Search results for "Bounded"
showing 10 items of 658 documents
Algebras with involution and multiplicities bounded by a constant
2020
Abstract Let A be an algebra with involution ⁎ over a field of characteristic zero. In this paper we characterize in two different ways when the multiplicities of the ⁎-cocharacter of A are bounded by a constant. As a consequence, we characterize the algebras with involution of bounded colength.
Codimensions of star-algebras and low exponential growth
2020
In this paper we prove that if A is any algebra with involution * satisfying a non-trivial polynomial identity, then its sequence of *-codimensions is eventually non-decreasing. Furthermore, by making use of the *-exponent we reconstruct the only two *-algebras, up to T*-equivalence, generating varieties of almost polynomial growth. As a third result we characterize the varieties of algebras with involution whose exponential growth is bounded by 2.
Classifying Algebras with Graded Involutions or Superinvolutions with Multiplicities of their Cocharacter Bounded by One
2020
Let A be superalgebra over a field of characteristic zero and let ∗ be either a graded involution or a superinvolution defined on A. In this paper we characterize the ∗-algebras whose ∗-cocharacter has multiplicities bounded by one, showing a set of ∗-polynomial identities satisfied by such algebras.
On the Kneser property for reaction–diffusion systems on unbounded domains
2009
Abstract We prove the Kneser property (i.e. the connectedness and compactness of the attainability set at any time) for reaction–diffusion systems on unbounded domains in which we do not know whether the property of uniqueness of the Cauchy problem holds or not. Using this property we obtain that the global attractor of such systems is connected. Finally, these results are applied to the complex Ginzburg–Landau equation.
Robust control in uncertain multi-inventory systems and consensus problems
2008
Abstract We consider a continuous time linear multi–inventory system with unknown demands bounded within ellipsoids and controls bounded within polytopes. We address the problem of ∈-stabilizing the inventory since this implies some reduction of the inventory costs. The main results are certain conditions under which ∈-stabilizability is possible through a saturated linear state feedback control. The idea of this approach is similar to the consensus problem solution for a network of continuous time dynamic agents, where each agent evolves according to a first order dynamics has bounded control and it is subject to unknown but bounded disturbances. In this context, we derive conditions under…
Large eddy simulation of inertial particles dispersion in a turbulent gas-particle channel flow bounded by rough walls
2020
The purpose of this paper is to understand the capability and consistency of large eddy simulation (LES) in Eulerian–Lagrangian studies aimed at predicting inertial particle dispersion in turbulent wall-bounded flows, in the absence of ad hoc closure models in the Lagrangian equations of particle motion. The degree of improvement granted by LES models is object of debate, in terms of both accurate prediction of particle accumulation and local particle segregation; therefore, we assessed the accuracy in the prediction of the particle velocity statistics by comparison against direct numerical simulation (DNS) of a finer computational mesh, under both one-way and two-way coupling regimes. We p…
Modelling of Systems with a Dispersed Phase: “Measuring” Small Sets in the Presence of Elliptic Operators
2016
When modelling systems with a dispersed phase involving elliptic operators, as is the case of the Stokes or Navier-Stokes problem or the heat equation in a bounded domain, the geometrical structure of the space occupied by the dispersed phase enters in the homogenization process through its capacity, a quantity which can be used to define the equivalence classes in \(H^1\). We shall review the relationship between capacity and homogenization terms in the limit when the number of inclusions becomes large, focusing in particular on the situation where the distribution of inclusions is not necessarily too regular (i.e. it is not periodic).
Bounded Palais–Smale sequences for non-differentiable functions
2011
The existence of bounded Palais-Smale sequences (briefly BPS) for functionals depending on a parameter belonging to a real interval and which are the sum of a locally Lipschitz continuous term and of a convex, proper, lower semicontinuous function, is obtained when the parameter runs in a full measure subset of the given interval. Specifically, for this class of non-smooth functions, we obtain BPS related to mountain pass and to global infima levels. This is done by developing a unifying approach, which applies to both cases and relies on a suitable deformation lemma. © 2011 Elsevier Ltd. All rights reserved.
Unbounded Linear Operators in Hilbert Spaces
2002
In order to make this monograph self-contained, we summarize in this chapter some basic definitions and results for unbounded linear operators in a Hilbert space. In Section 1.1, we recall the definitions of C*-algebras and von Neumann algebras. In Section 1.2, we define and investigate the notion of closedness, the closure and the adjoint of an unbounded linear operator in a Hilbert space. Section 1.3 is devoted to the Cayley transform approach to the self-adjointness of a symmetric operator. Section 1.4 deals with the self-adjoint extendability of a symmetric operator with help of the deficiency spaces. In Section 1.5, we extend to unbounded self-adjoint operators the spectral theorem and…
Nonlinear Analysis of Phase-Locked Loop (PLL): Global Stability Analysis, Hidden Oscillations and Simulation Problems
2013
In the middle of last century the problem of analyzing hidden oscillations arose in automatic control. In 1956 M. Kapranov considered a two-dimensional dynamical model of phase locked-loop (PLL) and investigated its qualitative behavior. In these investigations Kapranov assumed that oscillations in PLL systems can be self-excited oscillations only. However, in 1961, N. Gubar’ revealed a gap in Kapranov’s work and showed analytically the possibility of the existence of another type of oscillations, called later by the authors hidden oscillations, in a phase-locked loop model: from a computational point of view the system considered was globally stable (all the trajectories tend to equilibria…