Volume 49, Issue 3

The purpose of this note is two-fold. Firstly, we prove that the variety RDMSH 1 of regular De Morgan semi-Heyting algebras of level 1 satisfies Stone identity and present (equational) axiomatizations for several subvarieties of RDMSH 1 . Secondly, using our earlier results published in 2014, we give a concrete description of the lattice of subvarieties of the variety RDQDStSH 1 of regular dually quasi-De Morgan Stone semi- Heyting algebras that contains RDMSH 1 . Furthermore, we prove that every subvariety of RDQDStSH 1 , and hence of RDMSH 1 , has Amalgamation Property. The note concludes with some open problems for further investigation.

We give a combinatorial proof of an elementary property of generalized Lucas polynomials, inspired by [1]. These polynomials in s and t are defined by the recurrence relation 〈n〉 = s〈n-1〉+t〈n-2〉 for n ≥ 2. The initial values are 〈0〉 = 2; 〈1〉= s, respectively.

Intervals in binary or n-ary relations or other discrete structures generalize the concept of an interval in a linearly ordered set. They are defined abstractly as closed sets of a closure system on a set, satisfying certain axioms. Join-irreducible partitions into intervals are characterized in the lattice of all interval decompositions. This result is used to show that the lattice of interval decompositions is balanced, and the case when this lattice is distributive is also characterised.

In this paper, we provide some characterizations of semisimple rings, right V-rings, right hereditary and regular right FGC-rings in terms of C3-modules. The notions of C3-envelope and C3-cover are introduced.

In this paper, we shall discuss Bargmann type measures on C for several classes of probability measures on R. The unified interpolation expressions include not only the classical Bargmann measure and its q-deformation, but also their t-deformations and dilations. As a special case, we get conditions on existence and an explicit form of the Bargmann representation for the free Meixner family of probability measures.

In this paper, we construct a non-standard finite difference scheme for a general model of glucose-insulin interaction. We establish some new sufficient conditions to ensure that the discretized model preserves the persistence and global attractivity of the continuous model. One of the main findings in this paper is that we derive two important propositions (Proposition 3.1 and Proposition 3.2) which are used to prove the global attractivity of the discretized model. Furthermore, when investigating the persistence and, in some cases, the global attractivity of the discretized model, the nonlinear functions f and h are not required to be differentiable. Hence, our results are more realistic because the statistical data of glucose and insulin are collected and reported in discrete time. We also present some numerical examples and their simulations to illustrate our results.

In this paper, the author established the general solution and generalized Ulam-Hyers-Rassias stability of n-dimensional additive functional equation in generalized 2-normed space.

For an algebra A, an A-bimodule M, and m ∈ M, define a relation on A by R A (m,0)={(a, b) ∈A×A: amb =0}. We show that generalized derivations on unital standard algebras on Banach spaces can be characterized precisely as derivable maps on these relations. More precisely, if A is a unital standard algebra on a Banach space X then Δ ∈ L(A, B, (X)) is a generalized derivation if and only if Δ is derivable on R A (M, 0), for some M ∈ B(X). We give an example to show this is not the case in general for nest algebras. On the other hand, for an idempotent P in a nest algebra A = algN on a Hilbert space H such that P is either left-faithful to N or right-faithful to N ⊥ , if δ ∈ L(A, B(H)) is derivable on R A (P, 0) then Δ is a generalized derivation.

In this paper, we introduce semi-slant submersions from almost product Riemannian manifolds onto Riemannian manifolds. We give some examples, investigate the geometry of foliations which are arisen from the definition of a Riemannian submersion. We also find necessary and sufficient conditions for a semi-slant submersion to be totally geodesic.

In this paper, we introduce the concept of (CLR S )-property for mappings F : X × X→X and S : X → X (wherein X stands for a partial metric space) and utilize the same to prove two common fixed point theorems for two pairs of mappings in partial metric spaces. We also furnish two examples to illustrate our main theorems.