In this paper, we introduce a new generalization of weakly prime ideals called $I$-prime. Suppose $R$ is a commutative ring with identity and $I$ a fixed ideal of $R$. A proper ideal $P$ of $R$ is $I$-prime if for $a, b in R$ with $ab in P-IP$ implies either $a in P$ or $b in P$. We give some characterizations of $I$-prime ideals and study some of its properties.  Moreover, we give conditions  ...

Hypogonadotropic hypogonadism (HH) is an uncommon cause of male infertility and a congenital or secondary disorder characterized by delayed or absent sexual maturation. Congenital abnormalities leading to HH are usually the consequence of deficient GnRH secretion occurring either in isolation (idiopathic hypogonadotropic hypogonadism (IHH)), or in association with anosmia (Kallmann syndrome; KS...

The issue of relation, particularly that of human relation to God stands for one of the most significant concerns by all men of faith. To realize such a relation Martin Buber and Rumi, two globally acclaimed thinkers, have appropriated independent existences for both God and man to make them eligible for having a relation to each other, and they have brought this relationship to the fore in the...

Named a Program of Excellence by the Colorado Commission on Higher Education, the ITL Program provides summer engineering workshops and classes to extend hands-on learning to K-12 teachers and students, as part of its integrated K-16 engineering program. See its extensive K-12 curricula at TeachEngineering.org. " …one of the finer teaching environments on the planet. " — Hewlett-Packard Enginee...

SUMMARY. For a stationary *-mixing stochastic process, the law of iterated logarithm, asymptotic normality and weak convergence to Brownian motion processes

The object of the present investigation is to extend the findings of Hajek [5J on asymptotically most powerful rank order tests (AMPROT) to grouped data where the underlying distributions are essentially continuous but I the observable random variables correspond to a finite or countable set of contiguous class intervals. In this context, the two sample problem for grouped data is considered an...

in this paper, we introduce a new generalization of weakly prime ideals called $i$-prime. suppose $r$ is a commutative ring with identity and $i$ a fixed ideal of $r$. a proper ideal $p$ of $r$ is $i$-prime if for $a, b in r$ with $ab in p-ip$ implies either $a in p$ or $b in p$. we give some characterizations of $i$-prime ideals and study some of its properties.  moreover, we give conditions  ...