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Journal articles on the topic 'Correspondence manifold'

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Author: Grafiati

Published: 10 December 2022

Last updated: 28 January 2023

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1

Perego, Arvid. "Kobayashi—Hitchin correspondence for twisted vector bundles." Complex Manifolds 8, no. 1 (January 1, 2021): 1–95. http://dx.doi.org/10.1515/coma-2020-0107.

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Abstract We prove the Kobayashi—Hitchin correspondence and the approximate Kobayashi—Hitchin correspondence for twisted holomorphic vector bundles on compact Kähler manifolds. More precisely, if X is a compact manifold and g is a Gauduchon metric on X, a twisted holomorphic vector bundle on X is g−polystable if and only if it is g−Hermite-Einstein, and if X is a compact Kähler manifold and g is a Kähler metric on X, then a twisted holomorphic vector bundle on X is g−semistable if and only if it is approximate g−Hermite-Einstein.

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2

Cortés, Vicente, and Liana David. "Twist, elementary deformation and K/K correspondence in generalized geometry." International Journal of Mathematics 31, no. 10 (September 2020): 2050078. http://dx.doi.org/10.1142/s0129167x20500780.

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We define the conformal change and elementary deformation in generalized complex geometry. We apply Swann’s twist construction to generalized (almost) complex and Hermitian structures obtained by these operations and establish conditions for the Courant integrability of the resulting twisted structures. We associate to any appropriate generalized Kähler manifold [Formula: see text] with a Hamiltonian Killing vector field a new generalized Kähler manifold, depending on the choice of a pair of non-vanishing functions and compatible twist data. We study this construction when [Formula: see text] is toric, with emphasis on the four-dimensional case, and we apply it to deformations of the standard flat Kähler metric on [Formula: see text], the Fubini–Study metric on [Formula: see text] and the admissible Kähler metrics on Hirzebruch surfaces. As a further application, we recover the K/K (Kähler/Kähler) correspondence, by specializing to ordinary Kähler manifolds.

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3

LI, Xiang-Ru, Xiao-Ming LI, Hai-Ling LI, and Mao-Yong CAO. "Rejecting Outliers Based on Correspondence Manifold." Acta Automatica Sinica 35, no. 1 (April 7, 2009): 17–22. http://dx.doi.org/10.3724/sp.j.1004.2009.00017.

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4

Liu, Dongquan, Quan Chen, Jun Yu, Huiqin Gu, Dacheng Tao, and Hock Soon Seah. "Stroke Correspondence Construction Using Manifold Learning." Computer Graphics Forum 30, no. 8 (June 23, 2011): 2194–207. http://dx.doi.org/10.1111/j.1467-8659.2011.01969.x.

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5

LI, Xiang-Ru, Xiao-Ming LI, Hai-Ling LI, and Mao-Yong CAO. "Rejecting Outliers Based on Correspondence Manifold." Acta Automatica Sinica 35, no. 1 (January 2009): 17–22. http://dx.doi.org/10.1016/s1874-1029(08)60065-8.

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6

Baykur, R. İnanç, and Osamu Saeki. "Simplified broken Lefschetz fibrations and trisections of 4-manifolds." Proceedings of the National Academy of Sciences 115, no. 43 (October 22, 2018): 10894–900. http://dx.doi.org/10.1073/pnas.1717175115.

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Shapes of 4D spaces can be studied effectively via maps to standard surfaces. We explain, and illustrate by quintessential examples, how to simplify such generic maps on 4-manifolds topologically, to derive simple decompositions into much better-understood manifold pieces. Our methods not only allow us to produce various interesting families of examples but also to establish a correspondence between simplified broken Lefschetz fibrations and simplified trisections of closed, oriented 4-manifolds.

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7

Bejancu, Aurel, and Hani Reda Farran. "Curvature of Cr Manifolds." Annals of the Alexandru Ioan Cuza University - Mathematics 59, no. 1 (January 1, 2013): 43–72. http://dx.doi.org/10.2478/v10157-012-0021-z.

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Abstract We prove the existence and uniqueness of a torsion-free and h-metric linear connection ▽(CR connection) on the horizontal distribution of a CR manifold M. Then we define the CR sectional curvature of M and obtain a characterization of the CR space forms. Also, by using the CR Ricci tensor and the CR scalar curvature we define the CR Einstein gravitational tensor field on M. Thus, we can write down Einstein equations on the horizontal distribution of the 5-dimensional CR manifold involved in the Penrose correspondence. Finally, some CR differential operators are defined on M and two examples are given to illustrate the theory developed in the paper. Most of the results are obtained for CR manifolds that do not satisfy the integrability conditions

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8

Ferreira, Ana Cristina. "Induced three-forms on instanton moduli spaces." International Journal of Geometric Methods in Modern Physics 11, no. 09 (October 2014): 1460041. http://dx.doi.org/10.1142/s021988781460041x.

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In this note we study a correspondence between the space of three-forms on a four-manifold and the space of three-forms on the moduli space of instantons. We then specialize to the case where the base manifold is the four-sphere.

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9

HAMENSTÄDT, URSULA. "Cocycles, Hausdorff measures and cross ratios." Ergodic Theory and Dynamical Systems 17, no. 5 (October 1997): 1061–81. http://dx.doi.org/10.1017/s0143385797086379.

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Let $f$ be a flip-invariant Hölder continuous function on the unit tangent bundle $T^1 M$ of a closed negatively curved Riemannian manifold $M$. We show that conditionals on strong unstable manifolds of the Gibbs equilibrium state defined by $f$ can be realized as Hausdorff measures. Moreover, cohomology classes of flip invariant cocycles are in one-to-one correspondence to cross ratios on the space of four pairwise distinct points of the ideal boundary of the universal covering $\tilde M$ of $M$.

