LOCAL STABILITY, HOPF BIFURCATIONS FOR A SYSTEM OF HARMONIC OSCILLATORS WITH TIME DELAY
Idempotent hypergroups, Fixed points of endomorphisms, Theory of commutators on hypergroups, Theory of ideals on Boolean hyperrings. THE GENERAL STRICT TOPOLOGY IN LOCALLY CONVEX MODULES OVER LOCALLY CONVEX ALGEBRAS-II K.V. Shantha Let (X, Γ) be a locally convex left A-module over a locally convex algebra A with bounded approximate identity. In this paper we consider the strict topology β on X induced by A and characterize the strict dual (X β) * and the β-equicontinuos subsets of (X β) *. We
... so show that the strict topology β enjoys the classical property of earlier strict topologies, namely it is the finest locally convex topology on X which agrees with itself on its bounded sets. A system of harmonic oscillators with discrete time delay is considered. The local stability of the zero solution of theirs equations is investigated by analyzing the corresponding transcedental characteristic equation of the linearized equations. By choosing the delay as a bifurcation parameter, the model is found to undergo a sequence of Hopf bifurcations. The direction and the stability of the bifurcating periodic solutions are determined by using the normal form theory. Some numerical examples are finally given for justifying the theoretical results. ON I-CONVERGENCE FIELD Tiboř Salát, Binod Chandra Tripathy, Miloš Ziman In this paper we introduce the notion of c I A and m I A , the I-convergence field and bounded I-convergence field of an infinite matrix A. We restrict our study to diagonal matrices. We find necessary and/or sufficient conditions on the elements of A for solidity of c I A and m I A. ℵ-SPACES AND σ-MAPPINGS Jinjin Li In this paper, the relationships between metric spaces and ℵ-spaces are established by certain sequence-covering mappings. Those are some answers to Alexandroff's problems. UNIFORM STRUCTURE ON HYPER BCK-ALGEBRAS Borumand Saeid, M.M. Zahedi In this note by considering a reflexive hyper BCK-ideal in a hyper BCK-algebra H, we define a relation ∼ I on H, and then we show that this relation is an equivalence relation on H. Then we show that this equivalence relation gives a uniform structure on H, when this uniformity constructs a topology on H.