A necessary and sufficient condition of existence of positive solutions for nonlinear singular differential systems

In this paper, by means of monotone iterative technique, a necessary and sufficient condition of the existence of positive solution for a class of nonlinear singular differential system is established, the results of the existence and uniqueness of the positive solution and the iterative sequence of solution are given. In the end, two classes extending boundary value differential systems are discussed and some further results are obtained.     

The application of Hölder exponent to traffic congestion warning

In this paper, we applied multifractal modeling techniques to analyze the traffic data collected from the Beijing Yuquanying. The results indicated that multifractal characteristics obviously exist in the traffic system; the degree of fractality of these traffic data tends to increase as the traffic system becomes congested; the Hölder exponent that measures the local rate of fractality may be used as indicators to predict the presence of the traffic congestion.     

Oscillation of the solutions of parabolic equations with nonlinear neutral terms

In the present paper the oscillatory properties of the solutions of parabolic equations with nonlinear neutral terms are investigated. Our approach is to reduce the multi-dimensional problem to a one-dimensional problem for delay differential inequalities.     

Differential Pulse Polarographic Determination of Nitrate in AUT Solution

A differential pulse polarographic method for the determination of nitrate ion has been developed. With 0.5 M CaCl₂ as supporting electrolyte, NO^?₃ is reduced to give a peak with E_1/2=–1.836 Volt vs. the Ag/AgCl electrode. The differential pulse polarographic peak height is proportional to the nitrate concentration from 20 to 60 ppm. The detection limit for nitrate is 2 ppm in pure aqueous solution. In the determination of 40 ppm nitrate a relative precision (relative standard deviation) of less than 2% was achieved. Nitrite interferes seriously and should be absent if accurate results are required. The method has been applied to the determination of nitrate in Ammonium Uranyl Tricarbonate (AUT) Solution, results obtained by this method are compared to those obtained by ion chromatography. The agreement between the two sets of results suggests that the DPP method can be used with a fair degree of confidence.     

Semilinear Differential Inclusions in Separable Banach Spaces

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Equality and inequality constrained optimization algorithms with convergent stepsizes

In this paper, we consider two algorithms for nonlinear equality and inequality constrained optimization. Both algorithms utilize stepsize strategies based on differentiable penalty functions and quadratic programming subproblems. The essential difference between the algorithms is in the stepsize strategies used. The objective function in the quadratic subproblem includes a linear term that is dependent on the penalty functions. The quadratic objective function utilizes an approximate Hessian of the Lagrangian augmented by the penalty functions. In this approximation, it is possible to ignore the second-derivative terms arising from the constraints in the penalty functions.The penalty parameter is determined using a strategy, slightly different for each algorithm, that ensures boundedness as well as a descent property. In particular, the boundedness follows as the strategy is always satisfied for finite values of the parameter.These properties are utilized to establish global convergence and the condition under which unit stepsizes are achieved. There is also a compatibility between the quadratic objective function and the stepsize strategy to ensure the consistency of the properties for unit steps and subsequent convergence rates.This research was funded by SERC and ESRC research contracts. The author is grateful to Professors Laurence Dixon and David Mayne for their comments. The numerical results in the paper were obtained using a program written by Mr. Robin Becker.     

两种群竞争模型的奇摄动群

本文应用多重尺度法构造出非线性微分方程组的解的渐近展开式。并用微分不等式的技巧，证明原问题的解的存在性，且给出解的一致有效渐近估计．     

单个波长到多个波长的变换实验

报道一种波长变换的新方法.采用此方法不需要任何泵浦光便能够直接将信号光变换成在特定谱宽内的任意多个任意波长的变换光,这对于将来的波分复用光网络提供了较大的方便.此波长变换的原理是利用色散位移光纤的非线性效应产生超连续光谱(SC)信号,由于这种SC信号携带有变换光信号,对这种连续谱进行滤波便能够得到所需要的任意频率的变换信号.此变换方式具有变换频带宽,偏振不敏感的优点。     

Calorimetric analysis of the ethanolysis of 1,2-epoxybutane

Polyethers, which are produced by alcoholysis of oxiranes, are often used as solvents in chemical plants. The spectra of the products can be influenced by the choice of the catalyst (acid or base). The results of the base-catalyzed ethanolysis of 1,2-epoxybutane are displayed. The reaction was investigated calorimetrically by varying the molar ratio between ethanol and 1,2-epoxybutane, the starting temperature and the concentration of the catalyst sodium hydroxide. Additionally, the influence of the used alcohol will be shown in one example. To determine the activation parameters, the experiments were evaluated by the nonlinear software package TA-kin v3.3.     

SOME TOPICS ON WAVELET ANALYSIS

A review of the advance in the theory of wavelet analysis in recent years is given.