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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…
G. Upender Reddy
2-frames in 2-Hilbert spaces are studied and some results on it are presented. The tensor product of 2-frames in 2-Hilbert spaces is introduced. It is shown that the tensor product of two 2-frames is a 2-frame for the tensor product of Hilbert spaces. Some re…
Huabin Ge, Yipeng Shi
In this paper, we consider L ∞ estimates of eigenfunction, or more generally, the L ∞ estimates of equation -Δu= f u. We use heat flow to give a new proof of the L ∞ estimates for such type equations.
Qianqian Chu, Hailan Jin
This paper mainly studies some properties of skew polynomial ring related to Morita invariance, Armendariz and (quasi)-Baer. First, we show that skew polynomial ring has no Morita invariance by the counterexample. Then we prove a necessary condition that skew…
Yong Zhang, Wanzhou Ye
In this paper, we propose an efficient adaptive iteratively reweighted l 1 algorithm (A-IRL1 algorithm) for solving the elastic l q regularization problem. We prove that the sequence generated by the A-IRL1 algorithm is convergent for any rational and the lim…
Amiri Naser, Hasani Fysal
In this paper, we study about trigonometry in finite field, we know that , the field with p elements, where p is a prime number if and only if p = 8 k + 1 or p = 8 k -1. Let F and K be two fields, we say that F is an extension of K , if K ⊆ F or there ex…
Abdul Rauf Nizami, Mobeen Munir, Tanweer Sohail, Ammara Usman
Although computing the Khovanov homology of links is common in literature, no general formulae have been given for all of them. We give the graded Euler characteristic and the Khovanov homology of the 2-strand braid link , , and the 3-strand braid .
Konstantinos Goulianas, Athanasios Margaris, Ioannis Refanidis, Konstantinos Diamantaras, Theofilos Papadimitriou
The objective of this research is the presentation of a neural network capable of solving complete nonlinear algebraic systems of n equations with n unknowns. The proposed neural solver uses the classical back propagation algorithm with the identity function…
Mohamed S. El Naschie
The paper presents a very simple and straight forward yet pure mathematical derivation of the structure of actual spacetime from quantum set theory. This is achieved by utilizing elements of the topological theory of cobordism and the Menger-Urysohn dimension…
Thomas Beatty, Bradley Hansen
Double sequences have some unexpected properties which derive from the possibility of commuting limit operations. For example, may be defined so that the iterated limits and exist and are equal for all x , and yet the Pringsheim limit does not exist. The sequ…
Kung-Kuen Tse
We study projections onto a subspace and reflections with respect to a subspace in an arbitrary vector space with an inner product. We give necessary and sufficient conditions for two such transformations to commute. We then generalize the result to affine su…
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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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