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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…
Rostand S. Kuitché
For decades, Lychrel numbers have been studied on many bases. Their existence has been proven in base 2, 11 or 17. This paper presents a probabilistic proof of the existence of Lychrel number in base 10 and provides some properties which enable a mathematical…
Serdar Beji
An entirely new framework is established for developing various single- and multi-step formulations for the numerical integration of ordinary differential equations. Besides polynomials, unconventional base-functions with trigonometric and exponential terms s…
Fuzhang Zhao
The isotropic continuum stored energy (CSE) functional, fully combined with the Poisson function, has been applied to constitutively model compressible as well as incompressible rubberlike materials. The isotropic CSE constitutive model fits uniaxial tension…
Chuanmiao Chen, 1 1
Riemann (1859) had proved four theorems: analytic continuation ζ ( s ) , functional equation ξ ( z ) = G ( s ) ζ ( s ) ( s = 1 / 2 + i z , z = t − i ( σ − 1 / 2 ) ), product expression ξ 1 ( z ) and Riemann-Siegel formula Z ( z ) , and proposed Riemann conjec…
Anry Nersessian
In the author’s recent publications, a parametric system biorthogonal to the corresponding segment of the exponential Fourier system was unusually effective. On its basis, it was discovered that knowledge of a finite number of Fourier coefficients of function…
Alfred Wünsche
The Fourier series of the 2π-periodic functions tg ( x 2 ) and 1 sin ( x ) and some of their relatives (first of their integrals) are investigated and illustrated with respect to their convergence. These functions are Generalized functions and the convergence…
Stephen Macharia Gathigi, Moses Nderitu Gichuki, Kewamoi Chesire Sogomo
The concepts of connectedness play a critical role in digital picture segmentation and analyses. However, the crisp nature of set theory imposes hard boundaries that restrict the extension of the underlying topological notions and results. Whilst fuzzy set th…
Zhezhao Zeng, Yuqi Tang, 1 1
To address the challenge of achieving unified control across diverse nonlinear systems, a comprehensive control theory spanning from PID (Proportional-Integral-Derivative) to ACPID (Auto-Coupling PID) has been proposed. The primary concept is to unify all int…
Yingjun Ni, Fen Wang
This paper studied the invariance of the Cauchy mean with respect to the arithmetic mean when the denominator functions satisfy certain conditions. The partial derivatives of Cauchy’s mean on the diagonal are obtained by using the method of Wronskian determin…
Serdar Beji
A generalized form of the error function, G p ( x ) = p Γ ( 1 / p ) ∫ 0 x e − t p d t , which is directly associated with the gamma function, is evaluated for arbitrary real values of p > 1 and 0 < x ≤ + ∞ by employing a fast-converging power series expansion…
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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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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.
Use the journal's numbered (Vancouver) reference style. Cite sources consecutively in the order they appear, and ensure every reference is complete and retrievable.
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