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Oct 12, 2018Open    AccessArticle

On Semi π-Regular Local Ring

Zubayda M. Ibraheem, Raghad A. Mustafa, Maha F. Khalf
A ring R is said to be a right (left) semi π-regular local ring if and only if for all a in R, either a or (

Jun 07, 2018Open    AccessArticle

The Law of Self-Replication and the Birth of Life Science

Muying Zhou
The understanding of the unique replication facts of living things helps us to discover the basic law of the life world: the law of self-replication. This law re-veals the root causes of life arising and lays the foundation stone for life sci-ence. From now on, what is a living thing, what does life mean? There has been a standard (the definition).

Dec 20, 2017Open    AccessArticle

Derivatives over Certain Finite Rings

Soud K. Mohamed
We introduce a derivative of a relation over the ring of integers modulo an odd number which is based on the very fundamental concepts which helped in the evolution of derivative of a function over the real number field, namely slope. Then, for a prime field GF(p

May 15, 2017Open    AccessArticle

3D Matrix Ring with a “Common” Multiplication

Orgest ZAKA
In this article, starting from geometrical considerations, he was born with the idea of 3D matrices, which have developed in this article. A problem here was the definition of multiplication, which we have given in analogy with the usual 2D matrices. The goal here is 3D matrices to be a generalization of 2D matrices. Work initially we started with 3×3×3 matrix, and then we extended to m×n×matrices. In this article, we give the meaning of 3D matrices. We als...

Aug 23, 2016Open    AccessArticle

The Proof of Hilbert’s Seventh Problem about Transcendence of e+π

Jiaming Zhu
We prove that eπ is a transcendental number. We use proof by contradiction. The key to solve the problem is to establish a function that doesn’t satisfy the relational expression that we derive, thereby produce a conflicting result which can verify our assumption is incorrect.

Jun 25, 2015Open    AccessArticle

Special Matrices in Constructing Mutually Unbiased Maximally Entangled Bases in C2C4

Jun Zhang, Qiang Yang, Hua Nan, Yuanhong Tao
Some special matrices can really help us to construct more than two mutually unbiased maximally entangled bases in C2C4. Through detailed analysis of the necessary and sufficient conditions of two maximally entangled bases to be mutually unbiased, we find these special matrices. Taking one such kind of matrix, we present the steps of constructing five mutually unbia...