条件方程

InSection 2,we give several sufficient conditions for the existence of one solution,multiplesolutions and infinitely many solutions of the Sturm-Liouville bvps via the generalizedpolar coordinates.Then in Section 3,the existence of positive solutions are proved undersuperlinearity,sublinearity and many other conditions by a fixed point theorem in cones.Our results have generalized those in many articles.A detailed discussion of periodic solu-tions of a kind of functional differential equations with high-order Laplacian-like operatorcan be found in Section 4 and this subject has not been studied before.

在第二节，我们定义了一种新的坐标变换-广义极坐标，并利用它讨论了p-Laplacian算子和Laplacian-型算子的Sturm-Liouville边值问题，分别得到了存在一个解、多个解、无穷多个解的多个充分条件；第三节研究p-Laplacian算子的Sturm-Liouville边值问题正解的存在性与多重性，采用的是锥上的不动点定理，全面推广了这一方面已有的结果；对目前研究较少的高维Laplacian-型算子及带有Laplacian-型算子的泛函微分方程的周期解问题，我们在第四节做了一些研究，这也是拓扑方法的一个应用。

In chapter two, we discuss the existence of mild and strong solutions of a nonlinear integrodifferential systems of Sobolev type with nonlocal condition in Banach spaces.

第二章讨论了一类带有非局部条件的Sobolev型方程解的存在唯一性理论。

The modifined formula of interlaminar stresses is derived and by using continuous conditions.

给出了复合材料层合板壳弯曲变形的高阶位移模式，利用连续条件，导出了层间应力修正公式，并推导了相应的有限元方程。

Anon-Newtonian thermal elastohydrodynamic lubric ation model is set up to analyze running-in process under heavy load.

建立了非牛顿流体热弹流润滑数学模型，对重载条件下磨合过程进行数值分析，在考虑具有粘塑性本构的非牛顿流体时，采用了高效粘度法对建立的方程进行了解算。

Compared with determination of the chroma and melanoidin, the influences of drying temperature on two indexes were attained.

在凋萎温度48~52℃和焙焦温度78~82℃条件下麦芽色度与类黑精含量的回归方程为：y=1.7048χ+0.0554，r为0.995，呈良好的线性相关。

The equation of states under high temperatures and high pressures, phase -transition and metalization for H_2 and its isotopes are one of the hot topics of scientific studies for a long time.

氢及其同位素的高温高压状态方程、相变与金属化等问题是长期以来科学研究的热点课题之一；氢、氦分别是结构最简单的双原子和单原子分子，在冲击加载条件下，氢，氦材料的热力学特性一直是从事凝聚态物理研究的理论和实验工作者非常关注的前沿研究课题之一。

We analyzed primary test factor through multi-element linear regression model. We finally concluded the optimum conditions for tapioca starch micronization.

利用多元线性回归进行方差分析，分析了试验因素对回归方程的影响效应，最后得出优化的木薯淀粉微细化处理条件。

From Maxwell's equations, with material constitutive relation of optically active crystal and boundary conditions of electric field on the boundary between isotropic media and crystal, through coordinate transformation, the formula of the direction of refracted wave for arbitrary direction incident monochromic plane wave was derived. Furthermore, based on the unit vector of direction of refracted wave, eigen waves of electric field, electric displacement vectors and direction of energy flow can be easily obtained.

从麦克斯韦方程组出发，结合旋光晶体的物质方程以及单色平面波从各向同性介质入射到晶体界面时电场的连续性边界条件，通过晶体主轴坐标系和界面坐标系的坐标变换，推导了任意入射方向的单色平面波在晶体界面上的折射方向的求解公式，进而利用所得的折射方向求解晶体中折射波的电场本征模、电位移矢量本征模和光线方向。

It is shown that these two sequences converge monotonically to a unique solution of the finite difference system.

给出一类求解具时滞边界条件的时滞反应扩散方程的数值方法，证明了迭代序列的单调收敛性以及差分格式的收敛

Researches are made to find out the active tracing measurement strategy of crankshaft roundness error during noncircular grinding process .

本文对曲轴连杆颈非圆磨削过程中圆度误差的在线跟踪测量策略展开研究，推导了测量系统跟踪运动方程，针对在频域分析时对3个传感器之间线性相关性的要求，论述了满足均匀采样的约束条件。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。