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Magnetic Neumann Laplacian on a domain with a hole Rep. Math. Phys. (IF 0.8) Pub Date : 2023-12-30 Diana Barseghyan, Baruch Schneider, Swanhild Bernstein
In this article, we study the magnetic Neumann Laplacian on a domain with a small hole. Our attention is focused on the description of holes, which do not change the spectrum drastically. Moreover, we show that the spectrum of the magnetic Neumann Laplacian converges in the sense of the Hausdorff distance to the spectrum of the original operator defined on the unperturbed domain.
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On Construction of Darboux integrable discrete models Rep. Math. Phys. (IF 0.8) Pub Date : 2023-12-30 Kostyantyn Zheltukhin, Natalya Zheltukhina
The problem of discretization of Darboux integrable equations is considered. Given a Darboux integrable continuous equation, one can obtain a Darboux integrable differential-discrete equation, using the integrals of the continuous equation. In the present paper, the discretization of the differential-discrete equations is done using the corresponding characteristic algebras. New examples of integrable
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A categorical view on the principle of relativity Rep. Math. Phys. (IF 0.8) Pub Date : 2023-12-30 L.M. Gaio, B.F. Rizzuti
Category theory plays a special role in mathematics — it unifies distinct branches under the same formalism. Despite this integrative power in math, it also seems to provide the proper foundations to the experimental physicist. In this work, we present another application of category in physics, related to the principle of relativity. The operational construction of (inertial) frames of reference indicates
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Gradient Gibbs measures of an SOS model with alternating magnetism on Cayley trees Rep. Math. Phys. (IF 0.8) Pub Date : 2023-12-30 N.N. Ganikhodjaev, N.M. Khatamov, U.A. Rozikov
The work is devoted to gradient Gibbs measures (GGMs) of an SOS model with countable set Z of spin values and having alternating magnetism on Cayley trees. This model is defined by a nearest-neighbour gradient interaction potential. Using Külske-Schriever argument, based on boundary law equations, we give several q-height-periodic translations invariant GGMs for q = 2, 3, 4.
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Stäckel representations of stationary Kdv systems Rep. Math. Phys. (IF 0.8) Pub Date : 2023-12-30 Maciej Błaszak, Błażej M. Szablikowski, Krzysztof Marciniak
In this article we study Stäckel representations of stationary KdV systems. Using Lax formalism we prove that these systems have two different representations as separable Stäckel systems of Benenti type, related with different foliations of the stationary manifold. We do it by constructing an explicit transformation between the jet coordinates of stationary KdV systems and separation variables of
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Nonequilibrium thermodynamics as a symplecto-contact reduction and relative information entropy Rep. Math. Phys. (IF 0.8) Pub Date : 2023-12-30 Jin-wook Lim, Yong-Geun Oh
Both statistical phase space (SPS), which is Γ = T* R3N of N-body particle system, and kinetic theory phase space (KTPS), which is the cotangent bundle T* P(Γ) of the probability space P(Γ) thereon, carry canonical symplectic structures. Starting from this first principle, we provide a canonical derivation of thermodynamic phase space (TPS) of nonequilibrium thermodynamics as a contact manifold in
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An unbounded generalization of tomita's observable algebras III Rep. Math. Phys. (IF 0.8) Pub Date : 2023-11-01 Hiroshi Inoue
In this paper we shall continue the studies of T†-algebras done in [8, 9], and above all we investigate decompositions of the vector representation part of a T†-algebra and apply the results to invariant positive sesquilinear forms on *-algebras.
