems. We propose a natural way, mathematically analogous to renormalization in conventional quantum field theory, to construct unitary quantum evolution across the singularity. We carry out this procedure explicitly for free fields on the compactified Milne universe and compare our results with the matching conditions considered in earlier work (which were based on the covering Minkowski space)
Ishii, Shihoko
2014-01-01
This book is an introduction to singularities for graduate students and researchers. It is said that algebraic geometry originated in the seventeenth century with the famous work Discours de la méthode pour bien conduire sa raison, et chercher la vérité dans les sciences by Descartes. In that book he introduced coordinates to the study of geometry. After its publication, research on algebraic varieties developed steadily. Many beautiful results emerged in mathematicians’ works. Most of them were about non-singular varieties. Singularities were considered “bad” objects that interfered with knowledge of the structure of an algebraic variety. In the past three decades, however, it has become clear that singularities are necessary for us to have a good description of the framework of varieties. For example, it is impossible to formulate minimal model theory for higher-dimensional cases without singularities. Another example is that the moduli spaces of varieties have natural compactification, the boundar...
Principal Curves on Riemannian Manifolds.
Hauberg, Soren
2016-09-01
Euclidean statistics are often generalized to Riemannian manifolds by replacing straight-line interpolations with geodesic ones. While these Riemannian models are familiar-looking, they are restricted by the inflexibility of geodesics, and they rely on constructions which are optimal only in Euclidean domains. We consider extensions of Principal Component Analysis (PCA) to Riemannian manifolds. Classic Riemannian approaches seek a geodesic curve passing through the mean that optimizes a criteria of interest. The requirements that the solution both is geodesic and must pass through the mean tend to imply that the methods only work well when the manifold is mostly flat within the support of the generating distribution. We argue that instead of generalizing linear Euclidean models, it is more fruitful to generalize non-linear Euclidean models. Specifically, we extend the classic Principal Curves from Hastie & Stuetzle to data residing on a complete Riemannian manifold. We show that for elliptical distributions in the tangent of spaces of constant curvature, the standard principal geodesic is a principal curve. The proposed model is simple to compute and avoids many of the pitfalls of traditional geodesic approaches. We empirically demonstrate the effectiveness of the Riemannian principal curves on several manifolds and datasets.
Slow manifolds in chemical kinetics
International Nuclear Information System (INIS)
Shahzad, M.; Haq, I. U.; Sultan, F.; Wahab, A.; Faizullah, F.; Rahman, G. U.
2016-01-01
Modelling the chemical system, especially for complex and higher dimensional problems, gives an easy way to handle the ongoing reaction process with respect to time. Here, we will consider some of the newly developed computational methods commonly used for model reductions in a chemical reaction. An effective (simple) method is planned to measure the low dimensional manifold, which reduces the higher dimensional system in such a way that it may not affect the precision of the whole mechanism. The phase flow of the solution trajectories near the equilibrium point is observed while the initial approximation is measured with the spectral quasi equilibrium manifold, which starts from the equilibrium point. To make it an invariant curve, the approximated curve is first refined a certain number of times using the method of invariant grids. The other way of getting the reduced data in the low dimensional manifold is possible through the intrinsic low dimensional manifold. Then, we compare these two invariant curves given by both the methods. Finally, the idea is extended to the higher dimensional manifold, where more number of progress variables will be added. (author)
Manifold structure preservative for hyperspectral target detection
Imani, Maryam
2018-05-01
A nonparametric method termed as manifold structure preservative (MSP) is proposed in this paper for hyperspectral target detection. MSP transforms the feature space of data to maximize the separation between target and background signals. Moreover, it minimizes the reconstruction error of targets and preserves the topological structure of data in the projected feature space. MSP does not need to consider any distribution for target and background data. So, it can achieve accurate results in real scenarios due to avoiding unreliable assumptions. The proposed MSP detector is compared to several popular detectors and the experiments on a synthetic data and two real hyperspectral images indicate the superior ability of it in target detection.
Singularities and the geometry of spacetime
Hawking, Stephen
2014-11-01
The aim of this essay is to investigate certain aspects of the geometry of the spacetime manifold in the General Theory of Relativity with particular reference to the occurrence of singularities in cosmological solutions and their relation with other global properties. Section 2 gives a brief outline of Riemannian geometry. In Section 3, the General Theory of Relativity is presented in the form of two postulates and two requirements which are common to it and to the Special Theory of Relativity, and a third requirement, the Einstein field equations, which distinguish it from the Special Theory. There does not seem to be any alternative set of field equations which would not have some undeseriable features. Some exact solutions are described. In Section 4, the physical significance of curvature is investigated using the deviation equation for timelike and null curves. The Riemann tensor is decomposed into the Ricci tensor which represents the gravitational effect at a point of matter at that point and the Welyl tensor which represents the effect at a point of gravitational radiation and matter at other points. The two tensors are related by the Bianchi identities which are presented in a form analogous to the Maxwell equations. Some lemmas are given for the occurrence of conjugate points on timelike and null geodesics and their relation with the variation of timelike and null curves is established. Section 5 is concerned with properties of causal relations between points of spacetime. It is shown that these could be used to determine physically the manifold structure of spacetime if the strong causality assumption held. The concepts of a null horizon and a partial Cauchy surface are introduced and are used to prove a number of lemmas relating to the existence of a timelike curve of maximum length between two sets. In Section 6, the definition of a singularity of spacetime is given in terms of geodesic incompleteness. The various energy assumptions needed to prove
Ricci flow and geometrization of 3-manifolds
Morgan, John W
2010-01-01
This book is based on lectures given at Stanford University in 2009. The purpose of the lectures and of the book is to give an introductory overview of how to use Ricci flow and Ricci flow with surgery to establish the Poincar� Conjecture and the more general Geometrization Conjecture for 3-dimensional manifolds. Most of the material is geometric and analytic in nature; a crucial ingredient is understanding singularity development for 3-dimensional Ricci flows and for 3-dimensional Ricci flows with surgery. This understanding is crucial for extending Ricci flows with surgery so that they are defined for all positive time. Once this result is in place, one must study the nature of the time-slices as the time goes to infinity in order to deduce the topological consequences. The goal of the authors is to present the major geometric and analytic results and themes of the subject without weighing down the presentation with too many details. This book can be read as an introduction to more complete treatments of ...
Properties of kinematic singularities
Energy Technology Data Exchange (ETDEWEB)
Coley, A A [Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia B3H 3J5 (Canada); Hervik, S [Department of Mathematics and Natural Sciences, University of Stavanger, N-4036 Stavanger (Norway); Lim, W C [Albert-Einstein-Institut, Am Muehlenberg 1, D-14476 Potsdam (Germany); MacCallum, M A H, E-mail: aac@mathstat.dal.c, E-mail: sigbjorn.hervik@uis.n, E-mail: wclim@aei.mpg.d, E-mail: m.a.h.maccallum@qmul.ac.u [School of Mathematical Sciences, Queen Mary University of London, E1 4NS (United Kingdom)
2009-11-07
The locally rotationally symmetric tilted perfect fluid Bianchi type V cosmological model provides examples of future geodesically complete spacetimes that admit a 'kinematic singularity' at which the fluid congruence is inextendible but all frame components of the Weyl and Ricci tensors remain bounded. We show that for any positive integer n there are examples of Bianchi type V spacetimes admitting a kinematic singularity such that the covariant derivatives of the Weyl and Ricci tensors up to the nth order also stay bounded. We briefly discuss singularities in classical spacetimes.
Stein Manifolds and Holomorphic Mappings
Forstneric, Franc
2011-01-01
The main theme of this book is the homotopy principle for holomorphic mappings from Stein manifolds to the newly introduced class of Oka manifolds. This book contains the first complete account of Oka-Grauert theory and its modern extensions, initiated by Mikhail Gromov and developed in the last decade by the author and his collaborators. Included is the first systematic presentation of the theory of holomorphic automorphisms of complex Euclidean spaces, a survey on Stein neighborhoods, connections between the geometry of Stein surfaces and Seiberg-Witten theory, and a wide variety of applicat
Differential geometry curves, surfaces, manifolds
Kohnel, Wolfgang
2002-01-01
This carefully written book is an introduction to the beautiful ideas and results of differential geometry. The first half covers the geometry of curves and surfaces, which provide much of the motivation and intuition for the general theory. Special topics that are explored include Frenet frames, ruled surfaces, minimal surfaces and the Gauss-Bonnet theorem. The second part is an introduction to the geometry of general manifolds, with particular emphasis on connections and curvature. The final two chapters are insightful examinations of the special cases of spaces of constant curvature and Einstein manifolds. The text is illustrated with many figures and examples. The prerequisites are undergraduate analysis and linear algebra.
Blowup for flat slow manifolds
DEFF Research Database (Denmark)
Kristiansen, Kristian Uldall
2017-01-01
In this paper, we present a way of extending the blowup method, in the formulation of Krupa and Szmolyan, to flat slow manifolds that lose hyperbolicity beyond any algebraic order. Although these manifolds have infinite co-dimensions, they do appear naturally in certain settings; for example, in (a......) the regularization of piecewise smooth systems by tanh, (b) a particular aircraft landing dynamics model, and finally (c) in a model of earthquake faulting. We demonstrate the approach using a simple model system and the examples (a) and (b)....
Blowup for flat slow manifolds
Kristiansen, K. U.
2017-05-01
In this paper, we present a way of extending the blowup method, in the formulation of Krupa and Szmolyan, to flat slow manifolds that lose hyperbolicity beyond any algebraic order. Although these manifolds have infinite co-dimensions, they do appear naturally in certain settings; for example, in (a) the regularization of piecewise smooth systems by \\tanh , (b) a particular aircraft landing dynamics model, and finally (c) in a model of earthquake faulting. We demonstrate the approach using a simple model system and the examples (a) and (b).
Matrix regularization of 4-manifolds
Trzetrzelewski, M.
2012-01-01
We consider products of two 2-manifolds such as S^2 x S^2, embedded in Euclidean space and show that the corresponding 4-volume preserving diffeomorphism algebra can be approximated by a tensor product SU(N)xSU(N) i.e. functions on a manifold are approximated by the Kronecker product of two SU(N) matrices. A regularization of the 4-sphere is also performed by constructing N^2 x N^2 matrix representations of the 4-algebra (and as a byproduct of the 3-algebra which makes the regularization of S...
Connections and curvatures on complex Riemannian manifolds
International Nuclear Information System (INIS)
Ganchev, G.; Ivanov, S.
1991-05-01
Characteristic connection and characteristic holomorphic sectional curvatures are introduced on a complex Riemannian manifold (not necessarily with holomorphic metric). For the class of complex Riemannian manifolds with holomorphic characteristic connection a classification of the manifolds with (pointwise) constant holomorphic characteristic curvature is given. It is shown that the conformal geometry of complex analytic Riemannian manifolds can be naturally developed on the class of locally conformal holomorphic Riemannian manifolds. Complex Riemannian manifolds locally conformal to the complex Euclidean space are characterized with zero conformal fundamental tensor and zero conformal characteristic tensor. (author). 12 refs
Generalized graph manifolds and their effective recognition
International Nuclear Information System (INIS)
Matveev, S V
1998-01-01
A generalized graph manifold is a three-dimensional manifold obtained by gluing together elementary blocks, each of which is either a Seifert manifold or contains no essential tori or annuli. By a well-known result on torus decomposition each compact three-dimensional manifold with boundary that is either empty or consists of tori has a canonical representation as a generalized graph manifold. A short simple proof of the existence of a canonical representation is presented and a (partial) algorithm for its construction is described. A simple hyperbolicity test for blocks that are not Seifert manifolds is also presented
International Nuclear Information System (INIS)
Sitaramayya, M.
1993-11-01
After a brief review of the geometry of Moishezon spaces, their relation with l-convex spaces and a reasonable and up to date understanding of the obstructions for projectivity of Moishezon objects both in singular and non-singular case is given. The geometry of l-convex manifolds and with l-dimensional exceptional set is studied and some problems and conjectures are stated. The tools of cohomology vanishing theorems important for the subject are briefly sketched. Compactifications of C 3 and Stein spaces are finally outlined. given. 111 refs, 2 figs
Nonlinear singular elliptic equations
International Nuclear Information System (INIS)
Dong Minh Duc.
1988-09-01
We improve the Poincare inequality, the Sobolev imbedding theorem and the Trudinger imbedding theorem and prove a Mountain pass theorem. Applying these results we study a nonlinear singular mixed boundary problem. (author). 22 refs
International Nuclear Information System (INIS)
Berry, M.V.
2002-01-01
For illumination with white light, the spectra near a typical isolated phase singularity (nodal point of the component wavelengths) can be described by a universal function of position, up to linear distortion and a weak dependence on the spectrum of the source. The appearance of the singularity when viewed by a human observer is predicted by transforming the spectrum to trichromatic variables and chromaticity coordinates, and then rendering the colours, scaled to constant luminosity, on a computer monitor. The pattern far from the singularity is a white that depends on the source temperature, and the centre of the pattern is flanked by intensely coloured 'eyes', one orange and one blue, separated by red, and one of the eyes is surrounded by a bright white circle. Only a small range of possible colours appears near the singularity; in particular, there is no green. (author)
Directory of Open Access Journals (Sweden)
Gabriel Martínez-Niconoff
2012-01-01
Full Text Available With the purpose to compare the physical features of the electromagnetic field, we describe the synthesis of optical singularities propagating in the free space and on a metal surface. In both cases the electromagnetic field has a slit-shaped curve as a boundary condition, and the singularities correspond to a shock wave that is a consequence of the curvature of the slit curve. As prototypes, we generate singularities that correspond to fold and cusped regions. We show that singularities in free space may generate bifurcation effects while plasmon fields do not generate these kinds of effects. Experimental results for free-space propagation are presented and for surface plasmon fields, computer simulations are shown.
International Nuclear Information System (INIS)
Goswami, Rituparno; Joshi, Pankaj S.; Vaz, Cenalo; Witten, Louis
2004-01-01
We construct a class of spherically symmetric collapse models in which a naked singularity may develop as the end state of collapse. The matter distribution considered has negative radial and tangential pressures, but the weak energy condition is obeyed throughout. The singularity forms at the center of the collapsing cloud and continues to be visible for a finite time. The duration of visibility depends on the nature of energy distribution. Hence the causal structure of the resulting singularity depends on the nature of the mass function chosen for the cloud. We present a general model in which the naked singularity formed is timelike, neither pointlike nor null. Our work represents a step toward clarifying the necessary conditions for the validity of the Cosmic Censorship Conjecture
Directory of Open Access Journals (Sweden)
Hans Schonemann
1996-12-01
Full Text Available Some algorithms for singularity theory and algebraic geometry The use of Grobner basis computations for treating systems of polynomial equations has become an important tool in many areas. This paper introduces of the concept of standard bases (a generalization of Grobner bases and the application to some problems from algebraic geometry. The examples are presented as SINGULAR commands. A general introduction to Grobner bases can be found in the textbook [CLO], an introduction to syzygies in [E] and [St1]. SINGULAR is a computer algebra system for computing information about singularities, for use in algebraic geometry. The basic algorithms in SINGULAR are several variants of a general standard basis algorithm for general monomial orderings (see [GG]. This includes wellorderings (Buchberger algorithm ([B1], [B2] and tangent cone orderings (Mora algorithm ([M1], [MPT] as special cases: It is able to work with non-homogeneous and homogeneous input and also to compute in the localization of the polynomial ring in 0. Recent versions include algorithms to factorize polynomials and a factorizing Grobner basis algorithm. For a complete description of SINGULAR see [Si].
Numerical method of singular problems on singular integrals
International Nuclear Information System (INIS)
Zhao Huaiguo; Mou Zongze
1992-02-01
As first part on the numerical research of singular problems, a numerical method is proposed for singular integrals. It is shown that the procedure is quite powerful for solving physics calculation with singularity such as the plasma dispersion function. Useful quadrature formulas for some class of the singular integrals are derived. In general, integrals with more complex singularities can be dealt by this method easily
Cayley transform on Stiefel manifolds
Macías-Virgós, Enrique; Pereira-Sáez, María José; Tanré, Daniel
2018-01-01
The Cayley transform for orthogonal groups is a well known construction with applications in real and complex analysis, linear algebra and computer science. In this work, we construct Cayley transforms on Stiefel manifolds. Applications to the Lusternik-Schnirelmann category and optimization problems are presented.
Principal Curves on Riemannian Manifolds
DEFF Research Database (Denmark)
Hauberg, Søren
2015-01-01
Euclidean statistics are often generalized to Riemannian manifolds by replacing straight-line interpolations with geodesic ones. While these Riemannian models are familiar-looking, they are restricted by the inflexibility of geodesics, and they rely on constructions which are optimal only in Eucl...
Collective coordinates on symplectic manifolds
International Nuclear Information System (INIS)
Razumov, A.V.; Taranov, A.Yu.
1981-01-01
For an arbitrary Lie group of canonical transformations on a symplectic manifold collective coordinates are introduced. They describe a motion of the dynamical system as a whole under the group transformations. Some properties of Lie group of canonical transformations are considered [ru
An imbedding of Lorentzian manifolds
International Nuclear Information System (INIS)
Kim, Do-Hyung
2009-01-01
A new method for imbedding a Lorentzian manifold with a non-compact Cauchy surface is presented. As an application, it is shown that any two-dimensional globally hyperbolic spacetime with a non-compact Cauchy surface can be causally isomorphically imbedded into two-dimensional Minkowski spacetime.
Indian Academy of Sciences (India)
Abstract. This paper is concerned with the problem of the geometry of Norden manifolds. Some properties of Riemannian curvature tensors and curvature scalars of Kähler–Norden manifolds using the theory of Tachibana operators is presented.
Rank Two Affine Manifolds in Genus 3
Aulicino, David; Nguyen, Duc-Manh
2016-01-01
We complete the classification of rank two affine manifolds in the moduli space of translation surfaces in genus three. Combined with a recent result of Mirzakhani and Wright, this completes the classification of higher rank affine manifolds in genus three.
On a Monge-Amp\\`ere operator for plurisubharmonic functions with analytic singularities
Andersson, Mats; Błocki, Zbigniew; Wulcan, Elizabeth
2017-01-01
We study continuity properties of generalized Monge-Amp\\`ere operators for plurisubharmonic functions with analytic singularities. In particular, we prove continuity for a natural class of decreasing approximating sequences. We also prove a formula for the total mass of the Monge-Amp\\`ere measure of such a function on a compact K\\"ahler manifold.
Singular elliptic systems involving concave terms and critical Caffarelli-Kohn-Nirenberg exponents
Directory of Open Access Journals (Sweden)
Mohammed E. O. El Mokhtar
2012-03-01
Full Text Available In this article, we establish the existence of at least four solutions to a singular system with a concave term, a critical Caffarelli-Kohn-Nirenberg exponent, and sign-changing weight functions. Our main tools are the Nehari manifold and the mountain pass theorem.
Constructions of Calabi-Yau manifolds
International Nuclear Information System (INIS)
Hubsch, T.
1987-01-01
Among possible compactifications of Superstring Theories (defined in 9+1 dimensional space-time) it is argued that only those in Calabi-Yau manifolds may lead to phenomenologically acceptable models. Thus, constructions of such manifolds are studied and a huge sequence is presented, giving rise to many possibly applicable manifolds
Natural Connections on Riemannian Product Manifolds
Gribacheva, Dobrinka
2011-01-01
A Riemannian almost product manifold with integrable almost product structure is called a Riemannian product manifold. In the present paper the natural connections on such manifolds are studied, i.e. the linear connections preserving the almost product structure and the Riemannian metric.
A viewpoint on nearly conformally symmetric manifold
International Nuclear Information System (INIS)
Rahman, M.S.
1990-06-01
Some observations, with definition, on Nearly Conformally Symmetric (NCS) manifold are made. A number of theorems concerning conformal change of metric and parallel tensors on NCS manifolds are presented. It is illustrated that a manifold M = R n-1 x R + 1 , endowed with a special metric, is NCS but not of harmonic curvature. (author). 8 refs
Topological regularizations of the triple collision singularity in the 3-vortex problem
International Nuclear Information System (INIS)
Hiraoka, Yasuaki
2008-01-01
The triple collision singularity in the 3-vortex problem is studied in this paper. Under the necessary condition k 1 -1 +k 2 -1 +k 3 -1 =0 for vorticities to have the triple collision, the main results are summarized as follows: (i) For k 1 = k 2 , the triple collision singularity is topologically regularizable. (ii) For 0 1 − k 2 | < ε with a sufficiently small ε, the triple collision singularity is not topologically regularizable. First of all, in order to prove these statements, all singularities in the 3-vortex problem are classified. Then, we introduce a dynamical system by blowing up the triple collision singularity with an appropriate time scaling. Roughly speaking, it corresponds to pasting an invariant manifold at the triple collision singularity on the original phase space. This technique is well known as McGehee's collision manifold (1974 Inventions Math. 27 191–227) in the N-body problem of celestial mechanics. Finally, by adopting the viewpoint of Easton (1971 J. Diff. Eqns 10 92–9), topological regularizations of the triple collision singularity are studied in detail
Laplacian embedded regression for scalable manifold regularization.
Chen, Lin; Tsang, Ivor W; Xu, Dong
2012-06-01
Semi-supervised learning (SSL), as a powerful tool to learn from a limited number of labeled data and a large number of unlabeled data, has been attracting increasing attention in the machine learning community. In particular, the manifold regularization framework has laid solid theoretical foundations for a large family of SSL algorithms, such as Laplacian support vector machine (LapSVM) and Laplacian regularized least squares (LapRLS). However, most of these algorithms are limited to small scale problems due to the high computational cost of the matrix inversion operation involved in the optimization problem. In this paper, we propose a novel framework called Laplacian embedded regression by introducing an intermediate decision variable into the manifold regularization framework. By using ∈-insensitive loss, we obtain the Laplacian embedded support vector regression (LapESVR) algorithm, which inherits the sparse solution from SVR. Also, we derive Laplacian embedded RLS (LapERLS) corresponding to RLS under the proposed framework. Both LapESVR and LapERLS possess a simpler form of a transformed kernel, which is the summation of the original kernel and a graph kernel that captures the manifold structure. The benefits of the transformed kernel are two-fold: (1) we can deal with the original kernel matrix and the graph Laplacian matrix in the graph kernel separately and (2) if the graph Laplacian matrix is sparse, we only need to perform the inverse operation for a sparse matrix, which is much more efficient when compared with that for a dense one. Inspired by kernel principal component analysis, we further propose to project the introduced decision variable into a subspace spanned by a few eigenvectors of the graph Laplacian matrix in order to better reflect the data manifold, as well as accelerate the calculation of the graph kernel, allowing our methods to efficiently and effectively cope with large scale SSL problems. Extensive experiments on both toy and real
Flexible fuel cell gas manifold system
Cramer, Michael; Shah, Jagdish; Hayes, Richard P.; Kelley, Dana A.
2005-05-03
A fuel cell stack manifold system in which a flexible manifold body includes a pan having a central area, sidewall extending outward from the periphery of the central area, and at least one compound fold comprising a central area fold connecting adjacent portions of the central area and extending between opposite sides of the central area, and a sidewall fold connecting adjacent portions of the sidewall. The manifold system further includes a rail assembly for attachment to the manifold body and adapted to receive pins by which dielectric insulators are joined to the manifold assembly.
Singularities in FLRW spacetimes
het Lam, Huibert; Prokopec, Tomislav
2017-12-01
We point out that past-incompleteness of geodesics in FLRW spacetimes does not necessarily imply that these spacetimes start from a singularity. Namely, if a test particle that follows such a trajectory has a non-vanishing velocity, its energy was super-Planckian at some time in the past if it kept following that geodesic. That indicates a breakdown of the particle's description, which is why we should not consider those trajectories for the definition of an initial singularity. When one only considers test particles that do not have this breakdown of their trajectory, it turns out that the only singular FLRW spacetimes are the ones that have a scale parameter that vanishes at some initial time.
Minimal Webs in Riemannian Manifolds
DEFF Research Database (Denmark)
Markvorsen, Steen
2008-01-01
For a given combinatorial graph $G$ a {\\it geometrization} $(G, g)$ of the graph is obtained by considering each edge of the graph as a $1-$dimensional manifold with an associated metric $g$. In this paper we are concerned with {\\it minimal isometric immersions} of geometrized graphs $(G, g......)$ into Riemannian manifolds $(N^{n}, h)$. Such immersions we call {\\em{minimal webs}}. They admit a natural 'geometric' extension of the intrinsic combinatorial discrete Laplacian. The geometric Laplacian on minimal webs enjoys standard properties such as the maximum principle and the divergence theorems, which...... are of instrumental importance for the applications. We apply these properties to show that minimal webs in ambient Riemannian spaces share several analytic and geometric properties with their smooth (minimal submanifold) counterparts in such spaces. In particular we use appropriate versions of the divergence...
Invariance for Single Curved Manifold
Castro, Pedro Machado Manhaes de
2012-01-01
Recently, it has been shown that, for Lambert illumination model, solely scenes composed by developable objects with a very particular albedo distribution produce an (2D) image with isolines that are (almost) invariant to light direction change. In this work, we provide and investigate a more general framework, and we show that, in general, the requirement for such in variances is quite strong, and is related to the differential geometry of the objects. More precisely, it is proved that single curved manifolds, i.e., manifolds such that at each point there is at most one principal curvature direction, produce invariant is surfaces for a certain relevant family of energy functions. In the three-dimensional case, the associated energy function corresponds to the classical Lambert illumination model with albedo. This result is also extended for finite-dimensional scenes composed by single curved objects. © 2012 IEEE.
Invariance for Single Curved Manifold
Castro, Pedro Machado Manhaes de
2012-08-01
Recently, it has been shown that, for Lambert illumination model, solely scenes composed by developable objects with a very particular albedo distribution produce an (2D) image with isolines that are (almost) invariant to light direction change. In this work, we provide and investigate a more general framework, and we show that, in general, the requirement for such in variances is quite strong, and is related to the differential geometry of the objects. More precisely, it is proved that single curved manifolds, i.e., manifolds such that at each point there is at most one principal curvature direction, produce invariant is surfaces for a certain relevant family of energy functions. In the three-dimensional case, the associated energy function corresponds to the classical Lambert illumination model with albedo. This result is also extended for finite-dimensional scenes composed by single curved objects. © 2012 IEEE.
Numerical investigation of stress singularities in cracked bimaterial body
Czech Academy of Sciences Publication Activity Database
Náhlík, Luboš; Šestáková, Lucie; Hutař, Pavel
2008-01-01
Roč. 385-387, - (2008), s. 125-128 ISSN 1013-9826. [International Conference on Fracture and Damage Mechanics /7./. Seoul, 09.09.2008-11.09.2008] R&D Projects: GA AV ČR(CZ) KJB200410803; GA ČR GP106/06/P239; GA ČR GA106/08/1409 Institutional research plan: CEZ:AV0Z20410507 Keywords : bimaterial interface * stress singularity exponent * corner singularity * vertex singularity * general singular stress concentrator Subject RIV: JL - Materials Fatigue, Friction Mechanics
Torsions of 3-dimensional manifolds
Wurzbacher, T
2002-01-01
From the reviews: "This is an excellent exposition about abelian Reidemeister torsions for three-manifolds." ―Zentralblatt Math "This monograph contains a wealth of information many topologists will find very handy. …Many of the new points of view pioneered by Turaev are gradually becoming mainstream and are spreading beyond the pure topology world. This monograph is a timely and very useful addition to the scientific literature." ―Mathematical Reviews
Manifold seal structure for fuel cell stack
Collins, William P.
1988-01-01
The seal between the sides of a fuel cell stack and the gas manifolds is improved by adding a mechanical interlock between the adhesive sealing strip and the abutting surface of the manifolds. The adhesive is a material which can flow to some extent when under compression, and the mechanical interlock is formed providing small openings in the portion of the manifold which abuts the adhesive strip. When the manifolds are pressed against the adhesive strips, the latter will flow into and through the manifold openings to form buttons or ribs which mechanically interlock with the manifolds. These buttons or ribs increase the bond between the manifolds and adhesive, which previously relied solely on the adhesive nature of the adhesive.
Energy Technology Data Exchange (ETDEWEB)
Buehl, Heinz; Pietrowski, Herbert [Mann + Hummel GmbH, Ludwigsburg (Germany). Intake Manifolds; Kratzsch, Matthias [IAV GmbH, Berlin (Germany). Fachbereich Ottomotorenentwicklung; Guenther, Michael [IAV GmbH, Chemnitz (Germany). Abt. Verbrennung/Thermodynamik Ottomotoren
2013-11-01
Since the introduction of turbochargers the use of variable intake manifolds to increase performance has declined. In addition to influencing the full load characteristics, variable intake manifolds, however, offer advantages in part load. In a joint project, Mann + Hummel and IAV have examined the fuel saving potential of variable intake manifolds with two current gasoline engine concepts in the NEDC. (orig.)
Anomalies, conformal manifolds, and spheres
Energy Technology Data Exchange (ETDEWEB)
Gomis, Jaume [Perimeter Institute for Theoretical Physics,Waterloo, Ontario, N2L 2Y5 (Canada); Hsin, Po-Shen [Department of Physics, Princeton University,Princeton, NJ 08544 (United States); Komargodski, Zohar; Schwimmer, Adam [Weizmann Institute of Science,Rehovot 76100 (Israel); Seiberg, Nathan [School of Natural Sciences, Institute for Advanced Study,Princeton, NJ 08540 (United States); Theisen, Stefan [Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-Institut,14476 Golm (Germany)
2016-03-04
The two-point function of exactly marginal operators leads to a universal contribution to the trace anomaly in even dimensions. We study aspects of this trace anomaly, emphasizing its interpretation as a sigma model, whose target space M is the space of conformal field theories (a.k.a. the conformal manifold). When the underlying quantum field theory is supersymmetric, this sigma model has to be appropriately supersymmetrized. As examples, we consider in some detail N=(2,2) and N=(0,2) supersymmetric theories in d=2 and N=2 supersymmetric theories in d=4. This reasoning leads to new information about the conformal manifolds of these theories, for example, we show that the manifold is Kähler-Hodge and we further argue that it has vanishing Kähler class. For N=(2,2) theories in d=2 and N=2 theories in d=4 we also show that the relation between the sphere partition function and the Kähler potential of M follows immediately from the appropriate sigma models that we construct. Along the way we find several examples of potential trace anomalies that obey the Wess-Zumino consistency conditions, but can be ruled out by a more detailed analysis.
Yamazaki, Masahito
2012-05-01
We study 4d superconformal indices for a large class of {N} = 1 superconformal quiver gauge theories realized combinatorially as a bipartite graph or a set of "zig-zag paths" on a two-dimensional torus T 2. An exchange of loops, which we call a "double Yang-Baxter move", gives the Seiberg duality of the gauge theory, and the invariance of the index under the duality is translated into the Yang-Baxter-type equation of a spin system defined on a "Z-invariant" lattice on T 2. When we compactify the gauge theory to 3d, Higgs the theory and then compactify further to 2d, the superconformal index reduces to an integral of quantum/classical dilogarithm functions. The saddle point of this integral unexpectedly reproduces the hyperbolic volume of a hyperbolic 3-manifold. The 3-manifold is obtained by gluing hyperbolic ideal polyhedra in {{H}^3} , each of which could be thought of as a 3d lift of the faces of the 2d bipartite graph. The same quantity is also related with the thermodynamic limit of the BPS partition function, or equivalently the genus 0 topological string partition function, on a toric Calabi-Yau manifold dual to quiver gauge theories. We also comment on brane realization of our theories. This paper is a companion to another paper summarizing the results [1].
Pseudospherical surfaces with singularities
DEFF Research Database (Denmark)
Brander, David
2017-01-01
We study a generalization of constant Gauss curvature −1 surfaces in Euclidean 3-space, based on Lorentzian harmonic maps, that we call pseudospherical frontals. We analyse the singularities of these surfaces, dividing them into those of characteristic and non-characteristic type. We give methods...
Supersymmetry in singular spaces
Bergshoeff, Eric
2002-01-01
We discuss supersymmetry in spaces with a boundary, i.e. singular spaces. In particular, we discuss the situation in ten and five dimensions. In both these cases we review the construction of supersymmetric domain wall actions situated at the boundary. These domain walls act as sources inducing a
Singularities in FLRW Spacetimes
Lam, Huibert het; Prokopec, Tom
2017-01-01
We point out that past-incompleteness of geodesics in FLRW spacetimes does not necessarily imply that these spacetimes start from a singularity. Namely, if a test particle that follows such a trajectory has a non-vanishing velocity, its energy was super-Planckian at some time in the past if it kept
Charged singularities: repulsive effects
Energy Technology Data Exchange (ETDEWEB)
De Felice, F; Nobili, L [Padua Univ. (Italy). Ist. di Fisica; Calvani, M [Padua Univ. (Italy). Ist. di Astronomia
1980-07-01
The repulsive phenomena which a particle experiences in the vicinity of a naked singularity are investigated in the Kerr-Newman space-time. The aim is to extend the knowledge of this fact to charged solutions and to have a direct indication of how, in these situations, the gravitational and electrostatic interactions are competing.
Non-singular string-cosmologies from exact conformal field theories
International Nuclear Information System (INIS)
Vega, H.J. de; Larsen, A.L.; Sanchez, N.
2001-01-01
Non-singular two and three dimensional string cosmologies are constructed using the exact conformal field theories corresponding to SO(2,1)/SO(1,1) and SO(2,2)/SO(2,1). All semi-classical curvature singularities are canceled in the exact theories for both of these cosets, but some new quantum curvature singularities emerge. However, considering different patches of the global manifolds, allows the construction of non-singular space-times with cosmological interpretation. In both two and three dimensions, we construct non-singular oscillating cosmologies, non-singular expanding and inflationary cosmologies including a de Sitter (exponential) stage with positive scalar curvature as well as non-singular contracting and deflationary cosmologies. Similarities between the two and three dimensional cases suggest a general picture for higher dimensional coset cosmologies: Anisotropy seems to be a generic unavoidable feature, cosmological singularities are generically avoided and it is possible to construct non-singular cosmologies where some spatial dimensions are experiencing inflation while the others experience deflation
Papapetrou's naked singularity is a strong curvature singularity
International Nuclear Information System (INIS)
Hollier, G.P.
1986-01-01
Following Papapetrou [1985, a random walk in General Relativity ed. J. Krishna-Rao (New Delhi: Wiley Eastern)], a spacetime with a naked singularity is analysed. This singularity is shown to be a strong curvature singularity and thus a counterexample to a censorship conjecture. (author)
Transition Manifolds of Complex Metastable Systems
Bittracher, Andreas; Koltai, Péter; Klus, Stefan; Banisch, Ralf; Dellnitz, Michael; Schütte, Christof
2018-04-01
We consider complex dynamical systems showing metastable behavior, but no local separation of fast and slow time scales. The article raises the question of whether such systems exhibit a low-dimensional manifold supporting its effective dynamics. For answering this question, we aim at finding nonlinear coordinates, called reaction coordinates, such that the projection of the dynamics onto these coordinates preserves the dominant time scales of the dynamics. We show that, based on a specific reducibility property, the existence of good low-dimensional reaction coordinates preserving the dominant time scales is guaranteed. Based on this theoretical framework, we develop and test a novel numerical approach for computing good reaction coordinates. The proposed algorithmic approach is fully local and thus not prone to the curse of dimension with respect to the state space of the dynamics. Hence, it is a promising method for data-based model reduction of complex dynamical systems such as molecular dynamics.
Singular potentials in quantum mechanics
International Nuclear Information System (INIS)
Aguilera-Navarro, V.C.; Koo, E. Ley
1995-10-01
This paper is a review of some mathematical methods as recently developed and applied to deal with singular potentials in Quantum Mechanics. Regular and singular perturbative methods as well as variational treatments are considered. (author). 25 refs
Singularities: the Brieskorn anniversary volume
National Research Council Canada - National Science Library
Brieskorn, Egbert; Arnolʹd, V. I; Greuel, G.-M; Steenbrink, J. H. M
1998-01-01
...... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Main theorem ... 3 Ideals of ideal-unimodal plane curve singularities. . . . . . . . . . . . . . . . References ... Gert-Martin Greuel and Gerhard Pfister...
String theory and cosmological singularities
Indian Academy of Sciences (India)
Well-known examples are singularities inside black holes and initial or final singularities in expanding or contracting universes. In recent times, string theory is providing new perspectives of such singularities which may lead to an understanding of these in the standard framework of time evolution in quantum mechanics.
Holographic complexity and spacetime singularities
Energy Technology Data Exchange (ETDEWEB)
Barbón, José L.F. [Instituto de Física Teórica IFT UAM/CSIC,C/ Nicolás Cabrera 13, Campus Universidad Autónoma de Madrid,Madrid 28049 (Spain); Rabinovici, Eliezer [Racah Institute of Physics, The Hebrew University,Jerusalem 91904 (Israel); Laboratoire de Physique Théorique et Hautes Energies, Université Pierre et Marie Curie, 4 Place Jussieu, 75252 Paris Cedex 05 (France)
2016-01-15
We study the evolution of holographic complexity in various AdS/CFT models containing cosmological crunch singularities. We find that a notion of complexity measured by extremal bulk volumes tends to decrease as the singularity is approached in CFT time, suggesting that the corresponding quantum states have simpler entanglement structure at the singularity.
Are naked singularities really visible
Energy Technology Data Exchange (ETDEWEB)
Calvani, M [Padua Univ. (Italy). Ist. di Astronomia; De Felice, F [Alberta Univ., Edmonton (Canada); Nobili, L [Padua Univ. (Italy). Ist. di Fisica
1978-12-09
The question whether a Kerr naked singularity is actually visible from infinity is investigated; it is shown that in fact any signal which could be emitted from the singularity is infinitely red-shifted. This implies that naked singularities would be indistinguishable from a black hole.
Holographic complexity and spacetime singularities
International Nuclear Information System (INIS)
Barbón, José L.F.; Rabinovici, Eliezer
2016-01-01
We study the evolution of holographic complexity in various AdS/CFT models containing cosmological crunch singularities. We find that a notion of complexity measured by extremal bulk volumes tends to decrease as the singularity is approached in CFT time, suggesting that the corresponding quantum states have simpler entanglement structure at the singularity.
