几何的

Linear Algebra is mainly a subject which studies the linear structure of finite dimensional linear space and its linear transformation while linear concept is in itself from the old Euclid Geometry. The concept of "Linear Space" is a kind of algebraic abstract. In many fields of modern engineering project and technology, because of the influence of computer and graph showing, the algebraic disposal of geometric questions, the visual disposal of algebraic questions, algebra and geometry are tightly combined.

线性代数主要是研究有限维线性空间及其线性变换这一代数结构的学科，而线性概念究其根源则是来自古老的Euclid几何，线性空间概念是几何空间的一种代数抽象，在现代工程技术的许多领域里，由于计算机及图形显示的强大威力，几何问题的代数化处理，代数问题的可视化处理，把代数与几何更加紧密地结合在一起。

Then we re-sampling all signals defined on the surface of the original triangle mesh at the vertices of the spherical subdivision mesh and get a set of discrete geometry signals with subdivision topology which can be compressed by using spherical wavelet.

于是，在参数域内位于细分网格顶点处对定义在参数网格表面上的各种几何信号进行重采样，可得到新的具有细分结构的几何信号近似表示原始几何信号，以此满足球面细分小波对处理对象的细分结构要求，从而使得用球面细分小波对几何信号进行压缩得以实现。

The vector has the rich actual background and the widespread application function, it has the algebra and the geometry dual statuses, causes the algebra geometrization, the geometry algebra, has communicated the algebra, the geometry and the trigonometric function, has the good analysis method and the complete structure.

向量具有丰富的实际背景和广泛的应用功能，它具有代数和几何双重身份，使代数几何化、几何代数化，沟通了代数、几何与三角函数，具有良好的分析方法和完整的结构。

conformal geometric algebra is a kind of new geometric representation and geometric computation tool, and it has properties of geometric intuitiveness, compactness, high efficiency, unification and elegance.

摘 要：共形几何代数是一种新的几何表示和几何计算工具，它具有直观、简洁、高效、统一、雅致等特性。

Recent studies on the geometric inequality for the n-dimensional simplex produce many important geometric inequalities;however,the study on the problem of the geometric inequality for the pedal simplex has been very few.

关于n维单形的几何不等式研究，近期建立了许多重要几何不等式，然而，关于垂足单形几何不等式研究还是比较少。

We extended the Safety Margin theory, the flight parameters transferred to the singular space through the SVD method. This conception created the Safety Margin Terrain and showed the geometry properties of current flight.

而将飞航安全几何化的观点再做推展，透过奇异值分解的方法，将参数转换至奇异空间，再利用几何方程式，拟合飞航安全裕度於奇异空间中的曲线，求得安全裕度地形，并由此模型计算出每一航班之几何变化，并藉由此方法可求得当下飞航安全裕度的几何特性，表示当飞航安全的状态。

Many geometric properties of spaces may be pointwise, pointwise geometric properties were the localization and meticulous of properties of spaces.

空间中许多几何性质可以点态化，点态几何性质是空间几何性质的局部化、精细化。

Rresults from those studies can be summariazed as follow:(1) A preliminary study no correlationship between the UV-VIS reflection spectrum of tomato fruit surface and the lycopene amount of tomato fruit was undertaken. Based on observation from this study, a damage-free and in-situ detection technique of lycopene amount from tomato was developed with UV-VIS reflection spectroscopy;(2) The geometrical isomers of lycopene were separated successfully on C30-HPLC-PDA-ELSD. The absorption coefficients of Z-isomers were consequently dedermined. The geometrical isomer composition of lycopene could therefore be assessed. Those efforts formed a solid base to identify the natural product from synthetic compound of lycopene;(3) Lycopene resource from the fruit of Autumn oliver was proved to be available for industrial application. An extraction methos of lycopene from the fruit of Autumn oliver by supercritical carbon dioxide was developed at laboratory scale;(4) A method to extract lycopene by supercritical liquid with improved efficiency was developed; Data from this investigation suggested that a proper raw material pre-extraction process was important for a better extraction efficiency;(5) Variation in the geometrical isomer composition of lycopene during its metabolish in rat was assessed. A large amount of Z-isomers were observed. This variation took place in serum;(6) The absorption rate and accumulation in serum of natural lycopene in rat were assessed;(7) Ability to quench singlet oxygen by different geometrical isomers of lycopene was compared;(8) It was detected that whether natural lycopene had functions to regule blood-lipids and LDL antioxidation;(9) A C31 degradation piece of lycopene was found in the prostate gland of rat.

研究结果包括：[1]应用UV-VIS反射光谱法建立了番茄果实中番茄红素含量的无损伤、现场检测技术；[2]应用C30-HPLC-PDA-ELSD技术实现了对番茄红素几何异构体的分离，测定了不同顺式异构体的吸光系数，建立了天然番茄红素几何异构体组成的检测方法，为区分和鉴定人工合成品和天然产物奠定了基础；[3]证实了秋橄榄果实中的番茄红素资源具有工业开发价值，并建立了超临界CO_2萃取的实验室方法；[4]探索了提高番茄红素超临界流体萃取效率的方法，证明了物料前处理对提高萃取效率起了极其重要的作用；[5]观察了番茄红素在大鼠体内几何异构体组成的变化情况，发现了大量顺式异构体的存在，并证实了几何异构体组成在血清中发生了显著变化；[6]测定了天然番茄红素在大鼠体内的吸收率和在大鼠血清中的动态积累规律；[7]比较了不同番茄红素几何异构体淬灭单线态氧的能力；[8]检测了天然番茄红素是否具有调节血脂作用和抗低密度脂蛋白氧化的功能；[9]首次发现大鼠前列腺内存在番茄红素C31降解片段，并证实其仍具有淬灭单线态氧的能力。

The GSP computer-assisted instructional method is used in the former group while the traditional narrative teaching method is utilized in the latter group. The experiment is conducted for 5 weeks, and the teaching content is geometry,(the congruity of two triangles and the properties of parallelograms.) After the five weeks' experiment, a comparison of learning achievements and learning attitudes is made between the two groups. In addition, an investigation of the experimental group's learning attitude computer-assisted instructional method is made.

本实验教学为期五周，内容为国中几何课程，含两三角形全等与平行四边形，经实验教学之后，比较两组学生几何学习成就及数学学习态度之改变和针对实验组使用GSP 电脑辅助学习几何课程的态度调查，研究结果各项资料经统计处理分析之后获得下列三项主要结论

This paper discusses the close relation of geometry and architectural aesthetics in the aspects of ratio scale, geometric curved lines, geometric curved surfaces, etc.

几何与建筑美存在着密切关系，从比例分割、几何曲线、曲面等方面探寻了几何与建筑美的奇妙关系。

The labia have now been sutured together almost completely.The drains and the Foley catheter come out at the top.

此刻阴唇已经几乎完全的缝在一起了，排除多余淤血体液的管子和Foley导管从顶端冒出来。

To get the business done, I suggest we split the difference in price.

为了做成这笔生意，我建议我们在价格上大家各让一半。