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Magnetostatic levitation and two related linear pdes in unbounded domains Rep. Math. Phys. (IF 0.8) Pub Date : 2023-11-01 Bartosz Bieganowski, Jakub Siemianowski, Tomasz Cieślak
We consider a problem occurring in a magnetostatic levitation. The problem leads to a linear PDE in a strip. In engineering literature a particular solution is obtained. Such a solution enables one to compute lift and drag forces of the levitating object. It is in agreement with the experiment. We show that such a solution is unique in a class of bounded regular functions. Moreover, as a byproduct
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Constraints and interactions in quantization of Yukawa model with higher-order derivatives Rep. Math. Phys. (IF 0.8) Pub Date : 2023-11-01 Jan Żochowski
This work is dedicated to quantization of the light-front Yukawa model in D = 1 + 3 dimensions with higher-order derivatives of a scalar field. The problem of computing Dirac brackets and the (anti-)commutator algebra of interacting fields in the presence of constraints is discussed. The Dirac method and the Ostrogradski formalism of the higher-order derivatives are exploited. The systematic method
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A metrical approach to finsler geometry Rep. Math. Phys. (IF 0.8) Pub Date : 2023-11-01 E. Minguzzi
In the standard approach to Finsler geometry the metric is defined as a vertical Hessian and the Chern or Cartan connections appear as just two among many possible natural linear connections on the pullback tangent bundle. Here it is shown that the Hessian nature of the metric, the nonlinear connection and the Chern or Cartan connections can be derived from a few compatibility axioms between metric
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On the even-indexed eigenfunctions of the quantum harmonic oscillator Rep. Math. Phys. (IF 0.8) Pub Date : 2023-11-01 John M. Campbell
In 2021, Fassari et al. introduced a remarkable summation involving the even-indexed eigenfunctions of the quantum harmonic oscillator, and introduced a proof, based on manipulations of multiple elliptic integrals, for an evaluation involving Catalan's constant for the aforementioned summation. This motivates the development of generalizations and extensions of this evaluation. In this article, we
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Dynamical symmetry of a semiconfined harmonic oscillator model with a position-dependent effective mass Rep. Math. Phys. (IF 0.8) Pub Date : 2023-11-01 E.I. Jafarov, S.M. Nagiyev
Dynamical symmetry algebra for a semiconfined harmonic oscillator model with a position-dependent effective mass is constructed. Selecting the starting point as a well-known factorization method of the Hamiltonian under consideration, we have found three basis elements of this algebra. The algebra defined through those basis elements is an su (1,1) Heisenberg–Lie algebra. Different special cases and
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Ground state energies of the hubbard models and the hartree–fock approximation Rep. Math. Phys. (IF 0.8) Pub Date : 2023-11-01 Jacek Wojtkiewicz, Piotr H. Chankowski
According to the ‘folk knowledge', the Hartree–Fock (H-F) approximation applied to the Hubbard model becomes exact in the limit of small coupling U (the smaller |U|, the better is the H-F approximation). In [1] Bach and Poelchau have substantiated a certain version of this assertion by providing a rigorous estimate of the difference between the true ground-state energy of the simplest version of the
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Mittag-Leffler based Bessel and Tricomi functions via umbral approach Rep. Math. Phys. (IF 0.8) Pub Date : 2023-08-31 Tabinda Nahid, Hari Ponnama Rani
Various types of functions, their generalizations and extentions have been widely explored, especially for their applications in various fields of research. In this article, we show that the use of methods of an operational nature, such as umbral calculus, allows us to acquire the hybrid form of the Bessel and Tricomi functions in terms of Mittag-Leffler functions. Certain novel identities such as
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Integrable nonlocal nonlinear Schrödinger hierarchies of type (-λ*,λ) and soliton solutions Rep. Math. Phys. (IF 0.8) Pub Date : 2023-08-31 Wen-Xiu Ma
Two simultaneous nonlocal group constraints of the Ablowitz-Kaup-Newell-Segur matrix eigenvalue problems are discussed, of which one constraint changes the eigenvalue parameter into its negative of the complex conjugate and the other constraint does not change the eigenvalue parameter. Under those two constraints, mixed-type nonlocal integrable nonlinear Schrödinger hierarchies are generated. Further
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On umbral properties of a family of hyperbolic-like functions appearing in magnetic transport problem Rep. Math. Phys. (IF 0.8) Pub Date : 2023-08-31 Giuseppe Dattoli, Subuhi Khan, Mehnaz Haneef, Silvia Licciardi
Umbral operational techniques offer sturdy mechanism in the studies of special functions and special polynomials. The techniques of umbral calculus are employed to derive properties of families of exponential-like functions and their hyperbolic forms. The generalized forms of Mittag-Leffler functions are used to solve technical problems concerning transport of a charged beam in a solenoid magnet. The
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Exponential entropy on sequential effect algebras Rep. Math. Phys. (IF 0.8) Pub Date : 2023-08-31 Akhilesh Kumar Singh
The present paper introduces a new definition of entropy on sequential effect algebras. Unlike the logarithmic behaviour of the entropy defined in the literature, the entropy considered here is of exponential nature. Conditional entropy and entropy on the dynamical system are also introduced and studied. It is also proved that entropy of the dynamical system is invariant under isomorphism.
