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.

Planar cephalometry in essence provides only 2D information. CT scan provides 3D information for osseous and soft tissues but remains irradiant. STL dental models are interesting tools allowing for the production of 3D printed surgical splints. In orthognathic surgery planning, exploiting these three fields of information by linking them to the clinical findings and getting them all synchronize...

PURPOSE We assessed the potential ocular hazards of bright light therapy for patients with seasonal affective disorder, after both short- and long-term treatment, and identified prospective patients with pre-existing ocular abnormalities. METHODS Fifty patients with seasonal affective disorder received daily exposure to artificial light in the morning or evening for 30 minutes at an illuminan...

The variation of the lipophilic (carotenoids and α-tocopherol) and hydrophilic (glutathione and ascorbic acid) antioxidant contents, and the activities of antioxidant enzyme such superoxide dismutase (SOD), catalase (CAT) and peroxidase (POD), as well as cellular malonaldehyde and stable radicals of D. salina in response to ultraviolet B (UV-B radiation 290-320 nm) and secondary carotenoid indu...

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...

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...