The Generalized Uncertainty Principle

The uncertainty principle lies at the heart of quantum physics, and is widely thought of as a fundamental limit of the measurement precision of incompatible observables. Here it is shown that the traditional uncertainty relation in fact belongs to the leading order approximation of a generalized uncertainty relation. That is, the leading order linear dependence of observables gives the Heisenberg type of uncertainty relations, while higher order nonlinear dependence may reveal more different and interesting correlation properties. Applications of the generalized uncertainty relation and the high order nonlinear dependence between observables in quantum information science are also discussed.     

DIMENSIONS FORRANDOM SELF——CONFORMAL SETS

A set is called regular if its Hausdorff dimension and upper box-counting dimension coincide. In this paper, we prove that the random self-con formal set is regular almost surely. Also we determine the dimen-sions for a class of random self-con formal sets.     

Ideals and Subalgebras in BCI-Algebras

We prove that there exists a maximal ideal of a BCI-algebra X in which each subalgebra is an ideal.AMS Subject Classification (1991): 06F35, 03G25.The second author was supported by the LG Yonam Foundation (1995).     

A Comparative Study on Dynamic and Static Sparsity Patterns in Parallel Sparse Approximate Inverse Preconditioning

Sparse approximate inverse (SAI) techniques have recently emerged as a new class of parallel preconditioning techniques for solving large sparse linear systems on high performance computers. The choice of the sparsity pattern of the SAI matrix is probably the most important step in constructing an SAI preconditioner. Both dynamic and static sparsity pattern selection approaches have been proposed by researchers. Through a few numerical experiments, we conduct a comparable study on the properties and performance of the SAI preconditioners using the different sparsity patterns for solving some sparse linear systems. This revised version was published online in July 2006 with corrections to the Cover Date.     

A multilevel block incomplete cholesky preconditioner for solving normal equations in linear least squares problems

An incomplete factorization method for preconditioning symmetric positive definite matrices is introduced to solve normal equations. The normal equations are form to solve linear least squares problems. The procedure is based on a block incomplete Cholesky factorization and a multilevel recursive strategy with an approximate Schur complement matrix formed implicitly. A diagonal perturbation strategy is implemented to enhance factorization robustness. The factors obtained are used as a preconditioner for the conjugate gradient method. Numerical experiments are used to show the robustness and efficiency of this preconditioning technique, and to compare it with two other preconditioners.     

广义 Liénard 方程的整体渐近性态

我们研究如下的广义 Liénard 方程的整体渐近性态(?)+f(x)(?)+g(x)=e(t),或等价地,(?)其中,f(x),g(x)是实数轴上的连续函数,e(t)为正半轴上的连续函数.     

具有鉴相特性g()=(1+k)sin()/1+kcos()的三阶锁相环路方程奇点的拓扑结构

本文研究了具有鉴相特性g()=((1+k)sin())/(1+kcos())的三阶锁相环路方程奇点的拓扑结构.     

Ward-Takahashi Identity at Finite Temperature

A new real time formalism, based on the closed-time-path Green's function theory (CTPGF),is employed to obtain Ward-llfrkahashi identities of QED at finite temperature. It is shown that WT identity in coordinate space is of the same covariant form aa that in vacuum field theory. A perturbative check is provided to #how that in momentum spze, Takahashi's iden tities hold only in a weak sense.     

石墨炉原子吸收光谱法间接测量尿样中氨基多糖含量

本文采用阿利新蓝（ＡｌｃｉａｎＢｌｕｅ）与尿样中氨基多糖（以下称ＧＡＧ）在ｐＨ＝５．８的醋酸钠溶液中，发生沉淀反应生成ＧＡＧ铜复合物。离心分离沉淀物，以石墨炉原子吸收光谱测定沉淀物中铜含量，间接计算ＧＡＧ含量。本文对尿样加入染液浓度，沉淀反应平衡时间；沉淀物的洗涤剂、洗涤次数等进行了探讨，确定了最佳实验条件，实测了６０例健康人尿中ＧＡＧ含量，与文献报导值一致。     

质子交换光波导生长动力学研究

分析了质子交换光波导的生长动力学并给出了波导层厚度与生长时间的计算公式。