For a given standard Hamiltonian H with arbitrary complex scalar and vector potentials in one-dimension, we construct an invertible antilinear operator τ such that H is τ -anti-pseudo-Hermitian, i.e., H = τHτ−1. We use this result to give the explicit form of a linear Hermitian invertible operator with respect to which any standard PT symmetric Hamiltonian with a real degree of freedom is pseud...

For each prime p, a diffusion constant together with positive exponent specify Vladimirov operator and an associated p-adic equation. The fundamental solution of this pseudo-differential equation gives rise to measure on the Skorokhod space valued paths that is concentrated originating at origin. We calculate first exit probabilities from balls estimate these for Brownian bridges.

The aim of this paper is to introduce the notion of fantastic deductive systems on generalizations of fuzzy structures, and to emphasize their role in the probability theory on these algebras. We give a characterization of commutative pseudo-BE algebras and we generalize an axiom system consisting of four identities to the case of commutative pseudo-BE algebras. We define the fantastic deductiv...

We use Operator Ideals Theory and Gershgorin theory to obtain explicit information in terms of the symbol concerning spectrum pseudo-differential operators, on a smooth manifold ? with boundary ? , context non-harmonic analysis value problems introduced [29] model operator L. For symbols Hörmander class S 1 0 ( ¯ × I ) we provide version Gohberg's lemma, sufficient necessary condition ensure th...

In many calculations, spectral discretization in space is coupled with a standard ordinary differential equation formula in time. To analyze the stability of such a combination, one would like simply to test whether the eigenvalues of the spatial discretization operator (appropriately scaled by the time step k) lie in the stability region for the o.d.e. formula, but it is well known that this k...

The buckling and post-buckling behavior of a nonlinear discrete repetitive system, the discrete elastica, is studied herein. The nonlinearity essentially comes from the geometrical effect, whereas the constitutive law of each component is reduced to linear elasticity. The paper primarily focuses on the relevancy of higher-order continuum approximations of the difference equations, also called c...

a pseudo aneurysm results from leakage of blood from an artery after trauma or dehiscence or separation of a surgical anastomosis. the reported rate of pseudo aneurysm in access sites range from 0.88% to 8%. it has some cause like penetrating trauma, blunt trauma and endovascular procedure. the differential diagnoses of this lesion are hematoma, av fistula, lymphadenopathy, lymphocele, dvt, com...

in the present paper an operator-differential equation of second order in complex domain isconsidered when the coefficients have singularity of pole type at the point z=0. a theorem of existence of thesolution of the equation is proved and the spectral property of the solution is separately investigated when thecoefficients are spectral operators.