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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…
Michael M. Anthony
The Riemann hypothesis is intimately connected to the counting functions for the primes. In particular, Perron’s explicit formula relates the prime counting function to fixed points of iterations of the explicit formula with particular relations involving the…
Hidenori Tanaka, Shin-ya Koyama
In this paper, we calculate the absolute tensor square of the Dirichlet L -functions and show that it is expressed as an Euler product over pairs of primes. The method is to construct an equation to link primes to a series which has the factors of the absolut…
Giuseppina Guatteri, Federica Masiero
In this paper we study optimal advertising problems that model the introduction of a new product into the market in the presence of carryover effects of the advertisement and with memory effects in the level of goodwill. In particular, we let the dynamics of…
Kimou Kouadio Prosper, Kouakou Kouassi Vincent, Tanoé François
We analyse the Diophantine equation of Fermat <i>x</i><i><sup>p</sup></i> <i>y</i><i><sup>p</sup></i> = <i>z</i><i><sup>p</sup></i> with <i>p</i> > 2 a prime, <i>x</i>, <i>y</i>, <i>z</i> positive nonzero integers. We consider the hypothetical solution (<i>a<…
Han-Lin Li, Shu-Cherng Fang, Way Kuo
Over millennia, nobody has been able to predict where prime numbers sprout or how they spread. This study establishes the Periodic Table of Primes (PTP) using four prime numbers 2, 3, 5, and 7. We identify 48 integers out of a period <math display='inline' xm…
Moumouni Djassibo Woba
We have shown that certain non-commutative integral rings can be immersed in a field by a method which is not that of the construction of the field of fractions on the right <math display='inline' xmlns='http://www.w3.org/1998/Math/MathML'> <mrow> <mi>ℝ…
Vesna Gotovac Đogaš
This paper concerns the compactness and separability properties of the normed Boolean algebras (N.B.A.) with respect to topology generated by a distance equal to the square root of a measure of symmetric difference between two elements. The motivation arises…
Mark Jones
The stability of a set of spatially constant plane wave solutions to a pair of damped coupled nonlinear Schrödinger evolution equations is considered. The equations could model physical phenomena arising in fluid dynamics, fibre optics or electron plasma…
Najah A. AlSaedi
In this paper, we introduce and study the notion of <i>HB</i>-closed sets in <i>L</i>-topological space. Then, <i>HB</i>-convergence theory for <i>L</i>-molecular nets and <i>L</i>-ideals is established in terms of <i>HB</i>-closedness. Finally, we give a new…
Mady Ndiaye
We have found through calculations that the differences between the closest supposed prime numbers other than 2 and 3 defined in the articles are: 2; 4: and 6. For those whose difference is equal to 6, we showed their origin then we classified them into two c…
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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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