Related papers: Multipliers and Disjointness from Mixing
Dynamic multipliers can be used to guarantee the stability of Lurye systems with slope-restricted nonlinearities, but give no guarantee that the closed-loop system has finite incremental gain. We show that multipliers guarantee the…
We present a new criterion, based on commutator methods, for the strong mixing property of unitary representations of topological groups equipped with a proper length function. Our result generalises and unifies recent results on the strong…
We study ultraproducts of finite residue rings $\underset{n\in\mathbb{N}}{\prod}\mathbb{Z}/n\mathbb{Z} \diagup \mathcal{U} $ where $\mathcal{U}$ is a non-principal ultrafilter. We find sufficient conditions of the ultrafilter $\mathcal{U}$…
To work more accurately with elements of the semigroup of the Stone Cech compactification of the discrete semigroup of natural numbers N under multiplication. We divided these elements into ultrafilters which are on finite levels and…
Multipliers can be used to guarantee both the Lyapunov stability and input-output stability of Lurye systems with time-invariant memoryless slope-restricted nonlinearities. If a dynamic multiplier is used there is no guarantee the…
We present the multiplier method of constructing conservative finite difference schemes for ordinary and partial differential equations. Given a system of differential equations possessing conservation laws, our approach is based on…
We introduces the umodules, a generalisation of the notion of graph module. The theory we develop captures among others undirected graphs, tournaments, digraphs, and $2-$structures. We show that, under some axioms, a unique decomposition…
The adjoint method introduced in [Eva] and [Tra] is used, to construct analogs to the Aubry-Mather measures for non convex Hamiltonians. More precisely, a general construction of probability measures, that in the convex setting agree with…
We investigate the strength of the existence of a non-principal ultrafilter over fragments of higher order arithmetic. Let U be the statement that a non-principal ultrafilter exists and let ACA_0^{\omega} be the higher order extension of…
Given a finite-to-one factor map $\pi: (X, T) \to (Y, S)$ between topological dynamical systems, we look into the pushforward map $\pi_*: M(X, T) \to M(Y,T)$ between sets of invariant measures. We investigate the structure of the measure…
In an industrial context, the activity of sensors is recorded at a high frequency. A challenge is to automatically detect abnormal measurement behavior. Considering the sensor measures as functional data, the problem can be formulated as…
The purpose of this paper is to point the effectiveness of the Jordan-Chevalley decomposition, i.e. the decomposition of a square matrix $U$ with coefficients in a field $k$ containing the eigenvalues of $U$ as a sum $U=D+N,$ where $D$ is a…
We consider the density properties of divergence-free vector fields $ b \in L^1([0,1],\textit{BV}([0,1]^2)) $ which are ergodic/weakly mixing/strongly mixing: this means that their Regular Lagrangian Flow $X_t$ is an ergodic/weakly…
In this article, we deal with the uniform effective disjunction property and the uniform effective interpolation property, which are weaker versions of the classical effective disjunction property and the effective interpolation property.\\…
In this paper we continue the analysis of non-diagonalisable hyperbolic systems initiated in \cite{GarJRuz, GarJRuz2}. Here we assume that the system has discontinuous coefficients or more in general distributional coefficients.…
We describe a supersymmetric Grand Unified Theory based on the gauge group $\SU(5)^3$, or $\SO(10)^3$, invariant under the interchange of any~SU(5), or~SO(10), with each family multiplet transforming non trivially under one different…
We construct and discuss a "realistic" example of SUSY SU(5) GUT model, with an additional U(1) flavour symmetry, that is not plagued by the need of large fine tunings, like those associated with doublet-triplet splitting in the minimal…
The existence of neutrino mass and mixing is a strong pointer towards physics beyond the standard model. An overview of the possibility of having neutrino masses in supersymmetric theories is attempted here. Some of the recent works…
For $\tau>2$, let $T$ be a $C^\tau$ skew product map of the form $(x+\alpha,y+h(x))$ on $\mathbb T^2$ over a rotation of the circle. We show that if $T$ preserves a measurable section, then it is disjoint to the M\"{o}bius sequence. This in…
We prove that for any fixed unitary matrix $U$, any abelian self-adjoint algebra of matrices that is invariant under conjugation by $U$ can be embedded into a maximal abelian self-adjoint algebra that is still invariant under conjugation by…