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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…
Thomas Beatty, Nicole Legge
The finite field F q has q elements, where q = p k for prime p and k ∈ N. Then F q [ x ] is a unique factorization domain and its polynomials can be bijectively associated with their unique (up to order) factorizations into irreducibles. Such a factorization…
Lyndon O. Barton
This paper presents a graphical procedure, using an unmarked straightedge and compass only , for trisecting an arbitrary acute angle. The procedure, when applied to the 30 ˚ angle that has been “proven” to be not trisectable, produced a construction havi…
Gonzalo Perera, Angel M. Segura
We present a novel method to analyze extreme events of flows over manifolds called Peaks Over Manifold (POM). Here we show that under general and realistic hypotheses, the distribution of affectation measures converges to a Generalized Pareto Distribution (GP…
Mohammad Rahman
We provide the derivation of a new formula for the approximation of an integral Markov process arising in the approximation of stochastic differential equations. This formula extends an existing formula derived in [1] . We have shown numerically that the lead…
Maoze Wang, Yongbao Yang, Zhenxiang He, Meiyi Wang
In this paper, we use two new effective tools and ingenious methods to prove the 3X + 1 conjecture. By using the recursive method, we firstly prove that any positive integer can be turned into an element of fourth column of the infinite-row-six-column-matrix…
Zengyong Liang
This paper introduces how to use geometric figures to represent integers, and successfully proves Goldbach’s conjecture by using the mapping relationship between the internal angles of circles and sectors and the number of integers. It is also explained and p…
Leo Depuydt
This article presents four (4) additions to a book on the brain’s OS published by SciRP in 2015 [1]. It is a kind of appendix to the book. Some familiarity with the earlier book is presupposed. The book itself proposes a complete physical and mathematical blu…
Tingting Juan, Xianming Hou
In this paper, we establish the weighted L p (1 < p < ∞) boundedness of variation operator for the commutators generated by one-sided Calderón-Zygmund singular integrals with Lipschitz functions.
Mamoudou Amadou Bondabou, Ousmane Moussa Tessa, Maimouna Salou
The goal of this study is to propose a method of estimation of bounds for roots of polynomials with complex coefficients. A well-known and easy tool to obtain such information is to use the standard Gershgorin’s theorem, however, it doesn’t take into account…
Fanhui Meng, Wenhua Qiu
This paper focuses on the reducibility of two-dimensional almost periodic system with small perturbation. We use the KAM iterative method to get the reducibility by an almost periodic transformation. The system has been reduced to a simple form. So we have de…
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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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At least two independent reviewers evaluate the manuscript under single-blind review. Where revisions are required, authors respond point by point.
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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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