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The multiple functions of Numb
Experimental Cell Research, 2010Numb is an evolutionary conserved protein that plays critical roles in cell fate determination. Mammalian Numb displays a higher degree of structural complexity compared to the Drosophila homolog based on the number of encoding genes (Numb and Numb-like) and of alternative spliced isoforms.
GULINO, Alberto +2 more
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Forum Mathematicum, 2003 This paper is an English version of a part of some lecture notes by N. Kurokawa from 1991, the notes having been taken by S. Koyama. In the paper, a theory of multiple sine functions is constructed which generalizes the usual sine function. The double sine function was introduced by Hölder in 1886, and the authors introduce the triple and higher sine ...
Kurokawa Nobushige, Koyama Shin-ya
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Summation of multiplicative functions [PDF]
Journal of Soviet Mathematics, 1983 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Heteroscedastic BART via Multiplicative Regression Trees
, 2020Bayesian additive regression trees (BART) has become increasingly popular as a flexible and scalable nonparametric regression approach for modern applied statistics problems. For the practitioner dealing with large and complex nonlinear response surfaces,
M. Pratola +3 more
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On a new multiplicative function [PDF]
Russian Mathematical Surveys, 1998 The author considers a generalized Arkhipov function \(\alpha_{k,m}(n)\), defined as the number of solutions of the simultaneous equations \(x_1\cdots x_k=n\), \(n\equiv 0\mod[x_1^m,\dots,x_k^m]\), where \([a,b]\) denotes the least common multiple of the integers \(a\) and \(b\). Arkhipov's function is the special case \(m=2\).
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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 ...
M. V. Subbarao, A. A. Gioia
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Almost multiplicative functions and almost linear multiplicative functionals
Aequationes mathematicae, 2002Among others the following result is offered. If \(\delta>0\), \(A\) is a real Banach algebra, and \(\varphi: A\to\mathbb{R}\) a \(\delta\)-homomorphism, that is, \[ |\varphi(x+y)-\varphi(x)-\varphi(y)|\leq\delta(\|x\|+\|y\|),\quad |\varphi(xy)-\varphi(x)\varphi(y)|\leq \delta\|x\|\|y\|, \] then \(2\sup_{x\in A\setminus \{0\}} |\varphi(x)|/\|x\|\leq 1+(
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MULTIPLICATION OF WEAK FUNCTIONS
Acta Mathematica Scientia, 2005This paper is a continuation of the authors' recent work [\textit{X. Ding} and \textit{P. Luo}, Acta Math. Sci., Ser. B, Engl. Ed. 24, 691--697 (2004; Zbl 1081.33012)] and is concerned with multiplication of weak functions. Here the weak functions are treated as generalized expansions in Hermite functions just as in the same authors' earlier paper ...
Zhen Wang, Xiaqi Ding
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2010
If X is an open subset of Rn, the function ψ belongs to \(C^\infty (X),\) and f is locally integrable on X, one has, for every test function \(\phi,\ ({\rm test}(\psi\ f))(\phi ) = ({\rm test}\ f)(\psi\ \phi ).\)
Johannes J. Duistermaat, J. A. C. Kolk
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If X is an open subset of Rn, the function ψ belongs to \(C^\infty (X),\) and f is locally integrable on X, one has, for every test function \(\phi,\ ({\rm test}(\psi\ f))(\phi ) = ({\rm test}\ f)(\psi\ \phi ).\)
Johannes J. Duistermaat, J. A. C. Kolk
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Summation of multiplicative functions
Russian Mathematical Surveys, 2002Es seien \(f_1(n)\) eine total und \(f_2(n)\) eine streng multiplikative zahlentheoretische Funktion und \(f(n)=f_1(n)f_2(n)\). \(f_2(n)\) heißt dabei streng multiplikativ, wenn \(f_2(p^a)= f_2(p)\) für jede Primzahl \(p\) und jede natürliche Zahl \(a\) ist. Es sei \(k\) eine natürliche Zahl.
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