2D curve representations usually take algebraic forms in ways not related to visual perception. This poses great difficulties in connecting curve representation with object recognition where information computed from raw images must be manipulated in a perceptually meaningful way and compared to the representation. In this paper we show that 2D curves can be represented compactly by imposing sh...

In this paper sixth order boundary value problems is solved numerically by collocation method. The solution is approximated as a linear combination of septic B-spline functions. The septic B-splines constitute a basis for the space of septic polynomial splines. In the method, the basis functions are redefined into a new set of basis functions which in number match with the number of selected co...

Kautz functions constitute a basis in L2 and can be used for filter synthesis starting from a prescribed transient response. In a practical situation, only truncated series are used and thus the speed of convergence of such series is of importance. This convergence speed is a function of the parameters. The Kautz functions that are considered can be generated by a line of identical Nth-order al...

We suggest the modification of the standard approach to TMDs. The modification consists in the consideration of the small bT operator product expansion in the different operator basis. Instead of power expansion we suggest to use the Laguerre polynomial expansion. Within such a scheme the first term of OPE saturates TMDs in the wider range of bT in comparison to the power expansion that decreas...

Several representations for the interpolating polynomial exist: Lagrange, Newton, orthogonal polynomials etc. Each representation is characterized by some basis functions. In this paper we investigate the transformations between the basis functions which map a specific representation to another. We show that for this purpose the LU and the QR decomposition of the Vandermonde matrix play a cruci...

in this article we decide to define a modified homotopy perturbation for solving non-linear integral equations. almost, all of the papers that was presented to solve non-linear problems by the homotopy method, they used from two non-linear and linear operators. but we convert a non-linear problem to two suitable non-linear operators also we use from appropriate bases functions such as legendre ...

Let X be a set of points whose coordinates are known with limited accuracy; our aim is to give a characterization of the vanishing ideal I(X) independent of the data uncertainty. We present a method to compute a polynomial basis B of I(X) which exhibits structural stability, that is, if e X is any set of points differing only slightly from X, there exists a polynomial set e B structurally simil...

Recently, Zharkov and Blinkov introduced the notion of involutive bases of polynomial ideals. This involutive approach has its origin in the theory of partial di erential equations and is a translation of results of Janet and Pommaret. In this paper we present a pure algebraic foundation of involutive bases of Pommaret type. In fact, they turn out to be generalized left Grobner bases of ideals...

We propose a method to generate pairs of relatively prime polynomials. The method is deterministic and depends on Gröbner basis techniques. A possible application to Cryptography is presented.