Time series in many areas of application often display local or global trends. Typical models that provide statistical \explanations" of such trends are, for example, polynomial regression, smooth bounded trends that are estimated nonparametrically, and di erence-stationary processes such as, for instance, integrated ARIMA processes. In addition, there is a fast growing literature on stationary...

The Newtonian divided-di¤erence operators generate the nil-Coxeter algebra and semigroup. A bijective correspondence between the nil-Coxeter semigroup and the symmetric group is used to provide braid-like diagrams for the former, and corresponding Reidemeister-type moves for the relations. Conditions are given for similar relations to hold in a skew group ring. Interesting extensions of the nil...

In this paper an exact model for a basic rst order -modulator is derived by means of a di erence equation. Furthermore, the second order di erence equation describing a second order -modulator is given. In addition, the conditions under which by using the exact rst order model this second order di erence equation is getting a simpler form is given too.

The iterated di erence of polyhedra V P n P n Pk has been proposed independently in and as a su cient condition for V to be exactly computable by a two layered neural network An algorithm checking whether V IR is an iterated di erence of polyhedra is proposed in However this algorithm is not practically usable because it has a high computational complexity and it was only conjectured to stop wi...

Introduction In this paper we consider cell centered nite di erence approximations for second order convection di usion equations of divergence type Our goal is to construct nite di erence methods of second order of approximation that satisfy the discrete maximum principle The error estimates are in the discrete Sobolev spaces associated with the considered boundary value problem Approximation ...

We develop a Finite Element method (FEM) which can adopt very general meshes with polygonal elements for the numerical approximation of elliptic obstacle problems. This kind of methods are also known as mimetic discretization schemes, which stem from the Mimetic Finite Di erence (MFD) method. The rst-order convergence estimate in a suitable (mesh-dependent) energy norm is established. Numerical...

In this article we present a new experimental paradigm: comparative visual search. Each half of a display contains simple geometrical objects of three di erent colors and forms. The two display-halves are identical except for one object mismatched in either color or form. The subject's task is to nd this mismatch. We illustrate the potential of this paradigm for investigating the underlying com...

in this paper, a fuzzy hunter-saxton equation is solved by using the adomian'sdecomposition method (adm) and homotopy analysis method (ham). theapproximation solution of this equation is calculated in the form of series whichits components are computed by applying a recursive relation. the existenceand uniqueness of the solution and the convergence of the proposed methodsare proved. a nume...

In this paper implementations of three numerical schemes for the numerical simulation of the complex modi ed Korteweg de Vries CMKdV equation are reported The rst is an integrable scheme derived by methods related to the Inverse Scattering Transform IST The second is derived from the rst and is called the local IST scheme The third is a standard nite di erence scheme for the CMKdV equation Trav...

Voronoi cells and the notion of natural neighbours are used to develop a nite di erence method for the di usion operator on arbitrary unstructured grids. Natural neighbours are based on the Voronoi diagram, which partitions space into closest-point regions. The Sibson and the Laplace (non-Sibsonian) interpolants which are based on natural neighbours have shown promise within a Galerkin framewor...