Results 31 to 40 of about 178,978 (284)

On the least common multiple of $q$-binomial coefficients

, 2009
In this paper, we prove the following identity $$ \lcm({n\brack 0}_q,{n\brack 1}_q,...,{n\brack n}_q) =\frac{\lcm([1]_q,[2]_q,...,[n+1]_q)}{[n+1]_q}, $$ where ${n\brack k}_q$ denotes the $q$-binomial coefficient and $[n]_q=\frac{1-q^n}{1-q}$. This result
Farhi B., Guo V. J. W., Hanson D., Knuth D., Nair M., Victor J. W. Guo   +5 more
core   +1 more source

Shared Genetic Effects and Antagonistic Pleiotropy Between Multiple Sclerosis and Common Cancers

Annals of Clinical and Translational Neurology, EarlyView.
ABSTRACT Objective Epidemiologic studies have reported inconsistent altered cancer risk in individuals with multiple sclerosis (MS). Factors such as immune dysregulation, comorbidities, and disease‐modifying therapies may contribute to this variability.
Asli Buyukkurt, Marius Ygonia, Ali Manouchehrinia, Philippe Lefrançois, Ingrid Kockum, Adil Harroud   +5 more
wiley   +1 more source

Lucas' theorem: its generalizations, extensions and applications (1878--2014) [PDF]

, 2014
In 1878 \'E. Lucas proved a remarkable result which provides a simple way to compute the binomial coefficient ${n\choose m}$ modulo a prime $p$ in terms of the binomial coefficients of the base-$p$ digits of $n$ and $m$: {\it If $p$ is a prime, $n=n_0 ...
Meštrović, Romeo
core  

Novel 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. For this purpose, a novel binomial series (new binomial theorem) without the binomial coefficients is introduced for computational applications.
openaire   +1 more source

Unraveling the Molecular Mechanisms of Glioma Recurrence: A Study Integrating Single‐Cell and Spatial Transcriptomics

Annals of Clinical and Translational Neurology, EarlyView.
ABSTRACT Objective Glioma recurrence severely impacts patient prognosis, with current treatments showing limited efficacy. Traditional methods struggle to analyze recurrence mechanisms due to challenges in assessing tumor heterogeneity, spatial dynamics, and gene networks.
Lei Qiu, Yinjiao Fei, Jiaxuan Ding, Kexin Shi, Jinyan Luo, Yuchen Zhu, Xingjian Sun, Gefei Jiang, Yuandong Cao, Weilin Xu, Shu Zhou   +10 more
wiley   +1 more source

Characteristic polynomials of some min and max matrices

Mathematics Open
In this paper, we investigate Min matrices [Formula: see text] and Max matrices [Formula: see text] whose entries are [Formula: see text] and [Formula: see text], respectively, where [Formula: see text] and [Formula: see text]. By utilizing combinatorial
Wei Xie
doaj   +1 more source

Some properties of binomial coefficients and their application to growth modelling

Arab Journal of Basic and Applied Sciences, 2018
Some properties of diagonal binomial coefficients were studied in respect to frequency of their units’ digits. An approach was formulated that led to the use of difference tables to predict if certain units’ digits can appear in the values of binomial ...
Vladimir L. Gavrikov
doaj   +1 more source

Hip Morphology–Based Osteoarthritis Risk Prediction Models: Development and External Validation Using Individual Participant Data From the World COACH Consortium

Arthritis Care &Research, EarlyView.
Objective This study aims to develop hip morphology‐based radiographic hip osteoarthritis (RHOA) risk prediction models and investigates the added predictive value of hip morphology measurements and the generalizability to different populations. Methods We combined data from nine prospective cohort studies participating in the Worldwide Collaboration ...
Myrthe A. van den Berg, Fleur Boel, Michiel M. A. van Buuren, Noortje S. Riedstra, Jinchi Tang, Harbeer Ahedi, Nigel K. Arden, Sita M. A. Bierma‐Zeinstra, Cindy G. Boer, Flavia M. Cicuttini, Timothy F. Cootes, David T. Felson, Willem Paul Gielis, Joshua Heerey, Graeme Jones, Stefan Kluzek, Nancy E. Lane, Claudia Lindner, Joyce B. J. van Meurs, Andrea Mosler, Amanda E. Nelson, Michael C. Nevitt, Edwin H. Oei, Jos Runhaar, Harrie Weinans, Jesse H. Krijthe, Rintje Agricola   +26 more
wiley   +1 more source

Some congruence properties of binomial coefficients and linear second order recurrences

International Journal of Mathematics and Mathematical Sciences, 1988
Using elementary methods, the following results are obtained:(I) If p is prime, 0≤m≤n ...
Neville Robbins
doaj   +1 more source

The cyclic coloring complex of a complete k-uniform hypergraph

, 2011
In this paper, we study the homology of the cyclic coloring complex of three different types of $k$-uniform hypergraphs. For the case of a complete $k$-uniform hypergraph, we show that the dimension of the $(n-k-1)^{st}$ homology group is given by a ...
Rundell, Sarah Crown
core   +2 more sources