Results 101 to 110 of about 55,236 (313)

Binomial Series without Binomial Coefficients

, 2023
Nowadays, the growing complexity of mathematical and computational modelling demands the simplicity of mathematical equations for solving today’s scientific problems and challenges. Also, the computational science is a rapidly growing interdisciplinary area where science, computation, mathematics, and its collaboration use advanced computing ...
openaire   +1 more source

Binomial Distribution with Optimized Combination of Combinatorics

, 2022
This paper presents the binomial distribution combined with the improved binomial coefficient (optimized combination).
Chinnaraji Annamalai
core   +1 more source

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

Well-poised q-series and new Fibonomial-like sums

Kuwait Journal of Science
We introduce various sum formulae involving products of two Fibonomial/Lucanomial coefficients or quotients of two such coefficients over a third one.
Chu W., Kılıç E.
doaj   +1 more source

On alternating sums of binomial coefficients and $q$-binomial coefficients

, 2016
In this paper we shall evaluate two alternating sums of binomial coefficients by a combinatorial argument. Moreover, by combining the same combinatorial idea with partition theoretic techniques, we provide $q$-analogues involving the $q$-binomial coefficients.
openaire   +2 more sources

Analysis of Combinatorial Binomial Coefficients and Series

, 2023
This paper analyzes the binomial coefficients used in the combinatorial geometric series. The analysis and design of the binomial coefficient can enable the researchers to solve the scientific ...
Chinnaraji Annamalai
core   +1 more source

Retinal Vessel Segmentation: A Comprehensive Review From Classical Methods to Deep Learning Advances (1982–2025)

Advanced Intelligent Systems, EarlyView.
Four decades of retinal vessel segmentation research (1982–2025) are synthesized, spanning classical image processing, machine learning, and deep learning paradigms. A meta‐analysis of 428 studies establishes a unified taxonomy and highlights performance trends, generalization capabilities, and clinical relevance.
Avinash Bansal, Jan Kubíček, Jana Bahrová, Alice Varyšová, Martin Augustýnek, Marek Penhaker, Juraj Timkovič   +6 more
wiley   +1 more source

Harmonic Series of Convergence Ratio “1/4" with Cubic Central Binomial Coefficients

Axioms
We examine a useful hypergeometric transformation formula by means of the coefficient extraction method. A large class of “binomial/harmonic series” (of convergence ratio “1/4”) containing the cubic central binomial coefficients and harmonic numbers is ...
Chunli Li, Wenchang Chu
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

q-analogs of the binomial coefficient congruences of Babbage, Wolstenholme and Glaisher

, 1999
The object of this paper is to provide q-analogs of several classical binomial coefficient congruences due to Babbage, Wolstenholme and Glaisher.
Andrews, George E.
core   +1 more source