Results 71 to 80 of about 46,123 (300)
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.
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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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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
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Note on the binomial partial difference equation
Electronic Journal of Qualitative Theory of Differential Equations, 2015 Some formulas for the "general solution" to the binomial partial difference equation $$c_{m,n}=c_{m-1,n}+c_{m-1,n-1},$$ are known in the literature. However, it seems that there is no such a formula on the most natural domain connected to the equation ...
Stevo Stevic
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Harmonic number identities via polynomials with r-Lah coefficients
Comptes Rendus. Mathématique, 2020 In this paper, polynomials whose coefficients involve $r$-Lah numbers are used to evaluate several summation formulae involving binomial coefficients, Stirling numbers, harmonic or hyperharmonic numbers.
Kargın, Levent, Can, Mümün
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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
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Some combinatorial identities concerning harmonic numbers and binomial coefficients [PDF]
Discrete Mathematics Letters, 2021 Dongwei Guo
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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
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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
Advanced Science, EarlyView.Single‐cell and spatial profiling of 110 human thoracic aortic samples reveals a stromal–immune circuit driving aortic dissection. An elastin‐rich fibroblast subset is depleted with age and markedly reduced in disease, weakening aortic wall integrity.
Jing Tao +25 more
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