Results 91 to 100 of about 174,940 (323)
Multiple Sums of Circular Binomial Products
MathematicsFive classes of multiple sums about circular products of binomial coefficients are investigated. Their generating functions are explicitly expressed as rational functions, with coefficients being Fibonacci and Lucas numbers.
Marta Na Chen, Wenchang Chu
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Advanced Intelligent Systems, EarlyView.This article offers a comprehensive review of topic modeling techniques, tracing their evolution from inception to recent developments. It explores methods such as latent Dirichlet allocation, latent semantic analysis, non‐negative matrix factorization, probabilistic latent semantic analysis, Top2Vec, and BERTopic, highlighting their strengths ...
Pratima Kumari +6 more
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Explicit formulae for Bernoulli numbers
AIMS MathematicsBy examining the connection coefficients, we systematically review and extend (with an extra integer parameter) several double sum expressions for the Bernoulli numbers. New summation formulae are also established explicitly.
Nadia N. Li , Wenchang Chu
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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.
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Commutative rings and binomial coefficients
Monatshefte f�r Mathematik, 1992 Let \(R\) be a domain with quotient field \(k\) and let \(S(R)\) be the \(R\)- module of all \(k\)-polynomials mapping \(R\) in \(R\). It has been shown by \textit{G. Pólya} [Rend. Circ. Mat. Palermo 40, 1-16 (1915; JFM 45.0655.02)] that \(S(Z)\) is generated by binomial coefficients. \textit{G. Gerboud} [C. R. Acad. Sci., Paris, Sér. A 307, 1-4 (1988;
Halter-Koch, F., NARKIEWICZ, W.
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Color polymorphism in Anemone coronaria: Correlations with soil, climate, and flowering phenology
American Journal of Botany, EarlyView.Abstract Premise Flower color polymorphism (FCP) is thought to be driven by multiple selection agents. Although widely associated with visual attraction of multiple pollinators, FCP is also often correlated with abiotic factors. We explored the links between abiotic conditions, flowering phenology, and FCP in the winter‐flowering geophyte Anemone ...
Tzlil Labin +4 more
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On the calculation of generalized binomial coefficients
Journal of Multivariate Analysis, 1974 AbstractThe generalized binomial coefficients (κλ) are defined by Cλ(Im + R)Cλ(Im) = Σk=0lΣκ(λκ)Cκ(R)Cκ(Im), where the Ck(R) are the zonal polynomials of the m × m matrix R. In this paper some simple expressions are derived which allow straightforward calculation of a large number of these coefficients.
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American Journal of Botany, EarlyView.Abstract Premise Rainforests are usually too wet to burn, acting as natural barriers to fire spread and as refuges for biodiversity. However, climate change is increasing the risk of fire incursion into rainforests. Our capacity to manage these impacts is hindered by limited research on rainforest flammability.
Jamie E. Burton +2 more
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Triple Symmetric Sums of Circular Binomial Products
MathematicsBy employing the generating function approach, 16 triple sums for circular binomial products of binomial coefficients are examined. Recurrence relations and generating functions are explicitly determined.
Marta Na Chen, Wenchang Chu
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Revista do Instituto de Latícinios Cândido Tostes, 2015 The aim of the present study was to evaluate whether the binomial temperature/time of 21 ºC for 25 hours, already validated for enumeration of psychrotrophics in milk, presents viability for enumeration of thermoduric psychrotrophic, comparing counts of ...
Vanerli Beloti +5 more
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