this paper describes an approximating solution, based on lagrange interpolation and spline functions, to treat functional integral equations of fredholm type and volterra type. this method can be extended to functional dierential and integro-dierential equations. for showing eciency of the method we give some numerical examples.

A variety of data analysis concerned with genome sequences support the proposal that each living organism owns a genomic signature. Classical approaches to the genomic signature deciphering are based on the counting of oligonucleotides in DNA sequences. Statistical tools as well as graphical representations have been used to associate genomic signatures with oligonucleotides frequencies in the ...

The concept of expo-rational B-spline (ERBS) was introduced in [6] where the ’superproperties’ of ERBS were studied for the first time. In 2006 the first author of the present paper proposed a framework for the generalization of ERBS, the so-called generalized ERBS (GERBS), and considered one important instance of GERBS, the so-called Euler Beta-function B-splines (BFBS) which offered a good tr...

A new class of spline curves in polar coordinates has been presented in 12] and independently considered in 3]. These are rational trigonometric curves in Cartesian coordinates and can be represented as NURBS. From the relationship existing with the correspondent curves in Cartesian coordinates an alternative way to derive some useful tools for modelling splines in polar coordinates has been pr...

Pseudo-splines are a rich family of functions that allows the user to meet various demands for balancing polynomial reproduction (i.e., approximation power), regularity and support size. Such a family includes, as special members, B-spline functions, universally known for their usefulness in different fields of application. When replacing polynomial reproduction by exponential polynomial reprod...

Dirichlet averages of multivariate functions are employed for a derivation of basic recurrence formulas for the moments of multivariate Dirichlet splines. An algorithm for computing the moments of multivariate simplex splines is presented. Applications to hypergeometric functions of several variables are discussed. Introduction. In [9], H.B. Curry and I.J. Schoenberg have pointed out that univa...

It is proved that, among all nonnegative bases of its space, the B-spline basis is optimally stable for evaluating spline functions.