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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
A family of prime constellation detectors D ( p , N ) expressed as rational powers of 2π, built from the sum-of-divisors function σ . The central object D ( p , N ) = ( 2 π ) p + N + 1 − [ σ ( p ) + σ ( p + 2 N ) ] / 2 equals 1 if and only if both p and p + 2…
Michael Mark Anthony
Starting from Jensen’s integral representation of the Riemann zeta function, I derive, by a chain of convergent algebraic manipulations, a self-referential integral equation that a complex number F must satisfy in order for ρ = F ( s ) / ( F ( s ) − 1 ) to be…
Adnan Altay Altınörs
Ensuring stability and accuracy is essential in numerical modeling of subsurface flow in fractured and heterogeneous media. This study investigates one-dimensional transient groundwater flow in a finite fractured confined aquifer using a double-porosity conti…
Gnouma Jérôme Kadouno
The original online version of this article (Kadouno, G.J. (2025) Analysis of Multiplication Tables by Sum, Difference and Product: A New Approach to Primality. Advances in Pure Mathematics, 15, 505-517. https://doi.org/10.4236/apm.2025.158025 ) unfortunately…
Serdar Beji
A recursive technique, termed method of successive polynomial substitutions for computing all the real and complex roots of a polynomial of any given degree, is introduced. The method proceeds by reducing the degree of polynomial by one at each stage of succe…
Han-Lin Li, Shu-Cherng Fang, Way Kuo
The famous Fermat’s Christmas Theorem states that all Pythagorean primes can be expressed as a sum of two squares of integers. This report specifies the conditions that a ( 4 k + 1 )-type integer expressed in a sum of two squares becomes prime.
Andras Szasz, 1 1
The exact analytical solution of the three-dimensional (3D) Ising model remains a central unresolved problem in statistical mechanics. While exact solutions exist in one and two dimensions, the three-dimensional case has resisted closed-form treatment. While…
Zhenmin Liu, Yifan Liu, Xin Zhao, Hanzhen Xiao, Shihui Yu, Jianhui Liu, Yifang Fu, Shuxiong Xiao, Hongsheng Yu
This study proposes a dynamic evaluation model for medical service quality that integrates proximity function, fuzzy mathematics, and hexahedral boundary function theory (a mathematical tool that defines the value range of evaluation indicators by setting thr…
Manfred Wiessner, Benoît Loridant, Paul Angerer, Martin Medebach, Ewald Werner, Ernst Gamsjäger
This work introduces a novel Bayesian inspired regression method for the simultaneous estimation of model parameters and data uncertainties. The key mathematical result of this framework is an extended least squares objective function. The conventional sum of…
Hanan S. Gafel
The natural transform ( nt ), a novel global method for solving fractional high-order differential equations (FDEs), is presented in this work. This technique functions as an all-encompassing integral transform that includes both Sumudu and Laplace transforms…
No articles in 2018.
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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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.
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