Let $Gamma$ be a group, $Gamma'$ a subgroup of $Gamma$ with finite index and $M$ be a $Gamma$-module. We show that $M$ is cotorsion if and only if it is cotorsion as a $Gamma'$-module. Using this result, we prove that the global cotorsion dimensions of rings $ZGamma$ and $ZGamma'$ are equal.

Positive, continuous, and right-skewed data are fit by a mixture of gamma inverse distributions. For 16 hierarchical models distributions, there only 8 them that have conjugate priors. We first discuss some common typical problems for the eight do not Then, we calculate Bayesian posterior densities marginal After that, relations among analytical densities. Furthermore, find random variables bet...

Povećanje incidencije otrovanja biljnim i životinjskim toksinima tijekom proteklih godina ukazuje na važnost poznavanja otrovnih vrsta području Republike Hrvatske. Od biljnih u Republici Hrvatskoj raste velebilje, kranjski bijeli bun, duhan, bunovina, crna bunika, kužnjak, crni kukurijek jesenski mrazovac. Većina biljaka pripada porodici pomoćnica (Solanaceae). To su biljke bogate tropanskim al...

let $r$ be a commutative ring with identity. let $g(r)$ denote the maximal graph associated to $r$, i.e., $g(r)$ is a graph with vertices as the elements of $r$, where two distinct vertices $a$ and $b$ are adjacent if and only if there is a maximal ideal of $r$ containing both. let $gamma(r)$ denote the restriction of $g(r)$ to non-unit elements of $r$. in this paper we study the various graphi...

This paper consider the   general  forms of $(alpha,beta)$-fuzzyleft ideals (right ideals, bi-ideals, interior ideals) of an orderedsemigroup, where$alpha,betain{in_{gamma},q_{delta},in_{gamma}wedgeq_{delta}, in_{gamma}vee q_{delta}}$ and $alphaneqin_{gamma}wedge q_{delta}$. Special attention is paid to$(in_{gamma},ivq)$-left ideals (right ideals, bi-ideals, interiorideals) and some related  pr...

In this paper, the new notions of ``belongingness ($in_{gamma}$)"and ``quasi-coincidence ($q_delta$)"  of a fuzzy point with a fuzzyset are  introduced. By means of this new idea, the  concept of$(alpha,beta)$-fuzzy $n$-ary subhypergroup of an $n$-aryhypergroup is given, where $alpha,betain{in_{gamma}, q_{delta},in_{gamma}wedge q_{delta}, ivq}$,  andit is shown that, in 16 kinds of $(alpha,beta...

apoptosis, a physiologic mechanism to eliminate unwanted cells, is also induced by ionizing irradiation, through production of free radicals. it has been demonstrated that antioxidants such as vitamin e are able to protect cells from damage caused by free radicals. taken together we found it reasonable to make an attempt to evaluate the protective effect of vitamin e against apoptosis. the irra...

the aim of this paper is to study the $(alpha‎, ‎gamma)$-prolongation of central extensions‎. ‎we obtain the obstruction theory for $(alpha‎, ‎gamma)$-prolongations and classify $(alpha‎, ‎gamma)$-prolongations thanks to low-dimensional cohomology groups of groups‎.

It is very likely that in 3-4 years the construction of one or two linear colliders with c.m.s energy up to 0.5–1.5 TeV will be started. Besides eecollisions, linear colliders give a unique possibility to study γγ and γe interactions at energies and luminosities comparable to those in ee collisions. High energy photons for γγ and γe collisions can be obtained using laser backscattering. These t...