Results 71 to 80 of about 55,236 (313)
Is the binomial coefficient $2n \choose n$ square free?
, 1995 In this paper, we prove the Erd\"os conjecture that the binomial coefficient ${2n \choose n}$ is never square free, for all $n>4$
Velammal, G
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Construction and Analysis of Binomial Coefficients
, 2022 This paper discusses the construction and analysis of the binomial coefficients for combinatorial geometric series. The coefficient for each term in combinatorial geometric series refers to a binomial coefficient.
Chinnaraji Annamalai
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Biolipid Film‐Fused Electrochemiluminescence for Multipurpose In Situ Bioassays
Advanced Science, EarlyView.An ECL‐emissive, membrane‐interactive scaffold was fabricated, and facilely fused with natural and non‐native phospholipids into multifactorial mimicries of cytomembranes and vesicles for in vitro representative membrane‐process probing. Such a biointerface‐based, state‐sensitive ECL paradigm not only pinpointed proximal phenomena, including channeling
Jialiang Chen +9 more
wiley +1 more source
Sum of Series of Binomial Coefficients
, 2022 This paper presents a summation of series of binomial coefficients in combinatorial geometric series. The coefficient for each term in combinatorial geometric series refers to a binomial coefficient.
Chinnaraji Annamalai
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Temporal Interference Stimulation Enhances Neural Regeneration
Advanced Science, EarlyView.Temporal interference (TI) stimulation is proposed as a non‐invasive approach to enhance neural regeneration in the deep brain. Theta‐band TI modulation selectively promotes neural progenitor cell differentiation in vitro and augments hippocampal neurogenesis in amouse model of Alzheimer's disease‐like amyloidosis.
Sofia Peressotti +15 more
wiley +1 more source
Estimates of the least prime factor of a binomial coefficient
, 1993 We estimate the least prime factor p of the binomial coefficient ( k N ) \left ( {_k^N} \right ) for k ≥ 2 k \geq 2
C. B. Lacampagne +2 more
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Advanced Science, EarlyView.SpaMode introduces a versatile framework for spatial multi‐omics integration across vertical, horizontal, and mosaic scenarios. By disentangling modality‐invariant and variant features through a mixture‐of‐experts mechanism, it adaptively reconfigures spatially heterogeneous signals.
Xubin Zheng +6 more
wiley +1 more source
A Note on Extended Binomial Coefficients
J. Integer Seq., 2014 We study the distribution of the extended binomial coefficients by deriving a complete asymptotic expansion with uniform error terms. We obtain the expansion from a local central limit theorem and we state all coefficients explicitly as sums of Hermite polynomials and Bernoulli numbers.
openaire +6 more sources
Some divisibility properties of binomial and q -binomial coefficients
Journal of Number Theory, 2014 We first prove that if $a$ has a prime factor not dividing $b$ then there are infinitely many positive integers $n$ such that $\binom {an+bn} {an}$ is not divisible by $bn+1$. This confirms a recent conjecture of Z.-W. Sun. Moreover, we provide some new divisibility properties of binomial coefficients: for example, we prove that $\binom {12n} {3n}$ and
Krattenthaler, Christian +1 more
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Theorems based on Annamalai’s Binomial Coefficient and Identity
, 2022 This paper presents a binomial theorem and proof based on Annamalai’s binomial identity. The factorial function defined for non-negative integers, denoted by n!, is the product of all positive integers less than or equal to n.
Chinnaraji Annamalai
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