从射影观点看焦点

用射影几何知识讨论欧氏平面上二次曲线焦点与准线的性质.     

Validity of nonlinear geometric optics with times growing logarithmically

The profiles (a.k.a. amplitudes) which enter in the approximate solutions of nonlinear geometric optics satisfy equations, sometimes called the slowly varying amplitude equations, which are simpler than the original hyperbolic systems. When the underlying problem is conservative one often finds that the amplitudes are defined for all time and are uniformly bounded. The approximations of nonlinear geometric optics typically have percentage error which tends to zero uniformly on bounded time intervals as the wavelength tends to zero. Under suitable hypotheses when the amplitude is uniformly bounded in space and time we show that the percentage error tends to zero uniformly on time intervals which grow logarithmically. The proof relies in an essential way on the fact that one has a corrector to the leading term of geometric optics.

     

生态系统中心焦点判定的新方法

给出在生态系统的研究中 ,中心焦点判定的一种新方法 .利用这种方法对一类生物化学反应模型进行了中心焦点的判定 ,从而比较完整地对相应的系统作了研究 .     

中心与焦点判定定理证明之补充

中心与焦点判定问题的研究是微分方程定性理论课程教学的重要内容之一,然而我们发现在近30年出版的10多种国内外教材中对其中一个主要定理的涉及Poincare形式级数的证明均有缺陷,本文之目的就是对这一证明做了完整的补充.     

A simple parabolic model for the optics of the atmospheric surface layer

A simple yet accurate model is developed for optical ray tracing in the surface layer of a refracting atmosphere. The model consists of a small number of concentric spherical layers or shells, the surface of each being isothermal. If the temperature is taken to vary linearly between the surfaces, then the curvature of nearly-horizontal rays is approximately constant within each layer. Replacement of circular by parabolic arcs produces simple quadratic expressions for the rays. The procedure is easily implemented on a minicomputer, and a compact version fits into a programmable pocket calculator. This is particularly convenient for checking field observations. An example is given, as well as a discussion on error sensitivity due to simplifying assumptions.     

球形脉冲波穿过聚焦点的分析

利用渐近分析的方法,讨论球型脉冲波在非线性焦散情形下,脉冲波穿过焦点时的性态.得到在时间趋于负无穷的初始条件下,脉冲波穿过焦点时,方程的非线性项可以忽略.     

一类非线性微分方程组中心和焦点判定的简便方法

本文讨论非线性微分方程组dxdt=-y +x F( x,y) ,dydt=x +y F( x,y)( 1 )在奇点 ( 0 ,0 )邻近积分曲线的结构 .得到了判定原点 ( 0 ,0 )是微分方程组 ( 1 )的焦点或中心的简便方法 .     

一类具细焦点的三次系统极限环的唯一性

继续相关文献的工作,给出与二次系统Ⅰ相伴的一类三次系统在奇点N(0,1/n)的焦点量公式,证明了系统在细焦点N外围至多有一个极限环,同时证明了当N或O为细焦点时,系统在另一个焦点外围无极限环,结合相关文献的结论,说明了具有细焦点的该系统在全平面至多有一个极限环.     

A Schrodinger formulation research for light beam propagation through the media of complex refractive index

The Helmhotz equation of light beam propagating through a medium of complex refractive index is reduced to the axial-coordinate-dependent Schr?dinger equation of complex potential. The new bra vector, the new expectation value of a dynamical variable and the extended Heisenberg picture are defined by the inverse of the evolution operator instead of its Hermitian adjoint, and the complex beam propagation parameters defined in terms of the new expectation value, the complex ABCD law and the ABCD formulation of the Huygens' integral are discussed in terms of quantum mechanics. It is shown that the evolution equations of the complex beam propagation parameters are the same as those of the beam propagation parameters of beam propagating through a medium of real refractive index. The research on an optical system of the conservative complex beam quality factor shows that the complex ABCD law holds, the evolution of its coordinate operator and the momentum operator is linear, and the Huygens' integral is of the ABCD formulation.     

二次系统二阶细焦点外围极限环的唯一性

本文证明了平面二次系统二阶细焦点外围至多存在一个极限环这一猜想,并证明了若第二、第三焦点量的乘积大于零,则在二阶细焦点外围不存在极限环．     

青海省重点开发区人口资源环境承载力评价研究

选择青海省重点开发区的26个县、市(区)为研究对象,利用全局主成分分析(GPCA)、聚类分析等方法,根据人口经济活动支撑力、资源供给支持力和生态环境承载力及综合人口资源环境承载力等四个方面对这些地区1999-2012年人口资源环境承载力状况进行了定量、动态评价和分析.指数化的评价结果表明,青海省重点开发区人口资源环境承载力逐年提高,综合人口资源环境承载力指数均值从1999年的-0.29365上升到2012年的0.336723.     

