Results 71 to 80 of about 90,542 (255)

On Some Series Involving the Central Binomial Coefficients

15 ...
Adegoke, K., Frontczak, R., Goy, T.
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On Sums Related to Central Binomial and Trinomial Coefficients [PDF]

, 2014
A generalized central trinomial coefficient $T_n(b,c)$ is the coefficient of $x^n$ in the expansion of $(x^2+bx+c)^n$ with $b,c\in\mathbb Z$. In this paper we investigate congruences and series for sums of terms related to central binomial coefficients and generalized central trinomial coefficients.
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Integral Representations of Catalan Numbers and Sums Involving Central Binomial Coefficients

, 2023
In the paper, the authors collect several integral representations of the Catalan numbers and central binomial coefficients, supply alternative proofs of two integral representations of the Catalan numbers, and apply these integral representations to alternatively prove several combinatorial identities for finite and infinite sums in which central ...
Guo, Bai-Ni, Lim, Dongkyu
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Interpretability and Representability of Commutative Algebra, Algebraic Topology, and Topological Spectral Theory for Real‐World Data

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
wiley   +1 more source

The Impact of Extreme Weather on Dengue Fever in Guangzhou, China: A Zero‐Inflated Negative Binomial Spatial Lag Analysis

GeoHealth
Climate change intensifies extreme weather, which in turn influences infectious disease transmission. As a dengue fever (DF) hotspot, Guangzhou lacks research on how extreme weather characteristics and spatial factors interact to shape DF patterns.
Xinqiu Ouyang, Fang Shi, Yang Qiu, Guangran Deng, Shujun Zhang   +4 more
doaj   +1 more source

Giving and receiving help in three contexts as predictors of alcohol outcomes in a longitudinal study of sober living house residents

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, Elizabeth Mahoney, Meenakshi S. Subbaraman, Amy A. Mericle, Douglas L. Polcin   +4 more
wiley   +1 more source

Three combinatorial sums involving central binomial coefficients

We study three classes of combinatorial sums involving central binomial coefficients and harmonic numbers, odd harmonic numbers, and even indexed harmonic numbers, respectively. In each case we use summation by parts to derive recursive expressions for these sums.
Adegoke, Kunle, Frontczak, Robert
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Some $q$-congruences involving central $q$-binomial coefficients

, 2021
Suppose that $p$ is an odd prime and $m$ is an integer not divisible by $p$. Sun and Tauraso [Adv. in Appl. Math., 45(2010), 125--148] gave $\sum_{k=0}^{n-1}\binom{2k}{k+d}/m^k$ and $\sum_{k=0}^{n-1}\binom{2k}{k+d}/(km^k)$ modulo $p$ for all $d=0,1, \ldots n$ and $n= p^a$, where $a$ is a positive integer. In this paper, we present some $q$-analogues of
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Associations between inclusive community coalition leadership and use of evidence‐based practices

American Journal of Community Psychology, EarlyView.
Abstract Community coalitions have the potential to elicit diverse participants' perspectives on complex issues and generate shared commitment to adaptive strategies. Ideally, these approaches have been found effective elsewhere. Despite evidence that leadership plays a generally important role in coalitions, there have been limited prior findings ...
Rebecca Wells, Nalini Ranjit, Louis D. Brown, Sarah M. Chilenski, Yvonne Mary Gaddy   +4 more
wiley   +1 more source

Series Containing Squared Central Binomial Coefficients and Alternating Harmonic Numbers [PDF]

Mediterranean Journal of Mathematics, 2019
The author presents an interesting integration technique in order to evaluate infinite sums containing harmonic or alternating harmonic numbers. He gives known as well as new results by applying his method. We quote the following formula: \[\sum^\infty_{n=1} \begin{pmatrix} 2n\\ n\end{pmatrix}^2\,H_{2n}/16^n(n+1)^2= \frac{16G+24-48\ln(2)}{\pi}+ 4-8\ln ...
openaire   +1 more source