Results 71 to 80 of about 180,364 (280)
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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A sum of binomial coefficients [PDF]
Mathematics of Computation, 1978 An explicit expression is derived for the sum of the ( k + 1 ) (k + 1) st binomial coefficients in the nth, ( n − m ) (n - m) th, ( n − 2 m ) (n - 2m) th,... row of the arithmetic triangle.
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Cross‐Modal Denoising and Integration of Spatial Multi‐Omics Data with CANDIES
Advanced Science, EarlyView.In this paper, we introduce CANDIES, which leverages a conditional diffusion model and contrastive learning to effectively denoise and integrate spatial multi‐omics data. We conduct extensive evaluations on diverse synthetic and real datasets, CANDIES shows superior performance on various downstream tasks, including denoising, spatial domain ...
Ye Liu +5 more
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ON DIVISIBILITY OF BINOMIAL COEFFICIENTS [PDF]
Journal of the Australian Mathematical Society, 2012 AbstractIn this paper, motivated by Catalan numbers and higher-order Catalan numbers, we study factors of products of at most two binomial coefficients.
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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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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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Gauss Sums and Binomial Coefficients
Journal of Number Theory, 2002 Let \(p= tn+r\) be a prime which splits in \(\mathbb{Q}(\sqrt{-t})\) where \(t\) has one of the following forms \[ \begin{aligned} t= k>3 &\;\text{ for a prime } k\equiv 3\pmod 4,\\ t= 4k &\;\text{ for a prime } k\equiv 1\pmod 4,\\ t= 8k &\;\text{ for an odd prime } k.
Lee, DH, Hahn, SG Hahn, Sang-Geun
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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 Peressott +15 more
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Well-poised q-series and new Fibonomial-like sums
Kuwait Journal of ScienceWe introduce various sum formulae involving products of two Fibonomial/Lucanomial coefficients or quotients of two such coefficients over a third one.
Chu W., Kılıç E.
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Binomial Coefficients and Lucas Sequences
Journal of Number Theory, 2002 Let sequences \(\{u_n\}_{n\geq 0}\) and \(\{v_n\}_{n\geq 0}\) be defined by \(u_n= \frac{a^n-b^n}{a-b}\), \(v_n= a^n+b^n\) where \(a,b\) are integers such that \(a>|b|\). (Such sequences are Lucas sequences such that the associated quadratic polynomial has integer roots.
Flammenkamp, Achim, Luca, Florian
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