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2010
We now begin our study of topological invariants, by considering the “Euler number” or “Euler characteristic.” This assigns an integer to each topological space in a way that tells us something about the topology of the space. In particular, it can sometimes tell if two spaces are not homotopy equivalent, since spaces which are homotopy equivalent have
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We now begin our study of topological invariants, by considering the “Euler number” or “Euler characteristic.” This assigns an integer to each topological space in a way that tells us something about the topology of the space. In particular, it can sometimes tell if two spaces are not homotopy equivalent, since spaces which are homotopy equivalent have
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Leonhard euler’s convenient numbers
The Mathematical Intelligencer, 1985Die Euler'schen ''numeri idonei'' sind jene natürlichen Zahlen m, für welche die Kompositionsklassengruppe binärer Formen der Diskriminante - 4m nur eine Klasse im Geschlecht hat; es wird über die wichtigsten Resultate von L. Euler, C. F. Gauss and \textit{F. Grube} [Über einige Euler'sche Sätze aus der Theorie der quadratischen Formen, Z. Math.
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Integral Transforms and Special Functions, 2013
These numbers are defined as the coefficients of the Euler–Frobenius polynomials which usually are introduced via the rational function expansion n being a nonnegative integer and λ∈[0, 1). The special case An, l (0) is known from combinatorics (Eulerian numbers) and the general one An, l (λ) occurs, for example, in approximation theory, summability ...
Wolfgang Gawronski, Thorsten Neuschel
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These numbers are defined as the coefficients of the Euler–Frobenius polynomials which usually are introduced via the rational function expansion n being a nonnegative integer and λ∈[0, 1). The special case An, l (0) is known from combinatorics (Eulerian numbers) and the general one An, l (λ) occurs, for example, in approximation theory, summability ...
Wolfgang Gawronski, Thorsten Neuschel
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Proceedings of the Steklov Institute of Mathematics, 2009
We give an account of the most important results obtained by Euler in number theory, including the main contribution of Euler, application of analysis to problems of number theory. We note an important role played in modern number theory by the function that was introduced by Euler and is called the Riemann zeta function.
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We give an account of the most important results obtained by Euler in number theory, including the main contribution of Euler, application of analysis to problems of number theory. We note an important role played in modern number theory by the function that was introduced by Euler and is called the Riemann zeta function.
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An Addendum on the Euler Numbers
Journal of the London Mathematical Society, 1971openaire +2 more sources
Identities for the Bernoulli and Euler numbers and polynomials.
Ars Comb., 2012Summary: In this paper, we investigate some interesting identities on the Euler numbers and polynomials arising from their generating functions and difference operators. Finally, we give some properties of Bernoulli and Euler polynomials by using \(p\)-adic integral on \(\mathbb Z_p\).
Taekyun Kim 0001 +3 more
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The Euler Number of a Riemann Manifold
American Journal of Mathematics, 1940openaire +2 more sources
Dynamic numerical simulation of gas-liquid two-phase flows Euler/Euler versus Euler/Lagrange
Chemical Engineering Science, 1997Gerhart Eigenberger
exaly
A-to-Z Guide to Thermodynamics, Heat and Mass Transfer, and Fluids Engineering, 2006
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