About a numerical method of successive interpolations for two-point boundary value problems with deviating argument

A new numerical method for two-point boundary value problems with deviating argument is obtained. The method uses the fixed point technique, the trapezoidal quadrature rule, and a Birkhoff interpolation procedure. The convergence of the method is proved without smoothness conditions, the kernel function being only Lipschitzian in each argument. The interpolation procedure is used only on the points where the argument is modified. A stopping criterion of the algorithm is obtained and the accuracy of the method is illustrated on four numerical examples of pantograph type.     

Equilibrium shape and hysteresis behavior of liquid jets in transverse electric fields

The stability of a liquid jet subject to a transverse electric field is investigated in the framework of electrohydrostatic theory. It is shown that depending on the magnitude of permittivity ratio of the involved fluids S = ε_i/ε_o (inner to outer) compared to a critical permittivity ratio S_cr ≈ 27.45 the jet exhibits distinct behaviors; for S < S_cr the jet is stable and elongates indefinitely as the electric field is increased, while for S > S_cr it shows hysteresis behavior and becomes unstable beyond a critical electric capillary number Ca_cr. The results suggest that the jets are generally more stable than liquid drops.     

Imposing boundary conditions in Sinc method using highest derivative approximation

Sinc approximate methods are often used to solve complex boundary value problems such as problems on unbounded domains or problems with endpoint singularities. A recent implementation of the Sinc method [Li, C. and Wu, X., Numerical solution of differential equations using Sinc method based on the interpolation of the highest derivatives, Applied Mathematical Modeling 31 (1) 2007 1–9] in which Sinc basis functions are used to approximate the highest derivative in the governing equation of the boundary value problem is evaluated for structural mechanics applications in which interlaminar stresses are desired. We suggest an alternative approach for specifying the boundary conditions, and we compare the numerical results for analysis of a laminated composite Timoshenko beam, implementing both Li and Wu’s approach and our alternative approach for applying the boundary conditions. For the Timoshenko beam problem, we obtain accurate results using both approaches, including transverse shear stress by integration of the 3D equilibrium equations of elasticity. The beam results indicate our approach is less dependent on the selection of the Sinc mesh size than Li and Wu’s SIHD. We also apply SIHD to analyze a classical laminated composite plate. For the plate example, we experience difficulty in obtaining a complete system of equations using Li and Wu’s approach. For our approach, we suggest that additional necessary information may be obtained by applying the derivatives of the boundary conditions on each edge. Using this technique, we obtain accurate results for deflection and stresses, including interlaminar stresses by integration of the 3D equilibrium equations of elasticity. Our results for both the beam and the plate problems indicate that this approach is easily implemented, has a high level of accuracy, and good convergence properties.     

关于广义Liénard系统解的唯一性

研究了广义Liénard系统初值问题解的唯一性问题.利用李普希兹条件和隐函数定理,我们得到了此系统解的存在唯一性定理,推广了相应的结果.     

在一个半无穷柱体上的非标准Stokes流体方程的二择一问题

考虑了定义在半无限柱体上的非标准Stokes流体方程的初边值问题,其中在柱体的有限端施加非线性边界条件,在柱体的侧面上满足零边界条件.在初始条件中参数的适当范围内,利用微分不等式技术,得到了Stokes流体方程的二择一结果.在衰减的情况下,证明了"全能量"可以由已知数据项控制.     

CGMY模型下 的欧式外汇期权定价

修正传统有效市场假说,重新假设外汇汇率存在扩散和跳跃,并结合CGMY模型,采用傅里叶变换方法,推导出了CGMY模型下欧式外汇期权价格满足的分数阶偏微分方程(FPDE).尽管因分数阶偏导数引发的“全局性”很难处理,仍然推导出CGMY模型下欧式外汇期权的定价公式及其满足的平价公式.同时,引入一个新的缩放参数m来控制指数函数的增长率以克服被积函数衰减引起的计算困难,使其与Lévy密度函数的衰减在速度上达到一个平衡.最后,从数学与金融意义上分析了关键参数变化对欧式外汇期权价格的影响.     

一类具有时滞的Liénard方程的调和解

利用Mawhin的重合度理论讨论一类具有时滞的Liénard方程x″(t)+f(x(t))x′+g(x(t-τ(t)))=p(t)的调和解,推广和改进了现有的结果.     

扰动Fej\'{e}r点上复Hermite插值的联合逼近

$D$是复平面中由闭Jordan曲线$\Ga$围成的单连区域. 考虑在$\Ga$上扰动Fej\''er点的 Hermite插值一致逼近、平均逼近和联合逼近于函数$f\in A^{(q)}(\o D)$. 该文中的逼近阶一般说来是不可再改进的, 区域的边界限制条件到目前为止是最少的. 以往的全部同类结果都包括在该文中作为特殊情形, 由于该文方法上的改进, 简化和省去了以往 某些证明过程.     

等电位间隔-电位滴定法

对两点电位滴定法作出改进,提出了等电位间隔-电位滴定法。由数学推导证明,当P1的数值(P1为V1与Ve的比值以百分率表示;V1为在第1测量点所耗滴定剂的体积;Ve为滴定终点时所耗滴定剂的体积)达到95%,且在两点间的电位差值(ΔE)大于30mV时,滴定的相对误差(T)的计算值可达到小于0.1%。据此,在滴定过程中,记录两测量点之间的ΔE为30mV时的V及E值,当有两组数据的ΔE达到30mV并算得此时的T值≤0.1%时,即可停止滴定,并根据所给公式计算Ve及滴定结果。将此方法应用于包括中和反应、沉淀反应及氧化还原反应等多种滴定体系的电位滴定,所得结果与常规电位滴定法的测定结果一致。