求解一类二阶非线性偏微分方程的新算法

在再生核空间中给出一类二阶非线性偏微分方程的一个新的求解方法,近似解un(x)是通过在再生核空间中截断精确解u(x)而得到的,最后,通过一个数值算例来说明该方法是有效的.     

Laminar flamelet modeling of a turbulent CH4/H2/N2 jet diffusion flame using artificial neural networks

The laminar flamelet concept is used in the prediction of mean reactive scalars in a non-premixed turbulent CH₄/H₂/N₂ flame. First, a databank for temperature and species concentrations is developed from the solutions of counter-flow diffusion flames. The effects of flow field on flamelets are considered by using mixture fraction and scalar dissipation rate. Turbulence-chemistry interactions are taken into account by integrating different quantities based on a presumed probability density function (PDF), to calculate the Favre-averaged values of scalars. Flamelet library is then generated. To interpolate in the generated library, one artificial neural network (ANN) is trained where the mean and variance of mixture fraction and the scalar dissipation rate are used as inputs, and species mean mass fractions and temperature are selected as outputs. The weights and biases of this ANN are implemented in a CFD flow solver code, to estimate mean values of the scalars. Results reveal that ANN yields good predictions and the computational time has decreased as compared to numerical integration for the estimation of mean thermo-chemical variables in the CFD code. Predicted thermo-chemical quantities are close to those from experimental measurements but some discrepancies exist, which are mainly due to the assumption of non-unity Lewis number in the calculations.     

Quantitative determination of n-alkanethiols in air and in a blended gas mixture of methane with air by gas chromatography/differential mobility spectrometry

Mixtures of n-alkanethiols, in solution with equi-molar amounts from 0.5 to 360 ng per compound, were determined using gas chromatography (GC) with a differential mobility spectrometer, operated with a flow of air at ambient pressure, as the GC detector. A homologous series of n-alkanethiols with carbon number from two to six showed baseline resolution in the GC separation and positive and negative ion chromatograms were produced simultaneously for the alkanethiols. Differential mobility spectra showed compensation voltages characteristic of each alkanethiol and plots of ion intensity, retention time, and compensation voltage yield contour plots illustrating the second dimension of analytical selectivity provided by the detector. Another yet undeveloped dimension of analytical information was found in the dependence of mobility coefficients on electric field. Mass-analysis of ions from thiols showed a hydrogen abstracted ion, protonated monomers, and proton bound dimers. Linear ranges were narrow and the minimum detectable limits were ~1 ng. Response in positive polarity provided a ten-fold improvement in detection limits though spectra were more complex than for negative ions. In a methane-rich air atmosphere, intended to simulate ambient air or the detection of leaks from natural gas pipelines, the response to thiols with negative ions was not degraded by the methane up to 50% v/v, the highest level tested.     

Equation of state and elastic properties of ACrO3 (A=Pb,Ca, Sr and Ba) perovskites under high pressure

We employ the spin-polarized generalized gradient approximation within the density functional theory to investigate the equation of state, magnetism and elastic constant of cubic ACrO₃ (A=Pb, Ca, Sr, and Ba) perovskite. The antiferromagnetic phase is the most stable state at zero pressure. Under pressure, the ferromagnetic state will transform to the non-magnetic state. Considering the effect of magnetism, the equilibrium lattice constant, the bulk modulus and the high pressure equations of state agree well with the available experiments. By using the energy-strain method, the predicted elastic properties are satisfactory.     

DSC法研究液晶物质2-(4-烷氧苯基)6-取代苯并噻唑的相变热性质

The phase transitions of a new group of mesogens, 2-(4-alkoxyphenyl)-6-substituted benzothiazoles were thermodynamically studied by DSC, and their transition temperatures and enthalpy changes were measured, from which the transition entropy changes were calculated. The results obtained were discussed. In addition, the phe-nomenon of super-cooling of the compounds were quantitatively observed.     

Maximum principle for functional equations in the space of discontinuous functions of three variables

The paper is devoted to the maximum principles for functional equations in the space of measurable essentially bounded functions. The necessary and sufficient conditions for validity of corresponding maximum principles are obtained in a form of theorems about functional inequalities similar to the classical theorems about differential inequalities of the Vallee Poussin type. Assertions about the strong maximum principle are proposed. All results are also true for difference equations, which can be considered as a particular case of functional equations. The problems of validity of the maximum principles are reduced to nonoscillation properties and disconjugacy of functional equations. Note that zeros and nonoscillation of a solution in a space of discontinuous functions are defined in this paper. It is demonstrated that nonoscillation properties of functional equations are connected with the spectral radius of a corresponding operator acting in the space of essentially bounded functions. Simple sufficient conditions of nonoscillation, disconjugacy and validity of the maximum principles are proposed. The known nonoscillation results for equation in space of functions of one variable follow as a particular cases of these assertions. It should be noted that corresponding coefficient tests obtained on this basis cannot be improved. Various applications to nonoscillation, disconjugacy and the maximum principles for partial differential equations are proposed.     

Some Properties of Quasi-keep-range Operators and Their Applications

ＳｏｍｅＰｒｏｐｅｒｔｉｅｓｏｆＱｕａｓｉ┐ｋｅｅｐ┐ｒａｎｇｅＯｐｅｒａｔｏｒｓａｎｄＴｈｅｉｒＡｐｐｌｉｃａｔｉｏｎｓＬａｉＣｈｕｎｈｕｉ（赖春晖）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＺｈａｎｇｚｈｏｕＴｅａｃｈｅｒｓＣｏｌｅｇｅ，...     

无穷时滞泛函微分方程的正周期解

利用范数形式的锥拉伸和锥压缩不动点定理讨论具有无穷时滞泛函微分方程的周期解问题,获得了正周期解的存在性定理,并给出了定理的若干应用.     

多孔功能梯度材料Timoshenko梁的自由振动分析

基于Timoshenko梁理论研究多孔功能梯度材料梁(FGMs)的自由振动问题.首先,考虑多孔功能梯度材料梁的孔隙率模型,建立了两种类型的孔隙分布.其次,基于Timoshenko梁变形理论,给出位移场方程、几何方程和本构方程,利用Hamilton原理推导多孔功能梯度材料梁的自由振动控制微分方程,并进行无量纲化,然后应用微分变换法(DTM)对无量纲控制微分方程及其边界条件进行变换,得到含有固有频率的等价代数特征方程.最后,计算了固定-固定(C-C)、固定-简支(C-S)和简支-简支(S-S)三种不同边界下多孔功能梯度材料梁自由振动的无量纲固有频率.将其退化为均匀材料与已有文献数据结果对照,验证了正确性.讨论了孔隙率、细长比和梯度指数对多孔功能梯度材料梁无量纲固有频率的影响.     

A zero sum differential game in a Hilbert space

We study a zero sum differential game of fixed duration in a separable Hilbert space. We prove a minimax principle and establish the equivalence between the dynamic programming principle and the existence of a saddle point equilibrium. We also prove sufficient conditions for optimality.