We consider a class of one-dimensional nonselfadjoint semiclassical pseudo-differential operators, subject to small random perturbations, and study the statistical properties their (discrete) spectra, in limit h → 0. compare two types perturbation: potential vs. matrix. Hager Sjostrand had shown that, with high probability, local spectral density perturbed operator follows form Weyl's law, depe...

We introduce a very natural class of potential submanifolds in pseudo-Euclidean spaces (each Ndimensional potential submanifold is a special flat torsionless submanifold in a 2N-dimensional pseudoEuclidean space) and prove that each N-dimensional Frobenius manifold can be locally represented as an N-dimensional potential submanifold. We show that all potential submanifolds bear natural special ...

We study the higher order Jacobi operator in pseudo-Riemannian geometry. We exhibit a family of manifolds so that this operator has constant Jordan normal form on the Grassmannian of subspaces of signature (r, s) for certain values of (r, s). These pseudo-Riemannian manifolds are new and nontrivial examples of higher order Osserman manifolds. Subject Classification: 53B20. PACS numbers: 0240, 0...

This paper is concerned with the numerical treatment of pseudo-diierential equations in I R 2 , employing wavelet Galerkin methods. We construct wavelet bases adapted to a given pseudo-diierential operator in the sense that functions on diierent reenement levels are orthogonal with respect to a certain bilinear form induced by the operator.

In this paper, for any non-empty subset C of a pseudo BCI-algebra X, the concept of p-closure of C, denoted by C(pc), is introduced and some related properties are investigated. Applying this concept, a characterization of the minimal elements of X is given. It is proved that C(pc) is the least closed pseudo BCI-ideal of X containing C and K(X) for any ideal C of X...

In this paper we investigate the nuclear trace of vector-valued Fourier multipliers on torus and its applications to index theory periodic pseudo-differential operators. First characterise nuclearity operators acting Bochner integrable functions. regards, consider discrete cases. We go address problem finding sharp sufficient conditions for torus. end our investigation with two formulae. First,...

In this paper, by the weighted ergodic function based on the measure theory, we study the pseudo asymptotic behavior of mild solution for semilinear fractional integro-differential equations. The existence, unique of -pseudo anti-periodic ( -pseudo periodic, -pseudo almost periodic, -pseudo almost automorphic) solution are investigated. Moreover, an application to fractional partial differentia...

Pseudo-differential and Fourier series operators on the torus T = (R/2πZ) are analyzed by using global representations by Fourier series instead of local representations in coordinate charts. Toroidal symbols are investigated and the correspondence between toroidal and Euclidean symbols of pseudo-differential operators is established. Periodization of operators and hyperbolic partial differenti...

A complexified von Roos Hamiltonian is considered and a Hermitian first-order intertwining differential operator is used to obtain the related position dependent mass η-weak-pseudo-Hermitian Hamiltonians. Two ”user -friendly” reference-target maps are introduced to serve for exactsolvability of some non-Hermitian η-weak-pseudo-Hermitian position dependent mass Hamiltonians. A non-Hermitian PT -...

in this paper, we study the existence of generalized solutions for the infinite dimensional nonlinear stochastic differential inclusions $dx(t) in f(t,x(t))dt +g(t,x(t))dw_t$ in which the multifunction $f$ is semimonotone and hemicontinuous and the operator-valued multifunction $g$ satisfies a lipschitz condition. we define the it^{o} stochastic integral of operator set-valued stochastic pr...