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Einstein algebras in a categorical context Rep. Math. Phys. (IF 0.8) Pub Date : 2023-08-31 Leszek Pysiak, Wiesław Sasin, Michael Heller, Tomasz Miller
According to the basic idea of category theory, any Einstein algebra, essentially an algebraic formulation of general relativity, can be considered from the point of view of any object of the category of C∞-algebras; such an object is then called a stage. If we contemplate a given Einstein algebra from the point of view of the stage, which we choose to be an “algebra with infinitesimals” (Weil algebra)
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Investigation of exact solutions and conservation laws for nonlinear fractional (2+1)-dimensional Burgers system of equations Rep. Math. Phys. (IF 0.8) Pub Date : 2023-08-31 Komal Singla
The exact solutions of fractional order (2+1)-dimensional Burgers system are determined by using symmetry approach and power series technique. Also, the graphical behaviour of the obtained solutions is provided for better interpretation. The conservation laws for the system are reported by using the new conservation theorem.
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On the discrete modified KP hierarchies: The Wronskian solutions for their constrained cases Rep. Math. Phys. (IF 0.8) Pub Date : 2023-08-31 Ge Yi, Liyun Wang, Kelei Tian, Ying Xu
The discrete modified KP hierarchies are compatible with generalized k-constraints. By means of the gauge transformation, a large class of solutions can be represented by the Wronskian determinants of functions satisfying a set of linear equations. In this paper, we give a sufficient and necessary condition to reduce the discrete mKP hierarchies obtained by the Wronskian solutions to the discrete k-constrained
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Almost Ricci-Bourguignon soliton on warped product space Rep. Math. Phys. (IF 0.8) Pub Date : 2023-08-31 Santosh Kumar, Pankaj Kumar, Buddhadev Pal
The purpose of this article is to study the almost Ricci-Bourguignon soliton on warped product space. Some results for solenoidal and concurrent vector fields are obtained on warped product space with almost Ricci-Bourguignon soliton. We provide the relation between the warped manifold and its base manifold (fiber manifold) for an almost Ricci-Bourguignon soliton. We also generalize the Bochner formula
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Coherent states associated with tridiagonal Hamiltonians Rep. Math. Phys. (IF 0.8) Pub Date : 2023-08-31 Hashim A. Yamani, Zouhaïr Mouayn
It has been shown that a positive semi-definite Hamiltonian H, that has a tridiagonal matrix representation in a given basis {|ϕn〉}, can be represented in the form H = A†A, where A is a forward shift operator satisfying A|ϕn〉=cn|ϕn〉+dn|ϕn-1〉 playing the role of an annihilation operator. Here, the coherent states |z) are defined as eigenstates of A. We also exhibit a complete set of coherent states
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Investigation on gradient solitons in perfect fluid spacetimes Rep. Math. Phys. (IF 0.8) Pub Date : 2023-06-30 Krishnendu De, Uday Chand De
This article concerns the study of perfect fluid spacetimes equipped with different types of gradient solitons. It is shown that if a perfect fluid spacetime with Killing velocity vector admits a τ-Einstein soliton of gradient type, then the spacetime represents phantom regime, or ψ remains invariant under the velocity vector field ρ. Besides, we establish that in a perfect fluid spacetime with constant
