We consider a nonlocal eigenvalue problem which arises in the study of stability of point-condensation solutions in the Gierer-Meinhardt system and generalized Gray-Scott system. We give some suucient conditions for stability and instability. The conditions are new and can be applied to the study of stability of single point-condensation solutions.

Levine , N., Semi-open sets and semi-continuity in topological spaces, Amer.Math.Monthly,70(1963),36-41. Levine , N., Generalized closed sets in topology, Rend. Circ. Mat. Palermo, 19(1970),89-96. Maki., Devi, R., and Balachandran, K., Generalized α-closed sets in topology, Bull. Fukuoka Univ. Ed. Part III, 42(1993), 13-21. Hatir, E., Noiri, T., and Yuksel, S., A decomposition of continuity, Ac...

In this paper, we define and study fuzzy generalized α-closed sets and r-open sets of a given L-fuzzy topological space and prime element r ∈ P (L) and coprime element α ∈ M(L). The concept of L-fuzzy ropen sets was introduced in [10], and it was proved that all r-open sets for L-fuzzy topological space form a new L-fuzzy topology, which is called stratiform L-fuzzy topology. Making use of the ...

This is a version from 29 Sept 2003 of the paper published under the same name in Theoretical Computer Science 316 (2004) 297–321. The double powerlocale P(X) (found by composing, in either order, the upper and lower powerlocale constructions PU and PL) is shown to be isomorphic in [Loc,Set] to the double exponential SS X where S is the Sierpiński locale. Further PU (X) and PL(X) are shown to b...

As Dag Normann has recently shown, the fully abstract model for PCF of hereditarily-sequential functionals is not ω-complete (in contrast to the old fully abstract continuous dcpo model of Milner). This is also applicable to a potentially wider class of models such as the recently constructed by the author fully abstract (universal) model for PCF = PCF + pif (parallel if). Here we will present ...