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10

BISWAS, INDRANIL, and GEORG SCHUMACHER. "YANG–MILLS EQUATION FOR STABLE HIGGS SHEAVES." International Journal of Mathematics 20, no. 05 (May 2009): 541–56. http://dx.doi.org/10.1142/s0129167x09005406.

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We establish a Kobayashi–Hitchin correspondence for the stable Higgs sheaves on a compact Kähler manifold. Using it, we also obtain a Kobayashi–Hitchin correspondence for the stable Higgs G-sheaves, where G is any complex reductive linear algebraic group.

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11

GONZÁLEZ-FERNÁNDEZ, B., and A. CAMACHO. "FLUID-GRAVITY CORRESPONDENCE UNDER THE PRESENCE OF VISCOSITY." Modern Physics Letters A 27, no. 32 (October 11, 2012): 1250185. http://dx.doi.org/10.1142/s0217732312501854.

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This work addresses the analogy between the speed of sound of a viscous, barotropic, and irrotational fluid and the equation of motion for a non-massive field in a curved manifold. It will be shown that the presence of viscosity implies the introduction, into the equation of motion of the gravitational analogue, of a source term which entails the flow of energy from the non-massive field to the curvature of the spacetime manifold. The stress–energy tensor is also computed and it is found not to be constant, which is consistent with such energy interchange.

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12

Kang, Ensil. "Normal surfaces in non-compact 3-manifolds." Journal of the Australian Mathematical Society 78, no. 3 (June 2005): 305–21. http://dx.doi.org/10.1017/s1446788700008557.

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AbstractWe extend the normal surface Q-theory to non-compact 3-manifolds with respect to ideal triangulations. An ideal triangulation of a 3-manifold often has a small number of tetrahedra resulting in a system of Q-matching equations with a small number of variables. A unique feature of our approach is that a compact surface F with boundary properly embedded in a non-compact 3-manifold M with an ideal triangulation with torus cusps can be represented by a normal surface in M as follows. A half-open annulus made up of an infinite number of triangular disks is attached to each boundary component of F. The resulting surface , when normalized, will contain only a finite number of Q-disks and thus correspond to an admissible solution to the system of Q-matching equations. The correspondence is bijective.

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13

BRADLOW, STEVEN B., FRANZ W. KAMBER, and JAMES F. GLAZEBROOK. "THE HITCHIN–KOBAYASHI CORRESPONDENCE FOR TWISTED TRIPLES." International Journal of Mathematics 11, no. 04 (June 2000): 493–508. http://dx.doi.org/10.1142/s0129167x00000246.

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We introduce the twisted coupled vortex equations defined over a closed Kähler manifold X. There is an associated notion of stability for certain triples of holomorphic data on X. We establish a Hitchin–Kobayashi correspondence which relates the existence of solutions to these equations and the stability of a corresponding triple.

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14

CASALI, MARIA RITA, and PAOLA CRISTOFORI. "A CATALOGUE OF ORIENTABLE 3-MANIFOLDS TRIANGULATED BY 30 COLORED TETRAHEDRA." Journal of Knot Theory and Its Ramifications 17, no. 05 (May 2008): 579–99. http://dx.doi.org/10.1142/s0218216508006312.

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The present paper follows the computational approach to 3-manifold classification via edge-colored graphs, already performed in [1] (with respect to orientable 3-manifolds up to 28 colored tetrahedra), in [2] (with respect to non-orientable 3-manifolds up to 26 colored tetrahedra), in [3] and [4] (with respect to genus two 3-manifolds up to 34 colored tetrahedra): in fact, by automatic generation and analysis of suitable edge-colored graphs, called crystallizations, we obtain a catalogue of all orientable 3-manifolds admitting colored triangulations with 30 tetrahedra. These manifolds are unambiguously identified via JSJ decompositions and fibering structures. It is worth noting that, in the present work, a suitable use of elementary combinatorial moves yields an automatic partition of the elements of the generated crystallization catalogue into equivalence classes, which turn out to be in one-to-one correspondence with the homeomorphism classes of the represented manifolds.

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15

Ida, Cristian, Alexandru Ionescu, and Adelina Manea. "A note on para-holomorphic Riemannian–Einstein manifolds." International Journal of Geometric Methods in Modern Physics 13, no. 09 (September 20, 2016): 1650107. http://dx.doi.org/10.1142/s0219887816501073.

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The aim of this note is the study of Einstein condition for para-holomorphic Riemannian metrics in the para-complex geometry framework. First, we make some general considerations about para-complex Riemannian manifolds (not necessarily para-holomorphic). Next, using a one-to-one correspondence between para-holomorphic Riemannian metrics and para-Kähler–Norden metrics, we study the Einstein condition for a para-holomorphic Riemannian metric and the associated real para-Kähler–Norden metric on a para-complex manifold. Finally, it is shown that every semi-simple para-complex Lie group inherits a natural para-Kählerian–Norden Einstein metric.

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16

Cardona, Robert, Eva Miranda, and Daniel Peralta-Salas. "Euler flows and singular geometric structures." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 377, no. 2158 (September 30, 2019): 20190034. http://dx.doi.org/10.1098/rsta.2019.0034.

