查看更多>>摘要：In the present paper we develop a method of the vector fields Z(i) [9] in the theory of separation of variables. For an integrable case of the complex Kirchhoff's problem on e* (3), which has been never considered before, we construct-with the help of this method-two types of separation of variables (SoV): symmetric and asymmetric ones. Our asymmetric SoV is unusual: it is characterized by the quadratures containing differentials defined on two different curves of separation. It is a direct analogue of asymmetric SoV for the Clebsch model [17]. In the case of symmetric SoV both curves of separation are the same. This case has an additional bonus: on zero level set of one of the Casimir functions it yields a direct analogue of the famous Weber-Neumann separated coordinates. They are also considered in the present paper in some details. (C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：This article studies rank 2 Backlund transformations of hyperbolic Monge-Ampere systems using Cartan's method of equivalence. Such Backlund transformations have two main types, which we call Type A and Type B. For Type A, we completely determine a subclass whose local invariants satisfy a specific but simple algebraic constraint. We show that such Backlund transformations are parametrized by a finite number of constants; in a subcase of maximal symmetry, we determine the coordinate form of the underlying PDEs, which turn out to be Darboux integrable. For Type B, we present an invariantly formulated condition that determines whether a Backlund transformation is one that, under suitable choices of local coordinates, relates solutions of two PDEs of the form z(xy) = F(x, y, z, z(x), z(y)) and preserves the x, y variables on solutions. (C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this work we study discrete analogues of an exact sequence of vector bundles introduced by M. Atiyah in 1957, associated to any smooth principal G-bundle pi : Q -> Q/G. In the original setting, the splittings of the exact sequence correspond to connections on the principal bundle pi. The discrete analogues that we consider here can be studied in two different categories: the category of fiber bundles with a (chosen) section, Fbs, and the category of local Lie groupoids, lLGpd. In Fbs we find a correspondence between a) (semi-local) splittings of the discrete Atiyah sequence (DAS) of pi, b) discrete connections on the same bundle pi, and c) isomorphisms of the DAS with certain fiber product extensions in Fbs. We see that the right splittings of the DAS (in Fbs) are not necessarily right splittings in lLGpd: we use this obstruction to define the discrete curvature of a discrete connection. Then, there is a correspondence between the right splittings of the DAS in lLGpd and discrete connections with trivial discrete curvature, that is, flat discrete connections. We also introduce a semidirect product between (some) local Lie groupoids and prove that there is a correspondence between semidirect product extensions and right splittings of the DAS in lLGpd. (C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：For a Riemannian manifold (N, g), we construct a scalar flat neutral metric G on the tangent bundle TN. The metric is locally conformally flat if and only if either N is a 2-dimensional manifold or (N, g) is a real space form. It is also shown that G is locally symmetric if and only if g is locally symmetric. We then study submanifolds in TN and, in particular, find the conditions for a curve to be geodesic. The conditions for a Lagrangian graph in the tangent bundle TN to have parallel mean curvature are studied. Finally, using the cross product in R-3 we show that the space of oriented lines in R-3 can be minimally isometrically embedded in TR3. (C) 2021 The Authors. Published by Elsevier B.V.
查看更多>>摘要：A (2+1)-dimensional new generalized Korteweg-de Vries (ngKdV) equation is educed from a bilinear differential equation by combining the logarithmic transformation u = 2(lnf)x. Depending on bilinear equation, we can compute the Hirota N-soliton condition and Nsoliton solutions. The D'Alembert type waves of the (2+1)-dimensional ngKdV equation are shown via introducing traveling-wave variables. By dealing with the matching bilinear form, the multiple solitary solution that should fulfill the velocity resonance condition is found in the egKdV equation. Some of the figures of two-soliton molecules and threesoliton molecules are obtained by determining the appropriate arguments. (c) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：We are going to a further development of relations between formal measurement theory and thermodynamics. Higher-order geometrical structures on Lagrangian manifolds are introduced and their relations with an accuracy of measurement and confidence domains as well as phase transitions in thermodynamics are discussed. The approach is illustrated for the case of real gases and in detail for methane. (c) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：We introduce the notion of tame rho-quaternionic manifold that permits the construction of a finite family of p-connections, significant for the geometry involved. This provides, for example, the following: A new simple global characterisation of flat (complex-)quaternionic manifolds. A new simple construction of the metric and the corresponding Levi-Civita connection of a quaternionic-Kahler manifold by starting from its twistor space; moreover, our method provides a natural generalization of this correspondence. Also, a new construction of quaternionic manifolds is obtained, and the properties of twistorial harmonic morphisms with one-dimensional fibres from quaternionic-Kahler manifolds are studied. (C) 2021 Elsevier B.V. All rights reserved.
Maria Camacho, LuisaMaria Navarro, RosaOmirov, Bakhrom A.
13页
查看更多>>摘要：Throughout this paper we show that the method for describing finite-dimensional solvable Leibniz superalgebras with a given nilradical can be extended to infinite-dimensional ones, or so-called residually solvable Leibniz superalgebras. Prior to that, we improve the solvable extension method for the finite-dimensional case obtaining new and important results. Additionally, we fully determine the residually solvable Lie and Leibniz superalgebras with maximal codimension of pro-nilpotent ideals the model filiform Lie and null-filiform Leibniz superalgebras, respectively. Moreover, we prove that the residually solvable superalgebras obtained are complete. (C) 2021 The Authors. Published by Elsevier B.V.
查看更多>>摘要：Given any half-sided modular inclusion of standard subspaces, we show that the entropy function associated with the decreasing one-parameter family of translated standard subspaces is convex for any given (not necessarily smooth) vector in the underlying Hilbert space. In second quantisation, this infers the convexity of the vacuum relative entropy with respect to the translation parameter of the modular tunnel of von Neumann algebras. This result allows us to study the QNEC inequality for coherent states in a free Quantum Field Theory on a stationary curved spacetime, given a KMS state. To this end, we define wedge regions and appropriate (deformed) subregions. Examples are given by the Schwarzschild spacetime and null translated subregions with respect to the time translation Killing flow. More generally, we define wedge and strip regions on a globally hyperbolic spacetime, so to have non trivial modular inclusions of von Neumann algebras, and make our analysis in this context. (C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：In previous papers, a geometric framework has been developed to describe non-conservative field theories as a kind of modified Lagrangian and Hamiltonian field theories. This approach is that of k-contact Hamiltonian systems, which is based on the k-symplectic formulation of field theories as well as on contact geometry. In this work we present the Skinner-Rusk unified setting for these kinds of theories, which encompasses both the Lagrangian and Hamiltonian formalisms into a single picture. This unified framework is specially useful when dealing with singular systems, since: (i) it incorporates in a natural way the second-order condition for the solutions of field equations, (ii) it allows to implement the Lagrangian and Hamiltonian constraint algorithms in a unique simple way, and (iii) it gives the Legendre transformation, so that the Lagrangian and the Hamiltonian formalisms are obtained straightforwardly. We apply this description to several interesting physical examples: the damped vibrating string, the telegrapher's equations, and Maxwell's equations with dissipation terms. (c) 2021 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
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