In this paper, we introduce and study recurrent B form manifolds, which serve as a natural generalization of weakly B-symmetric and pseudo B-symmetric manifolds. We begin by defining a B form associated with the B tensor and investigate the structure of recurrent B form manifolds in the context of general relativity. A nontrivial example is constructed to demonstrate the existence of a (RBF)(4) space-time. Subsequently, we prove that if the B tensor is of Codazzi type, the resulting recurrent B form space-time is quasi-Einstein. Under suitable conditions, we examine whether such a space-time can model a perfect fluid and further show that a conformally flat (RBF)(4) space-time exhibits infinitesimal spatial isotropy with respect to a unit time-like vector field rho. Then, we examine the setting in which the B tensor is of Codazzi type and the Weyl tensor C is harmonic. It is shown that, under certain geometric conditions, the associated vector field rho characterizes a static space-time. Additionally, we prove that this space-time admits a matter collineation, provided that further assumptions are satisfied.
In this paper, we consider a variable-coefficient linear thermoelastic system with interior localized damping and dynamic Wentzell boundary conditions with delay. The model describes the interaction between the mechanical displacement u and temperature B, and is subject to dynamic Wentzell-type boundary conditions. Our main result demonstrates that this internal damping, localized on a subset omega subset of Omega, where a(x) >= a(0) > 0 over omega subset of Omega, is sufficient to achieve exponential stabilization of the entire system. To establish the well-posedness of the system, we apply semigroup theory. Then, by combining the multiplier method and the Riemannian geometry approach, we derive suitable energy estimates and prove the exponential decay of energy. The stability result highlights the interplay between interior damping, boundary feedback, and the delay term, and provides a meaningful extension of existing stabilization results for thermoelastic systems.
The challenge of the vacuum catastrophe arises from the discrepancy between quantum field theoretical predictions and the observed vacuum energy density. Using analytic continuation techniques and asymptotic analysis to ensure physical consistency, we explored the Mittag-Leffler function (MLF), a generalized exponential function applied in fractional calculus and anomalous diffusion, as a potential framework to address the vacuum catastrophe. We computed the MLFregularized vacuum energy integral, evaluated renormalization group equations, derived modified field equations for different parameter choices and provided numerical solutions of the modified Friedmann equations to track the evolution of the scale factor. Unlike conventional approaches relying on arbitrary cutoffs and standard QFT predictions, which exhibit uncontrolled growth at high energies, MLF regulates coupling divergences by attenuating high-energy contributions while preserving Lorentz invariance and renormalization group consistency. The field propagation profile exhibited suppression of high-energy components, consistent with modified dispersion relations predicted by fractional-order formulations. The scale factor evolution indicated a reduced contribution from vacuum energy, aligning with the expectation that MLF diminishes the effective cosmological constant over cosmic timescales. We found minimal deviations in the cosmic microwave background power spectrum relative to the standard cosmological model, consistent with current observational constraints.
A type of group reduction or similarity transformation is proposed and studied for the matrix AKNS spectral problem with two square matrix potentials. The corresponding integrable hierarchies of the reduced matrix AKNS equations, including reduced matrix nonlinear Schrodinger equations, are presented, demonstrating the diversity of matrix AKNS soliton hierarchies. The zero curvature formulation plays a crucial role in the development of these integrable models.
We define the generalized symmetric metric connection of type (alpha, beta) on almost contact statistical manifolds and Sasakian statistical manifolds. The curvature properties of these manifolds admitting such a connection are derived. Additionally, we investigate the symmetry properties of the curvature tensor with respect to this metric connection. New results are presented for Sasakian statistical manifolds equipped with a generalized symmetric metric connection of type (alpha, beta). Finally, explicit examples of Sasakian statistical manifolds are constructed to illustrate the theoretical framework.
In this paper, the Lax pairs of the negative-order AKNS equations are presented. The explicit solutions (classical N-soliton and singular kink wave solutions) are derived using the inverse scattering method. The auxiliary spectral problem is formulated as the classical Zakharov-Shabat system with real symmetric and real anti-symmetric potentials. By recalling results from the inverse scattering problem and utilizing the time evolution of the scattering data, explicit solutions for the negative-order AKNS equations corresponding to symmetric and anti-symmetric potentials are obtained through the Gelfand-Levitan-Marchenko equation.
