Results 1 to 10 of about 188,120 (215)
Additive Function-on-Function Regression [PDF]
Journal of Computational and Graphical Statistics, 2018 We study additive function-on-function regression where the mean response at a particular time point depends on the time point itself as well as the entire covariate trajectory. We develop a computationally efficient estimation methodology based on a novel combination of spline bases with an eigenbasis to represent the trivariate kernel function.
Kim, Janet S. +4 more
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On additive representation functions [PDF]
International Journal of Number Theory, 2015 Let 𝒜 = {a1 < a2 < a3 < ⋯ < an < ⋯} be an infinite sequence of nonnegative integers and let R2(n) = |{(i, j) : ai + aj = n; ai, aj ∈ 𝒜; i ≤ j}|. We define [Formula: see text]. We prove that if the L∞-norm of [Formula: see text] is small, then the L1-norm of [Formula: see text] is large.
Balasubramanian, R., Giri, Sumit
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On an additive arithmetic function [PDF]
Pacific Journal of Mathematics, 1977 Let \(n\) be a positive integer, \(n=\prod\limits_{i=1}^rp_i^{\alpha_i}\) in canonical form, and let \(A(n)=\sum\limits_{i=1}^r\alpha_ip_i\). Clearly \(A\) is an additive arithmetic function.
Alladi, K., Erdős, P.
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AN ADDITIVE FUNCTIONAL INEQUALITY [PDF]
Korean Journal of Mathematics, 2014 Summary: In this paper, we solve the additive functional inequality \[\|f(x)+f(y)+f(z)\| \le \| \rho f( s (x+y+z)\| ,\] where \(s\) is a nonzero real number and \(\rho\) is a real number with \(|\rho| < 3\). Moreover, we prove the Hyers-Ulam stability of the above additive functional inequality in Banach spaces.
Lee, Sung Jin +2 more
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ON ADDITIVE REPRESENTATION FUNCTIONS [PDF]
Bulletin of the Australian Mathematical Society, 2017 For any finite abelian group$G$with$|G|=m$,$A\subseteq G$and$g\in G$, let$R_{A}(g)$be the number of solutions of the equation$g=a+b$,$a,b\in A$. Recently, Sándor and Yang [‘A lower bound of Ruzsa’s number related to the Erdős–Turán conjecture’, Preprint, 2016,arXiv:1612.08722v1] proved that, if$m\geq 36$and$R_{A}(n)\geq 1$for all$n\in \mathbb{Z}_{m ...
YA-LI LI, YONG-GAO CHEN
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On the Measurability of Additive Functionals [PDF]
gmj, 2007 Abstract For an infinite-dimensional separable Hilbert space 𝐻, the problem of measurability of additive functionals 𝑓 : 𝐻 → 𝐑 with respect to various extensions of σ-finite diffused Borel measures on 𝐻 is discussed. It is shown that there exists an everywhere discontinuous additive functional 𝑓 on 𝐻 such that, for any σ-finite diffused ...
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On an additive representation function
Journal of Number Theory, 2004 Let \(A\) be an infinite set of positive integers with the property that at most finitely many integers have exactly one representation in the form \(a+a'\), \(a\leq a'\), \(a,a'\in A\). \textit{J.-L. Nicolas}, \textit{I. Z. Ruzsa}, and \textit{A. Sárközy} [J. Number Theory 73, 292--317 (1998; Zbl 0921.11050)] proved that such sets must satisfy \(A(x)>
Balasubramanian, R., Prakash, Gyan
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Additive functions on trees [PDF]
Colloquium Mathematicum, 2001 Summary: The motivation for considering positive additive functions on trees was a characterization of extended Dynkin graphs (see \textit{I.~Reiten} [Notices Am. Math. Soc. 44, No. 5, 546-556 (1997; Zbl 0940.16009)]) and applications of additive functions in representation theory (see \textit{H.~Lenzing} and \textit{I.~Reiten} [Colloq. Math. 82, No. 1,
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Additively decomposed quasiconvex functions [PDF]
Mathematical Programming, 1982 Letf be a real-valued function defined on the product ofm finite-dimensional open convex setsX1, ź,Xm. Assume thatf is quasiconvex and is the sum of nonconstant functionsf1, ź,fm defined on the respective factor sets. Then everyfi is continuous; with at most one exception every functionfi is convex; if the exception arises, all the other functions ...
Gerard Debreu, Tjalling C. Koopmans
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Proceedings of the Japan Academy, Series A, Mathematical Sciences, 1983 One more summation formula for \(q\)-additive functions is given. For part I see ibid. 59, 274--276 (1983; Zbl 0518.10062).
Mauclaire, J.-L., Murata, Leo
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