查询词典 alternating tensor

Principal curvatures and principal directions are obtained by computing in closed form the eigenvalues and eigenvectors of certain 3×3 symmetric matrices defined by integral formulas, and closely related to the matrix representation of the tensor of curvature.

通过计算3×3对称矩阵的特征值和特征向量可以得出主曲率和主方向，而该对称矩阵是由积分公式定义并且与曲率张量的矩阵表达密切相关。

This paper proposes a robust filter function, called trilateral filter function, to filter the noises in the domains of surface curvature, normal and position at each sample point while the local surface is fitted in a quadratic form. By optimizing the filtering result of curvature tensor, our approach is capable of preserving the feature on the target model.

通过在扫描模型每个采样点处拟合一个二次型曲面，设计了一个鲁棒的滤波函数--三边滤波函数；应用该函数分别对模型表面上每个点的法线、曲率和位置进行滤波；通过对曲率的滤波结果进行优化，可有效地保持三维模型表面上的特征。

In this paper, a "rigid bar relative movement model" was established to illustrate the traces of the helices in wire ropes. The angular speed of a moving particle of the model was relatives to curvature tensor to derive the curvature components and torsion of helices in multi-layer wire ropes. According to long and thin rod theory of Love and Yen-Chen's theoretical model considered the contact force and frictional force, the force-deformation or force-strain relative of wire in curved wire ropes subjected axial force is derived from the curvature components and curvature increment.

本研究改以刚杆相对运动模型，直接描述钢索中钢绞线轨迹，并且透过角速度类比曲率张量之概念，推导圆弧型多层钢索内部之钢铰线之曲率分量与扭率；之后再依据Love的细长杆理论，辅以Yen-Chen在考虑接触力及摩擦力下所修正之理论模型，以曲率及曲率增量来探讨圆弧型钢索受静态荷重作用下，钢绞线之受力与变形或应变关系。

Concretely speaking, using the irreducible tensor theory, we deuced the formulism for fine-structure energies of boron-like atoms in the ground and first excited states, which involves spin-orbit, spin-spin and spin-other-orbit interactions; completing all the angular integrations and spin summations needed, we make the final expression for fine-structure energies of boron-like atoms in the ground and first excited states in a combination of radial integrations. Afterwards, employing the wave functions we got in Chapter Three, we accomplished all the radial integrations and so obtained the fine-structure energies.

具体地说，利用不可约张量理论导出了类硼离子基态以及第一激发态的精细结构的表达式，给出了自旋-轨道、自旋-自旋、自旋-其它轨道相互作用等所涉及的所有角向积分和自旋求和的解析计算方法，完成了角向积分、自旋求和的计算，使类硼离子基态以及第一激发态精细结构能级最终可以表示为径向积分之和；在此基础上利用以前所得到的非相对论性波函数，进一步完成了所有径向积分的计算，从而得到了对应能级的精细结构的理论计算值。

And had proven the essence of submit function on geo-technical material is under certain stress condition between the second deviator stress tensor invariant and the own attribute functional relation of materials.

证明了岩土类介质屈服函数的实质是在一定应力状态下偏应力张量第二不变量与材料自身属性之间的函数关系。

With the aids of the angular momentum coupling theory, the diagonal sum rule and the irreducible tensor theory, a formulism for calculating the matrix elements of Boron-like atoms' non-relativistic Hamilton between the Racah wave functions have been derived. Based on this approach, the non-relativistic energies of Boron-like atoms in the ground and the first excited states have been obtained.

本论文借助角动量耦合理论、对角和法则和不可约张量理论，导出了类硼离子基态和第一激发态非相对论性哈密顿在拉卡基函数之间的矩阵元的表达式，给出了计算类硼离子基态和第一激发态非相对论性能量的方法，并应用此法计算了类硼离子基态和第一激发态非相对论性能量。

This is a major difference between Boolean sum operator and Tensor product operator.

这是实际设计部门乐意接受的，也是张量积方法所不具备的。1

This paper have also explored the nonwandering property of sum of operator, direct sum of operator,tensor products of operators and differentiation operators which can be viewed as weighted shifts on some space.

本文也研究了和算子，直和算子，张量积算子以及在某种意义下可看成加权移位的微分算子在一定空间上的非游荡性。

By using the tensor product of matrix, stride permutation matrix and matrix power series under the meaning of matrix direct sum, the parallel algorithm, including the scrambling algorithm, can be expressed integrally. This description provides a convenient tool for the study and application of parallel FFT algorithm.

本文提出了矩阵直和意义下幂级数的矩阵运算，同时利用迭代形式的矩阵方程将混合基FFT的并行算法及其数码倒置算法完整地表示出来，为并行FFT算法的研究和应用提供了方便的表示手段。

A new structure tensor integrating the second-order directional derivative information is designed, which can precisely analyze complex weak edges in the image.

摘要一致性扩散是分析图像中定向结构的重要的预处理步骤，现有的一致性扩散图像增强方法难以识别图像中的弱边界。

The shaping method of noncircular part and the tool holder's radial motion characters in noncircular turning process are discussed in detail in the thesis.

论文详细研究了非圆零件的成型方法和加工过程中刀架的径向运动规律。

I have not really liked him,I do not like his this kind of disposition.

我没有真的喜欢他，我不喜欢他的这种性格。