‎this contribution mainly focuses on some aspects of lipschitz groups‎, ‎i.e.‎, ‎metrizable groups with lipschitz multiplication and inversion map‎. ‎in the main result it is proved that metric groups‎, ‎with a translation-invariant metric‎, ‎may be characterized as particular group objects in the category of metric spaces and lipschitz maps‎. ‎moreover‎, ‎up to an adjustment of the metric‎, ‎a...

a module is said to be $pi$-extending provided that every projection invariant submodule is essential in a direct summand of the module. in this paper, we focus on direct summands and indecomposable decompositions of $pi$-extending modules. to this end, we provide several counter examples including the tangent bundles of complex spheres of dimensions bigger than or equal to 5 and certain hyper ...

One step towards understanding the structure of a flow involves describing the behavior of orbits near selected invariant sets ; particularly that behavior common to all nearby flows. The invariant set chosen is often an isolated invariant set, which means it is the largest invariant set in some (closed) neighborhood of itself, (cf. [1]) A typical example is a hyperbolic (elementary) rest point...

We study the structure of a quantum Markov semigroup (Tt)t≥0 on a von Neumann algebra A starting from its decomposition by means of the transient and recurrent projections. The existence of invariant states and convergence to invariant state is also discussed. Applications to quantum Markov semigroups with Lindblad type infinitesimal generator are analysed.

We obtain analytic solutions for the density contrast and the anisotropic pressure in a multi-dimensional FRW cosmology with collisionless, massless matter. These are compared with perturbations of a perfect fluid universe. To describe the metric perturbations we use manifest gauge invariant metric potentials. The matter perturbations are calculated by means of (automatically gauge invariant) f...

In this article, we present a geometric framework to study invariant sets of dynamical systems associated with differential equations. This framework is based on properties of invariant sets for an area functional. We obtain existence results for heteroclinic and periodic orbits. We also implement this approach numerically by means of the steepest descent method.

We show that the Kervaire invariant one elements θj ∈ π2j+2−2S 0 exist only for j ≤ 6. By Browder’s Theorem, this means that smooth framed manifolds of Kervaire invariant one exist only in dimensions 2, 6, 14, 30, 62, and possibly 126. Except for dimension 126 this resolves a longstanding problem in algebraic topology.

The graph isomorphism problem is to determine whether two given graphs are iso-morphic or not. In this paper, we present a new graph invariant, called the probability propagation matrix. By means of this graph invariant, we present a heuristic algorithm for the problem. The algorithm is easy to implement and highly parallelizable.

We show that the Kervaire invariant one elements θj ∈ π2j+1−2S 0 exist only for j ≤ 6. By Browder’s Theorem, this means that smooth framed manifolds of Kervaire invariant one exist only in dimensions 2, 6, 14, 30, 62, and possibly 126. Except for dimension 126 this resolves a longstanding problem in algebraic topology.

In our recent paper we have established close relationships between state reduction of a fuzzy recognizer and resolution of a particular system of fuzzy relation equations. In that paper we have also studied reductions by means of those solutions which are fuzzy equivalences. In this paper we will see that in some cases better reductions can be obtained using the solutions of this system that a...