Results 61 to 70 of about 55,236 (313)

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{
openaire   +2 more sources

Factorials, Integers, Binomial Coefficient and Factorial Theorem

, 2022
This paper presents a factorial theorem using factorial functions, integers, and binomial coefficients.
Chinnaraji Annamalai
core   +1 more source

TME/NIR Dual‐Responsive Zinc‐Based Targeted Nanoagonist for Multimodal Amplification of STING‐Mediated Cancer Immunotherapy

Advanced Science, EarlyView.
A multifunctional nanoagonist (cDZ@IP) enables nano‐metabolite–driven multimodal activation of the STING pathway and enhanced immune recognition, achieving potent antitumor immunity and suppressing tumor growth and metastasis. This strategy highlights the rational design of therapeutic metabolites and establishes a new paradigm bridging nanomedicine ...
Kepeng Hu, Jiawei Wang, Wei Zhang, Zhixuan Wu, Jing Chen, Yujing He, Xiyue Duan, Yaoting He, Xin Xin, Haoyi Xiang, Yijing Wang, Chengwei Wu, Yang Yi, Qing Meng, Yuqian Qiao, Kui Cheng, Xiaojun Long, Zhangfa Song   +17 more
wiley   +1 more source

Bernstein-type approximations of smooth functions

Statistica, 2007
The Bernstein-type approximation for smooth functions is proposed and studied. We propose the Bernstein-type approximation with definitions that directly apply the binomial distribution and the multivariate binomial distribution.
Andrea Pallini
doaj   +1 more source

A Note on the Difference of Powers and Falling Powers

International Journal of Mathematics and Mathematical Sciences, 2021
Combinatorial sums and binomial identities have appeared in many branches of mathematics, physics, and engineering. They can be established by many techniques, from generating functions to special series.
Taoufik Sabar
doaj   +1 more source

Some functional equations related to binomial coefficient summation

, 1967
The general solution has been obtained of two functional equations suggested by a binomial coefficient identity proved by Gould and Kaucký[J. Combinatorial Theory. 1 (1966), 233–247]
Carlitz, L.
core   +1 more source

Summation of Series of Binomial Coefficients

, 2022
This paper presents a summation of series of binomial coefficients in combinatorial geometric series. The coefficient for each term in combinatorial geometric series refers to a binomial coefficient.
Chinnaraji Annamalai
core   +1 more source

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, Wanpeng Zou, Yuekai Li, Jiayi Wang, Mingxuan Cai, Hongmin Cai   +5 more
wiley   +1 more source

Cubic binomial Fibonacci sums [PDF]

Electronic Journal of Mathematics, 2021
Kunle Adegoke, Adenike Olatinwo, Sourangshu Ghosh   +2 more
doaj   +1 more source

The Janjić–Petković Inset Counting Function: Riordan Array Properties and a Thermodynamic Application

Mathematics
Let q1+⋯+qn+m objects be arranged in n rows with q1,…,qn objects and one last row with m objects. The Janjić–Petković counting function denotes the number of (n+k)-insets, defined as subsets containing n+k objects such that at least one object is chosen ...
Marcus Kollar
doaj   +1 more source