查看更多>>摘要：We introduce the notion of harmonic map from a graph into a Riemannian manifold via a discrete version of the energy density. Existence and basic properties are established. Global existence and convergence of the associated heat flow are proved without any assumption on the curvature of the target manifold. We discuss a variant of the Steiner problem which replaces length by elastic energy. (C)& nbsp;2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：We give the necessary and sufficient conditions for Jacobi operators that determine an algebraic curvature tensor. This motivates us to introduce the new concept of Jacobi proportional Riemannian tensors, whose special case is the Rakic acute accent duality principle. We prove that all known Osserman tensors (both two-root Osserman and Clifford) are Jacobi-proportional. After the results given by Nikolayevsky, it is known that possible counterexamples of the Osserman conjecture can occur in dimension 16 only, while the reduced Jacobi operator has an eigenvalue of multiplicity 7 or 8. We prove that Jacobi proportional Osserman tensors that do not satisfy the Osserman conjecture are 2-root with multiplicities 8 and 7, or 3-root with multiplicities 7, 7, and 1. (C)& nbsp;2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this paper, we take advantage of envelope theory and singularity theory to study the evolutoids and pedaloids in Minkowski plane. We illustrate an internal correlation from algebraic and geometric viewpoints, and give the geometric explanation of evolutoids and pedaloids. Then, we generalize the notions of evolutoids and pedaloids to the category of frontals in Minkowski plane. Furthermore, we apply the technique of singularity theory, using the discriminants and versal unfolding tools, to consider evolving evolutoids and give the classifications of singularities of the evolutoids, and explain when cusps and inflexions occur and how evolutoids evolving. Besides, we found that there is a close relationship between the evolutoids and pedaloids and good correspondence between their singularities.(c) 2022 Elsevier B.V. All rights reserved.
Seadawy, Aly R.Ahmed, S.Rizvi, Syed T. R.Ali, K....
22页
查看更多>>摘要：This article retrieves multiple lump, periodic cross kink, rogue wave, multiwave, breathers, M-shaped and interactional solutions for generalized Vakhnenko Parkes (gVP) equation via appropriate transformations. This leads to a transformed equation for which it is straightforward to evaluate the exact solutions. The gVP equation gives a description of high-frequency waves in the relaxation medium possessing periodic and solitary traveling wave solutions some of which are loop-like in nature. These types of solutions have been observed in wave propagations, rogue waves and many other physical systems. We also interpret some of our solutions in distinct dimensions via 3D, 2D, contours and density profiles.(c) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this paper we investigate the geometric structure and control of exponential families depending on additional parameters, called external parameters. These generalized exponential families emerge naturally when one applies the maximum entropy formalism to derive the equilibrium statistical mechanics framework. We study the associated statistical model, compute the Fisher metric and introduce a natural fibration of the parameter space over the external parameter space. The Fisher Riemannian metric allows to endow this fibration with an Ehresmann connection and to study the geometry and control of these statistical models. As an example, we show that horizontal lift of paths in the external parameter space corresponds to an isentropic evolution of the system. We apply the theory to the example of an ideal gas and an ideal gas in a rotating rigid container.(c) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：This paper introduces a new characterization of Kenmotsu manifolds and analyzes curvature conditions of Kenmotsu manifolds admitting the Q tensor whose trace is the well-known Z tensor. New types of Kenmotsu manifold are defined which are named phi - Q symmetric Kenmotsu manifold and phi - Q recurrent Kenmotsu manifold. Various properties of such a 2m + 1-dimensional Kenmotsu manifold are studied. A theorem is given which states that a three-dimensional locally phi - Q recurrent and locally phi - Q symmetric Kenmotsu manifold admitting Q tensor is a manifold of constant curvature. Some examples of locally phi- Q symmetric Kenmotsu manifolds and Kenmotsu manifolds admitting Q tensor are provided.(c) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：This study presents a semi-symmetric non-metric connection on statistical manifolds and their submanifolds. The study determines some fundamental properties for the curvature tensor and proves the induced connection on the submanifold with the semi-symmetric non-metric connection. Also, the Gauss, Codazzi, and Ricci equations admitting semi symmetric non-metric connection have been examined. Finally, a constructive example of such type manifolds is presented. (C)& nbsp;2022 Elsevier B.V. All rights reserved.
Samir, IslamBadra, NiveenSeadawy, Aly R.Ahmed, Hamdy M....
10页
查看更多>>摘要：In this work, the improved modified extended tanh function method will be applied to study the perturbed Gerdjikov-Ivanov equation (PGI) which describe the dynamics of the soliton in optical fibers. New exact solutions for the PGI equation will be introduced including Weierstrass elliptic, Jacobi elliptic, dark and bright solitons, singular periodic and rational type solutions. Moreover, for the physical illustration of the obtained solutions, 3D and 2D graphs are presented. (C) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this paper, we use the unified method to research the variable coefficients Sasa-Satsuma model equation, which describes the nonlinear phenomenon of pulse propagation in optical fiber communication. Optical soliton, elliptic function, rogue waves, bright and dark soliton solutions of Sasa-Satsuma equation have been obtained to study nonlinear phenomena in related fields. With the aid of symbolic calculation, the exact solutions that complex soliton solutions, complex elliptic solutions and complex rational function solutions of the equation are needed to deal with more related phenomena. Later on, two-dimensional and three-dimensional graphics plots of the resulting solutions are made using Maple, and we discuss the symmetric soliton wave, periodic wave and kinky symmetric periodic wave formed by distinct solutions. (C)& nbsp;2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this paper, we study gradient Einstein-type structure immersed into a Riemannian warped product manifold. We obtain some triviality results for the potential function and smooth map u. We investigate conditions for a gradient Einstein-type structure to be totally umbilical, or totally geodesic immersed into a warped product I x f Mn. Furthermore, we study rotational hypersurface into R x f Rn has a gradient Einstein-type structure. (c) 2022 Elsevier B.V. All rights reserved.
NSTL
Elsevier