In this paper, using the direct method we study the generalized Hyers-Ulam-Rassias stability of the following quadratic functional equations (2 ) ( ) 6 ( )     f x y f x y f x and (3 ) ( ) 16 ( )     f x y f x y f x for the mapping f from normed linear space in to 2-Banach spaces.

A monomial Hénon mapping is defined as the wellknown two-dimensional Hénon map with the quadratic term replaced by a monomial. This paper introduces a conjecture about monomial Hénon mappings: Even Hénon mappings are chaotic and odd Hénon mappings are not chaotic in the first quadrant of the bifurcation parameter space. This conjecture is based on numerical simulations of this type of map.

In this paper we consider enveloping C *-algebras of *-algebras given by generators and defining relations of the following form A = CX, X * | XX * = f (X * X), where f is a Hermitian mapping. Some properties of these algebras associated with simple dynamical systems (f, R) are studied. As an example quadratic dynamical systems are considered.

This paper proposes a novel optimization which named as Swarm based Mean-variance mapping optimization (MVMOS) for solving the economic dispatch. The proposed optimization algorithm is the extension of the original single particle mean-variance mapping optimization (MVMO). The novel feature is the special mapping function applied for the mutation base on the mean and variance of n-best populati...

We report on the development of algorithms for solving the Quadratic 3-dimensional Assignment Problem (Q3AP). The application is a hybrid ARQ scheme for enriching diversity among multiple packet transmissions by optimizing the mapping of transmission symbols to data. Our current exact algorithm, based on a reformulation linearization technique, solves Q3AP instances of size 13 or smaller. Our f...

In this paper, four kinds of chaos mapping equations such as Logistic, Henon, Quadratic and MacKeyGlass were discussed, and the numerical characteristics of those chaos mapping equations were analyzed and compared by histogram and correlation coefficient. Then the better chaos encryption system was selected according to analyzing result, and the encryption method of poor chaos encryption system...

The braid group Bn is the mapping class group of an n-times punctured disk. The Iwahori-Hecke algebra Hn is a quotient of the braid group algebra of Bn by a quadratic relation in the standard generators. We discuss how to use Hn to define the Jones polynomial of a knot or link. We also summarize the classification of the irreducible representations of Hn. We conclude with some directions for fu...

The shadowing property is to find an exact solution to an iterated map that remains close to an approximate solution. In this article, using shadowing property, we show the stability of the following equation in normed group: 4n−2Cn/2−1rf ∑n j 1 xj/r n ∑ ik∈{0,1}, ∑n k 1 ik n/2 r2f ∑n i 1 −1 ik xi/r 4n·n−2Cn/2−1 ∑n i 1 f xi , where n ≥ 2, r ∈ R r2 / n and f is a mapping. And we prove that the e...

Recently, in [5], Najati and Moradlou proved Hyers-Ulam-Rassias stability of the following quadratic mapping of Apollonius type Q(z − x) + Q(z − y) = 1 2 Q(x− y) + 2Q ( z − x + y 2 ) in non-Archimedean space. In this paper we establish Hyers-Ulam-Rassias stability of this functional equation in random normed spaces by direct method and fixed point method. The concept of Hyers-Ulam-Rassias stabi...

In this work we present a simple, but effective method of enhancing and exploiting diversity from multiple packet transmissions in systems that employ nonbinary linear modulations such as PSK and QAM. This diversity improvement results from redesigning the symbol mapping for each packet transmission. Using a general framework for evaluating the upper bound of bit error rate (BER) with multiple ...