We study the asymptotic behaviour of eigenvalues and eigenfunctions 2D vibrating systems with mass density perturbed in a vicinity closed curves. The threshold case which resonance frequencies membrane thin inclusion coincide or closely situated is investigated. eigenvalue problem can be realized as family self-adjoint operators acting on varying Hilbert spaces. However so-called limit operator...

An implication operator A is said to be tied if there is a binary operation T that ties A; that is, the identity A(a,A(b, z)) = A(T (a, b), z) holds for all a, b, z. We aim at the construction of a complete predicate logic for prelinear tied adjointness algebras. We realize this in three steps. In the first step, we establish a propositional calculus AdjTPC, complete for the class of all tied a...

We establish optimal order a priori error estimates for implicit– explicit BDF methods for abstract semilinear parabolic equations with timedependent operators in a complex Banach space setting, under a sharp condition on the non-self-adjointness of the linear operator. Our approach relies on the discrete maximal parabolic regularity of implicit BDF schemes for autonomous linear parabolic equat...

We consider a Schrödinger operator with a magnetic field (and no electric field) on a domain in the Euclidean space with a compact boundary. We give sufficient conditions on the behavior of the magnetic field near the boundary which guarantees essential self-adjointness of this operator. From the physical point of view, it means that the quantum particle is confined in the domain by the magneti...

of N links joined at a single point. Each link supports a real locally integrable potential Vj ; the self–adjointness is ensured by the δ type boundary condition at the vertex. If all the links are semiinfinite and ideally coupled, the potential decays as x−1−ǫ along each of them, is non–repulsive in the mean and weak enough, the corresponding Schrödinger operator has a single negative eigenval...

Lecture 2. Index problem for manifolds with a boundary. Index of the Dirac operator and anomalies. Lecture 3. Spectral asymmetry and Riemannian geometry. Heat equation and asymptotic heat kernel. The η-and ζ-functions. Lecture 4. Two-component spinor calculus. Dirac and Weyl equations in two-component spinor form. Weyl equation with spectral or local boundary conditions. Potentials for massless...

Let $X=\mathbb{R}\times M$ be the spacetime, where $M$ is a closed manifold equipped with Riemannian metric $g$, and we consider symmetric Klein-Gordon type operator $P$ on $X$, which asymptotically converges to $\partial_t^2-\triangle_g$ as $|t|\to\infty$, $\triangle_g$ Laplace-Beltrami $M$. We prove essential self-adjointness of $C_0^\infty(X)$. The idea proof closely related recent paper by ...