Cobordism independence of Grassmann manifolds
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
ν(m) divides m. Given a positive integer d, let G(d) denote the set of bordism classes of all non-bounding. Grassmannian manifolds Gk(Fn+k) having real dimension d such that k < n. The restric- tion k
Minimal genera of open 4-manifolds
Gompf, Robert E.
2013-01-01
We study exotic smoothings of open 4-manifolds using the minimal genus function and its analog for end homology. While traditional techniques in open 4-manifold smoothing theory give no control of minimal genera, we make progress by using the adjunction inequality for Stein surfaces. Smoothings can be constructed with much more control of these genus functions than the compact setting seems to allow. As an application, we expand the range of 4-manifolds known to have exotic smoothings (up to ...
Spectral gaps, inertial manifolds and kinematic dynamos
Energy Technology Data Exchange (ETDEWEB)
Nunez, Manuel [Departamento de Analisis Matematico, Universidad de Valladolid, 47005 Valladolid (Spain)]. E-mail: mnjmhd@am.uva.es
2005-10-17
Inertial manifolds are desirable objects when ones wishes a dynamical process to behave asymptotically as a finite-dimensional ones. Recently [Physica D 194 (2004) 297] these manifolds are constructed for the kinematic dynamo problem with time-periodic velocity. It turns out, however, that the conditions imposed on the fluid velocity to guarantee the existence of inertial manifolds are too demanding, in the sense that they imply that all the solutions tend exponentially to zero. The inertial manifolds are meaningful because they represent different decay rates, but the classical dynamos where the magnetic field is maintained or grows are not covered by this approach, at least until more refined estimates are found.
Topology of high-dimensional manifolds
Energy Technology Data Exchange (ETDEWEB)
Farrell, F T [State University of New York, Binghamton (United States); Goettshe, L [Abdus Salam ICTP, Trieste (Italy); Lueck, W [Westfaelische Wilhelms-Universitaet Muenster, Muenster (Germany)
2002-08-15
The School on High-Dimensional Manifold Topology took place at the Abdus Salam ICTP, Trieste from 21 May 2001 to 8 June 2001. The focus of the school was on the classification of manifolds and related aspects of K-theory, geometry, and operator theory. The topics covered included: surgery theory, algebraic K- and L-theory, controlled topology, homology manifolds, exotic aspherical manifolds, homeomorphism and diffeomorphism groups, and scalar curvature. The school consisted of 2 weeks of lecture courses and one week of conference. Thwo-part lecture notes volume contains the notes of most of the lecture courses.
Analysis of mixed mode microwave distribution manifolds
International Nuclear Information System (INIS)
White, T.L.
1982-09-01
The 28-GHz microwave distribution manifold used in the ELMO Bumpy Torus-Scale (EBT-S) experiments consists of a toroidal metallic cavity, whose dimensions are much greater than a wavelength, fed by a source of microwave power. Equalization of the mixed mode power distribution ot the 24 cavities of EBT-S is accomplished by empirically adjusting the coupling irises which are equally spaced around the manifold. The performance of the manifold to date has been very good, yet no analytical models exist for optimizing manifold transmission efficiency or for scaling this technology to the EBT-P manifold design. The present report develops a general model for mixed mode microwave distribution manifolds based on isotropic plane wave sources of varying amplitudes that are distributed toroidally around the manifold. The calculated manifold transmission efficiency for the most recent EBT-S coupling iris modification is 90%. This agrees with the average measured transmission efficiency. Also, the model predicts the coupling iris areas required to balance the distribution of microwave power while maximizing transmission efficiency, and losses in waveguide feeds connecting the irises to the cavities of EBT are calculated using an approach similar to the calculation of mainfold losses. The model will be used to evaluate EBT-P manifold designs
Belinski, Vladimir
2018-01-01
Written for researchers focusing on general relativity, supergravity, and cosmology, this is a self-contained exposition of the structure of the cosmological singularity in generic solutions of the Einstein equations, and an up-to-date mathematical derivation of the theory underlying the Belinski–Khalatnikov–Lifshitz (BKL) conjecture on this field. Part I provides a comprehensive review of the theory underlying the BKL conjecture. The generic asymptotic behavior near the cosmological singularity of the gravitational field, and fields describing other kinds of matter, is explained in detail. Part II focuses on the billiard reformulation of the BKL behavior. Taking a general approach, this section does not assume any simplifying symmetry conditions and applies to theories involving a range of matter fields and space-time dimensions, including supergravities. Overall, this book will equip theoretical and mathematical physicists with the theoretical fundamentals of the Big Bang, Big Crunch, Black Hole singula...
Deformations of surface singularities
Szilárd, ágnes
2013-01-01
The present publication contains a special collection of research and review articles on deformations of surface singularities, that put together serve as an introductory survey of results and methods of the theory, as well as open problems, important examples and connections to other areas of mathematics. The aim is to collect material that will help mathematicians already working or wishing to work in this area to deepen their insight and eliminate the technical barriers in this learning process. This also is supported by review articles providing some global picture and an abundance of examples. Additionally, we introduce some material which emphasizes the newly found relationship with the theory of Stein fillings and symplectic geometry. This links two main theories of mathematics: low dimensional topology and algebraic geometry. The theory of normal surface singularities is a distinguished part of analytic or algebraic geometry with several important results, its own technical machinery, and several op...
DEFF Research Database (Denmark)
Somchaipeng, Kerawit; Sporring, Jon; Johansen, Peter
2007-01-01
We propose MultiScale Singularity Trees (MSSTs) as a structure to represent images, and we propose an algorithm for image comparison based on comparing MSSTs. The algorithm is tested on 3 public image databases and compared to 2 state-of-theart methods. We conclude that the computational complexity...... of our algorithm only allows for the comparison of small trees, and that the results of our method are comparable with state-of-the-art using much fewer parameters for image representation....
International Nuclear Information System (INIS)
Habis, M.; Robichon, F.; Demonet, J.F.
1996-01-01
Of late ten years, neurologists are studying the brain of the dyslectics. The cerebral imagery (NMR imaging, positron computed tomography) has allowed to confirm the anatomical particularities discovered by some of them: asymmetry default of cerebral hemispheres, size abnormally large of the white substance mass which connect the two hemispheres. The functional imagery, when visualizing this singular brain at work, allows to understand why it labors to reading. (O.M.)
Holomorphic bundles over elliptic manifolds
International Nuclear Information System (INIS)
Morgan, J.W.
2000-01-01
In this lecture we shall examine holomorphic bundles over compact elliptically fibered manifolds. We shall examine constructions of such bundles as well as (duality) relations between such bundles and other geometric objects, namely K3-surfaces and del Pezzo surfaces. We shall be dealing throughout with holomorphic principal bundles with structure group GC where G is a compact, simple (usually simply connected) Lie group and GC is the associated complex simple algebraic group. Of course, in the special case G = SU(n) and hence GC = SLn(C), we are considering holomorphic vector bundles with trivial determinant. In the other cases of classical groups, G SO(n) or G = Sympl(2n) we are considering holomorphic vector bundles with trivial determinant equipped with a non-degenerate symmetric, or skew symmetric pairing. In addition to these classical cases there are the finite number of exceptional groups. Amazingly enough, motivated by questions in physics, much interest centres around the group E8 and its subgroups. For these applications it does not suffice to consider only the classical groups. Thus, while often first doing the case of SU(n) or more generally of the classical groups, we shall extend our discussions to the general semi-simple group. Also, we shall spend a good deal of time considering elliptically fibered manifolds of the simplest type, namely, elliptic curves
Boukraa, S.; Hassani, S.; Maillard, J.-M.
2012-12-01
Focusing on examples associated with holonomic functions, we try to bring new ideas on how to look at phase transitions, for which the critical manifolds are not points but curves depending on a spectral variable, or even fill higher dimensional submanifolds. Lattice statistical mechanics often provides a natural (holonomic) framework to perform singularity analysis with several complex variables that would, in the most general mathematical framework, be too complex, or simply could not be defined. In a learn-by-example approach, considering several Picard-Fuchs systems of two-variables ‘above’ Calabi-Yau ODEs, associated with double hypergeometric series, we show that D-finite (holonomic) functions are actually a good framework for finding properly the singular manifolds. The singular manifolds are found to be genus-zero curves. We then analyze the singular algebraic varieties of quite important holonomic functions of lattice statistical mechanics, the n-fold integrals χ(n), corresponding to the n-particle decomposition of the magnetic susceptibility of the anisotropic square Ising model. In this anisotropic case, we revisit a set of so-called Nickelian singularities that turns out to be a two-parameter family of elliptic curves. We then find the first set of non-Nickelian singularities for χ(3) and χ(4), that also turns out to be rational or elliptic curves. We underline the fact that these singular curves depend on the anisotropy of the Ising model, or, equivalently, that they depend on the spectral parameter of the model. This has important consequences on the physical nature of the anisotropic χ(n)s which appear to be highly composite objects. We address, from a birational viewpoint, the emergence of families of elliptic curves, and that of Calabi-Yau manifolds on such problems. We also address the question of singularities of non-holonomic functions with a discussion on the accumulation of these singular curves for the non-holonomic anisotropic full
International Nuclear Information System (INIS)
Boukraa, S; Hassani, S; Maillard, J-M
2012-01-01
Focusing on examples associated with holonomic functions, we try to bring new ideas on how to look at phase transitions, for which the critical manifolds are not points but curves depending on a spectral variable, or even fill higher dimensional submanifolds. Lattice statistical mechanics often provides a natural (holonomic) framework to perform singularity analysis with several complex variables that would, in the most general mathematical framework, be too complex, or simply could not be defined. In a learn-by-example approach, considering several Picard–Fuchs systems of two-variables ‘above’ Calabi–Yau ODEs, associated with double hypergeometric series, we show that D-finite (holonomic) functions are actually a good framework for finding properly the singular manifolds. The singular manifolds are found to be genus-zero curves. We then analyze the singular algebraic varieties of quite important holonomic functions of lattice statistical mechanics, the n-fold integrals χ (n) , corresponding to the n-particle decomposition of the magnetic susceptibility of the anisotropic square Ising model. In this anisotropic case, we revisit a set of so-called Nickelian singularities that turns out to be a two-parameter family of elliptic curves. We then find the first set of non-Nickelian singularities for χ (3) and χ (4) , that also turns out to be rational or elliptic curves. We underline the fact that these singular curves depend on the anisotropy of the Ising model, or, equivalently, that they depend on the spectral parameter of the model. This has important consequences on the physical nature of the anisotropic χ (n) s which appear to be highly composite objects. We address, from a birational viewpoint, the emergence of families of elliptic curves, and that of Calabi–Yau manifolds on such problems. We also address the question of singularities of non-holonomic functions with a discussion on the accumulation of these singular curves for the non
Covariant Schrödinger semigroups on Riemannian manifolds
Güneysu, Batu
2017-01-01
This monograph discusses covariant Schrödinger operators and their heat semigroups on noncompact Riemannian manifolds and aims to fill a gap in the literature, given the fact that the existing literature on Schrödinger operators has mainly focused on scalar Schrödinger operators on Euclidean spaces so far. In particular, the book studies operators that act on sections of vector bundles. In addition, these operators are allowed to have unbounded potential terms, possibly with strong local singularities. The results presented here provide the first systematic study of such operators that is sufficiently general to simultaneously treat the natural operators from quantum mechanics, such as magnetic Schrödinger operators with singular electric potentials, and those from geometry, such as squares of Dirac operators that have smooth but endomorphism-valued and possibly unbounded potentials. The book is largely self-contained, making it accessible for graduate and postgraduate students alike. Since it also inc...
Fold points and singularity induced bifurcation in inviscid transonic flow
International Nuclear Information System (INIS)
Marszalek, Wieslaw
2012-01-01
Transonic inviscid flow equation of elliptic–hyperbolic type when written in terms of the velocity components and similarity variable results in a second order nonlinear ODE having several features typical of differential–algebraic equations rather than ODEs. These features include the fold singularities (e.g. folded nodes and saddles, forward and backward impasse points), singularity induced bifurcation behavior and singularity crossing phenomenon. We investigate the above properties and conclude that the quasilinear DAEs of transonic flow have interesting properties that do not occur in other known quasilinear DAEs, for example, in MHD. Several numerical examples are included. -- Highlights: ► A novel analysis of inviscid transonic flow and its similarity solutions. ► Singularity induced bifurcation, singular points of transonic flow. ► Projection method, index of transonic flow DAEs, linearization via matrix pencil.
Invariant identification of naked singularities in spherically symmetric spacetimes
International Nuclear Information System (INIS)
Torres, R
2012-01-01
The study of generic naked singularities and their implications for the cosmic censorship conjecture is still an open issue in the framework of general relativity. One of the obstacles can be traced to the procedures for identifying naked singularities. Usually, the methods applied are not only model and coordinate dependent, but they very often rely in some strong assumptions on the degree of differentiability of the physical magnitudes of the model (such as the mass, density, etc) in the singularity. In this paper, we present a coordinate independent framework for identifying naked singularities based on invariants which is also devoid of strong differentiability requirements. The approach is intended to analyse whole families of models and to provide general results related to the cosmic censorship conjecture. Moreover, since the framework has a strict geometrical nature it can be used with alternative theories of gravitation as long as they assume the existence of a Lorentzian manifold. We exemplify its strength by applying it to the study of the collapse of radiation in radiative coordinates and the collapse of dust in comoving coordinates. (paper)
Nonassociative geometry of manifold with trajectories
International Nuclear Information System (INIS)
Bouetou, T.B.; Matveev, O.A.
2004-12-01
We give some properties of solution of second order differential or system of differential equations on the manifold. It turns out that such manifolds can be seen as quasigroups or loop under certain circumstances. Output of the operations are given and the connection defined. (author)
Strictly convex functions on complete Finsler manifolds
Indian Academy of Sciences (India)
convex functions on the metric structures of complete Finsler manifolds. More precisely we discuss ... map expp at some point p ∈ M (and hence at every point on M) is defined on the whole tangent space Mp to M at ... The influence of the existence of convex functions on the metric and topology of under- lying manifolds has ...
Harmonic manifolds with minimal horospheres are flat
Indian Academy of Sciences (India)
Abstract. In this note we reprove the known theorem: Harmonic manifolds with minimal horospheres are flat. It turns out that our proof is simpler and more direct than the original one. We also reprove the theorem: Ricci flat harmonic manifolds are flat, which is generally affirmed by appealing to Cheeger–Gromov splitting ...
Harmonic Manifolds with Minimal Horospheres are Flat
Indian Academy of Sciences (India)
In this note we reprove the known theorem: Harmonic manifolds with minimal horospheres are flat. It turns out that our proof is simpler and more direct than the original one. We also reprove the theorem: Ricci flat harmonic manifolds are flat, which is generally affirmed by appealing to Cheeger–Gromov splitting theorem.
Transversal lightlike submanifolds of indefinite sasakian manifolds
YILDIRIM, Cumali; Yıldırım, Cumali; Şahin, Bayram
2014-01-01
We study both radical transversal and transversal lightlike submanifolds of indefinite Sasakian manifolds. We give examples, investigate the geometry of distributions and obtain necessary and sufficient conditions for the induced connection on these submanifolds to be metric connection. We also study totally contact umbilical radical transversal and transversal lightlike submanifolds of indefinite Sasakian manifolds and obtain a classification theorem for totally contact umbilical tr...
Transversal lightlike submanifolds of indefinite sasakian manifolds
YILDIRIM, Cumali
2010-01-01
We study both radical transversal and transversal lightlike submanifolds of indefinite Sasakian manifolds. We give examples, investigate the geometry of distributions and obtain necessary and sufficient conditions for the induced connection on these submanifolds to be metric connection. We also study totally contact umbilical radical transversal and transversal lightlike submanifolds of indefinite Sasakian manifolds and obtain a classification theorem for totally contact umbilical tr...
Holomorphic curves in exploded manifolds: Kuranishi structure
Parker, Brett
2013-01-01
This paper constructs a Kuranishi structure for the moduli stack of holomorphic curves in exploded manifolds. To avoid some technicalities of abstract Kuranishi structures, we embed our Kuranishi structure inside a moduli stack of curves. The construction also works for the moduli stack of holomorphic curves in any compact symplectic manifold.
Chekroun, Mickaël D; Wang, Shouhong
2015-01-01
In this second volume, a general approach is developed to provide approximate parameterizations of the "small" scales by the "large" ones for a broad class of stochastic partial differential equations (SPDEs). This is accomplished via the concept of parameterizing manifolds (PMs), which are stochastic manifolds that improve, for a given realization of the noise, in mean square error the partial knowledge of the full SPDE solution when compared to its projection onto some resolved modes. Backward-forward systems are designed to give access to such PMs in practice. The key idea consists of representing the modes with high wave numbers as a pullback limit depending on the time-history of the modes with low wave numbers. Non-Markovian stochastic reduced systems are then derived based on such a PM approach. The reduced systems take the form of stochastic differential equations involving random coefficients that convey memory effects. The theory is illustrated on a stochastic Burgers-type equation.
Harmonic space and quaternionic manifolds
International Nuclear Information System (INIS)
Galperin, A.; Ogievetsky, O.; Ivanov, E.
1992-10-01
A principle of harmonic analyticity underlying the quaternionic (quaternion-Kaehler) geometry is found, and the differential constraints which define this geometry are solved. To this end the original 4n-dimensional quaternionic manifold is extended to a biharmonic space. The latter includes additional harmonic coordinates associated with both the tangent local Sp(1) group and an extra rigid SU(2) group rotating the complex structures. An one-to-one correspondence is established between the quaternionic spaces and off-shell N=2 supersymmetric sigma-models coupled to N=2 supergravity. Coordinates of the analytic subspace are identified with superfields describing N=2 matter hypermultiplets and a compensating hypermultiplet of N=2 supergravity. As an illustration the potentials for the symmetric quaternionic spaces are presented. (K.A.) 22 refs
Moving Manifolds in Electromagnetic Fields
Directory of Open Access Journals (Sweden)
David V. Svintradze
2017-08-01
Full Text Available We propose dynamic non-linear equations for moving surfaces in an electromagnetic field. The field is induced by a material body with a boundary of the surface. Correspondingly the potential energy, set by the field at the boundary can be written as an addition of four-potential times four-current to a contraction of the electromagnetic tensor. Proper application of the minimal action principle to the system Lagrangian yields dynamic non-linear equations for moving three dimensional manifolds in electromagnetic fields. The equations in different conditions simplify to Maxwell equations for massless three surfaces, to Euler equations for a dynamic fluid, to magneto-hydrodynamic equations and to the Poisson-Boltzmann equation.
Hamiltonian PDEs and Frobenius manifolds
International Nuclear Information System (INIS)
Dubrovin, Boris A
2008-01-01
In the first part of this paper the theory of Frobenius manifolds is applied to the problem of classification of Hamiltonian systems of partial differential equations depending on a small parameter. Also developed is a deformation theory of integrable hierarchies including the subclass of integrable hierarchies of topological type. Many well-known examples of integrable hierarchies, such as the Korteweg-de Vries, non-linear Schroedinger, Toda, Boussinesq equations, and so on, belong to this subclass that also contains new integrable hierarchies. Some of these new integrable hierarchies may be important for applications. Properties of the solutions to these equations are studied in the second part. Consideration is given to the comparative study of the local properties of perturbed and unperturbed solutions near a point of gradient catastrophe. A Universality Conjecture is formulated describing the various types of critical behaviour of solutions to perturbed Hamiltonian systems near the point of gradient catastrophe of the unperturbed solution.
Hamiltonian PDEs and Frobenius manifolds
Energy Technology Data Exchange (ETDEWEB)
Dubrovin, Boris A [Steklov Mathematical Institute, Russian Academy of Sciences, Moscow (Russian Federation)
2008-12-31
In the first part of this paper the theory of Frobenius manifolds is applied to the problem of classification of Hamiltonian systems of partial differential equations depending on a small parameter. Also developed is a deformation theory of integrable hierarchies including the subclass of integrable hierarchies of topological type. Many well-known examples of integrable hierarchies, such as the Korteweg-de Vries, non-linear Schroedinger, Toda, Boussinesq equations, and so on, belong to this subclass that also contains new integrable hierarchies. Some of these new integrable hierarchies may be important for applications. Properties of the solutions to these equations are studied in the second part. Consideration is given to the comparative study of the local properties of perturbed and unperturbed solutions near a point of gradient catastrophe. A Universality Conjecture is formulated describing the various types of critical behaviour of solutions to perturbed Hamiltonian systems near the point of gradient catastrophe of the unperturbed solution.
Function theory on symplectic manifolds
Polterovich, Leonid
2014-01-01
This is a book on symplectic topology, a rapidly developing field of mathematics which originated as a geometric tool for problems of classical mechanics. Since the 1980s, powerful methods such as Gromov's pseudo-holomorphic curves and Morse-Floer theory on loop spaces gave rise to the discovery of unexpected symplectic phenomena. The present book focuses on function spaces associated with a symplectic manifold. A number of recent advances show that these spaces exhibit intriguing properties and structures, giving rise to an alternative intuition and new tools in symplectic topology. The book provides an essentially self-contained introduction into these developments along with applications to symplectic topology, algebra and geometry of symplectomorphism groups, Hamiltonian dynamics and quantum mechanics. It will appeal to researchers and students from the graduate level onwards. I like the spirit of this book. It formulates concepts clearly and explains the relationship between them. The subject matter is i...
Conformal manifolds: ODEs from OPEs
Behan, Connor
2018-03-01
The existence of an exactly marginal deformation in a conformal field theory is very special, but it is not well understood how this is reflected in the allowed dimensions and OPE coefficients of local operators. To shed light on this question, we compute perturbative corrections to several observables in an abstract CFT, starting with the beta function. This yields a sum rule that the theory must obey in order to be part of a conformal manifold. The set of constraints relating CFT data at different values of the coupling can in principle be written as a dynamical system that allows one to flow arbitrarily far. We begin the analysis of it by finding a simple form for the differential equations when the spacetime and theory space are both one-dimensional. A useful feature we can immediately observe is that our system makes it very difficult for level crossing to occur.
Differential geometry of quasi-Sasakian manifolds
International Nuclear Information System (INIS)
Kirichenko, V F; Rustanov, A R
2002-01-01
The full system of structure equations of a quasi-Sasakian structure is obtained. The structure of the main tensors on a quasi-Sasakian manifold (the Riemann-Christoffel tensor, the Ricci tensor, and other tensors) is studied on this basis. Interesting characterizations of quasi-Sasakian Einstein manifolds are obtained. Additional symmetry properties of the Riemann-Christoffel tensor are discovered and used for distinguishing a new class of CR 1 quasi-Sasakian manifolds. An exhaustive description of the local structure of manifolds in this class is given. A complete classification (up to the B-transformation of the metric) is obtained for manifolds in this class having additional properties of the isotropy kind
CSIR Research Space (South Africa)
Roux, FS
2013-09-01
Full Text Available Roux Presented at the International Conference on Correlation Optics 2013 Chernivtsi, Ukraine 18-20 September 2013 CSIR National Laser Centre, Pretoria, South Africa – p. 1/24 Contents ⊲ Defining Stochastic Singular Optics (SSO) ⊲ Tools of Stochastic... of vortices: topological charge ±1 (higher order are unstable). Positive and negative vortex densities np(x, y, z) and nn(x, y, z) ⊲ Vortex density: V = np + nn ⊲ Topological charge density: T = np − nn – p. 4/24 Subfields of SSO ⊲ Homogeneous, normally...
Cosmological models without singularities
International Nuclear Information System (INIS)
Petry, W.
1981-01-01
A previously studied theory of gravitation in flat space-time is applied to homogeneous and isotropic cosmological models. There exist two different classes of models without singularities: (i) ever-expanding models, (ii) oscillating models. The first class contains models with hot big bang. For these models there exist at the beginning of the universe-in contrast to Einstein's theory-very high but finite densities of matter and radiation with a big bang of very short duration. After short time these models pass into the homogeneous and isotropic models of Einstein's theory with spatial curvature equal to zero and cosmological constant ALPHA >= O. (author)
Plane waves with weak singularities
International Nuclear Information System (INIS)
David, Justin R.
2003-03-01
We study a class of time dependent solutions of the vacuum Einstein equations which are plane waves with weak null singularities. This singularity is weak in the sense that though the tidal forces diverge at the singularity, the rate of divergence is such that the distortion suffered by a freely falling observer remains finite. Among such weak singular plane waves there is a sub-class which does not exhibit large back reaction in the presence of test scalar probes. String propagation in these backgrounds is smooth and there is a natural way to continue the metric beyond the singularity. This continued metric admits string propagation without the string becoming infinitely excited. We construct a one parameter family of smooth metrics which are at a finite distance in the space of metrics from the extended metric and a well defined operator in the string sigma model which resolves the singularity. (author)
King, Nathan D.; Ruuth, Steven J.
2017-05-01
Maps from a source manifold M to a target manifold N appear in liquid crystals, color image enhancement, texture mapping, brain mapping, and many other areas. A numerical framework to solve variational problems and partial differential equations (PDEs) that map between manifolds is introduced within this paper. Our approach, the closest point method for manifold mapping, reduces the problem of solving a constrained PDE between manifolds M and N to the simpler problems of solving a PDE on M and projecting to the closest points on N. In our approach, an embedding PDE is formulated in the embedding space using closest point representations of M and N. This enables the use of standard Cartesian numerics for general manifolds that are open or closed, with or without orientation, and of any codimension. An algorithm is presented for the important example of harmonic maps and generalized to a broader class of PDEs, which includes p-harmonic maps. Improved efficiency and robustness are observed in convergence studies relative to the level set embedding methods. Harmonic and p-harmonic maps are computed for a variety of numerical examples. In these examples, we denoise texture maps, diffuse random maps between general manifolds, and enhance color images.
Topology and Singularities in Cosmological Spacetimes Obeying the Null Energy Condition
Galloway, Gregory J.; Ling, Eric
2018-06-01
We consider globally hyperbolic spacetimes with compact Cauchy surfaces in a setting compatible with the presence of a positive cosmological constant. More specifically, for 3 + 1 dimensional spacetimes which satisfy the null energy condition and contain a future expanding compact Cauchy surface, we establish a precise connection between the topology of the Cauchy surfaces and the occurrence of past singularities. In addition to the Penrose singularity theorem, the proof makes use of some recent advances in the topology of 3-manifolds and of certain fundamental existence results for minimal surfaces.
Discriminative sparse coding on multi-manifolds
Wang, J.J.-Y.; Bensmail, H.; Yao, N.; Gao, Xin
2013-01-01
Sparse coding has been popularly used as an effective data representation method in various applications, such as computer vision, medical imaging and bioinformatics. However, the conventional sparse coding algorithms and their manifold-regularized variants (graph sparse coding and Laplacian sparse coding), learn codebooks and codes in an unsupervised manner and neglect class information that is available in the training set. To address this problem, we propose a novel discriminative sparse coding method based on multi-manifolds, that learns discriminative class-conditioned codebooks and sparse codes from both data feature spaces and class labels. First, the entire training set is partitioned into multiple manifolds according to the class labels. Then, we formulate the sparse coding as a manifold-manifold matching problem and learn class-conditioned codebooks and codes to maximize the manifold margins of different classes. Lastly, we present a data sample-manifold matching-based strategy to classify the unlabeled data samples. Experimental results on somatic mutations identification and breast tumor classification based on ultrasonic images demonstrate the efficacy of the proposed data representation and classification approach. 2013 The Authors. All rights reserved.
Discriminative sparse coding on multi-manifolds
Wang, J.J.-Y.
2013-09-26
Sparse coding has been popularly used as an effective data representation method in various applications, such as computer vision, medical imaging and bioinformatics. However, the conventional sparse coding algorithms and their manifold-regularized variants (graph sparse coding and Laplacian sparse coding), learn codebooks and codes in an unsupervised manner and neglect class information that is available in the training set. To address this problem, we propose a novel discriminative sparse coding method based on multi-manifolds, that learns discriminative class-conditioned codebooks and sparse codes from both data feature spaces and class labels. First, the entire training set is partitioned into multiple manifolds according to the class labels. Then, we formulate the sparse coding as a manifold-manifold matching problem and learn class-conditioned codebooks and codes to maximize the manifold margins of different classes. Lastly, we present a data sample-manifold matching-based strategy to classify the unlabeled data samples. Experimental results on somatic mutations identification and breast tumor classification based on ultrasonic images demonstrate the efficacy of the proposed data representation and classification approach. 2013 The Authors. All rights reserved.
Multidimensional flamelet-generated manifolds for partially premixed combustion
Energy Technology Data Exchange (ETDEWEB)
Nguyen, Phuc-Danh; Vervisch, Luc; Subramanian, Vallinayagam; Domingo, Pascale [CORIA - CNRS and INSA de Rouen, Technopole du Madrillet, BP 8, 76801 Saint-Etienne-du-Rouvray (France)
2010-01-15
Flamelet-generated manifolds have been restricted so far to premixed or diffusion flame archetypes, even though the resulting tables have been applied to nonpremixed and partially premixed flame simulations. By using a projection of the full set of mass conservation species balance equations into a restricted subset of the composition space, unsteady multidimensional flamelet governing equations are derived from first principles, under given hypotheses. During the projection, as in usual one-dimensional flamelets, the tangential strain rate of scalar isosurfaces is expressed in the form of the scalar dissipation rates of the control parameters of the multidimensional flamelet-generated manifold (MFM), which is tested in its five-dimensional form for partially premixed combustion, with two composition space directions and three scalar dissipation rates. It is shown that strain-rate-induced effects can hardly be fully neglected in chemistry tabulation of partially premixed combustion, because of fluxes across iso-equivalence-ratio and iso-progress-of-reaction surfaces. This is illustrated by comparing the 5D flamelet-generated manifold with one-dimensional premixed flame and unsteady strained diffusion flame composition space trajectories. The formal links between the asymptotic behavior of MFM and stratified flame, weakly varying partially premixed front, triple-flame, premixed and nonpremixed edge flames are also evidenced. (author)
Residues and duality for singularity categories of isolated Gorenstein singularities
Murfet, Daniel
2009-01-01
We study Serre duality in the singularity category of an isolated Gorenstein singularity and find an explicit formula for the duality pairing in terms of generalised fractions and residues. For hypersurfaces we recover the residue formula of the string theorists Kapustin and Li. These results are obtained from an explicit construction of complete injective resolutions of maximal Cohen-Macaulay modules.
Holomorphic Yukawa couplings for complete intersection Calabi-Yau manifolds
Energy Technology Data Exchange (ETDEWEB)
Blesneag, Stefan [Rudolf Peierls Centre for Theoretical Physics, Oxford University,1 Keble Road, Oxford, OX1 3NP (United Kingdom); Buchbinder, Evgeny I. [The University of Western Australia,35 Stirling Highway, Crawley WA 6009 (Australia); Lukas, Andre [Rudolf Peierls Centre for Theoretical Physics, Oxford University,1 Keble Road, Oxford, OX1 3NP (United Kingdom)
2017-01-27
We develop methods to compute holomorphic Yukawa couplings for heterotic compactifications on complete intersection Calabi-Yau manifolds, generalising results of an earlier paper for Calabi-Yau hypersurfaces. Our methods are based on constructing the required bundle-valued forms explicitly and evaluating the relevant integrals over the projective ambient space. We also show how our approach relates to an earlier, algebraic one to calculate the holomorphic Yukawa couplings. A vanishing theorem, which we prove, implies that certain Yukawa couplings allowed by low-energy symmetries are zero due to topological reasons. To illustrate our methods, we calculate Yukawa couplings for SU(5)-based standard models on a co-dimension two complete intersection manifold.
Laplacian manifold regularization method for fluorescence molecular tomography
He, Xuelei; Wang, Xiaodong; Yi, Huangjian; Chen, Yanrong; Zhang, Xu; Yu, Jingjing; He, Xiaowei
2017-04-01
Sparse regularization methods have been widely used in fluorescence molecular tomography (FMT) for stable three-dimensional reconstruction. Generally, ℓ1-regularization-based methods allow for utilizing the sparsity nature of the target distribution. However, in addition to sparsity, the spatial structure information should be exploited as well. A joint ℓ1 and Laplacian manifold regularization model is proposed to improve the reconstruction performance, and two algorithms (with and without Barzilai-Borwein strategy) are presented to solve the regularization model. Numerical studies and in vivo experiment demonstrate that the proposed Gradient projection-resolved Laplacian manifold regularization method for the joint model performed better than the comparative algorithm for ℓ1 minimization method in both spatial aggregation and location accuracy.
International Nuclear Information System (INIS)
Chiang, Yuan-Jen.
1989-01-01
Harmonic maps between manifolds are described as the critical maps of their associated energy functionals. By using Sampson's method [Sam1], the author constructs a Sobolev's chain on a compact V-manifold and obtain Rellich's Theorem (Theorem 3.1), Sobolev's Theorem (Theorem 3.2), the regularity theorem (Theorem 3.3), the property of the eigenspaces for the Laplacian (Theorem 3.5) and the solvability of Laplacian (Theorem 3.6). Then, with these results, he constructs the Green's functions for the Laplacian on a compact V-manifold M in Proposition 4.1; and obtain an orthonormal basis for L 2 (M) formed by the eigenfunctions of the Laplacian corresponding to the eigenvalues in Proposition 4.2. He also estimates the eigenvalues and eigenfunctions of the Laplacian in Theorem 4.3, which is used to construct the heat kernel on a compact V-manifold in Proposition 5.1. Afterwards, he compares the G-invariant heat kernel functions with the G-invariant fundamental solutions of heat equations in the finite V-charts of a compact V-manifold in Theorem 6.1, and then study two integral operators associated to the heat kernel on a compact V-manifold in section 7. With all the preceding results established, in Theorem 8.3 he uses successive approximations to prove the existence of the solutions of parabolic equations on V-manifolds. Finally, he uses Theorem 8.3 to show the existence of harmonic maps from compact V-manifolds into compact Riemannian manifolds in Theorem 9.1 which extends Eells-Sampson's results [E-S
Space time manifolds and contact structures
Directory of Open Access Journals (Sweden)
K. L. Duggal
1990-01-01
Full Text Available A new class of contact manifolds (carring a global non-vanishing timelike vector field is introduced to establish a relation between spacetime manifolds and contact structures. We show that odd dimensional strongly causal (in particular, globally hyperbolic spacetimes can carry a regular contact structure. As examples, we present a causal spacetime with a non regular contact structure and a physical model [Gödel Universe] of Homogeneous contact manifold. Finally, we construct a model of 4-dimensional spacetime of general relativity as a contact CR-submanifold.
Path integrals on curved manifolds
International Nuclear Information System (INIS)
Grosche, C.; Steiner, F.
1987-01-01
A general framework for treating path integrals on curved manifolds is presented. We also show how to perform general coordinate and space-time transformations in path integrals. The main result is that one has to subtract a quantum correction ΔV ∝ ℎ 2 from the classical Lagrangian L, i.e. the correct effective Lagrangian to be used in the path integral is L eff = L-ΔV. A general prescription for calculating the quantum correction ΔV is given. It is based on a canonical approach using Weyl-ordering and the Hamiltonian path integral defined by the midpoint prescription. The general framework is illustrated by several examples: The d-dimensional rotator, i.e. the motion on the sphere S d-1 , the path integral in d-dimensional polar coordinates, the exact treatment of the hydrogen atom in R 2 and R 3 by performing a Kustaanheimo-Stiefel transformation, the Langer transformation and the path integral for the Morse potential. (orig.)
Dimension counts for singular rational curves via semigroups
Cotterill, Ethan; Feital, Lia; Martins, Renato Vidal
2015-01-01
We study singular rational curves in projective space, deducing conditions on their parametrizations from the value semigroups $\\sss$ of their singularities. In particular, we prove that a natural heuristic for the codimension of the space of nondegenerate rational curves of arithmetic genus $g>0$ and degree $d$ in $\\mb{P}^n$, viewed as a subspace of all degree-$d$ rational curves in $\\mb{P}^n$, holds whenever $g$ is small.
Geometry of minimal rational curves on Fano manifolds
Energy Technology Data Exchange (ETDEWEB)
Hwang, J -M [Korea Institute for Advanced Study, Seoul (Korea, Republic of)
2001-12-15
This lecture is an introduction to my joint project with N. Mok where we develop a geometric theory of Fano manifolds of Picard number 1 by studying the collection of tangent directions of minimal rational curves through a generic point. After a sketch of some historical background, the fundamental object of this project, the variety of minimal rational tangents, is defined and various examples are examined. Then some results on the variety of minimal rational tangents are discussed including an extension theorem for holomorphic maps preserving the geometric structure. Some applications of this theory to the stability of the tangent bundles and the rigidity of generically finite morphisms are given. (author)
Pseudo-Kaehler quantization on flag manifolds
International Nuclear Information System (INIS)
Karabegov, A.V.
1997-07-01
A unified approach to geometric, symbol and deformation quantizations on a generalized flag manifold endowed with an invariant pseudo-Kaehler structure is proposed. In particular cases we arrive at Berezin's quantization via covariant and contravariant symbols. (author). 16 refs
Moduli space of Calabi-Yau manifolds
International Nuclear Information System (INIS)
Candelas, P.; De la Ossa, X.C.
1991-01-01
We present an accessible account of the local geometry of the parameter space of Calabi-Yau manifolds. It is shown that the parameter space decomposes, at least locally, into a product with the space of parameters of the complex structure as one factor and a complex extension of the parameter space of the Kaehler class as the other. It is also shown that each of these spaces is itself a Kaehler manifold and is moreover a Kaehler manifold of restricted type. There is a remarkable symmetry in the intrinsic structures of the two parameter spaces and the relevance of this to the conjectured existence of mirror manifolds is discussed. The two parameter spaces behave differently with respect to modular transformations and it is argued that the role of quantum corrections is to restore the symmetry between the two types of parameters so as to enforce modular invariance. (orig.)
Indian Academy of Sciences (India)
Kähler–Norden manifolds using the theory of Tachibana operators is presented. ... arguments is subject to the action of the affinor structure ϕ. ..... [20] Vishnevskii V V, Integrable affinor structures and their plural interpretations, J. Math. Sci.
Submanifolds of a Finsler manifold - I
International Nuclear Information System (INIS)
Rastogi, S.C.