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The construction of Gel'fand triplet space structure for Infinite Potential Well System Rep. Math. Phys. (IF 0.8) Pub Date : 2023-06-30 Onur Genç, Haydar Uncu
The Hilbert space is the space which is usually chosen as the space of state vectors. In addition, the operators of quantum mechanics act on that space. However, the Hilbert space cannot provide a proper mathematical structure to define Dirac formulation. In particular, the use of Dirac formalism on the domain of definition of an observable leads to some physical contradictions. One example arises
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Time of arrival operator in the momentum space Rep. Math. Phys. (IF 0.8) Pub Date : 2023-06-30 A.M. Schlichtinger, A. Jadczyk
It is shown that in presence of certain external fields a well-defined self-adjoint time operator exists, satisfying the standard canonical commutation relations with the Hamiltonian. Examples include uniform electric and gravitational fields with nonrelativistic and relativistic Hamiltonians. The physical intepretation of these operators is proposed in terms of time of arrival in the momentum space
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Quantum-like correlation of two-qubit open system in the Markovian regime Rep. Math. Phys. (IF 0.8) Pub Date : 2023-06-30 S. Bukbech, K. El Anouz, Z. El Allali, A. El Allati
A rigorous relationship between local quantum uncertainty and local quantum Fisher information as recent quantifiers of nonclassical correlations is investigated. It consists of analysing the quantum correlation rate ingrained in a bipartite quantum system interacting with its surrounding environment under the Markovian regime. Indeed, we quantify the separability between two qubits where each qubit
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Galois symmetry of energy levels of the XXX model for the case of octagonal two-magnon states on the generic star of quasimomentum Rep. Math. Phys. (IF 0.8) Pub Date : 2023-06-30 T. Lulek, M. Łabuz, J. Milewski, R. Stagraczyński
We consider the factor υ of the characteristic polynomial wH (x) of the Heisenberg Hamiltonian Ĥ of the XXX model, corresponding to the generic star [k = ±1, ±3] of quasimomentum k for octagonal (N = 8) magnetic ring in the two-magnon sector. This factor is recognized as the fourth-degree polynomial with integer coefficients, indecomposable over the prime number field ℚ of rationals. We demonstrate
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Conserved currents from nonlocal constants in relativistic scalar field theories Rep. Math. Phys. (IF 0.8) Pub Date : 2023-06-30 Mattia Scomparin
Nonlocal constants are functions that are constant along motion but whose value depends on the past history of the motion itself. They have been introduced to study ODEs and, among all applications, they provide first integrals in special cases. In this respect, a new approach to get nonlocal constants within the framework of Lagrangian scalar field theory is introduced. We derive locally-conserved
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Periodic ground states for the mixed spin ising model with competing interactions on a Cayley tree Rep. Math. Phys. (IF 0.8) Pub Date : 2023-06-30 Farrukh Mukhamedov, Muzaffar M. Rahmatullaev, Dilshodbek O. EgAMOV
In the present paper, translation-invariant and periodic ground states are described for a mixed spin Ising model with competing interactions on the Cayley tree of order two. The limiting behaviour of various Gibbs measures of our mixed spin Ising model is discussed as well.
