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Now showing items 31-40 of 42
Preprint
Approximate Approximations and a Boundary Point Method for the Linearized Stokes System
(2007)
The method of approximate approximations, introduced by Maz'ya [1], can also be used for the numerical solution of boundary integral equations. In this case, the matrix
of the resulting algebraic system to compute an approximate source density depends only on the position of a finite number of boundary points and on the direction of the normal vector in these points (Boundary Point Method). We investigate this approach for the Stokes problem in the whole space and for the Stokes boundary value problem in a bounded ...
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
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
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 ...
Preprint
On Oseen Resolvent Estimates: A Negative Result
(2009)
We consider the resolvent problem for the scalar Oseen equation in the whole space R^3. We show that for small values of the resolvent parameter it is impossible to obtain an L^2-estimate analogous to
the one which is valid for the Stokes resolvent, even if the resolvent parameter has positive real part.
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
Statistical Analysis of Diabetes Mellitus
(2009)
Diabetes mellitus is a disease where the glucosis-content of the blood does not automatically decrease to a ”normal” value between 70 mg/dl and 120 mg/dl (3,89 mmol/l and 6,67 mmol/l) between perhaps one hour (or two hours) after eating. Several instruments can be used to arrive at a relative low increase of the glucosis-content. Besides drugs (oral antidiabetica, insulin) the blood-sugar content can mainly be influenced by (i) eating, i.e., consumption of the right amount of food at the right time (ii) physical ...
Preprint
Duplication coefficients via generating functions
(2006)
In this paper, we solve the duplication problem P_n(ax) = sum_{m=0}^{n}C_m(n,a)P_m(x) where {P_n}_{n>=0} belongs to a wide class of polynomials, including the classical orthogonal polynomials (Hermite, Laguerre, Jacobi) as well as the classical discrete orthogonal polynomials (Charlier, Meixner, Krawtchouk) for the specific case a = −1. We give closed-form expressions as well as recurrence relations satisfied by the duplication coefficients.
Preprint
Approximate solutions and error estimates for a Stokes boundary value problem
(2009)
The aim of this paper is the numerical treatment of a boundary value problem for the system of Stokes' equations. For this we extend the method of approximate approximations to boundary value problems. This method was introduced by V. Maz'ya in 1991 and has been used until now for the approximation of smooth functions defined on the whole space and for the approximation of volume potentials. In the present paper we develop an approximation procedure for the solution of the interior Dirichlet problem for the system ...