We show for many strongly regular graphs ∆, and for all Taylor graphs ∆ except the hexagon, that locally ∆ graphs have bounded diameter.

An n-tournament is an orientation of a complete n-partite graph. It was proved by J.A. Bondy in 1976 that every strongly connected n-partite tournament has an n-cycle. We characterize strongly connected n-partite tournaments in which a longest cycle is of length n and, thus, settle a problem in L. Volkmann, Discrete Math. 245 (2002) 19-53.

This paper begins the project of adapting the 1992 book by Adams, Barbasch and Vogan on the Langlands classification of admissible representations of real groups, to padic groups, continuing in the direction charted by Vogan in his 1993 paper on the Langlands correspondence. This paper presents three theorems in that direction. The first theorem shows how Lusztig’s work on perverse sheaves aris...

A quasi-symmetric design (QSD) is a (v, k, λ) design with two intersection numbers x, y, where 0 ≤ x < y < k. The block graph of a QSD is a strongly regular graph (SRG), whereas the converse is not true. Using Neumaier’s classification of SRGs related to the smallest eigenvalue, a complete parametric classification of QSDs whose block graph is an SRG with smallest eigenvalue −3, or second large...

Cardinal invariants related to sequential separability of generalized Cantor cubes 2κ, introduced by M. Matveev, are studied here. In particular, it is shown that the following assertions are relatively consistent with ZFC: (1) 2ω1 is sequentially separable, yet there is a countable dense subset of 2ω1 containing no non-trivial convergent subsequence, (2) 2ω1 is not sequentially separable, yet ...

Let M be a module over the commutative ring R. In this paper we introduce two new notions, namely strongly coprimal and super coprimal modules. Denote by ZR(M) the set of all zero-divisors of R on M . M is said to be strongly coprimal (resp. super coprimal) if for arbitrary a, b ∈ ZR(M) (resp. every finite subset F of ZR(M)) the annihilator of {a, b} (resp. F ) in M is non-zero. In this paper w...

A well-studied class of functions in communication complexity are composed functions of the form (f ◦ g)(x, y) = f(g(x, y), . . . , g(x, y)). This is a rich family of functions which encompasses many of the important examples in the literature. It is thus of great interest to understand what properties of f and g affect the communication complexity of (f ◦ g), and in what way. Recently, Shersto...

Abstract In this paper, we prove the abundance theorem for numerically trivial canonical divisors on strongly F -regular varieties, assuming that geometric generic fibers of Albanese morphisms are -regular.

Let E be a real Banach space with uniformly Gâteaux differentiable norm possessing uniform normal structure. K is a nonempty bounded closed convex subset of E, and { } ( ) ... , 2 , 1 = n Tn is a sequence of − n k Lipschitzian nonexpansive mappings from K into itself such that 1 lim = ∞ → n n k and ( ) 0 1 / ≠ ∞ = n n T F ∩ and f be a contraction on K. Under sutiable conditions on sequence { },...