Let S be a locally compact foundation semigroup with identity and                          be its semigroup algebra. Let X be a weak*-closed left translation invariant subspace of    In this paper, we prove that  X  is invariantly  complemented in   if and  only if  the left ideal  of    has a bounded approximate identity. We also prove that a foundation semigroup with identity S is left amenab...

‎in this paper‎, ‎we study translation invariant surfaces in the‎ ‎3-dimensional heisenberg group $rm nil_3$‎. ‎in particular‎, ‎we‎ ‎completely classify translation invariant surfaces in $rm nil_3$‎ ‎whose position vector $x$ satisfies the equation $delta x = ax$‎, ‎where $delta$ is the laplacian operator of the surface and $a$‎ ‎is a $3 times 3$-real matrix‎.

We first verify the global well-posedness of impulsive reaction-diffusion equations on infinite lattices. Then we establish that generated process by solution operators has a pullback attractor and family Borel invariant probability measures. Furthermore, formulate definition statistical for addressed system prove existence. Our results show satisfies merely Liouville type theorem piecewise, eq...

In this paper, we investigate the possibility of using interval arithmetic for rigorous investigations of periodic orbits in discrete-time dynamical systems with special emphasis on chaotic systems. We show that methods based on interval arithmetic when implemented properly are capable of finding all period-n cycles for considerable large n. We compare several interval methods for finding perio...

We answer a question of Piotr Minc by proving that there is no compact metrizable space whose set components contains unique topological copy every compactification ray (i.e. half-open interval) with an arc closed bounded as the remainder. To this end we use concept Borel reductions coming from Invariant descriptive theory. It follows corollary such continuum homeomorphic to exactly one compone...

Ratios of excitations in each cone-photoreceptor class produced by light reflected from pairs of surfaces in a scene are almost invariant under natural illuminant changes. The stability of these spatially defined ratios may explain the remarkable ability of human observers to efficiently discriminate illuminant changes from changes in surface reflectances. Spatial cone-excitation ratios are not...

A Gabor system generated by a window function φ and a rectangular lattice aZ× Z/b is given by G(φ, aZ× Z/b) := {e−2πint/bφ(t−ma) : (m,n) ∈ Z× Z}. One of fundamental problems in Gabor analysis is to identify window functions φ and time-frequency shift lattices aZ × Z/b such that the corresponding Gabor system G(φ, aZ × Z/b) is a Gabor frame for L(R), the space of all square-integrable functions ...

This paper deals with the computational issues encountered in the construction of invariant sets of uncertainty LTI systems, the presented results being useful in the more general framework of piecewise linear systems affected by parametric uncertainty. The main contribution is the efficient computation of upper and lower bounds of the maximal positively invariant (MPI) set. These turn to be me...

A novel, transfer-function solution of the Kalman-Bucy time-invariant filtering problem is presented. It is assumed that both message model and noise intensities are time invariant and that the mixture of message and noise has been observed over an infinite interval. This transfer-function approach is based on matrix fractions and spectral factorization of polynomial matrices. It offers an inte...