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Tichler proved (Tischler D. 1970 Topology 9 , 153–154. ( doi:10.1016/0040-9383(70)90037-6 )) that a manifold admitting a smooth non-vanishing and closed one-form fibres over a circle. More generally, a manifold admitting k -independent closed one-form fibres over a torus T k . In this article, we explain a version of this construction for manifolds with boundary using the techniques of b -calculus (Melrose R. 1993 The Atiyah Patodi Singer index theorem . Research Notes in Mathematics. Wellesley, MA: A. K. Peters; Guillemin V, Miranda E, Pires AR. 2014 Adv. Math. ( N. Y. ) 264 , 864–896. ( doi:10.1016/j.aim.2014.07.032 )). We explore new applications of this idea to fluid dynamics and more concretely in the study of stationary solutions of the Euler equations. In the study of Euler flows on manifolds, two dichotomic situations appear. For the first one, in which the Bernoulli function is not constant, we provide a new proof of Arnold's structure theorem and describe b -symplectic structures on some of the singular sets of the Bernoulli function. When the Bernoulli function is constant, a correspondence between contact structures with singularities (Miranda E, Oms C. 2018 Contact structures with singularities. https://arxiv.org/abs/1806.05638 ) and what we call b -Beltrami fields is established, thus mimicking the classical correspondence between Beltrami fields and contact structures (see for instance Etnyre J, Ghrist R. 2000 Trans. Am. Math. Soc. 352 , 5781–5794. ( doi:10.1090/S0002-9947-00-02651-9 )). These results provide a new technique to analyse the geometry of steady fluid flows on non-compact manifolds with cylindrical ends. This article is part of the theme issue ‘Topological and geometrical aspects of mass and vortex dynamics’.

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17

Ahsan, Zafar. "Ricci Solitons and the Spacetime of General Relativity." Journal of the Tensor Society 12, no. 01 (June 30, 2007): 49–64. http://dx.doi.org/10.56424/jts.v12i01.10592.

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The vector fields associated with Ricci flow and Ricci solitons in Riemann manifold has been studied and the correspondence between these vector fields and symmetries of spacetime manifold of general relativity has been established. The relationships between the symmetries of Petrov type D and N pure radiation fields and Ricci solitons have been explored. The solitons corresponding to Schwarzschild solution and Reissner-Nordstrom spacetime have been obtained.

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18

Bruzzo, Ugo, and Beatriz Graña Otero. "Approximate Hitchin–Kobayashi correspondence for Higgs G-bundles." International Journal of Geometric Methods in Modern Physics 11, no. 07 (August 2014): 1460015. http://dx.doi.org/10.1142/s0219887814600159.

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We announce a result about the extension of the Hitchin–Kobayashi correspondence to principal Higgs bundles. A principal Higgs bundle on a compact Kähler manifold, with structure group a connected linear algebraic reductive group, is semistable if and only if it admits an approximate Hermitian–Yang–Mills structure.

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19

YU, BIN. "Smale solenoid attractors and affine Hirsch foliations." Ergodic Theory and Dynamical Systems 39, no. 2 (May 4, 2017): 531–53. http://dx.doi.org/10.1017/etds.2017.30.

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The main purpose of this paper is to study north–south Smale solenoid diffeomorphisms on$3$-manifolds by using affine Hirsch foliations. A north–south Smale solenoid diffeomorphism$f$on a closed$3$-manifold$M$is a diffeomorphism whose non-wandering set is composed of a Smale solenoid attractor$\unicode[STIX]{x1D6EC}_{a}$and a Smale solenoid repeller$\unicode[STIX]{x1D6EC}_{r}$. The key observation is that a north–south Smale solenoid diffeomorphism$f$automatically induces two non-isotopically leaf-conjugate affine Hirsch foliations${\mathcal{H}}^{s}$and${\mathcal{H}}^{u}$on the orbit space of the wandering set of$f$(abbreviated to thewandering orbit spaceof$f$) by the stable and unstable manifolds of$\unicode[STIX]{x1D6EC}_{a}$and$\unicode[STIX]{x1D6EC}_{r}$, respectively. Under this viewpoint, we build some close relationships between north–south Smale solenoid diffeomorphisms and Hirsch manifolds (the closed$3$-manifolds admitting two non-isotopically leaf-conjugate affine Hirsch foliations).∙On the one hand, the union of the wandering orbit spaces is nearly in one-to-one correspondence with the union of Hirsch manifolds.∙On the other hand, surprisingly, the topology of the wandering orbit space (Hirsch manifold) is nearly a complete invariant of north–south Smale solenoid diffeomorphisms up to semi-global conjugacy.Moreover, as applications, we consider several more concrete questions. For instance, we prove that every diffeomorphism in many semi-global conjugacy classes of north–south Smale solenoid diffeomorphisms are not structurally stable.

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20

Hou, Chenping, Feiping Nie, Hua Wang, Dongyun Yi, and Changshui Zhang. "Learning high-dimensional correspondence via manifold learning and local approximation." Neural Computing and Applications 24, no. 7-8 (March 30, 2013): 1555–68. http://dx.doi.org/10.1007/s00521-013-1369-z.

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21

Schwartzman, Sol. "Higher Dimensional Asymptotic Cycles." Canadian Journal of Mathematics 55, no. 3 (June 1, 2003): 636–48. http://dx.doi.org/10.4153/cjm-2003-026-0.

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AbstractGiven a p-dimensional oriented foliation of an n-dimensional compact manifold Mn and a transversal invariant measure τ, Sullivan has defined an element of Hp(Mn; R). This generalized the notion of a μ-asymptotic cycle, which was originally defined for actions of the real line on compact spaces preserving an invariant measure μ. In this one-dimensional case there was a natural 1—1 correspondence between transversal invariant measures τ and invariant measures μ when one had a smooth flow without stationary points.For what we call an oriented action of a connected Lie group on a compact manifold we again get in this paper such a correspondence, provided we have what we call a positive quantifier. (In the one-dimensional case such a quantifier is provided by the vector field defining the flow.) Sufficient conditions for the existence of such a quantifier are given, together with some applications.

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22

CIELIEBAK, K., and E. VOLKOV. "A note on the stationary Euler equations of hydrodynamics." Ergodic Theory and Dynamical Systems 37, no. 2 (October 6, 2015): 454–80. http://dx.doi.org/10.1017/etds.2015.50.

