the purpose of this study is to present an approximate numerical method for solving high order linear fredholm-volterra integro-differential equations in terms of rational chebyshev functions under the mixed conditions. the method is based on the approximation by the truncated rational chebyshev series. finally, the effectiveness of the method is illustrated in several numerical examples. the p...

Pop proved that a smooth curve C over an ample field K with C(K) 6= ∅ has |K| many rational points. We strengthen this result by showing that there are |K| many rational points that do not lie in a given proper subfield, even after applying a rational map. As a consequence we gain insight into the structure of existentially definable subsets of ample fields. In particular, we prove that a perfe...

This article is about the institutional collaboration in the management structure of a city-region. To achieve this purpose, corporate limits of Qazvin are studied as the city is becoming a region.  The possible institutional cooperative in the centralist governmental structure is planned based on the new regionalism theory and its governance pattern, new institutionalism theory and its emphas...

We review the theory of homogeneous splines and their relationship to special rational splines considered by J. SS anchez{Reyes and independently by P. de Casteljau who called them focal splines. Applying an appropriate duality, we transform focal splines into a remarkable class of rational curves with rational oosets. We investigate geometric properties of these dual focal splines, and discuss...