In this article, we proved the following results. Let L(F (ni)) be the free group factor on ni generators and λ(gi) be one of standard generators of L(F (ni)) for 1 ≤ i ≤ N . Let Ai be the abelian von Neumann subalgebra of L(F (ni)) generated by λ(gi). Then the abelian von Neumann subalgebra ⊗i=1Ai is a maximal injective von Neumann subalgebra of ⊗i=1L(F (ni)). When N is equal to infinity, we o...

We show  that a projective maximal submodule of afinitely generated, regular, extending module is a directsummand. Hence, every finitely generated, regular, extendingmodule with projective maximal submodules is semisimple. As aconsequence, we observe that every regular, hereditary, extendingmodule is semisimple. This generalizes and simplifies a result of  Dung and   Smith. As another consequen...

Purpose: Allometry is a method to express the relationship between physiological and anatomical variables. It can be used to measure the vital capacity through mathematical equations. This study aimed at evaluating lung function indices to estimate the maximal aerobic power by respiratory gas analysis device and the allometric equation. Methods: This study was a descriptive and correlational r...

Teichmüller’s classical mapping problem for plane domains concerns finding a lower bound for the maximal dilatation of a quasiconformal homeomorphism which holds the boundary pointwise fixed, maps the domain onto itself, and maps a given point of the domain to another given point of the domain. For a domain D ⊂ Rn , n ≥ 2 , we consider the class of all Kquasiconformal maps of D onto itself with...

The problem we want to handle in this p a p e r is vagueness. A notion of space, which we basically have, plays an important part in the faculty of thinking and speech. In this paper, we concentrate on a particular class of spatial descriptions, namely descriptions about positional relations on a two-dimensional space. A theoretical device we present in this paper is called the potential model ...