Using the methods of Brown and Walsh, we get condition guaranteeing that, for an ideal I of sets in a perfect Polish space some (s0) sets are not in I. A few examples and corollaries are given.

The purpose of this note is to analyze the conditions needed in geometry to introduce ideal points without using order relations. Since only incidence relations are used, it is convenient to use the notation of lattice theory. The actual introduction of the ideal elements is a purely algebraic process belonging to the theory of ideal extension and will be given elsewhere. (See abstracts 44-5-20...

In this article we study the structure of residual intersections via constructing a finite complex which is acyclic under some sliding depth conditions on the cycles of the Koszul complex. This complex provides information on an ideal which coincides with the residual intersection in the case of geometric residual intersection; and is closely related to it in general. A new success obtained thr...

In this work we consider the computation of Gröbner bases of the steady state ideal of reaction networks equipped with mass-action kinetics. Specifically, we focus on the role of intermediate species and the relation between the extended network (with intermediate species) and the core network (without intermediate species). We show that a Gröbner basis of the steady state ideal of the core net...

in this paper we define the notions of ultra and involution ideals in bck-algebras. then we get the relation among them and other ideals as (positive) implicative, associative, commutative and prime ideals. specially, we show that in a bounded implicative bck-algebra, any involution ideal is a positive implicative ideal and in a bounded positive implicative lower bck-semilattice, the notions of...

The shortage of pediatricians has been identified as one of the largest social problems in Japan. This study aimed to compare the assumed ideal nighttime working conditions of pediatric hospitalists in Japan with the actual current situation. By using available data on the age-related numbers of pediatricians in Japan, we described the ideal working conditions for pediatric hospitalists in Japa...

Modern ideals of female attractiveness include an extremely toned and fit appearance in addition to extreme thinness. Although viewing thin models has a negative effect on women's body image, research has not tested the effect of exposure to the ultra-fit physique separate from the thin-ideal. This randomized, posttest-only experiment tested the effects of the athletic aspect of the current ide...

The term “sustainability” is generally used to describe an ideal condition in which the Earth’s biosphere and human civilization can safely interact coexist [...]