Flexible waveguides for Er-YAG laser radiation delivery

Flexible plastic waveguides (FPW) were devised for the delivery of Er-YAG laser radiation. The FPW characteristics were studied under various conditions. In vitro studies were carried out to explore the drilling procedure on extracted teeth and the FPW-tissue mutual effects. The results which were obtained proved that the FPW as a delivery device might be a substitute hand applicator for the pneumatic turbine for drilling in teeth     

Extremal problems concerning transformations of the edges of the complete hypergraphs

We consider extremal problems concerning transformations of the edges of complete hypergraphs. We estimate the order of the largest subhypergraph K such that for every edge e ? E(K), f(e) ? E(K), assuming f(e) ≠ e. Several extensions and variations of this problem are also discussed here.     

On three zero-sum Ramsey-type problems

For a graph G whose number of edges is divisible by k, let R(G,Z_k) denote the minimum integer r such that for every function f: E(K_r) ? Z_k there is a copy G¹ of G in K_r so that Σe∈E(G¹) f(e) = 0 (in Z_k). We prove that for every integer k₁ R(K_n, Z_k) ≤ n + O(k³ log k) provided n is sufficiently large as a function of k and k divides (). If, in addition, k is an odd prime-power then R(K_n, Z_k) ≤ n + 2k - 2 and this is tight if k is a prime that divides n. A related result is obtained for hypergraphs. It is further shown that for every graph G on n vertices with an even number of edges R(G,Z₂) ≤ n + 2. This estimate is sharp. © 1993 John Wiley & Sons, Inc.     

Time-dependent exchange-correlation current density functionals with memory

Most present applications of time-dependent density functional theory use adiabatic functionals, i.e., the effective potential at time t is determined solely by the density at the same time. This paper discusses a method that aims to go beyond this approximation, by incorporating "memory" effects: the derived exchange-correlation potential will depend not only on present densities but also on the past. In order to ensure the potentials are causal, we formulate the action on the Keldysh contour for electrons in electromagnetic fields, from which we derive suitable Kohn-Sham equations. The exchange-correlation action is now a functional of the electron density and velocity field. A specific action functional is constructed which is Galilean invariant and yields a causal exchange-correlation vector potential for the Kohn-Sham equations incorporating memory effects. We show explicitly that the net exchange-correlation Lorentz force is zero. The potential is consistent with known dynamical properties of the homogeneous electron gas (in the linear response limit).     

Zero-sum delta-systems and multiple copies of graphs

A main result proved in this paper is the following. Theorem. Let G be a noncomplete graph on n vertices with degree sequence d₁ ≥ d₂ ≥ · · · ≥ d_n and t ≥ 2 be a prime. Let m = gcd{t, d_i − d_j: 1 ≤ i < j ≤ n} and set Then R(tG, ℤ_t) = t(n + d) − d, where R is the zero-sum Ramsey number. This settles, almost completely, problems raised in [Bialostocki & Dierker, J Graph Theory, 1994; Y. Caro, J Graph Theory, 1991]. © 1999 John Wiley & Sons, Inc. J Graph Theory 32: 207–216, 1999     

Signal enhancement using beamforming and nonstationarity withapplications to speech

We consider a sensor array located in an enclosure, where arbitrary transfer functions (TFs) relate the source signal and the sensors. The array is used for enhancing a signal contaminated by interference. Constrained minimum power adaptive beamforming, which has been suggested by Frost (1972) and, in particular, the generalized sidelobe canceler (GSC) version, which has been developed by Griffiths and Jim (1982), are the most widely used beamforming techniques. These methods rely on the assumption that the received signals are simple delayed versions of the source signal. The good interference suppression attained under this assumption is severely impaired in complicated acoustic environments, where arbitrary TFs may be encountered. In this paper, we consider the arbitrary TF case. We propose a GSC solution, which is adapted to the general TF case. We derive a suboptimal algorithm that can be implemented by estimating the TFs ratios, instead of estimating the TFs. The TF ratios are estimated by exploiting the nonstationarity characteristics of the desired signal. The algorithm is applied to the problem of speech enhancement in a reverberating room. The discussion is supported by an experimental study using speech and noise signals recorded in an actual room acoustics environment     

Continuous symmetry measures: A note in proof of the folding/unfolding method

The measurement of the degree of symmetry proved to be a useful tool in the prediction of quantitative structural–physical correlations. These measurements have been based, in the most general form, on the folding/unfolding algorithm, for which we provide here a new and simpler proof. We generalize this proof to the case of objects composed of more than one (full) orbit. An important practical issue we consider is the division of the graph into symmetry orbits and the mapping of the symmetry group elements onto the points of the graph. The logical constraints imposed by the edges of the graph are reviewed and used for the successful resolution of the coupling between different orbits.     

Model case analysis of an algebraic multilevel method

A multilevel method for the solution of sparse linear systems is introduced. The method is defined in terms of the coefficient matrix alone; no underlying PDE or mesh is assumed. An upper bound for the condition number is available for a class of SPD problems. In particular, for certain discretizations of diffusion boundary value problems, this bound grows only polynomially with the number of levels used, regardless of whether or not the discontinuities in the diffusion coefficient align with the coarse grids. Numerical results in line with the analysis are presented. Copyright © 1999 John Wiley & Sons, Ltd.     

Analysis of matrix-dependent multigrid algorithms

Convergence theory for a multigrid method with matrix-dependent restriction, prolongation and coarse-grid operators is developed for a class of SPD problems. It motivates the construction of improved multigrid versions for diffusion problems with discontinuous coefficients. A computational two-level analysis method for a class of separable problems is also available. It motivates the design of matrix-dependent multigrid algorithms and, in particular, multiple coarse-grid correction algorithms for highly indefinite equations. Numerical experiments show the advantage of the present methods for several examples. © 1998 John Wiley & Sons, Ltd.     

Packing and covering dense graphs

Let d be a positive integer. A graph G is called d-divisible if d divides the degree of each vertex of G. G is called nowhere d-divisible if no degree of a vertex of G is divisible by d. For a graph H, gcd(H) denotes the greatest common divisor of the degrees of the vertices of H. The H-packing number of G is the maximum number of pairwise edge disjoint copies of H in G. The H-covering number of G is the minimum number of copies of H in G whose union covers all edges of G. Our main result is the following: For every fixed graph H with gcd(H) = d, there exist positive constants ϵ(H) and N(H) such that if G is a graph with at least N(H) vertices and has minimum degree at least (1 − ϵ(H))|G|, then the H-packing number of G and the H-covering number of G can be computed in polynomial time. Furthermore, if G is either d-divisible or nowhere d-divisible, then there is a closed formula for the H-packing number of G, and the H-covering number of G. Further extensions and solutions to related problems are also given. © 1998 John Wiley & Sons, Inc. J Combin Designs 6: 451–472, 1998