Results 51 to 60 of about 1,205,068 (305)
Vieta's triangular array and a related family of polynomials
International Journal of Mathematics and Mathematical Sciences, 1991 If n≥1, let the nth row of an infinite triangular array consist of entries B(n,j)=nn−j(jn−j), where 0≤j≤[12n].
Neville Robbins
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Quotients of sequences under the binomial convolution [PDF]
Notes on Number Theory and Discrete MathematicsThis paper gives expressions for the solution {a(n)} of the equation Σ_{k=0}^{n} (n choose k)a(k)b(n-k)=c(n),n=0,1,2,..., where b(0) ≠ 0, that is, of the equation a ○ b = c in a, where ○ is the binomial convolution.
Pentti Haukkanen
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On sums of binomial coefficients [PDF]
Proyecciones (Antofagasta)We investigate the integral representation of infinite sums involving the ratio of binomial coefficients. We also recover some wellknown properties of ζ (3) and extend the range of results given by other authors.
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A Panel of Circulating Exosomal sncRNAs Associated With Lung Cancer Risk up to 10 Years in Advance
Advanced Science, EarlyView.Lung cancer is often diagnosed too late, and current screening overlooks many people at risk. In a long‐term study of smokers, a panel of small non‐coding RNAs carried in blood exosomes signals elevated lung cancer risk up to ten years before diagnosis, pointing toward a blood‐based tool for earlier risk detection.
Zhuokun Feng +12 more
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On divisibility of binomial coefficients
Discrete Mathematics, 1994 Let \(p\) be a prime and \(A(n,p)\) the \(p^ n\times p^ n\)-matrix with entries \(a_{ij}= \left(\begin{smallmatrix} i\\ j\end{smallmatrix}\right)\text{ mod }p\) for \(0\leq i,j< p^ n\). It is shown that \(A(n,p)\) is the \(n\)-fold tensor product of \(A(1,p)\) with itself. As an application a short proof is given that there are precisely \(\left(\begin{
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Extension of Binomial Series with Optimized Binomial Coefficient
, 2022 This paper presents the binomial expansion and series with optimized binomial coefficients. The binomial series is built on the building blocks of optimized binomial coefficients and multiple summations of geometric ...
Chinnaraji Annamalai
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Advanced Science, EarlyView.Heat stress promotes WNT5A secretion from fibroblasts via METTL3/YTHDC1‐dependent m6A methylation. Subsequently, WNT5A binds to FZD10 on melanocytes, activating β‐catenin‐driven melanogenesis. ABSTRACT As the impact of global warming continues to intensify, the effects of heat stress on the skin are becoming increasingly evident.
Yuanyuan Wan +13 more
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Combinadic Compression: An Order-0 Enumerative Byte-Stream Codec with Size-Preserving Encryption
AlgorithmsOrder-0 enumerative coding represents a fixed-length block not as a self-delimiting bitstream but as a short tuple of integer fields over known finite ranges: each value’s positions form a bitset, reduced to its colexicographic rank, leaving per-symbol ...
Anthony J. Rasmussen
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Estimation of Intracluster Correlation under the Negative Binomial Model [PDF]
The Egyptian Statistical Journal, 2012 Estimation of the Intracluster Correlation Coefficient (ICC) for the case of clustered count data is considered. Under the negative binomial model the method of moments estimators of both the dispersion parameter and the ICC are derived.
Marwa Abdel Gawad Ahmed
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