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Calculation of the electromagnetic self-force of a non-lorentz-contractible uniformly charged spherical shell in arbitrary rectilinear motion Rep. Math. Phys. (IF 0.8) Pub Date : 2023-06-30 G. Vaman
We write the electromagnetic self-force of a non-Lorentz-contractible uniformly charged shell of radius a as a series in powers of a, and we calculate the first three terms of this expansion. The method of calculation presented here allows the exact consideration of all linear and nonlinear terms in velocity and its derivatives corresponding to a given power of a. Our calculation is entirely done in
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Jacobi vector fields and conjugate points on warped product manifolds Rep. Math. Phys. (IF 0.8) Pub Date : 2023-06-30 Alexander Dirmeier, Mike Scherfner, Sameh Shenawy, Bülent ÜnAL
In this paper, the structure of Jacobi vector fields on warped product manifolds is investigated. Many characterizations of Jacobi vector fields on warped product manifolds are obtained. Consequently, conjugate points on warped product manifolds are also considered. Finally, we apply our results to characterize conjugate points of some well-known warped product spacetimes.
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MAGNETIC FIELDS ON THE TANGENT BUNDLE OVER KÄHLERIAN MANIFOLDS Rep. Math. Phys. (IF 0.8) Pub Date : 2023-04-12 Nour Elhouda Djaa, Aydin Gezer, Mustapha Djaa
This paper is devoted to the study of generalized magnetic vector fields as magnetic maps from a Kählerian manifold to its tangent bundle endowed with a Berger type deformed Sasaki metric. Some properties of Killing magnetic vector fields are provided specially in the case of an Einstein manifold and a space form. In the last section, we consider the case of unit tangent bundle.
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ON SPACETIME ALGEBRA AND ITS RELATIONS WITH NEGATIVE MASSES Rep. Math. Phys. (IF 0.8) Pub Date : 2023-04-12 N. Debergh, J.-P. Petit
We consider four subsets of the complexified spacetime algebra, namely the real even part, the real odd part, the imaginary even part and the imaginary odd part. This naturally leads to the four connected components of the Lorentz group, supplemented each time by an additional symmetry. We then examine how these four parts impact the Dirac equation and show that four types of matter arise with positive
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WEAKLY-EINSTEIN CONDITIONS OVER LOCALLY CONFORMALLY FLAT LORENTZIAN THREE-MANIFOLDS Rep. Math. Phys. (IF 0.8) Pub Date : 2023-04-12 Parvane Atashpeykar, Amirhesam Zaeim, Ali Haji-Badali
We classify the Lorentzian manifolds of dimension n ≥ 3 admitting some diagonalizable operators which satisfy the Codazzi equation. This classification is applied to characterize three-dimensional weakly-Einstein Lorentzian manifolds which fall in the conformal class of the flat metrics.
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ON BOUNDARY CONDITIONS AND THE RIGGED HILBERT SPACE FORMALISM OF QUANTUM MECHANICS Rep. Math. Phys. (IF 0.8) Pub Date : 2023-04-12 Nadia Boudi, Zakariae Ennadifi
We discuss canonical rigged Hilbert space constructions. We focus on cyclic self-adjoint operators and use the one-dimensional free Hamiltonian on the half-line as a model. We propose a nonstandard construction that can be generalized to many quantum systems. Our construction is motivated by the Stone–von Neumann uniqueness theorem.
