Highly nonlinear functions

HYBRID FUNCTIONS APPROACH AND PIECEWISE CONSTANT FUNCTION BY COLLOCATION METHOD FOR THE NONLINEAR VOLTERRA-FREDHOLM INTEGRAL EQUATIONS

In this work, we will compare two approximation method based on hybrid Legendre andBlock-Pulse functions and a computational method for solving nonlinear Fredholm-Volterraintegral equations of the second kind which is based on replacement of the unknown functionby truncated series of well known Block-Pulse functions (BPfs) expansion

New Lower Bounds on Nonlinearity and a Class of Highly Nonlinear Functions

Highly nonlinear Boolean functions occupy an important p o-sition in the design of secure block as well as stream ciphers. This paper proves two n e w l o wer bounds on the nonlinearity of Boolean functions. Based on the study of these new lower bounds, we introduce a class of highly nonlinear Boolean functions on odd dimensional spaces and show examples of such functions.

COVARIANCE MATRIX OF MULTIVARIATE REWARD PROCESSES WITH NONLINEAR REWARD FUNCTIONS

Multivariate reward processes with reward functions of constant rates, defined on a semi-Markov process, first were studied by Masuda and Sumita, 1991. Reward processes with nonlinear reward functions were introduced in Soltani, 1996. In this work we study a multivariate process , , where are reward processes with nonlinear reward functions respectively. The Laplace transform of the covar...

Application of new basis functions for solving nonlinear stochastic differential equations

This paper presents an approach for solving a nonlinear stochastic differential equations (NSDEs) using a new basis functions (NBFs). These functions and their operational matrices are used for representing matrix form of the NBFs. With using this method in combination with the collocation method, the NSDEs are reduced a stochastic nonlinear system of equations and unknowns. Then, the error ana...

Numerical solution of nonlinear integral equations by Galerkin methods with hybrid Legendre and Block-Pulse functions

In this paper, we use a combination of Legendre and Block-Pulse functionson the interval [0; 1] to solve the nonlinear integral equation of the second kind.The nonlinear part of the integral equation is approximated by Hybrid Legen-dre Block-Pulse functions, and the nonlinear integral equation is reduced to asystem of nonlinear equations. We give some numerical examples. To showapplicability of...

Asymptotic Behavior of Multivariate Reward Processes with Nonlinear Reward Functions