构造孤子方程的Weierstrass椭圆函数解的一个新方法

利用具有Weierstrass椭圆函数解的方程，首先获得了投影Riccati方程的两组新解.由于投影Riccati方程可用于多种具孤子解的非线性演化方程的求解，因而得到了一个可以构造这些方程的Weierstrass椭圆函数解的新方法. 关键词： Weierstrass椭圆函数解 投影Riccati方程 非线性演化方程     

Boussinesq-Burgers方程新的精确解

基于改进的投影Riccati方程的解,提出一种新的构造非线性演化方程精确解的方法.通过这种方法,我们得导到了Boussinesq-Burgers方程各种类型的精确解,包括Jacobi和Weierstrass周期函数解.这种方法与数学软件Maple结合,简单易行,有助于探索其他非线性演化方程的精确解.     

(2+1)维 Zakharov-Kuznetsov 方程的精确解和孤子结构

在符号计算软件Maple的帮助下,利用改进的Riccati方程映射法得到了(2+1)维Zakharov-Kuznetsov方程(ZK)的新显式精确解. 根据得到的解,研究了ZK方程的特殊孤子结构. 关键词： 改进的Riccati方程映射法 Zakharov-Kuznetsov方程 精确解 孤子结构     

非线性演化方程椭圆函数解的一种简单求法及其应用

非线性演化方程的许多行波解可以写成满足投影Riccati方程的两个基本函数的多项式形式.利用这一性质，通过建立一般的椭圆方程与投影Riccati方程解之间的关系，导出了一个构造这些解的新方法.该方法对类型Ⅰ的方程和类型Ⅱ的方程均有效，同时也回答了如何求出非线性演化方程分式形式椭圆函数解的问题. 关键词： 非线性演化方程 椭圆函数解     

构造非线性发展方程无穷序列复合型精确解的一种方法

为了获得非线性发展方程新的无穷序列复合型精确解,给出了Riccati方程的Bäcklund变换和解的非线性叠加公式,符号计算系统Mathematica的帮助下,以广义Boussinesq方程为应用实例,获得了无穷序列复合型精确解.这里包括双曲函数、三角函数与有理函数复合解、双曲函数与三角函数复合解等几种新的无穷序列复合型精确解.该方法在构造非线性发展方程无穷序列复合型精确解方面具有普遍意义. 关键词： 非线性发展方程 非线性叠加公式 Riccati方程 无穷序列精确解     

非线性发展方程的Riemann theta 函数等几种新解

为了构造非线性发展方程的复合型无穷序列精确解, 获得了第二种椭圆方程的Riemann theta 函数等几种新解.在此基础上,利用第二种椭圆方程与Riccati方程的Bäcklund变换和解的非线性叠加公式, 借助符号计算系统 Mathematica, 以mKdV方程为应用实例, 构造了该方程的复合型无穷序列新精确解.这里包括Riemann theta 函数、Jacobi椭圆函数、双曲函数、 三角函数和有理函数,通过几种形式构成的复合型无穷序列新精确解. 关键词： 第二种椭圆方程 Riccati方程 非线性发展方程 Riemann theta 函数无穷序列解     

构造非线性发展方程无穷序列类孤子精确解的一种方法

辅助方程法已构造了非线性发展方程的有限多个新精确解. 本文为了构造非线性发展方程的无穷序列类孤子精确解, 分析总结了辅助方程法的构造性和机械化性特点. 在此基础上,给出了一种辅助方程的新解与Riccati方程之间的拟Bäcklund变换. 选择了非线性发展方程的两种形式解,借助符号计算系统 Mathematica,用改进的(2+1) 维色散水波系统为应用实例,构造了该方程的无穷序列类孤子新精确解. 这些解包括无穷序列光滑类孤子解, 紧孤立子解和尖峰类孤立子解.     

Degasperis-Procesi 方程的无穷序列尖峰孤立波解

本文为了构造非线性发展方程的无穷序列尖峰精确解,给出了Riccati方程的Bäcklund 变换和解的非线性叠加公式,并借助符号计算系统Mathematica,用Degasperis-Procesi方程为应用实例,构造了无穷序列尖峰孤立波解和无穷序列尖峰周期解. 关键词： Riccati方程 解的非线性叠加公式 尖峰孤立波解 Degasperis-Procesi 方程     

