Search results for "Bounded function"
showing 10 items of 508 documents
Lazy consensus for networks with unknown but bounded disturbances
2007
We consider stationary consensus protocols for networks of dynamic agents. The measure of the neighbors' state is affected by Unknown But Bounded disturbances. Here the main contribution is the formulation and solution of what we call the isin-consensus problem, where the states are required to converge in a tube of ray isin asymptotically or in finite time.
High Precision Conservative Surface Mesh Generation for Swept Volumes
2015
We present a novel, efficient, and flexible scheme to generate a high-quality mesh that approximates the outer boundary of a swept volume. Our approach comes with two guarantees. First, the approximation is conservative, i.e., the swept volume is enclosed by the generated mesh. Second, the one-sided Hausdorff distance of the generated mesh to the swept volume is upper bounded by a user defined tolerance. Exploiting this tolerance the algorithm generates a mesh that is adapted to the local complexity of the swept volume boundary, keeping the overall output complexity remarkably low. The algorithm is two-phased: the actual sweep and the mesh generation. In the sweeping phase, we introduce a g…
Bounded approximation properties via integral and nuclear operators
2010
Published version of an article in the journal:Proceedings of the American Mathematical Society. Also available from the publisher, Open Access
(Regular) pseudo-bosons versus bosons
2012
We discuss in which sense the so-called {\em regular pseudo-bosons}, recently introduced by Trifonov and analyzed in some details by the author, are related to ordinary bosons. We repeat the same analysis also for {\em pseudo-bosons}, and we analyze the role played by certain intertwining operators, which may be bounded or not.
Mean ergodicity of weighted composition operators on spaces of holomorphic functions
2016
[EN] Let phi be a self-map of the unit disc D of the complex plane C and let psi be a holomorphic function on D. We investigate the mean ergodicity and power boundedness of the weighted composition operator C-phi,C-psi(f) = psi(f o phi) with symbol phi and multiplier psi on the space H(D). We obtain necessary and sufficient conditions on the symbol phi and on the multiplier psi which characterize when the weighted composition operator is power bounded and (uniformly) mean ergodic. One necessary condition is that the symbol phi has a fixed point in D. If phi is not a rational rotation, the sufficient conditions are related to the modulus of the multiplier on the fixed point of phi. Some of o…
A greedy perturbation approach to accelerating consensus algorithms and reducing its power consumption
2011
The average consensus is part of a family of algorithms that are able to compute global statistics by only using local data. This capability makes these algorithms interesting for applications in which these distributed philosophy is necessary. However, its iterative nature usually leads to a large power consumption due to the repetitive communications among the iterations. This drawback highlights the necessity of minimizing the power consumption until consensus is reached. In this work, we propose a greedy approach to perturbing the connectivity graph, in order to improve the convergence time of the consensus algorithm while keeping bounded the power consumption per iteration step. These …
On the Robust Synthesis of Logical Consensus Algorithms for Distributed Intrusion Detection
2013
We introduce a novel consensus mechanism by which the agents of a network can reach an agreement on the value of a shared logical vector function depending on binary input events. Based on results on the convergence of finite--state iteration systems, we provide a technique to design logical consensus systems that minimize the number of messages to be exchanged and the number of steps before consensus is reached, and that can tolerate a bounded number of failed or malicious agents. We provide sufficient joint conditions on the input visibility and the communication topology for the method's applicability. We describe the application of our method to two distributed network intrusion detecti…
Long-range cohesive interactions of non-local continuum faced by fractional calculus
2008
Abstract A non-local continuum model including long-range forces between non-adjacent volume elements has been studied in this paper. The proposed continuum model has been obtained as limit case of two fully equivalent mechanical models: (i) A volume element model including contact forces between adjacent volumes as well as long-range interactions, distance decaying, between non-adjacent elements. (ii) A discrete point-spring model with local springs between adjacent points and non-local springs with distance-decaying stiffness connecting non-adjacent points. Under the assumption of fractional distance-decaying interactions between non-adjacent elements a fractional differential equation in…
Orbits of bounded bijective operators and Gabor frames
2020
This paper is a contribution to frame theory. Frames in a Hilbert space are generalizations of orthonormal bases. In particular, Gabor frames of $L^2(\mathbb{R})$, which are made of translations and modulations of one or more windows, are often used in applications. More precisely, the paper deals with a question posed in the last years by Christensen and Hasannasab about the existence of overcomplete Gabor frames, with some ordering over $\mathbb{Z}$, which are orbits of bounded operators on $L^2(\mathbb{R})$. Two classes of overcomplete Gabor frames which cannot be ordered over $\mathbb{Z}$ and represented by orbits of operators in $GL(L^2(\mathbb{R}))$ are given. Some results about opera…
Approximations of Parabolic Equations at the Vicinity of Hyperbolic Equilibrium Point
2014
This article is devoted to the numerical analysis of the abstract semilinear parabolic problem u′(t) = Au(t) + f(u(t)), u(0) = u 0, in a Banach space E. We are developing a general approach to establish a discrete dichotomy in a very general setting and prove shadowing theorems that compare solutions of the continuous problem with those of discrete approximations in space and time. In [3] the discretization in space was constructed under the assumption of compactness of the resolvent. It is a well-known fact (see [10, 11]) that the phase space in the neighborhood of the hyperbolic equilibrium can be split in a such way that the original initial value problem is reduced to initial value prob…