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1

Integration on hypercircles in Rn

Biernat G., Ligus M., Siedlecki J.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

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2009

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Vol. 8, nr 2

13-19

EN

This paper presents the formulas parametrizing hypercircles (the intersections of hyperplanes with the sphere in Rn, n ≥ 3). A hypothesis concerning the integral on hypercircle Cn-2 of the n-2 - canonical form ω n-2 is proposed.

2

Dependence of the Brillouin precursor form on the initial signal rise-time

Ciarkowski A.

Journal of Technical Physics

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2003

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Vol. 44, no 2

181-192

EN

Propagation of a Brillouin precursor in a Lorentz dispersive medium is considered. The precursor is excited by a sine-modulated initial signal, with its envelope described by a hyperbolic tangent function. The purpose of the paper is to show how the rate of growth of the signal affects the form of the Brillouin precursor. Uniform asymptotic approach, pertinent to coalescing saddle points, is applied in the analysis. The results are illustrated with numerical examples.

3

Tworzenie numerycznych procedur całkowania i różniczkowania sygnałów w oparciu o uproszczone modele dynamiki

Żuchowski A.

Zeszyty Naukowe Politechniki Rzeszowskiej. Elektrotechnika

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2002

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z. 22 [192]

287-294

PL

Dla różnych zastosowań praktycznych zachodzi potrzeba obliczania całki z sygnału x(t) po czasie, lub jego pochodnej, przy wykorzystaniu dyskretnych wartości x(nΔT). Wykorzystanie uproszczonych modeli dynamiki tworzonych na bazie splotu prowadzi do typowych i nietypowych procedur takich operacji zapewniających wysoką dokładność.

EN

The digital measurement equipment makes, that integrals or derivatives of signal x(t) in respect to time have to be calculated on the base of discrete values x(nΔT). The simplified models created by expansion of integrand of convolution integral in Taylor's series allow to define "typical" and "non-typical", highly accurate procedures for mentioned operations.

4

On Sommerfeld precursor in a Lorentz medium

Ciarkowski A.

Journal of Technical Physics

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2002

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Vol. 43, no 2

187-203

EN

A one-dimensional electromagnetic problem of Sommerfeld precursor evolution, resulting from a finite rise-time signal excitation in a dispersive Lorentz medium is considered. The effect of the initial signal rate of growth as well as of the medium dumping on the precursor shape and its magnitude is discussed. The analysis applied is based on an approach employing uniform asymptotic expansions. In addition, new approximate formulas are given for the location of the distant saddle points which affect local frequency and dumping of the precursor. The results obtained are illustrated numerically and compared with the results known from the literature.

5

Magneto-static field distribution due to inherent magnetisation of permanent magnets

Pawluk K.

Journal of Technical Physics

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2002

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Vol. 43, no 4

443-452

EN

A boundary-integral model of the static magnetic field due to cylindrical permanent magnets that is put in free space is considered. Magnetic scalar potential quantities created by a virtual quantity "surface magnetic charge density" is expressed by means of Lipschitz-Hankel integrals that for the considered case are reducible (by the way of hypergeometric series) to some algebraic expressions, in which elliptic integrals of various kinds occur. This approach seems to be more effective than that can be reached by the use of a typical professional software for the field problems in which numerical integration, being not quite conform to the considered case, is common. The magnet subjected to the analysis has to be virtually subdivided in some number of elementary pieces, inside of which the uniform distribution of the inherent magnetization is supposed.