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A mathematical analysis of poroacoustic traveling wave phenomena is presented. Assuming that the fluid phase satisfies the perfect gas law and that the drag offered by the porous matrix is described by Darcy's law, exact traveling wave solutions (TWS)s, as well as asymptotic/approximate expressions, are derived and examined. In particular, stability issues are addressed, shock and acceleration waves are shown to arise, and special/limiting cases are noted. Lastly, connections to other fields are...

A note on $q$ -partial difference equations and some applications to generating functions and $q$ -integrals

Da-Wei Niu, Jian Cao (2019)

Czechoslovak Mathematical Journal

We study the condition on expanding an analytic several variables function in terms of products of the homogeneous generalized Al-Salam-Carlitz polynomials. As applications, we deduce bilinear generating functions for the homogeneous generalized Al-Salam-Carlitz polynomials. We also gain multilinear generating functions for the homogeneous generalized Al-Salam-Carlitz polynomials. Moreover, we obtain generalizations of Andrews-Askey integrals and Ramanujan $q$ -beta integrals. At last, we derive $U (n + 1)$ ...

A note on semi-classical orthogonal polynomials.

Branquinho, Amílcar (1996)

Bulletin of the Belgian Mathematical Society - Simon Stevin

A note on some expansions of p-adic functions

Grzegorz Szkibiel (1992)

Acta Arithmetica

Introduction. Recently J. Rutkowski (see [3]) has defined the p-adic analogue of the Walsh system, which we shall denote by ${(ϕ ₘ)}_{m \in ℕ ₀}$ . The system ${(ϕ ₘ)}_{m \in ℕ ₀}$ is defined in the space C(ℤₚ,ℂₚ) of ℂₚ-valued continuous functions on ℤₚ. J. Rutkowski has also considered some questions concerning expansions of functions from C(ℤₚ,ℂₚ) with respect to ${(ϕ ₘ)}_{m \in ℕ ₀}$ . This paper is a remark to Rutkowski’s paper. We define another system ${(h ₙ)}_{n \in ℕ ₀}$ in C(ℤₚ,ℂₚ), investigate its properties and compare it to the system defined by Rutkowski. The system...