DSpace Collection: Volume 31 Number 4
http://hdl.handle.net/10525/1769
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Rétractes Absolus de Voisinage Algébriques
http://hdl.handle.net/10525/1773
Title: Rétractes Absolus de Voisinage Algébriques<br/><br/>Authors: Cauty, Robert<br/><br/>Abstract: We introduce the class of algebraic ANRs. It is defined byreplacing continuous maps by chain mappings in Lefschetz’s characterization of ANRs. To a large extent, the theory of algebraic ANRs parallels the classical theory of ANRs. Every ANR is an algebraic ANR, but the class of algebraic ANRs is much larger; the most striking difference between these classes is that every locally equiconnected metrisable space is an algebraicANR, whereas there exist metric linear spaces which are not ARs. This is important for applications of topological fixed point theory to functional analysis because all known results of fixed point for compact maps of ANRsextend to the algebraic ANRs. We prove here two such generalizations: theLefschetz-Hopf fixed point theorem for compact maps of algebraic ANRs,and the fixed point theorem for compact upper semi-continuous multivalued maps with Q-acyclic compacts point images in a Q-acyclic algebraic ANR. We stress that these generalizations apply to all neighborhood retract of a metrisable linear space and, more generally, of a locally contractible metrisable group.<br/><br/>Description: 2000 Mathematics Subject Classification: 54C55, 54H25, 55M20.Quasi-Likelihood Estimation for Ornstein-Uhlenbeck Diffusion Observed at Random Time Points
http://hdl.handle.net/10525/1772
Title: Quasi-Likelihood Estimation for Ornstein-Uhlenbeck Diffusion Observed at Random Time Points<br/><br/>Authors: Adès, Michel; Dion, Jean-Pierre; MacGibbon, Brenda<br/><br/>Abstract: In this paper, we study the quasi-likelihood estimator of the drift parameter θ in the Ornstein-Uhlenbeck diffusion process, when theprocess is observed at random time points, which are assumed to be unobservable. These time points are arrival times of a Poisson process with known rate. The asymptotic properties of the quasi-likelihood estimator (QLE) of θ, as well as those of its approximations are also elucidated. An extensive simulation study of these estimators is also performed. As a corollary to this work, we obtain the quasi-likelihood estimator iteratively in the deterministic framework with non-equidistant time points.<br/><br/>Description: 2000 Mathematics Subject Classification: 60J60, 62M99.Necessary and Sufficient Condition for Oscillations of Neutral Differential Equation
http://hdl.handle.net/10525/1771
Title: Necessary and Sufficient Condition for Oscillations of Neutral Differential Equation<br/><br/>Authors: Elabbasy, E.; Hassan, T.; Saker, S.<br/><br/>Abstract: We obtain necessary and sufficient conditions for the oscillation of all solutions of neutral differential equation with mixed (delayed andadvanced) arguments ...<br/><br/>Description: 2000 Mathematics Subject Classification: 34K15, 34C10.Dispersive Estimates of Solutions to the Wave Equation with a Potential in Dimensions Two and Three
http://hdl.handle.net/10525/1770
Title: Dispersive Estimates of Solutions to the Wave Equation with a Potential in Dimensions Two and Three<br/><br/>Authors: Cardoso, Fernando; Cuevas, Claudio; Vodev, Georgi<br/><br/>Abstract: We prove dispersive estimates for solutions to the wave equation with a real-valued potential V.<br/><br/>Description: 2000 Mathematics Subject Classification: 35L15, 35B40, 47F05.