Fourier-Galerkin numerical technique for solitary waves of fifth order Korteweg-de Vries equation

The present paper is aimed to display the performance of the Fourier-Galerkin technique developed earlier by the authors for numerical treatment of localized solutions in ²(-∞, ∞) for higher-order equations. The solitary-wave solution of the Kortweg-de Vries fifth order equation is obtained numerically and compared with approximate results of other authors.     

Jordan homomorphisms,chain geometries and the fundamental theorem

This research was supported by M.P.I. (R.S. 40%).     

Detection of hepatocarcinoma in rats by integration of the fluorescence spectrum: Experimental model

The incorporation of spectroscopic techniques into diagnostic procedures may greatly improve the chances for precise diagnostics. One promising technique is fluorescence spectroscopy, which has recently been used to detect many different types of diseases. In this work, we use laser-induced tissue fluorescence to detect hepatocarcinoma in rats using excitation light at wavelengths of 443 and 532 nm. Hepatocarcinoma was induced chemically in Wistar rats. The collected fluorescence spectrum ranges from the excitation wavelength up to 850 nm. A mathematical procedure carried out on the spectrum determines a figure of merit value, which allows the detection of hepatocarcinoma. The figure of merit involves a procedure which evaluates the ratio between the backscattered excitation wavelength and the broad emission fluorescence band. We demonstrate that a normalization allowed by integration of the fluorescence spectra is a simple operation that may allow the detection of hepatocarcinoma.     

A Hybrid Multiobjective Evolutionary Algorithm for Solving Vehicle Routing Problem with Time Windows

Vehicle routing problem with time windows (VRPTW) involves the routing of a set of vehicles with limited capacity from a central depot to a set of geographically dispersed customers with known demands and predefined time windows. The problem is solved by optimizing routes for the vehicles so as to meet all given constraints as well as to minimize the objectives of traveling distance and number of vehicles. This paper proposes a hybrid multiobjective evolutionary algorithm (HMOEA) that incorporates various heuristics for local exploitation in the evolutionary search and the concept of Pareto's optimality for solving multiobjective optimization in VRPTW. The proposed HMOEA is featured with specialized genetic operators and variable-length chromosome representation to accommodate the sequence-oriented optimization in VRPTW. Unlike existing VRPTW approaches that often aggregate multiple criteria and constraints into a compromise function, the proposed HMOEA optimizes all routing constraints and objectives simultaneously, which improves the routing solutions in many aspects, such as lower routing cost, wider scattering area and better convergence trace. The HMOEA is applied to solve the benchmark Solomon's 56 VRPTW 100-customer instances, which yields 20 routing solutions better than or competitive as compared to the best solutions published in literature.     

Autour du théorème de Ferrand–Obata (Concerning the Theorem of Ferrand–Obata)

The aim of this article is to give a new dynamical proof of the Ferrand–Obata theorem when the manifold is compact. This will give us a generalisation of this theorem to transversally conformal foliations ofcodimension greater than three and constant basic functions.     

Study of the spectrum of cherenkov light

It is pessible to study experimentally Cherenkov light spectra in a liquid scintillation spectrometer with colour filters. Cherenkov light spectra of⁶⁰Co,¹⁹⁸Au,¹¹⁵Cd,¹⁴³Ce,¹⁴⁰La,³²P,⁸⁶Rb,⁷⁶As,⁴²K and an external standard were studied in a Packard 3375 type liquid scintillation spectrometer, using 11 various Kodak Wratten filters. The absorption maxima of the filters ware in the 410–796 nm interval.     

A note on the Lyapunov equation for discrete linear systems in Hilbert space

It is given a simple and unified new proof for the following well-known stability condition: an infinite-dimensional time-invariant discrete linear system is uniformly asymptotically stable if and only if the associate Lyapunov equation has a unique strictly positive solution. The proof is partially based on an application of Rota's model construction technique.     

Properties of (InGa)As/GaAs QW (λ ≈ 1.2 µm) facet-coated edge emitting diode laser

In this paper, we report on the design and optical properties of laser diodes with an emission wave-length of ～1170 nm based on an (InGa)As/GaAs double quantum well active layer. The back and front facet of the laser diodes were coated with SiO_x dielectric films that influence the output optical power by enhancing or lowering the facet reflectivity. The measurements show improvement of the facet-coated laser diode properties in the threshold-current-density reduction along with light output power enhancement. Furthermore, a narrow far field pattern and high side mode suppression have been observed.     

Dosimetric investigations of laser-induced phase transition of MX1-cell membranes by use of quantum dots

It is well known that laser scattered-light applicators when applied for laser-induced tumor therapy allow the precise thermal destruction of metastases. Using laser radiation in the NIR spectral range (usually, Nd:YAG laser systems λ = 1064 nm), a penetration depth of 5–10 cm (1/e is the decrease in radiation intensity) is achieved in biological tissues. The major tissue-optical parameters, i.e., absorption coefficient μ_a, scattering coefficient μ_s, and the anisotropy factor g, show biological tissues to be strongly scattering media which have a so-called optical window in the NIR. As a consequence, the therapeutic laser radiation is scattered and absorbed at a deeper level, leading to a virtual enlargement of the laser applicator. The thermal sclerotization and the thermal cell damage originate within the absorbing volume of the laser radiation and spread outward by thermal diffusion. There are three dosimetrically relevant zones of thermal and biological damage: (1) a zone of thermal coagulation; (2) a threshold of partial necrosis (destruction of all metabolic processes in the cell is the maintenance of essential parts of the cytoskeleton and the plasma membrane); this is characterized by a specific temperature range, the so-called phase transition, which refers to the transition from the gel phase of the biomembrane to the fluid phase; the determination of this temperature zone is an integral part of the following experimental investigations on MX1 cells; (3) an external zone of thermal effects made up of partial and multiple damage with a statistical chance of survival. This paper describes the investigations on heat stress in cancer cells to verify the maximum phase transition of the outer MX1 cell membranes and the related results. For this purpose, a novel method of quantum dot fluorescence dosimetry was developed. The evaluation of the measured laser-induced fluorescences yields a first approximation of the determination of the phase transition on MX1 cells.