Search results for "Bounded"
showing 10 items of 658 documents
A remark on weakly convex continuous mappings in topological linear spaces
2009
Abstract Let C be a compact convex subset of a Hausdorff topological linear space and T : C → C a continuous mapping. We characterize those mappings T for which T ( C ) is convexly totally bounded.
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…
Quasilinear Dirichlet Problems with Degenerated p-Laplacian and Convection Term
2021
The paper develops a sub-supersolution approach for quasilinear elliptic equations driven by degenerated p-Laplacian and containing a convection term. The presence of the degenerated operator forces a substantial change to the functional setting of previous works. The existence and location of solutions through a sub-supersolution is established. The abstract result is applied to find nontrivial, nonnegative and bounded solutions.
On dependence of sets of functions on the mean value of their elements
2009
The paper considers, for a given closed bounded set M ⊂ R m and K = (0,1) n ⊂ R n , the set M = {h ϵ L2 (K;R m ) | h(x) ϵ M a.e.x ϵ K} and its subsets It is shown that, if a sequence {hk } ⊂ coM converges to an element hk ϵ M(hk ) there is h‘k ϵ M(ho ) such that h'k - hk → 0 as k → ∞ . If, in addition, the set M is finite or M is the convex hull of a finite set of elements, then the multivalued mapping h → M(h) is lower semicontinuous on coM. First published online: 14 Oct 2010
On robustness and dynamics in (un)balanced coalitional games
2012
In this paper we investigate robustness and dynamics for coalitional games with transferable utilities (TU games). In particular we study sequences of TU games. These sequences model dynamic situations in which the values of coalitions of players are not known beforehand, and are subject to changes over time. An allocation rule assigns a payoff to each player in each time period. This payoff is bounded by external restrictions, for example due to contractual agreements. Our main questions are: (i) under which conditions do the allocations converge to a core-element of the game, and (ii) when do the allocations converge to some specific allocation, the so-called nominal allocation? The main …
Set-valued consensus for distributed clock synchronization
2009
This paper addresses the clock synchronization problem in a wireless sensor network (WSN) and proposes a distributed solution that consists of a form of consensus, where agents are able to exchange data representing intervals or sets. The solution is based on a centralized algorithm for clock synchronization, proposed by Marzullo, that determines the smallest interval that is in common with the maximum number of measured intervals. We first show how to convert such an algorithm into a problem involving only operations on sets, and then we convert it into a set–valued consensus. The solution is valid for more general scenarios where agents have uncertain measures of e.g. the position of an o…