101,962 research outputs found
Control and stabilization of degenerate wave equations
No full textWe study a wave equation in one space dimension with a general diffusion coefficient
which degenerates on part of the boundary. Degeneracy is measured by a real parameter μ > 0. We establish observability inequalities for weakly (when μ ∈ [0, 1[) as well as strongly (when μ ∈ [1, 2[) degenerate equations. We also prove a negative result when the diffusion coefficient degenerates too violently (i.e., when μ > 2) and prove the blowup of the observability time when μa converges to 2 from below. Thus, using the Hilbert uniqueness method we deduce the exact controllability of the corresponding degenerate control problem when μ ∈ [0, 2[. We conclude the paper by studying the
boundary stabilization of the degenerate linearly damped wave equation and show that a suitable boundary feedback stabilizes the system exponentially. We extend this stability analysis to the degenerate nonlinearly boundary-damped wave equation for an arbitrarily growing nonlinear feedback close to the origin. This analysis proves that the degeneracy does not affect the optimal energy decay rates at large time. We apply the optimal-weight convexity method of [F. Alabau-Boussouira, Appl. Math. Optim., 51 (2005), pp. 61–105], [F. Alabau-Boussouira, J. Differential Equations, 249 (2010),
pp. 1473–1517], together with our results for linear damping, to perform this stability analysis
On a classical spectral optimization problem in linear elasticity
No full textWe consider a classical shape optimization problem for the eigenvalues of elliptic operators with homogeneous boundary conditions on domains in the N-dimensional Euclidean space. We survey recent results concerning the analytic dependence of the elementary symmetric functions of the eigenvalues upon domain perturbation and the role of balls as critical points of such functions subject to volume constraint. Our discussion concerns Dirichlet and buckling-type problems for polyharmonic operators, the Neumann and the intermediate problems for the biharmonic operator, the Lame' and the Reissner-Mindlin systems
Stability for Lie–Trotter products for some operator matrix semigroups
No full textCoupled systems of linear differential equations in Banach spaces can be often handled by the theory of C 0 -semigroups of operator matrices. We study the stability of Lie–Trotter products of such matrix semigroups, and present three classes of examples (abstract delay equations, abstract inhomogeneous equations, abstract dynamic boundary value problems) and some open problems. This survey is based on the papers [1], [2] and [5], to which we refer the interested reader for more details and extensive bibliographical information
Bibliographie Hilarion G. Petzold 1958 – 2009 mit Anhang als Einführung
No full textDieses Archiv enthält die Gesamtbibliographie der Werke des Autors nebst einiger Texte „Über H. G. Petzold“ im Schlussteil der Bibliographie sowie einen Anhang mit einer Einführung in die Architektur des Werkes in seinem wissenslogischen Aufbau als Ausarbeitung seines „Tree of Science Modells“ (2007).This archive contains the complete bibliography of the author and some texts about H. G. Petzold, moreover an epilogue with an introduction to the architecture of the works in its epistemological structure and composition and as an elaborations of Petzold’s „Tree of Science Modell (2007).https://www.fpi-publikation.de/polyloge/01-2009-petzold-h-g-gesamtbibliographie-h-g-petzold-1958-2009-updating-november2009/peerReviewedpublishedVersio
Dispelling the Myths Behind First-author Citation Counts
Get PDFWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
Dynamics of discrete screw dislocations via discrete gradient flow
No full textWe present variational approaches (developed in [3,4,11]) to the study of statics and dynamics of screw dislocations in crystals.
We model the crystal as a cubic lattice and we give the asymptotic Γ‐convergence expansion of the elastic energy induced by a finite family of screw dislocations as the lattice spacing goes to zero. We show that the effective energy associated to the presence of a finite system of screw dislocations coincides with the renormalized energy, studied within the Ginzburg‐Landau framework and ruling the interactions between the dislocations. As a byproduct of this analysis, we show the existence of many metastable configurations of dislocations pinned by energy barries. Using the minimizing movement approach á la De Giorgi, we introduce a discrete‐in‐time variational dynamics, referred to as Discrete Gradient Flow, which allows to overcome these energy barriers. More precisely, we show that lettting first the lattice spacing and then the time step of minimizing movements tend to zero, dislocations move accordingly with the gradient flow of the renormalized energy
Recommended from our members
3346: Samuel G. Freedman, author, 2013
No full textPhotograph of author Samuel G. Freedman, at NT Daily Slash meeting in the Mayborn School of Journalism at UNT
The Right to Strike under the United States Constitution: Theory, Practice, and Possible Implications for Canada
No full textAnswering critics of the Canadian Supreme Court's judgment in B.C. Health, the author argues that the Court laid the foundation for a principled and durable doctrine protecting constitutional labour rights, one that goes directly to the heart of the matter — the inequality of workers’ power in the employment relation. In the author’s view, two paths could lead from B.C. Health to the recognition of Charter protec- tion for a right to strike: one that treats the right as an accessory to col- lective bargaining, and one that upholds the right directly on the basis of the Charter values of equality and participation. The author supports the latter approach, contending that constitutional rights should be defined in relation to fundamental values, in a way that is not contingent on time-bound or fact-sensitive assessments about the role of strikes within a particular collective bargaining regime. Although a Charter right to strike may involve the courts in difficult choices about when to defer to legislative policy decisions, and courts may lack the institutional capac- ity to deal effectively with labour law issues, the author points out that judges can look to ILO standards for expert guidance. Noting that the U.S. experience in this area might be of considerable use to Canadians, the author concludes by providing an overview of American case law concerning a constitutional right to strike.Peer reviewe
G-Rank: Unsupervised Continuous Learn-to-Rank for Edge Devices in a P2P Network
No full textRanking algorithms in traditional search engines are powered by enormous training data sets that are meticulously engineered and curated by a centralized entity. Decentralized peer-to-peer (p2p) networks such as torrenting applications and Web3 protocols deliberately eschew centralized databases and computational architectures when designing services and features. As such, robust search-and-rank algorithms designed for such domains must be engineered specifically for decentralized networks, and must be lightweight enough to operate on consumer-grade personal devices such as a smartphone or laptop computer. We introduce G-Rank, an unsupervised ranking algorithm designed exclusively for decentralized networks. We demonstrate that accurate, relevant ranking results can be achieved in fully decentralized networks without any centralized data aggregation, feature engineering, or model training. Furthermore, we show that such results are obtainable with minimal data preprocessing and computational overhead, and can still return highly relevant results even when a user’s device is disconnected from the network. G-Rank is highly modular in design, is not limited to categorical data, and can be implemented in a variety of domains with minimal modification. The results herein show that unsupervised ranking models designed for decentralized p2p networks are not only viable, but worthy of further research.https://github.com/awrgold/G-RankComputer Scienc
- …