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This note concerns stationary solutions of the Euler equations for an ideal fluid on a closed 3-manifold. We prove that if the velocity field of such a solution has no zeroes and real analytic Bernoulli function, then it can be rescaled to the Reeb vector field of a stable Hamiltonian structure. In particular, such a vector field has a periodic orbit unless the 3-manifold is a torus bundle over the circle. We provide a counterexample showing that the correspondence breaks down without the real analyticity hypothesis.

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23

Su, Rina, and Chunrui Zhang. "Hopf-zero bifurcation of the ring unidirectionally coupled Toda oscillators with delay." Nonlinear Analysis: Modelling and Control 26, no. 3 (May 1, 2021): 375–95. http://dx.doi.org/10.15388/namc.2021.26.23050.

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In this paper, the Hopf-zero bifurcation of the ring unidirectionally coupled Toda oscillators with delay was explored. First, the conditions of the occurrence of Hopf-zero bifurcation were obtained by analyzing the distribution of eigenvalues in correspondence to linearization. Second, the stability of Hopf-zero bifurcation periodic solutions was determined based on the discussion of the normal form of the system, and some numerical simulations were employed to illustrate the results of this study. Lastly, the normal form of the system on the center manifold was derived by using the center manifold theorem and normal form method.

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24

WRIGHT, GRETCHEN. "THE RESHETIKHIN-TURAEV REPRESENTATION OF THE MAPPING CLASS GROUP." Journal of Knot Theory and Its Ramifications 03, no. 04 (December 1994): 547–74. http://dx.doi.org/10.1142/s021821659400040x.

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The Reshetikhin-Turaev representation of the mapping class group of an orientable surface is computed explicitly in the case r = 4. It is then shown that the restriction of this representation to the Torelli group is equal to the sum of the Birman-Craggs homomorphisms. The proof makes use of an explicit correspondence between the basis vectors of the representation space, and the Z/2Z-quadratic forms on the first homology of the surface. This result corresponds to the fact, shown by Kirby and Melvin, that the three-manifold invariant when r = 4 is related to spin structures on the associated four-manifold.

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25

Planat, Michel, Raymond Aschheim, Marcelo Amaral, and Klee Irwin. "Universal Quantum Computing and Three-Manifolds." Symmetry 10, no. 12 (December 19, 2018): 773. http://dx.doi.org/10.3390/sym10120773.

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A single qubit may be represented on the Bloch sphere or similarly on the 3-sphere S 3 . Our goal is to dress this correspondence by converting the language of universal quantum computing (UQC) to that of 3-manifolds. A magic state and the Pauli group acting on it define a model of UQC as a positive operator-valued measure (POVM) that one recognizes to be a 3-manifold M 3 . More precisely, the d-dimensional POVMs defined from subgroups of finite index of the modular group P S L ( 2 , Z ) correspond to d-fold M 3 - coverings over the trefoil knot. In this paper, we also investigate quantum information on a few ‘universal’ knots and links such as the figure-of-eight knot, the Whitehead link and Borromean rings, making use of the catalog of platonic manifolds available on the software SnapPy. Further connections between POVMs based UQC and M 3 ’s obtained from Dehn fillings are explored.

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26

Belkin, Mikhail, and Partha Niyogi. "Laplacian Eigenmaps for Dimensionality Reduction and Data Representation." Neural Computation 15, no. 6 (June 1, 2003): 1373–96. http://dx.doi.org/10.1162/089976603321780317.

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One of the central problems in machine learning and pattern recognition is to develop appropriate representations for complex data. We consider the problem of constructing a representation for data lying on a low-dimensional manifold embedded in a high-dimensional space. Drawing on the correspondence between the graph Laplacian, the Laplace Beltrami operator on the manifold, and the connections to the heat equation, we propose a geometrically motivated algorithm for representing the high-dimensional data. The algorithm provides a computationally efficient approach to nonlinear dimensionality reduction that has locality-preserving properties and a natural connection to clustering. Some potential applications and illustrative examples are discussed.

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27

Li, Bang-He, and Gui-Song Li. "Immersions with non-zero normal vector fields." Mathematical Proceedings of the Cambridge Philosophical Society 112, no. 2 (September 1992): 281–85. http://dx.doi.org/10.1017/s0305004100070961.

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Let M be a smooth n-manifold, X be a smooth (2n − 1)-manifold, and g:M → X be a map. It was proved in [6] that g is always homotopic to an immersion. The set of homotopy classes of monomorphisms from TM into g*TX, which is denoted by Sg, may be enumerated either by the method of I. M. James and E. Thomas or by the singularity method of U. Koschorke (see [1] and references therein). When the natural action of π1(XM, g) on Sg is trivial, for example, if X is euclidean, the set Sg is in one-to-one correspondence with the set of regular homotopy classes of immersions homotopic to g (see e.g. [4]).

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28

LÖBUS, JÖRG-UWE. "A FLAT COPY OF THE ORNSTEIN–UHLENBECK OPERATOR ON THE PATH SPACE OVER A RIEMANNIAN MANIFOLD." Infinite Dimensional Analysis, Quantum Probability and Related Topics 05, no. 03 (September 2002): 351–94. http://dx.doi.org/10.1142/s0219025702000900.

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A representation of a diffusion operator A on a certain space of right continuous trajectories in ℝd is derived. This operator A can be regarded as a flat copy of the Ornstein–Uhlenbeck operator on the path space over a Riemannian manifold. The correspondence to E. P. Hsu's representation of the Ornstein–Uhlenbeck operator is shown. Furthermore, an alternative treatment of conditional expectations of A is given.

