Results 271 to 280 of about 107,051 (305)
Some of the next articles are maybe not open access.
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
openaire +2 more sources
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 ...
openaire +2 more sources
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
openaire +2 more sources
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
openaire +2 more sources
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.
openaire +2 more sources
Some theta-function identities
Applied Mathematics and Computation, 2007Using an identity obtained in an earlier paper [\textit{B. Srivastava}, Kyungpook Math. J. 45, 603--607 (2005; Zbl 1101.11005)] the author derives new theta-function identities. One of these leads to another proof of the classical formula for the number of representations of a positive integer as a sum of two squares.
openaire +1 more source
Various partition function identities
Ars Comb., 2000N. Robbins proves seven integer partitions identities. We give two of them. If \(p(n)\), \(q(n)\), and \(q_0(n)\) denote the numbers of unrestricted partitions, partitions into distinct parts, and partitions into distinct odd parts, and \(t(n)=n(n+1)/2\) are triangular numbers, then \[ \sum _{j=0}^nq_0(n-j)q_0(j)=p(n/2)+2\sum _{j\geq 1}p((n-j^2)/2 ...
openaire +1 more source
Ecto-ATPases: Identities and Functions
1995Ecto-ATPases are ubiquitous in eukaryotic cells. They hydrolyze extracellular nucleoside tri- and/or diphosphates, and, when isolated, they exhibit E-type ATPase activity, (that is, the activity is dependent on Ca2+ or Mg2+, and it is insensitive to specific inhibitors of P-type, F-type, and V-type ATPases; in addition, several nucleotide tri- and/or ...
openaire +2 more sources