The real analytic Eisenstein series is a special function that has been studied classically. Its generalization to the case of many variables extensively. Moreover, properties certain on Siegel modular groups have also investigated. purpose this study provide concrete forms residue $$E_0^{(m)}(z,s)$$ at $$s=m/2$$ .

We investigate some properties of the WKB series for arbitrary analytic potentials and then specifically for potentials x (N even), where more explicit formulae for the WKB terms are derived. Our main new results are: (i) We find the explicit functional form for the general WKB terms σ k, where one has only to solve a general recursion relation for the rational coefficients. (ii) We give a syst...

in this paper, genetic algorithms (gas) are employed to control simultaneous linear systems in both state and output feedback. first, the similarity transformation is applied to obtain parameterized controllers. this requires solution of a system of equations and also some non-linear inequalities. gas are used to solve these equations and inequalities. therefore, the paper presents an analytica...

In the present paper we investigate the following problems. Suppose an >O for n_-I and Z a,=-. n=1 N° 1. Does there exist a sequence of natural numbers No =O, Ni l-, such that it decomposes the series monotone decreasingly : In order to state the second problem we define the index nk (c) as the minimum m such that (2) Now the second problem is as follows. are equiconvergent. m kc a j. j=1 N° 2....

Well-known Box-Jenkins Autoregressive integrated moving average (ARIMA) methodology has virtually dominated analysis of time-series data since 1930s. However, it is applicable to only those data that are either stationary or can be made so. Another limitation is that the resultant model is “Linear”. During the last two decades or so, the area of “Nonlinear time-series” is rapidly growing. Here,...

the paper presents the semi-numerical solution for the magnetohydrodynamic (mhd) viscous flow due to a stretching sheet caused by boundary layer of an incompressible viscous flow. the governing partial differential equations of momentum equations are reduced into a nonlinear ordinary differential equation (node) by using a classical similarity transformation along with appropriate boundary cond...