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We provide a new simple and transparent proof of the version of Kummer's test given in [Tong, J. (1994). Amer. Math. Monthly. 101(5): 450--452]. Our proof is based on an application of a Hardy--Littlewood Tauberian theorem.
A new numerical method to solve an inverse source problem for the radiative transfer equation involving the absorption and scattering terms, with incomplete data, is proposed. No restrictive assumption on those absorption and scattering…
In this paper, we prove the infinitely many solutions to a class of sublinear Schr\"{o}dinger-Poisson equations by using an extension of Clark's theorem established by Zhaoli Liu and Zhi-Qiang Wang.
The paper [1] considers a spherical cloak described by three radially varying acoustical quantities. For a given radial mass density in the cloak the question posed is whether the remaining two parameters, tangential density and…
We present a solution of $3x+1$ problem. For a history of this problem we refer the reader to Lagarias, Jeffrey C.
An inverse scattering problem for the 3D acoustic equation in time domain is considered. The unknown spatially distributed speed of sound is the subject of the solution of this problem. A single location of the point source is used. Using a…
A novel approach to an old symmetry problem is developed. A new proof is given for the following symmetry problem, studied earlier.
This paper summarizes some recent advances on a set of tasks related to the processing of singing using state-of-the-art deep learning techniques. We discuss their achievements in terms of accuracy and sound quality, and the current…
We present a new proof to a general result due to Kestelman. Our proof differs completely from the other proofs we know and we hope that readers will find it clearer. We also include a quite exhaustive bibliographical analysis on related…
It is tried to axiomatize the transparent theory of music.
Using modular arithmetic of the ring $\mathbb{Z}_{n+1}$ we obtain a new short solution to the problem of existence of at least one solution to the $N$-Queens problem on an $N \times N$ chessboard. It was proved, that these solutions can be…
We provide a surprising answer to a question raised in S. Ahmad and A.C. Lazer [2], and extend the results of that paper.
We present a novel integral representation for the biharmonic Dirichlet problem. To obtain the representation, the Dirichlet problem is first converted into a related Stokes problem for which the Sherman-Lauricella integral representation…
A new simple proof of Stirling's formula via the partial fraction expansion for the tangent function is presented.
We discuss a method of solving $n^{th}$ order scalar ordinary differential equations by extending the ideas based on the Prelle-Singer (PS) procedure for second order ordinary differential equations. We also introduce a novel way of…
We give again (see also arXiv:1112.0676) a proof of weighted estimate of any Calder\'on-Zygmund operator. This is under a universal sharp sufficient condition that is weaker than the so-called bump condition. Bump conjecture was recently…
The speech-to-song illusion is a robust psychological phenomenon whereby a spoken sentence sounds increasingly more musical as it is repeated. Despite decades of research, a complete formal account of this transformation is still lacking,…
A new description is given of all solutions to the relaxed commutant lifting problem. The method of proof is also different from earlier ones, and uses only an operator-valued version of a classical lemma on harmonic majorants.
In this paper, we present a series of mathematical problems which throw interesting lights on flamenco music. More specifically, these are problems in discrete and computational mathematics suggested by an analytical (not compositional)…
A problem in representation theory of $p$-adic groups is the computation of the \textit{Casselman basis} of Iwahori fixed vectors in the spherical principal series representations, which are dual to the intertwining integrals. We shall…