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29

Dioos, Bart. "Non-conformal harmonic maps into the 3-sphere." International Journal of Geometric Methods in Modern Physics 12, no. 08 (September 2015): 1560012. http://dx.doi.org/10.1142/s0219887815600129.

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We present two transforms of non-conformal harmonic maps from a surface into the 3-sphere. With these transforms one can construct from one non-conformal harmonic map a sequence of non-conformal harmonic maps. We also discuss the correspondence between non-conformal harmonic maps into the 3-sphere, H-surfaces in Euclidean 3-space and almost complex surfaces in the nearly Kähler manifold S3 × S3.

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30

Borówka, Aleksandra. "Quaternion-Kähler manifolds near maximal fixed point sets of $$S^1$$-symmetries." Annali di Matematica Pura ed Applicata (1923 -) 199, no. 3 (October 17, 2019): 1243–62. http://dx.doi.org/10.1007/s10231-019-00920-2.

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Abstract Using quaternionic Feix–Kaledin construction, we provide a local classification of quaternion-Kähler metrics with a rotating $$S^1$$S1-symmetry with the fixed point set submanifold S of maximal possible dimension. For any real-analytic Kähler manifold S equipped with a line bundle with a real-analytic unitary connection with curvature proportional to the Kähler form, we explicitly construct a holomorphic contact distribution on the twistor space obtained by the quaternionic Feix–Kaledin construction from these data. Conversely, we show that quaternion-Kähler metrics with a rotating $$S^1$$S1-symmetry induce on the fixed point set of maximal dimension a Kähler metric together with a unitary connection on a holomorphic line bundle with curvature proportional to the Kähler form and the two constructions are inverse to each other. Moreover, we study the case when S is compact, showing that in this case the quaternion-Kähler geometry is determined by the Kähler metric on the fixed point set (of maximal possible dimension) and by the contact line bundle along the corresponding submanifold on the twistor space. Finally, we relate the results to the c-map construction showing that the family of quaternion-Kähler manifolds obtained from a fixed Kähler metric on S by varying the line bundle and the hyperkähler manifold obtained by hyperkähler Feix–Kaledin construction from S are related by hyperkähler/quaternion-Kähler correspondence.

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31

Abgaryan, Vahagn, and Arsen Khvedelidze. "On Families of Wigner Functions for N-Level Quantum Systems." Symmetry 13, no. 6 (June 4, 2021): 1013. http://dx.doi.org/10.3390/sym13061013.

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A method for constructing all admissible unitary non-equivalent Wigner quasiprobability distributions providing the Stratonovic-h-Weyl correspondence for an arbitrary N-level quantum system is proposed. The method is based on the reformulation of the Stratonovich–Weyl correspondence in the form of algebraic “master equations” for the spectrum of the Stratonovich–Weyl kernel. The later implements a map between the operators in the Hilbert space and the functions in the phase space identified by the complex flag manifold. The non-uniqueness of the solutions to the master equations leads to diversity among the Wigner quasiprobability distributions. It is shown that among all possible Stratonovich–Weyl kernels for a N=(2j+1)-level system, one can always identify the representative that realizes the so-called SU(2)-symmetric spin-j symbol correspondence. The method is exemplified by considering the Wigner functions of a single qubit and a single qutrit.

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32

Gillespie, Mark, Nicholas Sharp, and Keenan Crane. "Integer coordinates for intrinsic geometry processing." ACM Transactions on Graphics 40, no. 6 (December 2021): 1–13. http://dx.doi.org/10.1145/3478513.3480522.

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This paper describes a numerically robust data structure for encoding intrinsic triangulations of polyhedral surfaces. Many applications demand a correspondence between the intrinsic triangulation and the input surface, but existing data structures either rely on floating point values to encode correspondence, or do not support remeshing operations beyond basic edge flips. We instead provide an integer-based data structure that guarantees valid correspondence, even for meshes with near-degenerate elements. Our starting point is the framework of normal coordinates from geometric topology, which we extend to the broader set of operations needed for mesh processing (vertex insertion, edge splits, etc. ). The resulting data structure can be used as a drop-in replacement for earlier schemes, automatically improving reliability across a wide variety of applications. As a stress test, we successfully compute an intrinsic Delaunay refinement and associated subdivision for all manifold meshes in the Thingi10k dataset. In turn, we can compute reliable and highly accurate solutions to partial differential equations even on extremely low-quality meshes.

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33

FLOHR, MICHAEL A. I. "CURIOSITIES AT c-EFFECTIVE = 1." Modern Physics Letters A 09, no. 12 (April 20, 1994): 1071–82. http://dx.doi.org/10.1142/s0217732394000897.

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The moduli space of all rational conformal quantum field theories with effective central charge c eff = 1 is considered. Whereas the space pf unitary theories essentially forms a manifold, the nonunitary ones form a fractal which lies dense in the parameter plane. Moreover, the points of this set are shown to be in one-to-one correspondence with the elements of the modular group for which an action on this set is defined.

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34

D’Agnolo, Andrea, and Masaki Kashiwara. "Enhanced perversities." Journal für die reine und angewandte Mathematik (Crelles Journal) 2019, no. 751 (June 1, 2019): 185–241. http://dx.doi.org/10.1515/crelle-2016-0062.

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AbstractOn a complex manifold, the Riemann–Hilbert correspondence embeds the triangulated category of (not necessarily regular) holonomic {\mathcal{D}}-modules into the triangulated category of {\mathbb{R}}-constructible enhanced ind-sheaves. The source category has a standard t-structure. Here, we provide the target category with a middle perversity t-structure, and prove that the embedding is exact.In the paper, we also discuss general perversities in the framework of {\mathbb{R}}-constructible enhanced ind-sheaves on bordered subanalytic spaces.

