半线性映射

The reference domain is assumed to be a bounded open set of R~N with boundary Γ of class C~2. We investigate in this paper the null controllability for the semilinear parabolic equations in non-cylindrical domains. The fixed point method is used in the proof.

本文讨论了定义在上述非柱形区域中的半线性抛物方程零能控性，我们使用的方法主要是通过同胚映射将非柱形区域中的抛物方程转化为柱形区域中的抛物方程，再利用不动点方法得到半线性抛物方程的有关结果。

This paper researches linear maps preserving orthogonality,obtains the linear maps preserving othrogonality,it is either a rank -declining or rank -keeping map or a map with nilpotent element in its codomain.

利用分块成向量的方法证明了MnMn(F为域F上所有n×n矩阵构成的乘法半群上的n×n拟正交矩阵组至多含有n个矩阵，利用方程组的解的理论证明了Mn中与给定矩阵A构成两两拟正交矩阵组的矩阵个数不超过n-Rank+1，从而得到Mn上保持拟正交性的线性映射φ要么是降秩的或者保秩的映射，要么φ的值域中含有幂零元。

In this paper the topological properties of solution set of non-autonomous differential inclusions are discussed,and the fact that the mild solution set of Cauchy is a retract of a convex subset of a Banach space is proved.

讨论了半线性微分包含解的拓扑性质，证明了非自治情况下其适度解集是一Banach空间的凸子集的收缩核，且收缩映射连续依赖于初值。

For regular topology surface, intermediate surface local texture mapping are used; for irregular topology surface, subdivision surface local texture mapping are used. So different topology surface using different texture mapping methods can solve the contradiction between texture effect and processing speed when they are dealt with by single method. The three judge conditions of texture distortion in the process of mapping onto the sphere surface are discussed and the exiting algorithms of mapping are analyzed, the new algorithms of mapping onto the sphere surface are presented. In order to enhance the realistic of graphics, a new function of wood texture is presented. OpenGL is also introduced in this papers and some realization examples of texture mapping based on OpenGL under the environment of VC++ and POV-RAY are presented in some chapters.

对于简单拓扑表面，利用改进的两步纹理映射，对于复杂拓扑表面利用新的面片分割算法，初步解决了颜色纹理中速度与走样之间的矛盾；通过对球面纹理时纹理不变形的三个判断条件的研究，分析了现在各种球面纹理映射算法，并在此基础上提出了一种基于等面积的半球面纹理映射算法，明显减少了球面纹理的纹理变形；针对现有的木纹纹理中，两种表示木纹的颜色差距表现出的颜色突变问题进行研究，提出对这两种颜色进行线性插值或二次插值，使生成的木纹纹理颜色更加连续，更加逼真；在VC++环境下，通过调用Open GL的图形库及在Pov-Ray软件环境下，实现了参数化纹理、球面纹理、凹凸纹理及木纹纹理等各种算法。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。