## Search

Now showing items 31-40 of 61

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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.

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Preprint
On the relationship between the Method of Least Squares and Gram-Schmidt orthogonalization

(2010)

The method of Least Squares is due to Carl Friedrich Gauss. The Gram-Schmidt
orthogonalization method is of much younger date. A method for solving Least Squares Problems is developed which automatically results in the appearance of the Gram-Schmidt orthogonalizers. Given these orthogonalizers an induction-proof is available for solving Least Squares Problems.

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Preprint
On Solution Sets of Information Inequalities

(2011)

We investigate solution sets of a special kind of linear inequality systems. In particular, we derive characterizations of these sets in terms of minimal solution sets. The studied inequalities emerge as information inequalities in the context of Bayesian networks. This allows to deduce important properties of Bayesian networks, which is important within causal inference.

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Preprint
Exact algorithms for p-adic fields and epsilon constant conjectures

(2006)

We develop several algorithms for computations in Galois extensions of p-adic fields. Our algorithms are based on existing algorithms for number fields and are exact in the sense that we do not need to consider approximations to p-adic numbers. As an application we describe an algorithmic approach to prove or disprove various conjectures for local and global epsilon constants.

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Preprint
Church-Rosser groups and growing context-sensitive groups

(2006)

A finitely generated group is called a Church-Rosser group (growing context-sensitive group) if it admits a finitely generated presentation for which the word problem is a Church-Rosser (growing context-sensitive) language.
Although the Church-Rosser languages are incomparable to the context-free languages under set inclusion, they strictly contain the class of deterministic context-free languages.
As each context-free group language is actually deterministic context-free, it follows that all context-free groups ...

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Preprint
Solution properties of the de Branges differential recurrence equation

(2005)

In this 1984 proof of the Bieberbach and Milin conjectures de Branges used a positivity result of special functions which follows from an identity about Jacobi polynomial sums thas was published by Askey and Gasper in 1976. The de Branges functions Tn/k(t) are defined as the solutions of a system of differential recurrence equations with suitably given initial values. The essential fact used in the proof of the Bieberbach and Milin conjectures is the statement Tn/k(t)<=0. In 1991 Weinstein presented another proof of ...

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Preprint
Preconditioner updates applied to CFD model problems

(2007)

In the present paper we concentrate on solving sequences of nonsymmetric linear systems with block structure arising from compressible flow problems. We attempt to improve the solution process by sharing part of the computational effort throughout the sequence. This is achieved by application of a cheap updating technique for preconditioners which we adapted in order to be used for our applications. Tested on three benchmark compressible flow problems, the strategy speeds up the entire computation with an acceleration ...

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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.

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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.