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35

ÁLVAREZ-CÓNSUL, LUIS, and OSCAR GARCÍA-PRADA. "DIMENSIONAL REDUCTION, ${\rm SL} (2, {\mathbb C})$-EQUIVARIANT BUNDLES AND STABLE HOLOMORPHIC CHAINS." International Journal of Mathematics 12, no. 02 (March 2001): 159–201. http://dx.doi.org/10.1142/s0129167x01000745.

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In this paper we study gauge theory on [Formula: see text]-equivariant bundles over X × ℙ1, where X is a compact Kähler manifold, ℙ1 is the complex projective line, and the action of [Formula: see text] is trivial on X and standard on ℙ1. We first classify these bundles, showing that they are in correspondence with objects on X — that we call holomorphic chains — consisting of a finite number of holomorphic bundles ℰi and morphisms ℰi → ℰi-1. We then prove a Hitchin–Kobayashi correspondence relating the existence of solutions to certain natural gauge-theoretic equations and an appropriate notion of stability for an equivariant bundle and the corresponding chain. A central tool in this paper is a dimensional reduction procedure which allow us to go from X × ℙ1 to X.

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SHIPMAN, BARBARA A. "A UNIPOTENT GROUP ACTION ON A FLAG MANIFOLD AND "GAP SEQUENCES" OF PERMUTATIONS." Journal of Algebra and Its Applications 02, no. 02 (June 2003): 215–22. http://dx.doi.org/10.1142/s0219498803000507.

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There is a unipotent subgroup of Sl(n, C) whose action on the flag manifold of Sl(n, C) completes the flows of the complex Kostant–Toda lattice (a Hamiltonian system in Lax form) through initial conditions where all the eigenvalues coincide. The action preserves the Bruhat cells, which are in one-to-one correspondence with the elements of the permutation group Σn. A generic orbit in a given cell is homeomorphic to Cm, where m is determined by the "gap sequence" of the permutation, which lists the number inversions of each degree.

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ISIDRO, JOSÉ M. "MODULI OF QUANTA." International Journal of Geometric Methods in Modern Physics 03, no. 02 (March 2006): 177–86. http://dx.doi.org/10.1142/s0219887806001089.

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The classical phase of the matrix model of 11-dimensional M-theory is complex, infinite-dimensional Hilbert space. As a complex manifold, the latter admits a continuum of nonequivalent, complex-differentiable structures that can be placed in 1-to-1 correspondence with families of coherent states in the Hilbert space of quantum states. The moduli space of nonbiholomorphic complex structures on classical phase space turns out to be an infinite-dimensional symmetric space. We argue that each choice of a complex differentiable structure gives rise to a physically different notion of an elementary quantum.

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Gassner, Steven, Carlo Cafaro, Sean A. Ali, and Paul M. Alsing. "Information geometric aspects of probability paths with minimum entropy production for quantum state evolution." International Journal of Geometric Methods in Modern Physics 18, no. 08 (May 8, 2021): 2150127. http://dx.doi.org/10.1142/s0219887821501279.

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We present an information geometric analysis of both entropic speeds and entropy production rates arising from geodesic evolution on manifolds parametrized by pure quantum states. In particular, we employ pure states that emerge as outputs of suitably chosen [Formula: see text] time-dependent Hamiltonian operators that characterize analog quantum search algorithms of specific types. The [Formula: see text] Hamiltonian models under consideration are specified by external time-dependent magnetic fields within which spin-[Formula: see text] test particles are immersed. The positive definite Riemannian metrization of the parameter manifold is furnished by the Fisher information function. The Fisher information function is evaluated along parametrized squared probability amplitudes obtained from the temporal evolution of these spin-[Formula: see text] test particles. A minimum action approach is then utilized to induce the transfer of the quantum system from its initial state to its final state on the parameter manifold over a finite temporal interval. We demonstrate in an explicit manner that the minimal (that is, optimum) path corresponds to the shortest (that is, geodesic) path between the initial and final states. Furthermore, we show that the minimal path serves also to minimize the total entropy production occurring during the transfer of states. Finally, upon evaluating the entropic speed as well as the total entropy production along optimal transfer paths within several scenarios of physical interest in analog quantum searching algorithms, we demonstrate in a transparent quantitative manner a correspondence between a faster transfer and a higher rate of entropy production. We therefore conclude that higher entropic speed is associated with lower entropic efficiency within the context of quantum state transfer.

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FUCHSSTEINER, BENNO, and GUDRUN OEVEL. "GEOMETRY AND ACTION-ANGLE VARIABLES OF MULTI SOLITON SYSTEMS." Reviews in Mathematical Physics 01, no. 04 (January 1989): 415–79. http://dx.doi.org/10.1142/s0129055x8900016x.

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For all completely integrable nonlinear hamiltonian systems which have a localized hereditary recursion operator, a complete action-angle variable representation is given for the multisoliton manifolds. Here multisoliton manifolds are defined as reductions with respect to suitable linear sums of symmetry generators. The embedding of these multisoliton manifolds, into the manifold of all solutions, is described in terms of the construction of its tangent bundle. The basis vectors of the respective tangent spaces are given by local densities. This local geometrical description of the tangent bundle turns out to be independent of the special structure of the particular equation under consideration. The principal tool for finding the necessary geometrical quantities are the canonical commutation relations for the so called mastersymmetries. These relations reflect the hereditary structure. All mastersymmetries turn out to be elements of the tangent space. Although the mastersymmetries, in the case under consideration, principally cannot be hamiltonian, suitable integrating factors are found which make them hamiltonian on the reduced manifold. So, up to suitable linear combinations, the mastersymmetries are shown to correspond to the angle variables. The action-angle-structure found in this way is put into one-to-one correspondence with the spectrum of the recursion operator. The spectrum of this operator is shown to be of multiplicity two and all its eigenvectors are explicitly constructed. Again, this construction is of a canonical nature, i.e., independent of the particular equation under consideration. For vanishing boundary conditions the given action-angle-structure is compared to the asymptotic data (speeds and phases), and the gradients of these global asymptotic data are given in terms of local quantities. It turns out that for all times during the evolution the derivatives of the field function with respect to any particular asymptotic datum yields an eigenvector of the recursion operator. Thus a method is given for reconstructing the spectral resolution of the recursion operator by partial derivatives. This method yields new methods of solution for other equations (for example the singularity equation and the Harry Dym equation). The superposition formula for phase shifts is shown to hold in all generality for the systems under consideration. Several examples are given. An extensive comparison of the present results with the work of others is carried out.

