退化时滞差分系统的通解

讨论具有时滞的退化差分系统，给出其初始函数的相容性条件，并给出其通解，最后举例说明之．     

A numerical method for the first-order wave equation with discontinuous initial data

We introduce a method, constructed such that numerical solutions of the wave equation are well behaved when the solutions also contain discontinuities. The wave equation serves as a model problem for the Euler equations when the solution contains a contact discontinuity. Numerical computations of linear equations and the Euler equations in one and two dimensions are presented. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 353–365, 1998     

广义线性模型在汽车延保风险保费测算中的应用

基于保险公司2010年1月—2019年3月的实际保单数据样本,分别运用广义线性模型中的泊松模型和伽玛模型测算出险频率和案均赔款,构建风险保费测算模型,对影响风险保费的因素进行定量研究及分析.结果表明:该方法能够构建多个变量与风险保费的数值关系,减少了信息的损失,得到的费率表可作为实际应用的参考.最后,通过该方法测算结果与市场定价的实例比较对方法的合理性与优越性进行了说明.     

Necessary and sufficient conditions for the lipschitzian invertibility of nonlinear difference operators in the spacesl p (ℤ, ℝ) with 1≤p≤∞with 1≤p≤∞

Necessary and sufficient conditions for the Lipschitzian invertibility of the difference map

方程u_(tt)=u_(xxt) f(u_x)_x初边值问题的差分法

１．引言方程是在国内外引起广泛关注的一类重要的非线性发展方程．文［１］在函数ｆ（ｓ）满足局部 Ｌｉｐ－ｓｃｈｉｔｚ条件及单调性条件（ｆ（ｓ２）－ｆ（ｓ１））（ｓ２－ｓ１）＞ ０的假设下得到了（１．１）初边值问题整体弱解的存在与唯一性;文［２］用 Ｇａｌｅｒｋｉｎ方法,研究了（１．１）的初边值问题,周期边值问题和初值问题,并在函数ｆ’（ｓ）下方有界的假设下得到了整体强解的存在与唯一性． 本文在有限区域 ＱＴ＝［０,１］×［０,Ｔ］（Ｔ＞ ０）上讨论方程（１．１）带有初值条件和边值条件（ｕ（ｘ,ｔ）为未知…     

时间空间均为二阶的新型NND差分格式

张涵信的研究表明,为了避免激波前后差分解的波动,在差分格式的改型方程中三阶导数的系数在激波上游必须是正的,而在激波下游则必须是负的.据此提出了一种新型的无波动、无自由参数耗散性的差分格式,它对时间和空间都是二阶的.证明了此格式是TVD的,而且是推广的二阶Годунов格式.在处理有激波的流场时,此格式是Lax-Wendroff格式的改进和推广.给出了若干算例,计算结果表明,此格式不仅无波动,而且具有形式紧凑、应用方便、分辨率高、稳定性准则中的Courant数较大的优点.     

高阶非线性差分方程的全局吸引性

研究了差分方程 xn 1 =a - bxn- k A - xn( a≥ 0 ,A≥ b≥ 0 )的全局稳定性和正解的周期性质 .证明了方程的一个正平衡点是一个全局吸引子 ,并给出了相应的吸引域     

带强耗散项的拟线性波方程的数值解

研究了一类拟线性波方程的数值解．构造了带强耗散项的拟线性波方程的三级差分格式,并证明其收敛性,估计了差分解的误差．最后给出数值例子．     

On (p a , p b , p a , p a-b )-Relative Difference Sets

This paper provides new exponent and rank conditions for the existence of abelian relative (p ^a,p ^b,p ^a,p ^a–b)-difference sets. It is also shown that no splitting relative (2^2c,2^d,2^2c,2^2c–d)-difference set exists if d > c and the forbidden subgroup is abelian. Furthermore, abelian relative (16, 4, 16, 4)-difference sets are studied in detail; in particular, it is shown that a relative (16, 4, 16, 4)-difference set in an abelian group G Z₈ × Z₄ × Z₂ exists if and only if exp(G) 4 or G = Z₈ × (Z₂)³ with N Z₂ × Z₂.     

A highly accurate numerical solution of a biharmonic equation

The coefficients for a nine–point high–order accuracy discretization scheme for a biharmonic equation ∇ ⁴u = f(x, y) (∇² is the two–dimensional Laplacian operator) are derived. The biharmonic problem is defined on a rectangular domain with two types of boundary conditions: (1) u and ∂²u/∂n² or (2) u and ∂u/part;n (where ∂/part;n is the normal to the boundary derivative) are specified at the boundary. For both considered cases, the truncation error for the suggested scheme is of the sixth-order O(h⁶) on a square mesh (h_x = h_y = h) and of the fourth-order O(h⁴_xh²_xh²_y h⁴_y) on an unequally spaced mesh. The biharmonic equation describes the deflection of loaded plates. The advantage of the suggested scheme is demonstrated for solving problems of the deflection of rectangular plates for cases of different boundary conditions: (1) a simply supported plate and (2) a plate with built-in edges. In order to demonstrate the high–order accuracy of the method, the numerical results are compared with exact solutions. © John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 13: 375–391, 1997