利用耦合的Riccati方程组构造微分-差分方程精确解

通过引入耦合的Riccati方程组得到一个构造非线性微分-差分方程精确解的代数方法.作为实例，将该方法应用到了一般格子方程，相对论的Toda格子方程和(2+1)维Toda格子方程.借助符号计算软件Mathematica，获得了这些方程的扭结型孤波解和复数解.该方法也适合求解其他非线性微分-差分方程的精确解. 关键词： 耦合Riccati方程组 格子方程 相对论的Toda格子方程 (2+1)维Toda格子方程     

用Riccati方程构造非线性差分微分方程新的精确解

把Riccati方程应用到非线性差分微分方程求解领域,并相结合与一种函数变换,借助符号计算系统Mathematica构造了修正的Volterra方程和一般格子方程新的精确孤立波解和三角函数解. 关键词： Riccati方程 函数变换 非线性差分微分方程 孤立波解     

Numbers,scale and symbols: the public understanding of nanotechnology

Nanotechnology will be an increasing part of the everyday lives of most people in the world. There is a general recognition that few people understand the implications of the technology, the technology itself or even the definition of the word. This lack of understanding stems from a lack of knowledge about science in general but more specifically difficulty in grasping the size scale and symbolism of nanotechnology. A potential key to informing the general public is establishing the ability to comprehend the scale of nanotechnology. Transitioning from the macro to the nanoscale seems to require an ability to comprehend scales of one-billion. Scaling is a skill not common in most individuals and tests of their ability to extrapolate size based upon scaling a common object demonstrates that most individuals cannot scale to the extent needed to make the transition to nanoscale. Symbolism is another important vehicle to providing the general public with a basis to understand the concepts of nanotechnology. With increasing age, individuals are able to draw representations of atomic scale objects, but these tend to be iconic and the different representations not easily translated. Ball and stick models are most recognized by the public, which provides an opportunity to present not only useful symbolism but also a reference point for the atomic scale.     

Illusion and reality in the quantum world

Often considered as the last ‘encyclopedist’, Henri Poincaré died one hundred years ago. If he was a prominent man in 1900 French Society, his heritage is not so clearly recognised, particularly in France. Among his too often misunderstood works is his contribution to the theory of relativity, mainly because it is almost never presented within Poincaré's general approach to science, including his philosophical writings. Our aim is therefore to provide an historical account of the main steps (experimental as well as theoretical) which led Poincaré to contribute to the theory of relativity. Starting from the optical experiments which led to the inconsistency of the classical (Galilean) composition law for velocities to explain light propagation, we introduce the FitzGerald and Lorentz contraction which was viewed as the ‘sole hypothesis’ to explain the Michelson and Morley experiment. We then show that Poincaré's contribution starts with a discussion of the principles governing the mechanics and was built step by step up to express in all its generality the principle of relativity. Poincaré thus showed the invariance of the Maxwell equations under the Lorentz transformation. In doing so, he also discovered the right composition law for velocities. Poincaré's approach to philosophy is detailed to help the reader to understand what a theory meant to him.     

激光测距机三轴平行性智能检测校正方法研究

提出了一种激光测距机三轴平行性智能的检测校正方法。建立了光轴平行性偏差与偏心环(框)旋转角度之间的数学模型,利用传感器得到激光发射轴与瞄准轴之间的平行性偏差,根据所建立的数学模型计算出偏心环(框)需要调整的角度值,利用步进电机使偏心环(框)转动相应的角度,从而物镜产生径向移动,实现激光测距机光轴的校正。此方法在检测激光测距机光轴平行性的同时实现了光轴的自动校正,也适用于其它具有双偏心结构的光学仪器。     

A new method for quantitation of spin concentration by EPR spectroscopy: application to methemoglobin and metmyoglobin

A new method of EPR spectral analysis is developed to quantitate overlapping signals. The method requires double integration of a number of spectra containing the signals in different proportions and the subsequent solution of a system of linear equations. The result gives the double integral values of the individual lines, which can then be further used to find the concentrations of all the paramagnetic species present. There is no requirement to deconvolute the whole spectrum into its individual components. The method is employed to quantify different heme species in methemoglobin and metmyoglobin preparations. A significantly greater intensity of the high-spin signal in metmyoglobin, compared to methemoglobin at the same heme concentration, is shown to be due to larger amounts of low-spin forms in methemoglobin. Three low-spin types in methemoglobin and two in metmyoglobin are present in these samples. When their calculated concentrations are added to those of the high-spin forms, the results correspond to the total heme concentrations obtained by optical spectroscopy.     

