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对称部分是实模态摄动，反对称部分是复模态摄动。The symmetric perturbation is of real mode and the antisymmetric is of complex mode.

要求反对称波函数的粒子，如电子，叫做费米子。Particles, such as electrons, requiring antisymmetric wave functions are called fermions.

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分析还表明，扰动的对称运动和反对称运动具有明显的波动特征。Meanwhile, both the symmetric motion and antisymmetric motion possess wave characteristic.

旨在研究反对称角铺设层合板的动力响应。The research on the dynamic response of the antisymmetric angle- ply laminated plate is presented.

面力和分娩是通过两个独立的应用和“反对称”硬的铁笼里。Tractions and confinements are applied through two separate and "antisymmetric" stiff steel cages.

另外，随着非绝热加热增加，对称运动和反对称运动强度也增加。The amplitudes of symmetric and antisymmetric motions increase with the increasing of diabatic-heating intensity.

给出了实反对称矩阵的若干构建方法及部分方法的证明。This paper demonstrates some methods of the building of the real antisymmetric matrix and some detailed demonstrate.

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通过求解应力对称和反对称部分可以得到位错密度-应力的相关关系。The dislocation density stress relations are derived with the help of the symmetric and antisymmetric parts of stresses.

该算法利用这组新的递推关系，提出了分别适用于对称和反对称多项式的算法。By using these new recursive relations, we establish the new algorithm in the form of both symmetric and antisymmetric polynomials.

研究了由一个中心刚体带有一对柔性梁的航天器的神经网络控制问题。Problem of control of a spacecraft, a central rigid body with two flexible antisymmetric appendage, using neural networks is discussed.

数值算例研究了材料非线性对反对称复合材料层合板瞬态温度场的影响。The influence of material nonlinearity on the transient temperature field of antisymmetric laminated plate was studied by numerical results.

本文引入了卫星太阳帆板反对称弯曲振动动力学方程，在此基础上分析了经典控制律下帆板的弹性振动情况。In this paper, the antisymmetric flexure dynamics of satellites are introduced and the rigid body control law to flexible satellites is examined.

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本文以二维反对称水弹性理论分析了大开口船体结构的弯扭耦合响应。The bend-torsion coupling responses of ships with large open deck are calculated by two-dimensional antisymmetric hydroelasticity theory in this paper.

借助内积与长度与夹角给出了欧氏空间的变换是反对称变换的若干个充要条件。A few good necessary and sufficient conditions are given by using inner product and length relation for antisymmetric transformation on Euclidean space.

将耦合摆弹簧作为弹性均匀杆，导出了对称简正模与反对称简正模的本征方程，给出各角频率值的近似式，并进行了讨论。Taking the spring of coupled pendulums as an uniform elastic rod, characteristic equations are derived for symmetric normal mode and antisymmetric modes.

实验中，采用了一发一收法，并分别激励了对称模态S1和反对称模态A1对该缺陷进行了检测。In the experiments, the symmetric and antisymmetric modes, S1 and A1, were excited to detect hidden corrosion defect respectively using pitch-catch technique.

以九维超球谐为投影函数，构造置换群S_3一维不可约表示的全反称基函数。The total antisymmetric basis functions are constructed for irreducible representation of S3 permutation group from nine- dimensional hyperspherical harmonics.

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根据两幅图像中的平面约束，证明了图像对的基础矩阵和同形矩阵的乘积具有反对称的性质。According to the planar constraints, we proved that the product of the fundamental matrix and the homography matrix of an image pair is an antisymmetric matrix.

核自旋之间的各种各向异性相互作用都能用二阶张量表示，这些张量可分解成各向同性、对称以及反对称分量。The various anisotropic spin interactions which can be represented by the rank two tensors are decomposed into isotropic, symmetric, and antisymmetric constituents.

第一章、第二章分别利用幂等矩阵及反对称矩阵的标准型构造了卡氏认证码。Chapter one and chapter two use normal form of idempotent matrices and antisymmetric matrices over finite fields to construct cartesian authentication codes respectively.