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Dec 28, 2023Open Access
In this paper, we explore the inverse spectral problem for a kind of pseudo-symmetric matrix A(ε,c,s) that corresponds to a graph of a banana tree when all ε=1. The problem of reconstructing pseudo-symmetric matrices from their spectra was considered. The sufficient and necessary conditions for the existence of these matrices are provided, and an algorithm and numerical example were provided to illustrate their characteristics. In addition, the effectiveness of the solution was v...
Aug 18, 2022Open Access
We can say for a ring R weak JN-clean ring if all elements a in R it can be written as a sum or difference of nilpotent and idempotent. Further the nilpotent element belongs to the Jacobson radical of R. The purpose of this paper is to give some characterization and basic properties of this ring. Also we will studied the relationship between weak JN-clean rings and J-reduced ring, Boolean ring, local ring and clean ring: from the main result: 1) The ring R is w...
Jun 29, 2022Open Access
If a ring R is called weak nil clean if every element in R can be expressed as the sum or difference of nilpotent element and idempotent, if further the idempotent element and nilpotent element commute the ring is called weak* nil clean. The purpose of this paper is to give some characterization and basic properties of weak nil clean rings. The main results of this work are: 1) Let R be a ring, then R is weak nil clean if and only if R/ P( R) is wea...
Dec 06, 2019Open Access
A Ring R is called right JGP-ring; if for every a ∈ J (R), r (a) is a left GP-ideal. In this paper, we first introduced and characterize JGP-ring, which is a proper generalization of right GP-ideal. Next, various properties of right JGP-rings are developed; many of them extend known results.
Oct 12, 2018Open Access
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 Access
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 Access
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 Access
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× p matrices. In this article, we give the meaning of 3D matrices. We als...
Aug 23, 2016Open Access
We prove that e＋π 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 Access
Some special matrices can really help us to construct more than two
mutually unbiased maximally entangled bases in C2 C4. 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...
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