Stabilization of discotic liquid organic thin films by ITO surface treatment

Discotic liquid crystals (LCs) are promising materials in the field of electronic components and, in particular, to make efficient photovoltaic cells due to their good charge transport properties. These materials generally exhibit a mesophase in which the disk-shaped molecules can self-assemble into columns, which favorize charge displacement, and may align themselves uniformly on surfaces to form well-oriented thin films. In order to orientate such a columnar thin film on an indium tin oxide (ITO) substrate, the film is heated up to the temperature range of the isotropic liquid phase and subsequently cooled down again. This treatment may lead not only to the desired alignment, but also to dewetting, which leads to an appreciable inhomogeneity in film thickness and to short circuits during the realization of photovoltaic cells. In this article, we describe how this dewetting and the film morphology can be influenced by ITO surface treatments. The chemical modifications of the surface by these treatments were studied by X-ray photoelectron spectroscopy (XPS). Such ITO treatments are shown to be efficient to prevent thin film dewetting when combined with rapid cooling through the isotropic-to-LC phase transition.     

"电感和电容对交变电流的影响"演示实验的改进

"电感和电容对交变电流的影响"演示实验的操作难度大且现象不明显,为此介绍了2种演示该实验的方法,一是通过将电灯分别与电感(电容)和电阻串联对比进行实验来演示电感和电容对交变电流的影响;二是通过信号发生器和示波器来研究交流电对电感(电容)的影响.2种方法演示效果均较好.     

On the connection between the solutions to the Dirac and Weyl equations and the corresponding electromagnetic four-potentials

In this work we study in detail the connection between the solutions to the Dirac and Weyl equations and the associated electromagnetic four-potentials.First,it is proven that all solutions to the Weyl equation are degenerate,in the sense that they correspond to an infinite number of electromagnetic four-potentials.As far as the solutions to the Dirac equation are concerned,it is shown that they can be classified into two classes.The elements of the first class correspond to one and only one four-potential,and are called non-degenerate Dirac solutions.On the other hand,the elements of the second class correspond to an infinite number of four-potentials,and are called degenerate Dirac solutions.Further,it is proven that at least two of these fourpotentials are gauge-inequivalent,corresponding to different electromagnetic fields.In order to illustrate this particularly important result we have studied the degenerate solutions to the forcefree Dirac equation and shown that they correspond to massless particles.We have also provided explicit examples regarding solutions to the force-free Weyl equation and the Weyl equation for a constant magnetic field.In all cases we have calculated the infinite number of different electromagnetic fields corresponding to these solutions.Finally,we have discussed potential applications of our results in cosmology,materials science and nanoelectronics.     

光屏两点投射法测量超临界流体折射率的光路分析计算

由于超临界流体温度和压力较高，用于测量其折射率的光学池需要特殊设计。超临界流体(Super Critical Fluid，SCF)光学池设计为细长形体，以便控温和耐高压；光屏两点投射法测量超临界流体折射率应采用斜交光学池；分析了斜交光学池测量折射率的光路，推出了斜交光学池平行窗口和非平行窗口光路计算的方程，并给出了求解折射率的方法。     

Strong disorder renormalization group primer and the superfluid–insulator transition

This brief review introduces the method and application of real-space renormalization group to strongly disordered quantum systems. The focus is on recent applications of the strong disorder renormalization group to the physics of disordered-boson systems and the superfluid–insulator transition in one dimension. The fact that there is also a well-understood weak disorder theory for this problem allows us to illustrate what aspects of the physics change at strong disorder. In particular, the strong disorder RG analysis suggests that the transitions at weak disorder and strong disorder belong to distinct universality classes, but this question remains under debate and is not fully resolved to date. Further applications of the strong disorder renormalization group to higher-dimensional Bose systems and to bosons coupled to dissipation are also briefly reviewed.     

Influence of structural variability upon sound perception: Usefulness of fractional factorial designs

The present paper introduces an efficient and time-saving approach for the evaluation of the consequences of structural uncertainties on sound perception. Its aim is to validate the use of fractional factorial designs for perceptual assessment of a model system. A test bench was used, which allowed to accurately control the variability of several structural design parameters. Sounds emitted by the bench were recorded with a dummy head and submitted to listeners during two experiments, in which they had to evaluate the dissimilarity of each sound to a reference, representing the nominal state of the device. In the first experiment, six factors, assumed to be independent, were used to define a fractional factorial design. As an analysis of variance showed that two interactions between factors should have been taken into account, a second experimental design was developed to quantify these interactions. These two experiments allowed to define an accurate model of sound perception, describing the effect of each factor on the perceived dissimilarity. Thus, it was possible to relate the variability of the structure to the perception of the sound emitted with few experimental effort.