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本文研究了三维Minkowski空间中直线汇的一些性质,特别是关于类时线汇的性质.讨论了线汇基本元素的存在性,并证明了关于三维Minkowski空间中类时线汇的配分参数的一个结果,推广了苏步青1927年的—个成果. 相似文献
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In this article the reflection coefficient of linear transition wedges is discussed,and an analyticalexpression and a simple real expression of the reflection coefficient under W.K.B.approximationare derived.The approximate expression of the reflection coefficient proves to be simple and con-venient for the design of absorbers. The sound absorbent structure of rib is also computed and analyzed,with emphasis on the rela-tionship between the size of the structure and the parameters of the material. In design of two types of wedges mentioned above,for the required frequency range,the materialperameters can be chosen properly and the dependence of the Wedge length on the lower limit fre-quency can be determined easily based on the derived expression.The theoretical computationsagree well with the experimental results. 相似文献
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研究了由三维Minkowski空间$E^3_1$中一个类空曲面$S_1$上一个单参数测地曲线族的切线所构成的直线汇$T$,它以$S_1$为一个焦曲面.证明了$T$的两个可展曲面族沿着第二个焦曲面$S_2$的正交曲线网相交的充要条件是$S_1$是可展曲面.对于$T$的两个焦曲面$S_1$和$S_2$之间沿着同一光线的对应,还证明了其保持渐近曲线网的充要条件.最后,研究了$T$的正交曲面$S$,并且证明了如果$S$是$E^3_1$中的一个极大曲面,那么,$T$的焦曲面$S_1$和$S_2$之间沿着同一光线的对 相似文献
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In this paper, we construct a kind of Weingarten surfaces in E3 and study its geometric properties. We first derive an explicit diffierential relationship between the principal curvatures of them. Then we prove an existence theorem of this kind of surfaces with prescribed principal curvatures. At last, we present two examples involving the rotation surfaces as the special case, and present several figures to the second example. 相似文献
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Consider SE(3)as a submanifold of the Euclidean space E12.At first,the intrinsic and extrinsic geometries of SE(3)are studied.Then the Frenet typed equations for curves in SE(3)are derived.The relationship between the k-th order covariant curvatures of a curve in SE(3)and the parametric equation of its pre-image in se(3)is established.Finally,some kinds of curves in SE(3)with vanish 5-th order covariant curvature are constructed.The behaviours of these curves are exhibited. 相似文献
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We proved that there exists a family of complete oriented minimal surfaces in R3 with finite total curvature-4nπ,each of which has 0 genus and two ends,and both of the ends have winding order n,where n ∈ N,and discussed the symmetric property for special parameters. 相似文献
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Let M be a closed surface with positive Gauss curvature minimally immersed in a standard Euclidean unit sphere S~n.In this paper,we choose a local orthonormal frame field on M,under which the shape operators have very convenient form.We also give some applications of this kind of frame field. 相似文献
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