1986-06-01
In 1981, Hojo defined a scalar function φ (p) (x,y), where p is a real number (not= 1). He used this function to define a tensor φ ij (p) (x,y) and a c P Γ-connection which reduce to g ij (x,y) and cΓ-connection for p=2. The aim of this paper is to study submanifolds of a Finsler manifold admitting a c P Γ-connection. In this paper I have obtained four kinds of Gauss-Codazzi equations based on various derivatives in a Finsler manifold admitting a c P Γ-connection. The method used in this paper is similar to the one used by the author in obtaining generalized Gauss-Codazzi equations based on congruences of curves in a Finsler manifold. Besides considering some special cases we have also studied the relationship between the Riemannian curvatures and Ricci tensors of the submanifold and the enveloping manifold. (author)
Generalized regular genus for manifolds with boundary
Directory of Open Access Journals (Sweden)
Paola Cristofori
2003-05-01
Full Text Available We introduce a generalization of the regular genus, a combinatorial invariant of PL manifolds ([10], which is proved to be strictly related, in dimension three, to generalized Heegaard splittings defined in [12].
Polynomial chaos representation of databases on manifolds
Energy Technology Data Exchange (ETDEWEB)
Soize, C., E-mail: christian.soize@univ-paris-est.fr [Université Paris-Est, Laboratoire Modélisation et Simulation Multi-Echelle, MSME UMR 8208 CNRS, 5 bd Descartes, 77454 Marne-La-Vallée, Cedex 2 (France); Ghanem, R., E-mail: ghanem@usc.edu [University of Southern California, 210 KAP Hall, Los Angeles, CA 90089 (United States)
2017-04-15
Characterizing the polynomial chaos expansion (PCE) of a vector-valued random variable with probability distribution concentrated on a manifold is a relevant problem in data-driven settings. The probability distribution of such random vectors is multimodal in general, leading to potentially very slow convergence of the PCE. In this paper, we build on a recent development for estimating and sampling from probabilities concentrated on a diffusion manifold. The proposed methodology constructs a PCE of the random vector together with an associated generator that samples from the target probability distribution which is estimated from data concentrated in the neighborhood of the manifold. The method is robust and remains efficient for high dimension and large datasets. The resulting polynomial chaos construction on manifolds permits the adaptation of many uncertainty quantification and statistical tools to emerging questions motivated by data-driven queries.
Geometry of superconformal manifolds. Part 1
International Nuclear Information System (INIS)
Roslyi, A.A.; Schwarz, A.S.; Voronov, A.A.
1987-01-01
The main facts about complex curves are generalized to superconformal manifolds. The results thus obtained are relevant to the dermion string theory and, in particular, they are useful for computation of determinants of superlaplacians which enter the string partition function
Stable harmonic maps from complete manifolds
International Nuclear Information System (INIS)
Xin, Y.L.
1986-01-01
By choosing distinguished cross-sections in the second variational formula for harmonic maps from manifolds with not too fast volume growth into certain submanifolds in the Euclidean space some Liouville type theorems have been proved in this article. (author)
Noncommutative gauge theory for Poisson manifolds
Energy Technology Data Exchange (ETDEWEB)
Jurco, Branislav E-mail: jurco@mpim-bonn.mpg.de; Schupp, Peter E-mail: schupp@theorie.physik.uni-muenchen.de; Wess, Julius E-mail: wess@theorie.physik.uni-muenchen.de
2000-09-25
A noncommutative gauge theory is associated to every Abelian gauge theory on a Poisson manifold. The semi-classical and full quantum version of the map from the ordinary gauge theory to the noncommutative gauge theory (Seiberg-Witten map) is given explicitly to all orders for any Poisson manifold in the Abelian case. In the quantum case the construction is based on Kontsevich's formality theorem.
Noncommutative gauge theory for Poisson manifolds
International Nuclear Information System (INIS)
Jurco, Branislav; Schupp, Peter; Wess, Julius
2000-01-01
A noncommutative gauge theory is associated to every Abelian gauge theory on a Poisson manifold. The semi-classical and full quantum version of the map from the ordinary gauge theory to the noncommutative gauge theory (Seiberg-Witten map) is given explicitly to all orders for any Poisson manifold in the Abelian case. In the quantum case the construction is based on Kontsevich's formality theorem
Sasakian manifolds and M-theory
International Nuclear Information System (INIS)
Figueroa-O’Farrill, José; Santi, Andrea
2016-01-01
We extend the link between Einstein Sasakian manifolds and Killing spinors to a class of η-Einstein Sasakian manifolds, both in Riemannian and Lorentzian settings, characterizing them in terms of generalized Killing spinors. We propose a definition of supersymmetric M-theory backgrounds on such a geometry and find a new class of such backgrounds, extending previous work of Haupt, Lukas and Stelle. (paper)
Computer calculation of Witten's 3-manifold invariant
International Nuclear Information System (INIS)
Freed, D.S.; Gompf, R.E.
1991-01-01
Witten's 2+1 dimensional Chern-Simons theory is exactly solvable. We compute the partition function, a topological invariant of 3-manifolds, on generalized Seifert spaces. Thus we test the path integral using the theory of 3-manifolds. In particular, we compare the exact solution with the asymptotic formula predicted by perturbation theory. We conclude that this path integral works as advertised and gives an effective topological invariant. (orig.)
Online Manifold Regularization by Dual Ascending Procedure
Sun, Boliang; Li, Guohui; Jia, Li; Zhang, Hui
2013-01-01
We propose a novel online manifold regularization framework based on the notion of duality in constrained optimization. The Fenchel conjugate of hinge functions is a key to transfer manifold regularization from offline to online in this paper. Our algorithms are derived by gradient ascent in the dual function. For practical purpose, we propose two buffering strategies and two sparse approximations to reduce the computational complexity. Detailed experiments verify the utility of our approache...
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)
Robinson manifolds and Cauchy-Riemann spaces
Trautman, A
2002-01-01
A Robinson manifold is defined as a Lorentz manifold (M, g) of dimension 2n >= 4 with a bundle N subset of C centre dot TM such that the fibres of N are maximal totally null and there holds the integrability condition [Sec N, Sec N] subset of Sec N. The real part of N intersection N-bar is a bundle of null directions tangent to a congruence of null geodesics. This generalizes the notion of a shear-free congruence of null geodesics (SNG) in dimension 4. Under a natural regularity assumption, the set M of all these geodesics has the structure of a Cauchy-Riemann manifold of dimension 2n - 1. Conversely, every such CR manifold lifts to many Robinson manifolds. Three definitions of a CR manifold are described here in considerable detail; they are equivalent under the assumption of real analyticity, but not in the smooth category. The distinctions between these definitions have a bearing on the validity of the Robinson theorem on the existence of null Maxwell fields associated with SNGs. This paper is largely a re...
Naked singularities are not singular in distorted gravity
Energy Technology Data Exchange (ETDEWEB)
Garattini, Remo, E-mail: Remo.Garattini@unibg.it [Università degli Studi di Bergamo, Facoltà di Ingegneria, Viale Marconi 5, 24044 Dalmine (Bergamo) (Italy); I.N.F.N. – sezione di Milano, Milan (Italy); Majumder, Barun, E-mail: barunbasanta@iitgn.ac.in [Indian Institute of Technology Gandhinagar, Ahmedabad, Gujarat 382424 (India)
2014-07-15
We compute the Zero Point Energy (ZPE) induced by a naked singularity with the help of a reformulation of the Wheeler–DeWitt equation. A variational approach is used for the calculation with Gaussian Trial Wave Functionals. The one loop contribution of the graviton to the ZPE is extracted keeping under control the UltraViolet divergences by means of a distorted gravitational field. Two examples of distortion are taken under consideration: Gravity's Rainbow and Noncommutative Geometry. Surprisingly, we find that the ZPE is no more singular when we approach the singularity.
Naked singularities are not singular in distorted gravity
Garattini, Remo; Majumder, Barun
2014-07-01
We compute the Zero Point Energy (ZPE) induced by a naked singularity with the help of a reformulation of the Wheele-DeWitt equation. A variational approach is used for the calculation with Gaussian Trial Wave Functionals. The one loop contribution of the graviton to the ZPE is extracted keeping under control the UltraViolet divergences by means of a distorted gravitational field. Two examples of distortion are taken under consideration: Gravity's Rainbow and Noncommutative Geometry. Surprisingly, we find that the ZPE is no more singular when we approach the singularity.
Naked singularities are not singular in distorted gravity
International Nuclear Information System (INIS)
Garattini, Remo; Majumder, Barun
2014-01-01
We compute the Zero Point Energy (ZPE) induced by a naked singularity with the help of a reformulation of the Wheeler–DeWitt equation. A variational approach is used for the calculation with Gaussian Trial Wave Functionals. The one loop contribution of the graviton to the ZPE is extracted keeping under control the UltraViolet divergences by means of a distorted gravitational field. Two examples of distortion are taken under consideration: Gravity's Rainbow and Noncommutative Geometry. Surprisingly, we find that the ZPE is no more singular when we approach the singularity
Ultrasonic defect characterization using parametric-manifold mapping
Velichko, A.; Bai, L.; Drinkwater, B. W.
2017-06-01
The aim of ultrasonic non-destructive evaluation includes the detection and characterization of defects, and an understanding of the nature of defects is essential for the assessment of structural integrity in safety critical systems. In general, the defect characterization challenge involves an estimation of defect parameters from measured data. In this paper, we explore the extent to which defects can be characterized by their ultrasonic scattering behaviour. Given a number of ultrasonic measurements, we show that characterization information can be extracted by projecting the measurement onto a parametric manifold in principal component space. We show that this manifold represents the entirety of the characterization information available from far-field harmonic ultrasound. We seek to understand the nature of this information and hence provide definitive statements on the defect characterization performance that is, in principle, extractable from typical measurement scenarios. In experiments, the characterization problem of surface-breaking cracks and the more general problem of elliptical voids are studied, and a good agreement is achieved between the actual parameter values and the characterization results. The nature of the parametric manifold enables us to explain and quantify why some defects are relatively easy to characterize, whereas others are inherently challenging.
Robust head pose estimation via supervised manifold learning.
Wang, Chao; Song, Xubo
2014-05-01
Head poses can be automatically estimated using manifold learning algorithms, with the assumption that with the pose being the only variable, the face images should lie in a smooth and low-dimensional manifold. However, this estimation approach is challenging due to other appearance variations related to identity, head location in image, background clutter, facial expression, and illumination. To address the problem, we propose to incorporate supervised information (pose angles of training samples) into the process of manifold learning. The process has three stages: neighborhood construction, graph weight computation and projection learning. For the first two stages, we redefine inter-point distance for neighborhood construction as well as graph weight by constraining them with the pose angle information. For Stage 3, we present a supervised neighborhood-based linear feature transformation algorithm to keep the data points with similar pose angles close together but the data points with dissimilar pose angles far apart. The experimental results show that our method has higher estimation accuracy than the other state-of-art algorithms and is robust to identity and illumination variations. Copyright © 2014 Elsevier Ltd. All rights reserved.
Right-angled polyhedra and hyperbolic 3-manifolds
Vesnin, A. Yu.
2017-04-01
Hyperbolic 3-manifolds whose fundamental groups are subgroups of finite index in right-angled Coxeter groups are under consideration. The construction of such manifolds is associated with regular colourings of the faces of polyhedra and, in particular, with 4-colourings. The following questions are discussed: the structure of the set of right-angled polytopes in Lobachevskii space; examples of orientable and non-orientable manifolds, including the classical Löbell manifold constructed in 1931; connections between the Hamiltonian property of a polyhedron and the existence of hyperelliptic involutions of manifolds; the volumes and complexity of manifolds; isometry between hyperbolic manifolds constructed from 4-colourings. Bibliography: 89 titles.
On some classes of super quasi-Einstein manifolds
International Nuclear Information System (INIS)
Ozguer, Cihan
2009-01-01
Quasi-Einstein and generalized quasi-Einstein manifolds are the generalizations of Einstein manifolds. In this study, we consider a super quasi-Einstein manifold, which is another generalization of an Einstein manifold. We find the curvature characterizations of a Ricci-pseudosymmetric and a quasi-conformally flat super quasi-Einstein manifolds. We also consider the condition C ∼ .S=0 on a super quasi-Einstein manifold, where C ∼ and S denote the quasi-conformal curvature tensor and Ricci tensor of the manifold, respectively.
Loop quantum cosmology and singularities.
Struyve, Ward
2017-08-15
Loop quantum gravity is believed to eliminate singularities such as the big bang and big crunch singularity. This belief is based on studies of so-called loop quantum cosmology which concerns symmetry-reduced models of quantum gravity. In this paper, the problem of singularities is analysed in the context of the Bohmian formulation of loop quantum cosmology. In this formulation there is an actual metric in addition to the wave function, which evolves stochastically (rather than deterministically as the case of the particle evolution in non-relativistic Bohmian mechanics). Thus a singularity occurs whenever this actual metric is singular. It is shown that in the loop quantum cosmology for a homogeneous and isotropic Friedmann-Lemaître-Robertson-Walker space-time with arbitrary constant spatial curvature and cosmological constant, coupled to a massless homogeneous scalar field, a big bang or big crunch singularity is never obtained. This should be contrasted with the fact that in the Bohmian formulation of the Wheeler-DeWitt theory singularities may exist.
On Riemannian manifolds (Mn, g) of quasi-constant curvature
International Nuclear Information System (INIS)
Rahman, M.S.
1995-07-01
A Riemannian manifold (M n , g) of quasi-constant curvature is defined. It is shown that an (M n , g) in association with other class of manifolds gives rise, under certain conditions, to a manifold of quasi-constant curvature. Some observations on how a manifold of quasi-constant curvature accounts for a pseudo Ricci-symmetric manifold and quasi-umbilical hypersurface are made. (author). 10 refs
Singularity resolution in quantum gravity
International Nuclear Information System (INIS)
Husain, Viqar; Winkler, Oliver
2004-01-01
We examine the singularity resolution issue in quantum gravity by studying a new quantization of standard Friedmann-Robertson-Walker geometrodynamics. The quantization procedure is inspired by the loop quantum gravity program, and is based on an alternative to the Schroedinger representation normally used in metric variable quantum cosmology. We show that in this representation for quantum geometrodynamics there exists a densely defined inverse scale factor operator, and that the Hamiltonian constraint acts as a difference operator on the basis states. We find that the cosmological singularity is avoided in the quantum dynamics. We discuss these results with a view to identifying the criteria that constitute 'singularity resolution' in quantum gravity
The theory of singular perturbations
De Jager, E M
1996-01-01
The subject of this textbook is the mathematical theory of singular perturbations, which despite its respectable history is still in a state of vigorous development. Singular perturbations of cumulative and of boundary layer type are presented. Attention has been given to composite expansions of solutions of initial and boundary value problems for ordinary and partial differential equations, linear as well as quasilinear; also turning points are discussed. The main emphasis lies on several methods of approximation for solutions of singularly perturbed differential equations and on the mathemat
Van Hove singularities revisited
International Nuclear Information System (INIS)
Dzyaloshinskii, I.
1987-07-01
Beginning with the work of Hirsch and Scalapino the importance of ln 2 -Van Hove singularity in T c -enhancement in La 2 CuO 4 -based compounds was realized, which is nicely reviewed by Rice. However, the theoretical treatment carried out before is incomplete. Two things were apparently not paid due attention to: interplay of particle-particle and particle-hole channels and Umklapp processes. In what follows a two-dimensional weak coupling model of LaCuO 4 will be solved exactly in the ln 2 -approximation. The result in the Hubbard limit (one bare charge) is that the system is unstable at any sign of interaction. Symmetry breaking moreover is pretty peculiar. Of course, there are separate singlet superconducting pairings in the pp-channel (attraction) and SDW (repulsion) and CDW (attraction) in the ph-channel. It is natural that Umklapps produce an SDW + CDW mixture at either sign of the interaction. What is unusual is that both the pp-ph interplay and the Umklapps give rise to a monster-coherent SS + SDW + CDW mixture, again at either sign of the bare charge. In the general model where all 4 charges involved are substantially different, the system might remain metallic. A more realistic approach which takes into account dopping in La-M-Cu-O and interlayer interaction provides at least a qualitative understanding of the experimental picture. 10 refs, 5 figs
Critical manifold of the kagome-lattice Potts model
International Nuclear Information System (INIS)
Jacobsen, Jesper Lykke; Scullard, Christian R
2012-01-01
Any two-dimensional infinite regular lattice G can be produced by tiling the plane with a finite subgraph B⊆G; we call B a basis of G. We introduce a two-parameter graph polynomial P B (q, v) that depends on B and its embedding in G. The algebraic curve P B (q, v) = 0 is shown to provide an approximation to the critical manifold of the q-state Potts model, with coupling v = e K − 1, defined on G. This curve predicts the phase diagram not only in the physical ferromagnetic regime (v > 0), but also in the antiferromagnetic (v B (q, v) = 0 provides the exact critical manifold in the limit of infinite B. Furthermore, for some lattices G—or for the Ising model (q = 2) on any G—the polynomial P B (q, v) factorizes for any choice of B: the zero set of the recurrent factor then provides the exact critical manifold. In this sense, the computation of P B (q, v) can be used to detect exact solvability of the Potts model on G. We illustrate the method for two choices of G: the square lattice, where the Potts model has been exactly solved, and the kagome lattice, where it has not. For the square lattice we correctly reproduce the known phase diagram, including the antiferromagnetic transition and the singularities in the Berker–Kadanoff phase at certain Beraha numbers. For the kagome lattice, taking the smallest basis with six edges we recover a well-known (but now refuted) conjecture of F Y Wu. Larger bases provide successive improvements on this formula, giving a natural extension of Wu’s approach. We perform large-scale numerical computations for comparison and find excellent agreement with the polynomial predictions. For v > 0 the accuracy of the predicted critical coupling v c is of the order 10 −4 or 10 −5 for the six-edge basis, and improves to 10 −6 or 10 −7 for the largest basis studied (with 36 edges). This article is part of ‘Lattice models and integrability’, a special issue of Journal of Physics A: Mathematical and Theoretical in honour of
New complete noncompact Spin(7) manifolds
International Nuclear Information System (INIS)
Cvetic, M.; Gibbons, G.W.; Lue, H.; Pope, C.N.
2002-01-01
We construct new explicit metrics on complete noncompact Riemannian 8-manifolds with holonomy Spin(7). One manifold, which we denote by (A 8 , is topologically R 8 and another, which we denote by B 8 , is the bundle of chiral spinors over S 4 . Unlike the previously-known complete noncompact metric of Spin(7) holonomy, which was also defined on the bundle of chiral spinors over S 4 , our new metrics are asymptotically locally conical (ALC): near infinity they approach a circle bundle with fibres of constant length over a cone whose base is the squashed Einstein metric on CP 3 . We construct the covariantly-constant spinor and calibrating 4-form. We also obtain an L 2 -normalisable harmonic 4-form for the (A)) 8 manifold, and two such 4-forms (of opposite dualities) for the B 8 manifold. We use the metrics to construct new supersymmetric brane solutions in M-theory and string theory. In particular, we construct resolved fractional M2-branes involving the use of the L 2 harmonic 4-forms, and show that for each manifold there is a supersymmetric example. An intriguing feature of the new A 8 and B 8 Spin(7) metrics is that they are actually the same local solution, with the two different complete manifolds corresponding to taking the radial coordinate to be either positive or negative. We make a comparison with the Taub-NUT and Taub-BOLT metrics, which by contrast do not have special holonomy. In we construct the general solution of our first-order equations for Spin(7) holonomy, and obtain further regular metrics that are complete on manifolds B 8 + and B 8 - similar to B 8
Singularity: Raychaudhuri equation once again
Indian Academy of Sciences (India)
Cosmology; Raychaudhuri equation; Universe; quantum gravity; loop quan- tum gravity ... than the observation verifying the prediction of theory. This gave .... which was now expanding, would have had a singular beginning in a hot Big Bang.
The role of self-similarity in singularities of partial differential equations
International Nuclear Information System (INIS)
Eggers, Jens; Fontelos, Marco A
2009-01-01
We survey rigorous, formal and numerical results on the formation of point-like singularities (or blow-up) for a wide range of evolution equations. We use a similarity transformation of the original equation with respect to the blow-up point, such that self-similar behaviour is mapped to the fixed point of a dynamical system. We point out that analysing the dynamics close to the fixed point is a useful way of characterizing the singularity, in that the dynamics frequently reduces to very few dimensions. As far as we are aware, examples from the literature either correspond to stable fixed points, low-dimensional centre-manifold dynamics, limit cycles or travelling waves. For each 'class' of singularity, we give detailed examples. (invited article)
Unsupervised image matching based on manifold alignment.
Pei, Yuru; Huang, Fengchun; Shi, Fuhao; Zha, Hongbin
2012-08-01
This paper challenges the issue of automatic matching between two image sets with similar intrinsic structures and different appearances, especially when there is no prior correspondence. An unsupervised manifold alignment framework is proposed to establish correspondence between data sets by a mapping function in the mutual embedding space. We introduce a local similarity metric based on parameterized distance curves to represent the connection of one point with the rest of the manifold. A small set of valid feature pairs can be found without manual interactions by matching the distance curve of one manifold with the curve cluster of the other manifold. To avoid potential confusions in image matching, we propose an extended affine transformation to solve the nonrigid alignment in the embedding space. The comparatively tight alignments and the structure preservation can be obtained simultaneously. The point pairs with the minimum distance after alignment are viewed as the matchings. We apply manifold alignment to image set matching problems. The correspondence between image sets of different poses, illuminations, and identities can be established effectively by our approach.
Lie group structures on automorphism groups of real-analytic CR manifolds
ZAITSEV, DMITRI
2008-01-01
PUBLISHED Given any real-analytic CR manifold M, we provide general conditions on M guar- anteeing that the group of all its global real-analytic CR automorphisms AutCR(M) is a Lie group (in an appropriate topology). In particular, we obtain a Lie group structure for AutCR(M) when M is an arbitrary compact real-analytic hypersurface embedded in some Stein manifold. The first author was supported by the Austrian Science Fund FWF, Project P17111 and Project P19667. The second ...
Symplectic manifolds, coadjoint orbits, and Mean Field Theory
International Nuclear Information System (INIS)
Rosensteel, G.
1986-01-01
Mean field theory is given a geometrical interpretation as a Hamiltonian dynamical system. The Hartree-Fock phase space is the Grassmann manifold, a symplectic submanifold of the projective space of the full many-fermion Hilbert space. The integral curves of the Hartree-Fock vector field are the time-dependent Hartree-Fock solutions, while the critical points of the energy function are the time-independent states. The mean field theory is generalized beyond determinants to coadjoint orbit spaces of the unitary group; the Grassmann variety is the minimal coadjoint orbit
The quantum 2-sphere as a complex quantum manifold
International Nuclear Information System (INIS)
Chu Chongsun; Ho Peiming; Zumino, B.
1996-01-01
We describe the quantum sphere of Podles for c=0 by means of a stereographic projection which is analogous to that which exibits the classical sphere as a complex manifold. We show that the algebra of functions and the differential calculus on the sphere are covariant under the coaction of fractional transformations with SU q (2) coefficients as well as under the action of SU q (2) vector fields. Going to the classical limit we obtain the Poisson sphere. Finally, we study the invariant integration of functions on the sphere and find its relation with the translationally invariant integration on the complex quantum plane. (orig.)
Czech Academy of Sciences Publication Activity Database
Knésl, Zdeněk; Klusák, Jan; Náhlík, Luboš
2007-01-01
Roč. 14, č. 6 (2007), s. 399-408 ISSN 1802-1484 R&D Projects: GA ČR(CZ) GA101/05/0320; GA ČR GA101/05/0227 Institutional research plan: CEZ:AV0Z20410507 Keywords : fracture mechanics * stability criteria * singular stress concentrations * crack initiation * critical stress Subject RIV: JL - Materials Fatigue, Friction Mechanics
Local and nonlocal space-time singularities
International Nuclear Information System (INIS)
Konstantinov, M.Yu.
1985-01-01
The necessity to subdivide the singularities into two classes: local and nonlocal, each of them to be defined independently, is proved. Both classes of the singularities are defined, and the relation between the definitions introduced and the standard definition of singularities, based on space-time, incompleteness, is established. The relation between definitions introduced and theorems on the singularity existence is also established
Online Manifold Regularization by Dual Ascending Procedure
Directory of Open Access Journals (Sweden)
Boliang Sun
2013-01-01
Full Text Available We propose a novel online manifold regularization framework based on the notion of duality in constrained optimization. The Fenchel conjugate of hinge functions is a key to transfer manifold regularization from offline to online in this paper. Our algorithms are derived by gradient ascent in the dual function. For practical purpose, we propose two buffering strategies and two sparse approximations to reduce the computational complexity. Detailed experiments verify the utility of our approaches. An important conclusion is that our online MR algorithms can handle the settings where the target hypothesis is not fixed but drifts with the sequence of examples. We also recap and draw connections to earlier works. This paper paves a way to the design and analysis of online manifold regularization algorithms.
Maximum Solutions of Normalized Ricci Flow on 4-Manifolds
Fang, Fuquan; Zhang, Yuguang; Zhang, Zhenlei
2008-10-01
We consider the maximum solution g( t), t ∈ [0, + ∞), to the normalized Ricci flow. Among other things, we prove that, if ( M, ω) is a smooth compact symplectic 4-manifold such that {b_2^+(M) > 1} and let g( t), t ∈ [0, ∞), be a solution to (1.3) on M whose Ricci curvature satisfies that |Ric( g( t))| ≤ 3 and additionally χ( M) = 3τ ( M) > 0, then there exists an {min mathbb{N}} , and a sequence of points { x j, k ∈ M}, j = 1, . . . , m, satisfying that, by passing to a subsequence, {{(M, g(tk+t), x_{1,k},ldots, x_{m,k})stackrel{d_{GH}}longrightarrow ({\\coprod limitsm_{j=1}} N_j , g_{infty}, x_{1,infty}, ldots, x_{m,infty}),}} t ∈ [0, ∞), in the m-pointed Gromov-Hausdorff sense for any sequence t k → ∞, where ( N j , g ∞), j = 1, . . . , m, are complete complex hyperbolic orbifolds of complex dimension 2 with at most finitely many isolated orbifold points. Moreover, the convergence is C ∞ in the non-singular part of {\\coprod _1^m Nj} and {text{Vol}_{g0}(M)=sum_{j=1}mtext{Vol}_{g_{infty}}(Nj)} , where χ( M) (resp. τ( M)) is the Euler characteristic (resp. signature) of M.
Harmonic mappings into manifolds with boundary
International Nuclear Information System (INIS)
Chen Yunmei; Musina, R.
1989-08-01
In this paper we deal with harmonic maps from a compact Riemannian manifold into a manifold with boundary. In this case, a weak harmonic map is by definition a solution to a differential inclusion. In the first part of the paper we investigate the general properties of weak harmonic maps, which can be seen as solutions to a system of elliptic differential equations. In the second part we concentrate our attention on the heat flow method for harmonic maps. The result we achieve in this context extends a result by Chen and Struwe. (author). 21 refs
Manifolds for pose tracking from monocular video
Basu, Saurav; Poulin, Joshua; Acton, Scott T.
2015-03-01
We formulate a simple human-pose tracking theory from monocular video based on the fundamental relationship between changes in pose and image motion vectors. We investigate the natural embedding of the low-dimensional body pose space into a high-dimensional space of body configurations that behaves locally in a linear manner. The embedded manifold facilitates the decomposition of the image motion vectors into basis motion vector fields of the tangent space to the manifold. This approach benefits from the style invariance of image motion flow vectors, and experiments to validate the fundamental theory show reasonable accuracy (within 4.9 deg of the ground truth).
Effective Field Theory on Manifolds with Boundary
Albert, Benjamin I.
In the monograph Renormalization and Effective Field Theory, Costello made two major advances in rigorous quantum field theory. Firstly, he gave an inductive position space renormalization procedure for constructing an effective field theory that is based on heat kernel regularization of the propagator. Secondly, he gave a rigorous formulation of quantum gauge theory within effective field theory that makes use of the BV formalism. In this work, we extend Costello's renormalization procedure to a class of manifolds with boundary and make preliminary steps towards extending his formulation of gauge theory to manifolds with boundary. In addition, we reorganize the presentation of the preexisting material, filling in details and strengthening the results.
Matrix regularization of embedded 4-manifolds
International Nuclear Information System (INIS)
Trzetrzelewski, Maciej
2012-01-01
We consider products of two 2-manifolds such as S 2 ×S 2 , embedded in Euclidean space and show that the corresponding 4-volume preserving diffeomorphism algebra can be approximated by a tensor product SU(N)⊗SU(N) i.e. functions on a manifold are approximated by the Kronecker product of two SU(N) matrices. A regularization of the 4-sphere is also performed by constructing N 2 ×N 2 matrix representations of the 4-algebra (and as a byproduct of the 3-algebra which makes the regularization of S 3 also possible).
The Brownian traveller on manifolds
Czech Academy of Sciences Publication Activity Database
Kolb, M.; Krejčiřík, David
2014-01-01
Roč. 4, č. 2 (2014), s. 235-281 ISSN 1664-039X R&D Projects: GA MŠk LC06002; GA ČR GAP203/11/0701 Institutional support: RVO:61389005 Keywords : heat equation and curvature * hardy inequality Subject RIV: BE - Theoretical Physics Impact factor: 1.231, year: 2014
Dynamics on Networks of Manifolds
DeVille, Lee; Lerman, Eugene
2015-03-01
We propose a precise definition of a continuous time dynamical system made up of interacting open subsystems. The interconnections of subsystems are coded by directed graphs. We prove that the appropriate maps of graphs called graph fibrations give rise to maps of dynamical systems. Consequently surjective graph fibrations give rise to invariant subsystems and injective graph fibrations give rise to projections of dynamical systems.
Synchronization and Control of Linearly Coupled Singular Systems
Directory of Open Access Journals (Sweden)
Fang Qingxiang
2013-01-01
Full Text Available The synchronization and control problem of linearly coupled singular systems is investigated. The uncoupled dynamical behavior at each node is general and can be chaotic or, otherwise the coupling matrix is not assumed to be symmetrical. Some sufficient conditions for globally exponential synchronization are derived based on Lyapunov stability theory. These criteria, which are in terms of linear matrix inequality (LMI, indicate that the left and right eigenvectors corresponding to eigenvalue zero of the coupling matrix play key roles in the stability analysis of the synchronization manifold. The controllers are designed for state feedback control and pinning control, respectively. Finally, a numerical example is provided to illustrate the effectiveness of the proposed conditions.
On the singularities of solutions to singular perturbation problems
International Nuclear Information System (INIS)
Fruchard, A; Schaefke, R
2005-01-01
We consider a singularly perturbed complex first order ODE εu ' Φ(x, u, a, ε), x, u element of C, ε > 0 is a small complex parameter and a element of C is a control parameter. It is proven that the singularities of some solutions are regularly spaced and that they move from one to the next as a runs about a loop of index one around a value of overstability. This gives a positive answer to a question of J. L. Callot
On the singularities of solutions to singular perturbation problems
Energy Technology Data Exchange (ETDEWEB)
Fruchard, A [Laboratoire de Mathematiques, Informatique et Applications, Faculte des Sciences et Techniques, Universite de Haute Alsace, 4 rue des Freres Lumiere, 68093 Mulhouse cedex (France); Schaefke, R [Departement de Mathematiques, Universite Louis Pasteur, 7 rue Rene-Descartes, 67084 Strasbourg cedex (France)
2005-01-01
We consider a singularly perturbed complex first order ODE {epsilon}u ' {phi}(x, u, a, {epsilon}), x, u element of C, {epsilon} > 0 is a small complex parameter and a element of C is a control parameter. It is proven that the singularities of some solutions are regularly spaced and that they move from one to the next as a runs about a loop of index one around a value of overstability. This gives a positive answer to a question of J. L. Callot.
Hidden singularities in non-abelian gauge fields
International Nuclear Information System (INIS)
Bollini, C.G.; Giambiagi, J.J.; Tiomno, J.
1978-01-01
It is shown that the potential (and field) of a non-abelian gauge theory is not well determined when it has a singular point. When this is the cause, it is important to specify the regularization procedure used to give a precise definition of physical quantities at the singularity at any stage of the computation. The fact that a certain A sub(μ) (associated with the given regularization) represents the vacuum when F sub(μν) is a zero distribution not only on the global space but also in all its projections to arbitrary subspaces is discussed. The example used as a base for the discussion is A vetor = i (sigma vetor Λ r vetor / r 2 ). For this example it is shown that different regularizations give the same field in the global space but they give different distributions when projected to subspaces containing the singular point [pt
Four-manifolds, geometries and knots
Hillman, Jonathan A
2007-01-01
The goal of this book is to characterize algebraically the closed 4-manifolds that fibre nontrivially or admit geometries in the sense of Thurston, or which are obtained by surgery on 2-knots, and to provide a reference for the topology of such manifolds and knots. The first chapter is purely algebraic. The rest of the book may be divided into three parts: general results on homotopy and surgery (Chapters 2-6), geometries and geometric decompositions (Chapters 7-13), and 2-knots (Chapters 14-18). In many cases the Euler characteristic, fundamental group and Stiefel-Whitney classes together form a complete system of invariants for the homotopy type of such manifolds, and the possible values of the invariants can be described explicitly. The strongest results are characterizations of manifolds which fibre homotopically over S^1 or an aspherical surface (up to homotopy equivalence) and infrasolvmanifolds (up to homeomorphism). As a consequence 2-knots whose groups are poly-Z are determined up to Gluck reconstruc...
International Nuclear Information System (INIS)
Becker, Katrin; Becker, Melanie; Robbins, Daniel
2015-01-01
In this talk we report on recent progress in describing compactifications of string theory and M-theory on G 2 and Spin(7) manifolds. We include the infinite set of α’-corrections and describe the entire tower of massless and massive Kaluza–Klein modes resulting from such compactifications. (invited comment)
The Koch curve as a smooth manifold
International Nuclear Information System (INIS)
Epstein, Marcelo; Sniatycki, Jedrzej
2008-01-01
We show that there exists a homeomorphism between the closed interval [0,1] is contained in R and the Koch curve endowed with the subset topology of R 2 . We use this homeomorphism to endow the Koch curve with the structure of a smooth manifold with boundary
Duality constructions from quantum state manifolds
Kriel, J. N.; van Zyl, H. J. R.; Scholtz, F. G.
2015-11-01
The formalism of quantum state space geometry on manifolds of generalised coherent states is proposed as a natural setting for the construction of geometric dual descriptions of non-relativistic quantum systems. These state manifolds are equipped with natural Riemannian and symplectic structures derived from the Hilbert space inner product. This approach allows for the systematic construction of geometries which reflect the dynamical symmetries of the quantum system under consideration. We analyse here in detail the two dimensional case and demonstrate how existing results in the AdS 2 /CF T 1 context can be understood within this framework. We show how the radial/bulk coordinate emerges as an energy scale associated with a regularisation procedure and find that, under quite general conditions, these state manifolds are asymptotically anti-de Sitter solutions of a class of classical dilaton gravity models. For the model of conformal quantum mechanics proposed by de Alfaro et al. [1] the corresponding state manifold is seen to be exactly AdS 2 with a scalar curvature determined by the representation of the symmetry algebra. It is also shown that the dilaton field itself is given by the quantum mechanical expectation values of the dynamical symmetry generators and as a result exhibits dynamics equivalent to that of a conformal mechanical system.
Toric geometry of G2-manifolds
DEFF Research Database (Denmark)
Madsen, Thomas Bruun; Swann, Andrew Francis
We consider G2-manifolds with an effective torus action that is multi-Hamiltonian for one or more of the defining forms. The case of T3-actions is found to be distinguished. For such actions multi-Hamiltonian with respect to both the three- and four-form, we derive a Gibbons-Hawking type ansatz...
Conservative systems with ports on contact manifolds
Eberard, D.; Maschke, B.M.; van der Schaft, Arjan; Piztek, P.
In this paper we propose an extension of port Hamiltonian systems, called conservative systems with ports, which encompass systems arising from the Irreversible Thermodynamics. Firstly we lift a port Hamiltonian system from its state space manifold to the thermodynamic phase space to a contact
Foliations and the geometry of 3-manifolds
Calegari, Danny
2014-01-01
This unique reference, aimed at research topologists, gives an exposition of the 'pseudo-Anosov' theory of foliations of 3-manifolds. This theory generalizes Thurston's theory of surface automorphisms and reveals an intimate connection between dynamics, geometry and topology in 3 dimensions.
Is the cosmological singularity compulsory
International Nuclear Information System (INIS)
Bekenstein, J.D.; Meisels, A.
1980-01-01
The cosmological singularity is inherent in all conventional general relativistic cosmological models. There can be no question that it is an unphysical feature; yet there does not seem to be any convervative way of eliminating it. Here we present singularity-free isotropic cosmological models which are indistinguishable from general relativistic ones at late times. They are based on the general theory of variable rest masses that we developed recently. Outside cosmology this theory simulates general relativity well. Thus it provides a framework incorporating those features which have made geneal relativity so sucessful while providing a way out of singularity dilemma. The cosmological models can be made to incorporate Dirac's large numbers hypothesis. G(now)/G(0)approx.10 -38
A 1 + 5-dimensional gravitational-wave solution. Curvature singularity and spacetime singularity
Energy Technology Data Exchange (ETDEWEB)
Chen, Yu-Zhu [Tianjin University, Department of Physics, Tianjin (China); Li, Wen-Du [Tianjin University, Department of Physics, Tianjin (China); Nankai University, Theoretical Physics Division, Chern Institute of Mathematics, Tianjin (China); Dai, Wu-Sheng [Nankai University, Theoretical Physics Division, Chern Institute of Mathematics, Tianjin (China); Nankai University and Tianjin University, LiuHui Center for Applied Mathematics, Tianjin (China)
2017-12-15
We solve a 1 + 5-dimensional cylindrical gravitational-wave solution of the Einstein equation, in which there are two curvature singularities. Then we show that one of the curvature singularities can be removed by an extension of the spacetime. The result exemplifies that the curvature singularity is not always a spacetime singularity; in other words, the curvature singularity cannot serve as a criterion for spacetime singularities. (orig.)
