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Title: O jednom vzorci z operátorového počtu (Czech)
Title: On a certain operational formula (English)
Title: Über eine Formel der Operatorenrechnung (German)
Author: Vodička, Václav
Language: Czech
Journal: Aplikace matematiky
ISSN: 0373-6725
Volume: 12
Issue: 2
Year: 1967
Pages: 123-129
Summary lang: English
Summary lang: German
Summary lang: Russian
Category: math
Summary: This paper originates in the author's investigations on thermal and mechanical processes in semi-infinite continua. It presents a contribution to the theory of the Laplace transformation by deriving the original functions to the transforms $\frac{e^{-a\sqrt{(p+b^2)}}}{p\sqrt{(p+b^2)}},\ a\geq 0,\ b\neq 0$, $\frac{e^{-a\sqrt{(p^2+b^2)}}}{p^2\sqrt{(p^2+b^2)}},\ a>0,\ b\neq 0$. The significance and, may be, originality of the paper lies in that it is not easy to find reliable results in the existing literature, secondly in that the procedure works quickly and can be extended to deriving other useful operational formulae and finally in that there exist vast groups of physical and technical problems which are closely connected with the results given in the paper. Some examples concerning the heating of conducting semi-space by a variable heat flux through the surface are discussed in considerable details. They can serve to technicians and physicists as a kind of guide in treating other advanced questions of mathematical physics and egineering. (English)
Keyword: integral equations
Keyword: integral transforms
idZBL: Zbl 0145.15702
DOI: 10.21136/AM.1967.103078
Date available: 2008-05-20T17:38:13Z
Last updated: 2020-07-28
Stable URL:
Reference: [1] Диткин В. А,, Кузнецов П. И.: Справочник по операционному исчислению.ГИТТЛ, Москва-Ленинград 1951, стр. 159. Zbl 1165.94313
Reference: [2] Теумин И. И.: Справочник по переходным электрическим процессам.Связиздат, Москва 1951, стр. 369. Zbl 1165.94313
Reference: [3] Carslaw H. S., Jaeger J. С.: Conduction of Heat in Solids.Oxford 1959, str. 264.
Reference: [4] Vodička V.: O podélném kmitání polonekonečných tyčí.Čs. Čas. Fys. 13 (1963), 81.


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