Reports on Mathematical Physics最新文献

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.

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 currents from them, and we prove the consistency of our results by recovering some standard Noetherian results. Applications include the real/complex nonlinear interacting theory and the real dissipative Klein–Gordon theory.

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.

In this work, we study cyclic codes of length n over a finite commutative non-chain ring$ℛ=F_q\left[u,v\right]/〈u^2-\gamma u,v^2-ϵv,uv-vu〉$ where$\gamma ,ϵ\in F_q^{*}$ 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). We then verify that the Gray image of linear complementary dual codes of length n over$ℛ$ is a linear complementary dual code of length 4n over$F_q$ by establishing a Gray map.

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 and characterized them. In this paper we shall proceed further with our studies of T^†-algebras and investigate whether a T^†-algebra is decomposable into a regular part and a singular part.

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.

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.

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 forms of the coupled equations and present formulae for multisoliton solutions. Both plane wave factor and phase factor in two-soliton solutions indicate the coupled systems belong to the discrete Boussinesq family, but there is no continuous correspondence in terms of the Miwa coordinates.

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.