凸域内矩形的运动测度

本文研究了凸域内矩形的运动测度,通过对凸域内定长线段运动测度的推广,建立了包含在凸域内且长、宽都确定的矩形运动测度的一般公式,利用此公式得到了圆域和矩形域内此类矩形的运动测度,并以此为基础得到了推广后的Buffon投针问题的一些结果.     

Bispinor Space

In this paper, we give identifications of bispinor space with Grassmann algebra, and with Clifford algebra. The multiplication in Clifford algebra provides an action on them. Lastly we have researched on the geometry of bispinor space, and define Dirac operators to get a Pythagoras equality.     

Strictly nilpotent elements and bispectral operators in the Weyl algebra

In this paper we give another characterization of the strictly nilpotent elements in the Weyl algebra, which (apart from the polynomials) turn out to be all bispectral operators with polynomial coefficients. This also allows to reformulate in terms of bispectral operators the famous conjecture, that all the endomorphisms of the Weyl algebra are automorphisms (Dixmier, Kirillov, etc).     

两个高维loop代数及应用

借助于循环数,构造了维数分别是5(s+1)和4(s+1)的两个高维loop代数．为了计算方便,本文只考虑s=1时的应用．利用第一个loop代数■_1~*得到了具有4-Hamilton结构的一个广义AKNS族,该方程族可约化为著名的AKNS族．利用第二个loop代数■_2~*,得到了具有4个分量位势函数的4-Hamilton结构方程族,该族可约化为一个非线性耦合Burgers方程和一个耦合的KdV方程．     

在腔耦合的超导量子比特中实现几何量子信息处理

用量子空腔耦合的超导电荷比特器件被认为是实现量子信息处理的相当有希望的体系之一.如何在这种可集成的量子体系中实现高保真度的操作是量子信息处理领域的重要课题.文章介绍作者最近提出的在量子腔耦合的超导量子比特中用具有内禀容错功能的几何操作来实现普适量子逻辑门,产生多比特量子纠缠及实现量子纠错编码的一个可行方案.     

量子代数wsl_q(2)上的伴随作用

本文证明了量子代数wslq(2)在左伴随作用下是其自身上的拟模代数,并研究了wslq(2)的局部有限子模(?)(wslq(2))的子模结构．     

Pseudo-Kähler metrics on six-dimensional nilpotent Lie algebras

It is well known that any symplectic manifold (M,Ω) has an almost complex structure J which is compatible with Ω. In this paper, we deal with the existence of compatible pairs (J,Ω) on nilpotent Lie algebras of dimension ≤6, J being an integrable almost complex structure. We prove that if such a pair exists, J must satisfy some extra conditions, namely J must be nilpotent in the sense of [Trans. Am. Math. Soc. 352 (2000) 5405]. Associated to any such a compatible pair, there is a pseudo-Kähler metric g which cannot be positive definite unless be abelian. All these metrics are Ricci flat, although many of them are nonflat, and we study the behaviour of its curvature tensor under deformation.     

Quantum World with Quantum Time

Since the beginning of quantum mechanics there have been a lot of attempts to quantize time. In this paper we refer to the little known concept of quantum time proposed by E.Kapuscik [Hadronic J. 8 (1985) 75]. We analyze some properties of systems with quantum time. Moreover we comment and discuss the idea of quantum time.     

Function of a square matrix with repeated eigenvalues

An analytical function f(A) of an arbitrary n×n constant matrix A is determined and expressed by the “fundamental formula”, the linear combination of constituent matrices. The constituent matrices Z_kh, which depend on A but not on the function f(s), are computed from the given matrix A, that may have repeated eigenvalues. The associated companion matrix C and Jordan matrix J are then expressed when all the eigenvalues with multiplicities are known. Several other related matrices, such as Vandermonde matrix V, modal matrix W, Krylov matrix K and their inverses, are also derived and depicted as in a 2-D or 3-D mapping diagram. The constituent matrices Z_kh of A are thus obtained by these matrices through similarity matrix transformations. Alternatively, efficient and direct approaches for Z_kh can be found by the linear combination of matrices, that may be further simplified by writing them in “super column matrix” forms. Finally, a typical example is provided to show the merit of several approaches for the constituent matrices of a given matrix A.     

The Optical Implementation of High Efficiency Packed Redundant Binary Number Addition Based on Boolean Polarization－encoded Logic Algebra

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