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‎We consider the oscillator group equipped with‎ ‎a biinvariant Lorentzian metric‎. ‎Some geometrical properties of this space and the harmonicity properties of left-invariant vector fields on this space are determined‎. ‎In some cases‎, ‎all these vector fields are critical points for the energy functional‎ ‎restricted to vector fields‎. ‎Left-invariant vector fields defining harmonic maps are...

Reaction random walk systems are hyperbolic models for description of spatial motion (in one dimension) and reaction of particles. In contrast to reaction diiusion equations particles have nite propagation speed. For parabolic systems invariance results and maximum principles are well known. A convex set is positively invariant if at each boundary point an outer normal is a left eigenvector of ...

‎We consider four-dimensional lie groups equipped with‎ ‎left-invariant Lorentzian Einstein metrics‎, ‎and determine the harmonicity properties ‎of vector fields on these spaces‎. ‎In some cases‎, ‎all these vector fields are critical points for the energy functional ‎restricted to vector fields‎. ‎We also classify vector fields defining harmonic maps‎, ‎and calculate explicitly the energy of t...

The purpose of this article is to develop the notions of amenabilityfor vector valued group algebras. We prove that L1(G, A) is approximatelyweakly amenable where A is a unital separable Banach algebra. We givenecessary and sufficient conditions for the existence of a left invariant meanon L∞(G, A∗), LUC(G, A∗), WAP(G, A∗) and C0(G, A∗).

The polytope algebra is the universal group for translation invariant valuations on the family of polytopes in a nite dimensional vector space over an ordered eld. In an earlier paper, it was shown that the polytope algebra is, in all but one trivial respect, a graded (commutative) algebra over the base eld. Also described was a family of separating (group) homomorphisms, called frame functiona...

A vector …eld in n-space is reconstructed from a n-dimensional family of ray or line integrals. A similar problem is considered for di¤erential forms of higher order. Key words: Di¤erential form, ray integral, k-plane integral, reconstruction, support condition AMS subject classi…cation (2000): Primary, 53C65; Secondary, 65R32, 76M27 Abbreviated title: Doppler transform 1 Introduction Integrals...

Since 2005 a new powerful invariant of an algebra has emerged using the earlier work of Horvath, Hethelyi, Kulshammer and Murray. The authors studied Morita invariance of a sequence of ideals of the center of a nite dimensional algebra over a eld of nite characteristic. It was shown that the sequence of ideals is actually a derived invariant, and most recently a slightly modied version o...

In this paper we employ the topological concepts of index of an equilibrium point of a vector eld and of the Conley index of an isolated invariant set of a vector eld with the purpose of deriving necessary conditions for the design of global control dynamics. Our results are a generalization of those of Brockett, Coron and others, which were derived for the special case of stabilization.