Results 11 to 20 of about 24,612 (239)
The Design of the Internal Audit implementation Model in the Iranian Public Sector Institutions [PDF]
مطالعات تجربی حسابداری مالی, 2023 Public Sector Internal Audit, by delivering reliable and consulting services in line with improvement and eliminate challenges can support organizations to achieve goals and provide better services. The purpose of this study is to provide a model for the
Jafar Babajani +2 more
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Some combinatorial identities containing central binomial coefficients or Catalan numbers*
Applied Mathematics in Science and Engineering, 2023 In the article, by virtue of Maclaurin's expansions of the arcsine function and its square and cubic, the authors give a short proof of a sum formula of a Maclaurin's series with coefficients containing reciprocals of the Catalan numbers; establish four ...
Feng Qi, Da-Wei Niu, Dongkyu Lim
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Results in Nonlinear Analysis, 2021 In the paper, with the aid of the series expansions of the square or cubic of the arcsine function, the authors establish several possibly new combinatorial identities containing the ratio of two central binomial coefficients which are related to the ...
Feng Qi, Chao-Ping Chen , Dongkyu Lim
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Divisibility of the central binomial coefficient $\binom {2n}{n}$ [PDF]
Transactions of the American Mathematical Society, 2020 We show that for every fixed $\ell\in\mathbb{N}$, the set of $n$ with $n^\ell|\binom{2n}{n}$ has a positive asymptotic density $c_\ell$, and we give an asymptotic formula for $c_\ell$ as $\ell\to \infty$. We also show that $\# \{n\le x, (n,\binom{2n}{n})=1 \} \sim cx/\log x$ for some constant $c$.
Ford, Kevin, Konyagin, Sergei
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Practical central binomial coefficients [PDF]
Quaestiones Mathematicae, 2020 A practical number is a positive integer $n$ such that all positive integers less than $n$ can be written as a sum of distinct divisors of $n$. Leonetti and Sanna proved that, as $x \to +\infty$, the central binomial coefficient $\binom{2n}{n}$ is a practical number for all positive integers $n \leq x$ but at most $O(x^{0.88097})$ exceptions.
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On Divisibility of Convolutions of Central Binomial Coefficients [PDF]
The Electronic Journal of Combinatorics, 2014 Recently, Z. Sun proved that \[ 2(2m+1)\binom{2m}{m} \mid \binom{6m}{3m}\binom{3m}{m} \] for $m\in\mathbb{Z}_{>0}$. In this paper, we consider a generalization of this result by defining \[ b_{n,k}=\frac{2^{k}\, (n+2k-2)!!}{((n-2)!!\, k!}. \] In this notation, Sun's result may be expressed as $2\, (2m+1) \mid b_{(2m+1),(2m+1)-1}$ for $m\in\mathbb ...
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Clinical associations of Human T-Lymphotropic Virus type 1 infection in an indigenous Australian population. [PDF]
PLoS Neglected Tropical Diseases, 2014 INTRODUCTION: In resource-poor areas, infectious diseases may be important causes of morbidity among individuals infected with the Human T-Lymphotropic Virus type 1 (HTLV-1).
Lloyd Einsiedel +5 more
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New congruences for central binomial coefficients
Advances in Applied Mathematics, 2010 Let p be a prime and let a be a positive integer. In this paper we determine $\sum_{k=0}^{p^a-1}\binom{2k}{k+d}/m^k$ and $\sum_{k=1}^{p-1}\binom{2k}{k+d}/(km^{k-1})$ modulo $p$ for all d=0,...,p^a, where m is any integer not divisible by p. For example, we show that if $p\not=2,5$ then $$\sum_{k=1}^{p-1}(-1)^k\frac{\binom{2k}k}k=-5\frac{F_{p-(\frac p5)}
TAURASO, ROBERTO, Sun, ZW
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Prenatal factors associated with fetal visceral adiposity
Jornal de Pediatria, 2020 Objective: To assess fetal visceral adiposity and associated factors during pregnancy. Methods: Secondary analysis of prospective cohort data with 172 pairs (pregnant woman/fetus) treated at public health units.
Aline Silva Santos Sena +5 more
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Factors of certain sums involving central q-binomial coefficients [PDF]
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2021 Recently, Ni and Pan proved a $q$-congruence on certain sums involving central $q$-binomial coefficients, which was conjectured by Guo. In this paper, we give a generalization of this $q$-congruence and confirm another $q$-congruence, also conjectured by Guo.
Guo, Victor J. W., Wang, Su-Dan
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