Search results for "Bounded function"
showing 10 items of 508 documents
(Bounded) Traveling combustion fronts with degenerate kinetics
2022
Abstract We consider the propagation of a flame front in a solid periodic medium. It is governed by an equation of Hamilton–Jacobi type, whose front’s velocity depends on the temperature via a nonlinear degenerate kinetic rate. The temperature solves a free boundary problem subject to boundary conditions depending on the front’s velocity itself. We show the existence of nonplanar traveling wave solutions which are bounded and global. Previous results by the same authors (cf. Alibaud and Namah, 2017) were obtained for essentially positively lower bounded kinetics or eventually which have some very weak degeneracy. Here we consider very general degenerate kinetics, including for the first tim…
Direct adaptive tracking control for a class of pure-feedback stochastic nonlinear systems based on fuzzy-approximation
2014
Published version of an article in the journal: Abstract and Applied Analysis. Also available from the publisher at: http://dx.doi.org/10.1155/2014/462468 Open Access The problem of fuzzy-based direct adaptive tracking control is considered for a class of pure-feedback stochastic nonlinear systems. During the controller design, fuzzy logic systems are used to approximate the packaged unknown nonlinearities, and then a novel direct adaptive controller is constructed via backstepping technique. It is shown that the proposed controller guarantees that all the signals in the closed-loop system are bounded in probability and the tracking error eventually converges to a small neighborhood around …
Solutions of the Einstein field equations for a bounded and finite discontinuous source, and its generalization: Metric matching conditions and jumpi…
2019
We consider the metrics of the General Relativity, whose energy-momentum tensor has a bounded support where it is continuous except for a finite step across the corresponding boundary surface. As a consequence, the first derivative of the metric across this boundary could perhaps present a finite step too. However, we can assume that the metric is ${\cal C}^1$ class everywhere. In such a case, although the partial second derivatives of the metric exhibit finite (no Dirac $\delta$ functions) discontinuities, the Dirac $\delta$ functions will still appear in the conservation equation of the energy-momentum tensor. As a consequence, strictly speaking, the corresponding metric solutions of the …
On vibrating thin membranes with mass concentrated near the boundary: an asymptotic analysis
2018
We consider the spectral problem \begin{equation*} \left\{\begin{array}{ll} -\Delta u_{\varepsilon}=\lambda(\varepsilon)\rho_{\varepsilon}u_{\varepsilon} & {\rm in}\ \Omega\\ \frac{\partial u_{\varepsilon}}{\partial\nu}=0 & {\rm on}\ \partial\Omega \end{array}\right. \end{equation*} in a smooth bounded domain $\Omega$ of $\mathbb R^2$. The factor $\rho_{\varepsilon}$ which appears in the first equation plays the role of a mass density and it is equal to a constant of order $\varepsilon^{-1}$ in an $\varepsilon$-neighborhood of the boundary and to a constant of order $\varepsilon$ in the rest of $\Omega$. We study the asymptotic behavior of the eigenvalues $\lambda(\varepsilon)$ and the eige…
Robust H-Infinity Filter Design for Uncertain Linear Systems Over Network with Network-Induced Delays and Output Quantization
2009
This paper investigates a convex optimization approach to the problem of robust H-Infinity filtering for uncertain linear systems connected over a common digital communication network. We consider the case where quantizers are static and the parameter uncertainties are norm bounded. Firstly, we propose a new model to investigate the effect of both the output quantization levels and the network conditions. Secondly, by introducing a descriptor technique, using Lyapunov-Krasovskii functional and a suitable change of variables, new required sufficient conditions are established in terms of delay-dependent linear matrix inequalities (LMIs) for the existence of the desired network-based quantize…
A NEW COMPLEXITY FUNCTION FOR WORDS BASED ON PERIODICITY
2013
Motivated by the extension of the critical factorization theorem to infinite words, we study the (local) periodicity function, i.e. the function that, for any position in a word, gives the size of the shortest square centered in that position. We prove that this function characterizes any binary word up to exchange of letters. We then introduce a new complexity function for words (the periodicity complexity) that, for any position in the word, gives the average value of the periodicity function up to that position. The new complexity function is independent from the other commonly used complexity measures as, for instance, the factor complexity. Indeed, whereas any infinite word with bound…
Representable and Continuous Functionals on Banach Quasi *-Algebras
2017
In the study of locally convex quasi *-algebras an important role is played by representable linear functionals; i.e., functionals which allow a GNS-construction. This paper is mainly devoted to the study of the continuity of representable functionals in Banach and Hilbert quasi *-algebras. Some other concepts related to representable functionals (full-representability, *-semisimplicity, etc) are revisited in these special cases. In particular, in the case of Hilbert quasi *-algebras, which are shown to be fully representable, the existence of a 1-1 correspondence between positive, bounded elements (defined in an appropriate way) and continuous representable functionals is proved.
Bergman and Bloch spaces of vector-valued functions
2003
We investigate Bergman and Bloch spaces of analytic vector-valued functions in the unit disc. We show how the Bergman projection from the Bochner-Lebesgue space Lp(, X) onto the Bergman space Bp(X) extends boundedly to the space of vector-valued measures of bounded p-variation Vp(X), using this fact to prove that the dual of Bp(X) is Bp(X*) for any complex Banach space X and 1 < p < ∞. As for p = 1 the dual is the Bloch space ℬ(X*). Furthermore we relate these spaces (via the Bergman kernel) with the classes of p-summing and positive p-summing operators, and we show in the same framework that Bp(X) is always complemented in p(X). (© 2003 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
Variational Aspects of the Physically-Based Approach to 3D Non-Local Continuum Mechanics
2010
This paper deals with the generalization to three-dimensional elasticity of the physically-based approach to non-local mechanics, recently proposed by the authors in one-dimensional case. The proposed model assumes that the equilibrium of a volume element is attained by contact forces between adjacent elements and by long-range central forces exerted by non-adjacent elements. Specifically, the long-range forces are modeled as central body forces depending on the relative displacements between the centroids of the volume elements, measured along the line connecting the centroids. Furthermore, the long-range forces are assumed to be proportional to a proper, material-dependent, distance-decay…
Robust Allocation Rules in Dynamical Cooperative TU Games
2011
Robust dynamic coalitional TU games are repeated TU games where the values of the coalitions are unknown but bounded variables. We set up the game supposing that the Game Designer uses a vague measure of the extra reward that each coalition has received up to the current time to re-adjust the allocations among the players. As main result, we provide a constructive method for designing allocation rules that converge to the core of the average game. Both the set up and the solution approach also provide an insight on commonalities between coalitional games and stability theory.