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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…
Alfred Wünsche
To the Riemann hypothesis, we investigate first the approximation by step-wise Omega functions Ω( u ) with commensurable step lengths u 0 concerning their zeros in corresponding Xi functions Ξ( z ). They are periodically on the y -axis with period proportiona…
Dorin Ghisa
The Cauchy integral formula expresses the value of a function f ( z ), which is analytic in a simply connected domain D , at any point z 0 interior to a simple closed contour C situated in D in terms of the values of on C . We deal in this paper with the ques…
Weikang Chen
In this paper, we prove an existence theory for ring-profiled optical vortex solitons via constrained minimization, which are considered in the context of an electromagnetic light wave propagating in a nonlinear media and governed by a nonlinear Schrödinger t…
Yufeng Xia
The most interesting and famous problem that puzzled the mathematicians all around the world is much likely to be the Fermat’s Last Theorem. However, since the Theorem was proposed, people can’t find a way to solve the problem until Andrew Wiles proved the Fe…
Thomas Beatty, Gabriela von Linden
Factoring quadratics over Z is a staple of introductory algebra and textbooks tend to create the impression that doable factorizations are fairly common. To the contrary, if coefficients of a general quadratic are selected randomly without restriction, the pr…
Jing Liu, Wanzhou Ye
In this paper, we research the regression problem of time series data from heterogeneous populations on the basis of the finite mixture regression model. We propose two finite mixed time-varying regression models to solve this. A regularization method for var…
Xiaochun Mei
A standard method is proposed to prove strictly that the Riemann Zeta function equation has no non-trivial zeros. The real part and imaginary part of the Riemann Zeta function equation are separated completely. Suppose ξ ( s ) = ξ 1 ( a , b ) + i ξ 2 ( a , b…
Yukun Liu, Yong Yue, Dongwen Zhang, Chunhua Li
This paper presents a new scheme of flaw searching in surface modeling based on Euler Characteristic. This scheme can be applied to surface construction or reconstruction in computer. It is referred to as Euler Accompanying Test (EAT) algorithm in this paper.…
Jiangtao Wang, Wanzhou Ye
The traditional estimation of Gaussian mixture model is sensitive to heavy-tailed errors; thus we propose a robust mixture regression model by assuming that the error terms follow a Laplace distribution in this article. And for the variable selection problem…
Yukun Liu, Yong Yue
There are two classes of continuities, parametric continuities and geometric continuities, which are used to illuminate the smoothness of a composite surface in surface construction and reconstruction in computer graphics (CG) and computer aided design (CAD).…
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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.
The editorial office screens the manuscript for scope, completeness, and formatting before assigning a handling editor.
At least two independent reviewers evaluate the manuscript under single-blind review. Where revisions are required, authors respond point by point.
On acceptance the article processing charge is invoiced and the CC BY 4.0 copyright handover is signed.
The article is copyedited, typeset, and given a DOI, then publishes open access with a permanent link.
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.
Use the journal's numbered (Vancouver) reference style. Cite sources consecutively in the order they appear, and ensure every reference is complete and retrievable.
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