* Professor Jacobson, Editor of these Proceedings, in a letter to me dated June 15, 1951, says in part: The referee "noted that the second theorem can be formulated in terms of groups with operators from a principal ideal domain." And he expressed the opinion that a formulation in finite abelian groups may serve the same purpose. Subsequently, the writer has read, perhaps with insufficient unde...

in this study, we introduce the classes of $phi$-strongly pseudocontractive mappings in the intermediate sense and generalized $phi$-pseudocontractive mappings in the intermediate sense and prove the existence of fixed points for those maps. the results generalise the results of several authors in literature including xiang [chang he xiang, fixed point theorem for generalized $phi$-pseudocontra...

Based on some earlier findings on Banach Category Theorem for some “nice” σ-ideals by J. Kaniewski, D. Rose and myself. I introduce the h operator (h stands for “heavy points”) to refine and generalize kernel constructions of A. H. Stone. Having obtained this way a generalized Kuratowski’s decomposition theorem I prove some characterizations of the domains of functions having “many” points of h...

Khutoretskii’s Theorem states that the Rogers semilattice of any family of c.e. sets has either at most one or infinitely many elements. A lemma in the inductive step of the proof shows that no Rogers semilattice can be partitioned into a principal ideal and a principal filter. We show that such a partitioning is possible for some family of d.c.e. sets. In fact, we construct a family of c.e. se...

1. Introduction. When studying ideal theory in semirings, it is natural to consider the quotient structure of a semiring modulo an ideal. If 7 is an ideal in a semiring R, the collection {x+l}xeit oí sets x + I={x+i\iEl} need not be a partition of R. Faced with this problem, [2] used equivalence relations to determine cosets relative to an ideal. La Torre successfully established analogues of s...

The notions of a S fuzzy ∧ sub semi lattice, a S fuzzy ideal and a S fuzzy prime ideal of a bounded lattice with truth values in a bounded ∧ sub semi lattice S are introduced which generalize the existing notions with truth values in a unit interval of real numbers. Finally, S fuzzy prime ideal theorem is proved. 2010 AMS Classification: 03G10, 46H10, 06D50, 08A72

In this paper, we considered the half logistic model and derived a probability density function that generalized it. The cumulative distribution function, the $n^{th}$ moment, the median, the mode and the 100$k$-percentage points of the generalized distribution were established. Estimation of the parameters of the distribution through maximum likelihood method was accomplished with the aid of c...

We establish a Hessian geometric structure in chemical thermodynamics, which describes reaction networks (CRNs) with equilibrium states. In our setup, the ideal gas assumption and mass action kinetics are not required. The existence uniqueness condition of state is derived by using Legendre duality inherent to structure. entropy production during relaxation can be evaluated Bregman divergence. ...