On the set of values of the Euler function.
Tasoev, B.G. (1999)
Vladikavkazskiĭ Matematicheskiĭ Zhurnal
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Tasoev, B.G. (1999)
Vladikavkazskiĭ Matematicheskiĭ Zhurnal
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Florian Luca, Pantelimon Stănică (2007)
Acta Arithmetica
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William D. Banks, John B. Friedlander, Florian Luca, Francesco Pappalardi, Igor E. Shparlinski (2006)
Acta Arithmetica
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William D. Banks, Florian Luca (2005)
Acta Arithmetica
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Hao Pan, Zhi-Wei Sun (2006)
Acta Arithmetica
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Sabine Roller, Thomas Schwartzkopff, Roland Fortenbach, Michael Dumbser, Claus-Dieter Munz (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
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The calculation of sound generation and propagation in low Mach number flows requires serious reflections on the characteristics of the underlying equations. Although the compressible Euler/Navier-Stokes equations cover all effects, an approximation via standard compressible solvers does not have the ability to represent acoustic waves correctly. Therefore, different methods have been developed to deal with the problem. In this paper, three of them are considered and compared...
Hirotaka Akatsuka (2006)
Acta Arithmetica
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Ji-Cai Liu (2017)
Czechoslovak Mathematical Journal
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Euler's pentagonal number theorem was a spectacular achievement at the time of its discovery, and is still considered to be a beautiful result in number theory and combinatorics. In this paper, we obtain three new finite generalizations of Euler's pentagonal number theorem.
Hiroshi Isozaki (1986)
Journées équations aux dérivées partielles
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Thomas C. Sideris (1991-1992)
Séminaire Équations aux dérivées partielles (Polytechnique)
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Sz. Tengely (2008)
Acta Arithmetica
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Kumbakonam R. Rajagopal (2023)
Applications of Mathematics
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The aim of this short paper is threefold. First, we develop an implicit generalization of a constitutive relation introduced by Korteweg (1901) that can describe the phenomenon of capillarity. Second, using a sub-class of the constitutive relations (implicit Euler equations), we show that even in that simple situation more than one of the members of the sub-class may be able to describe one or a set of experiments one is interested in describing, and we must determine which amongst these...
Ken Shirakawa (2009)
Banach Center Publications
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In this paper, a one-dimensional Euler-Lagrange equation associated with the total variation energy, and Euler-Lagrange equations generated by approximating total variations with linear growth, are considered. Each of the problems presented can be regarded as a governing equation for steady-states in solid-liquid phase transitions. On the basis of precise structural analysis for the solutions, the continuous dependence between the solution classes of approximating problems and that of...
Miloš Čanak (1994)
Matematički Vesnik
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