Zeroth Poisson Homology, Foliated Cohomology and Perfect Poisson Manifolds
Martínez-Torres, David; Miranda, Eva
2018-01-01
We prove that, for compact regular Poisson manifolds, the zeroth homology group is isomorphic to the top foliated cohomology group, and we give some applications. In particular, we show that, for regular unimodular Poisson manifolds, top Poisson and foliated cohomology groups are isomorphic. Inspired by the symplectic setting, we define what a perfect Poisson manifold is. We use these Poisson homology computations to provide families of perfect Poisson manifolds.
Hyperbolic manifolds as vacuum solutions in Kaluza-Klein theories
International Nuclear Information System (INIS)
Aref'eva, I.Ya.; Volovich, I.V.
1985-08-01
The relevance of compact hyperbolic manifolds in the context of Kaluza-Klein theories is discussed. Examples of spontaneous compactification on hyperbolic manifolds including d dimensional (d>=8) Einstein-Yang-Mills gravity and 11-dimensional supergravity are considered. Some mathematical facts about hyperbolic manifolds essential for the physical content of the theory are briefly summarized. Non-linear σ-models based on hyperbolic manifolds are discussed. (author)
Fluid manifold design for a solar energy storage tank
Humphries, W. R.; Hewitt, H. C.; Griggs, E. I.
1975-01-01
A design technique for a fluid manifold for use in a solar energy storage tank is given. This analytical treatment generalizes the fluid equations pertinent to manifold design, giving manifold pressures, velocities, and orifice pressure differentials in terms of appropriate fluid and manifold geometry parameters. Experimental results used to corroborate analytical predictions are presented. These data indicate that variations in discharge coefficients due to variations in orifices can cause deviations between analytical predictions and actual performance values.
Some theorems on a class of harmonic manifolds
International Nuclear Information System (INIS)
Rahman, M.S.; Chen Weihuan.
1993-08-01
A class of harmonic n-manifold, denoted by HM n , is, in fact, focussed on a Riemannian manifold with harmonic curvature. A variety of results, with properties, on HM n is presented in a fair order. Harmonic manifolds are then touched upon manifolds with recurrent Ricci curvature, biRicci-recurrent curvature and recurrent conformal curvature, and, in consequence, a sequence of theorems are deduced. (author). 21 refs
A Combination Theorem for Convex Hyperbolic Manifolds, with Applications to Surfaces in 3-Manifolds
Baker, Mark; Cooper, Daryl
2005-01-01
We prove the convex combination theorem for hyperbolic n-manifolds. Applications are given both in high dimensions and in 3 dimensions. One consequence is that given two geometrically finite subgroups of a discrete group of isometries of hyperbolic n-space, satisfying a natural condition on their parabolic subgroups, there are finite index subgroups which generate a subgroup that is an amalgamated free product. Constructions of infinite volume hyperbolic n-manifolds are described by gluing lo...
Singularities in geodesic surface congruence
International Nuclear Information System (INIS)
Cho, Yong Seung; Hong, Soon-Tae
2008-01-01
In the stringy cosmology, we investigate singularities in geodesic surface congruences for the timelike and null strings to yield the Raychaudhuri type equations possessing correction terms associated with the novel features owing to the strings. Assuming the stringy strong energy condition, we have a Hawking-Penrose type inequality equation. If the initial expansion is negative so that the congruence is converging, we show that the expansion must pass through the singularity within a proper time. We observe that the stringy strong energy conditions of both the timelike and null string congruences produce the same inequality equation.
Singular perturbation of simple eigenvalues
International Nuclear Information System (INIS)
Greenlee, W.M.
1976-01-01
Two operator theoretic theorems which generalize those of asymptotic regular perturbation theory and which apply to singular perturbation problems are proved. Application of these theorems to concrete problems is involved, but the perturbation expansions for eigenvalues and eigenvectors are developed in terms of solutions of linear operator equations. The method of correctors, as well as traditional boundary layer techniques, can be used to apply these theorems. The current formulation should be applicable to highly singular ''hard core'' potential perturbations of the radial equation of quantum mechanics. The theorems are applied to a comparatively simple model problem whose analysis is basic to that of the quantum mechanical problem
Singularity Theory and its Applications
Stewart, Ian; Mond, David; Montaldi, James
1991-01-01
A workshop on Singularities, Bifuraction and Dynamics was held at Warwick in July 1989, as part of a year-long symposium on Singularity Theory and its applications. The proceedings fall into two halves: Volume I mainly on connections with algebraic geometry and volume II on connections with dynamical systems theory, bifurcation theory and applications in the sciences. The papers are original research, stimulated by the symposium and workshop: All have been refereed and none will appear elsewhere. The main topic of volume II is new methods for the study of bifurcations in nonlinear dynamical systems, and applications of these.
Ambient cosmology and spacetime singularities
International Nuclear Information System (INIS)
Antoniadis, Ignatios; Cotsakis, Spiros
2015-01-01
We present a new approach to the issues of spacetime singularities and cosmic censorship in general relativity. This is based on the idea that standard 4-dimensional spacetime is the conformal infinity of an ambient metric for the 5-dimensional Einstein equations with fluid sources. We then find that the existence of spacetime singularities in four dimensions is constrained by asymptotic properties of the ambient 5-metric, while the non-degeneracy of the latter crucially depends on cosmic censorship holding on the boundary. (orig.)
Ambient cosmology and spacetime singularities
Antoniadis, Ignatios
2015-01-01
We present a new approach to the issues of spacetime singularities and cosmic censorship in general relativity. This is based on the idea that standard 4-dimensional spacetime is the conformal infinity of an ambient metric for the 5-dimensional Einstein equations with fluid sources. We then find that the existence of spacetime singularities in four dimensions is constrained by asymptotic properties of the ambient 5-metric, while the non-degeneracy of the latter crucially depends on cosmic censorship holding on the boundary.
Singular moduli and Arakelov intersection
International Nuclear Information System (INIS)
Weng Lin.
1994-05-01
The value of the modular function j(τ) at imaginary quadratic arguments τ in the upper half plane is usually called singular moduli. In this paper, we use Arakelov intersection to give the prime factorizations of a certain combination of singular moduli, coming from the Hecke correspondence. Such a result may be considered as the degenerate one of Gross and Zagier on Heegner points and derivatives of L-series in their paper [GZ1], and is parallel to the result in [GZ2]. (author). 2 refs
Normal pure states of the von Nuemann algebra of bounded operators as Kaehler manifold
International Nuclear Information System (INIS)
Cirelli, R.; Lanzavecchia, P.; Mania, A.
1983-01-01
The projective space of a complex Hilbert space H is considered both as a Kaehler manifold and as the set of pure states of the von Neumann algebra B(H). A link is given between these two structures. Special attention is devoted to topology, orientation and automorphisms of the structures and Wigner's theorem. (author)
Quantum filter reduction for measurement-feedback control via unsupervised manifold learning
DEFF Research Database (Denmark)
Nielsen, Anne E. B.; Hopkins, Asa S .; Mabuchi, Hideo
2009-01-01
We derive simple models for the dynamics of a single atom coupled to a cavity field mode in the absorptive bistable parameter regime by projecting the time evolution of the state of the system onto a suitably chosen nonlinear low-dimensional manifold, which is found by use of local tangent space ...
Singularities in minimax optimization of networks
DEFF Research Database (Denmark)
Madsen, Kaj; Schjær-Jacobsen, Hans
1976-01-01
A theoretical treatment of singularities in nonlinear minimax optimization problems, which allows for a classification in regular and singular problems, is presented. A theorem for determining a singularity that is present in a given problem is formulated. A group of problems often used in the li......A theoretical treatment of singularities in nonlinear minimax optimization problems, which allows for a classification in regular and singular problems, is presented. A theorem for determining a singularity that is present in a given problem is formulated. A group of problems often used...
Harmonic Riemannian Maps on Locally Conformal Kaehler Manifolds
Indian Academy of Sciences (India)
We study harmonic Riemannian maps on locally conformal Kaehler manifolds ( l c K manifolds). We show that if a Riemannian holomorphic map between l c K manifolds is harmonic, then the Lee vector field of the domain belongs to the kernel of the Riemannian map under a condition. When the domain is Kaehler, we ...
Higher-order Jordan Osserman pseudo-Riemannian manifolds
International Nuclear Information System (INIS)
Gilkey, Peter B; Ivanova, Raina; Zhang Tan
2002-01-01
We study the higher-order Jacobi operator in pseudo-Riemannian geometry. We exhibit a family of manifolds so that this operator has constant Jordan normal form on the Grassmannian of subspaces of signature (r, s) for certain values of (r, s). These pseudo-Riemannian manifolds are new and non-trivial examples of higher-order Osserman manifolds
Higher-order Jordan Osserman pseudo-Riemannian manifolds
Energy Technology Data Exchange (ETDEWEB)
Gilkey, Peter B [Mathematics Department, University of Oregon, Eugene, OR 97403 (United States); Ivanova, Raina [Mathematics Department, University of Hawaii - Hilo, 200 W Kawili St, Hilo, HI 96720 (United States); Zhang Tan [Department of Mathematics and Statistics, Murray State University, Murray, KY 42071 (United States)
2002-09-07
We study the higher-order Jacobi operator in pseudo-Riemannian geometry. We exhibit a family of manifolds so that this operator has constant Jordan normal form on the Grassmannian of subspaces of signature (r, s) for certain values of (r, s). These pseudo-Riemannian manifolds are new and non-trivial examples of higher-order Osserman manifolds.
Wave equations on anti self dual (ASD) manifolds
Bashingwa, Jean-Juste; Kara, A. H.
2017-11-01
In this paper, we study and perform analyses of the wave equation on some manifolds with non diagonal metric g_{ij} which are of neutral signatures. These include the invariance properties, variational symmetries and conservation laws. In the recent past, wave equations on the standard (space time) Lorentzian manifolds have been performed but not on the manifolds from metrics of neutral signatures.
Hasan, Cris R; Krauskopf, Bernd; Osinga, Hinke M
2018-04-19
Many physiological phenomena have the property that some variables evolve much faster than others. For example, neuron models typically involve observable differences in time scales. The Hodgkin-Huxley model is well known for explaining the ionic mechanism that generates the action potential in the squid giant axon. Rubin and Wechselberger (Biol. Cybern. 97:5-32, 2007) nondimensionalized this model and obtained a singularly perturbed system with two fast, two slow variables, and an explicit time-scale ratio ε. The dynamics of this system are complex and feature periodic orbits with a series of action potentials separated by small-amplitude oscillations (SAOs); also referred to as mixed-mode oscillations (MMOs). The slow dynamics of this system are organized by two-dimensional locally invariant manifolds called slow manifolds which can be either attracting or of saddle type.In this paper, we introduce a general approach for computing two-dimensional saddle slow manifolds and their stable and unstable fast manifolds. We also develop a technique for detecting and continuing associated canard orbits, which arise from the interaction between attracting and saddle slow manifolds, and provide a mechanism for the organization of SAOs in [Formula: see text]. We first test our approach with an extended four-dimensional normal form of a folded node. Our results demonstrate that our computations give reliable approximations of slow manifolds and canard orbits of this model. Our computational approach is then utilized to investigate the role of saddle slow manifolds and associated canard orbits of the full Hodgkin-Huxley model in organizing MMOs and determining the firing rates of action potentials. For ε sufficiently large, canard orbits are arranged in pairs of twin canard orbits with the same number of SAOs. We illustrate how twin canard orbits partition the attracting slow manifold into a number of ribbons that play the role of sectors of rotations. The upshot is that we
Latash, Mark L
2018-02-21
The main goal of this paper is to introduce the concept of iso-perceptual manifold for perception of body configuration and related variables (kinesthetic perception) and to discuss its relation to the equilibrium-point hypothesis and the concepts of reference coordinate and uncontrolled manifold. Hierarchical control of action is postulated with abundant transformations between sets of spatial reference coordinates for salient effectors at different levels. Iso-perceptual manifold is defined in the combined space of afferent and efferent variables as the subspace corresponding to a stable percept. Examples of motion along an iso-perceptual manifold (perceptually equivalent motion) are considered during various natural actions. Some combinations of afferent and efferent signals, in particular those implying a violation of body's integrity, give rise to variable percepts by artificial projection onto iso-perceptual manifolds. This framework is used to interpret unusual features of vibration-induced kinesthetic illusions and to predict new illusions not yet reported in the literature. Copyright © 2017 IBRO. Published by Elsevier Ltd. All rights reserved.
Boundary triples for Schrodinger operators with singular interactions on hypersurfaces
Czech Academy of Sciences Publication Activity Database
Behrndt, J.; Langer, M.; Lotoreichik, Vladimir
2016-01-01
Roč. 7, č. 2 (2016), s. 290-302 ISSN 2220-8054 R&D Projects: GA ČR(CZ) GA14-06818S Institutional support: RVO:61389005 Keywords : boundary triple * Weyl function * Schrodinger operator * singular potential * delta-interaction * hypersurface Subject RIV: BE - Theoretical Physics
String theory and cosmological singularities
Indian Academy of Sciences (India)
recent times, string theory is providing new perspectives of such singularities which .... holes appear as stacks of a large number of D-branes wrapped in internal .... results into a well-known measure factor which makes the wave function into a.
Charged singularities: the causality violation
Energy Technology Data Exchange (ETDEWEB)
De Felice, F; Nobili, L [Padua Univ. (Italy). Ist. di Fisica; Calvani, M [Padua Univ. (Italy). Ist. di Astronomia
1980-12-01
A search is made for examples of particle trajectories which, approaching a naked singularity from infinity, make up for lost time before going back to infinity. In the Kerr-Newman metric a whole family of such trajectories is found showing that the causality violation is indeed a non-avoidable pathology.
Interval matrices: Regularity generates singularity
Czech Academy of Sciences Publication Activity Database
Rohn, Jiří; Shary, S.P.
2018-01-01
Roč. 540, 1 March (2018), s. 149-159 ISSN 0024-3795 Institutional support: RVO:67985807 Keywords : interval matrix * regularity * singularity * P-matrix * absolute value equation * diagonally singilarizable matrix Subject RIV: BA - General Mathematics Impact factor: 0.973, year: 2016
Singular solitons of generalized Camassa-Holm models
International Nuclear Information System (INIS)
Tian Lixin; Sun Lu
2007-01-01
Two generalizations of the Camassa-Holm system associated with the singular analysis are proposed for Painleve integrability properties and the extensions of already known analytic solitons. A remarkable feature of the physical model is that it has peakon solution which has peak form. An alternative WTC test which allowed the identifying of such models directly if formulated in terms of inserting a formed ansatz into these models. For the two models have Painleve property, Painleve-Baecklund systems can be constructed through the expansion of solitons about the singularity manifold. By the implementations of Maple, plentiful new type solitonic structures and some kink waves, which are affected by the variation of energy, are explored. If the energy is infinite in finite time, there will be a collapse in soliton systems by direct numerical simulations. Particularly, there are two collapses coexisting in our regular solitons, which occurred around its central regions. Simulation shows that in the bottom of periodic waves arises the non-zero parts of compactons and anti-compactons. We also get floating solitary waves whose amplitude is infinite. In contrary to which a finite-amplitude blow-up soliton is obtained. Periodic blow-ups are found too. Special kinks which have periodic cuspons are derived
Cosmological solutions and finite time singularities in Finslerian geometry
Paul, Nupur; de, S. S.; Rahaman, Farook
2018-03-01
We consider a very general scenario of our universe where its geometry is characterized by the Finslerian structure on the underlying spacetime manifold, a generalization of the Riemannian geometry. Now considering a general energy-momentum tensor for matter sector, we derive the gravitational field equations in such spacetime. Further, to depict the cosmological dynamics in such spacetime proposing an interesting equation of state identified by a sole parameter γ which for isotropic limit is simply the barotropic equation of state p = (γ ‑ 1)ρ (γ ∈ ℝ being the barotropic index), we solve the background dynamics. The dynamics offers several possibilities depending on this sole parameter as follows: (i) only an exponential expansion, or (ii) a finite time past singularity (big bang) with late accelerating phase, or (iii) a nonsingular universe exhibiting an accelerating scenario at late time which finally predicts a big rip type singularity. We also discuss several energy conditions and the possibility of cosmic bounce. Finally, we establish the first law of thermodynamics in such spacetime.
Nonlinear dynamical modes of climate variability: from curves to manifolds
Gavrilov, Andrey; Mukhin, Dmitry; Loskutov, Evgeny; Feigin, Alexander
2016-04-01
The necessity of efficient dimensionality reduction methods capturing dynamical properties of the system from observed data is evident. Recent study shows that nonlinear dynamical mode (NDM) expansion is able to solve this problem and provide adequate phase variables in climate data analysis [1]. A single NDM is logical extension of linear spatio-temporal structure (like empirical orthogonal function pattern): it is constructed as nonlinear transformation of hidden scalar time series to the space of observed variables, i. e. projection of observed dataset onto a nonlinear curve. Both the hidden time series and the parameters of the curve are learned simultaneously using Bayesian approach. The only prior information about the hidden signal is the assumption of its smoothness. The optimal nonlinearity degree and smoothness are found using Bayesian evidence technique. In this work we do further extension and look for vector hidden signals instead of scalar with the same smoothness restriction. As a result we resolve multidimensional manifolds instead of sum of curves. The dimension of the hidden manifold is optimized using also Bayesian evidence. The efficiency of the extension is demonstrated on model examples. Results of application to climate data are demonstrated and discussed. The study is supported by Government of Russian Federation (agreement #14.Z50.31.0033 with the Institute of Applied Physics of RAS). 1. Mukhin, D., Gavrilov, A., Feigin, A., Loskutov, E., & Kurths, J. (2015). Principal nonlinear dynamical modes of climate variability. Scientific Reports, 5, 15510. http://doi.org/10.1038/srep15510
Remarks on gauge variables and singular Lagrangians
International Nuclear Information System (INIS)
Chela-Flores, J.; Janica-de-la-Torre, R.; Kalnay, A.J.; Rodriguez-Gomez, J.; Rodriguez-Nunez, J.; Tascon, R.
1977-01-01
The relevance is discussed of gauge theory, based on a singular Lagrangian density, to the foundations of field theory. The idea that gauge transformations could change the physics of systems where the Lagrangian is singular is examined. (author)
Singular multiparameter dynamic equations with distributional ...
African Journals Online (AJOL)
Singular multiparameter dynamic equations with distributional potentials on time scales. ... In this paper, we consider both singular single and several multiparameter ... multiple function which is of one sign and nonzero on the given time scale.
Topological quantum field theory and four manifolds
Marino, Marcos
2005-01-01
The present book is the first of its kind in dealing with topological quantum field theories and their applications to topological aspects of four manifolds. It is not only unique for this reason but also because it contains sufficient introductory material that it can be read by mathematicians and theoretical physicists. On the one hand, it contains a chapter dealing with topological aspects of four manifolds, on the other hand it provides a full introduction to supersymmetry. The book constitutes an essential tool for researchers interested in the basics of topological quantum field theory, since these theories are introduced in detail from a general point of view. In addition, the book describes Donaldson theory and Seiberg-Witten theory, and provides all the details that have led to the connection between these theories using topological quantum field theory. It provides a full account of Witten’s magic formula relating Donaldson and Seiberg-Witten invariants. Furthermore, the book presents some of the ...
Modular categories and 3-manifold invariants
International Nuclear Information System (INIS)
Tureav, V.G.
1992-01-01
The aim of this paper is to give a concise introduction to the theory of knot invariants and 3-manifold invariants which generalize the Jones polynomial and which may be considered as a mathematical version of the Witten invariants. Such a theory was introduced by N. Reshetikhin and the author on the ground of the theory of quantum groups. here we use more general algebraic objects, specifically, ribbon and modular categories. Such categories in particular arise as the categories of representations of quantum groups. The notion of modular category, interesting in itself, is closely related to the notion of modular tensor category in the sense of G. Moore and N. Seiberg. For simplicity we restrict ourselves in this paper to the case of closed 3-manifolds
Topological anomalies for Seifert 3-manifolds
Energy Technology Data Exchange (ETDEWEB)
Imbimbo, Camillo [Dipartimento di Fisica, Università di Genova,Via Dodecaneso 33, 16146 Genova (Italy); INFN - Sezione di Genova,Via Dodecaneso 33, 16146, Genova (Italy); Rosa, Dario [School of Physics and Astronomy andCenter for Theoretical Physics Seoul National University,Seoul 151-747 (Korea, Republic of); Dipartimento di Fisica, Università di Milano-Bicocca,I-20126 Milano (Italy); INFN - Sezione di Milano-Bicocca,I-20126 Milano (Italy)
2015-07-14
We study globally supersymmetric 3d gauge theories on curved manifolds by describing the coupling of 3d topological gauge theories, with both Yang-Mills and Chern-Simons terms in the action, to background topological gravity. In our approach, the Seifert condition for manifolds supporting global supersymmetry is elegantly deduced from the BRST transformations of topological gravity. A cohomological characterization of the geometrical moduli which affect the partition function is obtained. In the Seifert context the Chern-Simons topological (framing) anomaly is BRST trivial. We compute explicitly the corresponding local Wess-Zumino functional. As an application, we obtain the dependence on the Seifert moduli of the partition function of 3d supersymmetric gauge theory on the squashed sphere by solving the anomalous topological Ward identities, in a regularization independent way and without the need of evaluating any functional determinant.
Dynamical systems on 2- and 3-manifolds
Grines, Viacheslav Z; Pochinka, Olga V
2016-01-01
This book provides an introduction to the topological classification of smooth structurally stable diffeomorphisms on closed orientable 2- and 3-manifolds.The topological classification is one of the main problems of the theory of dynamical systems and the results presented in this book are mostly for dynamical systems satisfying Smale's Axiom A. The main results on the topological classification of discrete dynamical systems are widely scattered among many papers and surveys. This book presents these results fluidly, systematically, and for the first time in one publication. Additionally, this book discusses the recent results on the topological classification of Axiom A diffeomorphisms focusing on the nontrivial effects of the dynamical systems on 2- and 3-manifolds. The classical methods and approaches which are considered to be promising for the further research are also discussed. < The reader needs to be familiar with the basic concepts of the qualitative theory of dynamical systems which are present...
Convex nonnegative matrix factorization with manifold regularization.
Hu, Wenjun; Choi, Kup-Sze; Wang, Peiliang; Jiang, Yunliang; Wang, Shitong
2015-03-01
Nonnegative Matrix Factorization (NMF) has been extensively applied in many areas, including computer vision, pattern recognition, text mining, and signal processing. However, nonnegative entries are usually required for the data matrix in NMF, which limits its application. Besides, while the basis and encoding vectors obtained by NMF can represent the original data in low dimension, the representations do not always reflect the intrinsic geometric structure embedded in the data. Motivated by manifold learning and Convex NMF (CNMF), we propose a novel matrix factorization method called Graph Regularized and Convex Nonnegative Matrix Factorization (GCNMF) by introducing a graph regularized term into CNMF. The proposed matrix factorization technique not only inherits the intrinsic low-dimensional manifold structure, but also allows the processing of mixed-sign data matrix. Clustering experiments on nonnegative and mixed-sign real-world data sets are conducted to demonstrate the effectiveness of the proposed method. Copyright © 2014 Elsevier Ltd. All rights reserved.
Symposium on Singularities, Representation of Algebras, and Vector Bundles
Trautmann, Günther
1987-01-01
It is well known that there are close relations between classes of singularities and representation theory via the McKay correspondence and between representation theory and vector bundles on projective spaces via the Bernstein-Gelfand-Gelfand construction. These relations however cannot be considered to be either completely understood or fully exploited. These proceedings document recent developments in the area. The questions and methods of representation theory have applications to singularities and to vector bundles. Representation theory itself, which had primarily developed its methods for Artinian algebras, starts to investigate algebras of higher dimension partly because of these applications. Future research in representation theory may be spurred by the classification of singularities and the highly developed theory of moduli for vector bundles. The volume contains 3 survey articles on the 3 main topics mentioned, stressing their interrelationships, as well as original research papers.
Sasakian manifolds with purely transversal Bach tensor
Ghosh, Amalendu; Sharma, Ramesh
2017-10-01
We show that a (2n + 1)-dimensional Sasakian manifold (M, g) with a purely transversal Bach tensor has constant scalar curvature ≥2 n (2 n +1 ) , equality holding if and only if (M, g) is Einstein. For dimension 3, M is locally isometric to the unit sphere S3. For dimension 5, if in addition (M, g) is complete, then it has positive Ricci curvature and is compact with finite fundamental group π1(M).
CFD simulations for engine intake manifolds
International Nuclear Information System (INIS)
Witry, A.; Zhao, A.
2002-01-01
This paper attempts to explain a procedure for using Computational Fluid Dynamics (CFD) for product development of engine intake manifolds. The paper uses the development of an intake manifold as an example of such a process. Using the commercial FLUENT solver, its standard wall functions and k-ε model, a four runner intake manifold with an average mesh size of 300, 000 hexa elements created in ICEM-CFD with a maximum skewness of 0.85 produces rapid results for quick product turn-around times. The setup used allows for compressibility and viscous heating effects to be modeled whilst ignoring wall heat transfer due to the high speeds of the air/foil mixture and low residence times. Eight consecutive models were modeled here whilst carrying out continuous enhancements. For every iteration, four different so called 'static' runs with only one runner open at any one time using a steady state assumption were calculated further assuming that only one intake valve is open at any one time. Even flow distributions between the runner are deemed to be 'dynamically' obtained once the pressure drops between the manifold's inlet and runner outlets are equalized. Furthermore, different modifications were attempted to ensure that the fluid's particle tracks show very little particle return tendencies along with excellent nonuniformity indexes at the runners outlets. Confirmation of these results were obtained from test data showing CFD pressure drop predictions to be within 4% error with 67% of any runner's pressure losses being caused in the runner itself due to the small cross sectional area(s). (author)
Fine topology and locally Minkowskian manifolds
Agrawal, Gunjan; Sinha, Soami Pyari
2018-05-01
Fine topology is one of the several well-known topologies of physical and mathematical relevance. In the present paper, it is obtained that the nonempty open sets of different dimensional Minkowski spaces with the fine topology are not homeomorphic. This leads to the introduction of a new class of manifolds. It turns out that the technique developed here is also applicable to some other topologies, namely, the s-topology, space topology, f-topology, and A-topology.
On complete manifolds supporting a weighted Sobolev type inequality
International Nuclear Information System (INIS)
Adriano, Levi; Xia Changyu
2011-01-01
Highlights: → We study manifolds supporting a weighted Sobolev or log-Sobolev inequality. → We investigate manifolds of asymptotically non-negative Ricci curvature. → The constant in the weighted Sobolev inequality on complete manifolds is studied. - Abstract: This paper studies the geometric and topological properties of complete open Riemannian manifolds which support a weighted Sobolev or log-Sobolev inequality. We show that the constant in the weighted Sobolev inequality on a complete open Riemannian manifold should be bigger than or equal to the optimal one on the Euclidean space of the same dimension and that a complete open manifold of asymptotically non-negative Ricci curvature supporting a weighted Sobolev inequality must have large volume growth. We also show that a complete manifold of non-negative Ricci curvature on which the log-Sobolev inequality holds is not very far from the Euclidean space.
Sasaki-Einstein Manifolds and Volume Minimisation
Martelli, D; Yau, S T; Martelli, Dario; Sparks, James; Yau, Shing-Tung
2006-01-01
We study a variational problem whose critical point determines the Reeb vector field for a Sasaki-Einstein manifold. This extends our previous work on Sasakian geometry by lifting the condition that the manifolds are toric. We show that the Einstein-Hilbert action, restricted to a space of Sasakian metrics on a link L in a Calabi-Yau cone M, is the volume functional, which in fact is a function on the space of Reeb vector fields. We relate this function both to the Duistermaat-Heckman formula and also to a limit of a certain equivariant index on M that counts holomorphic functions. Both formulae may be evaluated by localisation. This leads to a general formula for the volume function in terms of topological fixed point data. As a result we prove that the volume of any Sasaki-Einstein manifold, relative to that of the round sphere, is always an algebraic number. In complex dimension n=3 these results provide, via AdS/CFT, the geometric counterpart of a-maximisation in four dimensional superconformal field theo...
Manifold learning in machine vision and robotics
Bernstein, Alexander
2017-02-01
Smart algorithms are used in Machine vision and Robotics to organize or extract high-level information from the available data. Nowadays, Machine learning is an essential and ubiquitous tool to automate extraction patterns or regularities from data (images in Machine vision; camera, laser, and sonar sensors data in Robotics) in order to solve various subject-oriented tasks such as understanding and classification of images content, navigation of mobile autonomous robot in uncertain environments, robot manipulation in medical robotics and computer-assisted surgery, and other. Usually such data have high dimensionality, however, due to various dependencies between their components and constraints caused by physical reasons, all "feasible and usable data" occupy only a very small part in high dimensional "observation space" with smaller intrinsic dimensionality. Generally accepted model of such data is manifold model in accordance with which the data lie on or near an unknown manifold (surface) of lower dimensionality embedded in an ambient high dimensional observation space; real-world high-dimensional data obtained from "natural" sources meet, as a rule, this model. The use of Manifold learning technique in Machine vision and Robotics, which discovers a low-dimensional structure of high dimensional data and results in effective algorithms for solving of a large number of various subject-oriented tasks, is the content of the conference plenary speech some topics of which are in the paper.
Analysis of singularity in redundant manipulators
International Nuclear Information System (INIS)
Watanabe, Koichi
2000-03-01
In the analysis of arm positions and configurations of redundant manipulators, the singularity avoidance problems are important themes. This report presents singularity avoidance computations of a 7 DOF manipulator by using a computer code based on human-arm models. The behavior of the arm escaping from the singular point can be identified satisfactorily through the use of 3-D plotting tools. (author)
Nonplanar on-shell diagrams and leading singularities of scattering amplitudes
Energy Technology Data Exchange (ETDEWEB)
Chen, Baoyi; Cheung, Yeuk-Kwan E.; Li, Yunxuan; Xie, Ruofei; Xin, Yuan [Nanjing University, Department of Physics, Nanjing (China); Chen, Gang [Zhejiang Normal University, Department of Physics, Jinhua, Zhejiang (China); Nanjing University, Department of Physics, Nanjing (China)
2017-02-15
Bipartite on-shell diagrams are the latest tool in constructing scattering amplitudes. In this paper we prove that a Britto-Cachazo-Feng-Witten (BCFW) decomposable on-shell diagram process a rational top form if and only if the algebraic ideal comprised the geometrical constraints are shifted linearly during successive BCFW integrations. With a proper geometric interpretation of the constraints in the Grassmannian manifold, the rational top form integration contours can thus be obtained, and understood, in a straightforward way. All rational top form integrands of arbitrary higher loops leading singularities can therefore be derived recursively, as long as the corresponding on-shell diagram is BCFW decomposable. (orig.)
Fundamental solutions of singular SPDEs
International Nuclear Information System (INIS)
Selesi, Dora
2011-01-01
Highlights: → Fundamental solutions of linear SPDEs are constructed. → Wick-convolution product is introduced for the first time. → Fourier transformation maps Wick-convolution into Wick product. → Solutions of linear SPDEs are expressed via Wick-convolution with fundamental solutions. → Stochastic Helmholtz equation is solved. - Abstract: This paper deals with some models of mathematical physics, where random fluctuations are modeled by white noise or other singular Gaussian generalized processes. White noise, as the distributional derivative od Brownian motion, which is the most important case of a Levy process, is defined in the framework of Hida distribution spaces. The Fourier transformation in the framework of singular generalized stochastic processes is introduced and its applications to solving stochastic differential equations involving Wick products and singularities such as the Dirac delta distribution are presented. Explicit solutions are obtained in form of a chaos expansion in the Kondratiev white noise space, while the coefficients of the expansion are tempered distributions. Stochastic differential equations of the form P(ω, D) ◊ u(x, ω) = A(x, ω) are considered, where A is a singular generalized stochastic process and P(ω, D) is a partial differential operator with random coefficients. We introduce the Wick-convolution operator * which enables us to express the solution as u = s*A ◊ I ◊(-1) , where s denotes the fundamental solution and I is the unit random variable. In particular, the stochastic Helmholtz equation is solved, which in physical interpretation describes waves propagating with a random speed from randomly appearing point sources.
Why the Singularity Cannot Happen
Modis, Theodore
2012-01-01
The concept of a Singularity as described in Ray Kurzweil's book cannot happen for a number of reasons. One reason is that all natural growth processes that follow exponential patterns eventually reveal themselves to be following S-curves thus excluding runaway situations. The remaining growth potential from Kurzweil's ''knee'', which could be approximated as the moment when an S-curve pattern begins deviating from the corresponding exponential, is a factor of only one order of magnitude grea...
Black holes, singularities and predictability
International Nuclear Information System (INIS)
Wald, R.M.
1984-01-01
The paper favours the view that singularities may play a central role in quantum gravity. The author reviews the arguments leading to the conclusion, that in the process of black hole formation and evaporation, an initial pure state evolves to a final density matrix, thus signaling a breakdown in ordinary quantum dynamical evolution. Some related issues dealing with predictability in the dynamical evolution, are also discussed. (U.K.)
On singularities of lattice varieties
Mukherjee, Himadri
2013-01-01
Toric varieties associated with distributive lattices arise as a fibre of a flat degeneration of a Schubert variety in a minuscule. The singular locus of these varieties has been studied by various authors. In this article we prove that the number of diamonds incident on a lattice point $\\a$ in a product of chain lattices is more than or equal to the codimension of the lattice. Using this we also show that the lattice varieties associated with product of chain lattices is smooth.
Quantum propagation across cosmological singularities
Gielen, Steffen; Turok, Neil
2017-05-01
The initial singularity is the most troubling feature of the standard cosmology, which quantum effects are hoped to resolve. In this paper, we study quantum cosmology with conformal (Weyl) invariant matter. We show that it is natural to extend the scale factor to negative values, allowing a large, collapsing universe to evolve across a quantum "bounce" into an expanding universe like ours. We compute the Feynman propagator for Friedmann-Robertson-Walker backgrounds exactly, identifying curious pathologies in the case of curved (open or closed) universes. We then include anisotropies, fixing the operator ordering of the quantum Hamiltonian by imposing covariance under field redefinitions and again finding exact solutions. We show how complex classical solutions allow one to circumvent the singularity while maintaining the validity of the semiclassical approximation. The simplest isotropic universes sit on a critical boundary, beyond which there is qualitatively different behavior, with potential for instability. Additional scalars improve the theory's stability. Finally, we study the semiclassical propagation of inhomogeneous perturbations about the flat, isotropic case, at linear and nonlinear order, showing that, at least at this level, there is no particle production across the bounce. These results form the basis for a promising new approach to quantum cosmology and the resolution of the big bang singularity.
Faria, T.; Magalhaes, L. T.
The paper addresses, for retarded functional differential equations (FDEs), the computation of normal forms associated with the flow on a finite-dimensional invariant manifold tangent to invariant spaces for the infinitesimal generator of the linearized equation at a singularity. A phase space appropriate to the computation of these normal forms is introduced, and adequate nonresonance conditions for the computation of the normal forms are derived. As an application, the general situation of Bogdanov-Takens singularity and its versal unfolding for scalar retarded FDEs with nondegeneracy at second order is considered, both in the general case and in the case of differential-delay equations of the form ẋ( t) = ƒ( x( t), x( t-1)).
Singularities in Free Surface Flows
Thete, Sumeet Suresh
Free surface flows where the shape of the interface separating two or more phases or liquids are unknown apriori, are commonplace in industrial applications and nature. Distribution of drop sizes, coalescence rate of drops, and the behavior of thin liquid films are crucial to understanding and enhancing industrial practices such as ink-jet printing, spraying, separations of chemicals, and coating flows. When a contiguous mass of liquid such as a drop, filament or a film undergoes breakup to give rise to multiple masses, the topological transition is accompanied with a finite-time singularity . Such singularity also arises when two or more masses of liquid merge into each other or coalesce. Thus the dynamics close to singularity determines the fate of about-to-form drops or films and applications they are involved in, and therefore needs to be analyzed precisely. The primary goal of this thesis is to resolve and analyze the dynamics close to singularity when free surface flows experience a topological transition, using a combination of theory, experiments, and numerical simulations. The first problem under consideration focuses on the dynamics following flow shut-off in bottle filling applications that are relevant to pharmaceutical and consumer products industry, using numerical techniques based on Galerkin Finite Element Methods (GFEM). The second problem addresses the dual flow behavior of aqueous foams that are observed in oil and gas fields and estimates the relevant parameters that describe such flows through a series of experiments. The third problem aims at understanding the drop formation of Newtonian and Carreau fluids, computationally using GFEM. The drops are formed as a result of imposed flow rates or expanding bubbles similar to those of piezo actuated and thermal ink-jet nozzles. The focus of fourth problem is on the evolution of thinning threads of Newtonian fluids and suspensions towards singularity, using computations based on GFEM and experimental
Mathematical models with singularities a zoo of singular creatures
Torres, Pedro J
2015-01-01
The book aims to provide an unifying view of a variety (a 'zoo') of mathematical models with some kind of singular nonlinearity, in the sense that it becomes infinite when the state variable approaches a certain point. Up to 11 different concrete models are analyzed in separate chapters. Each chapter starts with a discussion of the basic model and its physical significance. Then the main results and typical proofs are outlined, followed by open problems. Each chapter is closed by a suitable list of references. The book may serve as a guide for researchers interested in the modelling of real world processes.
Monoids of moduli spaces of manifolds
DEFF Research Database (Denmark)
Galatius, Søren; Randal-Williams, Oscar
2010-01-01
We study categories of d–dimensional cobordisms from the perspective of Tillmann [Invent. Math. 130 (1997) 257–275] and Galatius, Madsen, Tillman and Weiss [Acta Math. 202 (2009) 195–239]. There is a category C¿ of closed smooth (d - 1)–manifolds and smooth d–dimensional cobordisms, equipped...... with generalised orientations specified by a map ¿: X ¿ BO(d). The main result of [Acta Math. 202 (2009) 195–239] is a determination of the homotopy type of the classifying space BC¿. The goal of the present paper is a systematic investigation of subcategories D¿C¿ with the property that BD¿ BC¿, the smaller...
Rational Homological Stability for Automorphisms of Manifolds
DEFF Research Database (Denmark)
Grey, Matthias
In this thesis we prove rational homological stability for the classifying spaces of the homotopy automorphisms and block di↵eomorphisms of iterated connected sums of products of spheres of a certain connectivity.The results in particular apply to the manifolds Npg,q = (#g(Sp x Sq)) - int...... with coefficients in the homology of the universal covering, which is studied using rational homology theory. The result for the block di↵eomorphisms is deduced from the homological stability for the homotopy automorphisms upon using Surgery theory. Themain theorems of this thesis extend the homological stability...
