Results 61 to 70 of about 41,390 (232)
A sum of binomial coefficients [PDF]
Mathematics of Computation, 1978 An explicit expression is derived for the sum of the ( k + 1 ) (k + 1) st binomial coefficients in the nth, ( n − m ) (n - m) th, ( n − 2 m ) (n - 2m) th,... row of the arithmetic triangle.
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Agribusiness, EarlyView.ABSTRACT The cocoa‐chocolate value chain faces significant environmental and social challenges, driving firms to adopt sustainability strategies ranging from individual practices to third‐party certifications. This study investigates the factors associated with these strategies by analyzing 304 cocoa‐chocolate companies using firm‐level data from the ...
Stella Marschner +3 more
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The update exposition of the components organisig the sum of weighted equal powers
Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2012 The sum of the weighted equal powers with natural bases and parameters is organized of components, which are independent or dependent on weight coefficients.
Alexander I Nikonov
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Some congruence properties of binomial coefficients and linear second order recurrences
International Journal of Mathematics and Mathematical Sciences, 1988 Using elementary methods, the following results are obtained:(I) If p is prime, 0≤m≤n ...
Neville Robbins
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ON DIVISIBILITY OF BINOMIAL COEFFICIENTS [PDF]
Journal of the Australian Mathematical Society, 2012 AbstractIn this paper, motivated by Catalan numbers and higher-order Catalan numbers, we study factors of products of at most two binomial coefficients.
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Advanced Intelligent Discovery, EarlyView.This article investigates how persistent homology, persistent Laplacians, and persistent commutative algebra reveal complementary geometric, topological, and algebraic invariants or signatures of real‐world data. By analyzing shapes, synthetic complexes, fullerenes, and biomolecules, the article shows how these mathematical frameworks enhance ...
Yiming Ren, Guo‐Wei Wei
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Abstract and Applied Analysis, 2014 A variety of identities involving harmonic numbers and generalized harmonic numbers have been investigated since the distant past and involved in a wide range of diverse fields such as analysis of algorithms in computer science, various branches of ...
Junesang Choi
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Note on the binomial partial difference equation
Electronic Journal of Qualitative Theory of Differential Equations, 2015 Some formulas for the "general solution" to the binomial partial difference equation $$c_{m,n}=c_{m-1,n}+c_{m-1,n-1},$$ are known in the literature. However, it seems that there is no such a formula on the most natural domain connected to the equation ...
Stevo Stevic
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Gauss Sums and Binomial Coefficients
Journal of Number Theory, 2002 Let \(p= tn+r\) be a prime which splits in \(\mathbb{Q}(\sqrt{-t})\) where \(t\) has one of the following forms \[ \begin{aligned} t= k>3 &\;\text{ for a prime } k\equiv 3\pmod 4,\\ t= 4k &\;\text{ for a prime } k\equiv 1\pmod 4,\\ t= 8k &\;\text{ for an odd prime } k.
Lee, DH, Hahn, SG Hahn, Sang-Geun
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American Journal of Community Psychology, EarlyView.Abstract Although peer support is central to the social model approach emphasized in sober living houses (SLHs), no longitudinal studies have examined helping among SLH residents. This longitudinal study examined benefits of helping in three contexts among SLH residents. Data were from 205 participants entering 28 SLHs across 2021–2023. Interviews were
Sarah E. Zemore +4 more
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