Results 51 to 60 of about 9,502,067 (333)
Stochastic heat engines beyond a unique definition of temperature
Physical Review Research, 2023 When Carnot and Stirling initially conceptualized heat engines, temperature unambiguously represented our everyday perception of cold and hot. However, as this energy scale is expanded to measure the strength of noise in general nonequilibrium heat baths,
Chia-Hao Chang +4 more
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Acta Universitatis Sapientiae: Mathematica, 2016 In the paper, the authors find several identities, including a new recurrence relation for the Stirling numbers of the first kind, involving the falling and rising factorials and the Cauchy, Lah, and Stirling numbers.
Qi Feng, Shi Xiao-Ting, Liu Fang-Fang
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A Closed Form for the Stirling Polynomials in Terms of the Stirling Numbers
Tbilisi Mathematical Journal, 2017 In the paper, by virtue of the Faá di Bruno formula and two identities for the Bell polynomial of the second kind, the authors find a closed form for the Stirling polynomials in terms of the Stirling numbers of the first and second kinds.
Feng Qi, Feng Qi, Bai-Ni Guo
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Mixed restricted Stirling numbers [PDF]
Acta Mathematica Hungarica, 2019 12 pages,
Somaya Barati +3 more
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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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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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A generalization of the Stirling numbers
Discrete Mathematics, 1992 AbstractWe generalize the Stirling numbers of the first kind s(a, k) to the case where a may be an arbitrary real number. In particular, we study the case in which a is an integer. There, we discover new combinatorial properties held by the classical Stirling numbers, and analogous properties held by the Stirling numbers s(n, k) with n a negative ...
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Journal of Combinatorial Theory, Series A, 1983 AbstractThe equivalence of two classical sums giving the Stirling numbers of first kind results from a joint law for records.
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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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A Perspective on the Origin of High‐Entropy Solid Electrolytes
Advanced Materials, EarlyView.This perspective critically examines HE approaches in SEs, highlighting how compositional complexity induces system disorder and local‐structure evolution to enhance stability and properties. While HE concepts are attractive, establishing rigorous structure‐property relationships requires further investigation.
Feipeng Zhao, Shumin Zhang, Xueliang Sun
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