A new method of obtaining exact solution for the rate matrix R in the Matrix-Analytic method in case of the phase state of dimension two is proposed. The method is based on symbolic solution of the determinental polynomial equation, and obtaining a linear matrix equation for the unknown rate matrix R by Cayley–Hamilton theorem. The method is applied to analyze the EnergyPerformance tradeoff of ...

in the present paper a solution of the generalizedquadratic functional equation$$f(kx+ y)+f(kx+sigma(y))=2k^{2}f(x)+2f(y),phantom{+} x,yin{e}$$ isgiven where $sigma$ is an involution of the normed space $e$ and$k$ is a fixed positive integer. furthermore we investigate thehyers-ulam-rassias stability of the functional equation. thehyers-ulam stability on unbounded domains is also studied.applic...

The solution for the above formulated problems are well known (Anderson, Moore, 1990), (Kuo, 1992), but there are some difficulties in implementation of the algorithms. The solution to the P1 problem is usually presented as an open loop control u(k) because the feedback control u(x(k)) has a complicated form. The P2 problem is the most frequently meet linear quadratic problem with finite final ...

Solving a quadratic equation P (x) = ax + bx+ c = 0 with real coefficients is known to middle school students. Solving the equation over the quaternions is not straightforward. Huang and So [2] give a complete set of formulas, breaking it into several cases depending on the coefficients. From a result of the second author in [10], zeros of P (x) can be expressed in terms of the zeros of a real ...

In this paper we introduce a general class of level dependent Quasi-Birth-and-Death (QBD) processes and their stationary solution. We obtain the complete characterization of their fundamental matrices in terms of minimal non-negative solution of number of matrix quadratic equations. Our results will provide mixed-geometric solution for the stationary solution of level dependent chains. Applicat...

In this paper we study a very general quadratic integral equation of fractional order. We show that the quadratic integral equations of fractional orders has at least one monotonic solution in the Banach space of all real functions defined and continuous on a bounded and closed interval. The concept of a measure of noncompactness related to monotonicity, introduced by J. Banaś and L. Olszowy, a...

In [12] a Zero-Knowledge scheme ZK(2) was designed from a solution of a set of multivariate quadratic equations over a finite field. In this paper we will give two methods to generalize this construction for polynomials of any degree d, i.e. we will design two Zero-Knowledge schemes ZK(d) and ̃ ZK(d) from a set of polynomial equations of degree d. We will show that ̃ ZK(d) is optimal in term of...

In this paper, a generalization of the level dependent Quasi-Birth-and-Death (QBD) chains is presented. We analyze nested level dependent QBD chains and provide the complete characterization of their fundamental matrices in terms of minimal non-negative solutions of a number of matrix quadratic equations. Our results provide mixed matrix-geometric solution for the stationary distribution of nes...

where f, g : I × → are given functions, λ ∈ (0, 1]. The study of quadratic integral equation has received much attention over the last thirty years or so. For instance, Cahlon and Eskin [1] prove the existence of positive solutions in the space C[0, 1] and Cα[0, 1] of an integral equation of the Chandrasekhar H-equation with perturbation. Argyros [2] investigates a class of quadratic equations ...