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ON A SPECIAL COUPLED LATTICE SYSTEM OF THE DISCRETE BOUSSINESQ TYPE Rep. Math. Phys. (IF 0.8) Pub Date : 2023-04-12 Guesh Yfter Tela, Da-jun Zhang
In this paper, we investigate a multidimensionally consistent coupled quadrilateral system of the discrete Boussinesq type, proposed by Fordy and Xenitidis recently. It is distinguished from the known discrete Boussinesq type equations by a special dispersion relation. A Bäcklund transformation is constructed and a one-soliton solution is derived using the Bäcklund transformation. We also give bilinear
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NEW QUANTUM AND LCD CODES FROM CYCLIC CODES OVER A FINITE NON-CHAIN RING Rep. Math. Phys. (IF 0.8) Pub Date : 2023-04-12 Nadeem ur Rehman, Mohd Azmi, Ghulam Mohammad
In this work, we study cyclic codes of length n over a finite commutative non-chain ring ℛ=Fq[u,v]/〈u2−γu,v2−ϵv,uv−vu〉 where γ,ϵ∈Fq* and we find new and better quantum error-correcting codes than previously known quantum error correcting codes. Then certain constraints are imposed on the generator polynomials of cyclic codes, so these codes become linear complementary dual codes (in short LCD codes)
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AN UNBOUNDED GENERALIZATION OF TOMITA's OBSERVABLE ALGEBRAS II Rep. Math. Phys. (IF 0.8) Pub Date : 2023-04-12 Hiroshi Inoue
In a previous paper [4] we tried to build the basic theory of unbounded Tomita's observable algebras called T†-algebras which are related to unbounded operator algebras, especially unbounded Tomita-Takesaki theory, operator algebras on Krein spaces, studies of positive linear functionals on *-algebras and so on. And we defined the notions of regularity, semisimplicity and singularity of T†-algebras
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LIE-POISSON REDUCTION FOR OPTIMAL CONTROL OF LEFT-INVARIANT CONTROL SYSTEMS WITH SUBGROUP SYMMETRY Rep. Math. Phys. (IF 0.8) Pub Date : 2023-02-20 Leonardo Colombo, Efstratios Stratoglou
We study the reduction by symmetries for optimality conditions in optimal control problems of left-invariant affine control systems with partial symmetry breaking cost functions. We recast the optimal control problem as a constrained problem with a partial symmetry breaking Hamiltonian and we obtain the reduced optimality conditions for normal extrema from Pontryagin's Maximum Principle and a Lie--Poisson
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NEW CRITERION OF STABILITY FOR TIME-VARYING DYNAMICAL SYSTEMS: APPLICATION TO SPRING-MASS-DAMPER MODEL Rep. Math. Phys. (IF 0.8) Pub Date : 2023-02-20 Ezzine Faten, Mohamed Ali Hammami
In this paper, we investigate the problem of stability with respect to a part of variables of nonlinear time-varying systems. We derive some sufficient conditions that guarantee exponential stability and practical exponential stability with respect to a part of the variables of perturbed systems based on Lyapunov techniques where converse theorems are stated. Furthermore, illustrative examples to show
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CHARACTERIZATIONS OF ALMOST PSEUDO-RICCI SYMMETRIC SPACETIMES UNDER GRAY's DECOMPOSITION Rep. Math. Phys. (IF 0.8) Pub Date : 2023-02-20 Dipankar Hazra, Uday Chand De
In this study, we analyze almost pseudo-Ricci symmetric spacetimes endowed with Gray's decomposition, as well as generalized Robertson—Walker spacetimes. For almost pseudo-Ricci symmetric spacetimes, we determine the form of the Ricci tensor in all the O (n)-invariant subspaces provided by Gray's decomposition of the gradient of the Ricci tensor. In three cases we obtain that the Ricci tensor is in
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FUNDAMENTAL GROUP AND FINE TOPOLOGY ON MINKOWSKI SPACE Rep. Math. Phys. (IF 0.8) Pub Date : 2023-02-20 Gunjan Agrawal
The present paper focuses on the study of fundamental group of Minkowski space with the fine topology which has been found to contain uncountably many subgroups isomorphic to the additive group of integers.
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GAUSS DECOMPOSITION AND NONSTANDARD DEFORMATION OF GL(1|1) Rep. Math. Phys. (IF 0.8) Pub Date : 2023-02-20 Salih Celik
We present the standard and nonstandard one-parameter deformations of two supergroups, one of which is the lower and the other upper triangular matrices, and using these we show that the two-parameter nonstandard deformation of the supergroup GL(1|1) can be achieved.
