‎let $i$ be an ideal in a regular local ring $(r,n)$‎, ‎we will find‎ ‎bounds on the first and the last betti numbers of‎ ‎$(a,m)=(r/i,n/i)$‎. ‎if $a$ is an artinian ring of the embedding‎ ‎codimension $h$‎, ‎$i$ has the initial degree $t$ and $mu(m^t)=1$‎, ‎we call $a$ a {it $t-$extended stretched local ring}‎. ‎this class of‎ ‎local rings is a natural generalization of the class of stretched ...

an important factor in the growth medium of plants and chemical plants. native substrates can be used to improve plant performance. to evaluate the effect of growth medium on the herb f. benjamina experimental design was completely randomized with eight treatments and four replications were carried out in the research greenhouse of islamic azad university of jiroft. f. benjamina  plants from ve...

background: polycystic ovaries syndrome (pcos) is the most common disorder in infertile women with ovulation sterility. there are some instances of abnormal endocrine in the women stricken by this syndrome and so the clinical results of ovulating induction in them, because of severe response of ovary against ovulating induction, are very discussing and may lead to different results from those w...

the main idea of this paper is to study the dependence between the probability of default and the recovery rate on credit portfolio and to seek empirically this relationship. we examine the dependence between pd and rr by theoretical approach. for the empirically methodology, we use the bootstrapped quantile regression and the simultaneous quantile regression. these methods allow to determinate...

mathematics curriculum in schools is always a key position and is considered as an essential knowledge. so it is taught in the first years of school curriculum. this knowledge has focused on calculating the initial period. so this part of mathematics play an important role in lives of all people so this knowledge is essential for learning today. in the early years of primary school children, th...

We introduce the notion of uniform number of a graph. The  uniform number of a connected graph $G$ is the least cardinality of a nonempty subset $M$ of the vertex set of $G$ for which the function $f_M: M^crightarrow mathcal{P}(X) - {emptyset}$ defined as $f_M(x) = {D(x, y): y in M}$ is a constant function, where $D(x, y)$ is the detour distance between $x$ and $y$ in $G$ and $mathcal{P}(X)$ ...