数的几何

First we prove that 0 is an eigenvalue of the operator with geometric multiplicity one,next we prove that all points on the imaginary axis except for zero belong to the resolvent set of the operator,last we prove that 0 is an eigenvalue of the adjoint operator of the operator.

首先证明0是对应于该排队模型的主算子的几何重数为1的特征值，其次证明在虚轴上除了0以外其他所有点都属于该算子的豫解集，然后证明0是该主算子共轭算子的特征值。

First we prove that all points on the imaginary axis except for zero belong to the resolvent set of the operator corresponding to the model, second prove that 0 is an eigenvalue of the operator and its adjoint operator with geometric multiplicity and algebraic multiplicity one,last by using theabove results we obtain that the time-dependent solution of the model str.

首先证明在虚轴上除了0以外其他所有点都属于该算子的豫解集，其次证明0是对应于该系统的主算子及其共轭算子的几何与代数重数为1的特征值，由此推出该系统的时间依赖解当时刻趋向于无穷时强收敛于系统的稳态解。

Ringel realized positive parts of semisimple Lie algebras in the framework of Ringel-Hall algebras. The main result of this thesis is to build a geometric and topological model over triangulated categories such as derived categories and stable module categories of repetitive algebras. We defines a Lie bracket by Euler characteristics of constructible subsets and thus realizes infinite dimensional Lie algebras of various types with non-degenerated bilinear form.

本文的主要结果是在导出范畴和重复代数的稳定模范畴等三角范畴水平上建立相应的几何-拓扑模型，并利用相应可构集的欧拉示性数定义了一个Hall代数的交换子乘法，从而在三角范畴水平上实现了一大类无限维李代数的整体构造，并且这类李代数本质上都具有非退化的不变双线性型。

It defines the vector norms as satisfaction function to revise the weighting factors of metrics given by analytic hierarchy process. Meanwhile, the scheme exploits vector geometrical relationships in Hilbert sub-space basing on revised weights to measure similarities between vectors of network ability and user target.

该算法定义Hilbert空间中的向量范数表征满意函数，以修正由层次分析法给出的各指标权重因子；并利用基于修正权重因子的Hilbert子空间中向量间的几何关系，衡量网络参考向量与用户目标向量间的相似性，选择与用户需求最匹配的网络。

The new technique reduced the distance ladder to three "rungs":(1) The distance to galaxy NGC4258 is measured using straightforward geometry and Kepler's laws;(2)Cepheids in six more distant galaxies are used to calibrate the luminosity of Type Ia supernovae;(3) The Hubble constant is measured by observing a brighter milepost marker, Type Ia supernovae, in more distant galaxies hundreds of millions of light-years away, embedded in the expanding universe.

这种新技巧简化了距离跳跃为三个"阶梯"：1、星系NGC 4258的距离采用开普勒定律和简单直接的几何方法精确测量；2、在6个更远的星系中的造父变星用来校准Ia超新星的光度；3、深嵌于数亿光年外的膨胀宇宙中的星系中的Ia超新星——一种遥远而明亮的量天尺，被用于精确测定哈勃常数。

In order to find a powerful assistant computation tool for further analysis and design of multilayer optical coatings,an analytical model is mathematically established for accurate calculation of the first and second derivatives of the spectral coefficients of multilayer optical coatings with respect to layer parameters like thickness,real refractive index and extinction coefficient. It is based on the matrix theory of calculating the spectral coefficients of multilayer optical coatings and is achieved by perfectly using the trace operation of matrix.

为了寻找一种膜系深入分析与设计的有力辅助计算工具，从光学薄膜光谱系数的矩阵计算理论出发，基于对矩阵求迹运算的巧妙运用，从数学上建立了准确计算膜系光谱系数关于膜层几何厚度、实际折射率和消光系数等膜层参数的一阶和二阶偏导数的解析模型。

Using quasi birth and death chain and matrix-geometric solution method, we obtain the distribution of the number of customers in the system, the average number of the customers and the average sojourn time of a customer in the stationary state.

