1991 Mathematics Subject Classi cation: Primary, 11K31, 11K38, 11K55; Secondary: 11B85.

1991 Mathematics Subject Classi cation. Primary 20C10; Secondary 20H15, 11E12, 20F29, 20E28, 20-04.

In this paper we underline the importance of the parametric subregularity property of setvalued mappings, de…ned with respect to …xed sets. We show that this property appears naturally for some very simple mappings which play an important role in the theory of metric regularity. We prove a result concerning the preservation of metric subregularity at generalized compositions. Then we obtain, on...

Abstract_ _ We prove a common coincidence point theorem for a non-fuzzy mapping and a pair of fuzzy mappings under a ' contraction condition on a metric space in the context of Hausdor¤ metric on the family of fuzzy sets. Further, we establish a common coincidence point theorem on a metric space with the d1 metric on fuzzy sets, which extends a number of recent results. As applications, we obta...

Truncated correlation and convolution operators is a general operator-class containing popular operators such as Toeplitz (WienerHopf), Hankel and nite interval convolution operators as well as small and big Hankel operators in several variables. We completely characterize the symbols for which such operators have nite rank, and develop methods for determining the rank in concrete cases. Such r...

We analyze spectrum of Laplacian supported by a periodic honeycomb lattice with generally unequal edge lengths and a δ type coupling in the vertices. Such a quantum graph has nonempty point spectrum with compactly supported eigenfunctions provided all the edge lengths are commensurate. We derive conditions determining the continuous spectral component and show that existence of gaps may depend ...

We describe a few applications of semide nite programming in combinatorial optimization Mathematics Subject Classi cation C C C C C R

The possible dimensions of a composition algebra are 1, 2, 4, or 8. We give a tensor categorical argument. 1991 Mathematics Subject Classi cation: Primary 17A75; Secondary 57M25.

An estimate is given of the size of a solution n 2 N of the inequality (an+ b) < (an), gcd(a; b) = 1. Experiments indicate that this gives a useful indication of the size of the minimal solution. 2000 Mathematics Subject Classi cation: Primary 11A25. Secondary 11Y70. 1998 ACM Computing Classi cation System: F.2.1.

We give a simple proof of I. Krichever’s theorem on rational reductions of the Kadomtsev^Petviashvili hierarchy by using the Poisson^Lie structure on the group of pseudo-differential symbols. Mathematics Subject Classi¢cations (2000). 58F07, 22E65.