Narrow Results

We investigate the asymptotic behavior of large eigenvalues for a class of finite difference self-adjoint operators with compact resolvent in l².

The chaotic system is widely used in chaotic cryptosystem and chaotic secure communication. In this paper, a universal method for designing the discrete chaotic system with any desired number of positive Lyapunov exponents is proposed to meet the needs of hyperchaotic systems in chaotic cryptosystem and chaotic secure communication, and three examples of eight-dimensional discrete system with chaotic attractors, eight-dimensional discrete system with fixed point attractors and eight-dimensional discrete system with periodic attractors are given to illustrate how the proposed methods control the Lyapunov exponents. Compared to the previous methods, the positive Lyapunov exponents are used to reconstruct a hyperchaotic system.

The purpose of this paper is to demonstrate the use of the results from [5, 6] for the explicit computation of the spectrum of two-sided infinite matrices with random diagonals. Here we consider the case of two random diagonals, one of them the main diagonal. Our result is a generalization of [24, Theorem 8.1] by Trefethen, Contedini and Embree from the case of one random and one constant diagonal to the case of two random diagonals.

In this paper, we present a method for constructing a Jacobi matrix $J\in {ℝ}^{n\times n}$ using $n$ known eigenvalues ${\lambda }_1,{\lambda }_2,\dots ,{\lambda }_n$. Some conditions are also given under which the constructed matrix is nonnegative and its diagonal entries are specified. Finally, we present a technique for constructing symmetric and nonsymmetric nonnegative matrices by their eigenvalues.

Functional and linear-algebraic approaches to the Delsarte problem of upper bounds on codes are discussed. We show that Christoffel-Darboux kernels and Levenshtein polynomials related to them arise as stationary points of the moment functionals of some distributions. We also show that they can be derived as eigenfunctions of the Jacobi operator.