Exact Polynomial Eigenmodes for Homogeneous Spherical 3-Manifolds
Weeks, Jeffrey R.
2005-01-01
Observational data hints at a finite universe, with spherical manifolds such as the Poincare dodecahedral space tentatively providing the best fit. Simulating the physics of a model universe requires knowing the eigenmodes of the Laplace operator on the space. The present article provides explicit polynomial eigenmodes for all globally homogeneous 3-manifolds: the Poincare dodecahedral space S3/I*, the binary octahedral space S3/O*, the binary tetrahedral space S3/T*, the prism manifolds S3/D...
Strong Proximities on Smooth Manifolds and Vorono\\" i Diagrams
Peters, J. F.; Guadagni, C.
2015-01-01
This article introduces strongly near smooth manifolds. The main results are (i) second countability of the strongly hit and far-miss topology on a family $\\mathcal{B}$ of subsets on the Lodato proximity space of regular open sets to which singletons are added, (ii) manifold strong proximity, (iii) strong proximity of charts in manifold atlases implies that the charts have nonempty intersection. The application of these results is given in terms of the nearness of atlases and charts of proxim...
Some problems of dynamical systems on three dimensional manifolds
International Nuclear Information System (INIS)
Dong Zhenxie.
1985-08-01
It is important to study the dynamical systems on 3-dimensional manifolds, its importance is showing up in its close relation with our life. Because of the complication of topological structure of Dynamical systems on 3-dimensional manifolds, generally speaking, the search for 3-dynamical systems is not easier than 2-dynamical systems. This paper is a summary of the partial result of dynamical systems on 3-dimensional manifolds. (author)
Total Generalized Variation for Manifold-valued Data
Bredies, K.; Holler, M.; Storath, M.; Weinmann, A.
2017-01-01
In this paper we introduce the notion of second-order total generalized variation (TGV) regularization for manifold-valued data. We provide an axiomatic approach to formalize reasonable generalizations of TGV to the manifold setting and present two possible concrete instances that fulfill the proposed axioms. We provide well-posedness results and present algorithms for a numerical realization of these generalizations to the manifold setup. Further, we provide experimental results for syntheti...
CT Image Reconstruction in a Low Dimensional Manifold
Cong, Wenxiang; Wang, Ge; Yang, Qingsong; Hsieh, Jiang; Li, Jia; Lai, Rongjie
2017-01-01
Regularization methods are commonly used in X-ray CT image reconstruction. Different regularization methods reflect the characterization of different prior knowledge of images. In a recent work, a new regularization method called a low-dimensional manifold model (LDMM) is investigated to characterize the low-dimensional patch manifold structure of natural images, where the manifold dimensionality characterizes structural information of an image. In this paper, we propose a CT image reconstruc...
Czech Academy of Sciences Publication Activity Database
Krepl, Ondřej; Klusák, Jan
2017-01-01
Roč. 90, AUG (2017), s. 85-99 ISSN 0167-8442 R&D Projects: GA MŠk(CZ) LQ1601; GA ČR(CZ) GA16-18702S Institutional support: RVO:68081723 Keywords : General singular stress concentrator * Generalized fracture mechanics * Muskhelishvili plane elasticity * Sharp material inclusion * Singular and non-singular stress terms Subject RIV: JL - Materials Fatigue, Friction Mechanics OBOR OECD: Audio engineering, reliability analysis Impact factor: 2.659, year: 2016
On the trace-manifold generated by the deformations of a body-manifold
Directory of Open Access Journals (Sweden)
Boja Nicolae
2003-01-01
Full Text Available In this paper, concerned to the study of continuous deformations of material media using some tools of modem differential geometry, a moving frame of Frenet type along the orbits of an one-parameter group acting on a so-called "trace-manifold", M, associated to the deformations, is constructed. The manifold M is defined as an infinite union of non-disjoint compact manifolds, generated by the consecutive positions in the Euclidean affine 3-space of a body-manifold under deformations in a closed time interval. We put in evidence a skew-symmetric band tensor of second order, ω, which describes the deformation in a small neighborhood of any point along the orbits. The non-null components ωi,i+i, (i =1,2, of ω are assimilated as like curvatures at each point of an orbit in the planes generated by the pairs of vectors (ĕi,ĕi+i of a moving frame in M associated to the orbit in a similar way as the Frenet's frame is. Also a formula for the energy of the orbits is given and its relationship with some stiffness matrices is established.
LCD OF AIR INTAKE MANIFOLDS PHASE 2: FORD F250 AIR INTAKE MANIFOLD
The life cycle design methodology was applied to the design analysis of three alternatives for the lower plehum of the air intake manifold for us with a 5.4L F-250 truck engine: a sand cast aluminum, a lost core molded nylon composite, and a vibration welded nylon composite. The ...
On important precursor of singular optics (tutorial)
Polyanskii, Peter V.; Felde, Christina V.; Bogatyryova, Halina V.; Konovchuk, Alexey V.
2018-01-01
The rise of singular optics is usually associated with the seminal paper by J. F. Nye and M. V. Berry [Proc. R. Soc. Lond. A, 336, 165-189 (1974)]. Intense development of this area of modern photonics has started since the early eighties of the XX century due to invention of the interfrence technique for detection and diagnostics of phase singularities, such as optical vortices in complex speckle-structured light fields. The next powerful incentive for formation of singular optics into separate area of the science on light was connectected with discovering of very practical technique for creation of singular optical beams of various kinds on the base of computer-generated holograms. In the eghties and ninetieth of the XX century, singular optics evolved, almost entirely, under the approximation of complete coherency of light field. Only at the threshold of the XXI century, it has been comprehended that the singular-optics approaches can be fruitfully expanded onto partially spatially coherent, partially polarized and polychromatic light fields supporting singularities of new kinds, that has been resulted in establishing of correlation singular optics. Here we show that correlation singular optics has much deeper roots, ascending to "pre-singular" and even pre-laser epoch and associated with the concept of partial coherence and polarization. It is remarcable that correlation singular optics in its present interpretation has forestalled the standard coherent singular optics. This paper is timed to the sixtieth anniversary of the most profound precursor of modern correlation singular optics [J. Opt. Soc. Am., 47, 895-902 (1957)].
Variable area manifolds for ring mirror heat exchangers
Eng, Albert; Senterfitt, Donald R.
1988-05-01
A laser ring mirror assembly is disclosed which supports and cools an annular ring mirror of a high powered laser with a cooling manifold which has a coolant flow design which is intended to reduce thermal distortions of the ring mirror by minimizing azimuthal variations in temperature around its circumference. The cooling manifold has complementary pairs of cooling passages each of which conduct coolant in opposite flow directions. The manifold also houses adjusters which vary the depth between the annular ring mirror and each cooling, and which vary the flow area of the cooling passage to produce a control over the cooling characteristics of the cooling manifold.
Totally Contact Umbilical Lightlike Hypersurfaces of Indefinite -Manifolds
Directory of Open Access Journals (Sweden)
Rachna Rani
2013-01-01
Full Text Available We study totally contact umbilical lightlike hypersurfaces of indefinite -manifolds and prove the nonexistence of totally contact umbilical lightlike hypersurface in indefinite -space form.
Directory of Open Access Journals (Sweden)
Zena M Hira
Full Text Available Microarray databases are a large source of genetic data, which, upon proper analysis, could enhance our understanding of biology and medicine. Many microarray experiments have been designed to investigate the genetic mechanisms of cancer, and analytical approaches have been applied in order to classify different types of cancer or distinguish between cancerous and non-cancerous tissue. However, microarrays are high-dimensional datasets with high levels of noise and this causes problems when using machine learning methods. A popular approach to this problem is to search for a set of features that will simplify the structure and to some degree remove the noise from the data. The most widely used approach to feature extraction is principal component analysis (PCA which assumes a multivariate Gaussian model of the data. More recently, non-linear methods have been investigated. Among these, manifold learning algorithms, for example Isomap, aim to project the data from a higher dimensional space onto a lower dimension one. We have proposed a priori manifold learning for finding a manifold in which a representative set of microarray data is fused with relevant data taken from the KEGG pathway database. Once the manifold has been constructed the raw microarray data is projected onto it and clustering and classification can take place. In contrast to earlier fusion based methods, the prior knowledge from the KEGG databases is not used in, and does not bias the classification process--it merely acts as an aid to find the best space in which to search the data. In our experiments we have found that using our new manifold method gives better classification results than using either PCA or conventional Isomap.
Efficient orbit integration by manifold correction methods.
Fukushima, Toshio
2005-12-01
Triggered by a desire to investigate, numerically, the planetary precession through a long-term numerical integration of the solar system, we developed a new formulation of numerical integration of orbital motion named manifold correct on methods. The main trick is to rigorously retain the consistency of physical relations, such as the orbital energy, the orbital angular momentum, or the Laplace integral, of a binary subsystem. This maintenance is done by applying a correction to the integrated variables at each integration step. Typical methods of correction are certain geometric transformations, such as spatial scaling and spatial rotation, which are commonly used in the comparison of reference frames, or mathematically reasonable operations, such as modularization of angle variables into the standard domain [-pi, pi). The form of the manifold correction methods finally evolved are the orbital longitude methods, which enable us to conduct an extremely precise integration of orbital motions. In unperturbed orbits, the integration errors are suppressed at the machine epsilon level for an indefinitely long period. In perturbed cases, on the other hand, the errors initially grow in proportion to the square root of time and then increase more rapidly, the onset of which depends on the type and magnitude of the perturbations. This feature is also realized for highly eccentric orbits by applying the same idea as used in KS-regularization. In particular, the introduction of time elements greatly enhances the performance of numerical integration of KS-regularized orbits, whether the scaling is applied or not.
Manifold-Based Visual Object Counting.
Wang, Yi; Zou, Yuexian; Wang, Wenwu
2018-07-01
Visual object counting (VOC) is an emerging area in computer vision which aims to estimate the number of objects of interest in a given image or video. Recently, object density based estimation method is shown to be promising for object counting as well as rough instance localization. However, the performance of this method tends to degrade when dealing with new objects and scenes. To address this limitation, we propose a manifold-based method for visual object counting (M-VOC), based on the manifold assumption that similar image patches share similar object densities. Firstly, the local geometry of a given image patch is represented linearly by its neighbors using a predefined patch training set, and the object density of this given image patch is reconstructed by preserving the local geometry using locally linear embedding. To improve the characterization of local geometry, additional constraints such as sparsity and non-negativity are also considered via regularization, nonlinear mapping, and kernel trick. Compared with the state-of-the-art VOC methods, our proposed M-VOC methods achieve competitive performance on seven benchmark datasets. Experiments verify that the proposed M-VOC methods have several favorable properties, such as robustness to the variation in the size of training dataset and image resolution, as often encountered in real-world VOC applications.
Lagrangian descriptors of driven chemical reaction manifolds.
Craven, Galen T; Junginger, Andrej; Hernandez, Rigoberto
2017-08-01
The persistence of a transition state structure in systems driven by time-dependent environments allows the application of modern reaction rate theories to solution-phase and nonequilibrium chemical reactions. However, identifying this structure is problematic in driven systems and has been limited by theories built on series expansion about a saddle point. Recently, it has been shown that to obtain formally exact rates for reactions in thermal environments, a transition state trajectory must be constructed. Here, using optimized Lagrangian descriptors [G. T. Craven and R. Hernandez, Phys. Rev. Lett. 115, 148301 (2015)PRLTAO0031-900710.1103/PhysRevLett.115.148301], we obtain this so-called distinguished trajectory and the associated moving reaction manifolds on model energy surfaces subject to various driving and dissipative conditions. In particular, we demonstrate that this is exact for harmonic barriers in one dimension and this verification gives impetus to the application of Lagrangian descriptor-based methods in diverse classes of chemical reactions. The development of these objects is paramount in the theory of reaction dynamics as the transition state structure and its underlying network of manifolds directly dictate reactivity and selectivity.
Symmetry generators in singular theories
International Nuclear Information System (INIS)
Lavrov, P.M.; Tyutin, I.V.
1989-01-01
It is proved that in the singular nondegenerate theories any symmetry of the lagrangian under non-point transformations of lagrangian variables with the open (in the general case) algebra in the hamiltonian approach generates corresponding transformations of canonical variables the generator of which is the Noether charge with respect to the Dirac brackets. On the surface of all constraints these transformations leave the hamiltonian invariant and the algebra of the Noether charges is closed. As a consequence it is shown that the nilpotent BRST charge operator always exists in gauge theories of the general form (if possible anomalies are not taken into account)
Integral manifolding structure for fuel cell core having parallel gas flow
Herceg, Joseph E.
1984-01-01
Disclosed herein are manifolding means for directing the fuel and oxidant gases to parallel flow passageways in a fuel cell core. Each core passageway is defined by electrolyte and interconnect walls. Each electrolyte and interconnect wall consists respectively of anode and cathode materials layered on the opposite sides of electrolyte material, or on the opposite sides of interconnect material. A core wall projects beyond the open ends of the defined core passageways and is disposed approximately midway between and parallel to the adjacent overlaying and underlying interconnect walls to define manifold chambers therebetween on opposite sides of the wall. Each electrolyte wall defining the flow passageways is shaped to blend into and be connected to this wall in order to redirect the corresponding fuel and oxidant passageways to the respective manifold chambers either above or below this intermediate wall. Inlet and outlet connections are made to these separate manifold chambers respectively, for carrying the fuel and oxidant gases to the core, and for carrying their reaction products away from the core.
Space-by-time manifold representation of dynamic facial expressions for emotion categorization
Delis, Ioannis; Chen, Chaona; Jack, Rachael E.; Garrod, Oliver G. B.; Panzeri, Stefano; Schyns, Philippe G.
2016-01-01
Visual categorization is the brain computation that reduces high-dimensional information in the visual environment into a smaller set of meaningful categories. An important problem in visual neuroscience is to identify the visual information that the brain must represent and then use to categorize visual inputs. Here we introduce a new mathematical formalism—termed space-by-time manifold decomposition—that describes this information as a low-dimensional manifold separable in space and time. We use this decomposition to characterize the representations used by observers to categorize the six classic facial expressions of emotion (happy, surprise, fear, disgust, anger, and sad). By means of a Generative Face Grammar, we presented random dynamic facial movements on each experimental trial and used subjective human perception to identify the facial movements that correlate with each emotion category. When the random movements projected onto the categorization manifold region corresponding to one of the emotion categories, observers categorized the stimulus accordingly; otherwise they selected “other.” Using this information, we determined both the Action Unit and temporal components whose linear combinations lead to reliable categorization of each emotion. In a validation experiment, we confirmed the psychological validity of the resulting space-by-time manifold representation. Finally, we demonstrated the importance of temporal sequencing for accurate emotion categorization and identified the temporal dynamics of Action Unit components that cause typical confusions between specific emotions (e.g., fear and surprise) as well as those resolving these confusions. PMID:27305521
Topological resolution of gauge theory singularities
Saracco, Fabio; Tomasiello, Alessandro; Torroba, Gonzalo
2013-08-01
Some gauge theories with Coulomb branches exhibit singularities in perturbation theory, which are usually resolved by nonperturbative physics. In string theory this corresponds to the resolution of timelike singularities near the core of orientifold planes by effects from F or M theory. We propose a new mechanism for resolving Coulomb branch singularities in three-dimensional gauge theories, based on Chern-Simons interactions. This is illustrated in a supersymmetric SU(2) Yang-Mills-Chern-Simons theory. We calculate the one-loop corrections to the Coulomb branch of this theory and find a result that interpolates smoothly between the high-energy metric (that would exhibit the singularity) and a regular singularity-free low-energy result. We suggest possible applications to singularity resolution in string theory and speculate a relationship to a similar phenomenon for the orientifold six-plane in massive IIA supergravity.
Topological resolution of gauge theory singularities
Energy Technology Data Exchange (ETDEWEB)
Saracco, Fabio; Tomasiello, Alessandro; Torroba, Gonzalo
2013-08-21
Some gauge theories with Coulomb branches exhibit singularities in perturbation theory, which are usually resolved by nonperturbative physics. In string theory this corresponds to the resolution of timelike singularities near the core of orientifold planes by effects from F or M theory. We propose a new mechanism for resolving Coulomb branch singularities in three-dimensional gauge theories, based on Chern-Simons interactions. This is illustrated in a supersymmetric S U ( 2 ) Yang-Mills-Chern-Simons theory. We calculate the one-loop corrections to the Coulomb branch of this theory and find a result that interpolates smoothly between the high-energy metric (that would exhibit the singularity) and a regular singularity-free low-energy result. We suggest possible applications to singularity resolution in string theory and speculate a relationship to a similar phenomenon for the orientifold six-plane in massive IIA supergravity.
Singularities of Type-Q ABS Equations
Directory of Open Access Journals (Sweden)
James Atkinson
2011-07-01
Full Text Available The type-Q equations lie on the top level of the hierarchy introduced by Adler, Bobenko and Suris (ABS in their classification of discrete counterparts of KdV-type integrable partial differential equations. We ask what singularities are possible in the solutions of these equations, and examine the relationship between the singularities and the principal integrability feature of multidimensional consistency. These questions are considered in the global setting and therefore extend previous considerations of singularities which have been local. What emerges are some simple geometric criteria that determine the allowed singularities, and the interesting discovery that generically the presence of singularities leads to a breakdown in the global consistency of such systems despite their local consistency property. This failure to be globally consistent is quantified by introducing a natural notion of monodromy for isolated singularities.
The dominant balance at cosmological singularities
International Nuclear Information System (INIS)
Cotsakis, Spiros; Barrow, John D
2007-01-01
We define the notion of a finite-time singularity of a vector field and then discuss a technique suitable for the asymptotic analysis of vector fields and their integral curves in the neighborhood of such a singularity. Having in mind the application of this method to cosmology, we also provide an analysis of the time singularities of an isotropic universe filled with a perfect fluid in general relativity
Exact solutions and singularities in string theory
International Nuclear Information System (INIS)
Horowitz, G.T.; Tseytlin, A.A.
1994-01-01
We construct two new classes of exact solutions to string theory which are not of the standard plane wave of gauged WZW type. Many of these solutions have curvature singularities. The first class includes the fundamental string solution, for which the string coupling vanishes near the singularity. This suggests that the singularity may not be removed by quantum corrections. The second class consists of hybrids of plane wave and gauged WZW solutions. We discuss a four-dimensional example in detail
Dressing up a Kerr naked singularity
Energy Technology Data Exchange (ETDEWEB)
Calvani, M [Padua Univ. (Italy). Ist. di Astronomia; Nobili, L [Padua Univ. (Italy). Ist. di Fisica
1979-06-11
The evolution of a naked singularity surrounded by an accreting disk of matter is studied; two kinds of disks are considered: the standard thin-disk model and the thick barytropic model, for several initial conditions. It is shown that any Kerr naked singularity slows down in a finite time to a maximal Kerr black hole. The final mass, the luminosity and the time of evolution of the singularity are evaluated.
Type IIA orientifolds on SU(2)-structure manifolds
Energy Technology Data Exchange (ETDEWEB)
Danckaert, Thomas
2010-11-15
We investigate the possible supersymmetry-preserving orientifold projections of type IIA string theory on a six-dimensional background with SU(2)-structure. We find two categories of projections which preserve half of the low-energy supersymmetry, reducing the effective theory from an N=4 supergravity theory, to an N=2 supergravity. For these two cases, we impose the projection on the low-energy spectrum and reduce the effective N=4 supergravity action accordingly. We can identify the resulting gauged N=2 supergravity theory and bring the action into canonical form. We compute the scalar moduli spaces and characterize the gauged symmetries in terms of the geometry of these moduli spaces. Due to their origin in N=4 supergravity, which is a highly constrained theory, the moduli spaces are of a very simple form. We find that, for suitable background manifolds, isometries in all scalar sectors can become gauged. The obtained gaugings share many features with those of N=2 supergravities obtained previously from other G-structure compactifications. (orig.)
Naked singularity, firewall, and Hawking radiation.
Zhang, Hongsheng
2017-06-21
Spacetime singularity has always been of interest since the proof of the Penrose-Hawking singularity theorem. Naked singularity naturally emerges from reasonable initial conditions in the collapsing process. A recent interesting approach in black hole information problem implies that we need a firewall to break the surplus entanglements among the Hawking photons. Classically, the firewall becomes a naked singularity. We find some vacuum analytical solutions in R n -gravity of the firewall-type and use these solutions as concrete models to study the naked singularities. By using standard quantum theory, we investigate the Hawking radiation emitted from the black holes with naked singularities. Here we show that the singularity itself does not destroy information. A unitary quantum theory works well around a firewall-type singularity. We discuss the validity of our result in general relativity. Further our result demonstrates that the temperature of the Hawking radiation still can be expressed in the form of the surface gravity divided by 2π. This indicates that a naked singularity may not compromise the Hakwing evaporation process.
Spacetime averaging of exotic singularity universes
International Nuclear Information System (INIS)
Dabrowski, Mariusz P.
2011-01-01
Taking a spacetime average as a measure of the strength of singularities we show that big-rips (type I) are stronger than big-bangs. The former have infinite spacetime averages while the latter have them equal to zero. The sudden future singularities (type II) and w-singularities (type V) have finite spacetime averages. The finite scale factor (type III) singularities for some values of the parameters may have an infinite average and in that sense they may be considered stronger than big-bangs.
Coupled singular and non singular thermoelastic system and double lapalce decomposition methods
Hassan Gadain; Hassan Gadain
2016-01-01
In this paper, the double Laplace decomposition methods are applied to solve the non singular and singular one dimensional thermo-elasticity coupled system and. The technique is described and illustrated with some examples
Singular value decomposition methods for wave propagation analysis
Czech Academy of Sciences Publication Activity Database
Santolík, Ondřej; Parrot, M.; Lefeuvre, F.
2003-01-01
Roč. 38, č. 1 (2003), s. 10-1-10-13 ISSN 0048-6604 R&D Projects: GA ČR GA205/01/1064 Grant - others:Barrande(CZ) 98039/98055 Institutional research plan: CEZ:AV0Z3042911; CEZ:MSM 113200004 Keywords : wave propagation * singular value decomposition Subject RIV: DG - Athmosphere Sciences, Meteorology Impact factor: 0.832, year: 2003
Fatigue crack shape prediction based on vertex singularity
Czech Academy of Sciences Publication Activity Database
Hutař, Pavel; Náhlík, Luboš
2008-01-01
Roč. 2, č. 1 (2008), s. 45-52 ISSN 1802-680X R&D Projects: GA ČR GA101/08/1623; GA ČR GP106/06/P239 Institutional research plan: CEZ:AV0Z20410507 Keywords : 3D vertex singularity * crack shape * fatigue crack propagation Subject RIV: JL - Materials Fatigue, Friction Mechanics
Solving singular convolution equations using the inverse fast Fourier transform
Czech Academy of Sciences Publication Activity Database
Krajník, E.; Montesinos, V.; Zizler, P.; Zizler, Václav
2012-01-01
Roč. 57, č. 5 (2012), s. 543-550 ISSN 0862-7940 R&D Projects: GA AV ČR IAA100190901 Institutional research plan: CEZ:AV0Z10190503 Keywords : singular convolution equations * fast Fourier transform * tempered distribution Subject RIV: BA - General Mathematics Impact factor: 0.222, year: 2012 http://www.springerlink.com/content/m8437t3563214048/
Geomechanical time series and its singularity spectrum analysis
Czech Academy of Sciences Publication Activity Database
Lyubushin, Alexei A.; Kaláb, Zdeněk; Lednická, Markéta
2012-01-01
Roč. 47, č. 1 (2012), s. 69-77 ISSN 1217-8977 R&D Projects: GA ČR GA105/09/0089 Institutional research plan: CEZ:AV0Z30860518 Keywords : geomechanical time series * singularity spectrum * time series segmentation * laser distance meter Subject RIV: DC - Siesmology, Volcanology, Earth Structure Impact factor: 0.347, year: 2012 http://www.akademiai.com/content/88v4027758382225/fulltext.pdf
Patterns and singular features of extreme fluctuational paths of a periodically driven system
International Nuclear Information System (INIS)
Chen, Zhen; Liu, Xianbin
2016-01-01
Large fluctuations of an overdamped periodically driven oscillating system are investigated theoretically and numerically in the limit of weak noise. Optimal paths fluctuating to certain point are given by statistical analysis using the concept of prehistory probability distribution. The validity of statistical results is verified by solutions of boundary value problem. Optimal paths are found to change topologically when terminating points lie at opposite side of a switching line. Patterns of extreme paths are plotted through a proper parameterization of Lagrangian manifold having complicated structures. Several extreme paths to the same point are obtained by multiple solutions of boundary value solutions. Actions along various extreme paths are calculated and associated analysis is performed in relation to the singular features of the patterns. - Highlights: • Both extreme and optimal paths are obtained by various methods. • Boundary value problems are solved to ensure the validity of statistical results. • Topological structure of Lagrangian manifold is considered. • Singularities of the pattern of extreme paths are studied.
Manifold corrections on spinning compact binaries
International Nuclear Information System (INIS)
Zhong Shuangying; Wu Xin
2010-01-01
This paper deals mainly with a discussion of three new manifold correction methods and three existing ones, which can numerically preserve or correct all integrals in the conservative post-Newtonian Hamiltonian formulation of spinning compact binaries. Two of them are listed here. One is a new momentum-position scaling scheme for complete consistency of both the total energy and the magnitude of the total angular momentum, and the other is the Nacozy's approach with least-squares correction of the four integrals including the total energy and the total angular momentum vector. The post-Newtonian contributions, the spin effects, and the classification of orbits play an important role in the effectiveness of these six manifold corrections. They are all nearly equivalent to correct the integrals at the level of the machine epsilon for the pure Kepler problem. Once the third-order post-Newtonian contributions are added to the pure orbital part, three of these corrections have only minor effects on controlling the errors of these integrals. When the spin effects are also included, the effectiveness of the Nacozy's approach becomes further weakened, and even gets useless for the chaotic case. In all cases tested, the new momentum-position scaling scheme always shows the optimal performance. It requires a little but not much expensive additional computational cost when the spin effects exist and several time-saving techniques are used. As an interesting case, the efficiency of the correction to chaotic eccentric orbits is generally better than one to quasicircular regular orbits. Besides this, the corrected fast Lyapunov indicators and Lyapunov exponents of chaotic eccentric orbits are large as compared with the uncorrected counterparts. The amplification is a true expression of the original dynamical behavior. With the aid of both the manifold correction added to a certain low-order integration algorithm as a fast and high-precision device and the fast Lyapunov
Czech Academy of Sciences Publication Activity Database
Krisztin, T.; Rezunenko, Oleksandr
2016-01-01
Roč. 260, č. 5 (2016), s. 4454-4472 ISSN 0022-0396 R&D Projects: GA ČR GAP103/12/2431 Institutional support: RVO:67985556 Keywords : Parabolic partial differential equations * State dependent delay * Solution manifold Subject RIV: BC - Control Systems Theory Impact factor: 1.988, year: 2016 http://library.utia.cas.cz/separaty/2016/AS/rezunenko-0457879.pdf
Upper bound theorem for odd-dimensional flag triangulations of manifolds
Czech Academy of Sciences Publication Activity Database
Adamaszek, M.; Hladký, Jan
2016-01-01
Roč. 62, č. 3 (2016), s. 909-928 ISSN 0025-5793 EU Projects: European Commission(XE) 628974 - PAECIDM Institutional support: RVO:67985840 Keywords : f-vector * manifold * extremal graph theory Subject RIV: BA - General Mathematics Impact factor: 0.667, year: 2016 http:// journals .cambridge.org/action/displayAbstract?fromPage=online&aid=10346369&fulltextType=RA&fileId=S0025579316000115
The quantum equivariant cohomology of toric manifolds through mirror symmetry
Baptista, J. M.
2008-01-01
Using mirror symmetry as described by Hori and Vafa, we compute the quantum equivariant cohomology ring of toric manifolds. This ring arises naturally in topological gauged sigma-models and is related to the Hamiltonian Gromov-Witten invariants of the target manifold.
Conformal Vector Fields on Doubly Warped Product Manifolds and Applications
Directory of Open Access Journals (Sweden)
H. K. El-Sayied
2016-01-01
Full Text Available This article aimed to study and explore conformal vector fields on doubly warped product manifolds as well as on doubly warped spacetime. Then we derive sufficient conditions for matter and Ricci collineations on doubly warped product manifolds. A special attention is paid to concurrent vector fields. Finally, Ricci solitons on doubly warped product spacetime admitting conformal vector fields are considered.
The quantum equivariant cohomology of toric manifolds through mirror symmetry
Baptista, J.M.
2009-01-01
Using mirror symmetry as described by Hori and Vafa, we compute the quantum equivariant cohomology ring of toric manifolds. This ring arises naturally in topological gauged sigma-models and is related to the Hamiltonian Gromov-Witten invariants of the target manifold.
Variable volume combustor with nested fuel manifold system
McConnaughhay, Johnie Franklin; Keener, Christopher Paul; Johnson, Thomas Edward; Ostebee, Heath Michael
2016-09-13
The present application provides a combustor for use with a gas turbine engine. The combustor may include a number of micro-mixer fuel nozzles, a fuel manifold system in communication with the micro-mixer fuel nozzles to deliver a flow of fuel thereto, and a linear actuator to maneuver the micro-mixer fuel nozzles and the fuel manifold system.
Generalized Transversal Lightlike Submanifolds of Indefinite Sasakian Manifolds
Yaning Wang; Ximin Liu
2012-01-01
We introduce and study generalized transversal lightlike submanifold of indefinite Sasakian manifolds which includes radical and transversal lightlike submanifolds of indefinite Sasakian manifolds as its trivial subcases. A characteristic theorem and a classification theorem of generalized transversal lightlike submanifolds are obtained.
Papapetrou's naked singularity is a strong curvature singularity
Energy Technology Data Exchange (ETDEWEB)
Hollier, G.P.
1986-11-01
Following Papapetrou (1985, a random walk in General Relativity ed. J. Krishna-Rao (New Delhi: Wiley Eastern)), a spacetime with a naked singularity is analysed. This singularity is shown to be a strong curvature singularity and thus a counterexample to a censorship conjecture.
Geometric solitons of Hamiltonian flows on manifolds
Energy Technology Data Exchange (ETDEWEB)
Song, Chong, E-mail: songchong@xmu.edu.cn [School of Mathematical Sciences, Xiamen University, Xiamen 361005 (China); Sun, Xiaowei, E-mail: sunxw@cufe.edu.cn [School of Applied Mathematics, Central University of Finance and Economics, Beijing 100081 (China); Wang, Youde, E-mail: wyd@math.ac.cn [Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190 (China)
2013-12-15
It is well-known that the LIE (Locally Induction Equation) admit soliton-type solutions and same soliton solutions arise from different and apparently irrelevant physical models. By comparing the solitons of LIE and Killing magnetic geodesics, we observe that these solitons are essentially decided by two families of isometries of the domain and the target space, respectively. With this insight, we propose the new concept of geometric solitons of Hamiltonian flows on manifolds, such as geometric Schrödinger flows and KdV flows for maps. Moreover, we give several examples of geometric solitons of the Schrödinger flow and geometric KdV flow, including magnetic curves as geometric Schrödinger solitons and explicit geometric KdV solitons on surfaces of revolution.
Contact manifolds, Lagrangian Grassmannians and PDEs
Directory of Open Access Journals (Sweden)
Eshkobilov Olimjon
2018-02-01
Full Text Available In this paper we review a geometric approach to PDEs. We mainly focus on scalar PDEs in n independent variables and one dependent variable of order one and two, by insisting on the underlying (2n + 1-dimensional contact manifold and the so-called Lagrangian Grassmannian bundle over the latter. This work is based on a Ph.D course given by two of the authors (G. M. and G. M.. As such, it was mainly designed as a quick introduction to the subject for graduate students. But also the more demanding reader will be gratified, thanks to the frequent references to current research topics and glimpses of higher-level mathematics, found mostly in the last sections.
Evolutionary global optimization, manifolds and applications
Aguiar e Oliveira Junior, Hime
2016-01-01
This book presents powerful techniques for solving global optimization problems on manifolds by means of evolutionary algorithms, and shows in practice how these techniques can be applied to solve real-world problems. It describes recent findings and well-known key facts in general and differential topology, revisiting them all in the context of application to current optimization problems. Special emphasis is put on game theory problems. Here, these problems are reformulated as constrained global optimization tasks and solved with the help of Fuzzy ASA. In addition, more abstract examples, including minimizations of well-known functions, are also included. Although the Fuzzy ASA approach has been chosen as the main optimizing paradigm, the book suggests that other metaheuristic methods could be used as well. Some of them are introduced, together with their advantages and disadvantages. Readers should possess some knowledge of linear algebra, and of basic concepts of numerical analysis and probability theory....
Manifold Adaptive Label Propagation for Face Clustering.
Pei, Xiaobing; Lyu, Zehua; Chen, Changqing; Chen, Chuanbo
2015-08-01
In this paper, a novel label propagation (LP) method is presented, called the manifold adaptive label propagation (MALP) method, which is to extend original LP by integrating sparse representation constraint into regularization framework of LP method. Similar to most LP, first of all, MALP also finds graph edges from given data and gives weights to the graph edges. Our goal is to find graph weights matrix adaptively. The key advantage of our approach is that MALP simultaneously finds graph weights matrix and predicts the label of unlabeled data. This paper also derives efficient algorithm to solve the proposed problem. Extensions of our MALP in kernel space and robust version are presented. The proposed method has been applied to the problem of semi-supervised face clustering using the well-known ORL, Yale, extended YaleB, and PIE datasets. Our experimental evaluations show the effectiveness of our method.
Model Transport: Towards Scalable Transfer Learning on Manifolds
DEFF Research Database (Denmark)
Freifeld, Oren; Hauberg, Søren; Black, Michael J.
2014-01-01
We consider the intersection of two research fields: transfer learning and statistics on manifolds. In particular, we consider, for manifold-valued data, transfer learning of tangent-space models such as Gaussians distributions, PCA, regression, or classifiers. Though one would hope to simply use...... ordinary Rn-transfer learning ideas, the manifold structure prevents it. We overcome this by basing our method on inner-product-preserving parallel transport, a well-known tool widely used in other problems of statistics on manifolds in computer vision. At first, this straightforward idea seems to suffer...... “commutes” with learning. Consequently, our compact framework, applicable to a large class of manifolds, is not restricted by the size of either the training or test sets. We demonstrate the approach by transferring PCA and logistic-regression models of real-world data involving 3D shapes and image...
Quaternionic Kaehler and hyperkaehler manifolds with torsion and twistor spaces
International Nuclear Information System (INIS)
Ivanov, Stefan; Minchev, Ivan
2001-12-01
The target space of a (4,0) supersymmetric two-dimensional sigma model with Wess-Zumino term has a connection with totally skew-symmetric torsion and holonomy contained in Sp(n)Sp(l) (resp. Sp(n)), QKT (resp. HKT)-spaces. We study the geometry of QKT, HKT manifold and their twistor spaces. We show that the Swann bundle of a QKT manifold admits a HKT structure with special symmetry if and only if the twistor space of the QKT manifold admits an almost hermitian structure with totally skew-symmetric Nijenhuis tensor, thus connecting two structures arising from quantum field theories and supersymmetric sigma models with Wess- Zumino term. We discovered that a HKT manifold has always co-closed Lee form. Applying this property to compact HKT manifold we get information about the plurigenera. (author)
Convex functions and optimization methods on Riemannian manifolds
Udrişte, Constantin
1994-01-01
This unique monograph discusses the interaction between Riemannian geometry, convex programming, numerical analysis, dynamical systems and mathematical modelling. The book is the first account of the development of this subject as it emerged at the beginning of the 'seventies. A unified theory of convexity of functions, dynamical systems and optimization methods on Riemannian manifolds is also presented. Topics covered include geodesics and completeness of Riemannian manifolds, variations of the p-energy of a curve and Jacobi fields, convex programs on Riemannian manifolds, geometrical constructions of convex functions, flows and energies, applications of convexity, descent algorithms on Riemannian manifolds, TC and TP programs for calculations and plots, all allowing the user to explore and experiment interactively with real life problems in the language of Riemannian geometry. An appendix is devoted to convexity and completeness in Finsler manifolds. For students and researchers in such diverse fields as pu...
Investigating performance of microchannel evaporators with different manifold structures
Energy Technology Data Exchange (ETDEWEB)
Shi, Junye; Qu, Xiaohua; Qi, Zhaogang; Chen, Jiangping [Institute of Refrigeration and Cryogenics, Shanghai Jiao Tong University, No. 800, Dongchuan Rd, Shanghai 200240 (China)
2011-01-15
In this paper, the performances of microchannel evaporators with different manifold structures are experimentally investigated. Eight evaporator samples with 7 different designs of the I/O manifold and 5 different designs of the return manifold are made for this study. The performances of the evaporator samples are tested on a psychometric calorimeter test bench with the refrigerant 134A at a real automotive AC condition. The results on the variations of the cooling capacity and air temperature distribution of the evaporator due to the deflector designs in the I/O manifold and flow hole arrangements in the return manifold are presented and analyzed. By studying the KPI's for the performance of an evaporator, the design trade-off for an evaporator designer is summarized and discussed. (author)
The Semantics of Plurals: A Defense of Singularism
Florio, Salvatore
2010-01-01
In this dissertation, I defend "semantic singularism", which is the view that syntactically plural terms, such as "they" or "Russell and Whitehead", are semantically singular. A semantically singular term is a term that denotes a single entity. Semantic singularism is to be distinguished from "syntactic singularism", according to which…
Topology of quasi-projective varieties and Lefschetz theory
International Nuclear Information System (INIS)
Eyral, Christophe
2001-11-01
This paper surveys Lefschetz's theory on the topology of non-singular complex projective varieties. It also includes the more recent generalizations to (singular) quasi-projective varieties, and a discussion on some related questions which are still open. (author)
Stable singularities in string theory
International Nuclear Information System (INIS)
Aspinwall, P.S.; Morrison, D.R.; Gross, M.
