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Advances in Pure Mathematics (APM) is an openly accessible journal published monthly. The goal of this journal is to provide a platform for scientists and academicians all over the world to promote, share, and discuss various new issues and developments in different areas of ordered algebraic structures. All the manus…
Kazuyuki Fujii, 1 1
The least squares method is one of the most fundamental methods in Statistics to estimate correlations among various data. On the other hand, Deep Learning is the heart of Artificial Intelligence and it is a learning method based on the least squares. In this…
Yoshihiro Hamaya
In this paper, we consider an almost periodic system which includes a system of the type , where <i>k</i> is a positive integer, a<sub>ij</sub> are almost periodic in n and satisfy a<sub>ij</sub>(n)≥0 for i≠j, for 1≤j≤m. In the special case where a<sub>ij</su…
Nicholas S. Gonchar
In the paper, the martingales and super-martingales relative to a convex set of equivalent measures are systematically stu died. The notion of local regular super-martingale relative to a convex set of equivalent measures is introduced and the necessary and s…
Chenghong Yang, Hongjuan Zhang
At present, although the human speech separation has achieved fruitful results, it is not ideal for the separation of singing and accompaniment. Based on low-rank and sparse optimization theory, in this paper, we propose a new singing voice separation algorit…
Lucian M. Ionescu
A canonical p-adic Frobenius lift is defined in the context of p-adic numbers, viewed as deformations of the corresponding finite field. Applications to p-adic periods are considered, including to the classical Euler gamma and beta functions and their p-adic…
Siqi Tao
In this paper, we first reformulate the max-min dispersion problem as a saddle-point problem. Specifically, we introduce an auxiliary problem whose optimum value gives an upper bound on that of the original problem. Then we propose the saddle-point problem to…
José Bavio, Melina Guardiola, Gonzalo Perera
In this work we study virtual social networks known as Facebook. It is used by millions of people worldwide, gathering a combination of virtual elements and real world components. We suggest a probabilistic model to describe the long-term behavior of Facebook…
Yongyi Lan
This paper is devoted to the following high order elliptic problems under the Navier boundary condition: Without assuming the standard subcritical polynomial growth condition ensuring the compactness of a bounded (P.S.) sequence, we show that the Navier bound…
Sumitra Dalal, Ibtisam A. Masmali, Ghaliah Y. Alhamzi
In this paper, we prove common fixed point results for quadruple self-mappings satisfying an implicit function which is general enough to cover a multitude of known as well as unknown contractions. Our results modify, unify, extend and generalize many relevan…
Alfred Wünsche
We generalize the Eulerian numbers to sets of numbers E μ ( k,l ), ( μ =0,1,2, · · ·) where the Eulerian numbers appear as the special case μ =1 . This can be used for the evaluation of generalizations E μ ( k,Z ) of the Geometric series G 0 (k;Z)=G 1 (0;Z) b…
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Advances in Pure Mathematics (APM) is an openly accessible journal published monthly. The goal of this journal is to provide a platform for scientists and academicians all over the world to promote, share, and discuss various new issues and developments in different areas of ordered algebraic structures. All the manus… All articles are open access under a CC BY 4.0 licence, with authors retaining copyright.
Authors submit their manuscript, metadata, and declarations through the portal. There is no submission fee.
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Manuscripts must be original and not under consideration elsewhere. Submit in Microsoft Word or LaTeX with figures at 300 dpi minimum. Structure research articles as Abstract, Introduction, Methods, Results, Discussion, and References.
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