一类相空间中的准几率分布函数系

定义了一类相空间中的准几率分布函数系，这个准几率分布函数系直接建立在具有更加广泛意义的量子相空间Schr?dinger方程解的基础之上，其中定义_α=αp-i?q和_α=(1-α)q+i?p.发现了两个有趣的关系.(1)建立的量子相空间Schr?dinger方程的解实际上是对函数φ(λ)exp［i(1-α)qp］做窗口Fourier变换.(2)这个窗口函数g(λ)起着选择窗口形式的作用，而且不同的窗口对应着不同的分布函数.当g(λ)是一个代表Gauss窗的Gauss函数的时候，准几率分布函数就是一个类似于Husimi的分布函数f^HL_α(q,p)；当g(λ)是一个表示椭圆的复函数时，准几率分布函数就是一个椭圆分布函数f^E_α(q,p)；再在g(λ)为复函数的基础上附加α=0，就可得到标准序分布函数f^S(q,p)、反标准序分布函数f^AS(q,p)和Wigner分布函数f^W(q,p)，此时g(λ)表示高度为1/12π?而长度为λ的矩形窗. 关键词： 窗口Fourier变换 相空间 Wigner分布函数     

Classification of Gauge Orbit Types for SU(n)-Gauge Theories

A method for determining the orbit types of the action of the group of gauge transformations on the space of connections for gauge theories with gauge group SU(n) in spacetime dimension d4 is presented. The method is based on the one-to-one correspondence between orbit types and holonomy-induced reductions of the underlying principal SU(n)-bundle. It is shown that the orbit types are labelled by certain cohomology elements of spacetime satisfying two relations. Thus, for every principal SU(n)-bundle the corresponding stratification of the gauge orbit space can be explicitly determined. As an application, a criterion characterizing kinematical nodes for physical states in Yang–Mills theory with the Chern–Simons term proposed by Asorey et al. is discussed.     

Exploiting the diversity of time scales in the immune system: A B-cell antibody model

Using the continuous shape space formalism, we develop an immune system model involving both B lymphocytes and antibody molecules. The binding and cross-linking of receptors on B cells stimulates the cells to divide and, with a lag, to secrete antibody. Using the method of multiple scales, we show how to correctly formulate long-time-scale equations for the population dynamics of B cells, the total antibody concentration, and rate of antibody secretion. We compare our model with previous phenomenological formulations.     

光致折射效应中空间电荷场建立过程的研究

本文推导了包含自衍射及非线性吸收影响、用以描述空间电荷场建立过程的微分方程组,阐明了周期性的空间电荷场与光强干涉条纹之间的相位差在建立过程中所起的作用,并推导了描述条纹倾斜和弯曲的微分方程。通过数值计算找到了硅酸铋(BSO)晶体中能量转移的规律,讨论了材料特性对过程快慢的影响,提出了用CW激光来探讨瞬态过程快慢的可能性。     

A Classical Formulation of Quantum Theory?

We explore a particular way of reformulating quantum theory in classical terms, starting with phase space rather than Hilbert space, and with actual probability distributions rather than quasiprobabilities. The classical picture we start with is epistemically restricted, in the spirit of a model introduced by Spekkens. We obtain quantum theory only by combining a collection of restricted classical pictures. Our main challenge in this paper is to find a simple way of characterizing the allowed sets of classical pictures. We present one promising approach to this problem and show how it works out for the case of a single qubit.     

A Time-Symmetric Formulation of Quantum Entanglement

I numerically simulate and compare the entanglement of two quanta using the conventional formulation of quantum mechanics and a time-symmetric formulation that has no collapse postulate. The experimental predictions of the two formulations are identical, but the entanglement predictions are significantly different. The time-symmetric formulation reveals an experimentally testable discrepancy in the original quantum analysis of the Hanbury Brown–Twiss experiment, suggests solutions to some parts of the nonlocality and measurement problems, fixes known time asymmetries in the conventional formulation, and answers Bell’s question “How do you convert an ’and’ into an ’or’?”     

一种混沌映射的相空间去噪方法

对于混沌映射来说,它们的频谱比混沌流的频谱更广阔,与噪声频谱的重叠率更高,所以混沌流的去噪方法对它们并不适用. 在半盲分析法的框架下,混沌系统的参数估计问题终将归结为最小二乘估计问题. 本文从最小二乘拟合的角度出发估计混沌映射的演化参数,进而通过相空间重构以及投影操作,实现对观测信号的噪声抑制. 实验结果表明,该算法的去噪效果优于扩展卡尔曼滤波器（extended Kalman filter,EKF）和无先导卡尔曼滤波器（unscneted Kalman filter,UKF）,并且能够较大程度地将信号源的混沌特征量还原. 关键词： 混沌 噪声抑制 相空间重构 投影     

Standard pseudo-Hermitian structure on manifolds and seifert fibration

A strictly pseudoconvex pseudo-Hermitian manifoldM admits a canonical Lorentz metric as well as a canonical Riemannian metric. Using these metrics, we can define a curvaturelike function onM. AsM supports a contact form, there exists a characteristic vector field dual to the contact structure. If induces a local one-parameter group ofCR transformations, then a strictly pseudoconvex pseudo-Hermitian manifoldM is said to be a standard pseudo-Hermitian manifold. We study topological and geometric properties of standard pseudo-Hermitian manifolds of positive curvature or of nonpositive curvature . By the definition, standard pseudo-Hermitian manifolds are calledK-contact manifolds by Sasaki. In particular, standard pseudo-Hermitian manifolds of constant curvature turn out to be Sasakian space forms. It is well known that a conformally flat manifold contains a class of Riemannian manifolds of constant curvature. A sphericalCR manifold is aCR manifold whose Chern-Moser curvature form vanishes (equivalently, Weyl pseudo-conformal curvature tensor vanishes). In contrast, it is emphasized that a sphericalCR manifold contains a class of standard pseudo-Hermitian manifolds of constant curvature (i.e., Sasakian space forms). We shall classify those compact Sasakian space forms. When 0, standard pseudo-Hermitian closed aspherical manifolds are shown to be Seifert fiber spaces. We consider a deformation of standard pseudo-Hermitian structure preserving a sphericalCR structure.Dedicated to Professor Sasao Seiya for his sixtieth birthday     

Lipschitz局部严格伪压缩映象的迭代逼近

设Ｋ是一致光滑Ｂａｎａｃｈ空间Ｋ的非空子集，Ｔ：Ｋ→Ｘ是Ｌｉｐｓｃｈｉｔｚ局部严格伪压缩映象。本文给出一个迭代序列强收敛到Ｔ的唯一不动点，并给出一个涉及Ｌｉｐｓｃｈｉｔｚ局部强增殖映象Ｔ的非线性方程Ｔｘ＝ｆ的解的迭代逼近。     

CHAOS FOR MIXING TRANSFORMATIONS

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