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Journal of the Australian Mathematical Society, 2016
Poly-Euler numbers are introduced as a generalization of the Euler numbers in a manner similar to the introduction of the poly-Bernoulli numbers. In this paper, some number-theoretic properties of poly-Euler numbers, for example, explicit formulas, a Clausen–von Staudt type formula, congruence relations and duality formulas, are given together with ...
Ohno, Yasuo, Sasaki, Yoshitaka
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Poly-Euler numbers are introduced as a generalization of the Euler numbers in a manner similar to the introduction of the poly-Bernoulli numbers. In this paper, some number-theoretic properties of poly-Euler numbers, for example, explicit formulas, a Clausen–von Staudt type formula, congruence relations and duality formulas, are given together with ...
Ohno, Yasuo, Sasaki, Yoshitaka
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Estimation of the number of alveolar capillaries by the Euler number (Euler-Poincaré characteristic)
American Journal of Physiology-Lung Cellular and Molecular Physiology, 2015The lung parenchyma provides a maximal surface area of blood-containing capillaries that are in close contact with a large surface area of the air-containing alveoli. Volume and surface area of capillaries are the classic stereological parameters to characterize the alveolar capillary network (ACN) and have provided essential structure-function ...
Willführ, Alper +6 more
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A proof of image Euler Number formula
Science in China Series F, 2006zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xiaozhu Lin +3 more
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On Distribution of the Number of Peaks and the Euler Numbers of Permutations
Methodology and Computing in Applied Probability, 2023zbMATH Open Web Interface contents unavailable due to conflicting licenses.
James C. Fu +2 more
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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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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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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
A-to-Z Guide to Thermodynamics, Heat and Mass Transfer, and Fluids Engineering, 2006
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