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Applying whitening process and Gram-Schimdt orthogonalization and orthogonal subspace projection, an optimal transformation matrix is designed to minimize the ratio of intra-class distance to inter-class distance while imposing the constraint that different class centers after transformation are along specifically directions that are orthogonal each other.

以线性变换后样本的类内距离与类间距离之比最小作为准则函数，同时加上约束条件使变换后的样本中心沿着特定的正交方向，通过白化变换、Gram-Schimdt正交化和正交子空间投影求解约束准则函数得到最优变换矩阵。

Through S-wave polarization scanning mode of ultrasonic impulse testing, rock samples with three different properties are measured to evaluate the variation of S-wave velocity in three perpendicular coordinates. By analyzing S-wave splitting of three directions and polarization of the maximum or minimum speed S-wave amplitudes, we think that the velocity orthotropy and fracture orientation observed in the grain sandstones and crack marble samples can be estimated in terms of the polarization and velocity of S-wave. Also, perpendicularity characteristics on the two types of rocks can attribute to the bedding and structure of rocks (directional grains or crystallize).

在实验室通过选择了三种不同岩性的岩石，采用超声脉冲测试方法中的横波偏振扫描方式，观测了岩石样品三个坐标方向上的横波速度变化，通过分析三个传播方向上出现横波分裂的差异，以及出现最大或最小快慢横波振幅的偏振方向发现，可从横波偏振方向和速度值判断出纹理砂岩和裂隙大理岩样品存在不同程度的速度正交各向异性和裂隙方向等特征，认为这两种岩石的正交特性的原因是岩石的层理或裂隙与岩石本身的结构构成的。

Finally, it reflects the problems in this study, and points out the directions of further step.

最后，反思了本文研究存在的问题，指出了进一步研究的方向。

Outside from the inside and outside the tangent way to cut into the curved outer edge to the APEX point, then along the outer edge of the exit turn driving directions ...

外内外的切线方式就是由弯道外沿向APEX点切入，再沿着弯道外沿驶出的驾驶路线。。。。

Finally in this thesis,the problems of research and directions of research in the future have been outlined.

最后，本文还指出了一些实验过程中的不足之处，并为今后类似课题提出了进一步研究发展的方向。

At last, this paper outlines future research directions.

最后，对未来的工作进行了展望。

If you are using an over-the-counter medicine, follow the directions on the label unless otherwise directed by your doctor.

服用非处方药时，如无医嘱规定，应按药品标签说明服药。

At last, the possible future research directions are discussed as references for the research of Internet overlay routing.

最后讨论了未来可能的研究方向，为互联网覆盖路由的研究提供参考。

He twirls in reversed directions a clouded cane, then wedges it tight in his oxter.

他朝相反的方向旋转着一根有云状花纹的手杖，随后又把它紧紧夹在腋下。

Carefully follow the directions in the pamphlet provided in order to avoid damaging your watch.

仔细按照我们提供的小册子的指示，以避免损坏您的手表。

It has been put forward that there exists single Ball point and double Ball points on the symmetrical connecting-rod curves of equilateral mechanisms.

从鲍尔点的形成原理出发，分析对称连杆曲线上鲍尔点的产生条件，提出等边机构的对称连杆曲线上有单鲍尔点和双鲍尔点。

The factory affiliated to the Group primarily manufactures multiple-purpose pincers, baking kits, knives, scissors, kitchenware, gardening tools and beauty care kits as well as other hardware tools, the annual production value of which reaches US$ 30 million dollars.

集团所属工厂主要生产多用钳、烤具、刀具、剪刀、厨具、花园工具、美容套等五金产品，年生产总值3000万美元，产品价廉物美、选料上乘、质量保证，深受国内外客户的青睐