Article history: Received 7 October 2011 Accepted 21 May 2012 Available online 23 May 2012

López-Dahab coordinates are usually the system of choice for implementations of elliptic curves over binary fields. We give new formulas for doubling which need one squaring less and one more addition. This leads to a speed-up for binary fields in polynomial basis representation if the parameters are not fixed.

We consider several simple combinatorial problems and discuss different ways to express them using polynomial equations and try to describe the Gröbner basis of the corresponding ideals. The main instruments are complete symmetric polynomials that help to express different conditions in rather compact way.

In remote sensing, because of the wide diversity of image characteristics (size, spatial and radiometric resolution, terrain relief, observation poses, etc.), image registration methods that may work well on certain satellite images will not produce acceptable results for others, requiring more powerful techniques. A variety of registration techniques for images with non-rigid geometric differe...

In this talk, it is shown that a space curve in $\R^d$ can be approximated by a piecewise polynomial curve of degree $m$ with order $ (m+1)+ \lfloor (m+1)/(2d-1) \rfloor$ rather than $m+1$. Moreover, we show that the optimal order $(m+1)+\lfloor (m-1)/(d-1)\rfloor$ is possible for a particular set of curves.

Matrix functions are used in many areas of linear algebra and arise in numerical applications in science and engineering. In this paper, we introduce an effective approach for determining matrix function f(A)=g(q(A)) of a square matrix A, where q is a polynomial function from a degree of m and also function g can be a transcendental function. Computing a matrix function f(A) will be time- consu...

We introduce a reverse variant of the dual immaculate quasisymmetric functions, mirroring dichotomy between Schur functions and Young establish lift this basis to polynomial ring. show that taking stable limits these slide polynomials produces we positive formulas for expansions into fundamental quasi-key bases polynomials. These mirror connections extending from ring full also use provide anal...

The aim of this paper is to explore whether the generalized polynomial chaos (gPC) and random Fröbenius methods preserve the first three statistical moments of random differential equations. There exist exact solutions only for a few cases, so there is a need to use other techniques for validating the aforementioned methods in regards to their accuracy and convergence. Here we present a techniq...

Numerical solutions of the Helmholtz equation suffer from numerical pollution especially for the case of high wavenumbers. The major component of the numerical pollution is, as has been reported in the literature, the dispersion error which is defined as the phase difference between the numerical and the exact wave. The dispersion error for the meshless methods can be a priori determined at an ...