In this paper we prove a Hölder and Lipschitz stability estimates of determining the residual stress by a single pair of observations from a part of the lateral boundary or from the whole boundary. These estimates imply first uniqueness results for determination of residual stress from few boundary measurements.

In this paper we prove existence results for extremal solutions of the first order discontinuous impulsive differential inclusions with periodic boundary conditions and impulses at the fixed times under certain monotonicity conditions of the multi-valued functions.

We construct examples, that log Hölder continuity of the integrated density of states cannot be improved. Our examples are limit-periodic.

In two-dimensional lattice fermion model a determinant representation for the twopoint correlation function of the twist field in the disorder phase is obtained. This field is defined by twisted boundary conditions for lattice fermion field. The large distance asymptotics of the correlation function is calculated at the critical point and in the scaling region. The result is compared with the v...

We consider the convective Cahn–Hilliard equation with periodic boundary conditions as an infinite dimensional dynamical system and establish the existence of a compact attractor and a finite dimensional inertial manifold that contains it. Moreover, Gevrey regularity of solutions on the attractor is established and used to prove that four nodes are determining for each solution on the attractor...

It is shown that certain natural maps between the ideal, Gromov, and end boundaries of a complete CAT(0) space can fail to be either injective or surjective. Additionally the natural map from the Gromov boundary to the end boundary of a complete CAT(−1) space can fail to be either injective or surjective.

— We prove that the subquartic wave equation on the three dimensional ball Θ, with Dirichlet boundary conditions admits global strong solutions for a large set of random supercritical initial data in ∩s<1/2H (Θ). We obtain this result as a consequence of a general random data Cauchy theory for supercritical wave equations developed in our previous work [6] and invariant measure considerations w...

We consider the problem of enumerating spanning trees on lattices. Closed-form expressions are obtained for the spanning tree generating function for a hypercubic lattice of size N1×N2×· · ·×Nd in d dimensions under free, periodic, and a combination of free and periodic boundary conditions. Results are also obtained for a simple quartic net embedded on two non-orientable surfaces, a Möbius stri...

Size-dependent longitudinal and torsional vibrations of nano-beams are examined by two-phase mixture integral elasticity. A new and efficient elastodynamic model is conceived by convexly combining the local phase with strain- and stress-driven purely nonlocal phases. The proposed stress-driven nonlocal integral mixture leads to well-posed structural problems for any value of the scale parameter...

A path-integral representation for the kernel of the evolution operator of general Hamiltonian systems is reviewed. We study the models with bosonic and fermionic degrees of freedom. A general scheme for introducing boundary conditions in the path-integral is given. We calculate the path-integral for the systems with quadratic first class constraints and present an explicit formula for the heat...