A very classical subject in Commutative Algebra is the Invariant Theory of finite groups. In our work on 3–dimensional topology [12], we found certain examples of group actions on polynomial rings. When we tried to compute the invariant ring using Singular [6] or Magma [1], it turned out that the existing algorithms did not suffice. We present here a new algorithm for the computation of seconda...

‎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 ...

In 1981, Thompson proved that, if n > 1 is any integer and G is any finite subgroup of GLn(C), then G has a semi-invariant of degree at most 4n2. He conjectured that, in fact, there is a universal constant C such that for any n ∈ N and any finite subgroup G < GLn(C), G has a semi-invariant of degree at most Cn. This conjecture would imply that the α-invariant αG(P), as introduced by Tian in 198...

The Ornstein-Uhlenbeck semigroup combines Gaussian diffusion with the flow of a linear vector field. In infinite dimensional settings there can be non-Gaussian invariant measures. This gives a context for one version of the renormalization group. The adjoint of the OrnsteinUhlenbeck semigroup with respect to an invariant measure need not be an Ornstein-Uhlenbeck semigroup. This adjoint is the a...

As a generalization of the Fourier transform, the fractional Fourier transform was introduced and has been further investigated both in theory and in applications of signal processing. We obtain a sampling theorem on shift-invariant spaces associated with the fractional Fourier transform domain. The resulting sampling theorem extends not only the classical Whittaker-Shannon-Kotelnikov sampling ...

We survey examples of dynamical systems on non–compact spaces which exhibit measure rigidity on the level of infinite invariant measures in one or more of the following ways: all locally finite ergodic invariant measures can be described; exactly one (up to scaling) admits a generalized law of large numbers; the generic points can be specified. The examples are horocycle flows on hyperbolic sur...

Outlier detection methods are fundamental to all of data analysis. They are desirably robust, affine invariant, and computationally easy in any dimension. The powerful projection pursuit approach yields the “projection outlyingness”, which is affine invariant and highly robust and does not impose ellipsoidal contours like the Mahalanobis distance approach. However, it is highly computationally ...

An integral criterion for the existence of an invariant measure of an Itô process is developed. This new criterion is based on the probabilistic symbol of the Itô process. In contrast to the standard integral criterion for invariant measures of Markov processes based on the generator, no test functions and hence no information on the domain of the generator is needed. 2010 Mathematics subject c...