基于线性偏振光子对学说的数学建模与仿真

北京大学学者猜想单个光子只有左旋光子、右旋光子两种.一个左旋光子与一个右旋光子可以组成一个线性偏振光子对.在合理假设基础上,从光的波粒二象性的认识出发,基于这种猜想分别对双缝干涉、单缝衍射、多缝衍射等实验建立光子的运动方程,利用复数积分法得到相应的光强分布模型.并用Matlab软件进行数学仿真,得到猜想的实验结果与波恩的实验结果相符合.     

光子结构的猜想及其数学仿真

通过研究光的波粒二象性,对光子结构进行了研究并提出了自建光子模型.自建光子模型具有以下特性:①光子与原子核存在引力作用;②光子的电场与磁场交替变换使其具备了相位效应,且光强由光子数与光子相位和两个因素决定.在此基础上,通过借鉴天体物理中关于二体运动的三种轨迹,利用其中结论对大量原子核的引力作用进行概率分析,使用中心极限定理提出出射角度基本符合高斯分布的假设.接着对光子的相位叠加效应进行了分析.最后,对大量光子进行模拟仿真,并将仿真结果与单缝衍射、双缝干涉、多缝干涉现象等实验现象进行了对比.     

光子结构猜想的仿真验证

从龚祖同院士的类氢光子结构模型和北大学者的电磁场粒子模型出发,提出了等效作用和动态光子层的概念,并在此基础上,利用蒙特卡罗法和伽尔顿板法,对光的干涉、衍射现象进行了定量分析和仿真实验,验证了光子结构猜想的正确性.     

基于光的波粒二象性猜想的数学仿真

从现有的经典物理光学理论和专业实验结果出发,运用数学思维,综合光子理论,建立了基于光的波粒二象性猜想的四种数学模型.针对光微子碰撞猜想,建立了基于光子碰撞后概率分布的模型.针对光子作为电磁场自我旋转的猜想,分别从专业证明和数学模型分析方面建立了电磁场偏转模型和光子旋转模型.最后建立了我们自己的猜想模型——光子蜂窝网络模型.该模型引入了"光子域"、"光子电力"、"光子磁力"、"光子键"等概念,从五个子模型出发,定性解释了四个光学现象,合理回答了题目提出的三大问题,并定量证明了衍射光强分布.     

光的波粒二象性探索

光具有波粒二象性,但很难从光的某一特定现象中同时看到这两种性质.如果能用粒子性解释波动性,光的两种性质就能得到完美的统一.分别对龚祖同光子模型、前进电磁场光子模型进行数学建模和MATLAB仿真,并与已有的实验结果比较.发现两个模型都存在不足,进而提出改进的光子模型,从粒子的角度,对展现光的波动性质的干涉、衍射以及偏振现象进行解释.     

基于光的波粒二象性猜想的数学建模与仿真

光具有波粒二象性,诸多学者都对此提出了不同猜想,用以合理解释光的直线传播、衍射和干涉等问题.对三种基于光的波粒二象性的猜想进行了数学建模与仿真验证.以Matlab为工具对光的衍射等现象的进行了数学仿真,并与《光学原理》中的相关结果作了对比,最终验证了猜想的正确性.     

关于双随机循环矩阵中的素元(英文)

非负矩阵中的素元分类问题在控制和系统论中有重要的应用.本文将研究由G.Picci等所提出的关于双随机循环矩阵中素元的一个问题和一个猜想,得到了一个判别具有位数5的n阶双随机循环矩阵不是素元的充要条件,给出了猜想成立的一些充分条件.     

关于K(B)-L(B)=1的块

运用局部表示论以及Brauer的一些原始思想研究了满足条件K(B)-L(B)=1的块,得到了这种块的结构及其亏群的一些性质.特别地,作为这些性质的一个推论,对这种块证明了K(B)猜想.     

中考数学猜想题例说

数学家弗赖登塔尔说 :“真正的数学家常常借数学的直觉思维作出各种猜想 ,然后加以证实的 .猜想是一种探索性活动 ,具有一定的规律和方法 ,在探索中 ,这些规律和思维方法的实践与邻悟 ,必然会对学生智能的开发和数学思维的发展具有重要的推进作用 .”由此可见 ,数学猜想是数学发展的源动力 ,是解决数学问题的先行军 .数学就在不断的证明或否定猜想的过程中得到发展 .数学猜想是对研究的对象或问题进行观察、实验、分析、比较、联想、类比、归纳等 ,依据已有的材料和知识作出符合一定的经验与事实的推测性想象的思维形式 .(任樟辉著《数学思…     

浅谈高中“数学实验”教学的教学设计

从五个方面入手对高中"数学实验"教学的教学设计进行探讨,包括:创设情境、明确目标;动手实验;验证规律或提出猜想;验证猜想;反思、体验、提高.     

