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Bessel Functions and Their Applications
TLDR
The theory of Bessel functions and its application in the theory of Oscillations, Hydrodynamics, and Heat Transfer were discussed in this paper, with a focus on Bessel Equation.Abstract:
Foundation of the Theory of Bessel Functions Bessel Equation. Properties of Bessel Functions. Definite and Improper Integrals. Series in Bessel Functions. Applications of Bessel Functions. Problems of the Theory of Plates and Shells. Problems of the Theory of Oscillations, Hydrodynamics and Heat Transfer. Appendix A. Brief Information on Gamma Functions.read more
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The Surprising Mathematics of Longest Increasing Subsequences
TL;DR: In a surprising sequence of developments, the longest increasing subsequence problem has proven to have deep connections to many seemingly unrelated branches of mathematics, such as random permutations, random matrices, Young tableaux, and the corner growth model as discussed by the authors.
Journal ArticleDOI
Analytical modeling of PCM solidification in a shell and tube finned thermal storage for air conditioning systems
TL;DR: In this paper, a comparative study of phase change materials (PCM) solidification in cylindrical shell and rectangular storages having the same volume and heat transfer surface area is presented.
Journal ArticleDOI
Wave propagation in a duct with a periodic Helmholtz resonators array
Xu Wang,Cheuk Ming Mak +1 more
TL;DR: This paper presents a theoretical study of sound propagation in a one-dimensional duct with identical side-branch resonators mounted periodically and indicates that the wave coupling in this periodic system results in the dispersion of the frequency band into the stop and the pass bands.
Book ChapterDOI
Karhunen-Loève Expansions for Weighted Wiener Processes and Brownian Bridges via Bessel Functions
Paul Deheuvels,Guennady Martynov +1 more
TL;DR: In this article, Karhunen-Loeve expansions on (0, 1) for the processes t θ B (tρ) and T θ W (tθ) were provided for the Brownian process, where B is a bridge, W is a Wiener process, and ρ and θ are arbitrary real numbers such that ρ > −(ρ + 1)/2.
MonographDOI
Special Functions and Orthogonal Polynomials
Richard Beals,Roderick Wong +1 more
TL;DR: The subject of special functions is often presented as a collection of disparate results, rarely organized in a coherent way as discussed by the authors, and the authors of this book emphasize general principles that unify and demarcate the subjects of study.