Volume 49, Issue 2

We associate a semigroup B(S) to every semiring S with semilattice additive reduct, namely the semigroup of all k-bi-ideals of S; and such semirings S have been characterized by this associated semigroup B(S). A semiring S is k-regular if and only if B(S) is a regular semigroup. For the left k-Clifford semirings S, B(S) is a left normal band; and consequently, B(S) is a semilattice if S is a k-Clifford semiring. Also we show that the set B m (S) of all minimal k-bi-ideals of S forms a rectangular band and B m (S) is a bi-ideal of the semigroup B(S).

In this note, we give a self-contained proof of the following classification (up to conjugation) of finite subgroups of GSp n (F̅ ℓ ) containing a nontrivial transvection for ℓ ≥ 5, which can be derived from work of Kantor: G is either reducible, symplectically imprimitive or it contains Sp n (F̅ ℓ ). This result is for instance useful for proving ‘big image’ results for symplectic Galois representations.

The purpose of this corrigendum is to correct an error in the earlier paper by the authors: Generalizations of Opial-type inequalities in several independent variables, Demonstratio Math.

In 1972, S. Valenti introduced the definition of k-pseudo symmetric derivative and has shown that the set of all points of a continuous function, at which there exists a finite k-pseudo symmetric derivative but the finite ordinary derivative does not exist, is of Lebesgue measure zero. In 1993, L. Zajícek has shown that for a continuous function f, the set of all points, at which f is symmetrically differentiable but no differentiable, is σ-(1 - ε) symmetrically porous for every ε > 0. The question arises: can we transferred the Zajícek’s result to the case of the k-pseudo symmetric derivative? In this paper, we shall show that for each 0 < ε < 1 the set of all points of a continuous function, at which there exists a finite k-pseudo symmetric derivative but the finite ordinary derivative does not exist, is σ-(1 - ε)-porous.

The purpose of the paper is to study the uniqueness of meromorphic functions sharing a nonzero polynomial. The results of the paper improve and generalize the recent results due to X. B. Zhang and J. F. Xu [19]. We also solve an open problem as posed in the last section of [19].

The concepts of Wijsman asymptotically equivalence, Wijsman asymptotically statistically equivalence, Wijsman asymptotically lacunary equivalence and Wijsman asymptotically lacunary statistical equivalence for sequences of sets were studied by Ulusu and Nuray [24]. In this paper, we get analogous results for double sequences of sets.

In this paper, we characterize local exponential monomials and polynomials on different types of Abelian groups and we prove Montel-type theorems for these function classes.

The intrinsic flexibility of probabilistic metric spaces makes it possible to extend the idea of contraction mapping in several inequivalent ways, one of which being the C-contraction. Cyclic contractions are another type of contractions used extensively in global optimization problems. We introduced here p-cyclic contractions which are probabilistic C-contraction types. It involves p numbers of subsets of the spaces and involves two control functions for its definitions. We show that such contractions have fixed points in a complete probabilistic metric space. The main result is supported with an example and extends several existing results.

The device named autoclave used in pharma industries has been studied in this paper. This study provides the discussion how to obtain the reliability testing strategy of two dis-similar parallel units. The system is considered to be in operative condition if at least one out of two is in operative state. A single repair facility is available for repairing both kinds of failed units. In addition to repair mechanism, inspection policy has also been introduced for failed automatic unit. But the manual one does not require any such supervision facilty. Various essential measures of system effectiveness such as mean time to system failure (MTSF), steady state availability, busy period of supervisor and repairman are examined probabilistically by using geometric distribution and regenerative point techniques. A graph has been plotted to represent the behaviour of profit function and MTSF with respect to different failure and repair rate.

Random integral mappings give isomorphism between the subsemigroups of the classical (I D, *) and the free-infinite divisible (I D, ⊞) probability measures. This allows us to introduce new examples of such measures, more precisely their corresponding characteristic functionals.