in this paper, we have dened and studied a generalized form of topological vectorspaces called s-topological vector spaces. s-topological vector spaces are dened by using semi-open sets and semi-continuity in the sense of levine. along with other results, it is provedthat every s-topological vector space is generalized homogeneous space. every open subspaceof an s-topological vector space is ...

One may assume w.l.o.g. that p(x) is a homogeneous polynomial (form). Indeed, as observed in [2], if p(x) = ∑d l=0 pl(x), where pl(x) is homogeneous of degree l, then minimizing p(x) over ∆ is equivalent to minimizing the degree d form p(x) := ∑d l=0 pl(x)( ∑n i=1 xi) . Problem (1) is an NP-hard problem, already for forms of degree d = 2, as it contains the maximum stable set problem. Indeed, f...

Let \(X\) be a real reflexive Banach space and \(X^*\) its dual space. \(G_1\) \(G_2\) open subsets of such that \(\overline G_2\subset G_1\), \(0\in G_2\), is bounded. \(L: X\supset D(L)\to X^*\) densely defined linear maximal monotone operator, \(A:X\supset D(A)\to 2^{X^*}\) positively homogeneous operator degree \(\gamma>0\), \(C:X\supset D(C)\to bounded demicontinuous type \((S_+)\) with...

We investigate some logics with Henkin quantifiers. For a given logic L, we consider questions of the form: what is the degree of the set of L–tautologies in a poor vocabulary (monadic or empty)? We prove that the set of tautologies of the logic with all Henkin quantifiers in empty vocabulary L∗∅ is of degree 0 . We show that the same holds also for some weaker logics like L∅(Hω) and L∅(Eω). We...

With the unit interval [0,1] as the truth value table, Chen and Wupresented the concept of  possibility computation over dcpos.Indeed, every possibility computation can be considered as a[0,1]-valued Scott open set on a dcpo. The aim of this paper is tostudy Chen-Wu's duality on quantale-valued setting. For clarity,with a commutative unital quantale $L$ as the truth value table, weintroduce a c...

Let T be a symmetric directed tree, i.e., a tree with each edge viewed as two opposite directed links. We consider the problem of routing arbitrary sets of connection requests in T. In all-optical communication tree networks with WDM (wavelength-division multiplexing) this is equivalent to color (assign wavelengths to) a given set of directed paths so that no two directed paths of the same colo...