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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…
A. Gnanam, B. Anitha
Polygonal numbers and sums of squares of primes are distinct fields of number theory. Here we consider sums of squares of consecutive (of order and rank) polygonal numbers. We try to express sums of squares of polygonal numbers of consecutive orders in matrix…
Barış Kendirli
Here, we determine formulae, for the numbers of representations of a positive integer by certain sextenary quadratic forms whose coefficients are 1, 2, 3 and 6.
Oded Kafri
When P indistinguishable balls are randomly distributed among L distinguishable boxes, and considering the dense system , our natural intuition tells us that the box with the average number of balls P / L has the highest probability and that none of boxes are…
Xiang Liu, Rybachuk Ekaterina, Fasheng Liu
Using the properties of theta-series and Schwarz reflection principle, a proof for Riemann hypothesis (RH) is directly presented and the first ten nontrivial zeros are easily obtained. From now on RH becomes Riemann Theorem (RT) and all its equivalent results…
Tohru Morita, Ken-ichi Sato
We know that the hypergeometric function, which is a solution of the hypergeometric differential equation, is expressed in terms of the Riemann-Liouville fractional derivative (fD). The solution of the differential equation obtained by the Euler method takes…
Md. Nur Alam, Fethi Bin Muhammad Belgacem
The new generalized (G'/G)-expansion method is one of the powerful and competent methods that appear in recent time for establishing exact solutions to nonlinear evolution equations (NLEEs). We apply the new generalized (G'/G)-expansion method to solve exact…
Arif M. Khan
The present paper aims at introducing and investigating a new class of generalized double zeta function i.e . modified double zeta function which involves the Riemann, Hurwitz, Hurwitz-Lerch, Barnes double zeta function and Bin-Saad generalized double zeta fu…
Edgar E. Escultura
The paper resolves the great debate of the 20th century between the three philosophies of mathematics-logicism, intuitionism and formalism—founded by Bertrand Russell and A. N. Whitehead, L. E. J. Brouwer and David Hilbert, respectively. The issue: which one…
Slaviša V. Djordjević, Fernando Hernández-Díaz
The purpose of this article is to present Schechter’s manner to introduce α -Wayl operators and compare this definition with another one given by Yadav and Arora. Moreover, we introduce generalized Weyl operator in the way that we keep many properties of the…
Madjid Allili, David Corriveau
In this paper, we propose a new algorithm to compute the homology of a finitely generated chain complex. Our method is based on grouping several reductions into structures that can be encoded as directed acyclic graphs. The organized reduction pairs lead to s…
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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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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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