应用拟生灭链以及矩阵几何解的方法，本文给出了稳态下顾客数的概率分布、平均队长以及顾客的平均逗留时间，最后通过数值例子说明我们的模型可以较好的模拟一些实际问题。

It points out: a rational arrangement of supplementary cathode can greatly uniformize the handsaw temperature duo to its double actions of redistributing heat source and reducing thermal radiation; less shield layers at the top of the furnace leads to more uniform horizontal temperature distribution. The horizontal plate between two rows of handsaws can enhance the radiative heat transfer at the center place, and therefore can reduce the temperature difference along both horizontal and vertical directions.

指出：辅助阴极具有重新分配炉内的热源分布和隔热保温的双重作用，合理添加辅助阴极对改善料筐内温度场的均匀性具有重要的作用；在渗金属炉的顶部减少辐射屏层数，可以在保证竖直方向满足工艺要求的同时改善水平方向的温度场的均匀性；料筐的几何结构对温度场有重要影响，锯条背之间的距离以60毫米为好；减少料筐材料的发射率有利于局部控制料筐温度。

Study: the first day: ceramic perm on the theory and analysis of the principles of ceramic perm hair physi sign Pi and mathematics, made a single film roll with the law, made into bars at the end of the display, three bars into technology, into the bars of the nine changes in the bar when the bar into the core of the film made with the point of view, the core of the ring a few bars And calculation of the perm and the relationship between the separation and shape the relationship between the perm, hair texture and appearance to the effect, the geometric shapes scald Division

陶瓷烫发原理毛发生理学知识，设计原则分析，设计的适应性，陶瓷烫的元素解析，发质与烫发的关系，裁剪结构与烫发的关系，烫发设计与数学圆周率，单片发片与卷法，进杠时发尾的摆放情况，三个进杠技术，九个进杠变化，进杠时杠芯与发片的角度，杠芯的圈数和计算与烫发的关系，分出形状与烫发的关系，发丝的纹理走向与外观效果，造型烫的几何分区

Study: the first day: ceramic perm on the theory and analysis of the principles of ceramic perm hair physiology knowledge, design principles, the design of adaptive, hot ceramic element analysis, hair perm and the relationship between structure and cut the relationship between the perm, Hair Design Pi and mathematics, made a single film roll with the law, made into bars at the end of the display, three bars into technology, into the bars of the nine changes in the bar when the bar into the core of the film made with the point of view, the core of the ring a few bars And calculation of the perm and the relationship between the separation and shape the relationship between the perm, hair texture and appearance to the effect, the geometric shapes scald Division

陶瓷烫发原理毛发生理学知识，设计原则分析，设计的适应性，陶瓷烫的元素解析，发质与烫发的关系，裁剪结构与烫发的关系，烫发设计与数学圆周率，单片发片与卷法，进杠时发尾的摆放情况，三个进杠技术，九个进杠变化，进杠时杠芯与发片的角度，杠芯的圈数和计算与烫发的关系，分出形状与烫发的关系，发丝的纹理走向与外观效果，造型烫的几何分区

We have no common name for a mime of Sophron or Xenarchus and a Socratic Conversation; and we should still be without one even if the imitation in the two instances were in trimeters or elegiacs or some other kind of verse--though it is the way with people to tack on 'poet' to the name of a metre, and talk of elegiac-poets and epic-poets, thinking that they call them poets not by reason of the imitative nature of their work, but indiscriminately by reason of the metre they write in.

索夫农 、森那库斯和苏格拉底式的对话采用的模仿没有一个公共的名称；三音步诗、挽歌体或其他类型的诗的模仿也没有——人们把&诗人&这一名词和格律名称结合到一起，称之为挽歌体诗人或者史诗诗人，他们被称为诗人，似乎只是因为遵守格律写作，而非他们作品的模仿本质。

The relationship between communicative competence and grammar teaching should be that of the ends and the means.

交际能力和语法的关系应该是目标与途径的关系。