一类三阶中立型时滞方程的周期解

利用Fourier级数理论和实分析不等式技巧，讨论了一类三阶中立型时滞差分方程∑i=0^3aix^(i)(t) ∑j=1^m∑i=0^3ujix^(i)(t-hj)=f(t)的周期解的存在性与唯一性，给出了若干新的充分判据，并完善一些己知文献的结果。     

矩阵方程X-m∑i-1A*iXδAi=Q的正定解

基于正规锥上单调算子的不动点定理,本文研究非线性矩阵方程X-m∑i-1A*iXδAi=Q的正定解.给出了正定解的存在性定理,并且构造了求解的m步定常迭代方法,最后证明了该迭代法的收敛性.     

一类四阶方程边值问题正解的存在性与多重性

本文得到了四阶方程边值问题u^（4）=f（u（x）），u′（0）=u″（0）=u′″（0）=0，ku（1）=u′″（1）相应的Green函数G（x，t）。从而将该问题转化为Hammerstein型积分方程，并利用锥拉伸与锥压缩不动点定理，讨论了其正解的存在性与多重性，得到了相应的结论。     

超级电容器用活性炭中钾离子的解吸动力学研究

利用解吸动力学的4个方程,Elovich方程:qt=a+blnt;一级动力学方程:ln(1-qt/qe)=-ka t;指数方程:lnqt=lna+blnt;抛物线扩散方程:qt=a+bt,对超级电容器用活性炭中钾离子的解吸过程进行了模拟,Elovich方程的拟合关系最好,r=0.994;一级动力学方程次之,r=0.992,指数方程和抛物线方程的拟合结果一般,两者r均为0.973。     

矩阵方程X-A~TX~(-1)A=Q的牛顿迭代解法

非线性矩阵方程X-A~TX~(-1)A=Q在控制理论、动态规划、插值理论和随机滤波等领域中具有广泛的应用.本文给出了该矩阵方程的等价形式并利用牛顿法对该等价矩阵方程进行求解.通过定义一类用牛顿法求根时产生的矩阵序列与用牛顿法求解矩阵方程时产生的矩阵序列相同的矩阵函数,证明了由牛顿迭代法求解矩阵方程时产生的矩阵序列包含在具有唯一解的闭球内,并收敛到闭球内的唯一解.给出了该方程近似解与真解的误差估计式,并给出了说明牛顿算法对该方程求解有效性的数值例子.     

梯度涂层高炉风口的涂层梯度方程选择

采用有限元分析软件研究了具有不同梯度方程的梯度涂层高炉风口温度及应力的分布状况。结果表明：梯度涂层能够明显改变高炉风口的温度分布，缓和了涂层与基体接合界面处的应力。组成分布规律指数P=1时，涂层中应力缓和效果明显且应力值较小，从而确定最优涂层梯度方程为c=x／5。     

高阶中立型差分方程正解的存在性和渐近性

研究了一类高阶中立型差分方程△^l(Xn-CnXn-m) PnXn-k=0,n=N,N 1,N 2……正解的存在性和渐近性。利用Krasnoselskii不动点定理，给出了该类方程存在有界最终正解及当n→ ∞时其解渐近趋于零的几个充分条件。     

关于Fuzzy综合评价模型的研究

讨论了Fuzzy模型P=A(×)B=(p1,p2,…,pn)的算法规则(×)的三种情形,即Pj=max1≤i≤n[min(αi,rij)],pj=∑n)/(i=1αirij,Pj=∑n)/(i=1min(αi,rij), 以及二种评定法则:(1)简单评定法:当pk=max1≤j≤mpj时定为k级.(2)复合评定法:当∑k-1)/(j=1pj≤∑m)/(j=kpj且∑m)/(j=k+1pj≤∑k-1)/(j=1pj时定为k级,当∑k-1)/(j=1pj≥∑m)/(j=kpj且∑k-2)/(j=1pj≤∑m)/(j=k-1pj时定为(k-1)级,当∑m)/(j=k+1pj≥∑k-1)/(j=1pj且∑k-1)/(j=1pj≤∑m)/(j=kpj时定为(k+1)级.当模糊复杂度rij具有一定实际含义下,可能引发误判的三个定理.在三个定理条件下,一次性判定及联合判定均判定为k级,但当模糊复杂度rij有一定实际含义时,会发生不应判定为k级的现象.同时给出了减少误判的措施.     

