Results 221 to 230 of about 549,143 (266)
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Identities for Multiplicative Functions
Canadian Mathematical Bulletin, 1967Throughout this paper the arithmetic functions L(n) and w(n) denote respectively the number and product of the distinct prime divisors of the integer n > 1, with L(1) = 0 and w(1) = 1. Also letWe recall that an arithmetic function f(n) is said to be multiplicative if f(1) = 1 and f(mn) = f(m)f(n) whenever (m, n) = 1, where (m, n) denotes as usual ...
Subbarao, M. V., Gioia, A. A.
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COMBINATORIAL IDENTITIES AND HYPERGEOMETRIC FUNCTIONS
Rocky Mountain Journal of Mathematics, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Alzer, Horst, Richards, Kendall C.
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Wigner Function for Identical Particles
Journal of Computational Electronics, 2004In this work the Wigner function approach to quantum transport developed for the single electron case is extended to a more complicated system for n indistingushable particles. In particular we study how the Monte Carlo tecnique and the Wigner paths method can be applyed to a single particle Wigner function defined for a system of n interacting ...
E. Cancellieri +4 more
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Simple Collective Identity Functions
Theory and Decision, 2008zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Cengelci, Murat Ali, Sanver, M. Remzi
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Arithmetical identities and zeta‐functions
Mathematische Nachrichten, 2010AbstractIn this paper we establish a class of arithmetical Fourier series as a manifestation of the intermediate modular relation, which is equivalent to the functional equation of the relevant zeta‐functions. One of the examples is the one given by Riemann as an example of a continuous non‐differentiable function.
Kanemitsu, Shigeru +2 more
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Functional Identities and Rings of Quotients
Algebras and Representation Theory, 2016Let \(R\) be a prime ring of degree \(\deg R\geq d\), it is well known that \(R\) is a \(d\)-free set of its maximal (left) ring of quotients \(Q_{ml}(R)\). (The exact definitions are given in the paper, there is a small misprint in that of the degree: on page 1443, line \(-2\) of the paper it should read \(\deg(R)=\sup\{\deg(t)\mid t\in R\}\).) Denote
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Cubic Identities of Theta Functions
The Ramanujan Journal, 1998A number of useful and interesting cubic identities involving theta functions are available in Ramanujan's Lost Note book. In this paper several theorems are established, in order to prove, some of these cubic identities. For proving the theorems the author employed addition formulas, the Jacobi triple product identity and the quintuple product ...
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The Enteric Glia: Identity and Functions
Glia, 2015Enteric glial cells were first described at the end of the 19th century, but they attracted more interest from researchers only in the last decades of the 20th. Although, they have a different embryological origin, the enteric GLIA share many characteristics with astrocytes, the main glial cell type of the central nervous system (CNS), such as in their
Juliana de Mattos, Coelho-Aguiar +9 more
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The identity and function of microglia in neurodegeneration
Nature Immunology, 2018The predominant type of immune cell in the brain is the microglia, a type of tissue-resident macrophage. In a variety of neurodegenerative settings, microglia alter their transcriptional profile, morphology and function in similar ways; thus, these activated cells have been called 'degeneration- or disease-associated microglia' (DAM).
Wilbur M. Song, Marco Colonna
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A characterization of the identity function
1997\textit{C. A. Spiro} [J. Number Theory 42, No. 2, 232--246 (1992; Zbl 0756.11027)] showed that if \(f\) is a multiplicative arithmetical function satisfying \(f(p+q)=f(p)+f(q)\) for all primes \(p\) and \(q\), then \(f(n)=n\). A related result was proved by \textit{J.-M. De Koninck, I. Kátai} and \textit{B. M. Phong} [J. Number Theory 63, No.
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