For graphs G and H , a homomorphism from G to H is a function φ : V (G) → V (H), which maps vertices adjacent in G to adjacent vertices of H . A homomorphism is locally injective if no two vertices with a common neighbor are mapped to a single vertex in H . Many cases of graph homomorphism and locally injective graph homomorphism are NPcomplete, so there is little hope to design polynomial-time...

Let A and B be commutative rings such that B is an A-algebra. We define ΩB/A to be the B-module of regular differentials over A. By definition, this B-module ΩB/A is a unique B-module which has the following property. For a B-module M we denote by DerA(B,M ) the set of all A-derivations (an A-homomorphism φ:B → M is called an A-derivation if φ(xy) = xφ(y) + yφ(x) and φ(x) = 0 for any x ∈ A ). T...

Let X,Y be locally compact Hausdorff spaces and M,N be Banach algebras. Let θ : C0(X,M) → C0(Y,N ) be a zero-product preserving bounded linear map with dense range. We show that θ is given by a continuous field of algebra homomorphisms from M into N if N is irreducible. As corollaries, such a surjective θ arises from an algebra homomorphism, provided thatM is a W*-algebra and N is a semi-simple...

Let A and B be two Banach algebras and let M be a Banach B-bimodule. Suppose that σ : A → B is a linear mapping and d : A → M is a σ-derivation. We prove several results about automatic continuity of σderivations on Banach algebras. In addition, we define a notion for m-weakly continuous linear mapping and show that, under certain conditions, d and σ are m-weakly continuous. Moreover, we prove ...

We show that every closed nonpositively curved manifold with non-trivial volume flux group has zero minimal volume, and admits a finite covering with circle actions whose orbits are homologically essential. This proves a conjecture of Kedra– Kotschick–Morita for this class of manifolds. Let M be a closed smooth manifold and μ a volume form on M . Denote by Diff the group of μ–preserving diffeom...

We propose a new class of mathematical structures called (m, n)-semirings (which generalize the usual semirings) and describe their basic properties. We define partial ordering and generalize the concepts of congruence, homomorphism, and so forth, for (m, n)-semirings. Following earlier work by Rao (2008), we consider systems made up of several components whose failures may cause them to fail a...

i=1 aiφ(u′′(ξi)), u(0) = 0, u(1) = m−2 ∑ i=1 biu(ξi), where φ : R −→ R is an increasing homeomorphism and homomorphism and φ(0) = 0. The nonlinear term f may change sign. As an application, an example to demonstrate our results is given. © 2008 Elsevier B.V. All rights reserved.

Let G be an unramified group over a p-adic field. This article introduces a base change homomorphism for Bernstein centers of depth-zero principal series blocks for G and proves the corresponding base change fundamental lemma. This result is used in the approach to Shimura varieties with Γ1(p)-level structure initiated by M. Rapoport and the author in [HR2].

Vx = {yeP:xSy} is the principal filter generated by x. The filters on P are easily seen to be the open sets for a topology on P, and the increasing maps from P to another locally finite partially ordered set Q are precisely the continuous functions from P to Q [5]. For each filter V on P, let M(P9 V\ or simply M(V) when reference to P is understood, denote the free abelian group on V. For filte...

We investigate how a C*-algebra could consist of functions on a noncommutative set: a discretization of a C*-algebra A is a ∗-homomorphism A → M that factors through the canonical inclusion C(X) ⊆ `∞(X) when restricted to a commutative C*-subalgebra. Any C*-algebra admits an injective but nonfunctorial discretization, as well as a possibly noninjective functorial discretization, where M is a C*...