let r be an associative ring with identity, c(r) be the category of com-plexes of r-modules and flat(c(r)) be the class of all at complexes of r-modules. we show that the at cotorsion theory (flat(c(r)); flat(c(r))−)have enough injectives in c(r). as an application, we prove that for each atcomplex f and each complex y of r-modules, exti (f,x)= 0, whenever ris n-perfect and i > n.

the aim of this study was to estimate body fat percentage through circumference of different parts of body by hydrodensitometry (hydrostatic underwater weighing) as the criterion method and to develop related equations. 158 male students of isfahan university (mean age: 21.6 yrs, height: 174 cm, weight: 69.04 kg, body fat percentage: 15.61 kg, bmi: 22.59) were randomly selected. these subjects ...

Body image is an internal representation of the external appearance which includes physical and perceptual aspects and attitudes toward them. Body image anxiety can cause weight problems. In addition, perfectionism, the trend or effort to be perfect and flawless can cause extreme thinking and self-criticism. Perfectionism can provoke anxiety and concerns for body image and weight, especially in...

1. The idea that species occupy distinct niches is a fundamental concept in ecology. Classically, the niche was described as an n-dimensional hypervolume where each dimension represents a biotic or abiotic characteristic. More recently, it has been hypothesised that a single dimension may be sufficient to explain the system-level organization of trophic interactions observed between species in ...

We solved analytically the three-body mass-imbalanced problem embedded in $D$ dimensions for zero-range resonantly interacting particles. derived negative energy eigenstates of Schr\"odinger equation by imposing Bethe-Peierls boundary conditions zero-energy two-body bound states. The solution retrieves Efimov-like discrete scaling factor dependence with dimension. analytical form bound-state wa...

The Vapnik-Chervonenkis dimension of a set K in R n is the maximal dimension of the coordinate cube of a given size, which can be found in coordinate projections of K. We show that the VC dimension of a convex body governs its entropy. This has a number of consequences, including the optimal Elton's theorem and a uniform central limit theorem in the real valued case.

We study geometric properties of coordinate projections. Among other results, we show that if a body K ⊂ R has an “almost extremal” volume ratio, then it has a projection of proportional dimension which is close to the cube. We also establish a sharp estimate on the shattering dimension of the convex hull of a class of functions in terms of the shattering dimension of the class itself.

Many classical geometric inequalities on functionals of convex bodies depend on the dimension of the ambient space. We show that this dimension dependence may often be replaced (totally or partially) by different symmetry measures of the convex body. Since these coefficients are bounded by the dimension but possibly smaller, our inequalities sharpen the original ones. Since they can often be co...