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ONE-PARAMETER GENERALISED FISHER INFORMATION MATRIX: ONE RANDOM VARIABLE Rep. Math. Phys. (IF 0.8) Pub Date : 2023-02-20 Worachet Bukaew, Sikarin Yoo-Kong
We propose a generalised Fisher information or a one-parameter extended class of the Fisher information for the case of one random variable. This new form of the Fisher information is obtained from the intriguing connection between the standard Fisher information and the variational principle together with the nonuniqueness property of the Lagrangian. A generalised Cramér--Rao inequality is also derived
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3-JACK POLYNOMIALS AND YANG--BAXTER EQUATION Rep. Math. Phys. (IF 0.8) Pub Date : 2023-02-20 Na Wang
Every slice of a 3D Young diagram on the plane z = n in the coordinate system O - xyz is a 2D Young diagram. In this paper, we show how Jack polynomials of 2D Young diagrams constitute a Jack polynomial of 3D Young diagram, which is called 3-Jack polynomial. We give the specific expressions of 3-Jack polynomials of 3D Young diagrams of total box number less than 4, and we find a method to obtain 3-Jack
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GRAY's DECOMPOSITION AND WARPED PRODUCT OF GENERALIZED RICCI RECURRENT SPACETIMES Rep. Math. Phys. (IF 0.8) Pub Date : 2023-02-20 Uday Chand De, Sameh Shenawy, Abdallah Abdelhameed Syied
Generalized Ricci recurrent spacetimes (GR)n are investigated in Gray's seven subspaces. It is proved that a (GR)n spacetime in all subspaces but one is an Einstein spacetime. The subspace ℐ cannot contain a (GR)n spacetime. Further, the subspaces ℐ⊕A and ℐ⊕B reduce to A and B, respectively. Next, we prove that a (GR)n spacetime is Ricci semi-symmetric if and only if either the spacetime is Einstein
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APPROXIMATION STATES AND FIXED POINTS OF QUANTUM CHANNELS* Rep. Math. Phys. (IF 0.8) Pub Date : 2023-02-20 Yuan Li, Fan Li, Shan Chen, Yanni Chen
In this note, we extend some results on positive and completely positive trace-preserving maps (called quantum channels in the CPTP case) from finite-dimensional to infinite-dimensional Hilbert space. Specifically, we mainly consider whether the fixed state of a quantum channel Φ on T(ℋ) exists, where T(ℋ) is the Banach algebra of all trace-class operators on the Hilbert space ℋ. We show that there
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Algebraic Construction of Associated Functions of Nondiagonalizable Models with Anharmonic Oscillator Complex Interaction Rep. Math. Phys. (IF 0.8) Pub Date : 2022-11-30 I. Marquette, C. Quesne
A shape invariant nonseparable and nondiagonalizable two-dimensional model with anharmonic complex interaction, first studied by Cannata, Ioffe, and Nishnianidze, is re-examined with the purpose of providing an algebraic construction of the associated functions to the excited-state wavefunctions, needed to complete the basis. The two operators A+ and A-, coming from the shape invariant supersymmetric
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Anti- PT-Symmetric Harmonic Oscillator and its Relation to the Inverted Harmonic Oscillator Rep. Math. Phys. (IF 0.8) Pub Date : 2022-11-30 Nadjat Amaouche, Ishak Bouguerche, Rahma Zerimeche, Mustapha Maamache
We treat the quantum dynamics of a harmonic oscillator as well as its inverted counterpart in the Schrödinger picture. Generally in the most papers in the literature, the inverted harmonic oscillator is formally obtained from the harmonic oscillator by the replacement of ωby iω, this leads to unbounded eigenvectors. This explicitly demonstrates that there are some unclear points involved in redefining
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Poisson Structures on the Conifold and Local Calabi-Yau Threefolds Rep. Math. Phys. (IF 0.8) Pub Date : 2022-11-30 Eduardo Ballico, Elizabeth Gasparim, Thomas Köppe, Bruno Suzuki
We describe bivector fields and Poisson structures on local Calabi-Yau threefolds which are total spaces of vector bundles on a contractible rational curve. In particular, we calculate all possible holomorphic Poisson structures on the conifold.
