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ISSN : 1226-0657
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Vol.9 No.1
Abstract
For A bounded subset G of a metric Space (X,d) and <TEX>$\chi \in X$</TEX>, let <TEX>$f_{G}$</TEX> be the real-valued function on X defined by <TEX>$f_{G}$</TEX>(<TEX>$\chi$</TEX>)=sup{<TEX>$d (\chi, g)\in:G$</TEX>}, and <TEX>$F(G,\chi)$</TEX>={<TEX>$z \in X:sup_{g \in G}d(g,z)=sup_{g \in G}d(g,\chi)+d(\chi,z)$</TEX>}. In this paper we discuss some properties of the map <TEX>$f_G$</TEX> and of the set <TEX>$ F(G, \chi)$</TEX> in convex metric spaces. A sufficient condition for an element of a convex metric space X to lie in <TEX>$ F(G, \chi)$</TEX> is also given in this pope.
Abstract
In this Paper, we will show that every basically disconnected space is a projective object in the category <TEX>$Tych_{\sigma}$</TEX> of Tychonoff spaces and <TEX>$_{\sigma}Z^{#}$</TEX> -irreducible maps and that if X is a space such that <TEX>${\Beta} {\Lambda} X={\Lambda} {\Beta} X$</TEX>, then X has a projective cover in <TEX>$Tych_{\sigma}$</TEX>. Moreover, observing that for any weakly Linde1of space, <TEX>${\Lambda} X : {\Lambda} X\;{\longrightarrow}\;X$</TEX> is <TEX>$_{\sigma}Z^{#}$</TEX>-irreducible, we will show that the projective objects in <TEX>$wLind_{\sigma}$</TEX>/ of weakly Lindelof spaces and <TEX>$_{\sigma}Z^{#}$</TEX>-irreducible maps are precisely the basically disconnected spaces.
Abstract
We consider one class of bursting oscillation models, that is square-wave burster. One of the interesting features of these models is that periodic bursting solution need not to be unique or stable for arbitrarily small values of a singular perturbation parameter <TEX>$\epsilon$</TEX>. Recent results show that the bursting solution is uniquely determined and stable for most of the ranges of the small parameter <TEX>$\epsilon$</TEX>. In this paper, we present a condition of uniqueness and stability of periodic bursting solutions for all sufficiently small values of <TEX>$\epsilon$</TEX> > 0.
Abstract
In this paper, we find explicitly the eigenvalues and the eigenfunctions of Laplace operator on a triangle domain with a mixed boundary condition. We also show that a weaker form of the principle of spatial averaging holds for this domain under suitable boundary condition.
Abstract
In this paper, we study the space of almost continuous functions with the topology of uniform convergence. And we investigate some properties of this space.
Abstract
In this pope., we consider a Minty's lemma for (<TEX>$\theta ,\eta$</TEX>)-pseudomonotone-type set-valued mappings in real Banach spaces and then we show the existence of solutions to variational-type inequality problems for (<TEX>$\theta ,\eta$</TEX>)-pseudomonotone-type set-valued mappings in nonreflexive Banach spaces.
Abstract
Let G be a connected graph. A pebbling move on a graph G is the movement of taking two pebbles off from a vertex and placing one of them onto an adjacent vertex. The pebbling number f(G) of a connected graph G is the least n such that any distribution of n pebbles on the vertices of G allows one pebble to be moved to any specified, but arbitrary vertex by a sequence of pebbling moves. In this paper, the pebbling numbers of the compositions of two graphs are computed.
Abstract
An inverse interpolation problem for rational matrix functions with a certain type of symmetricity in zero-pole structure is studied.
Abstract
In this paper, We Characterize the Pettis integrability for the Dunford integrable functions on a perfect finite measure space.