The integrable discretization of a nonlinear partial differential equation and the continuous limits of the relevant discrete integrability properties are one of the most important research subjects in soliton theory. In this paper we construct the spatial discrete version of the focusing and defocusing fifth-order mKdV equation and study the continuous limits of the related discrete integrable properties. Firstly, starting from a discrete spectral problem, we derive integrable equation hierarchies and then obtain the focusing and defocusing fifth-order semi-discrete mKdV equation by using a linear combination of them. Secondly, the Backlund transformation and soliton solutions of the equation are presented, the relationship between parameters and solutions' structures is discussed, some important physical quantities related to solutions are analyzed, the dynamics of soliton solutions are illustrated graphically. Thirdly, we show that the fifth-order mKdV theory including the Lax pairs, the Backlund transformation and soliton solutions is recovered through the continuous limits of corresponding theory for the fifth-order semi-discrete mKdV equation. As a conclusion, we believe that the focusing and defocusing fifth-order semi-discrete mKdV equation which we construct in this paper is an extremely useful model for the numerical analysis for considering the Cauchy problem with a general initial data of the fifth-order mKdV equation.
In the present article, we consider mixed generalized quasi-Einstein manifolds in the perspective of Gray's decomposition. We begin by analyzing the properties of these manifolds in the context of the subspaces defined by Gray. Furthermore, we apply principles of general relativity to derive significant physical results.
The content of this paper includes two parts: (i) A detailed analysis for constructing integrable (4+2)-dimensional generalized fifth-order Korteweg-de Vries (KdV) equation by complexifying the independent variables is presented. Two three-spatial-dimensions equations are obtained by concrete reduction. The spectral analysis of the t-independent part of the Lax pair yields the nonlinear Fourier transform pair comprising both direct and inverse transforms, which is used to solve the Cauchy initial value problem of the three-spatial-dimensions KdV equation with two temporal variables after taking into account the appropriate time evolution. (ii) We initially impose this real condition on the potential function u, thereby deriving the restriction on the degenerate kernel R-0 in the limit of weak field. Several kernel functions R-0 that satisfy the restriction are selected to construct solutions with functional parameters, line soliton solutions, and rational solutions of (2+ 1)-dimensional generalized fifth-order KdV equation in terms of Zakharov-Manakov (ZM) partial derivative-dressing method.
This article is mainly devoted to tackling the stability result of the Cauchy-Wentzell problem with internal delay. Our focus is to show the exponential decay of the energy of the system. Throughout our investigation, we will use the multiplier method by making suitable choices of Lyapunov functions.
In this article some geometric properties of a relativistic string cloud spacetime coupled with magnetized quark matter are illustrated. Then, we discuss conformal eta-Ricci-Yamabe soliton of type (K, l) on a string cloud spacetime coupled with magnetized quark matter with a Z-Ric vector field. Furthermore, we analyze some physical significance of conformal pressure in terms of such soliton concerning a Z-Ric vector field on a string cloud spacetime. Besides, we deduce a modified Poisson and Liouville equation from the conformal eta-Ricci-Yamabe soliton of type (K, l) on a relativistic string cloud spacetime. In addition, we light up the harmonic aspect of a conformal j7-Ricci-Yamabe soliton of type (K, l) on a relativistic string cloud spacetime with magnetized quark matter and we establish a necessary and sufficient condition for a 1-form eta, which is the g-dual of the vector field xi to be a solution of the Schrodinger-Ricci equation. Finally, we produce an example of eta-Ricci-Yamabe soliton.
This paper extends Remling's theorem to vector-valued discrete Schrodinger operators, showing that the omega limit points of the matrix potentials, under the shift map, are reflectionless on the absolutely continuous spectrum with full multiplicity.
Einstein algebra, the concept due to Geroch, is essentially general relativity in an algebraic disguise. We introduce the concept of Einstein-Grassmann algebra as a superalgebra (defining a supermanifold) which is also an Einstein algebra. We employ this concept to confront the supermanifold structure with the structure of strong singularity, the so-called malicious singularity, in general relativity. Einstein-Grassmann algebras consist of two parts: a part called body and a part called soul. For the body part, the singularity theorems apply and the singularities persist as the conclusions of the classical theorems on the existence of singularities require. We prove that, if we relax algebraical requirements, the soul part of the algebra can survive the malicious singularity. In particular, we study the behaviour of supercurves in the presence of malicious singularity.