一种新型高淬透性Ni-Cr-Mo-B钢的热变形本构分析

基于Gleeble单道次热压缩实验并结合OM表征手段及回归方法,研究了一种新型高淬透性Ni-Cr-Mo-B特厚板钢在850～1 150℃和0. 01～10 s-1热变形参数下的热变形行为。结果表明,Ni-Cr-Mo-B钢在热变形过程中流变应力随变形温度的升高而减小,随应变速率的增加而增大。建立的典型应变补偿Arrhenius型本构方程可用于粗略预测Ni-Cr-Mo-B钢的流变行为。考虑到应变速率、变形热对变形过程的影响,提出修正应变补偿Arrhenius型本构方程,其统计学参量Rc=0. 994 68、AARE=3. 69%、RMSE=6. 44 MPa、NMBE=1. 25%,相对误差大部分(94. 87%)在±10%之内,表明该方程具有极高的流变应力预测精度。     

对贝塞尔公式证法的探讨

根据∑^nj，k=1δjδk=0证明贝塞尔公式，长期以来被一些尝得所认同，现对此提出质疑和讨论，并从其它途径推证贝塞尔公式。     

Kovacic's algorithm and its application to some families of special functions

We apply the Kovacic algorithm to some families of special functions, mainly the hypergeometric one and that of Heun, in order to discuss the existence of closed-form solutions. We begin by giving a slightly modified version of the Kovacic algorithm and a sketch proof.     

复合材料任意壳稳定性研究(Ⅰ)──几何方程的新研究

从三维非线性理论导出,任意曲线坐标系中任意壳体的几何非线性微分方程,并修正K.Washizu的公式,以期得到更加准确的稳定方程。      

随机系统能稳性的一个注记

研究随机系统ｄｘ＝（Ａｘ－Ｂｕ）ｄｔ－（Ｃｘ＋Ｄｕ）ｄＷ的能稳性,首先组出了系统能稳性的一个充分必要条件,并通过构造一个反例指出了以往文献中的一个错误。     

复合材料任意壳稳定性研究（Ⅰ）──几何方程的新研究

从三维非线性理论导出，任意曲线坐标系中任意壳体的几何非线性微分方程，并修正Ｋ．Ｗａｓｈｉｚｕ的公式，以期得到更加准确的稳定方程。     

求解Poisson方程改进的交替方向隐式迭代格式

本文以 Poisson 方程为例,在不对节点进行重新排列的前提下,通过求解较低维数的矩阵方程,对交替方向隐式迭代格式进行了改进,降低了程序实现难度．以 Gauss 消去法为例,对改进的交替方向隐式迭代格式的计算量进行估计,发现改进的交替方向隐式迭代格式大大减少了计算量,并进一步证明了改进的交替方向隐式迭代格式与经典的交替方向隐式迭代格式的等价性．数值算例验证了改进的交替方向隐式迭代格式与经典的交替方向隐式迭代格式的等价性和改进的交替方向隐式迭代格式在计算量等方面的优越性．     

Principle of Virtual Power for thermomechanics of fluids and solids with dissipation

A fundamental variational principle, called the Principle of Virtual Power, is proposed in this paper to govern the irreversible thermomechanical processes for a material body. The principle and the corresponding variational equation of virtual velocity are formulated by integrating the classical field theories of continuum mechanics and thermodynamics. From the variational equation, we establish simultaneously the balance equations of linear momentum, of angular momentum, and of virtual internal power by applying the procedure of relaxation in Lagrangian mechanics. By assuming different types of system functions for internal power consisting of internal energy and newly introduced working dissipation, we are able to derive the constitutive equations for gas, liquid, or solid and the Fourier equation of heat conduction from the balance of virtual internal power. The combination of the law of conservation of mass, the first law of thermodynamics, and the proposed principle forms a complete set of fundamental principles for the thermomechanics of deformable bodies.     

Nonlinear electric flow across parallel plates

The electric current flowing across two parallel plates that touch each other over a circular contact is calculated. The change in the physical properties due to temperature rise caused by Joule heating is taken into account so that the current is not linearly proportional to the voltage difference. The resistance is calculated and an accurate approximation for the resistance, based on minimizing the power, is presented.     

Mean stress effects in stress-life fatigue and the Walker equation

Mean stress effects in finite-life fatigue are studied for a number of sets of experimental data for steels, aluminium alloys and one titanium alloy. Specifically, the agreement with these data is examined for the Goodman, Morrow, Smith–Watson–Topper and Walker equations. The Goodman relationship is found to be highly inaccurate. Reasonable accuracy is provided by the Morrow and by the Smith–Watson–Topper equations. But the Morrow method should not be used for aluminium alloys unless the true fracture strength is employed, instead of the more usual use of the stress-life intercept constant. The Walker equation with its adjustable fitting parameter γ gives superior results. For steels, γ is found to correlate with the ultimate tensile strength, and a linear relationship permits γ to be estimated for cases where non-zero mean stress data are not available. Relatively high-strength aluminium alloys have γ≈ 0.5, which corresponds with the SWT method, but higher values of γ apply for relatively low-strength aluminium alloys. For both steels and aluminium alloys, there is a trend of decreasing γ with increasing strength, indicating an increasing sensitivity to mean stress.     

微分方程和差分方程的多解存在性

本文首先讨论了差映射的一个映射性质:某元有无映射原象等价于映射象集是否包含此元,等价于以此元为象的映射方程的解是否存在.若有两个映射,其中一个映射的象集较大,另一个映射的象集较小,则在一定条件下,可以确定此二映射的差映射象集包含一集合,此集合的差映射原象非空,以此集合中的元为映射象的差映射方程的解存在.其次,我们运用此结论讨论了几个微分方程、差分方程多解的存在性.