一类二阶非线性常微分方程非线性边界条件的两点边值问题

本文讨论了一类二阶非线性常微分方程之具有线性边界条件的和具有非线性边界条件的两点边值问题解的存在性.     

金属切削刀具新材料的发展、应用及展望

结合国内外研究情况 ,对刀具材料的种类、性能、发展和应用情况进行了综合评述 ,并总结了切削刀具材料当前的研究特点及发展趋势     

Rational approximation in the complex plane using a τ-method and computer algebra

Numerous versions of the Lanczos τ-methods have been extensively used to produce polynomial approximations for functions verifying a linear differential equation with polynomial coefficients. In the case of an initial-value problem, an adapted τ-method based on Chebyshev series and the use of symbolic computation lead to a rational approximation of the solution on a region of the complex plane. Numerical examples show that the simplicity of the method does not prevent a high accuracy of results. This revised version was published online in June 2006 with corrections to the Cover Date.     

Cutting tool materials for high speed machining

High speed machining (HSM) is one of the emerging cutting processes, which is machining at a speed significantly higher than the speed commonly in use on the shop floor. In the last twenty years, high speed machining has received great attentions as a technological solution for high productivity in manufacturing. This article reviews the developments of tool materials in high speed machining operations, and the properties, applications and prospective developments of tool materials in HSM are also presented.     

Spline Techniques for Solving Singularly-Perturbed Nonlinear Problems on Nonuniform Grids

A numerical method based on cubic splines with nonuniform grid is given for singularly-perturbed nonlinear two-point boundary-value problems. The original nonlinear equation is linearized using quasilinearization. Difference schemes are derived for the linear case using a variable-mesh cubic spline and are used to solve each linear equation obtained via quasilinearization. Second-order uniform convergence is achieved. Numerical examples are given in support of the theoretical results.     

Nondegeneracy and uniqueness of positive solutions for Robin problem of second order ordinary differential equations and its applications

This article studies positive solutions of Robin problem for semi-linear second order ordinary differential equations. Nondegeneracy and uniqueness results are proven for homogeneous differential equations. Necessary and sufficient conditions for the existence of one or two positive solutions for inhomogeneous differential equations or differential equations with concave-convex nonlinearities are obtained by making use of the nondegeneracy and uniqueness results for positive solutions of homogeneous differential equations.     

高精度步进压印机热误差的建模分析

为了消除由紫外光曝光所引起的步进压印机的热误差，以提高压印机的套刻对准精度，运用逐步回归分析法选取了压印机上温度测量点的数量，将压印机上布置的温度传感器从15个减少到6个，并建立了压印机温度测量关键点处的温度与压头在x、z方向热误差关系的数学模型．实验结果与模型计算结果的对比分析表明，模型的热误差预测精度在x方向可以达到899／6，而在z方向可以达到939／6．应用表明，该方法是一种在压印机热误差建模中选择温度测量关键点的有效方法，可避免热误差建模过程中的变量耦合问题，从而提高了模型的精确性．     

A trajectory-following method for unconstrained optimization

A trajectory-following method with interesting properties is considered for solving unconstrained nonlinear programming problems. The trajectory is defined by a special system of ordinary differential equations. This system uses only the gradient of the objective function. Numerical examples are given.The work of the second author was supported by the DFG Schwerpunkt Anwendungs-bezogene Optimierung and Steuerung.     

关子齐次微分方程的积分曲线

记所论微分方程为(E_λ)_n,本文拓广的不变直线法,在(E_λ)_n的“有理相曲线”与临界、中介水平线”的交、切点与型号间建立起对应关系.依次以各水平线上交、切点型号串得的型列为行,使构成(E_λ)_n的型阵.它表达出λ遍取不同实数值(由-∞至,+∞)时,(E_λ)_n积分曲线的定性变化图景.实际上,它就是的均匀旋转向量场的完全族.     

切削刀具倒棱刃口挤压力的理论计算

根据试验观察．揭出了刀具刃口带负倒棱时的切削模型。在此模型中,刀具刃口 存在一个“金属死区”。以新模型为基础．采用能量法,对高温、高应变率下刀具刃 口的挤压力进行了理论计算。所做工作的特点是：１）在材料变形分析中计入了挤压 层金属绕过刀具刃口时的过剩变形;２）进行有关材料变形与物理特性的计算时,考 虑了温度与应变率的影响。利用新研制的压电式切削测力仪进行验证试验,其结果表 明,理论计算值与实测数据较好一致。