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1)  Singular pseudosymplectic space
奇异伪辛空间
2)  Singular symplectic space
奇异辛空间
3)  affine singular symplectic space
仿射奇异辛空间
1.
In this paper,the concepts of affine singular symplectic spaces ASG(2v + l, IFq)and singular symplectic group ASp2v+l,v(IFq)over IFq are given,and some Anzahl theorems in ASG(2v + l, IFq)are obtained using actions of ASP2V+l,v(IFq)on ASG(2v+l, IFq), Moreover,we construct an associative scheme and an authentication code in view of singular affine symplectic spaces.
给出了有限域IFq上的2v+l维仿射奇异辛空间ASG(2v+l,IFq)和2v+l次仿射奇异辛群ASP2v+l,v(IFq)的概念,然后讨论了ASP2v+l,v(IFq)作用在ASG(2v+l,IFq)上的可迁性及一些相关的计数定理,最后给出应用仿射奇异辛空问构作结合方案和认证码的例子。
4)  Singular Pseudo-symplectic Groups
奇异伪辛群
5)  bogus symplectic space
伪辛空间
1.
The forming of concept of bogus symplectic space is studied.
论述了伪辛空间概念的形成,深入阐述了其本质属性及分化、演变和扩张,揭示了伪辛空间与辛空间及欧氏空间的内在联系和区别。
2.
The essential property and developmental course of Euclidean space,symplectic space and bogus symplectic space are studied.
论述欧氏空间、辛空间、伪辛空间的本质属性及演变过程 。
3.
In this paper,we construct the concept of bogus symplectic space,discuss the motion of bogus symplectic space and discribe the property of the motion by showing the composition and manifestation form of the motion,the generation and decomposition of the matrix of motion.
给出伪辛空间的概念,论述伪辛空间中的运动。
6)  pseudo-symplectic space
伪辛空间
1.
The association schemes of a kind of 2-dimensional subspaces of pseudo-symplectic space F_q~((2v+1+l)) and its structure;
伪辛空间F_q~(2v+1+l)中一类2-维子空间的结合方案及其结构
2.
After illustrating the conception pseudo-symplectry ,the evolvement and extension of the conception symplectry and the formation of pseudo-symplectic space,the nature of pseudo-symplectic space and the inner relationship and differences between pseudo-symplectic space and symplectic space are reflected here.
通过对辛空间的深入分析和研究,从空间中的度量与向量的迷向性问题入手并展开较为详细的讨论,定义"伪辛"的概念,阐述"辛"概念的演变、扩充与伪辛空间生成的事实,进而揭示伪辛空间的本质属性及其与辛空间的内在联系与区别。
补充资料:半伪Euclid空间


半伪Euclid空间
semi-pseudo-Euclidean space

半伪五”d记空间f胭I幼一碑”心一h凶山汾n习.Ce;n。刃-nce.月oe卿“月OBo nP0c甲明cTBO] 具有退化的不定度量的向量空间.半伪Euclid空间‘’‘,R:”’,一’定义为一个刀维空间,在其中给定了厂个数量积 (二,力“二艺气二味y’u,这里O=椒(、<俐l<一
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