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40

Ramtke, Nora. "Kotzebues journalliterarisches Nachleben." Internationales Archiv für Sozialgeschichte der deutschen Literatur 44, no. 1 (June 4, 2019): 3–38. http://dx.doi.org/10.1515/iasl-2019-0002.

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Abstract Introduced in response to the assassination of August von Kotzebue, the Carlsbad Decrees of 1819 marked a new era in German press and censorship history. Whereas the historical developments surrounding the Decrees have been well researched, this article traces Kotzebue’s literary afterlife by focusing on a series of fictional letters ostensibly written by the dead author. Drawing on the genre tradition of the dialogues of the dead, this fictional correspondence was published (and occasionally censored) in various periodicals of the early 1820 s and thus explored the manifold ramifications of the new restrictive press law.

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41

Mayer, Martin. "Prescribing Morse scalar curvatures: Critical points at infinity." Advances in Calculus of Variations 15, no. 2 (January 20, 2022): 151–90. http://dx.doi.org/10.1515/acv-2019-0009.

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Abstract The problem of prescribing conformally the scalar curvature of a closed Riemannian manifold as a given Morse function reduces to solving an elliptic partial differential equation with critical Sobolev exponent. Two ways of attacking this problem consist in subcritical approximations or negative pseudogradient flows. We show under a mild nondegeneracy assumption the equivalence of both approaches with respect to zero weak limits, in particular a one-to-one correspondence of zero weak limit finite energy subcritical blow-up solutions, zero weak limit critical points at infinity of negative type and sets of critical points with negative Laplacian of the function to be prescribed.

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Jiao, Shichao, Xie Han, Fengguang Xiong, Fusheng Sun, Rong Zhao, and Liqun Kuang. "Cross-Domain Correspondence for Sketch-Based 3D Model Retrieval Using Convolutional Neural Network and Manifold Ranking." IEEE Access 8 (2020): 121584–95. http://dx.doi.org/10.1109/access.2020.3006585.

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Spera, Mauro, and Tilmann Wurzbacher. "Determinants, Pfaffians and Quasi-Free Representations of the CAR Algebra." Reviews in Mathematical Physics 10, no. 05 (July 1998): 705–21. http://dx.doi.org/10.1142/s0129055x98000227.

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In this paper we apply the theory of quasi-free states of CAR algebras and Bogolubov automorphisms to give an alternative C*-algebraic construction of the Determinant and Pfaffian line bundles discussed by Pressley and Segal and by Borthwick. The basic property of the Pfaffian of being the holomorphic square root of the Determinant line bundle (after restriction from the Hilbert space Grassmannian to the Siegel manifold, or isotropic Grassmannian, consisting of all complex structures on an associated Hilbert space) is derived from a Fock–anti-Fock correspondence and an application of the Powers–Størmer purification procedure. A Borel–Weil type description of the infinite dimensional Spin c- representation is obtained, via a Shale–Stinespring implementation of Bogolubov transformations.

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SCORPAN, ALEXANDRU. "NOWHERE-ZERO HARMONIC SPINORS AND THEIR ASSOCIATED SELF-DUAL 2-FORMS." Communications in Contemporary Mathematics 04, no. 01 (February 2002): 45–63. http://dx.doi.org/10.1142/s0219199702000580.

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Let M be a closed oriented 4-manifold, with Riemannian metric g, and a [Formula: see text]-structure induced by an almost-complex structure ω. Each connection A on the determinant line bundle induces a unique connection ∇A, and Dirac operator [Formula: see text] on spinor fields. Let [Formula: see text] be the natural squaring map, taking self-dual spinors to self-dual 2-forms. In this paper, we characterize the self-dual 2-forms that are images of self-dual spinor fields through σ. They are those α for which (off zeros) c1(α)=c1(ω), where c1(α) is a suitably defined Chern class. We also obtain the formula: [Formula: see text]. Using these, we establish a bijective correspondence between: {Kähler forms α compatible with a metric scalar-multiple of g, and with c1(α)=c1(ω)} and {gauge classes of pairs (φ,A), with ∇Aφ=0}, as well as a bijective correspondence between: {Symplectic forms α compatible with a metric conformal to g, and with c1(α)=c1(ω)} and {gauge classes of pairs (φ,A), with [Formula: see text], and <∇Aφ,iφ>ℝ=0, and φ nowhere-zero}.

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45

Planat, Michel, Raymond Aschheim, Marcelo M. Amaral, and Klee Irwin. "Quantum Computing, Seifert Surfaces, and Singular Fibers." Quantum Reports 1, no. 1 (April 24, 2019): 12–22. http://dx.doi.org/10.3390/quantum1010003.

