On the number of full levels in tries

We study the asymptotic distribution of the fill‐up level in a binary trie built over n independent strings generated by a biased memoryless source. The fill‐up level is the number of full levels in a tree. A level is full if it contains the maximum allowable number of nodes (e.g., in a binary tree level k can have up to 2^k nodes). The fill‐up level finds many interesting applications, e.g., in the internet IP lookup problem and in the analysis of level compressed tries (LC tries). In this paper, we present a complete asymptotic characterization of the fill‐up distribution. In particular, we prove that this distribution concentrates on one or two points around the most probably value k = ?log_1/qn ? log log log n + 1 + log log(p/q)?, where p > q = 1 ? p is the probability of generating the more likely symbol (while q = 1 ? p is the probability of the less likely symbol). We derive our results by analytic methods such as generating functions, Mellin transform, the saddle point method, and analytic depoissonization. We also present some numerical verification of our results. © 2004 Wiley Periodicals, Inc. Random Struct. Alg., 2004     

Sinc-Galerkin method for solving linear sixth-order boundary-value problems

There are few techniques available to numerically solve sixth-order boundary-value problems with two-point boundary conditions. In this paper we show that the Sinc-Galerkin method is a very effective tool in numerically solving such problems. The method is then tested on examples with homogeneous and nonhomogeneous boundary conditions and a comparison with the modified decomposition method is made. It is shown that the Sinc-Galerkin method yields better results.

     

Natural vibrations of a strip made of a composite material with a locally curved structure

The possibility of using the finite-element method for investigating two-dimensional problems on natural vibrations in the mechanics of composite materials with curved structures is considered. With the example of a hinge-supported strip made of a composite material with a locally curved structure, the influence of geometrical and mechanical parameters of the strip on its eigenfrequencies is examined. It is established that the presence of local curving in the structure of strip material decreases the magnitude of eigenfrequencies.Translated from Mekhanika Kompozitnykh Materialov, Vol. 41, No. 1, pp. 71–78, January–February, 2005.     

Development of a parallel storm surge model

A new parallel storm surge model, the Parallel Environmental Model (PEM), is developed and tested by comparisons with analytic solutions. The PEM is a 2‐D vertically averaged, wetting and drying numerical model and can be operated in explicit, semi‐implicit and fully implicit modes. In the implicit mode, the propagation, Coriolis and bottom friction terms can all be treated implicitly. The advection and diffusion terms are solved with a parallel Eulerian–Lagrangian scheme developed for this study. The model is developed specifically for use on parallel computer systems and will function accordingly in either explicit of implicit modes. Storm boundary conditions are based on a simple exponential decay of pressure from the centre of a storm. The simulated flooding caused by a major Category 5 hurricane making landfall in the Indian River Lagoon, Florida is then presented as an example application of the PEM. Copyright © 2003 John Wiley & Sons, Ltd.     

Shape Optimization and Fictitious Domain Approach for Solving Free Boundary Problems of Bernoulli Type

This contribution deals with an efficient method for the numerical realization of the exterior and interior Bernoulli free boundary problems. It is based on a shape optimization approach. The state problems are solved by a fictitious domain solver using boundary Lagrange multipliers.     

Interior point cutting plane method for optimal power flow

In this paper, an interior point cutting plane method (IPCPM)is applied to solve optimal power flow (OPF) problems. Comparedwith the simplex cutting plane method (SCPM), the IPCPM is simpler,and efficient because of its polynomial-time characteristic.Issues in implementing IPCPM for OPF problems are addressed,including (1) how to generate cutting planes without using thesimplex tableau, (2) how to identify the basis variables inIPCPM, and (3) how to generate mixed integer cutting planes.The calculation speed of the proposed algorithm is further enhancedby utilizing the sparsity features of the OPF formulation. Numericalsimulations on IEEE 14-300-bus test systems have shown thatthe proposed method is effective.     

Time-resolved imaging of latent fingerprints with nanosecond resolution

Imaging of latent fingerprints using time-resolved (TR) method offers a broader platform to eliminate the unwanted background emission. In this paper, a novel TR imaging technique is demonstrated and implemented, which facilitates the detection of latent fingerprints with nanosecond resolution. Simulated experiments were carried out with two overlapping fingerprints treated with two fluorescent powders having different lifetimes in nanosecond range. The dependence of the fluorescence emission intensity in nanosecond resolution of TR imaging is also revealed.     

Nonvolatile photorefractive holographic recording in Sc:Ce:Cu:LiNbO3

In this paper experimental studies of nonvolatile photorefractive holographic recording in Ce:Cu:LiNbO₃ crystals doped with Sc(0,1,2,3 mol%) were carried out. The Sc:Ce:Cu:LiNbO₃ crystals were grown by the Czochralski method and oxidized in Nb₂O₅ powders. The nonvolatile holographic recording in Sc:Ce:Cu:LiNbO₃ crystals was realized by the two-photon fixed method. We found that the recording time of Sc:Ce:Cu:LiNbO₃ crystal became shorter with the increase of Sc doping concentration, especially doping with Sc(3 mol%), which exceeds the so-called threshold, and there was little loss of nonvolatile diffraction efficiencies between Sc(3 mol%):Ce:Cu:LiNbO₃ and Ce:Cu:LiNbO₃ crystals.     

A boundary element method for the calculation of noise barrier insertion loss in the presence of atmospheric turbulence

Atmospheric turbulence is an important factor that limits the amount of attenuation a barrier can provide in the outdoor environment. It is therefore important to develop a reliable method to predict its effect on barrier performance. The boundary element method (BEM) has been shown to be a very effective technique for predicting barrier insertion loss in the absence of turbulence. This paper develops a simple and efficient modification of the BEM formulation to predict the insertion loss of a barrier in the presence of atmospheric turbulence. The modification is based on two alternative methods: (1) random realisations of log-amplitude and phase fluctuations of boundary sources and (2) de-correlation of source coherence using the mutual coherence function (MCF). An investigation into the behaviours of these two methods is carried out and simplified forms of the methods developed. Some systematic differences between the predictions from the methods are found. When incorporated into the BEM formulation, the method of random realisations and the method of MCF de-correlation provide predictions that agree well with predictions by the parabolic equation method and by the scattering cross-section method on a variety of thin barrier configurations.     

Lame Function and Its Application to Some Nonlinear Evolution Equations

In this paper, based on the Lame function and Jacobi elliptic function, the perturbation method is appliedto some nonlinear evolution equations to derive their multi-order solutions.