Let $X$ be a $BCH$-algebra and $I$ be an ideal of $X$. In this paper, we introduce the concept of $sqrt{I}$. We show that it is an ideal of $X$, when $I$ is closed ideal of $X$. Then we verify some useful properties of it. We prove that it is the ::::union:::: of all $k-$nil ideals of $I$. Moreover, if $I$ is a closed ideal of $X$, then $sqrt{I}$ is a closed translation ideal and so we can cons...

in this paper we will prove that if $l$ is a continuous symmetric n-linear form on a hilbert spaceand $widehat{l}$ is the associated continuous n-homogeneous polynomial, then $||l||=||widehat{l}||$.for the proof we are using a classical generalized  inequality due to s. bernstein for entire functions of exponential type. furthermore we study the case that if x is a banach space then we have tha...

Let R be an associative ring with unity. An element a in R is said to be r-clean if a = e+r, where e is an idempotent and r is a regular (von Neumann) element in R. If every element of R is r-clean, then R is called an r-clean ring. In this paper, we prove that the concepts of clean ring and r-clean ring are equivalent for abelian rings. Further we prove that if 0 and 1 are the only idempotents...

when the parties enter into a contract it is valid and binds the parties: that meams one of them cannot terminate the contract without an agreement; in this article we try to prove the base of this principle: in islamic law if the evidence of the sources are not sufficient we can accompany the effects of the contract if it is unconditional and absolute in islamic law it is known as esteshaab.

Prediction of future observations is an important and challenging problem. The two mainstream approaches for quantifying prediction uncertainty use regions predictive distributions, respectively, with the latter believed to be more informative because it can perform other prediction-related tasks. standard notion validity, what we refer here as Type-1 focuses on coverage probability regions, wh...