Abstract In this paper, we analyze some properties of a sixth-order elliptic operator arising in the framework strain gradient linear elasticity theory for nanoplates flexural deformation. We first rigorously deduce weak formulation underlying Neumann problem as well its posedness. Under suitable smoothness assumptions on coefficients and geometry, derive interior boundary regularity estimates ...

We prove that the resolvent of renormalised Nelson Hamiltonian at fixed total momentum P improves positivity in (momentum) Fock-representation, for every P. Our argument is based on an explcit representation operator and its domain using interior boundary conditions.

Rough set theory is an excellent mathematical tool for the analysis of a vague description actions in decision problems. Now, this paper by considering notion equality algebra, lower and upper approximations are introduced some properties them given. Moreover, it proved that define interior operator closure operator, respectively. Also, using D-lower D-upper approximation, conditions nonempty s...

We give a solution, via operator spaces, of an old problem in the Morita equivalence of C*-algebras. Namely, we show that C*-algebras are strongly Morita equivalent in the sense of Rieffel if and only if their categories of left operator modules are isomorphic via completely contractive functors. Moreover, any such functor is completely isometrically isomorphic to the Haagerup tensor product (=...

Microlocal analysis of a seismic linearized inverse problem. Abstract: The seismic inverse problem is to determine the wavespeed c(x) in the interior of a medium from measurements at the boundary. In this paper we analyze the linearized inverse problem in general acoustic media. The problem is to nd a left inverse of the linearized forward map F, or, equivalently, to nd the inverse of the norma...

The paper presents a cheap technique for the approximation of the harmonic extension from the boundary into the interior of a domain with respect to a given diierential operator. The new extension operator is based on the hierarchical splitting of the given f.e. space together with smoothing sweeps and an exact discrete harmonic extension on the lowest level and will be used as a component in a...

Any compact C∞ manifold with boundary admits a Riemann metric on its interior taking the form x−4dx2 + x−2h′ near the boundary, where x is a boundary defining function and h′ is a smooth symmetric 2-cotensor restricting to be positive-definite, and hence a metric, h, on the boundary. The scattering theory associated to the Laplacian for such a ‘scattering metric’ was discussed by the first auth...

For a positive integer k, the rank-k numerical range Λk(A) of an operator A acting on a Hilbert space H of dimension at least k is the set of scalars λ such that PAP = λP for some rank k orthogonal projection P . In this paper, a close connection between low rank perturbation of an operator A and Λk(A) is established. In particular, for 1 ≤ r < k it is shown that Λk(A) ⊆ Λk−r(A + F ) for any op...