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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 existence of “strange trees” is proven and their paradoxical nature is discussed, due to which set theory is suspected of being contradictory. All proofs rely on informal set-theoretic reasoning, but without using elements that were prohibited in axiomati…
Carlos Antonio Marin-Mendoza, Rogelio Valdez-Delgado
A novel method of renormalization called Pacman renormalization allows us to study (unicritical) Siegel functions through Pacman-type functions. It has been used to investigate the Siegel parameters with combinatorially periodic rotation number in the main ca…
Hong Sun, Fang Liu
In this paper, we study the Dirichlet boundary value problem involving the highly degenerate and h -homogeneous quasilinear operator associated with the infinity Laplacian, where the right hand side term is and the boundary value is . First, we establish the…
Lijun Hao, Liangliang Xu
In the literature, the Bailey transform has many applications in basic hypergeometric series. In this paper, we derive many new transformation formulas for q -series by means of the Bailey transform. Meanwhile, We also obtain some new terminated identities. F…
Fate Shan, Liping Zhu
In this paper, we study the relationship between the convergence of the sinusoidal series and the infinity integrals (any real number α ∈[0,1] , parameter p > 0 ). First of all, we study the convergence of the series (any real number α ∈[0,1], parameter p > 0…
Susmita Pramanik, Deepak Kumar Das, Panchanan Pramanik
Fermat’s last theorem, had the statement that there are no natural numbers A, B, and C such that A n + B n = C n , in which n is a natural number greater than 2. We have shown that any product of two odd numbers can generate Fermat or Pythagoras triple ( A, B…
Lyndon O. Barton
This paper describes the methodology (or approach) that was key to the solution of the angle trisection problem published earlier in article entitled, “A Procedure For Trisecting An Acute Angle.” It was an approach that required first, designing a working mod…
Ola A. Jarab’ah
The constrained motion of a particle on an elliptical path is studied using Hamiltonian mechanics through Poisson bracket and Lagrangian mechanics through Euler Lagrange equation using non-natural Lagrangian. We calculate the generalized momentum p θ and we f…
Xinxue Zhang, Guanggang Liu
In this paper, we consider the following noncooperative elliptic systems where Ω is a bounded domain in R N with smooth boundary ∂ Ω, λ , δ , γ are real parameters, and . We assume that F is subquadratic at zero with respect to the variables u , v . By…
Musa O. Tijani, Adefisayo Ojo, Oludotun Akinsola
Holder’s inequality, its refinement, and reverse have received considerable attention in the theory of mathematical analysis and differential equations. In this paper, we give some refinements of Holder’s inequality and its reverse using a simple analytical t…
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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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