Results 31 to 40 of about 152,514 (291)
Some results on p-adic valuations of Stirling numbers of the second kind
AIMS Mathematics, 2020 Let $n$ and $k$ be nonnegative integers. The Stirling number of the second kind, denoted by $S(n, k)$, is defined as the number of ways to partition a set of $n$ elements into exactly $k$ nonempty subsets and we have $$ S(n, k)=\frac{1}{k!}\sum_{i=0}^{k}(
Yulu Feng, Min Qiu
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Solar powered stirling engine for domestic household and rural areas in Karachi, Pakistan
Memoria Investigaciones en Ingeniería, 2023 There is a critical need to use the abundantly available solar energy worldwide due to the global energy crisis. The goal of this study is to demonstrate the residential use of a stirling engine powered by solar energy in Karachi, Pakistan.
Muhammad Uzair +4 more
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Congruences for the Stirling numbers and associated Stirling numbers [PDF]
Acta Arithmetica, 1990 Let s(n,k) and S(n,k) be the Stirling numbers of the first and second kind, respectively. The author proves that if \(k+n\) is odd, then \[ s(n,k)\equiv 0 (mod\left( \begin{matrix} n\\ 2\end{matrix} \right)),\quad S(n,k)\equiv 0 (mod\left( \begin{matrix} k+1\\ 2\end{matrix} \right)).
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Generalized Bell Numbers and Peirce Matrix via Pascal Matrix
International Journal of Mathematics and Mathematical Sciences, 2018 With the Stirling matrix S and the Pascal matrix T, we show that TkS (k≥0) satisfies a type of generalized Stirling recurrence. Then, by expressing the sum of components of each row of TkS as k-Bell number, we investigate properties of k-Bell numbers as ...
Eunmi Choi
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Generalized Fock spaces and the Stirling numbers [PDF]
, 2018 The Bargmann-Fock-Segal space plays an important role in mathematical physics, and has been extended into a number of directions. In the present paper we imbed this space into a Gelfand triple. The spaces forming the Fr\'echet part (i.e.
Alpay D. +14 more
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Energies, 2022 This study aimed at the development of an algorithm for the computational optimization of free-piston Stirling engines. The design algorithm includes an optimization method and two compatible strategies.
Chin-Hsiang Cheng, Yu-Ting Lin
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Normal Ordering for Deformed Boson Operators and Operator-valued Deformed Stirling Numbers
, 1992 The normal ordering formulae for powers of the boson number operator $\hat{n}$ are extended to deformed bosons. It is found that for the `M-type' deformed bosons, which satisfy $a a^{\dagger} - q a^{\dagger} a = 1$, the extension involves a set of ...
Abramowitz M +17 more
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Combinatorially interpreting generalized Stirling numbers [PDF]
, 2014 Let $w$ be a word in alphabet $\{x,D\}$ with $m$ $x$'s and $n$ $D$'s. Interpreting "$x$" as multiplication by $x$, and "$D$" as differentiation with respect to $x$, the identity $wf(x) = x^{m-n}\sum_k S_w(k) x^k D^k f(x)$, valid for any smooth function ...
Engbers, John +2 more
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Enumeration of a dual set of Stirling permutations by their alternating runs
, 2015 In this paper, we count a dual set of Stirling permutations by the number of alternating runs. Properties of the generating functions, including recurrence relations, grammatical interpretations and convolution formulas are studied.Comment: 8 ...
Ma, Shi-Mei, Wang, Hai-Na
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Two problems of binomial sums involving harmonic numbers
Advances in Difference Equations, 2021 Two open problems recently proposed by Xi and Luo (Adv. Differ. Equ. 2021:38, 2021) are resolved by evaluating explicitly three binomial sums involving harmonic numbers, that are realized mainly by utilizing the generating function method and symmetric ...
Nadia N. Li, Wenchang Chu
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