Results 81 to 90 of about 46,123 (300)
Sum of the Reciprocals of the Binomial Coefficients
European Journal of Combinatorics, 1993 Let \(S_ n=\sum^ n_{k=0}{1 \over {n \choose k}}\). It is shown that \(S_ n\) satisfies the recurrence \(S_ n={n+1 \over 2n}S_{n-1}+1\). The proof can be simplified by observing that \[ n!S_ n=\sum^ n_{k=0}k!(n-k)!=n!+\sum^{n-1}_{k=0}k!(n-k-1)!(n+1-k-1) =n!+(n+ 1)(n-1)!S_{n-1}-(n!S_ n-n!). \]
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A divisibility property of binomial coefficients viewed as an elementary sieve
International Journal of Mathematics and Mathematical Sciences, 1981 The triangular array of binomial coefficients 012301111212131331… is said to have undergone a j-shift if the r-th row of the triangle is shifted rj units to the right (r=0,1,2,…). Mann and Shanks have proved that in a 2-shifted array a column number c>
Richard H. Hudson, Kenneth S. Williams
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Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2013 The correctness of equality which gives the combinatorial expression for the sum of the weighted equal powers of members of an arithmetical progression is found out.
Alexander I Nikonov
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Advanced Science, EarlyView.A self‐supervised multi‐view graph fusion framework integrates spatial multi‐omics, excelling in domain identification and denoising. It reconstructs spatial pseudo‐expression, jointly analyzes multi‐omics data, infers RNA velocity, predicts spatial omics features from single‐cell multi‐omics, and detects spatially dark genes and transcription factors,
Yuejing Lu +8 more
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The update exposition of the components organisig the sum of weighted equal powers
Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2012 The sum of the weighted equal powers with natural bases and parameters is organized of components, which are independent or dependent on weight coefficients.
Alexander I Nikonov
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stMixer for Scalable Mosaic Integration and Label Transfer in Spatial Histology and Multi‐Omics
Advanced Science, EarlyView.stMixer is an unsupervised framework for scalable integration and label transfer across spatial histology and multi‐slide multi‐omics data with incomplete modality overlap. It combines self‐looped cross‐attention, multimodal metric learning, and graph‐guided cluster voting to align heterogeneous sections, correct batch effects, and propagate ...
Qixing Yang +3 more
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Agribusiness, EarlyView.ABSTRACT This paper explores the convergence in on‐farm diversification strategies of agricultural holdings, between remote areas and more central ones. Using Italian farm‐level data, we explore the determinants of diversification strategies across farms.
Gianluca Grilli +2 more
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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 ...
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Annals of Gastroenterological Surgery, EarlyView.Robotic‐assisted rectal resection in Japan increased markedly after national insurance reimbursement in 2018, with a concurrent decline in open surgery. Using NDB Open Data, we found substantial inter‐prefectural heterogeneity in surgical volume and robotic utilization that persisted after age and sex standardization (SCR). Urban–rural differences were
Ryo Ohta +9 more
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On prime divisors of binomial coefficients
, 1988 This paper, using computational and theoretical methods, deals with prime divisors of binomial coefficients: Geometric distribution and number of distinct prime divisors are studied.
Pierre Goetgheluck
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