1996-01-01
We study a topological obstruction of a very stringy nature concerned with deforming the target space of an N=2 non-linear σ-model. This target space has a singularity which may be smoothed away according to the conventional rules of geometry, but when one studies the associated conformal field theory one sees that such a deformation is not possible without a discontinuous change in some of the correlation functions. This obstruction appears to come from torsion in the homology of the target space (which is seen by deforming the theory by an irrelevant operator). We discuss the link between this phenomenon and orbifolds with discrete torsion as studied by Vafa and Witten. (orig.). With 3 figs
Directory of Open Access Journals (Sweden)
Elvio Alccinelli
2001-07-01
Full Text Available En este artículo pretendemos mostrar que le conjunto de las economías singulares, si bien pequeño desde el punto de vista de la topología y/o desde el punto de vista de la teoría de la medida, tiene importantes efectos en el desarrollo de los regímenes económicos. Es el responsable de los cambios abruptos en los estados de equilibrio y de la multiplicidad de tales estados. Permite además establecer a partir de los tipos de singularidades posibles, una partición del conjunto de economías según tenga lugar uno u otro tipo de singularidad cuya presencia o no, caracteriza el comportamiento posible de la economía en cuestión.
Quantum transitions through cosmological singularities
Energy Technology Data Exchange (ETDEWEB)
Bramberger, Sebastian F.; Lehners, Jean-Luc [Max Planck Institute for Gravitational Physics (Albert Einstein Institute), 14476 Potsdam-Golm (Germany); Hertog, Thomas; Vreys, Yannick, E-mail: sebastian.bramberger@aei.mpg.de, E-mail: thomas.hertog@kuleuven.be, E-mail: jlehners@aei.mpg.de, E-mail: yannick.vreys@kuleuven.be [Institute for Theoretical Physics, KU Leuven, 3001 Leuven (Belgium)
2017-07-01
In a quantum theory of cosmology spacetime behaves classically only in limited patches of the configuration space on which the wave function of the universe is defined. Quantum transitions can connect classical evolution in different patches. Working in the saddle point approximation and in minisuperspace we compute quantum transitions connecting inflationary histories across a de Sitter like throat or a singularity. This supplies probabilities for how an inflating universe, when evolved backwards, transitions and branches into an ensemble of histories on the opposite side of a quantum bounce. Generalising our analysis to scalar potentials with negative regions we identify saddle points describing a quantum transition between a classically contracting, crunching ekpyrotic phase and an inflationary universe.
Coulomb branches with complex singularities
Argyres, Philip C.; Martone, Mario
2018-06-01
We construct 4d superconformal field theories (SCFTs) whose Coulomb branches have singular complex structures. This implies, in particular, that their Coulomb branch coordinate rings are not freely generated. Our construction also gives examples of distinct SCFTs which have identical moduli space (Coulomb, Higgs, and mixed branch) geometries. These SCFTs thus provide an interesting arena in which to test the relationship between moduli space geometries and conformal field theory data. We construct these SCFTs by gauging certain discrete global symmetries of N = 4 superYang-Mills (sYM) theories. In the simplest cases, these discrete symmetries are outer automorphisms of the sYM gauge group, and so these theories have lagrangian descriptions as N = 4 sYM theories with disconnected gauge groups.
Quantum transitions through cosmological singularities
International Nuclear Information System (INIS)
Bramberger, Sebastian F.; Lehners, Jean-Luc; Hertog, Thomas; Vreys, Yannick
2017-01-01
In a quantum theory of cosmology spacetime behaves classically only in limited patches of the configuration space on which the wave function of the universe is defined. Quantum transitions can connect classical evolution in different patches. Working in the saddle point approximation and in minisuperspace we compute quantum transitions connecting inflationary histories across a de Sitter like throat or a singularity. This supplies probabilities for how an inflating universe, when evolved backwards, transitions and branches into an ensemble of histories on the opposite side of a quantum bounce. Generalising our analysis to scalar potentials with negative regions we identify saddle points describing a quantum transition between a classically contracting, crunching ekpyrotic phase and an inflationary universe.
Discrete variable representation for singular Hamiltonians
DEFF Research Database (Denmark)
Schneider, B. I.; Nygaard, Nicolai
2004-01-01
We discuss the application of the discrete variable representation (DVR) to Schrodinger problems which involve singular Hamiltonians. Unlike recent authors who invoke transformations to rid the eigenvalue equation of singularities at the cost of added complexity, we show that an approach based...
Reasons for singularity in robot teleoperation
DEFF Research Database (Denmark)
Marhenke, Ilka; Fischer, Kerstin; Savarimuthu, Thiusius Rajeeth
2014-01-01
In this paper, the causes for singularity of a robot arm in teleoperation for robot learning from demonstration are analyzed. Singularity is the alignment of robot joints, which prevents the configuration of the inverse kinematics. Inspired by users' own hypotheses, we investigated speed and dela...
The Geometry of Black Hole Singularities
Directory of Open Access Journals (Sweden)
Ovidiu Cristinel Stoica
2014-01-01
Full Text Available Recent results show that important singularities in General Relativity can be naturally described in terms of finite and invariant canonical geometric objects. Consequently, one can write field equations which are equivalent to Einstein's at nonsingular points but, in addition remain well-defined and smooth at singularities. The black hole singularities appear to be less undesirable than it was thought, especially after we remove the part of the singularity due to the coordinate system. Black hole singularities are then compatible with global hyperbolicity and do not make the evolution equations break down, when these are expressed in terms of the appropriate variables. The charged black holes turn out to have smooth potential and electromagnetic fields in the new atlas. Classical charged particles can be modeled, in General Relativity, as charged black hole solutions. Since black hole singularities are accompanied by dimensional reduction, this should affect Feynman's path integrals. Therefore, it is expected that singularities induce dimensional reduction effects in Quantum Gravity. These dimensional reduction effects are very similar to those postulated in some approaches to make Quantum Gravity perturbatively renormalizable. This may provide a way to test indirectly the effects of singularities, otherwise inaccessible.
Singularities in the nonisotropic Boltzmann equation
International Nuclear Information System (INIS)
Garibotti, C.R.; Martiarena, M.L.; Zanette, D.
1987-09-01
We consider solutions of the nonlinear Boltzmann equation (NLBE) with anisotropic singular initial conditions, which give a simplified model for the penetration of a monochromatic beam on a rarified target. The NLBE is transformed into an integral equation which is solved iteratively and the evolution of the initial singularities is discussed. (author). 5 refs
Cold atoms in singular potentials
International Nuclear Information System (INIS)
Denschlag, J. P.
1998-09-01
We studied both theoretically and experimentally the interaction between cold Li atoms from a magnetic-optical trap (MOT) and a charged or current-carrying wire. With this system, we were able to realize 1/r 2 and 1/r potentials in two dimensions and to observe the motion of cold atoms in both potentials. For an atom in an attractive 1/r 2 potential, there exist no stable trajectories, instead there is a characteristic class of trajectories for which atoms fall into the singularity. We were able to observe this falling of atoms into the center of the potential. Moreover, by probing the singular 1/r 2 potential with atomic clouds of varying size and temperature we extracted scaling properties of the atom-wire interaction. For very cold atoms, and very thin wires the motion of the atoms must be treated quantum mechanically. Here we predict that the absorption cross section for the 1/r 2 potential should exhibit quantum steps. These quantum steps are a manifestation of the quantum mechanical decomposition of plane waves into partial waves. For the second part of this work, we realized a two dimensional 1/r potential for cold atoms. If the potential is attractive, the atoms can be bound and follow Kepler-like orbits around the wire. The motion in the third dimension along the wire is free. We were able to exploit this property and constructed a novel cold atom guide, the 'Kepler guide'. We also demonstrated another type of atom guide (the 'side guide'), by combining the magnetic field of the wire with a homogeneous offset magnetic field. In this case, the atoms are held in a potential 'tube' on the side of the wire. The versatility, simplicity, and scaling properties of this guide make it an interesting technique. (author)
An adaptive singular ES-FEM for mechanics problems with singular field of arbitrary order
Nguyen-Xuan, H.; Liu, G. R.; Bordas, Stéphane; Natarajan, S.; Rabczuk, T.
2013-01-01
This paper presents a singular edge-based smoothed finite element method (sES-FEM) for mechanics problems with singular stress fields of arbitrary order. The sES-FEM uses a basic mesh of three-noded linear triangular (T3) elements and a special layer of five-noded singular triangular elements (sT5) connected to the singular-point of the stress field. The sT5 element has an additional node on each of the two edges connected to the singular-point. It allows us to represent simple and efficient ...
DEFF Research Database (Denmark)
Cappellin, Cecilia; Breinbjerg, Olav; Frandsen, Aksel
2008-01-01
An effective technique for extracting the singularity of plane wave spectra in the computation of antenna aperture fields is proposed. The singular spectrum is first factorized into a product of a finite function and a singular function. The finite function is inverse Fourier transformed...... numerically using the Inverse Fast Fourier Transform, while the singular function is inverse Fourier transformed analytically, using the Weyl-identity, and the two resulting spatial functions are then convolved to produce the antenna aperture field. This article formulates the theory of the singularity...
Biclustering via Sparse Singular Value Decomposition
Lee, Mihee
2010-02-16
Sparse singular value decomposition (SSVD) is proposed as a new exploratory analysis tool for biclustering or identifying interpretable row-column associations within high-dimensional data matrices. SSVD seeks a low-rank, checkerboard structured matrix approximation to data matrices. The desired checkerboard structure is achieved by forcing both the left- and right-singular vectors to be sparse, that is, having many zero entries. By interpreting singular vectors as regression coefficient vectors for certain linear regressions, sparsity-inducing regularization penalties are imposed to the least squares regression to produce sparse singular vectors. An efficient iterative algorithm is proposed for computing the sparse singular vectors, along with some discussion of penalty parameter selection. A lung cancer microarray dataset and a food nutrition dataset are used to illustrate SSVD as a biclustering method. SSVD is also compared with some existing biclustering methods using simulated datasets. © 2010, The International Biometric Society.
One dimensional systems with singular perturbations
International Nuclear Information System (INIS)
Alvarez, J J; Gadella, M; Nieto, L M; Glasser, L M; Lara, L P
2011-01-01
This paper discusses some one dimensional quantum models with singular perturbations. Eventually, a mass discontinuity is added at the points that support the singular perturbations. The simplest model includes an attractive singular potential with a mass jump both located at the origin. We study the form of the only bound state. Another model exhibits a hard core at the origin plus one or more repulsive deltas with mass jumps at the points supporting these deltas. We study the location and the multiplicity of these resonances for the case of one or two deltas and settle the basis for a generalization. Finally, we consider the harmonic oscillator and the infinite square well plus a singular potential at the origin. We see how the energy of bound states is affected by the singular perturbation.
Noncrossing timelike singularities of irrotational dust collapse
International Nuclear Information System (INIS)
Liang, E.P.T.
1979-01-01
Known naked singularities in spherical dust collapse are either due to shell-crossing or localized to the central world line. They will probably be destroyed by pressure gradients or blue-shift instabilities. To violate the cosmic censorship hypothesis in a more convincing and general context, collapse solutions with naked singularities that are at least nonshell-crossing and nonlocalized need to be constructed. Some results concerning the probable structure of a class of nonshellcrossing and nonlocalized timelike singularities are reviewed. The cylindrical dust model is considered but this model is not asymptotically flat. To make these noncrossing singularities viable counter examples to the cosmic censorship hypothesis, the occurrence of such singularities in asymptotically flat collapse needs to be demonstrated. (UK)
Application of wavelets to singular integral scattering equations
International Nuclear Information System (INIS)
Kessler, B.M.; Payne, G.L.; Polyzou, W.N.
2004-01-01
The use of orthonormal wavelet basis functions for solving singular integral scattering equations is investigated. It is shown that these basis functions lead to sparse matrix equations which can be solved by iterative techniques. The scaling properties of wavelets are used to derive an efficient method for evaluating the singular integrals. The accuracy and efficiency of the wavelet transforms are demonstrated by solving the two-body T-matrix equation without partial wave projection. The resulting matrix equation which is characteristic of multiparticle integral scattering equations is found to provide an efficient method for obtaining accurate approximate solutions to the integral equation. These results indicate that wavelet transforms may provide a useful tool for studying few-body systems
Discriminative clustering on manifold for adaptive transductive classification.
Zhang, Zhao; Jia, Lei; Zhang, Min; Li, Bing; Zhang, Li; Li, Fanzhang
2017-10-01
In this paper, we mainly propose a novel adaptive transductive label propagation approach by joint discriminative clustering on manifolds for representing and classifying high-dimensional data. Our framework seamlessly combines the unsupervised manifold learning, discriminative clustering and adaptive classification into a unified model. Also, our method incorporates the adaptive graph weight construction with label propagation. Specifically, our method is capable of propagating label information using adaptive weights over low-dimensional manifold features, which is different from most existing studies that usually predict the labels and construct the weights in the original Euclidean space. For transductive classification by our formulation, we first perform the joint discriminative K-means clustering and manifold learning to capture the low-dimensional nonlinear manifolds. Then, we construct the adaptive weights over the learnt manifold features, where the adaptive weights are calculated through performing the joint minimization of the reconstruction errors over features and soft labels so that the graph weights can be joint-optimal for data representation and classification. Using the adaptive weights, we can easily estimate the unknown labels of samples. After that, our method returns the updated weights for further updating the manifold features. Extensive simulations on image classification and segmentation show that our proposed algorithm can deliver the state-of-the-art performance on several public datasets. Copyright © 2017 Elsevier Ltd. All rights reserved.
Introduction to global analysis minimal surfaces in Riemannian manifolds
Moore, John Douglas
2017-01-01
During the last century, global analysis was one of the main sources of interaction between geometry and topology. One might argue that the core of this subject is Morse theory, according to which the critical points of a generic smooth proper function on a manifold M determine the homology of the manifold. Morse envisioned applying this idea to the calculus of variations, including the theory of periodic motion in classical mechanics, by approximating the space of loops on M by a finite-dimensional manifold of high dimension. Palais and Smale reformulated Morse's calculus of variations in terms of infinite-dimensional manifolds, and these infinite-dimensional manifolds were found useful for studying a wide variety of nonlinear PDEs. This book applies infinite-dimensional manifold theory to the Morse theory of closed geodesics in a Riemannian manifold. It then describes the problems encountered when extending this theory to maps from surfaces instead of curves. It treats critical point theory for closed param...
Piping structural design for the ITER thermal shield manifold
Energy Technology Data Exchange (ETDEWEB)
Noh, Chang Hyun, E-mail: chnoh@nfri.re.kr [ITER Korea, National Fusion Research Institute, Daejeon 305-333 (Korea, Republic of); Chung, Wooho, E-mail: whchung@nfri.re.kr [ITER Korea, National Fusion Research Institute, Daejeon 305-333 (Korea, Republic of); Nam, Kwanwoo; Kang, Kyoung-O. [ITER Korea, National Fusion Research Institute, Daejeon 305-333 (Korea, Republic of); Bae, Jing Do; Cha, Jong Kook [Korea Marine Equipment Research Institute, Busan 606-806 (Korea, Republic of); Kim, Kyoung-Kyu [Mecha T& S, Jinju-si 660-843 (Korea, Republic of); Hamlyn-Harris, Craig; Hicks, Robby; Her, Namil; Jun, Chang-Hoon [ITER Organization, Route de Vinon-sur-Verdon, CS 90 046, 13067 St. Paul Lez Durance Cedex (France)
2015-10-15
Highlights: • We finalized piping design of ITER thermal shield manifold for procurement. • Support span is determined by stress and deflection limitation. • SQP, which is design optimization method, is used for the pipe design. • Benchmark analysis is performed to verify the analysis software. • Pipe design is verified by structural analyses. - Abstract: The thermal shield (TS) provides the thermal barrier in the ITER tokamak to minimize heat load transferred by thermal radiation from the hot components to the superconducting magnets operating at 4.2 K. The TS is actively cooled by 80 K pressurized helium gas which flows from the cold valve box to the cooling tubes on the TS panels via manifold piping. This paper describes the manifold piping design and analysis for the ITER thermal shield. First, maximum allowable span for the manifold support is calculated based on the simple beam theory. In order to accommodate the thermal contraction in the manifold feeder, a contraction loop is designed and applied. Sequential Quadratic Programming (SQP) method is used to determine the optimized dimensions of the contraction loop to ensure adequate flexibility of manifold pipe. Global structural behavior of the manifold is investigated when the thermal movement of the redundant (un-cooled) pipe is large.
Minimal solution for inconsistent singular fuzzy matrix equations
Directory of Open Access Journals (Sweden)
M. Nikuie
2013-10-01
Full Text Available The fuzzy matrix equations $Ailde{X}=ilde{Y}$ is called a singular fuzzy matrix equations while the coefficients matrix of its equivalent crisp matrix equations be a singular matrix. The singular fuzzy matrix equations are divided into two parts: consistent singular matrix equations and inconsistent fuzzy matrix equations. In this paper, the inconsistent singular fuzzy matrix equations is studied and the effect of generalized inverses in finding minimal solution of an inconsistent singular fuzzy matrix equations are investigated.
Cohomological rigidity of manifolds defined by 3-dimensional polytopes
Buchstaber, V. M.; Erokhovets, N. Yu.; Masuda, M.; Panov, T. E.; Park, S.
2017-04-01
A family of closed manifolds is said to be cohomologically rigid if a cohomology ring isomorphism implies a diffeomorphism for any two manifolds in the family. Cohomological rigidity is established here for large families of 3-dimensional and 6-dimensional manifolds defined by 3-dimensional polytopes. The class \\mathscr{P} of 3-dimensional combinatorial simple polytopes P different from tetrahedra and without facets forming 3- and 4-belts is studied. This class includes mathematical fullerenes, that is, simple 3- polytopes with only 5-gonal and 6-gonal facets. By a theorem of Pogorelov, any polytope in \\mathscr{P} admits in Lobachevsky 3-space a right-angled realisation which is unique up to isometry. Our families of smooth manifolds are associated with polytopes in the class \\mathscr{P}. The first family consists of 3-dimensional small covers of polytopes in \\mathscr{P}, or equivalently, hyperbolic 3-manifolds of Löbell type. The second family consists of 6-dimensional quasitoric manifolds over polytopes in \\mathscr{P}. Our main result is that both families are cohomologically rigid, that is, two manifolds M and M' from either family are diffeomorphic if and only if their cohomology rings are isomorphic. It is also proved that if M and M' are diffeomorphic, then their corresponding polytopes P and P' are combinatorially equivalent. These results are intertwined with classical subjects in geometry and topology such as the combinatorics of 3-polytopes, the Four Colour Theorem, aspherical manifolds, a diffeomorphism classification of 6-manifolds, and invariance of Pontryagin classes. The proofs use techniques of toric topology. Bibliography: 69 titles.
Stochastic development regression on non-linear manifolds
DEFF Research Database (Denmark)
Kühnel, Line; Sommer, Stefan Horst
2017-01-01
We introduce a regression model for data on non-linear manifolds. The model describes the relation between a set of manifold valued observations, such as shapes of anatomical objects, and Euclidean explanatory variables. The approach is based on stochastic development of Euclidean diffusion...... processes to the manifold. Defining the data distribution as the transition distribution of the mapped stochastic process, parameters of the model, the non-linear analogue of design matrix and intercept, are found via maximum likelihood. The model is intrinsically related to the geometry encoded...
Scientific data interpolation with low dimensional manifold model
Zhu, Wei; Wang, Bao; Barnard, Richard; Hauck, Cory D.; Jenko, Frank; Osher, Stanley
2018-01-01
We propose to apply a low dimensional manifold model to scientific data interpolation from regular and irregular samplings with a significant amount of missing information. The low dimensionality of the patch manifold for general scientific data sets has been used as a regularizer in a variational formulation. The problem is solved via alternating minimization with respect to the manifold and the data set, and the Laplace-Beltrami operator in the Euler-Lagrange equation is discretized using the weighted graph Laplacian. Various scientific data sets from different fields of study are used to illustrate the performance of the proposed algorithm on data compression and interpolation from both regular and irregular samplings.
Topological field theory and surgery on three-manifolds
International Nuclear Information System (INIS)
Guadagnini, E.; Panicucci, S.
1992-01-01
The solution of the SU(2) quantum Chern-Simons field theory defined on a closed, connected and orientable three-manifold is presented. The vacuum expectation values of Wilson line operators, associated with framed links in a generic manifold, are computed in terms of the expectation values of the three-sphere. The method consists of using an operator realization of Dehn surgery. The rules, corresponding to the surgery instructions in the three-sphere, are derived and the three-manifold invariant defined by the Chern-Simons theory is constructed. Several examples are considered and explicit results are reported. (orig.)
Mechanical systems with closed orbits on manifolds of revolution
International Nuclear Information System (INIS)
Kudryavtseva, E A; Fedoseev, D A
2015-01-01
We study natural mechanical systems describing the motion of a particle on a two-dimensional Riemannian manifold of revolution in the field of a central smooth potential. We obtain a classification of Riemannian manifolds of revolution and central potentials on them that have the strong Bertrand property: any nonsingular (that is, not contained in a meridian) orbit is closed. We also obtain a classification of manifolds of revolution and central potentials on them that have the 'stable' Bertrand property: every parallel is an 'almost stable' circular orbit, and any nonsingular bounded orbit is closed. Bibliography: 14 titles
Geometric transitions, flops and non-Kahler manifolds: I
International Nuclear Information System (INIS)
Becker, Melanie; Dasgupta, Keshav; Knauf, Anke; Tatar, Radu
2004-01-01
We construct a duality cycle which provides a complete supergravity description of geometric transitions in type II theories via a flop in M-theory. This cycle connects the different supergravity descriptions before and after the geometric transitions. Our construction reproduces many of the known phenomena studied earlier in the literature and allows us to describe some new and interesting aspects in a simple and elegant fashion. A precise supergravity description of new torsional manifolds that appear on the type IIA side with branes and fluxes and the corresponding geometric transition are obtained. A local description of new G2 manifolds that are circle fibrations over non-Kahler manifolds is presented
Scientific data interpolation with low dimensional manifold model
International Nuclear Information System (INIS)
Zhu, Wei; Wang, Bao; Barnard, Richard C.; Hauck, Cory D.
2017-01-01
Here, we propose to apply a low dimensional manifold model to scientific data interpolation from regular and irregular samplings with a significant amount of missing information. The low dimensionality of the patch manifold for general scientific data sets has been used as a regularizer in a variational formulation. The problem is solved via alternating minimization with respect to the manifold and the data set, and the Laplace–Beltrami operator in the Euler–Lagrange equation is discretized using the weighted graph Laplacian. Various scientific data sets from different fields of study are used to illustrate the performance of the proposed algorithm on data compression and interpolation from both regular and irregular samplings.
Quantum cosmology and late-time singularities
International Nuclear Information System (INIS)
Kamenshchik, A Yu
2013-01-01
The development of dark energy models has stimulated interest to cosmological singularities, which differ from the traditional Big Bang and Big Crunch singularities. We review a broad class of phenomena connected with soft cosmological singularities in classical and quantum cosmology. We discuss the classification of singularities from the geometrical point of view and from the point of view of the behavior of finite size objects, crossing such singularities. We discuss in some detail quantum and classical cosmology of models based on perfect fluids (anti-Chaplygin gas and anti-Chaplygin gas plus dust), of models based on the Born–Infeld-type fields and of the model of a scalar field with a potential inversely proportional to the field itself. We dwell also on the phenomenon of the phantom divide line crossing in the scalar field models with cusped potentials. Then we discuss the Friedmann equations modified by quantum corrections to the effective action of the models under considerations and the influence of such modification on the nature and the existence of soft singularities. We review also quantum cosmology of models, where the initial quantum state of the universe is presented by the density matrix (mixed state). Finally, we discuss the exotic singularities arising in the braneworld cosmological models. (topical review)
Directory of Open Access Journals (Sweden)
Borbon Martin de
2017-02-01
Full Text Available The goal of this article is to provide a construction and classification, in the case of two complex dimensions, of the possible tangent cones at points of limit spaces of non-collapsed sequences of Kähler-Einstein metrics with cone singularities. The proofs and constructions are completely elementary, nevertheless they have an intrinsic beauty. In a few words; tangent cones correspond to spherical metrics with cone singularities in the projective line by means of the Kähler quotient construction with respect to the S1-action generated by the Reeb vector field, except in the irregular case ℂβ₁×ℂβ₂ with β₂/ β₁ ∉ Q.
Singularity fitting in hydrodynamical calculations II
International Nuclear Information System (INIS)
Richtmyer, R.D.; Lazarus, R.B.
1975-09-01
This is the second report in a series on the development of techniques for the proper handling of singularities in fluid-dynamical calculations; the first was called Progress Report on the Shock-Fitting Project. This report contains six main results: derivation of a free-surface condition, which relates the acceleration of the surface with the gradient of the square of the sound speed just behind it; an accurate method for the early and middle stages of the development of a rarefaction wave, two orders of magnitude more accurate than a simple direct method used for comparison; the similarity theory of the collapsing free surface, where it is shown that there is a two-parameter family of self-similar solutions for γ = 3.9; the similarity theory for the outgoing shock, which takes into account the entropy increase; a ''zooming'' method for the study of the asymptotic behavior of solutions of the full initial boundary-value problem; comparison of two methods for determining the similarity parameter delta by zooming, which shows that the second method is preferred. Future reports in the series will contain discussions of the self-similar solutions for this problem, and for that of the collapsing shock, in more detail and for the full range (1, infinity) of γ; the values of certain integrals related to neutronic and thermonuclear rates near collapse; and methods for fitting shocks, contact discontinuities, interfaces, and free surfaces in two-dimensional flows
Manifold Regularized Experimental Design for Active Learning.
Zhang, Lining; Shum, Hubert P H; Shao, Ling
2016-12-02
Various machine learning and data mining tasks in classification require abundant data samples to be labeled for training. Conventional active learning methods aim at labeling the most informative samples for alleviating the labor of the user. Many previous studies in active learning select one sample after another in a greedy manner. However, this is not very effective because the classification models has to be retrained for each newly labeled sample. Moreover, many popular active learning approaches utilize the most uncertain samples by leveraging the classification hyperplane of the classifier, which is not appropriate since the classification hyperplane is inaccurate when the training data are small-sized. The problem of insufficient training data in real-world systems limits the potential applications of these approaches. This paper presents a novel method of active learning called manifold regularized experimental design (MRED), which can label multiple informative samples at one time for training. In addition, MRED gives an explicit geometric explanation for the selected samples to be labeled by the user. Different from existing active learning methods, our method avoids the intrinsic problems caused by insufficiently labeled samples in real-world applications. Various experiments on synthetic datasets, the Yale face database and the Corel image database have been carried out to show how MRED outperforms existing methods.
Killing superalgebras for Lorentzian four-manifolds
International Nuclear Information System (INIS)
Medeiros, Paul de; Figueroa-O’Farrill, José; Santi, Andrea
2016-01-01
We determine the Killing superalgebras underpinning field theories with rigid unextended supersymmetry on Lorentzian four-manifolds by re-interpreting them as filtered deformations of ℤ-graded subalgebras with maximum odd dimension of the N=1 Poincaré superalgebra in four dimensions. Part of this calculation involves computing a Spencer cohomology group which, by analogy with a similar result in eleven dimensions, prescribes a notion of Killing spinor, which we identify with the defining condition for bosonic supersymmetric backgrounds of minimal off-shell supergravity in four dimensions. We prove that such Killing spinors always generate a Lie superalgebra, and that this Lie superalgebra is a filtered deformation of a subalgebra of the N=1 Poincaré superalgebra in four dimensions. Demanding the flatness of the connection defining the Killing spinors, we obtain equations satisfied by the maximally supersymmetric backgrounds. We solve these equations, arriving at the classification of maximally supersymmetric backgrounds whose associated Killing superalgebras are precisely the filtered deformations we classify in this paper.
Killing superalgebras for Lorentzian four-manifolds
Energy Technology Data Exchange (ETDEWEB)
Medeiros, Paul de [Department of Mathematics and Natural Sciences, University of Stavanger,4036 Stavanger (Norway); Figueroa-O’Farrill, José; Santi, Andrea [Maxwell Institute and School of Mathematics, The University of Edinburgh,James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh EH9 3FD, Scotland (United Kingdom)
2016-06-20
We determine the Killing superalgebras underpinning field theories with rigid unextended supersymmetry on Lorentzian four-manifolds by re-interpreting them as filtered deformations of ℤ-graded subalgebras with maximum odd dimension of the N=1 Poincaré superalgebra in four dimensions. Part of this calculation involves computing a Spencer cohomology group which, by analogy with a similar result in eleven dimensions, prescribes a notion of Killing spinor, which we identify with the defining condition for bosonic supersymmetric backgrounds of minimal off-shell supergravity in four dimensions. We prove that such Killing spinors always generate a Lie superalgebra, and that this Lie superalgebra is a filtered deformation of a subalgebra of the N=1 Poincaré superalgebra in four dimensions. Demanding the flatness of the connection defining the Killing spinors, we obtain equations satisfied by the maximally supersymmetric backgrounds. We solve these equations, arriving at the classification of maximally supersymmetric backgrounds whose associated Killing superalgebras are precisely the filtered deformations we classify in this paper.
Geometric transitions on non-Kaehler manifolds
International Nuclear Information System (INIS)
Knauf, A.
2007-01-01
We study geometric transitions on the supergravity level using the basic idea of an earlier paper (M. Becker et al., 2004), where a pair of non-Kaehler backgrounds was constructed, which are related by a geometric transition. Here we embed this idea into an orientifold setup. The non-Kaehler backgrounds we obtain in type IIA are non-trivially fibered due to their construction from IIB via T-duality with Neveu-Schwarz flux. We demonstrate that these non-Kaehler manifolds are not half-flat and show that a symplectic structure exists on them at least locally. We also review the construction of new non-Kaehler backgrounds in type I and heterotic theory. They are found by a series of T- and S-duality and can be argued to be related by geometric transitions as well. A local toy model is provided that fulfills the flux equations of motion in IIB and the torsional relation in heterotic theory, and that is consistent with the U-duality relating both theories. For the heterotic theory we also propose a global solution that fulfills the torsional relation because it is similar to the Maldacena-Nunez background. (Abstract Copyright [2007], Wiley Periodicals, Inc.)
Solution path for manifold regularized semisupervised classification.
Wang, Gang; Wang, Fei; Chen, Tao; Yeung, Dit-Yan; Lochovsky, Frederick H
2012-04-01
Traditional learning algorithms use only labeled data for training. However, labeled examples are often difficult or time consuming to obtain since they require substantial human labeling efforts. On the other hand, unlabeled data are often relatively easy to collect. Semisupervised learning addresses this problem by using large quantities of unlabeled data with labeled data to build better learning algorithms. In this paper, we use the manifold regularization approach to formulate the semisupervised learning problem where a regularization framework which balances a tradeoff between loss and penalty is established. We investigate different implementations of the loss function and identify the methods which have the least computational expense. The regularization hyperparameter, which determines the balance between loss and penalty, is crucial to model selection. Accordingly, we derive an algorithm that can fit the entire path of solutions for every value of the hyperparameter. Its computational complexity after preprocessing is quadratic only in the number of labeled examples rather than the total number of labeled and unlabeled examples.
Initial singularity and pure geometric field theories
Wanas, M. I.; Kamal, Mona M.; Dabash, Tahia F.
2018-01-01
In the present article we use a modified version of the geodesic equation, together with a modified version of the Raychaudhuri equation, to study initial singularities. These modified equations are used to account for the effect of the spin-torsion interaction on the existence of initial singularities in cosmological models. Such models are the results of solutions of the field equations of a class of field theories termed pure geometric. The geometric structure used in this study is an absolute parallelism structure satisfying the cosmological principle. It is shown that the existence of initial singularities is subject to some mathematical (geometric) conditions. The scheme suggested for this study can be easily generalized.
Discrete variable representation for singular Hamiltonians
DEFF Research Database (Denmark)
Schneider, B. I.; Nygaard, Nicolai
2004-01-01
We discuss the application of the discrete variable representation (DVR) to Schrodinger problems which involve singular Hamiltonians. Unlike recent authors who invoke transformations to rid the eigenvalue equation of singularities at the cost of added complexity, we show that an approach based...... solely on an orthogonal polynomial basis is adequate, provided the Gauss-Lobatto or Gauss-Radau quadrature rule is used. This ensures that the mesh contains the singular points and by simply discarding the DVR functions corresponding to those points, all matrix elements become well behaved. the boundary...
Transmutation of singularities in optical instruments
Energy Technology Data Exchange (ETDEWEB)
Tyc, Tomas [Institute of Theoretical Physics and Astrophysics, Masaryk University, Kotlarska 2, 61137 Brno (Czech Republic); Leonhardt, Ulf [School of Physics and Astronomy, University of St Andrews, North Haugh, St Andrews KY16 9SS (United Kingdom)], E-mail: tomtyc@physics.muni.cz
2008-11-15
We propose a method for eliminating a class of singularities in optical media where the refractive index goes to zero or infinity at one or more isolated points. Employing transformation optics, we find a refractive index distribution equivalent to the original one that is nonsingular but shows a slight anisotropy. In this way, the original singularity is 'transmuted' into another, weaker type of singularity where the permittivity and permeability tensors are discontinuous at one point. The method is likely to find applications in designing and improving optical devices by making them easier to implement or to operate in a broad band of the spectrum.
Quantum dress for a naked singularity
Directory of Open Access Journals (Sweden)
Marc Casals
2016-09-01
Full Text Available We investigate semiclassical backreaction on a conical naked singularity space–time with a negative cosmological constant in (2+1-dimensions. In particular, we calculate the renormalized quantum stress–energy tensor for a conformally coupled scalar field on such naked singularity space–time. We then obtain the backreacted metric via the semiclassical Einstein equations. We show that, in the regime where the semiclassical approximation can be trusted, backreaction dresses the naked singularity with an event horizon, thus enforcing (weak cosmic censorship.
Cirant, Marco; Gomes, Diogo A.; Pimentel, Edgard A.; Sá nchez-Morgado, Hé ctor
2016-01-01
Here, we prove the existence of smooth solutions for mean-field games with a singular mean-field coupling; that is, a coupling in the Hamilton-Jacobi equation of the form $g(m)=-m^{-\\alpha}$. We consider stationary and time-dependent settings. The function $g$ is monotone, but it is not bounded from below. With the exception of the logarithmic coupling, this is the first time that MFGs whose coupling is not bounded from below is examined in the literature. This coupling arises in models where agents have a strong preference for low-density regions. Paradoxically, this causes the agents to spread and prevents the creation of solutions with a very-low density. To prove the existence of solutions, we consider an approximate problem for which the existence of smooth solutions is known. Then, we prove new a priori bounds for the solutions that show that $\\frac 1 m$ is bounded. Finally, using a limiting argument, we obtain the existence of solutions. The proof in the stationary case relies on a blow-up argument and in the time-dependent case on new bounds for $m^{-1}$.
Cirant, Marco
2016-11-22
Here, we prove the existence of smooth solutions for mean-field games with a singular mean-field coupling; that is, a coupling in the Hamilton-Jacobi equation of the form $g(m)=-m^{-\\\\alpha}$. We consider stationary and time-dependent settings. The function $g$ is monotone, but it is not bounded from below. With the exception of the logarithmic coupling, this is the first time that MFGs whose coupling is not bounded from below is examined in the literature. This coupling arises in models where agents have a strong preference for low-density regions. Paradoxically, this causes the agents to spread and prevents the creation of solutions with a very-low density. To prove the existence of solutions, we consider an approximate problem for which the existence of smooth solutions is known. Then, we prove new a priori bounds for the solutions that show that $\\\\frac 1 m$ is bounded. Finally, using a limiting argument, we obtain the existence of solutions. The proof in the stationary case relies on a blow-up argument and in the time-dependent case on new bounds for $m^{-1}$.
Hybrid direct and iterative solvers for h refined grids with singularities
Paszyński, Maciej R.
2015-04-27
This paper describes a hybrid direct and iterative solver for two and three dimensional h adaptive grids with point singularities. The point singularities are eliminated by using a sequential linear computational cost solver O(N) on CPU [1]. The remaining Schur complements are submitted to incomplete LU preconditioned conjugated gradient (ILUPCG) iterative solver. The approach is compared to the standard algorithm performing static condensation over the entire mesh and executing the ILUPCG algorithm on top of it. The hybrid solver is applied for two or three dimensional grids automatically h refined towards point or edge singularities. The automatic refinement is based on the relative error estimations between the coarse and fine mesh solutions [2], and the optimal refinements are selected using the projection based interpolation. The computational mesh is partitioned into sub-meshes with local point and edge singularities separated. This is done by using the following greedy algorithm.
International Nuclear Information System (INIS)
Rodriguez-Bernal, A.
1993-01-01
On a model example, the Kuramoto-Velarde equation, which includes the Kuramoto-Sivashin-sky and the Cahn-Hilliard models, and under suitable and reasonable hypothesis, we show the dimension and determining modes of inertial manifolds for several classes of solutions. We also give bounds for the dimensions of inertial manifolds of the full system as a parameter is varied. The results are pointed out to be almost model-independent. The same ideas are also applied to a class of parabolic equations in higher space dimension, obtaining results about inertial manifolds on thin and small domains. (Author). 30 refs
Pseudo-Kähler Quantization on Flag Manifolds
Karabegov, Alexander V.
A unified approach to geometric, symbol and deformation quantizations on a generalized flag manifold endowed with an invariant pseudo-Kähler structure is proposed. In particular cases we arrive at Berezin's quantization via covariant and contravariant symbols.
Natural differential operations on manifolds: an algebraic approach
International Nuclear Information System (INIS)
Katsylo, P I; Timashev, D A
2008-01-01
Natural algebraic differential operations on geometric quantities on smooth manifolds are considered. A method for the investigation and classification of such operations is described, the method of IT-reduction. With it the investigation of natural operations reduces to the analysis of rational maps between k-jet spaces, which are equivariant with respect to certain algebraic groups. On the basis of the method of IT-reduction a finite generation theorem is proved: for tensor bundles V,W→M all the natural differential operations D:Γ(V)→Γ(W) of degree at most d can be algebraically constructed from some finite set of such operations. Conceptual proofs of known results on the classification of natural linear operations on arbitrary and symplectic manifolds are presented. A non-existence theorem is proved for natural deformation quantizations on Poisson manifolds and symplectic manifolds. Bibliography: 21 titles.
