Grover’s equation [L.K. Grover, Local search and the local structure of some NP-complete problems, Operations Research Letters 12 (1992)] and, equivalently, the Laplacian equation [J.W. Barnes, S. Dokov, B. Dimova, A. Solomon, A theory of elementary landscapes, Applied Mathematics Letters 16 (2003)] define an elementary landscape which has favorable properties for direct search methods. Dimova ...

There are numerous papers in the literature, which analyze the behavior of specific queueing systems in terms of certain roots of a nonlinear equation. In this paper we show that a very general class of queueing systems, including queues with heterogeneous servers, multiple arrival streams, bulk queues and feedback, is described by a characteristic equation. We prove that the number in queue an...

We discuss how properties of Hecke symmetry (i.e., Hecke type R-matrix) influence the algebraic structure of the corresponding Reflection Equation (RE) algebra. Analogues of the Newton relations and Cayley-Hamilton theorem for the matrix of generators of the RE algebra related to a finite rank even Hecke symmetry are derived.

in this paper, operational matrices of riemann-liouville fractional integration and caputo fractional differentiation for shifted jacobi polynomials are considered. using the given initial conditions, we transform the fractional differential equation (fde) into a modified fractional differential equation with zero initial conditions. next, all the existing functions in modified differential equ...