关于有限域上最优正规基的分布(英文)

设E/F_q为q元有限域F_q的扩域.如果α∈E生成E/F_q的一个正规基,则称α∈E为E的一个正规基生成元.本文证明了:对于任何中间域K,E的正规元被E到K的迹映射均匀的映到K的正规元.另一方面,给出了所有这样的中间域K:K中的正规元在E到K的迹映射下的完全原像中的元均为E中的正规元.     

Chebyshev Spaces and Bernstein Bases

We characterize extended Chebyshev spaces by the fact that any Hermite interpolation problem involving at most two different points has a unique solution. This enables us to prove that, in a given space, Bernstein bases exist if and only if the space obtained by differentiation is an extended Chebyshev space.     

Selective Hydroxy Group Protection of Gallic Acid

An efficient procedure allowing selective differentiation of the 4-hydroxy group of methyl gallate was reported.     

Thermal Behaviour of Complexes of Antipyrine Derivatives

Parent and mixed ligand complexes of cobalt and copper with antipyrine derivatives of 1,2-ethanediamine or piperazine and with 2-aminobenzothiazole (TAB) were synthesized and their thermal behaviour was investigated. The complexes contain N,N′-bis(4-antipyrylmethyl)-piperazine (BAMP) or N,N′-tetra(4-antipyrylmethyl)-1,2-diaminoethane (TAMEN) or/and TAB as ligand, and Cl⁻, ClO₄ ⁻ or SCN⁻. The complexes decompose with the evolution of heat. The decomposition route depends on the presence of ClO₄ ⁻. If the ClO₄ ⁻ is not coordinated, it oxidizes the TAB and BAMP or TAMEN and the decomposition is explosive. This revised version was published online in August 2006 with corrections to the Cover Date.     

单个N维量子系统的量子秘密共享

提出了一种单个N维量子系统的量子秘密共享方案.在该方案中，利用对Bennett和Brassard协议(BB84协议)中使用的两基四态扩展到多基多态，分发者对要共享的秘密采用多基多态编码，将被编码的单个N维量子系统发送给他的两个代理人之一，该代理人利用一个N维克隆机对接收到的粒子做幺正操作，然后把粒子发送给另一代理人.在得知最后一个代理人接收到该粒子之后，分发者告知两个代理人他所用的制备基，然后两个代理人分别对自己的系统进行测量并在合作之后获知分发者所发送的粒子的量子态.该方案的安全性基于量子不可克隆定理. 关键词： 量子秘密共享 多基多态编码 N维克隆机 量子不可克隆定理     

G-frames and g-Riesz bases

G-frames are generalized frames which include ordinary frames, bounded invertible linear operators, as well as many recent generalizations of frames, e.g., bounded quasi-projectors and frames of subspaces. G-frames are natural generalizations of frames and provide more choices on analyzing functions from frame expansion coefficients. We give characterizations of g-frames and prove that g-frames share many useful properties with frames. We also give a generalized version of Riesz bases and orthonormal bases. As an application, we get atomic resolutions for bounded linear operators.     

Airy传递矩阵法与偏压下多势垒结构的准束缚能级

使用Airy函数和传递矩阵方法精确计算了一维定态薛定谔方程，并推广到多势垒结构，求解出有/无偏压作用的2,3势垒结构的准束缚能级，进一步研究了有/无偏压作用的2,3势垒结构的准束缚能级与有效质量和外加电压的关系，并对结论的正确性进行了验证． 另外，文中 还指出了有些文章中关于Airy传递矩阵法与计算偏压下多势垒结构的准束缚能级的错误陈述 . 关键词： 准束缚能级 有/无偏压作用的多势垒结构 Airy函数 透射系数