Stochastic development regression on non-linear manifolds
DEFF Research Database (Denmark)
Kühnel, Line; Sommer, Stefan Horst
2017-01-01
We introduce a regression model for data on non-linear manifolds. The model describes the relation between a set of manifold valued observations, such as shapes of anatomical objects, and Euclidean explanatory variables. The approach is based on stochastic development of Euclidean diffusion...... processes to the manifold. Defining the data distribution as the transition distribution of the mapped stochastic process, parameters of the model, the non-linear analogue of design matrix and intercept, are found via maximum likelihood. The model is intrinsically related to the geometry encoded...... in the connection of the manifold. We propose an estimation procedure which applies the Laplace approximation of the likelihood function. A simulation study of the performance of the model is performed and the model is applied to a real dataset of Corpus Callosum shapes....
Example-driven manifold priors for image deconvolution.
Ni, Jie; Turaga, Pavan; Patel, Vishal M; Chellappa, Rama
2011-11-01
Image restoration methods that exploit prior information about images to be estimated have been extensively studied, typically using the Bayesian framework. In this paper, we consider the role of prior knowledge of the object class in the form of a patch manifold to address the deconvolution problem. Specifically, we incorporate unlabeled image data of the object class, say natural images, in the form of a patch-manifold prior for the object class. The manifold prior is implicitly estimated from the given unlabeled data. We show how the patch-manifold prior effectively exploits the available sample class data for regularizing the deblurring problem. Furthermore, we derive a generalized cross-validation (GCV) function to automatically determine the regularization parameter at each iteration without explicitly knowing the noise variance. Extensive experiments show that this method performs better than many competitive image deconvolution methods.
Partial Synchronization Manifolds for Linearly Time-Delay Coupled Systems
Steur, Erik; van Leeuwen, Cees; Michiels, Wim
2014-01-01
Sometimes a network of dynamical systems shows a form of incomplete synchronization characterized by synchronization of some but not all of its systems. This type of incomplete synchronization is called partial synchronization. Partial synchronization is associated with the existence of partial synchronization manifolds, which are linear invariant subspaces of C, the state space of the network of systems. We focus on partial synchronization manifolds in networks of system...
Two-dimensional manifolds with metrics of revolution
International Nuclear Information System (INIS)
Sabitov, I Kh
2000-01-01
This is a study of the topological and metric structure of two-dimensional manifolds with a metric that is locally a metric of revolution. In the case of compact manifolds this problem can be thoroughly investigated, and in particular it is explained why there are no closed analytic surfaces of revolution in R 3 other than a sphere and a torus (moreover, in the smoothness class C ∞ such surfaces, understood in a certain generalized sense, exist in any topological class)
Radical Transversal Lightlike Submanifolds of Indefinite Para-Sasakian Manifolds
Shukla S.S.; Yadav Akhilesh
2014-01-01
In this paper, we study radical transversal lightlike submanifolds and screen slant radical transversal lightlike submanifolds of indefinite para-Sasakian manifolds giving some non-trivial examples of these submanifolds. Integrability conditions of distributions D and RadTM on radical transversal lightlike submanifolds and screen slant radical transversal lightlike submanifolds of indefinite para-Sasakian manifolds, have been obtained. We also study totally contact umbilical radical transvers...
Renormalization, unstable manifolds, and the fractal structure of mode locking
International Nuclear Information System (INIS)
Cvitanovic, P.; Jensen, M.H.; Kadanoff, L.P.; Procaccia, I.
1985-01-01
The apparent universality of the fractal dimension of the set of quasiperiodic windings at the onset of chaos in a wide class of circle maps is described by construction of a universal one-parameter family of maps which lies along the unstable manifold of the renormalization group. The manifold generates a universal ''devil's staircase'' whose dimension agrees with direct numerical calculations. Applications to experiments are discussed
Reduction of Nambu-Poisson Manifolds by Regular Distributions
Das, Apurba
2018-03-01
The version of Marsden-Ratiu reduction theorem for Nambu-Poisson manifolds by a regular distribution has been studied by Ibáñez et al. In this paper we show that the reduction is always ensured unless the distribution is zero. Next we extend the more general Falceto-Zambon Poisson reduction theorem for Nambu-Poisson manifolds. Finally, we define gauge transformations of Nambu-Poisson structures and show that these transformations commute with the reduction procedure.
Singularities in cosmologies with interacting fluids
International Nuclear Information System (INIS)
Cotsakis, Spiros; Kittou, Georgia
2012-01-01
We study the dynamics near finite-time singularities of flat isotropic universes filled with two interacting but otherwise arbitrary perfect fluids. The overall dynamical picture reveals a variety of asymptotic solutions valid locally around the spacetime singularity. We find the attractor of all solutions with standard decay, and for ‘phantom’ matter asymptotically at early times. We give a number of special asymptotic solutions describing universes collapsing to zero size and others ending at a big rip singularity. We also find a very complicated singularity corresponding to a logarithmic branch point that resembles a cyclic universe, and give an asymptotic local series representation of the general solution in the neighborhood of infinity.
Singularities: the state of the art
International Nuclear Information System (INIS)
Clarke, C.J.S.; Schmidt, B.G.
1977-01-01
A brief, but precise and unified account is given of the results that have been rigorously established at the time of writing concerning the existence and nature of singularities in classical relativity. (author)
Technological Singularity: What Do We Really Know?
Directory of Open Access Journals (Sweden)
Alexey Potapov
2018-04-01
Full Text Available The concept of the technological singularity is frequently reified. Futurist forecasts inferred from this imprecise reification are then criticized, and the reified ideas are incorporated in the core concept. In this paper, I try to disentangle the facts related to the technological singularity from more speculative beliefs about the possibility of creating artificial general intelligence. I use the theory of metasystem transitions and the concept of universal evolution to analyze some misconceptions about the technological singularity. While it may be neither purely technological, nor truly singular, we can predict that the next transition will take place, and that the emerged metasystem will demonstrate exponential growth in complexity with a doubling time of less than half a year, exceeding the complexity of the existing cybernetic systems in few decades.
Algunas aclaraciones acerca del conocimiento del singular.
Directory of Open Access Journals (Sweden)
Carlos Llano Cifuentes
2013-11-01
Full Text Available Llano tries to explain the main purpose of El Conocimiento del Singular, showing how the individuals about which the book is concerned are basically human individuals: people as decision makers.
Topological Signals of Singularities in Ricci Flow
Directory of Open Access Journals (Sweden)
Paul M. Alsing
2017-08-01
Full Text Available We implement methods from computational homology to obtain a topological signal of singularity formation in a selection of geometries evolved numerically by Ricci flow. Our approach, based on persistent homology, produces precise, quantitative measures describing the behavior of an entire collection of data across a discrete sample of times. We analyze the topological signals of geometric criticality obtained numerically from the application of persistent homology to models manifesting singularities under Ricci flow. The results we obtain for these numerical models suggest that the topological signals distinguish global singularity formation (collapse to a round point from local singularity formation (neckpinch. Finally, we discuss the interpretation and implication of these results and future applications.
Asymptotic safety, singularities, and gravitational collapse
International Nuclear Information System (INIS)
Casadio, Roberto; Hsu, Stephen D.H.; Mirza, Behrouz
2011-01-01
Asymptotic safety (an ultraviolet fixed point with finite-dimensional critical surface) offers the possibility that a predictive theory of quantum gravity can be obtained from the quantization of classical general relativity. However, it is unclear what becomes of the singularities of classical general relativity, which, it is hoped, might be resolved by quantum effects. We study dust collapse with a running gravitational coupling and find that a future singularity can be avoided if the coupling becomes exactly zero at some finite energy scale. The singularity can also be avoided (pushed off to infinite proper time) if the coupling approaches zero sufficiently rapidly at high energies. However, the evolution deduced from perturbation theory still implies a singularity at finite proper time.
Stable computation of generalized singular values
Energy Technology Data Exchange (ETDEWEB)
Drmac, Z.; Jessup, E.R. [Univ. of Colorado, Boulder, CO (United States)
1996-12-31
We study floating-point computation of the generalized singular value decomposition (GSVD) of a general matrix pair (A, B), where A and B are real matrices with the same numbers of columns. The GSVD is a powerful analytical and computational tool. For instance, the GSVD is an implicit way to solve the generalized symmetric eigenvalue problem Kx = {lambda}Mx, where K = A{sup {tau}}A and M = B{sup {tau}}B. Our goal is to develop stable numerical algorithms for the GSVD that are capable of computing the singular value approximations with the high relative accuracy that the perturbation theory says is possible. We assume that the singular values are well-determined by the data, i.e., that small relative perturbations {delta}A and {delta}B (pointwise rounding errors, for example) cause in each singular value {sigma} of (A, B) only a small relative perturbation {vert_bar}{delta}{sigma}{vert_bar}/{sigma}.
Dimensionality reduction of collective motion by principal manifolds
Gajamannage, Kelum; Butail, Sachit; Porfiri, Maurizio; Bollt, Erik M.
2015-01-01
While the existence of low-dimensional embedding manifolds has been shown in patterns of collective motion, the current battery of nonlinear dimensionality reduction methods is not amenable to the analysis of such manifolds. This is mainly due to the necessary spectral decomposition step, which limits control over the mapping from the original high-dimensional space to the embedding space. Here, we propose an alternative approach that demands a two-dimensional embedding which topologically summarizes the high-dimensional data. In this sense, our approach is closely related to the construction of one-dimensional principal curves that minimize orthogonal error to data points subject to smoothness constraints. Specifically, we construct a two-dimensional principal manifold directly in the high-dimensional space using cubic smoothing splines, and define the embedding coordinates in terms of geodesic distances. Thus, the mapping from the high-dimensional data to the manifold is defined in terms of local coordinates. Through representative examples, we show that compared to existing nonlinear dimensionality reduction methods, the principal manifold retains the original structure even in noisy and sparse datasets. The principal manifold finding algorithm is applied to configurations obtained from a dynamical system of multiple agents simulating a complex maneuver called predator mobbing, and the resulting two-dimensional embedding is compared with that of a well-established nonlinear dimensionality reduction method.
Semisupervised Support Vector Machines With Tangent Space Intrinsic Manifold Regularization.
Sun, Shiliang; Xie, Xijiong
2016-09-01
Semisupervised learning has been an active research topic in machine learning and data mining. One main reason is that labeling examples is expensive and time-consuming, while there are large numbers of unlabeled examples available in many practical problems. So far, Laplacian regularization has been widely used in semisupervised learning. In this paper, we propose a new regularization method called tangent space intrinsic manifold regularization. It is intrinsic to data manifold and favors linear functions on the manifold. Fundamental elements involved in the formulation of the regularization are local tangent space representations, which are estimated by local principal component analysis, and the connections that relate adjacent tangent spaces. Simultaneously, we explore its application to semisupervised classification and propose two new learning algorithms called tangent space intrinsic manifold regularized support vector machines (TiSVMs) and tangent space intrinsic manifold regularized twin SVMs (TiTSVMs). They effectively integrate the tangent space intrinsic manifold regularization consideration. The optimization of TiSVMs can be solved by a standard quadratic programming, while the optimization of TiTSVMs can be solved by a pair of standard quadratic programmings. The experimental results of semisupervised classification problems show the effectiveness of the proposed semisupervised learning algorithms.
On Borel singularities in quantum field theory
International Nuclear Information System (INIS)
Chadha, S.; Olesen, P.
1977-10-01
The authors consider the effective one-loop Lagrangian in a constant electric field. It is shown that perturbation theory behaves as n factorial giving rise to singularities in the Borel plane. Comparing with the known exact result it is shown how to integrate these singularities. It is suggested that renormalons in QED and QCD should be integrated in a similar way. A speculation is made on a possible interpretation of this integration. (Auth.)
Singularity theorems from weakened energy conditions
International Nuclear Information System (INIS)
Fewster, Christopher J; Galloway, Gregory J
2011-01-01
We establish analogues of the Hawking and Penrose singularity theorems based on (a) averaged energy conditions with exponential damping; (b) conditions on local stress-energy averages inspired by the quantum energy inequalities satisfied by a number of quantum field theories. As particular applications, we establish singularity theorems for the Einstein equations coupled to a classical scalar field, which violates the strong energy condition, and the nonminimally coupled scalar field, which also violates the null energy condition.
On the de Rham–Wu decomposition for Riemannian and Lorentzian manifolds
International Nuclear Information System (INIS)
Galaev, Anton S
2014-01-01
It is explained how to find the de Rham decomposition of a Riemannian manifold and the Wu decomposition of a Lorentzian manifold. For that it is enough to find parallel symmetric bilinear forms on the manifold, and do some linear algebra. This result will allow to compute the connected holonomy group of an arbitrary Riemannian or Lorentzian manifold. (paper)
Folding-retraction of chaotic dynamical manifold and the VAK of vacuum fluctuation
International Nuclear Information System (INIS)
El-Ghoul, M.; El-Ahmady, A.E.; Rafat, H.
2004-01-01
In this paper we introduce the retraction of chaos dynamical manifold. Some properties of chaos dynamical manifold will be deduced. Theorems governing the relation between the folding and retraction of chaos dynamical manifold will be discussed. Some applications of chaos dynamical manifolds and their retractions are achieved in particular high energy particle physics
One-dimensional super Calabi-Yau manifolds and their mirrors
Energy Technology Data Exchange (ETDEWEB)
Noja, S. [Dipartimento di Matematica, Università degli Studi di Milano,Via Saldini 50, I-20133 Milano (Italy); Cacciatori, S.L. [Dipartimento di Scienza e Alta Tecnologia, Università dell’Insubria, Via Valleggio 11, I-22100 Como (Italy); INFN, Sezione di Milano,Via Celoria 16, I-20133 Milano (Italy); Piazza, F. Dalla [Dipartimento di Scienza e Alta Tecnologia, Università dell’Insubria, Via Valleggio 11, I-22100 Como (Italy); Marrani, A. [Centro Studi e Ricerche ‘Enrico Fermi’,Via Panisperna 89A, I-00184 Roma (Italy); Dipartimento di Fisica e Astronomia ‘Galileo Galilei’, Università di Padova,and INFN, Sezione di Padova,Via Marzolo 8, I-35131 Padova (Italy); Re, R. [Dipartimento di Matematica e Informatica, Università degli Studi di Catania,Viale Andrea Doria 6, 95125 Catania (Italy)
2017-04-18
We apply a definition of generalised super Calabi-Yau variety (SCY) to supermanifolds of complex dimension one. One of our results is that there are two SCY’s having reduced manifold equal to ℙ{sup 1}, namely the projective super space ℙ{sup 1|2} and the weighted projective super space Wℙ{sub (2)}{sup 1|1}. Then we compute the corresponding sheaf cohomology of superforms, showing that the cohomology with picture number one is infinite dimensional, while the de Rham cohomology, which is what matters from a physical point of view, remains finite dimensional. Moreover, we provide the complete real and holomorphic de Rham cohomology for generic projective super spaces ℙ{sup n|m}. We also determine the automorphism groups: these always match the dimension of the projective super group with the only exception of ℙ{sup 1|2}, whose automorphism group turns out to be larger than the projective super group. By considering the cohomology of the super tangent sheaf, we compute the deformations of ℙ{sup 1|m}, discovering that the presence of a fermionic structure allows for deformations even if the reduced manifold is rigid. Finally, we show that ℙ{sup 1|2} is self-mirror, whereas Wℙ{sub (2)}{sup 1|1} has a zero dimensional mirror. Also, the mirror map for ℙ{sup 1|2} naturally endows it with a structure of N=2 super Riemann surface.
Simulating triangulations. Graphs, manifolds and (quantum) spacetime
International Nuclear Information System (INIS)
Krueger, Benedikt
2016-01-01
Triangulations, which can intuitively be described as a tessellation of space into simplicial building blocks, are structures that arise in various different branches of physics: They can be used for describing complicated and curved objects in a discretized way, e.g., in foams, gels or porous media, or for discretizing curved boundaries for fluid simulations or dissipative systems. Interpreting triangulations as (maximal planar) graphs makes it possible to use them in graph theory or statistical physics, e.g., as small-world networks, as networks of spins or in biological physics as actin networks. Since one can find an analogue of the Einstein-Hilbert action on triangulations, they can even be used for formulating theories of quantum gravity. Triangulations have also important applications in mathematics, especially in discrete topology. Despite their wide occurrence in different branches of physics and mathematics, there are still some fundamental open questions about triangulations in general. It is a prior unknown how many triangulations there are for a given set of points or a given manifold, or even whether there are exponentially many triangulations or more, a question that relates to a well-defined behavior of certain quantum geometry models. Another major unknown question is whether elementary steps transforming triangulations into each other, which are used in computer simulations, are ergodic. Using triangulations as model for spacetime, it is not clear whether there is a meaningful continuum limit that can be identified with the usual and well-tested theory of general relativity. Within this thesis some of these fundamental questions about triangulations are answered by the use of Markov chain Monte Carlo simulations, which are a probabilistic method for calculating statistical expectation values, or more generally a tool for calculating high-dimensional integrals. Additionally, some details about the Wang-Landau algorithm, which is the primary used
Simulating triangulations. Graphs, manifolds and (quantum) spacetime
Energy Technology Data Exchange (ETDEWEB)
Krueger, Benedikt
2016-07-01
Triangulations, which can intuitively be described as a tessellation of space into simplicial building blocks, are structures that arise in various different branches of physics: They can be used for describing complicated and curved objects in a discretized way, e.g., in foams, gels or porous media, or for discretizing curved boundaries for fluid simulations or dissipative systems. Interpreting triangulations as (maximal planar) graphs makes it possible to use them in graph theory or statistical physics, e.g., as small-world networks, as networks of spins or in biological physics as actin networks. Since one can find an analogue of the Einstein-Hilbert action on triangulations, they can even be used for formulating theories of quantum gravity. Triangulations have also important applications in mathematics, especially in discrete topology. Despite their wide occurrence in different branches of physics and mathematics, there are still some fundamental open questions about triangulations in general. It is a prior unknown how many triangulations there are for a given set of points or a given manifold, or even whether there are exponentially many triangulations or more, a question that relates to a well-defined behavior of certain quantum geometry models. Another major unknown question is whether elementary steps transforming triangulations into each other, which are used in computer simulations, are ergodic. Using triangulations as model for spacetime, it is not clear whether there is a meaningful continuum limit that can be identified with the usual and well-tested theory of general relativity. Within this thesis some of these fundamental questions about triangulations are answered by the use of Markov chain Monte Carlo simulations, which are a probabilistic method for calculating statistical expectation values, or more generally a tool for calculating high-dimensional integrals. Additionally, some details about the Wang-Landau algorithm, which is the primary used
Observational constraints on cosmological future singularities
Energy Technology Data Exchange (ETDEWEB)
Beltran Jimenez, Jose [Aix Marseille Univ, Universite de Toulon CNRS, CPT, Marseille (France); Lazkoz, Ruth [Euskal Herriko Unibertsitatea, Fisika Teorikoaren eta Zientziaren Historia Saila, Zientzia eta Teknologia Fakultatea, Bilbao (Spain); Saez-Gomez, Diego [Faculdade de Ciencias da Universidade de Lisboa, Departamento de Fisica, Instituto de Astrofisica e Ciencias do Espaco, Lisbon (Portugal); Salzano, Vincenzo [University of Szczecin, Institute of Physics, Szczecin (Poland)
2016-11-15
In this work we consider a family of cosmological models featuring future singularities. This type of cosmological evolution is typical of dark energy models with an equation of state violating some of the standard energy conditions (e.g. the null energy condition). Such a kind of behavior, widely studied in the literature, may arise in cosmologies with phantom fields, theories of modified gravity or models with interacting dark matter/dark energy. We briefly review the physical consequences of these cosmological evolution regarding geodesic completeness and the divergence of tidal forces in order to emphasize under which circumstances the singularities in some cosmological quantities correspond to actual singular spacetimes. We then introduce several phenomenological parameterizations of the Hubble expansion rate to model different singularities existing in the literature and use SN Ia, BAO and H(z) data to constrain how far in the future the singularity needs to be (under some reasonable assumptions on the behavior of the Hubble factor). We show that, for our family of parameterizations, the lower bound for the singularity time cannot be smaller than about 1.2 times the age of the universe, what roughly speaking means ∝2.8 Gyrs from the present time. (orig.)
Observational constraints on cosmological future singularities
International Nuclear Information System (INIS)
Beltran Jimenez, Jose; Lazkoz, Ruth; Saez-Gomez, Diego; Salzano, Vincenzo
2016-01-01
In this work we consider a family of cosmological models featuring future singularities. This type of cosmological evolution is typical of dark energy models with an equation of state violating some of the standard energy conditions (e.g. the null energy condition). Such a kind of behavior, widely studied in the literature, may arise in cosmologies with phantom fields, theories of modified gravity or models with interacting dark matter/dark energy. We briefly review the physical consequences of these cosmological evolution regarding geodesic completeness and the divergence of tidal forces in order to emphasize under which circumstances the singularities in some cosmological quantities correspond to actual singular spacetimes. We then introduce several phenomenological parameterizations of the Hubble expansion rate to model different singularities existing in the literature and use SN Ia, BAO and H(z) data to constrain how far in the future the singularity needs to be (under some reasonable assumptions on the behavior of the Hubble factor). We show that, for our family of parameterizations, the lower bound for the singularity time cannot be smaller than about 1.2 times the age of the universe, what roughly speaking means ∝2.8 Gyrs from the present time. (orig.)
Quantized Abelian principle connections on Lorentzian manifolds
International Nuclear Information System (INIS)
Benini, Marco; Schenkel, Alexander
2013-03-01
We construct a covariant functor from a category of Abelian principal bundles over globally hyperbolic spacetimes to a category of *-algebras that describes quantized principal connections. We work within an appropriate differential geometric setting by using the bundle of connections and we study the full gauge group, namely the group of vertical principal bundle automorphisms. Properties of our functor are investigated in detail and, similar to earlier works, it is found that due to topological obstructions the locality property of locally covariant quantum field theory is violated. Furthermore, we prove that, for Abelian structure groups containing a nontrivial compact factor, the gauge invariant Borchers- Uhlmann algebra of the vector dual of the bundle of connections is not separating on gauge equivalence classes of principal connections. We introduce a topological generalization of the concept of locally covariant quantum fields. As examples, we construct for the full subcategory of principal U(1)-bundles two natural transformations from singular homology functors to the quantum field theory functor that can be interpreted as the Euler class and the electric charge. In this case we also prove that the electric charges can be consistently set to zero, which yields another quantum field theory functor that satisfies all axioms of locally covariant quantum field theory.
Quantized Abelian principle connections on Lorentzian manifolds
Energy Technology Data Exchange (ETDEWEB)
Benini, Marco [Pavia Univ. (Italy); Istituto Nazionale di Fisica Nucleare, Pavia (Italy); Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Dappiaggi, Claudio [Pavia Univ. (Italy); Istituto Nazionale di Fisica Nucleare, Pavia (Italy); Schenkel, Alexander [Bergische Univ., Wuppertal (Germany). Fachgruppe Mathematik
2013-03-15
We construct a covariant functor from a category of Abelian principal bundles over globally hyperbolic spacetimes to a category of *-algebras that describes quantized principal connections. We work within an appropriate differential geometric setting by using the bundle of connections and we study the full gauge group, namely the group of vertical principal bundle automorphisms. Properties of our functor are investigated in detail and, similar to earlier works, it is found that due to topological obstructions the locality property of locally covariant quantum field theory is violated. Furthermore, we prove that, for Abelian structure groups containing a nontrivial compact factor, the gauge invariant Borchers- Uhlmann algebra of the vector dual of the bundle of connections is not separating on gauge equivalence classes of principal connections. We introduce a topological generalization of the concept of locally covariant quantum fields. As examples, we construct for the full subcategory of principal U(1)-bundles two natural transformations from singular homology functors to the quantum field theory functor that can be interpreted as the Euler class and the electric charge. In this case we also prove that the electric charges can be consistently set to zero, which yields another quantum field theory functor that satisfies all axioms of locally covariant quantum field theory.
Naked singularities and cosmic censorship: comment on the current situation
International Nuclear Information System (INIS)
Seifert, H.J.
1979-01-01
The current discussion is mainly concerned with how, or indeed, whether space-times possessing naked singularities can be ruled out as being too unrealistic or not being singular at all. The present position is summarized, with references, under the following headings: the Hawking-Penrose existence theorems, hydrodynamical singularities and the strength of naked singularities. (UK)
Directory of Open Access Journals (Sweden)
Elias Zafiris
2016-08-01
Full Text Available The existence of singularities alerts that one of the highest priorities of a centennial perspective on general relativity should be a careful re-thinking of the validity domain of Einstein’s field equations. We address the problem of constructing distinguishable extensions of the smooth spacetime manifold model, which can incorporate singularities, while retaining the form of the field equations. The sheaf-theoretic formulation of this problem is tantamount to extending the algebra sheaf of smooth functions to a distribution-like algebra sheaf in which the former may be embedded, satisfying the pertinent cohomological conditions required for the coordinatization of all of the tensorial physical quantities, such that the form of the field equations is preserved. We present in detail the construction of these distribution-like algebra sheaves in terms of residue classes of sequences of smooth functions modulo the information of singular loci encoded in suitable ideals. Finally, we consider the application of these distribution-like solution sheaves in geometrodynamics by modeling topologically-circular boundaries of singular loci in three-dimensional space in terms of topological links. It turns out that the Borromean link represents higher order wormhole solutions.
Energy Technology Data Exchange (ETDEWEB)
Gary D. Bourn; Ford A. Phillips; Ralph E. Harris
2005-12-01
This document provides results and conclusions for Task 15.0--Detailed Analysis of Air Balance & Conceptual Design of Improved Air Manifolds in the ''Technologies to Enhance the Operation of Existing Natural Gas Compression Infrastructure'' project. SwRI{reg_sign} is conducting this project for DOE in conjunction with Pipeline Research Council International, Gas Machinery Research Council, El Paso Pipeline, Cooper Compression, and Southern Star, under DOE contract number DE-FC26-02NT41646. The objective of Task 15.0 was to investigate the perceived imbalance in airflow between power cylinders in two-stroke integral compressor engines and develop solutions via manifold redesign. The overall project objective is to develop and substantiate methods for operating integral engine/compressors in gas pipeline service, which reduce fuel consumption, increase capacity, and enhance mechanical integrity.
Cosmologies with quasiregular singularities. II. Stability considerations
International Nuclear Information System (INIS)
Konkowski, D.A.; Helliwell, T.M.
1985-01-01
The stability properties of a class of spacetimes with quasiregular singularities is discussed. Quasiregular singularities are the end points of incomplete, inextendible geodesics at which the Riemann tensor and its derivatives remain at least bounded in all parallel-propagated orthonormal (PPON) frames; observers approaching such a singularity would find that their world lines come to an end in a finite proper time. The Taub-NUT (Newman-Unti-Tamburino)-type cosmologies investigated are R 1 x T 3 and R 3 x S 1 flat Kasner spacetimes, the two-parameter family of spatially homogeneous but anisotropic Bianchi type-IX Taub-NUT spacetimes, and an infinite-dimensional family of Einstein-Rosen-Gowdy spacetimes studied by Moncrief. The behavior of matter near the quasiregular singularity in each of these spacetimes is explored through an examination of the behavior of the stress-energy tensors and scalars for conformally coupled and minimally coupled, massive and massless scalar waves as observed in both coordinate and PPON frames. A conjecture is postulated concerning the stability of the nature of the singularity in these spacetimes. The conjecture for a Taub-NUT-type background spacetime is that if a test-field stress-energy tensor evaluated in a PPON frame mimics the behavior of the Riemann tensor components which indicate a particular type of singularity (quasiregular, nonscalar curvature, or scalar curvature), then a complete nonlinear backreaction calculation, in which the fields are allowed to influence the geometry, would show that this type of singularity actually occurs. Evidence supporting the conjecture is presented for spacetimes whose symmetries are unchanged when fields with the same symmetries are added
Generalized teleparallel cosmology and initial singularity crossing
Energy Technology Data Exchange (ETDEWEB)
Awad, Adel; Nashed, Gamal, E-mail: Adel.Awad@bue.edu.eg, E-mail: gglnashed@sci.asu.edu.eg [Center for Theoretical Physics, the British University in Egypt, Suez Desert Road, Sherouk City 11837 (Egypt)
2017-02-01
We present a class of cosmological solutions for a generalized teleparallel gravity with f ( T )= T +α̃ (− T ) {sup n} , where α̃ is some parameter and n is an integer or half-integer. Choosing α̃ ∼ G {sup n} {sup −1}, where G is the gravitational constant, and working with an equation of state p = w ρ, one obtains a cosmological solution with multiple branches. The dynamics of the solution describes standard cosmology at late times, but the higher-torsion correction changes the nature of the initial singularity from big bang to a sudden singularity. The milder behavior of the sudden singularity enables us to extend timelike or lightlike curves, through joining two disconnected branches of solution at the singularity, leaving the singularity traversable. We show that this extension is consistent with the field equations through checking the known junction conditions for generalized teleparallel gravity. This suggests that these solutions describe a contracting phase a prior to the expanding phase of the universe.
Compactifications of IIA supergravity on SU(2)-structure manifolds
Energy Technology Data Exchange (ETDEWEB)
Spanjaard, B.
2008-07-15
In this thesis, we study compactifications of type IIA supergravity on six-dimensional manifolds with an SU(2)-structure. A general study of six-dimensional manifolds with SU(2)-structure shows that IIA supergravity compactified on such a manifold should yield a four-dimensional gauged N=4 supergravity. We explicitly derive the bosonic spectrum, gauge transformations and action for IIA supergravity compactified on two different manifolds with SU(2)-structure, one of which also has an H{sup (3)}{sub 10}-flux, and confirm that the resulting four-dimensional theories are indeed N=4 gauged supergravities. In the second chapter, we study an explicit construction of a set of SU(2)-structure manifolds. This construction involves a Scherk-Schwarz duality twist reduction of the half-maximal six-dimensional supergravity obtained by compactifying IIA supergravity on a K3. This reduction results in a gauged N=4 four-dimensional supergravity, where the gaugings can be divided into three classes of parameters. We relate two of the classes to parameters we found before, and argue that the third class of parameters could be interpreted as a mirror flux. (orig.)
Algebras and manifolds: Differential, difference, simplicial and quantum
International Nuclear Information System (INIS)
Finkelstein, D.; Rodriguez, E.
1986-01-01
Generalized manifolds and Clifford algebras depict the world at levels of resolution ranging from the classical macroscopic to the quantum microscopic. The coarsest picture is a differential manifold and algebra (dm), direct integral of familiar local Clifford algebras of spin operators in curved time-space. Next is a finite difference manifold (Δm) of Regge calculus. This is a subalgebra of the third, a Minkowskian simplicial manifold (Σm). The most detailed description is the quantum manifold (Qm), whose algebra is the free Clifford algebra S of quantum set theory. We surmise that each Σm is a classical 'condensation' of a Qm. Quantum simplices have both integer and half-integer spins in their spectrum. A quantum set theory of nature requires a series of reductions leading from the Qm and a world descriptor W up through the intermediate Σm and Δm to a dm and an action principle. What may be a new algebraic language for topology, classical or quantum, is a by-product of the work. (orig.)
Group manifold approach to gravity and supergravity theories
International Nuclear Information System (INIS)
d'Auria, R.; Fre, P.; Regge, T.
1981-05-01
Gravity theories are presented from the point of view of group manifold formulation. The differential geometry of groups and supergroups is discussed first; the notion of connection and related Yang-Mills potentials is introduced. Then ordinary Einstein gravity is discussed in the Cartan formulation. This discussion provides a first example which will then be generalized to more complicated theories, in particular supergravity. The distinction between ''pure'' and ''impure' theories is also set forth. Next, the authors develop an axiomatic approach to rheonomic theories related to the concept of Chevalley cohomology on group manifolds, and apply these principles to N = 1 supergravity. Then the panorama of so far constructed pure and impure group manifold supergravities is presented. The pure d = 5 N = 2 case is discussed in some detail, and N = 2 and N = 3 in d = 4 are considered as examples of the impure theories. The way a pure theory becomes impure after dimensional reduction is illustrated. Next, the role of kinematical superspace constraints as a subset of the group-manifold equations of motion is discussed, and the use of this approach to obtain the auxiliary fields is demonstrated. Finally, the application of the group manifold method to supersymmetric Super Yang-Mills theories is addressed
Quasi-Newton Exploration of Implicitly Constrained Manifolds
Tang, Chengcheng
2011-08-01
A family of methods for the efficient update of second order approximations of a constraint manifold is proposed in this thesis. The concept of such a constraint manifold corresponds to an abstract space prescribed by implicit nonlinear constraints, which can be a set of objects satisfying certain desired properties. This concept has a variety of applications, and it has been successfully introduced to fabrication-aware architectural design as a shape space consisting of all the implementable designs. The local approximation of such a manifold can be first order, in the tangent space, or second order, in the osculating surface, with higher precision. For a nonlinearly constrained manifold with rather high dimension and codimension, the computation of second order approximants (osculants) is time consuming. In this thesis, a type of so-called quasi-Newton manifold exploration methods which approximate the new osculants by updating the ones of a neighbor point by 1st-order information is introduced. The procedures are discussed in detail and the examples implemented to visually verify the methods are illustrated.
Enhanced manifold regularization for semi-supervised classification.
Gan, Haitao; Luo, Zhizeng; Fan, Yingle; Sang, Nong
2016-06-01
Manifold regularization (MR) has become one of the most widely used approaches in the semi-supervised learning field. It has shown superiority by exploiting the local manifold structure of both labeled and unlabeled data. The manifold structure is modeled by constructing a Laplacian graph and then incorporated in learning through a smoothness regularization term. Hence the labels of labeled and unlabeled data vary smoothly along the geodesics on the manifold. However, MR has ignored the discriminative ability of the labeled and unlabeled data. To address the problem, we propose an enhanced MR framework for semi-supervised classification in which the local discriminative information of the labeled and unlabeled data is explicitly exploited. To make full use of labeled data, we firstly employ a semi-supervised clustering method to discover the underlying data space structure of the whole dataset. Then we construct a local discrimination graph to model the discriminative information of labeled and unlabeled data according to the discovered intrinsic structure. Therefore, the data points that may be from different clusters, though similar on the manifold, are enforced far away from each other. Finally, the discrimination graph is incorporated into the MR framework. In particular, we utilize semi-supervised fuzzy c-means and Laplacian regularized Kernel minimum squared error for semi-supervised clustering and classification, respectively. Experimental results on several benchmark datasets and face recognition demonstrate the effectiveness of our proposed method.
Phantom cosmology without Big Rip singularity
Energy Technology Data Exchange (ETDEWEB)
Astashenok, Artyom V. [Baltic Federal University of I. Kant, Department of Theoretical Physics, 236041, 14, Nevsky st., Kaliningrad (Russian Federation); Nojiri, Shin' ichi, E-mail: nojiri@phys.nagoya-u.ac.jp [Department of Physics, Nagoya University, Nagoya 464-8602 (Japan); Kobayashi-Maskawa Institute for the Origin of Particles and the Universe, Nagoya University, Nagoya 464-8602 (Japan); Odintsov, Sergei D. [Department of Physics, Nagoya University, Nagoya 464-8602 (Japan); Institucio Catalana de Recerca i Estudis Avancats - ICREA and Institut de Ciencies de l' Espai (IEEC-CSIC), Campus UAB, Facultat de Ciencies, Torre C5-Par-2a pl, E-08193 Bellaterra (Barcelona) (Spain); Tomsk State Pedagogical University, Tomsk (Russian Federation); Yurov, Artyom V. [Baltic Federal University of I. Kant, Department of Theoretical Physics, 236041, 14, Nevsky st., Kaliningrad (Russian Federation)
2012-03-23
We construct phantom energy models with the equation of state parameter w which is less than -1, w<-1, but finite-time future singularity does not occur. Such models can be divided into two classes: (i) energy density increases with time ('phantom energy' without 'Big Rip' singularity) and (ii) energy density tends to constant value with time ('cosmological constant' with asymptotically de Sitter evolution). The disintegration of bound structure is confirmed in Little Rip cosmology. Surprisingly, we find that such disintegration (on example of Sun-Earth system) may occur even in asymptotically de Sitter phantom universe consistent with observational data. We also demonstrate that non-singular phantom models admit wormhole solutions as well as possibility of Big Trip via wormholes.
Radioanatomy of the singular nerve canal
Energy Technology Data Exchange (ETDEWEB)
Muren, C. [Dept. of Diagnostic Radiology, Sabbatsbergs Hospital, Stockholm (Sweden); Wadin, K. [University Hospital, Uppsala (Sweden); Dimopoulos, P. [University Hospital, Uppsala (Sweden)
1991-08-01
The singular canal conveys vestibular nerve fibers from the ampulla of the posterior semicircular canal to the posteroinferior border of the internal auditory meatus. Radiographic identification of this anatomic structure helps to distinguish it from a fracture. It is also a landmark in certain surgical procedures. Computed tomography (CT) examinations of deep-frozen temporal bone specimens were compared with subsequently prepared plastic casts of these bones, showing good correlation between the anatomy and the images. The singular canal and its variable anatomy were studied in CT examinations of 107 patients. The singular canal could be identified, in both the axial and in the coronal planes. Its point of entry into the internal auditory meatus varied considerably. (orig.)
Enveloping branes and brane-world singularities
Energy Technology Data Exchange (ETDEWEB)
Antoniadis, Ignatios; Cotsakis, Spiros [CERN-Theory Division, Department of Physics, Geneva 23 (Switzerland); Klaoudatou, Ifigeneia [University of the Aegean, Research Group of Geometry, Dynamical Systems and Cosmology, Department of Information and Communication Systems Engineering, Samos (Greece)
2014-12-01
The existence of envelopes is studied for systems of differential equations in connection with the method of asymptotic splittings which allows one to determine the singularity structure of the solutions. The result is applied to brane-worlds consisting of a 3-brane in a five-dimensional bulk, in the presence of an analog of a bulk perfect fluid parameterizing a generic class of bulk matter. We find that all flat brane solutions suffer from a finite-distance singularity contrary to previous claims. We then study the possibility of avoiding finite-distance singularities by cutting the bulk and gluing regular solutions at the position of the brane. Further imposing physical conditions such as finite Planck mass on the brane and positive energy conditions on the bulk fluid, excludes, however, this possibility as well. (orig.)
