## Search

Now showing items 1-8 of 8

####
Preprint
Parity of the Number of Irreducible Factors for Composite Polynomials

(2008)

Various results on parity of the number of irreducible factors of given polynomials over finite fields have been obtained in the recent literature. Those are mainly based on Swan’s theorem in which discriminants of polynomials over a finite field or the integral ring Z play an important role. In this paper we consider discriminants of the composition of some polynomials over finite fields. The relation between the discriminants of composed polynomial and the original ones will be established. We apply this to obtain ...

####
Preprint
Construction of recurrent fractal interpolation surfaces(RFISs) on rectangular grids

(2008)

A recurrent iterated function system (RIFS) is a genaralization of an IFS and provides
nonself-affine fractal sets which are closer to natural objects. In general, it's attractor
is not a continuous surface in R3. A recurrent fractal interpolation surface (RFIS) is an
attractor of RIFS which is a graph of bivariate continuous interpolation function. We
introduce a general method of generating recurrent interpolation surface which are at-
tractors of RIFSs about any data set on a grid.

####
Preprint
Construction of fractal interpolation surfaces on rectangular grids

(2008)

We present a general method of generating continuous fractal interpolation surfaces
by iterated function systems on an arbitrary data set over rectangular grids and estimate
their Box-counting dimension.

####
Preprint
The Parity of the Number of Irreducible Factors for Some Pentanomials

(2008)

It is well known that Stickelberger-Swan theorem is very important for determining reducibility of polynomials over a binary field. Using this theorem it was determined the parity of the number of irreducible factors for some kinds of polynomials over a binary field, for instance, trinomials,
tetranomials, self-reciprocal polynomials and so on. We discuss this problem for type II pentanomials namely x^m +x^{n+2} +x^{n+1} +x^n +1 \in\ IF_2 [x].
Such pentanomials can be used for efficient implementing multiplication ...

####
Preprint
On Nonlinear Preconditioners in Newton-Krylov-Methods for Unsteady Flows

(2008)

The application of nonlinear schemes like dual time stepping as preconditioners in matrix-free Newton-Krylov-solvers is considered and analyzed. We provide a novel formulation of the left preconditioned operator that says it is in fact linear in the matrix-free sense, but changes the Newton scheme. This allows to get some insight in the convergence properties of these schemes which are demonstrated through numerical results.

####
Preprint
Numerical Methods for Non-Stationary Stokes Flow

(2008)

We consider a first order implicit time stepping procedure (Euler scheme)
for the non-stationary Stokes equations in smoothly bounded domains of R3. Using
energy estimates we can prove optimal convergence properties in the Sobolev
spaces Hm(G) (m = 0;1;2) uniformly in time, provided that the solution of the
Stokes equations has a certain degree of regularity. For the solution of the resulting
Stokes resolvent boundary value problems we use a representation in form of
hydrodynamical volume and boundary layer ...

####
Preprint
Image compression predicated on recurrent iterated function systems

(2008)

Recurrent iterated function systems (RIFSs) are improvements of
iterated function systems (IFSs) using elements of the theory of Marcovian
stochastic processes which can produce more natural looking images. We
construct new RIFSs consisting substantially of a vertical contraction factor
function and nonlinear transformations. These RIFSs are applied to image
compression.

####
Preprint
Divisibility of Trinomials by Irreducible Polynomials over F_2

(2008)

Irreducible trinomials of given degree n over F_2 do not always exist and in the cases that there is no irreducible trinomial of degree n it may be effective to use trinomials with an irreducible factor of degree n. In this paper we consider some conditions under which irreducible polynomials divide trinomials over F_2. A condition for divisibility of self-reciprocal trinomials by irreducible polynomials over F_2 is established. And we extend Welch's criterion for testing if an irreducible polynomial divides trinomials ...