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By utilizing the concepts and methods developed in Algebra Topology,Algebra Geometry and Algebra Representations,we first depicted the concepts and results of Incidence Algebra which reflects the linear structure of underlying posets and Sheaf theory which reflects the topological structure of underlying poset in the framework of Category Theory.

本文综合运用了代数拓扑、代数几何及代数表示论里发展起来的概念与方法，首先在范畴的框架下，对和偏序集的线性结构密切相关的Incidence代数，及与偏序集的拓扑结构紧密联系的层，进行了刻画。

This allows us to save bandwidth in video and image representations by subsampling the color information.

这使得我们可以借助对色彩信息的子采样来节省视频和图像信息的带宽。

The third chapter deduces the universal rules in the process of derivation. The substitution rule shows the nature of representations in two levels, the structure and the semantic levels with the features of combinatory and paradigmatic relations. The major parameter variations are interpreted with a weight on dislocation of word and the multi-functions of Wh-word in the frame work of the syntactical asymmetry. The fourth chapter further discusses the innate reasons of the English Wh-move and Korean Wh-in-situ in the syntactical system after summarizing the main findings of the comparison.

而后，在第三章采用演绎方法对英朝Wh-问句转换生成的共性规则，即指代规则在结构和语义两个层级上的指代特征及其聚合组合关系特征进行了分析；以句法不对称性为理论依据，以错位语序和wh-词的一词多功能为着眼点，对主要参数差异进行了生成解析；在第四章，对英朝Wh-问句对应关系和上述对比研究进行归纳总结的基础上，在句法系统中进一步讨论了英语WH-移位与朝鲜语WH-原位的言内原因。

The fact that a real number might have two different decimal representations is merely a reflection of the fact that two different sets of real numbers can have the same supremum.

一个实数可以有两种不同的小数表示法，仅仅是两个不同的实数集合可以有相同的最小上界的一个反映。

The fact that a real number might have two different decimal representations is merely a reflection of the fact that two different sets of real numbers can have the same supremum.）refApostol p.12/ref /blockquote

汤姆·阿波斯托尔得出结论： blockquote 一个实数可以有两种不同的小数表示法，仅仅是两个不同的实数集合可以有相同的最小上界的一个反映。

得 (1 2r ) A 1 + A2 = 0 由条件得 4π(1 )A1 + 2A2 = P P (1 2) A1 =, A2 = P 2π 2π由及二式的联立求解,得 42 Substitute the obtained A1 and A2 into the forgoing representations, we get (1 +)P rz (1 2)r ur = R2 R + z 2πER (1 +)P z2 ω= 2(1 )+ 2 2πER R P (1 2)R 3r 2 z σr = 3 2 2πR R + z R (1 2)P z R σθ= 2 R R + z 2πR 3Pz3 3Pr z 2 σ z = 5 ,τ zr =τ rz = 2πR 2πR5 43 将得出的A1及A2回代,得(1 +)P rz (1 2)r ur = R2 R + z 2πER (1 +)P z2 ω= 2(1 )+ 2 2πER R P (1 2)R 3r 2 z σr = 3 2 2πR R + z R (1 2)P z R σθ= 2 R R + z 2πR 3Pz3 3Pr z 2 σ z = 5 ,τ zr =τ rz = 2πR 2πR5 44 §8-4 Spherically Symmetric Problem For Space Among spatial problems, if the elasticity body's geometric shape,restraint condition and any external factors are symmetrical in a certain point (any plane which passes this point is all symmetrical one),then all stresses,strains and displacements are symmetrical in this point.

§8-4 空间球对称问题在空间问题中，如果弹性体的几何形状，约束情况以及所受的外来因素，都对称于某一点(通过这一点的任意平面都是对称面)，则所有的应力，形变和位移也对称于这一点。这种问题称为空间球对称问题。

And local coordinate representations of left invariant symplectic structure and symplectic left invariant vector field on the Symplectic-Lie group are given.

还给出了辛李群上左不变辛结构和辛左不变向量场的局部坐标表示。

Objective: To evaluate the MRI representations of pigmented villonodular synovitis of the knee joint, and increase the recognition of the disease.

目的：分析膝关节色素沉着绒毛结节性滑膜炎的MRI影像表现，提高对本病的认识。

These names are used to signify either a series of pictures or tableaux representing certain scenes in the Passion of Christ, each corresponding to a particular incident, or the special form of devotion connected with such representations.

这些名称是用来表明要么一系列图片或tableaux代表某些场景耶稣受难记，每个对应於一个特定的事件，或特殊形式的奉献与这种表述。

Some of Mr. Talbot's early models were non-functional representations like the ones shown here.

一些Talbot先生的早期模型，非功能性的陈述一样，那些在这里显示。

Foods high in this vitamin include oily fish such as salmon, tuna and, and fish liver oils.

维生素D含量高的食物包括诸如大麻哈鱼、金枪鱼和鲭鱼之类的油鱼以及鱼肝油。

We need you to cosign our public letter demanding that press intimidation cease immediately, and that all charges be dropped.

我们需要您cosign我们的公共信，要求记者立即停止恐吓，并要求所有收费下降。