The error estimation for eigenvalues and eigenvectors of a small positive symmetric perturbation on the spectrum of a graph Laplacian is related to Gauss hypergeometric functions. Based on this, a heuristic polynomial-time algorithm for finding an optimal locally ultrametric approximation of a graph-distance power Laplacian matrix via the Vietoris-Rips graph based on the graph distance function is proposed. In the end, the error in the solution to the graph Laplacian heat equation given by extension to a locally p-adic equation is estimated.
We consider isomonodromic deformations of connections with a simple pole on the torus, motivated by the elliptic version of the sixth Painlevé equation. We establish an extended symmetry, complementing known results. The Calogero-Moser system in its elliptic version is shown to fit nicely in the geometric framework, the extended symplectic two-form is introduced and shown to be closed.
A Skyr me-type energy functional for maps phi : M -> N from an oriented Riemannian 3-manifold M to a contact 3-manifold N is defined, generalizing the Bogomol'nyi-Prasad-Sommerfeld (BPS) Skyrme energy of Ferreira and Zakrzewski. This energy has a topological lower bound, attained by solutions of a first-order self-duality equation which we call (strong) Beltrami maps. In the case where N is the 3-sphere, we show that the original Ferreira-Zakrzewski model (which has N = S-3 with the standard contact structure) can have no BPS solutions on M = S-3 with | deg(phi) | > 1 if the coupling constant has the lowest admissible value.
In continuation of the similarly titled paper on the e(2 )< m(2) Reissner-Nordstrom (RN) metric, in this paper it was verified whether it is possible to send (by means of timelike and null geodesics) messages to one's own past in the maximally extended extreme (e(2 )= m(2) ) RN spacetime with the asymptotically flat regions being identified. Numerical examples show that timelike and nonradial null geodesics originating outside the horizon have their turning points to the future of the past light cone of the future copy of the emitter. This means that they cannot reach the causal past of the emitter's future copy. Ingoing radial null geodesics hit the singularity at r = 0 and stop there. So, unlike in the e(2 )< m(2) case, identification of the asymptotically flat regions does not lead to causality breaches. A formal mathematical proof of this thesis (as opposed to the numerical examples given in this paper) is still lacking and desired.
The paper presents an interesting mathematical feedback between the formalism of coherent states and the field of integrals and integral representations involving special functions. This materializes through an easy and fast method to calculate integrals or integral representations of different functions, expressible by means of Meijer's G-, as well as hypergeometric generalized functions. The feedback starts from a fundamental integral that comes from the decomposition of the unity operator in the language of coherent states from quantum mechanics. In this way, integrals and integral representations are obtained, some of them do not appear in the literature, and others are already known, which can be verified by orthodox methods. All calculations are made using the properties of the diagonal operators ordering technique (DOOT), a relatively new technique of normal ordering of the creation and annihilation operators in quantum mechanics. The paper contributes to increasing the number of solvable integrals involving special functions.
The generalized knots-quivers correspondence extends the original knots-quivers correspondence by allowing higher level generators of quiver generating series. In this paper we explore the underlying combinatorics of such generating series, relationship with the Bogomol'nyi-Prasad-Sommer field (BPS) numbers of a corresponding knot, and new combinatorial interpretations of the coefficients of generating series in terms of the count of lattice paths.
We propose a solution formula for chemical diffusion master equations of birth and death type. These equations, proposed and formalized in the recent paper [5], aim at incorporating the spatial diffusion of molecules into the description provided by the classical chemical master equation. We start from the general approach developed in [20] and perform a more detailed analysis of the representation found there. This leads to a solution formula for birth-death chemical diffusion master equations which is expressed in terms of the solution to the reaction-diffusion partial differential equation associated with the system under investigation. Such representation also reveals a striking analogy with the solution to the classical birth-death chemical master equations. The solutions of our findings are also illustrated for several examples.
