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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…
Guo Zhao
A newly developed approach without crack surface discretization for modeling 2D solids with large number of cracks in linear elastic fracture mechanics is proposed with the eigen crack opening displacement (COD) boundary integral equations in this paper. The…
Xinru Ma, Heguo Liu, Honglian Zhang
In this note, we provide an effective proof of the fundamental structure theorem of finitely generated modules over a principal ideal domain, from which we find the minimality of decomposition for a finitely generated module over a principal ideal domain.
Wiesław Grzesikiewicz, Artur Zbiciak
Planar motion of a non-deformable wheel under the action of non-ideal unilateral constraints is considered. The mathematical description of this phenomenon has a form of a non-smooth initial value problem. The non-smoothness of this problem means that its sol…
M. Y. Youssif, Elhadi E. E. Dalam
Scattering theory plays the main role in the study of manifolds and the Laplacian spectrum. In this article, we process justifying the continuous Laplacian spectrum and on a complete Riemannian manifold. ( M , g i ) is categorized by the use of bounded curvat…
Yueming Sun
This paper mainly investigates the semicontinuity of solution mappings for set optimization problems under a partial order set relation instead of upper and lower set less order relations. To this end, we propose two types of monotonicity definition for the s…
Ibrahim Ly, Sadou Tao
The purpose of the research is to assign a formally exact elliptic complex of length two to the Cauchy-Riemann Operator. The Neumann problem for this complex in a bounded domain with smooth boundary in R 2 will be studied, helping therefore to solve a usual b…
Zhongyan Shen, Tianxin Cai
Let p be an odd prime, the harmonic congruence such as , and many different variations and generalizations have been studied intensively. In this note, we consider the congruences involving the combination of alternating harmonic sums, where P P denotes the s…
Chuanmiao Chen, 1 1
Riemann hypothesis (RH) is a difficult problem. So far one doesn’t know how to go about it. Studying ζ and using analysis method likely are two incor-rect guides. Actually, a unique hope may study Riemann function , , by geometric analysis, which has the symm…
Prodromos Char. Papadopoulos
This article B is almost autonomous because it can be read independently from the first published article A [1] using only a few parts of the article A. Be-low are given instructions so to need the reader study only on few places of the article A. Also, in th…
Gerd Kaupp
The original online version of this article (Gerd Kaupp 2020) Valid Geometric Solutions for Indentations with Algebraic Calculations, (Volume, 10, 322-336, https://doi.org/10.4236/apm.2020.105019) needs some further amendments and clarification.
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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.
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