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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…
Pingyuan Zhou
By our suggested definition, an even number L n is called the largest strong Goldbach number generated by the n -th prime P n if every even number from 4 to L n is the sum of two primes not greater than P n but L n + 2 is not such a sum. We discovered the exi…
Philip C. Jackson
A 2023 paper discussed how the real numbers between 0 and 1 could be represented by an infinite tree structure called the “infinity tree”, which contains only a countably infinite number of nodes and arcs. A 2025 paper discussed how a finite-state Turing mach…
Lionel Laurore
The Collatz Conjecture asserts that for all positive integers s , every Syracuse integer sequence defined by T ( s ) = s / 2 if s is even, and T ( s ) = ( 3 s + 1 ) / 2 otherwise, eventually reaches 1 after a finite number of iterations. The stopping time of…
Paul Bracken
Properties of Hilbert spaces, projections and spectral measures are introduced and studied. Spectral integrals and the related operator are considered, and their relationship with the spectrum of an operator is given. The theorems that result yield a version…
Qinqin Gan, Wanzhou Ye
Regression models with intractable normalizing constants are valuable tools for analyzing complex data structures, yet parameter inference for such models remains highly challenging—particularly when observations are discrete. In statistical inference, discre…
Mengyu Hu
Stable distributions are well-known for their desirable properties and can effectively fit data with heavy tail. However, due to the lack of an explicit probability density function and finite second moments in most cases, traditional parametric inference met…
Mustapha Laayouni
Compact sets have important properties, and their studies have contributed to the development of functional analysis, particularly in the field of compact operators. In this paper, we introduce the concept of order compactness in Riesz spaces as an analog to…
Zhongcui Ma, Dandan Lai, Jianxiang Zhu, Yaxin Peng
Offline reinforcement learning (RL) focuses on learning policies using static datasets without further exploration. With the introduction of distributional reinforcement learning into offline RL, current methods excel at quantifying the risk and ensuring the…
Han-Lin Li, Shu-Cherng Fang, Way Kuo, Nianrui Lin
Over millennia, people have considered prime numbers as unpredictable and hard to list. This study confirms that all positive integers without factors of 2, 3, 5 and 7 can be regarded as the offspring of 48 roots in the interval [11, 220]. These roots are to…
Xin’ai Fu
This paper is devoted to studying the global existence of smooth solutions for the Timoshenko-Cattaneo system with two sound waves. In the case of equal wave speeds and non-equal wave speeds, the Timoshenko-Cattaneo system exhibits regularity loss in the high…
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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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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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