abstract. in this paper we study some relations between the power andquotient power graph of a finite group. these interesting relations motivateus to find some graph theoretical properties of the quotient power graphand the proper quotient power graph of a finite group g. in addition, weclassify those groups whose quotient (proper quotient) power graphs areisomorphic to trees or paths.

An immediate generalization of the classical McKay correspondence for Gorenstein quotient spaces C/G in dimensions r ≥ 4 would primarily demand the existence of projective, crepant, full desingularizations. Since this is not always possible, it is natural to ask about special classes of such quotient spaces which would satisfy the above property. In this paper we give explicit necessary and suf...

We study linear actions of algebraic groups on smooth projective varieties X. A guiding goal for us is to understand the cohomology of “quotients” under such actions, by generalizing (from reductive to non-reductive group actions) existing methods involving Mumford’s geometric invariant theory (GIT). We concentrate on actions of unipotent groups H, and define sets of stable points X and semista...

In this paper, we consider quotient structure and quotient difunctions in the context of interior and closure operators on textures in the sense of Dikranjan-Giuli. The generalizations of several results concerning separation and quotient mapping are presented. It is shown that the category of interior-closure spaces and bicontinuous difunctions has a T0 reflection. Finally, we introduce some c...

BACKGROUND Elderly patients with chronic obstructive pulmonary disease (COPD) usually have a compromised nutritional status which is an independent predictor of morbidity and mortality. To know the Resting Energy Expenditure (REE) and the substrate oxidation measurement is essential to prevent these complications. This study aimed to compare the REE, respiratory quotient (RQ) and body compositi...

The availability of mice lacking the mitochondrial uncoupling protein UCP1, has provided an opportunity to analyze the relationship between the capacity for energy expenditure and the development of obesity in response to a high-fat, high-sucrose diet. Congenic UCP1-deficient mice on a C57BL/6J genetic background show a temperature-dependent resistance to diet-induced obesity when compared with...