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The fundamental group π 1 ( L ) of a knot or link L may be used to generate magic states appropriate for performing universal quantum computation and simultaneously for retrieving complete information about the processed quantum states. In this paper, one defines braids whose closure is the L of such a quantum computer model and computes their braid-induced Seifert surfaces and the corresponding Alexander polynomial. In particular, some d-fold coverings of the trefoil knot, with d = 3 , 4, 6, or 12, define appropriate links L, and the latter two cases connect to the Dynkin diagrams of E 6 and D 4 , respectively. In this new context, one finds that this correspondence continues with Kodaira’s classification of elliptic singular fibers. The Seifert fibered toroidal manifold Σ ′ , at the boundary of the singular fiber E 8 ˜ , allows possible models of quantum computing.

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46

Graf, Rüdiger. "OF ALCOHOL, APES, AND TAXES: GÜNTER SCHMÖLDERS AND THE REINVENTION OF ECONOMICS IN BEHAVIORAL TERMS." Journal of the History of Economic Thought 43, no. 4 (October 11, 2021): 564–86. http://dx.doi.org/10.1017/s1053837220000267.

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The article examines an early and idiosyncratic version of behavioral economics or “empirical socio-economics,” which the German economist and taxation expert Günter Schmölders developed in the postwar decades. Relying on both his published papers and his lecture notes and correspondence, it scrutinizes Schmölders’s intellectual upbringing in the tradition of the Historical School of Economics (Historische Schule der Nationalökonomie) and his relation to the emerging ordoliberalism, demonstrating that the roads that led to dissatisfaction with the emerging neoclassical mainstream and the unrealistic behavioral assumptions of macroeconomic models were manifold. Accordingly, it shows that behavioral economics is compatible with various intellectual and political backgrounds and convictions. Yet, it still forms a distinct entity: comparing Schmölders with contemporary and later behavioral economists, I will show that they shared essential methodological assumptions as well as an understanding of human beings as decision-making organisms.

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47

Belfakir, A., A. belhaj, Y. El Maadi, S. E. Ennadifi, Y. Hassouni, and A. Segui. "Stringy dyonic solutions and clifford structures." International Journal of Geometric Methods in Modern Physics 16, no. 09 (September 2019): 1950138. http://dx.doi.org/10.1142/s021988781950138x.

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Using the toroidal compactification of string theory on [Formula: see text]-dimensional tori, [Formula: see text], we investigate dyonic objects in arbitrary dimensions. First, we present a class of dyonic black solutions formed by two different D-branes using a correspondence between toroidal cycles and objects possessing both magnetic and electric charges, belonging to [Formula: see text] dyonic gauge symmetry. This symmetry could be associated with electrically charged magnetic monopole solutions in stringy model buildings of the standard model (SM) extensions. Then, we consider in some detail such black hole classes obtained from even-dimensional toroidal compactifications, and we find that they are linked to [Formula: see text] Clifford algebras using the vee product. It is believed that this analysis could be extended to dyonic objects which can be obtained from local Calabi–Yau manifold compactifications.

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48

Loop, Jan. "Johann Heinrich Hottinger (1620–1667) and the “Historia Orientalis”." Church History and Religious Culture 88, no. 2 (2008): 169–203. http://dx.doi.org/10.1163/187124108x354312.

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AbstractGenerally neglected by scholars of the history of oriental studies, Johann Heinrich Hottinger's Historia Orientalis (1651, 2nd ed. 1660) is one of the most significant contributions to the history of Islam to have been published in the seventeenth century. This article analyses Hottinger's interest in Islam and in Arabic sources across the range of his writings and his correspondence, with a special focus on the Historia Orientalis. It discusses the philological and antiquarian standards by which he assessed Arab history and it describes the numerous Islamic manuscripts he exploited. It also examines the manifold ways in which Hottinger used the Koran and other Islamic sources to corroborate his apologetic Protestant interpretation of Church history. It thus sheds a light on the impact that a combination of confessional commitment, antiquarianism, and philology had on the rise of oriental studies in seventeenth-century Europe.

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KLEBANOV, IGOR R. "QCD AND STRING THEORY." International Journal of Modern Physics A 21, no. 08n09 (April 10, 2006): 1831–43. http://dx.doi.org/10.1142/s0217751x06032794.

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This talk begins with some history and basic facts about string theory and its connections with strong interactions. Comparisons of stacks of Dirichlet branes with curved backgrounds produced by them are used to motivate the AdS/CFT correspondence between superconformal gauge theory and string theory on a product of Anti-de Sitter space and a compact manifold. The ensuing duality between semi-classical spinning strings and long gauge theory operators is briefly reviewed. Strongly coupled thermal SYM theory is explored via a black hole in 5-dimensional AdS space, which leads to explicit results for its entropy and shear viscosity. A conjectured universal lower bound on the viscosity to entropy density ratio, and its possible relation to recent results from RHIC, are discussed. Finally, some available results on string duals of confining gauge theories are briefly reviewed.

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CHENG, TAIWANG, JIE LIU, and SHIGANG CHEN. "IONIZATION AND STABILIZATION OF A ONE-DIMENSIONAL MODEL ATOM: MAP APPROACH." International Journal of Modern Physics B 13, no. 12 (May 20, 1999): 1489–502. http://dx.doi.org/10.1142/s0217979299001533.

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In this paper, the interactions between a one-dimensional model atom and intense laser field is approximately described by a map. Both the classical version and quantum version of this map are studied. It is shown that besides classical stable islands which can bound some phase space region against ionization and then are responsible for the atomic stabilization, there is another structure in phase space, the unstable manifold, which can determine the ionization process of the system. Quantumly, the quantum quasienergy eigenstates (QE state) under absorptive boundaries, which directly related to the ionization process, are calculated. We define the QE state with smallest ionization rate as QE0 state, which represents the stabilization degree. The Wigner distribution of such QE0 state show clear fringe structures. Finally we show that the classical description and quantum description are in a correspondence manner.

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