Applied Mathematics

In mathematics or its applications, a functional equation is an equation in terms of independent variables, and also unknown functions, which are to be solved for. Many properties of functions can be determined by studying the types of functional equations they satisfy. Usually the term functional equation is reserved for equations that are not in some simple sense reducible to algebraic equations, often because two or more known functions of the variables are substituted as arguments into an unknown function to be solved for. For example: The commutative and associative laws are functional equations. When the associative law is expressed in its familiar form, one lets some symbol between two variables represent a binary operation, thus: (a * b) * c = a * (b * c) But if we write f (a, b) instead of a * b, then the associative law looks more like what one conventionally thinks of as a functional equation: f (f(a, b), c) = f(a, f(b, c))We study generalized quadratic functional equations on quasigroups. These are equations s = t, where each variable appears exactly twice in s = t and each Operational symbol is assumed to be a quasigroup operation on a (fixed) set. A fundamental problem in this class of equations is to investigate their structure and classify them accordingly.

Mean labeling of graphs was discussed in [24-28].Different kinds of mean labeling were discussed in [17]. In this paper, we have proved the Cycle related mean graphs.

Half a variable coefficient model is a variable coefficient model, this paper mainly discusses the useful promotion in linear equality constraints in the second half of variable coefficient model parameter estimation problem, this paper presents parameters in part equality constraints under double parameters of the conjugate gradient method and the parameters of part estimate, on the double parameters conjugate gradient method of the decline of the projection and convergence is proved by an example, the algorithm of the optimal inspection benign.