On a certain operational formula

Václav Vodička

Aplikace matematiky (1967)

  • Volume: 12, Issue: 2, page 123-129
  • ISSN: 0862-7940

Abstract

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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 e - a ( p + b 2 ) p ( p + b 2 ) , a ≥ 0 , b ≠ 0 , e - a ( p 2 + b 2 ) p 2 ( p 2 + b 2 ) , a > 0 , b ≠ 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.

How to cite

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Vodička, Václav. "O jednom vzorci z operátorového počtu." Aplikace matematiky 12.2 (1967): 123-129. <http://eudml.org/doc/14461>.

@article{Vodička1967,
author = {Vodička, Václav},
journal = {Aplikace matematiky},
keywords = {integral equations; integral transforms},
language = {cze},
number = {2},
pages = {123-129},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {O jednom vzorci z operátorového počtu},
url = {http://eudml.org/doc/14461},
volume = {12},
year = {1967},
}

TY - JOUR
AU - Vodička, Václav
TI - O jednom vzorci z operátorového počtu
JO - Aplikace matematiky
PY - 1967
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 12
IS - 2
SP - 123
EP - 129
LA - cze
KW - integral equations; integral transforms
UR - http://eudml.org/doc/14461
ER -

References

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  1. Диткин В. А,, Кузнецов П. И., Справочник по операционному исчислению, ГИТТЛ, Москва-Ленинград 1951, стр. 159. (1951) Zbl1165.94313
  2. Теумин И. И., Справочник по переходным электрическим процессам, Связиздат, Москва 1951, стр. 369. (1951) Zbl1165.94313
  3. Carslaw H. S., Jaeger J. С., Conduction of Heat in Solids, Oxford 1959, str. 264. (1959) 
  4. Vodička V., O podélném kmitání polonekonečných tyčí, Čs. Čas. Fys. 13 (1963), 81. (1963) 

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