Phantom cosmology without Big Rip singularity
International Nuclear Information System (INIS)
Astashenok, Artyom V.; Nojiri, Shin'ichi; Odintsov, Sergei D.; Yurov, Artyom V.
2012-01-01
We construct phantom energy models with the equation of state parameter w which is less than -1, w<-1, but finite-time future singularity does not occur. Such models can be divided into two classes: (i) energy density increases with time (“phantom energy” without “Big Rip” singularity) and (ii) energy density tends to constant value with time (“cosmological constant” with asymptotically de Sitter evolution). The disintegration of bound structure is confirmed in Little Rip cosmology. Surprisingly, we find that such disintegration (on example of Sun-Earth system) may occur even in asymptotically de Sitter phantom universe consistent with observational data. We also demonstrate that non-singular phantom models admit wormhole solutions as well as possibility of Big Trip via wormholes.
Holographic subregion complexity for singular surfaces
Energy Technology Data Exchange (ETDEWEB)
Bakhshaei, Elaheh [Isfahan University of Technology, Department of Physics, Isfahan (Iran, Islamic Republic of); Mollabashi, Ali [Institute for Research in Fundamental Sciences (IPM), School of Physics, Tehran (Iran, Islamic Republic of); Shirzad, Ahmad [Isfahan University of Technology, Department of Physics, Isfahan (Iran, Islamic Republic of); Institute for Research in Fundamental Sciences (IPM), School of Particles and Accelerators, Tehran (Iran, Islamic Republic of)
2017-10-15
Recently holographic prescriptions were proposed to compute the quantum complexity of a given state in the boundary theory. A specific proposal known as 'holographic subregion complexity' is supposed to calculate the complexity of a reduced density matrix corresponding to a static subregion. We study different families of singular subregions in the dual field theory and find the divergence structure and universal terms of holographic subregion complexity for these singular surfaces. We find that there are new universal terms, logarithmic in the UV cut-off, due to the singularities of a family of surfaces including a kink in (2 + 1) dimensions and cones in even dimensional field theories. We also find examples of new divergent terms such as squared logarithm and negative powers times the logarithm of the UV cut-off parameter. (orig.)
Singularity hypotheses a scientific and philosophical assessment
Moor, James; Søraker, Johnny; Steinhart, Eric
2012-01-01
Singularity Hypotheses: A Scientific and Philosophical Assessment offers authoritative, jargon-free essays and critical commentaries on accelerating technological progress and the notion of technological singularity. It focuses on conjectures about the intelligence explosion, transhumanism, and whole brain emulation. Recent years have seen a plethora of forecasts about the profound, disruptive impact that is likely to result from further progress in these areas. Many commentators however doubt the scientific rigor of these forecasts, rejecting them as speculative and unfounded. We therefore invited prominent computer scientists, physicists, philosophers, biologists, economists and other thinkers to assess the singularity hypotheses. Their contributions go beyond speculation, providing deep insights into the main issues and a balanced picture of the debate.
Singularities in four-body final-state amplitudes
International Nuclear Information System (INIS)
Adhikari, S.K.
1978-01-01
Like three-body amplitudes, four-body amplitudes have subenergy threshold singularities over and above total-energy singularities. In the four-body problem we encounter a new type of subenergy singularity besides the usual two- and three-body subenergy threshold singularities. This singularity will be referred to as ''independent-pair threshold singularity'' and involves pair-subenergy threshold singularities in each of the two independent pair subenergies in four-body final states. We also study the particularly interesting case of resonant two- and three-body interactions in the four-body isobar model and the rapid (singular) dependence of the isobar amplitudes they generate in the four-body phase space. All these singularities are analyzed in the multiple-scattering formalism and it is shown that they arise from the ''next-to-last'' rescattering and hence may be represented correctly by an approximate amplitude which has that rescattering
Gene selection for microarray data classification via subspace learning and manifold regularization.
Tang, Chang; Cao, Lijuan; Zheng, Xiao; Wang, Minhui
2017-12-19
With the rapid development of DNA microarray technology, large amount of genomic data has been generated. Classification of these microarray data is a challenge task since gene expression data are often with thousands of genes but a small number of samples. In this paper, an effective gene selection method is proposed to select the best subset of genes for microarray data with the irrelevant and redundant genes removed. Compared with original data, the selected gene subset can benefit the classification task. We formulate the gene selection task as a manifold regularized subspace learning problem. In detail, a projection matrix is used to project the original high dimensional microarray data into a lower dimensional subspace, with the constraint that the original genes can be well represented by the selected genes. Meanwhile, the local manifold structure of original data is preserved by a Laplacian graph regularization term on the low-dimensional data space. The projection matrix can serve as an importance indicator of different genes. An iterative update algorithm is developed for solving the problem. Experimental results on six publicly available microarray datasets and one clinical dataset demonstrate that the proposed method performs better when compared with other state-of-the-art methods in terms of microarray data classification. Graphical Abstract The graphical abstract of this work.
Total Variation Regularization for Functions with Values in a Manifold
Lellmann, Jan; Strekalovskiy, Evgeny; Koetter, Sabrina; Cremers, Daniel
2013-01-01
While total variation is among the most popular regularizers for variational problems, its extension to functions with values in a manifold is an open problem. In this paper, we propose the first algorithm to solve such problems which applies to arbitrary Riemannian manifolds. The key idea is to reformulate the variational problem as a multilabel optimization problem with an infinite number of labels. This leads to a hard optimization problem which can be approximately solved using convex relaxation techniques. The framework can be easily adapted to different manifolds including spheres and three-dimensional rotations, and allows to obtain accurate solutions even with a relatively coarse discretization. With numerous examples we demonstrate that the proposed framework can be applied to variational models that incorporate chromaticity values, normal fields, or camera trajectories. © 2013 IEEE.
Total Variation Regularization for Functions with Values in a Manifold
Lellmann, Jan
2013-12-01
While total variation is among the most popular regularizers for variational problems, its extension to functions with values in a manifold is an open problem. In this paper, we propose the first algorithm to solve such problems which applies to arbitrary Riemannian manifolds. The key idea is to reformulate the variational problem as a multilabel optimization problem with an infinite number of labels. This leads to a hard optimization problem which can be approximately solved using convex relaxation techniques. The framework can be easily adapted to different manifolds including spheres and three-dimensional rotations, and allows to obtain accurate solutions even with a relatively coarse discretization. With numerous examples we demonstrate that the proposed framework can be applied to variational models that incorporate chromaticity values, normal fields, or camera trajectories. © 2013 IEEE.
Para-Hermitian and para-quaternionic manifolds
International Nuclear Information System (INIS)
Ivanov, S.; Zamkovoy, S.
2003-10-01
A set of canonical para-Hermitian connections on an almost para-Hermitian manifold is defined. A Para-hermitian version of the Apostolov-Gauduchon generalization of the Goldberg-Sachs theorem in General Relativity is given. It is proved that the Nijenhuis tensor of a Nearly para-Kaehler manifolds is parallel with respect to the canonical connection. Salamon's twistor construction on quaternionic manifold is adapted to the para-quaternionic case. A locally conformally hyper-para-Kaehler (hypersymplectic) flat structure with parallel Lee form on the Kodaira-Thurston complex surfaces modeled on S 1 x SL (2, R)-tilde is constructed. Anti-self-dual locally conformally hyper-para-Kaehler (hypersymplectic) neutral metrics with non vanishing Weyl tensor are obtained on the Inoe surfaces. An example of anti-self-dual neutral metric which is not locally conformally hyper-para-Kaehler (hypersymplectic) is constructed. (author)
Rigidity of complete noncompact bach-flat n-manifolds
Chu, Yawei; Feng, Pinghua
2012-11-01
Let (Mn,g) be a complete noncompact Bach-flat n-manifold with the positive Yamabe constant and constant scalar curvature. Assume that the L2-norm of the trace-free Riemannian curvature tensor R∘m is finite. In this paper, we prove that (Mn,g) is a constant curvature space if the L-norm of R∘m is sufficiently small. Moreover, we get a gap theorem for (Mn,g) with positive scalar curvature. This can be viewed as a generalization of our earlier results of 4-dimensional Bach-flat manifolds with constant scalar curvature R≥0 [Y.W. Chu, A rigidity theorem for complete noncompact Bach-flat manifolds, J. Geom. Phys. 61 (2011) 516-521]. Furthermore, when n>9, we derive a rigidity result for R<0.
Weyl-Euler-Lagrange Equations of Motion on Flat Manifold
Directory of Open Access Journals (Sweden)
Zeki Kasap
2015-01-01
Full Text Available This paper deals with Weyl-Euler-Lagrange equations of motion on flat manifold. It is well known that a Riemannian manifold is said to be flat if its curvature is everywhere zero. Furthermore, a flat manifold is one Euclidean space in terms of distances. Weyl introduced a metric with a conformal transformation for unified theory in 1918. Classical mechanics is one of the major subfields of mechanics. Also, one way of solving problems in classical mechanics occurs with the help of the Euler-Lagrange equations. In this study, partial differential equations have been obtained for movement of objects in space and solutions of these equations have been generated by using the symbolic Algebra software. Additionally, the improvements, obtained in this study, will be presented.
Schoen manifold with line bundles as resolved magnetized orbifolds
Energy Technology Data Exchange (ETDEWEB)
Groot Nibbelink, Stefan [Muenchen Univ. (Germany). Arnold Sommerfeld Center for Theoretical Physics; Vaudrevange, Patrick K.S. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2012-12-15
We give an alternative description of the Schoen manifold as the blow-up of a Z{sub 2} x Z{sub 2} orbifold in which one Z{sub 2} factor acts as a roto-translation. Since for this orbifold the fixed tori are only identified in pairs but not orbifolded, four-dimensional chirality can never be obtained using standard techniques alone. However, chirality is recovered when its tori become magnetized. To exemplify this, we construct an SU(5) GUT on the Schoen manifold with Abelian gauge fluxes, which becomes an MSSM with three generations after an appropriate Wilson line is associated to its freely acting involution. We reproduce this model as a standard orbifold CFT of the (partially) blown down Schoen manifold with a magnetic flux. Finally, in analogy to a proposal for non-perturbative heterotic models by Aldazabal et al. we suggest modifications to the heterotic orbifold spectrum formulae in the presence of magnetized tori.
Adaptive Sampling for Nonlinear Dimensionality Reduction Based on Manifold Learning
DEFF Research Database (Denmark)
Franz, Thomas; Zimmermann, Ralf; Goertz, Stefan
2017-01-01
We make use of the non-intrusive dimensionality reduction method Isomap in order to emulate nonlinear parametric flow problems that are governed by the Reynolds-averaged Navier-Stokes equations. Isomap is a manifold learning approach that provides a low-dimensional embedding space that is approxi...... to detect and fill up gaps in the sampling in the embedding space. The performance of the proposed manifold filling method will be illustrated by numerical experiments, where we consider nonlinear parameter-dependent steady-state Navier-Stokes flows in the transonic regime.......We make use of the non-intrusive dimensionality reduction method Isomap in order to emulate nonlinear parametric flow problems that are governed by the Reynolds-averaged Navier-Stokes equations. Isomap is a manifold learning approach that provides a low-dimensional embedding space...
Para-Hermitian and para-quaternionic manifolds
Energy Technology Data Exchange (ETDEWEB)
Ivanov, S [University of Sofia ' St. Kl. Ohridski' , Faculty of Mathematics and Informatics, Sofia (Bulgaria) and Abdus Salam International Centre for Theoretical Physics, Trieste (Italy); Zamkovoy, S [University of Sofia ' St. Kl. Ohridski' , Faculty of Mathematics and Informatics, Sofia (Bulgaria)
2003-10-01
A set of canonical para-Hermitian connections on an almost para-Hermitian manifold is defined. A Para-hermitian version of the Apostolov-Gauduchon generalization of the Goldberg-Sachs theorem in General Relativity is given. It is proved that the Nijenhuis tensor of a Nearly para-Kaehler manifolds is parallel with respect to the canonical connection. Salamon's twistor construction on quaternionic manifold is adapted to the para-quaternionic case. A locally conformally hyper-para-Kaehler (hypersymplectic) flat structure with parallel Lee form on the Kodaira-Thurston complex surfaces modeled on S{sup 1} x SL (2, R)-tilde is constructed. Anti-self-dual locally conformally hyper-para-Kaehler (hypersymplectic) neutral metrics with non vanishing Weyl tensor are obtained on the Inoe surfaces. An example of anti-self-dual neutral metric which is not locally conformally hyper-para-Kaehler (hypersymplectic) is constructed. (author)
On the geometry of some special projective varieties
Russo, Francesco
2016-01-01
Providing an introduction to both classical and modern techniques in projective algebraic geometry, this monograph treats the geometrical properties of varieties embedded in projective spaces, their secant and tangent lines, the behavior of tangent linear spaces, the algebro-geometric and topological obstructions to their embedding into smaller projective spaces, and the classification of extremal cases. It also provides a solution of Hartshorne’s Conjecture on Complete Intersections for the class of quadratic manifolds and new short proofs of previously known results, using the modern tools of Mori Theory and of rationally connected manifolds. The new approach to some of the problems considered can be resumed in the principle that, instead of studying a special embedded manifold uniruled by lines, one passes to analyze the original geometrical property on the manifold of lines passing through a general point and contained in the manifold. Once this embedded manifold, usually of lower codimension, is classi...
Rigid Body Attitude Control Based on a Manifold Representation of Direction Cosine Matrices
International Nuclear Information System (INIS)
Nakath, David; Clemens, Joachim; Rachuy, Carsten
2017-01-01
Autonomous systems typically actively observe certain aspects of their surroundings, which makes them dependent on a suitable controller. However, building an attitude controller for three degrees of freedom is a challenging task, mainly due to singularities in the different parametrizations of the three dimensional rotation group SO (3). Thus, we propose an attitude controller based on a manifold representation of direction cosine matrices: In state space, the attitude is globally and uniquely represented as a direction cosine matrix R ∈ SO (3). However, differences in the state space, i.e., the attitude errors, are exposed to the controller in the vector space ℝ 3 . This is achieved by an operator, which integrates the matrix logarithm mapping from SO (3) to so(3) and the map from so(3) to ℝ 3 . Based on this representation, we derive a proportional and derivative feedback controller, whose output has an upper bound to prevent actuator saturation. Additionally, the feedback is preprocessed by a particle filter to account for measurement and state transition noise. We evaluate our approach in a simulator in three different spacecraft maneuver scenarios: (i) stabilizing, (ii) rest-to-rest, and (iii) nadir-pointing. The controller exhibits stable behavior from initial attitudes near and far from the setpoint. Furthermore, it is able to stabilize a spacecraft and can be used for nadir-pointing maneuvers. (paper)
Quantization of Poisson Manifolds from the Integrability of the Modular Function
Bonechi, F.; Ciccoli, N.; Qiu, J.; Tarlini, M.
2014-10-01
We discuss a framework for quantizing a Poisson manifold via the quantization of its symplectic groupoid, combining the tools of geometric quantization with the results of Renault's theory of groupoid C*-algebras. This setting allows very singular polarizations. In particular, we consider the case when the modular function is multiplicatively integrable, i.e., when the space of leaves of the polarization inherits a groupoid structure. If suitable regularity conditions are satisfied, then one can define the quantum algebra as the convolution algebra of the subgroupoid of leaves satisfying the Bohr-Sommerfeld conditions. We apply this procedure to the case of a family of Poisson structures on , seen as Poisson homogeneous spaces of the standard Poisson-Lie group SU( n + 1). We show that a bihamiltonian system on defines a multiplicative integrable model on the symplectic groupoid; we compute the Bohr-Sommerfeld groupoid and show that it satisfies the needed properties for applying Renault theory. We recover and extend Sheu's description of quantum homogeneous spaces as groupoid C*-algebras.
Postoperative 3D spine reconstruction by navigating partitioning manifolds
Energy Technology Data Exchange (ETDEWEB)
Kadoury, Samuel, E-mail: samuel.kadoury@polymtl.ca [Department of Computer and Software Engineering, Ecole Polytechnique Montreal, Montréal, Québec H3C 3A7 (Canada); Labelle, Hubert, E-mail: hubert.labelle@recherche-ste-justine.qc.ca; Parent, Stefan, E-mail: stefan.parent@umontreal.ca [CHU Sainte-Justine Hospital Research Center, Montréal, Québec H3T 1C5 (Canada)
2016-03-15
Purpose: The postoperative evaluation of scoliosis patients undergoing corrective treatment is an important task to assess the strategy of the spinal surgery. Using accurate 3D geometric models of the patient’s spine is essential to measure longitudinal changes in the patient’s anatomy. On the other hand, reconstructing the spine in 3D from postoperative radiographs is a challenging problem due to the presence of instrumentation (metallic rods and screws) occluding vertebrae on the spine. Methods: This paper describes the reconstruction problem by searching for the optimal model within a manifold space of articulated spines learned from a training dataset of pathological cases who underwent surgery. The manifold structure is implemented based on a multilevel manifold ensemble to structure the data, incorporating connections between nodes within a single manifold, in addition to connections between different multilevel manifolds, representing subregions with similar characteristics. Results: The reconstruction pipeline was evaluated on x-ray datasets from both preoperative patients and patients with spinal surgery. By comparing the method to ground-truth models, a 3D reconstruction accuracy of 2.24 ± 0.90 mm was obtained from 30 postoperative scoliotic patients, while handling patients with highly deformed spines. Conclusions: This paper illustrates how this manifold model can accurately identify similar spine models by navigating in the low-dimensional space, as well as computing nonlinear charts within local neighborhoods of the embedded space during the testing phase. This technique allows postoperative follow-ups of spinal surgery using personalized 3D spine models and assess surgical strategies for spinal deformities.
Conservation laws in quantum mechanics on a Riemannian manifold
International Nuclear Information System (INIS)
Chepilko, N.M.
1992-01-01
In Refs. 1-5 the quantum dynamics of a particle on a Riemannian manifold V n is considered. The advantage of Ref. 5, in comparison with Refs. 1-4, is the fact that in it the differential-geometric character of the theory and the covariant definition (via the known Lagrangian of the particle) of the algebra of quantum-mechanical operators on V n are mutually consistent. However, in Ref. 5 the procedure for calculating the expectation values of operators from the known wave function of the particle is not discussed. In the authors view, this question is problematical and requires special study. The essence of the problem is that integration on a Riemannian manifold V n , unlike that of a Euclidean manifold R n , is uniquely defined only for scalars. For this reason, the calculation of the expectation value of, e.g., the operator of the momentum or angular momentum of a particle on V n is not defined in the usual sense. However, this circumstance was not taken into account by the authors of Refs. 1-4, in which quantum mechanics on a Riemannian manifold V n was studied. In this paper the author considers the conservation laws and a procedure for calculating observable quantities in the classical mechanics (Sec. 2) and quantum mechanics (Sec. 3) of a particle on V n . It is found that a key role here is played by the Killing vectors of the Riemannian manifold V n . It is shown that the proposed approach to the problem satisfies the correspondence principle for both the classical and the quantum mechanics of a particle on a Euclidean manifold R n
Postoperative 3D spine reconstruction by navigating partitioning manifolds
International Nuclear Information System (INIS)
Kadoury, Samuel; Labelle, Hubert; Parent, Stefan
2016-01-01
Purpose: The postoperative evaluation of scoliosis patients undergoing corrective treatment is an important task to assess the strategy of the spinal surgery. Using accurate 3D geometric models of the patient’s spine is essential to measure longitudinal changes in the patient’s anatomy. On the other hand, reconstructing the spine in 3D from postoperative radiographs is a challenging problem due to the presence of instrumentation (metallic rods and screws) occluding vertebrae on the spine. Methods: This paper describes the reconstruction problem by searching for the optimal model within a manifold space of articulated spines learned from a training dataset of pathological cases who underwent surgery. The manifold structure is implemented based on a multilevel manifold ensemble to structure the data, incorporating connections between nodes within a single manifold, in addition to connections between different multilevel manifolds, representing subregions with similar characteristics. Results: The reconstruction pipeline was evaluated on x-ray datasets from both preoperative patients and patients with spinal surgery. By comparing the method to ground-truth models, a 3D reconstruction accuracy of 2.24 ± 0.90 mm was obtained from 30 postoperative scoliotic patients, while handling patients with highly deformed spines. Conclusions: This paper illustrates how this manifold model can accurately identify similar spine models by navigating in the low-dimensional space, as well as computing nonlinear charts within local neighborhoods of the embedded space during the testing phase. This technique allows postoperative follow-ups of spinal surgery using personalized 3D spine models and assess surgical strategies for spinal deformities
Endpoint singularities in unintegrated parton distributions
Hautmann, F
2007-01-01
We examine the singular behavior from the endpoint region x -> 1 in parton distributions unintegrated in both longitudinal and transverse momenta. We identify and regularize the singularities by using the subtraction method, and compare this with the cut-off regularization method. The counterterms for the distributions with subtractive regularization are given in coordinate space by compact all-order expressions in terms of eikonal-line operators. We carry out an explicit calculation at one loop for the unintegrated quark distribution. We discuss the relation of the unintegrated parton distributions in subtractive regularization with the ordinary parton distributions.
Characteristic classes, singular embeddings, and intersection homology.
Cappell, S E; Shaneson, J L
1987-06-01
This note announces some results on the relationship between global invariants and local topological structure. The first section gives a local-global formula for Pontrjagin classes or L-classes. The second section describes a corresponding decomposition theorem on the level of complexes of sheaves. A final section mentions some related aspects of "singular knot theory" and the study of nonisolated singularities. Analogous equivariant analogues, with local-global formulas for Atiyah-Singer classes and their relations to G-signatures, will be presented in a future paper.
Cosmic censorship and the strengths of singularities
International Nuclear Information System (INIS)
Newman, R.P.
1986-01-01
This paper considers the principal definitions concerning limiting curvature strength on geodesics, and on non-spacelike geodesics in particular. They are formulated in terms of focussing conditions. Two definitions suggest themselves, and these are given in terms of a concept of a generalized Jacobi field. An historical survey is presented on some important developments concerning examples of naked singularities. The historical context is recalled in which these models, and cosmic censorship in general, have arisen. It is the author's opinion that one can expect to obtain theoretical limitations on the strengths of any naked singularities which do occur
Robust Covariance Estimators Based on Information Divergences and Riemannian Manifold
Directory of Open Access Journals (Sweden)
Xiaoqiang Hua
2018-03-01
Full Text Available This paper proposes a class of covariance estimators based on information divergences in heterogeneous environments. In particular, the problem of covariance estimation is reformulated on the Riemannian manifold of Hermitian positive-definite (HPD matrices. The means associated with information divergences are derived and used as the estimators. Without resorting to the complete knowledge of the probability distribution of the sample data, the geometry of the Riemannian manifold of HPD matrices is considered in mean estimators. Moreover, the robustness of mean estimators is analyzed using the influence function. Simulation results indicate the robustness and superiority of an adaptive normalized matched filter with our proposed estimators compared with the existing alternatives.
Hamilton's gradient estimate for the heat kernel on complete manifolds
Kotschwar, Brett
2007-01-01
In this paper we extend a gradient estimate of R. Hamilton for positive solutions to the heat equation on closed manifolds to bounded positive solutions on complete, non-compact manifolds with $Rc \\geq -Kg$. We accomplish this extension via a maximum principle of L. Karp and P. Li and a Bernstein-type estimate on the gradient of the solution. An application of our result, together with the bounds of P. Li and S.T. Yau, yields an estimate on the gradient of the heat kernel for complete manifol...
Distributed mean curvature on a discrete manifold for Regge calculus
International Nuclear Information System (INIS)
Conboye, Rory; Miller, Warner A; Ray, Shannon
2015-01-01
The integrated mean curvature of a simplicial manifold is well understood in both Regge Calculus and Discrete Differential Geometry. However, a well motivated pointwise definition of curvature requires a careful choice of the volume over which to uniformly distribute the local integrated curvature. We show that hybrid cells formed using both the simplicial lattice and its circumcentric dual emerge as a remarkably natural structure for the distribution of this local integrated curvature. These hybrid cells form a complete tessellation of the simplicial manifold, contain a geometric orthonormal basis, and are also shown to give a pointwise mean curvature with a natural interpretation as the fractional rate of change of the normal vector. (paper)
Tops as building blocks for G 2 manifolds
Braun, Andreas P.
2017-10-01
A large number of examples of compact G 2 manifolds, relevant to supersymmetric compactifications of M-Theory to four dimensions, can be constructed by forming a twisted connected sum of two building blocks times a circle. These building blocks, which are appropriate K3-fibred threefolds, are shown to have a natural and elegant construction in terms of tops, which parallels the construction of Calabi-Yau manifolds via reflexive polytopes. In particular, this enables us to prove combinatorial formulas for the Hodge numbers and other relevant topological data.
Distributed mean curvature on a discrete manifold for Regge calculus
Conboye, Rory; Miller, Warner A.; Ray, Shannon
2015-09-01
The integrated mean curvature of a simplicial manifold is well understood in both Regge Calculus and Discrete Differential Geometry. However, a well motivated pointwise definition of curvature requires a careful choice of the volume over which to uniformly distribute the local integrated curvature. We show that hybrid cells formed using both the simplicial lattice and its circumcentric dual emerge as a remarkably natural structure for the distribution of this local integrated curvature. These hybrid cells form a complete tessellation of the simplicial manifold, contain a geometric orthonormal basis, and are also shown to give a pointwise mean curvature with a natural interpretation as the fractional rate of change of the normal vector.
Gauge groups and topological invariants of vacuum manifolds
International Nuclear Information System (INIS)
Golo, V.L.; Monastyrsky, M.I.
1978-01-01
The paper is concerned with topological properties of the vacuum manifolds in the theories with the broken gauge symmetry for the groups of the type SO(k) x U(n), SO(k) x SO(p) x U(r). For the Ginsburg-Landau theory of the superfluid 3 He the gauge transformations are discussed. They provide the means to indicate all possible types of the vacuum manifolds, which are likely to correspond to distinct phases of the superfluid 3 He. Conditions on the existence of the minimums of the Ginsburg-Landau functional are discussed
Prescribed curvature tensor in locally conformally flat manifolds
Pina, Romildo; Pieterzack, Mauricio
2018-01-01
A global existence theorem for the prescribed curvature tensor problem in locally conformally flat manifolds is proved for a special class of tensors R. Necessary and sufficient conditions for the existence of a metric g ¯ , conformal to Euclidean g, are determined such that R ¯ = R, where R ¯ is the Riemannian curvature tensor of the metric g ¯ . The solution to this problem is given explicitly for special cases of the tensor R, including the case where the metric g ¯ is complete on Rn. Similar problems are considered for locally conformally flat manifolds.
Spontaneous compactification and Ricci-flat manifolds with torsion
International Nuclear Information System (INIS)
McInnes, B.
1985-06-01
The Freund-Rubin mechanism is based on the equation Rsub(ik)=lambdagsub(ik) (where lambda>0), which, via Myers' Theorem, implies ''spontaneous'' compactification. The difficulties connected with the cosmological constant in this approach can be resolved if torsion is introduced and lambda set equal to zero, but then compactification ''by hand'' is necessary, since the equation Rsub(ik)=0 can be satisfied both on compact and on non-compact manifolds. In this paper we discuss the global geometry of Ricci-flat manifolds with torsion, and suggest ways of restoring the ''spontaneity'' of the compactification. (author)
Markov's theorem and algorithmically non-recognizable combinatorial manifolds
International Nuclear Information System (INIS)
Shtan'ko, M A
2004-01-01
We prove the theorem of Markov on the existence of an algorithmically non-recognizable combinatorial n-dimensional manifold for every n≥4. We construct for the first time a concrete manifold which is algorithmically non-recognizable. A strengthened form of Markov's theorem is proved using the combinatorial methods of regular neighbourhoods and handle theory. The proofs coincide for all n≥4. We use Borisov's group with insoluble word problem. It has two generators and twelve relations. The use of this group forms the base for proving the strengthened form of Markov's theorem
Rotation vectors for homeomorphisms of non-positively curved manifolds
International Nuclear Information System (INIS)
Lessa, Pablo
2011-01-01
Rotation vectors, as defined for homeomorphisms of the torus that are isotopic to the identity, are generalized to such homeomorphisms of any complete Riemannian manifold with non-positive sectional curvature. These generalized rotation vectors are shown to exist for almost every orbit of such a dynamical system with respect to any invariant measure with compact support. The concept is then extended to flows and, as an application, it is shown how non-null rotation vectors can be used to construct a measurable semi-conjugacy between a given flow and the geodesic flow of a manifold
PT-symmetric models in curved manifolds
Czech Academy of Sciences Publication Activity Database
Krejčiřík, David; Siegl, Petr
2010-01-01
Roč. 43, č. 48 (2010), 485204/1-485204/30 ISSN 1751-8113 R&D Projects: GA MŠk LC06002 Institutional research plan: CEZ:AV0Z10480505 Keywords : NON-HERMITIAN HAMILTONIANS * SCHRODINGER -TYPE OPERATORS * PSEUDO-HERMITICITY Subject RIV: BA - General Mathematics Impact factor: 1.641, year: 2010
Spectral Analysis of a Quantum System with a Double Line Singular Interaction
Czech Academy of Sciences Publication Activity Database
Kondej, S.; Krejčiřík, David
2013-01-01
Roč. 49, č. 4 (2013), s. 831-859 ISSN 0034-5318 R&D Projects: GA ČR GAP203/11/0701 Institutional support: RVO:61389005 Keywords : Schrödinger operator * singular perturbation * spectral analysis * Hardy inequality * resonance Subject RIV: BE - Theoretical Physics Impact factor: 0.614, year: 2013
Czech Academy of Sciences Publication Activity Database
Exner, Pavel; Pankrashkin, K.
2014-01-01
Roč. 39, č. 2 (2014), s. 193-212 ISSN 0360-5302 R&D Projects: GA ČR GAP203/11/0701 Institutional support: RVO:61389005 Keywords : Eigenvalue * Schrödinger operator * singular interaction * strong coupling * 35Q40 * 35P15 * 35J10 Subject RIV: BE - Theoretical Physics Impact factor: 1.013, year: 2014
Feature extraction for SAR target recognition based on supervised manifold learning
International Nuclear Information System (INIS)
Du, C; Zhou, S; Sun, J; Zhao, J
2014-01-01
On the basis of manifold learning theory, a new feature extraction method for Synthetic aperture radar (SAR) target recognition is proposed. First, the proposed algorithm estimates the within-class and between-class local neighbourhood surrounding each SAR sample. After computing the local tangent space for each neighbourhood, the proposed algorithm seeks for the optimal projecting matrix by preserving the local within-class property and simultaneously maximizing the local between-class separability. The use of uncorrelated constraint can also enhance the discriminating power of the optimal projecting matrix. Finally, the nearest neighbour classifier is applied to recognize SAR targets in the projected feature subspace. Experimental results on MSTAR datasets demonstrate that the proposed method can provide a higher recognition rate than traditional feature extraction algorithms in SAR target recognition
Singular Linear Differential Equations in Two Variables
Braaksma, B.L.J.; Put, M. van der
2008-01-01
The formal and analytic classification of integrable singular linear differential equations has been studied among others by R. Gerard and Y. Sibuya. We provide a simple proof of their main result, namely: For certain irregular systems in two variables there is no Stokes phenomenon, i.e. there is no
Singular continuous spectrum for palindromic Schroedinger operators
International Nuclear Information System (INIS)
Hof, A.; Knill, O.; Simon, B.
1995-01-01
We give new examples of discrete Schroedinger operators with potentials taking finitely many values that have purely singular continuous spectrum. If the hull X of the potential is strictly ergodic, then the existence of just one potential x in X for which the operator has no eigenvalues implies that there is a generic set in X for which the operator has purely singular continuous spectrum. A sufficient condition for the existence of such an x is that there is a z element of X that contains arbitrarily long palindromes. Thus we can define a large class of primitive substitutions for which the operators are purely singularly continuous for a generic subset in X. The class includes well-known substitutions like Fibonacci, Thue-Morse, Period Doubling, binary non-Pisot and ternary non-Pisot. We also show that the operator has no absolutely continuous spectrum for all x element of X if X derives from a primitive substitution. For potentials defined by circle maps, x n =l J (θ 0 +nα), we show that the operator has purely singular continuous spectrum for a generic subset in X for all irrational α and every half-open interval J. (orig.)
'Footballs', conical singularities, and the Liouville equation
International Nuclear Information System (INIS)
Redi, Michele
2005-01-01
We generalize the football shaped extra dimensions scenario to an arbitrary number of branes. The problem is related to the solution of the Liouville equation with singularities, and explicit solutions are presented for the case of three branes. The tensions of the branes do not need to be tuned with each other but only satisfy mild global constraints
Mobile communications technology: The singular factor responsible ...
African Journals Online (AJOL)
This paper investigated the factors responsible for the growth of Internet usage on the African continent. The principal finding was that increasing growth of Internet usage is also down to one singular factor: mobile communications technology. The proliferation of mobile phone usage in Africa has resulted in the sustained ...
Diamagnetism of quantum gases with singular potentials
DEFF Research Database (Denmark)
Briet, Philippe; Cornean, Horia; Savoie, Baptiste
2010-01-01
We consider a gas of quasi-free quantum particles confined to a finite box, subjected to singular magnetic and electric fields. We prove in great generality that the finite volume grand-canonical pressure is analytic with respect to the chemical potential and the intensity of the external magnetic...
Supersymmetric quantum mechanics under point singularities
International Nuclear Information System (INIS)
Uchino, Takashi; Tsutsui, Izumi
2003-01-01
We provide a systematic study on the possibility of supersymmetry (SUSY) for one-dimensional quantum mechanical systems consisting of a pair of lines R or intervals [-l, l] each having a point singularity. We consider the most general singularities and walls (boundaries) at x = ±l admitted quantum mechanically, using a U(2) family of parameters to specify one singularity and similarly a U(1) family of parameters to specify one wall. With these parameter freedoms, we find that for a certain subfamily the line systems acquire an N = 1 SUSY which can be enhanced to N = 4 if the parameters are further tuned, and that these SUSY are generically broken except for a special case. The interval systems, on the other hand, can accommodate N = 2 or N = 4 SUSY, broken or unbroken, and exhibit a rich variety of (degenerate) spectra. Our SUSY systems include the familiar SUSY systems with the Dirac δ(x)-potential, and hence are extensions of the known SUSY quantum mechanics to those with general point singularities and walls. The self-adjointness of the supercharge in relation to the self-adjointness of the Hamiltonian is also discussed
A singularity theorem based on spatial averages
Indian Academy of Sciences (India)
journal of. July 2007 physics pp. 31–47. A singularity theorem based on spatial ... In this paper I would like to present a result which confirms – at least partially – ... A detailed analysis of how the model fits in with the .... Further, the statement that the spatial average ...... Financial support under grants FIS2004-01626 and no.
Resolving curvature singularities in holomorphic gravity
Mantz, C.L.M.; Prokopec, T.
2011-01-01
We formulate a holomorphic theory of gravity and study how the holomorphy symmetry alters the two most important singular solutions of general relativity: black holes and cosmology. We show that typical observers (freely) falling into a holomorphic black hole do not encounter a curvature
Classical resolution of singularities in dilaton cosmologies
Bergshoeff, EA; Collinucci, A; Roest, D; Russo, JG; Townsend, PK
2005-01-01
For models of dilaton gravity with a possible exponential potential, such as the tensor-scalar sector of ITA supergravity, we show how cosmological solutions correspond to trajectories in a 2D Milne space (parametrized by the dilaton and the scale factor). Cosmological singularities correspond to
Normal forms of Hopf-zero singularity
International Nuclear Information System (INIS)
Gazor, Majid; Mokhtari, Fahimeh
2015-01-01
The Lie algebra generated by Hopf-zero classical normal forms is decomposed into two versal Lie subalgebras. Some dynamical properties for each subalgebra are described; one is the set of all volume-preserving conservative systems while the other is the maximal Lie algebra of nonconservative systems. This introduces a unique conservative–nonconservative decomposition for the normal form systems. There exists a Lie-subalgebra that is Lie-isomorphic to a large family of vector fields with Bogdanov–Takens singularity. This gives rise to a conclusion that the local dynamics of formal Hopf-zero singularities is well-understood by the study of Bogdanov–Takens singularities. Despite this, the normal form computations of Bogdanov–Takens and Hopf-zero singularities are independent. Thus, by assuming a quadratic nonzero condition, complete results on the simplest Hopf-zero normal forms are obtained in terms of the conservative–nonconservative decomposition. Some practical formulas are derived and the results implemented using Maple. The method has been applied on the Rössler and Kuramoto–Sivashinsky equations to demonstrate the applicability of our results. (paper)
Normal forms of Hopf-zero singularity
Gazor, Majid; Mokhtari, Fahimeh
2015-01-01
The Lie algebra generated by Hopf-zero classical normal forms is decomposed into two versal Lie subalgebras. Some dynamical properties for each subalgebra are described; one is the set of all volume-preserving conservative systems while the other is the maximal Lie algebra of nonconservative systems. This introduces a unique conservative-nonconservative decomposition for the normal form systems. There exists a Lie-subalgebra that is Lie-isomorphic to a large family of vector fields with Bogdanov-Takens singularity. This gives rise to a conclusion that the local dynamics of formal Hopf-zero singularities is well-understood by the study of Bogdanov-Takens singularities. Despite this, the normal form computations of Bogdanov-Takens and Hopf-zero singularities are independent. Thus, by assuming a quadratic nonzero condition, complete results on the simplest Hopf-zero normal forms are obtained in terms of the conservative-nonconservative decomposition. Some practical formulas are derived and the results implemented using Maple. The method has been applied on the Rössler and Kuramoto-Sivashinsky equations to demonstrate the applicability of our results.
A Systolic Architecture for Singular Value Decomposition,
1983-01-01
Presented at the 1 st International Colloquium on Vector and Parallel Computing in Scientific Applications, Paris, March 191J Contract N00014-82-K.0703...Gene Golub. Private comunication . given inputs x and n 2 , compute 2 2 2 2 /6/ G. H. Golub and F. T. Luk : "Singular Value I + X1 Decomposition