‎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...

BACKGROUND Dedicated storage organs in the form of tubers are evolutionary novelties that share a common function but originate in diverse species from different organs. Tubers in potato, Solanum tuberosum, are derived from the swollen tips of specialized basal lateral juvenile shoots, called stolons. Lateral buds of tomato, Solanum lycopersicum, a potato sibling species, only form regular shoo...