Weberized Mumford-Shah Model with Bose-Einstein Photon Noise

Human vision works equally well in a large dynamic range of light intensities, from only a few photons to typical midday sunlight. Contributing to such remarkable flexibility is a famous law in perceptual (both visual and aural) psychology and psychophysics known as Weber's Law. The current paper develops a new segmentation model based on the integration of Weber's Law and the celebrated Mumford-Shah segmentation model (Comm. Pure Appl. Math., vol. 42, pp. 577-685, 1989). Explained in detail are issues concerning why the classical Mumford-Shah model lacks light adaptivity, and why its "weberized" version can more faithfully reflect human vision's superior segmentation capability in a variety of illuminance conditions from dawn to dusk. It is also argued that the popular Gaussian noise model is physically inappropriate for the weberization procedure. As a result, the intrinsic thermal noise of photon ensembles is introduced based on Bose and Einstein's distributions in quantum statistics, which turns out to be compatible with weberization both analytically and computationally. The current paper focuses on both the theory and computation of the weberized Mumford-Shah model with Bose-Einstein noise. In particular, Ambrosio-Tortorelli's Γ-convergence approximation theory is adapted (Boll. Un. Mat. Ital. B, vol. 6, pp. 105-123, 1992), and stable numerical algorithms are developed for the associated pair of nonlinear Euler-Lagrange PDEs.     

The Wave Function of the Lyman-Alpha Photon Part II. The Shape,Position, and Trajectory of the Photon

In Part I of the present paper we derived the wave function of the Lyman-a \alpha photon in both the linear and angular momentum bases using relativistic concepts for the photon wave function. In the present paper, Part II, we derive two [(X)\vec] \vec{X} -representations. In the first we assume one-particle theory for the photon wave function and the usual commutation rules for the position operators X_i X_i and linear momentum operators P_i P_i . The second representation employs the quantized photon field to derive an [(X)\vec] \vec{X} -representation. The stress, energy tensor density is used to provide a probability density in [(x)\vec] \vec{x} -space which is relativistic. The two methods of defining [(x)\vec] \vec{x} -space are compared.¶It is found in the present case that, despite the use of particle operators, the photon resembles a field far more than it does a particle.     

Commensurated Subgroups of Arithmetic Groups, Totally Disconnected Groups and Adelic Rigidity

The paper establishes a substantial number of cases of a conjecture regarding commensurated subgroups of S-arithmetic groups made by Margulis and Zimmer in the late 1970s. New results in the structure theory of totally disconnected groups are established along the way and are of independent interest. Other ideas in the argument motivate a sweeping conjecture, presented in the last section of the paper, which naturally unifies in an adelic setting deep results and fundamental conjectures in the rigidity theory of arithmetic groups.     

The eigenvalues of a tridiagonal matrix in biogeography

We derive the eigenvalues of a tridiagonal matrix with a special structure. A conjecture about the eigenvalues was presented in a previous paper, and here we prove the conjecture. The matrix structure that we consider has applications in biogeography theory.     

Photon transport with a localized source in locally convex spaces

This paper deals with the study of a mathematical model of photon transport in an interstellar cloud where a localized source is present. The source is represented by a Dirac delta functional. The problem is studied in the setting of locally convex spaces. By means of the theory of semigroups on locally convex spaces and the adjoint approach, we prove existence and uniqueness of the solution. Copyright © 2006 John Wiley & Sons, Ltd.     

Circular Distributions and Euler Systems, II

The purpose of this paper is to investigate a conjecture about the universality of the circular distribution made by Robert Coleman. The algebraic property of the universal distribution is the main ingredient in studying Euler system of Kolyvagin and Rubin. We study the universality of the circular distribution by using the Iwasawa theory and the theory of the Euler systems. The conjecture is a characterization of Euler systems in the case of number field. The results here assert that Euler systems are essentially made out of cyclotomic units.     

Photon structure of stationary spaces

Theoretical and Mathematical Physics - This work is devoted to the analysis of photon surfaces and photon regions in the stationary Plebański–Demiański space–time, including...