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Global Existence Theorem of Mild Solutions of the Boltzmann Equation for Short Range Interactions Rep. Math. Phys. (IF 0.8) Pub Date : 2022-11-30 Emmanuel Kamdem Tchtjengtje, Etienne Takou
In this paper, we consider the Cauchy problem for the relativistic Boltzmann equation with near vacuum initial data where the distribution function depends on time, position and momenta. The collision kernel considered here corresponds to short range interactions and the background space-time is fixed and is of Bianchi type I. The existence of a unique global (in time) mild solution is obtained in
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Some Details Concerning Transition from the Hubbard Model to the Heisenberg Model Rep. Math. Phys. (IF 0.8) Pub Date : 2022-11-30 Dorota Jakubczyk
In this paper we present the example the details of the transition of the Hubbard model to the Heisenberg model in the limit of on-site repulsion constant u → ∞. We explore the models with respect to the nearest and the next-nearest-neighbour hopping. We construct the next-nearest-neighbour hopping free subspaces for the considered example and find the procedure applicable to any number and any configuration
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Weyl Moments and Quantum Gaussian States Rep. Math. Phys. (IF 0.8) Pub Date : 2022-11-30 Jorge R. Bolaños-Servín, Roberto Quezada, Josué I. Rios-Cangas
We give a rigorous definition of moments of an unbounded observable with respect to a quantum state in terms of Yosida's approximations of unbounded generators of contractions semigroups. We use this notion to characterize Gaussian states in terms of the moments of the field operator, which we call Weyl moments. As a by-product, rigorous formulae for the mean value vector and the covariance matrix
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A Note on Generalized Vitali Sets with Respect to Some Arbitrary Deformed Sums Rep. Math. Phys. (IF 0.8) Pub Date : 2022-11-30 Brian Villegas-Villalpando, Jorge E. Macías-Díaz
In this manuscript, we present a generalized deformed sum inspired by the nonadditive property of entropies such as those investigated by Tsallis and Shannon in the context of information theory. From this deformed sum, we define a generalization of the Vitali set and prove its nonmeasurability. Moreover, the standard sum is recovered as the deforming parameter tends to zero, and Vitali's theorem is
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Density Operator Formulation for a Supersymmetric Harmonic Oscillator: Vector Coherent State Construction and Statistical Properties Rep. Math. Phys. (IF 0.8) Pub Date : 2022-11-30 Isiaka Aremua, Mahouton Norbert Hounkonnou, Komi Sodoga, Paalamwé Komi Tchakpélé
Motivated by our recent work published in [23], we achieve, in this paper, a matrix formulation of the density operator to construct a two-component vector coherent state representation for a supersymmetric harmonic oscillator. We investigate and discuss the main relevant statistical properties. We use the completeness relation to perform the thermodynamic analysis in the diagonal P-representation
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Sasakian structure on the unit tangent bundle of a Finsler manifold Rep. Math. Phys. (IF 0.8) Pub Date : 2022-11-01 Hassan Attarchi
In this work, we introduce an adopted local frame on the tangent bundle of a Finsler manifold with respect to the natural foliations of the tangent bundle. We show the prominence of using this local frame by studying some geometric properties of the foliations and distributions on the tangent bundle of a Finsler manifold. Moreover, we find the necessary and sufficient conditions on the Finsler manifold
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Darboux transformation of two novel two-component generalized complex short pulse equations Rep. Math. Phys. (IF 0.8) Pub Date : 2022-11-01 Xinyue Li, Zhixin Zhang, Qiulan Zhao, Chuanzhong Li
The short pulse equation is able to describe ultra short pulse, which plays a crucial part in the field of optical fiber propagation. In this paper, we investigate a generalized complex short pulse equation and its two-component generalization. We first prove that they are Lax integrable. Subsequently, we obtain their new Lax pairs through hodograph transformation to carry out Darboux transformation