The most primitive form of a stadium is a circle, say of radius r. If we separate the left and right halves of the circle slightly and connect these two semi circles at the top and bottom by straight lines we have a classical stadium (racetrack). Let a be the horizontal distance from the center of the figure to either the left or right semi circle; that is, the distance of each ‘straightaway’ i...

An odd Sugihara monoid is a residuated distributive latticeordered commutative idempotent monoid with an order-reversing involution that fixes the monoid identity. The main theorem of this paper establishes a category equivalence between odd Sugihara monoids and relative Stone algebras. In combination with known results, it swiftly determines which varieties of odd Sugihara monoids are [strongl...

The structure of the isometric representations of unital discrete semi-groups with the left cancellation property and no divisors of the identity is studied. We obtain Wold decompositions and prove that the left regular representation of such semigroups is irreducible.

Zadeh in 1965 introduce the concept of a fuzzy set which now have a wide range of applications in various fields of Engineering Sciences, Computer Science and Management Sciences. It is worth mentioning here that for applications of fuzzy sets mostly associative algebraic structures are used such as in 2003, Mordeson, Malik and Kuroki have discovered the applications of fuzzy semigroups in fuzz...

Let R be a right GF-closed ring with finite left and right Gorenstein global dimension. We prove that if I is an ideal of R such that R/I is a semi-simple ring, then the Gorensntein flat dimensnion of R/I as a right R-module and the Gorensntein injective dimensnnion of R/I as a left R-module are identical. In particular, we show that for a simple module S over a commutative Gorensntein ring R, ...

[Purpose] Clarification of the differences in the compression volume of the lungs by the heart (CVLH) between postures may facilitate the selection of optimal postures in respiratory care. Determining CVLH in the supine, semi-prone (Sim's position), and side-lying positions was the aim of this study. [Subjects and Methods] Eight healthy volunteers (six males, two females; mean age, 29.0 ± 9.2 y...