用定义求解高等数学中的有关问题

应用导数的定义，为分段函数的分界点提供了一种行之有效的求导方法，利用微分的定义判断函数在分界点及其他特殊点的可微性，运用定和分的定义求一类特殊类型的极限．     

Enthalpies of sorption of linear hydrocarbons (C2–C8) and chloroderivatives of methane and ethylene on the surface of hydrotalcite

Differential molar adsorption enthalpies (DMAE) were determined by gas chromatographic measurements of specific retention volume of vapors on the surface of two forms of Mg–Al hydrotalcite. A linear dependence of the DMAE on the number of the carbon atoms in hydrocarbons was observed for both form of hydrotalcite. The dependence of the differential molar adsorption enthalpies on the number of chlorine atoms in organic molecules is discussed. A linear dependence of DMAE on the molecular weight of chloroderivatives of methane and ethylene on the basic form in an order monochloromethane < dichloromethane < trichloromethane or vinylidene chloride < 1,1-dichloroethylene < trichloroethylene was found.     

Linearized and rational approximation method for solving non‐linear Burgers' equation

A new numerical method called linearized and rational approximation method is presented to solve non‐linear evolution equations. The utility of the method is demonstrated for the case of differentiation of functions involving steep gradients. The solution of Burgers' equation is presented to illustrate the effectiveness of the technique for the solution of non‐linear evolution equations exhibiting nearly discontinuous solutions. Copyright © 2004 John Wiley & Sons, Ltd.     

60keV质子辐照对TiNi记忆合金薄膜马氏体相变的影响

 利用磁控溅射的方法在氧化后的单晶Si基片上制备了TiNi形状记忆合金薄膜，利用示差扫描量热法和原位X射线衍射研究了薄膜的马氏体相变特征。通过60keV质子注入（辐照）薄膜样品研究了H+离子对合金薄膜马氏体相变特征的影响，结果表明氢离子注入后引起了马氏体相变开始Ms和结束点Mf以及逆马氏体相变开始As和结束温度Af的下降，而对R相变开始Rs和结束温度Rf影响不大。掠入射X射线衍射表明H+离子注入后有氢化物形成。H⁺离子注入形成的氢化物是引起相变点的变化的主要因素。     

Differential FBG sensor for temperature-compensated high-pressure (or displacement) measurement

A differential fiber Bragg grating (FBG) sensor with a free active element bulk-modulus for high-pressure (or displacement) measurement is presented. Based on the differential measurement method and an isosceles triangle cantilever structure, problems of cross-sensitivity and chirped signal in FBG sensor are improved both theoretically and experimentally. Preliminary experiments indicate that temperature-compensated measurement results agree well with the theoretical analysis. Displacement measurement sensitivity is 1.75 pm/μm, and the estimated pressure measurement resolution can reach 0.27 MPa in case the wavelength shift measurement resolution is 0.01 nm.     

Surjectivity and fixed points of relaxed dissipative multifunctions. Differential inclusions approach

One from the most important properties of accretive and monotone operators is the existence of zeros and surjectivity. In the paper we introduce relaxed variants of dissipative, accretive and monotone operators. Using essentially the properties of the solution set of appropriate differential inclusions we study the existence of zeros of such operators. As corollaries the existence of fixed points of relaxed contractive and relaxed nonexpansive multifunctions are obtained.     

An existence result for a quadrature surface free boundary problem

The aim of this paper is to present two different approachs in order to obtain an existence result to the so-called quadrature surface free boundary problem. The first one requires the shape derivative calculus while the second one depends strongly on the compatibility condition of the Neumann problem. A necessary and sufficient condition of existences is given in the radial case.     

The variational Lyapunov function and strict stability theory for differential systems

In this paper, we investigate strict stability of differential systems by variational Lyapunov function. We obtain some sufficient conditions and comparison theorems.     

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.     

A note on generalized averaged Gaussian formulas

We have recently proposed a very simple numerical method for constructing the averaged Gaussian quadrature formulas. These formulas exist in many more cases than the real positive Gauss–Kronrod formulas. In this note we try to answer whether the averaged Gaussian formulas are an adequate alternative to the corresponding Gauss–Kronrod quadrature formulas, to estimate the remainder term of a Gaussian rule.