Impact of Partial Separability on Large-Scale Optimization

ELSO is an environment for the solution oflarge-scale optimization problems. With ELSO the user is required to provide only code for the evaluation of a partially separable function. ELSO exploits the partialseparability structure of the function to computethe gradient efficiently using automatic differentiation.We demonstrate ELSO's efficiency by comparing thevarious options available in ELSO.Our conclusion is that the hybrid option in ELSOprovides performance comparable to the hand-coded option, while having the significantadvantage of not requiring a hand-coded gradient orthe sparsity pattern of the partially separable function.In our test problems, which have carefully coded gradients,the computing time for the hybrid AD option is within a factor of two of thehand-coded option.     

Order conditions for linearly implicit fractional step Runge Kutta methods

^{In this paper, we study the consistency of a variant of fractionalstep Runge–Kutta methods. These methods are designed tointegrate efficiently semi-linear multidimensional parabolicproblems by means of linearly implicit time integration processes.Such time discretization procedures are also related to a splittingof the space differential operator (or the spatial discretizationof it) as a sum of ‘simpler’ linear differentialoperators and a nonlinear term.}     

Preparation and properties of homogeneous V2O5-SiO2 xerogel composite based on interpenetrating polymer network

In this paper, we report the conducting and electrochemical properties of a homogeneous V₂O₅-SiO₂ xerogel composite obtained from the simultaneous polymerization in both inorganic components (Si-O and V-O based polymers) forming an interpenetrating polymer network, where a mutual “solubility” due to cross-links and entanglements was observed. The presence of V₂O₅ inside the silica matrix has a strong effect on electrical conductivity; measurements showed room temperature conductivity almost 1000 times higher than what is found in the literature. In addition, the electrochemical behavior is quite similar to that found in V₂O₅ xerogel. Moreover, the effects of thermal treatment on the conducting and electrochemical properties were investigated. It was found that both properties were improved with no significant effect on V₂O₅ xerogel layered structure.     

Reliability and expectation bounds for coherent systems with exchangeable components

Sharp upper and lower bounds are obtained for the reliability functions and the expectations of lifetimes of coherent systems based on dependent exchangeable absolutely continuous components with a given marginal distribution function, by use of the concept of Samaniego's signature. We first show that the distribution of any coherent system based on exchangeable components with absolutely continuous joint distribution is a convex combination of distributions of order statistics (equivalent to the k-out-of-n systems) with the weights identical with the values of the Samaniego signature of the system. This extends the Samaniego representation valid for the case of independent and identically distributed components. Combining the representation with optimal bounds on linear combinations of distribution functions of order statistics from dependent identically distributed samples, we derive the corresponding reliability and expectation bounds, dependent on the signature of the system and marginal distribution of dependent components. We also present the sequences of exchangeable absolutely continuous joint distributions of components which attain the bounds in limit. As an application, we obtain the reliability bounds for all the coherent systems with three and four exchangeable components, expressed in terms of the parent marginal reliability function and specify the respective expectation bounds for exchangeable exponential components, comparing them with the lifetime expectations of systems with independent and identically distributed exponential components.     

Production and characterization of refractive index gratings in high-birefringence fibre optics

In this work, we report production and modelling of both Bragg gratings and rocking filters in high birefringence fibre optics. Bragg gratings are produced by UV (257.0 nm) external interferometric exposition of a frequency-doubled Ar⁺ ion laser, whereas for rocking filters formation the visible Ar⁺ ion laser lines in 488.0 and 514.5 nm are used in an internal method. The spectral characteristics due to the birefringence properties are studied through numerical methods and experimental techniques. The spectral responsivity of the structures under temperature changes and stress application is presented.     

Lattices contained in planar orders are planar

The covering graph of a lattice which is contained in an ordered set with a planar covering graph is itself planar.Presented by R. W. Quackenbush.     

Local solution for the Kadomtsev-Petviashvili equation with periodic conditions

In this article we prove a local existence and uniqueness theorem for the Kadomtsev-Petviashvili Equation (u _t +u _xxx +uu _x ) _x −u _yy =0) in the Sobolev spaces of orders≥3, with initial values in the same spaces, and periodic boundary conditions. This theorem improves previous results based upon the application of singular perturbation techniques.     

The semiclassical limit of a quantum Fermi accelerator

A classical Fermi accelerator model (FAM) is known to show chaotic behavior. The FAM is defined by a free particle bouncing elastically from two rigid walls, one fixed and the other oscillating periodically in time. The central aim of this paper is to connect the quantum and the classical solutions to the FAM in the semiclassical limit. This goal is accomplished using a finite inverted parametric oscillator (FIPO), confined to a box withfixed walls, as an alternative representation of the FAM. In the FIPO representation, an explicit correspondence between classical and quantum limits is accomplished using a Husimi representation of the quasienergy eigenfunctions.     

Point-to-Periodic and Periodic-to-Periodic Connections

In this work we consider computing and continuing connecting orbits in parameter dependent dynamical systems. We give details of algorithms for computing connections between equilibria and periodic orbits, and between periodic orbits. The theoretical foundation for these techniques is given by the seminal work of Beyn in 1994, “On well-posed problems for connecting orbits in dynamical systems”, where a numerical technique is also proposed. Our algorithms consist of splitting the computation of the connection from that of the periodic orbit(s). To set up appropriate boundary conditions, we follow the algorithmic approach used by Demmel, Dieci, and Friedman, for the case of connecting orbits between equilibria, and we construct and exploit the smooth block Schur decomposition of the monodromy matrices associated to the periodic orbits. Numerical examples illustrate the performance of the algorithms. This revised version was published online in July 2006 with corrections to the Cover Date.     

An approximation property of harmonic functions in Lipschitz domains and some of its consequences

An extension of an inequality of J. B. Garnett (1979), with improvements by B. E. J. Dahlberg (1980), on an approximation property of harmonic functions is proved. The weighted inequality proved here was suggested by the work of J. Pipher (1993) and it implies an extension of a result of S. Y. A. Chang, J. Wilson and T. Wolff (1985) and C. Sweezy (1991) on exponential square integrability of the boundary values of solutions to second-order linear differential equations in divergence form. This implies a solution of a problem left open by R. Bañuelos and C. N. Moore (1989) on sharp estimates for the area integral of harmonic functions in Lipschitz domains.