Results 81 to 90 of about 165,496 (329)
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
openaire +2 more sources
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
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
doaj +1 more source
Axioms, 2019 The aim of this paper is to construct generating functions for new families of combinatorial numbers and polynomials. By using these generating functions with their functional and differential equations, we not only investigate properties of these new ...
Irem Kucukoglu +2 more
doaj +1 more source
Binomial Coefficients and Lucas Sequences
Journal of Number Theory, 2002 Let sequences \(\{u_n\}_{n\geq 0}\) and \(\{v_n\}_{n\geq 0}\) be defined by \(u_n= \frac{a^n-b^n}{a-b}\), \(v_n= a^n+b^n\) where \(a,b\) are integers such that \(a>|b|\). (Such sequences are Lucas sequences such that the associated quadratic polynomial has integer roots.
Flammenkamp, Achim, Luca, Florian
openaire +2 more sources
Wind‐driven seed dispersal differentially promotes seed trapping and retention across alpine plants
American Journal of Botany, EarlyView.Abstract Premise Seed dispersal can mediate species interactions between plants across life stages. Plants can physically stop seed movement (seed trapping) and prevent further dispersal following entrapment (seed retention). We therefore hypothesized seed trapping and retention rates depend on the physical attributes of interacting seeds and plants ...
Courtenay A. Ray +7 more
wiley +1 more source
Repeated sums and binomial coefficients
Open Journal of Discrete Applied Mathematics, 2021 Binomial coefficients have been used for centuries in a variety of fields and have accumulated numerous definitions. In this paper, we introduce a new way of defining binomial coefficients as repeated sums of ones. A multitude of binomial coefficient identities will be shown in order to prove this definition.
openaire +2 more sources
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
wiley +1 more source
Ascending and Descending Orders of Annamalai's Binomial Coefficient
, 2022 Chinnaraji Annamalai
openalex +2 more sources
Reduction of the sum of the weighted equal powers to explicit combinatorial representation
Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2012 The paper contains the proof of the statement that the component of the sum of weighted powers with natural bases and equal parameters, dependent on weight coefficients, is equal to the sum of products of binomial and weight coefficients.
Alexander I Nikonov
doaj