Study of combined electroreflectance and double layer effects at lead electrodes

Reflectance changes at lead electrodes have been measured as a function of surface charge at 45° and 70° angles of incidence using solutions of sodium fluoride and quaternary ammonium salts. These solutions were chosen so as to provide quite different composition for the inner layer at the metal/solution interface, and hence different optical contributions there from. Linear reflectance-surface charge relation has been observed for NaF solutions only at a number of wavelengths. The optical effects from the inner layer has been recognized but could not be separated out from the main er effect by comparative measurements at two angles of incidence. This has been rationalized on the basis of similar variation of the er effect and the optical effect from the double-layer as a function of angle of incidence of light.     

Estimates for multigrid methods based on red-black Gauss-Seidel smoothings

Summary TheMGR[v] algorithms of Ries, Trottenberg and Winter, the Algorithms 2.1 and 6.1 of Braess and the Algorithm 4.1 of Verfürth are all multigrid algorithms for the solution of the discrete Poisson equation (with Dirichlet boundary conditions) based on red-black Gauss-Seidel smoothing. Both Braess and Verfürth give explicit numerical upper bounds on the rate of convergence of their methods in convex polygonal domains. In this work we reconsider these problems and obtain improved estimates for theh–2h Algorithm 4.1 as well asW-cycle estimates for both schemes in non-convex polygonal domains. The proofs do not depend on the strengthened Cauchy inequality.Sponsored by the Air Force Office of Scientific Research under Contract No. AFOSR-86-0163     

Efficient parallel algorithms for shortest paths in planar digraphs

Efficient parallel algorithms are presented, on the CREW PRAM model, for generating a succinct encoding of all pairs shortest path information in a directed planar graphG with real-valued edge costs but no negative cycles. We assume that a planar embedding ofG is given, together with a set ofq faces that cover all the vertices. Then our algorithm runs inO(log² n) time and employsO(nq+M(q)) processors (whereM(t) is the number of processors required to multiply twot×t matrices inO(logt) time). Let us note here that wheneverq<n then our processor bound is better than the best previous one (M(n)).O(log² n) time,n-processor algorithms are presented for various subproblems, including that of generating all pairs shortest path information in a directedouterplanar graph. Our work is based on the fundamental hammock-decomposition technique of G. Frederickson. We achieve this decomposition inO(logn log*n) parallel time by usingO(n) processors. The hammock-decomposition seems to be a fundamental operation that may help in improving efficiency of many parallel (and sequential) graph algorithms.This work was partially supported by the EEC ESPRIT Basic Research Action No. 3075 (ALCOM) and by the Ministry of Industry, Energy and Technology of Greece.     

Page usage in a quadtree index

This paper provides a characterization of the storage needs of a quadtree when used as an index to access large volumes of 2-dimensional data. It is shown that the page occupancy for data in random order approaches 33%. A precise mathematical analysis that involves a modicum of hypergeometric functions and dilogarithms, together with some computer algebra is presented.A brief survey of the analysis of storage usage in tree structures is included. The 33% ratio for quadtrees is to be compared to the figures for binary search trees (50%), tries (69%), and quadtries (46%).The research of this author was done while visiting INRIA, Rocquencourt, France under support from the Ministry of Education of Japanese Government.Work of this author was supported in part by the Basic Research Action of the E.C. under contract No. 3075 (Project ALCOM).     

Approximation of tricomi problem with Neumann boundary condition

Summary The Tricomi problem with Neumann boundary condition is reduced to a degenerate problem in the elliptic region with a non-local boundary condition and to a Cauchy problem in the hyperbolic region. A variational formulation is given to the elliptic problem and a finite element approximation is studied. Also some regularity results in weighted Sobolev spaces are discussed.     

Calculation of light pulses with chirp in passively mode-locked lasers taking into account the phase memory of absorber and amplifier

Starting from the complete set of Maxwell's equations and density matrix equations for the atomic systems, the change of amplitude and phase of light pulses in passing through absorbing and amplifying samples has been calculated by using certain approximations. It is shown that the phase modulation originates from saturation and phase memory in off-resonance interaction. The use of the simple rate-equation approximations.is only justified if saturation dominates. The full cavity round-trip equation has been established and solved for steady-state pulses under different conditions. For the case of pulses being outside resonance with the media we take into account a linear optical element for intracavity chirp compensation in order to describe the regime, where in experiment the shortest pulses have been found.     

Reaction of N-acylthioureas with electrophilic reagents : Synthesis of 1,3,5-oxadiazinium salts, 1,3,5-thiadiazinium salts, 1,2,4-dithiazolium salts and benzothiazoles

N-Acylthioureas 1 can be easily transformed into 2,4-diamino-6-aryl-1,3,5-oxadiazinium salts 12, 2,4-diamino-6-aryl-1,3,5-thiadiazinium salts 13,3-amino-5-aryl-1,2,4-dithiazolium salts 19 and 2-acylimino-benzothiazolines 22, respectively by reaction with different electrophiles. The structure of the compounds prepared is confirmed by analytical data as well as by chemical transformations.     

Stability and robustness of collocation methods for Abel-type integral equations

Summary We study stability aspects of collocation methods for Abel-type integral equations of the first kind using piecewise polynomials. These collocation methods may be formulated as projection methods. Stability is defined as the boundedness of the sequence of projectors in their natural setting. Robustness is essentially the optimal asymptotic insensitivity to perturbations in the data. We show that stability and robustness are equivalent for the above collocation methods. This allows us to obtain optimal error estimates for some methods that are well-known to be robust. We also present numerical results for some methods which appear to be robust.Research supported in part by the United States Army under Contract No. DAAG 29-83-K-0109