高速运算可挖掘更多大脑潜能

2012年《科学画报》2期新闻广角"脑科学"专栏刊文——《数学家挖掘更多大脑潜能》介绍:据法国和比利时科学家合作进行的一项新研究,数学家在作运算,特别是高速心算时,能利用一般人不能利用的大脑部位。这就是说,他们能使用更多的大脑部位。专家们利用正电子x射线扫描(PET)技术,首先对     

Probabilistically implementing nonlocal operations between two distant qutrits

We propose a method to probabilistically implement a nonlocal operation, $% \exp {[}\i\xi U_{A}U_{B}{]}$, between two distant qutrits $A$ and $B$, where $% \xi \in [0,2\pi ]$ and $U_{A}$, $U_{B}$ are local unitary and Hermitian operations for qutrits $A$ and $B$ respectively. The consumptions of resource for one performance of the method are a single non-maximally entangled qutrit state and 1-trit classical communication. For a given $\xi $% , the successful probability of the method depends on the forms of both entanglement resource and Bob's partial-measurement basis. We systematically discuss the optimal successful probabilities and their corresponding conditions for three cases: adjustable entanglement resource, adjustable partial-measurement basis, adjustable entanglement resource and partial-measurement basis. It is straightforward to generalize the method for producing nonlocal unitary operations between any two $N$-level systems.     

模糊运算和模糊有限元静力控制方程的求解

根据模糊数的区间形式表达和区间运算的性质,给出了模糊数和模糊变量的运算规则.据此并依据区间有限元理论,提出了结构模糊有限元静力控制方程的几种求解方法.方法可根据输入模糊数的隶属函数,给出结构响应量的可能性分布.且计算量小,易于实施.算例分析说明了方法是实用和可行的.     

On the General Algebraic Inverse Eigenvalue Problems

A number of new results on sufficient conditions for the solvability and numerical algorithms of the following general algebraic inverse eigenvalue problem are obtained: Given $n+1$ real $n\times n$ matrices $A=(a_{ij}),A_k=(a_{ij}^{(k)})(k=1,2,\cdots,n)$ and $n$ distinct real numbers $\lambda_1,\lambda_2,\cdots,\lambda_n,$ find $n$ real number $c_1,c_2,\cdots,c_n$ such that the matrix $A(c)=A+\sum\limits_{k=1}^{n}c_k A_k$ has eigenvalues $\lambda_1,\lambda_2,\cdots,\lambda_n.$     

多重尺度法的计算机计算——一类非线性方程组的狄立克雷问题

应用多重尺度的边界层方法和计算机符号运算研究一类非线性方程组的边值问题解的渐近性质,构造出解的渐近展开式和估计了余项.并分析一个实例.为多重尺度方法的应用提供新的前景.     

Obtaining the band structure of a complicated photonic crystal by linear operations

Absolute band gaps can be created by lifting the degeneracy in the bands of a photonic crystal.To calculate the band structure of a complicated photoinc crystal generated by e.g.symmetry breaking ,general forms of all possible linear operations are presented in terms of matrices and procedure to combine these operations in given.Other forms of linear operations (Such as the addition,subtraction,and translation transforms)are also presented to obtain an explicit expression for the Fourier coefficient of the dielectric function in the plane-wave expansion method.With the present method,band structures for various complicated photoinc crystals(related through these linear operations)can be obtained easily and quickly.As a numerical example,a large absolute and gap for a complicated photonic crystal structure of GaAs is found in the high reglon of normalized frequency.     

Antinormally Ordering the Power of Radial Operator in Quantum Optics Theory

We derive a general formula for arranging the power of radial operators into antinormal ordering product of optical fields by using the technique of integration within antinormally ordered product of operators.     

A Series of Soliton-like and Double-like Periodic Solutions of a （2＋1）-Dimensional Asymmetric Nizhnik-Novikov-Vesselov Equation

We generalize the algebraic method presented by Fan [J.Phys. A: Math. Gen. 36 (2003) 7009)] to uniformly construct a series of soliton-like solutions and double-like periodic solutions for nonlinear partial differential equations (NPDE). As an application of the method, we choose a (2 1)-dimensional asymmetric Nizhnik Novikov Vesselov equation and successfully construct new and more general solutions including a series of nontraveling wave and coefficient functions‘soliton-like solutions, double-like periodic and trigonometric-like function solutions.     

长周期扫描电路的设计与应用

本文鉴于常用的基于电容充放电的运算放大器积分式长周期扫描电路输出电压线性差,设计了基于计数器和D／A转换的数字式线性功率扫描电路。     

线性子空间关系运算的Pluecker坐标表示

本讨论了线性子空间Pluecker的线性表示,给出了Pluecker关系式的矩阵形式,并由之导出了子空间关联关系、零化子空间、和子空间与交子空间Pluecker坐标的矩阵表达式。