Applications of the growth characteristics induced by the spectral distance

Let A be a complex unital Banach algebra. Using a connection between the spectral distance and the growth characteristics of a certain entire map into A, we derive a generalization of Gelfand’s famous power boundedness theorem. Elaborating on these ideas, with the help of a Phragm´en-Lindel¨of device for subharmonic functions, it is then shown, as the main result, that two normal elements of a C^?-algebra are equal if and only if they are quasinilpotent equivalent.     

Frequency and dependence of long range temporal correlations in human hippocampal energy fluctuations

Spontaneous energy fluctuations in human hippocampal EEG show prominent amplitude and temporal variability. Here we show hippocampal energy fluctuations often exhibit long‐range temporal correlations with power‐law scaling. In most cases this scaling behavior persisted on time scales in excess of 10 minutes, the maximum duration we could detect with our recording durations. During these epochs we find that the energy fluctuations exhibit long‐range correlations over a broad frequency range (0.5–100 Hz) with greater persistence of the correlations in the lower frequency bands (0.5–30 Hz) than the higher (30–100 Hz). The correlation in hippocampal energy fluctuations is characterized by a bias for energy fluctuations to be followed by similar magnitude fluctuations over all energy scales, i.e. large fluctuations begets large fluctuations and small begets small. © 2005 Wiley Periodicals, Inc. Complexity 10: 35–45, 2005     

Four Wave Mixing of the Signal and ASE Noisein Long Distance Optical Communication System

ＦｏｕｒＷａｖｅＭｉｘｉｎｇｏｆｔｈｅＳｉｇｎａｌａｎｄＡＳＥＮｏｉｓｅｉｎＬｏｎｇＤｉｓｔａｎｃｅＯｐｔｉｃａｌＣｏｍｍｕｎｉｃａｔｉｏｎＳｙｓｔｅｍ１１ＴｈｅｐａｐｅｒｗａｓｒｅｃｅｉｖｅｄｏｎＳｅｐｔ．２９，１９９６ＨｏｎｇＹＵＡＮ，Ａｎｓｈｉ...     

用群方法求解幂律非牛顿导电流体的Raleigh问题

研究了如下磁流体Rayleigh问题：一块半无限大平板受瞬态冲击后以恒定速度在无限大非牛顿幂律流体的区域内运动。讨论了在横向外在磁场作用下非牛顿导电流体在无限大区域内的非定常流动。用变换群理论得到了这个强非线性问题的解。通过单参数群变换减少了一个自变量，并使带边界条件的偏微分方程转化为带合适边界条件的常微分方程。同时研究了某些参数对流体速度的影响。     

Experimental studies of high order soliton compression effect and gain characteristics in femtosecond laser pulses E3+r-doped fiber amplifier

Seed laser pulses with average power of 146 μW and pulse duration of 480 fs were amplified to 14.5 mW. The pulse duration was compressed to 260 fs using 6 m high concentration E3+r-doped fiber under forward pumping. The amplified signal pulse energy was 0.691 nJ (corresponding to a peak power of 2 657.7 W) and the repetition rate was 20.84 MHz. Spectrum breakup was observed simultaneously. The spectrum of pulses amplified by 3 m E3+r-doped fiber remains a single peak under different pump power. The amplified pulse duration was compressed abnormally with the increasing pump power using the backward pumping; that is, the amplified pulses were compressed with the increasing pump power under low pump power. When the pump power reached 38 mW, the shortest amplified pulse duration was 309 fs. With further increase in pump power, the amplified pulses began broadening, accompanied by a single peak spectrum under different pump power.     

Stationary measures and hydrodynamics of zero range processes with several species of particles

We study general zero range processes with different types of particles on a d-dimensional lattice with periodic boundary conditions. A necessary and sufficient condition on the jump rates for the existence of stationary product measures is established. For translation invariant jump rates we prove the hydrodynamic limit on the Euler scale using Yaus relative entropy method. The limit equation is a system of conservation laws, which is hyperbolic and has a globally convex entropy. We analyze this system in terms of entropy variables. In addition we obtain stationary density profiles for open boundaries.     

Experimental studies of high order soliton compression effect and gain characteristics in femtosecond laser pulses Er3+-doped fiber amplifier

Seed laser pulses with average power of 146 μW and pulse duration of 480 fs were amplified to 14.5 mW. The pulse duration was compressed to 260 fs using 6 m high concentration E³⁺ _r -doped fiber under forward pumping. The amplified signal pulse energy was 0.691 nJ (corresponding to a peak power of 2 657.7 W) and the repetition rate was 20.84 MHz. Spectrum breakup was observed simultaneously. The spectrum of pulses amplified by 3 m E³⁺ _r -doped fiber remains a single peak under different pump power. The amplified pulse duration was compressed abnormally with the increasing pump power using the backward pumping; that is, the amplified pulses were compressed with the increasing pump power under low pump power. When the pump power reached 38 mW, the shortest amplified pulse duration was 309 fs. With further increase in pump power, the amplified pulses began broadening, accompanied by a single peak spectrum under different pump power.