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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…
Yury M. Volin
The article is devoted to proving the inconsistency of set theory arising from the existence of strange trees. All steps of the proof rely on common informal set-theoretic reasoning, but they take into account the prohibitions that were introduced into axioma…
Terry E. Moschandreou
This article gives a general model using specific periodic special functions, which is degenerate elliptic Weierstrass P functions whose presence in the governing equations through the forcing terms simplify the periodic Navier Stokes equations (PNS) at the c…
Lily Gebhart, John Kolassa
The test of Prentice [1] is a non-parametric statistical test for the two-way analysis of variance using ranks. The null distribution of this test typically is approximated using the Chi-square distribution. However, the exact null distribution deviates from…
Jean-Francois Pommaret
When D : ξ → η is a linear ordinary differential (OD) or partial differential (PD) operator, a “direct problem” is to find the generating compatibility conditions (CC) in the form of an operator D 1: η → ξ such that D ξ = η implies D 1 η = 0. When D is involu…
Mady Ndiaye
The application of the Euclidean division theorem for the positive integers allowed us to establish a set which contains all the prime numbers and this set we called it set of supposedly prime numbers and we noted it E sp . We subsequently established from th…
Sudhindra B. Kittur
An elementary formula to know the number of primes in the interval ( x , 2 x ) close to the exact figure for a fixed x is given here. A new elementary equation is derived (a relation between prime numbers and composite numbers distributed in the interval [1,…
Alfred Wünsche
The Pythagorean triples ( a, b | c ) of planar geometry which satisfy the equation a 2 +b 2 =c 2 with integers ( a, b, c ) are generalized to 3D-Pythagorean quadruples ( a, b, c | d ) of spatial geometry which satisfy the equation a 2 +b 2 +c 2 =d 2 with inte…
Pal Doroszlai, Horacio Keller
The present paper gives the proof of the set of primes as a continuum. It starts with the density of the primes, and shortly recapitulates the prime-number-formula and the complete-prime-number-formula. Reflecting the series of the primes over any prime gives…
Solomon Jekel
In our paper Simplicial K(G , 1)’s we constructed a sub-complex of the nerve of a group G determined by a partial group structure, and we proved, under a generalized associativity condition called regularity, that the sub-complex realizes as a K(G , 1). This…
Ruhua Zhang
This paper discusses further the roughness of Riemann-Liouville fractional integral on an arbitrary fractal continuous functions that follows Rfs. [1] . A novel method is used to reach a similar result for an arbitrary fractal function , where is the Riemann-…
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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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