On the approximate functional equation of Hecke's Z-functions

the effect of functional/notional approach on the proficiency level of efl learners and its evaluation through functional test

in fact, this study focused on the following questions: 1. is there any difference between the effect of functional/notional approach and the structural approaches to language teaching on the proficiency test of efl learners? 2. can a rather innovative language test referred to as "functional test" ge devised so so to measure the proficiency test of efl learners, and thus be as much reliable an...

On Approximate Solutions of the Generalized Radical Cubic Functional Equation in Quasi-$beta$-Banach Spaces

In this paper, we prove the generalized Hyers-Ulam-Rassias stability of the generalized radical cubic functional equation[    fleft( sqrt[3]{ax^3 + by^3}right)=af(x) + bf(y),]    where $a,b in mathbb{R}_+$ are fixed positive real numbers, by using direct method in quasi-$beta$-Banach spaces. Moreover, we use subadditive functions to investigate stability of the generaliz...

Uniform Approximate Functional Equation for Principal L-functions

C terms, C = C(π) = C(π̃) being the analytic conductor introduced by Iwaniec and Sarnak [IS]. We investigate the decay rate of the cutoff function and its derivatives (Theorem 1). We also see that the truncation can be made uniformly explicit at the cost of an error term (Theorem 2). Straightforward extensions of these results exist for products of central values. We hope that these formulae wil...

An efficient approximate method for solution of the heat equation using Laguerre-Gaussians radial functions

In the present paper, a numerical method is considered for solving one-dimensional heat equation subject to both Neumann and Dirichlet initial boundary conditions. This method is a combination of collocation method and radial basis functions (RBFs). The operational matrix of derivative for Laguerre-Gaussians (LG) radial basis functions is used to reduce the problem to a set of algebraic equatio...

On the Stability of the Orthogonally Quartic Functional Equation