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Based on our derivation of finite temperature reduced density matrix functional theory and the discussion of the performance of its first-order functional this work presents several different correlation-energy functionals and applies them…

In this paper, we consider limit laws for the model, which is a generalisation of the random energy model (REM) to the case when the energy levels have the mixture distribution. More precisely, the distribution of the energy levels is…

This paper extends the nonlinear ISS small-gain theorem to a large-scale time delay system composed of three or more subsystems. En route to proving this small-gain theorem for systems of differential equations with delays, a small-gain…

An overview of stability conditions in terms of the Lyapunov matrix for time-delay systems is presented. The main results and proof are presented in details for the case of systems with multiple delays. The state of the art, ongoing…

On compact Riemannian manifolds, we prove a decomposition theorem for arbitrarily bounded energy sequence of solutions of a singular elliptic equation.

In this paper we present a short and elementary proof for the error in Simpson's rule.

Here we simplify the proof of the de Rham theorem for Schwartz functions on affine Nash manifolds and generalize the result to the case of non affine Nash manifolds.

Synchronization in an array of mutually coupled systems with a finite time-delay in coupling is studied using Josephson junction as a model system. The sum of the transverse Lyapunov exponents is evaluated as a function of the parameters by…

For a relativistic particle moving in the presence of mean scalar and vector fields, the energy at second order in the scalar field is shown to contain two contributions in general. One is a momentum-dependent repulsive interaction…

In this paper, we prove several generalizations and applications of a fixed point theorem. This theorem is used to prove the existence and uniqueness of solutions of the linear sparse matrix problem considered.

We study minimizers of non-autonomous energies with minimal growth and coercivity assumptions on the energy. We show that the minimizer is nevertheless the solution of the relevant Euler--Lagrange equation or inequality. The main tool is an…

We discuss the possibility of generalizing some aspects of the C-theorem within two different approaches, the conventional RG and the Wilson RG flows. We show that the original Zamolodchikov's theorem is related to the existence of the…

A class of semilinear parabolic reaction diffusion equations with multiple time delays is considered. These time delays and corresponding weights are to be optimized such that the associated solution of the delay equation is the best…

The chapter from the book introduces the delay theory, whose purpose is the modeling of the asynchronous circuits from digital electrical engineering with ordinary and differential pseudo-boolean equations.

Rosenbrock's theorem on polynomial system matrices is a classical result in linear systems theory that relates the Smith-McMillan form of a rational matrix $G$ with the Smith forms of an irreducible polynomial system matrix $P$ giving rise…

We study the minimum energy null-controllability problem for differential equations with point-wise delays. For the equations of both neutral and retarded type we reduce the problem of finding the optimal control to a Volterra integral…

We prove that if a globally minimizing solution to the vectorial Allen-Cahn equation has finite potential energy, then it is a constant.

Under integral restrictions on dilatations, it is proved existence theorems for the degenerate Beltrami equations with two characteristics and, in particular, to the Beltrami equations of the second type that play a great role in many…

An analog of Picard's little theorem for entire functions of matrices is proved.

We consider the energy of smooth generalized distributions and also of singular foliations on compact Riemannian manifolds for which the set of their singularities consists of a finite number of isolated points and of pairwise disjoint…