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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…
Mohamed Bekkali
The Intermediate Value Theorem (for short, TVI) is a real analysis concept that one encounters in her/his College first calculus course. It is stated for a real continuous function, f , on a closed non empty interval I ⊂ ℝ . These two hypothesis, on the funct…
James Evans, Andrzej Korzeniowski
We obtain a closed form expression for the joint probability mass function of the occupation times for a Three-State Markov chain. Our representation extends the long-standing result for a Two-State Markov chain by utilizing the method of probability generati…
Zengyong Liang
High degree algebraic equations are an unsolved problem in algebra. The author has been able to solve high-order algebraic equations using elementary algebraic methods through exploration. This article will introduce new methods for solving algebraic equation…
Hawazin Daif Allah Alzahrani
This paper investigates the homological structures in L ∞ -algebras and their behavior under various conditions, with a focus on the excision theorem, simplicial homology, and bar homology. We introduce the key concepts of excision in the context of L ∞ -alge…
Yong Seung Cho
The Hodge conjecture states that the Hodge group of Hodge classes is equal to the algebraic group generated by algebraic subvarieties on a Hodge manifold. To prove the conjecture, we introduce the Hodge structure, the Lefschetz decomposition, and polarization…
Gnouma Jérôme Kadouno
This paper systematically studies the properties of multiplication tables through three fundamental operations: Σ T , Δ T , Π T . We show how these operations reveal deep arithmetic structures, leading to an innovative primality test. A logarithmic version op…
Alemayehu Negash, Meaza Bogale
In this paper, our purpose is to establish a common fixed point result for a pair of self-mappings satisfying some generalized cyclic contraction type conditions involving altering distance and control function with two variables in partial metric spaces. Mor…
Hawazin Daif Allah Alzahrani
This paper explores the foundational and advanced aspects of A ∞ -algebras. We present a comprehensive study of A ∞ -algebras and their homology, emphasizing the construction of long exact sequences in simplicial homology and their implications for short exac…
Gnouma Jérôme Kadouno
This article proposes an algorithmic method for testing divisibility, grounded in the relationships between the multiplication tables of consecutive divisors. The algorithm generates, through an iterative process, a sequence of quotients and differences that…
Ángel Padilla, Ronald Ramírez, Maira Valera-López
In this paper, we present some properties of m -convex stochastic processes. The most important results are: a generalization of the sandwich theorem and a result on Hyers-Ulam stability, given for m -convex functions. The first result allows us to bound an m…
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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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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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