Painleve properties and exact solutions for the high-dimensional Schwartz Boussinesq equation

The usual （1＋1）-dimensional Schwartz Boussinesq equation is extended to the （1＋1）-dimensional space-time symmetric form and the general （n＋1）-dimensional space-time symmetric form. These extensions are Painleve integrable in the sense that they possess the Painleve property. The single soliton solutions and the periodic travelling wave solutions for arbitrary dimensional space-time symmetric form are obtained by the Painleve-Backlund transformation.     

A Miura of the Painlevé I Equation and Its Discrete Analogs

We present Miura transformations for the continuous and several discrete Painlev\'e I equations. In the case of the continuous P_I, we use the Hamiltonian formulation of the Painlev\'e equations and show that there exists a Miura transformation between P_I and the binomial, second degree, equation of Cosgrove SD_V. In the case of the discrete P_I's we obtain two different kinds of Miuras. One kind relates a d-P_I to some other d-P_I while the other leads to discrete four-point equations which are the discrete analogs of the derivative of Cosgrove's equation SD_V.     

Statistical-Mechanical Entropies of Schwarzschild Black Hole due to Arbitrary Spin Fields in Different Coordinates

The statistical-mechanical entropies of the Schwarzschild black hole arising from the scalar, Weyl neutrino, electromagnetic, Rarita-Schwinger and gravitational fields are investigated in the Painlevg and Lemaitre coordinates. Although the metrics in the Painlevg and the Lemaitre coordinates do not obviously possess the singularity as that in the Schwarzschild coordinate, we find that the entropies of the arbitrary spin fields in both the Painlevd and Lemaitre coordinates are exactly equivalent to that in the Schwarzschild coordinate.     

Lie symmetry analysis and reduction of a new integrable coupled KdV system

In this paper, Lie symmetry is investigated for a new integrable coupled Korteweg--de Vries (KdV) equation system. Using some symmetry subalgebra of the equation system, we obtain five types of the significant similarity reductions. Abundant solutions of the coupled KdV equation system, such as the solitary wave solution, exponential solution, rational solution and polynomial solution, etc. are obtained from the reduced equations. Especially, one type of group-invariant solution of reduced equations can be acquired by means of the Painlev\'e I transcendent function.     

The model of the black hole enclosed in dust: the flat space case

The model is constructed to describe the Schwarzschild-like black hole enclosed in the dust cosmological background. It is an exact solution of Einstein equations for spherically symmetric dust distribution, and is a special case of Lemaitre–Tolman–Bondi solutions. The motion of the test particle in the model is investigated in comoving coordinate frame. Observable velocity of the particle is found from geodesic equations. It is shown that chosen reference system does not allow to solve the problem of ’all or nothing’ behavior.     

耦合Burgers系统的Painlevé性质分析，对称和对称约化

本文给出了耦合Burgers系统的Painlevé性质，逆强对称算子，无穷多对称和李对称约化。通过把强对称和逆强对称算子重复多次作用到耦合Burgers模型的一些平庸对称，如恒等变换，空间平移变换和标度变换上，我们得到了三族无穷多对称。这些对称构成了无穷维李代数。用其中的有限维子代数——点李代数对模型进行对称约化，得到了模型的群不变解。     

对气象常用坐标系中位涡形式的探讨

气象常用垂直坐标系中的位涡方程及位涡形式是位涡理论及位涡诊断技术的基础.本文依据坐标转换的观点,分别用两种不同的方法推导出等压坐标和等熵坐标中的位涡方程及相应的位涡表达式.一是从三维矢量运动方程出发,由三维涡度方程、连续方程和热力学方程推导位涡方程;二是直接从等压坐标和等熵坐标中的标量运动方程组出发推导位涡方程.结果表明,用两种方法所得到的等压坐标中的位涡方程和位涡表达式形式有所不同,而等熵坐标中用两种方法所得到的位涡方程和位涡形式相同.对垂直坐标系的物理本质分析表明,采用第一种方法时尽管矢量运动方程中的 关键词： 位涡 坐标转换 等压坐标 等熵坐标     

Exact Solutions of Bogoyavlenskii Coupled KdV Equations

The special soliton solutions of Bogoyavlenskii coupled KdV equations are obtained by means of the standard Weiss-Tabor-Carnvale Painlev\'{e} truncation expansion and the nonstandard truncation of a modified Conte's invariant Painlev\'{e} expansion.     

基于天顶观测的光学系统精确标定方法

针对光学系统在实际应用中与载体坐标系协调的问题,将光学系统基准面放置于站心地平坐标系水平面上并摄取星图,对星图处理获取星像坐标,应用天体自动辨识技术和恒星视位置计算技术得到对应天体的赤道坐标,以天顶点为原点建立天球切平面基准坐标系,把星体赤道坐标转化为所对应的基准坐标,利用天顶点切平面与站心地平坐标系的对应关系,将天体基准坐标转换为站心像平面坐标,建立星体站心像平面坐标与星图像平面坐标的标定方程,解算光学系统综合标定参数。实验结果表明:标定精度达到角秒量级,实现光学系统像平面坐标系到载体坐标系的高精度转换。     

SYMMETRIES AND DROMION SOLUTION OF A (2+1)-DIMENSIONAL NONLINEAR SOHR?DINGER EQUATION

The Painlevé property, infinitely many symmetries and exact solutions of a (2+1)-dimensional nonlinear Schr?dinger equation, which are obtained from the constraints of the Kadomtsev-Petviashvili equation, are studied in this paper. The Painlevé property is proved by the Weiss-Kruskal approach, the infinitely many symmetries are obtained by the formal series symmetry method and the dromion-like solution which is localized exponentially in all directions is obtained by a variable separation method.     

基于SLAM的连续运动测量坐标转换算法研究

本文基于同步定位与地图创建(Simultaneous Localization and Mapping,SLAM)原理,通过双目视觉系统的坐标转换方法,建立动态坐标系与静态基准点之间的关系,实现连续运动测量。通过实验,设计运动路线,验证坐标转换算法,并得到了建立在世界坐标系下的空间线形曲线。实验结果表明：转换后的坐标,x、y、z三个方向的最大误差不超过0.734mm。     

A new supersymmetric classical Boussinesq equation

In this paper, we obtain a supersymmetric generalization for the classical Boussinesq equation. We show that the supersymmetric equation system passes the Painlev\'{e test and we also calculate its one- and two-soliton solutions.     

A new supersymmetric classical Boussinesq equation

In this paper, we obtain a supersymmetric generalization for the classical Boussinesq equation. We show that the supersymmetric equation system passes the Painlev\'{e test and we also calculate its one- and two-soliton solutions.     

Coordinates Used in Derivation of Hawking Radiation via Hamilton-Jacobi Method

Coordinates used in derivation of Hawking radiation via Hamilton-Jacobi method are investigated more deeply. In the case of a 4-dimensional Schwarzschild black hole, a direct computation leads to a wrong result. In the meantime, making use of the isotropic coordinate or invariant radial distance, we can get the correct conclusion. More coordinates including Painleve and Eddington-Finkelstein are tried to calculate the semi-classical Hawking emission rate. The reason of the discrepancy between naive coordinate and well-behaved coordinates is also discussed.     

狭义相对论中没有“矛盾方程”

根据洛伦兹变换把两个惯性系的坐标原点的时空坐标从一个坐标系变换到另一坐标系,从相对运动的角度说明洛伦兹变换是自洽的,运动物体上发生的自然过程比起静止物体的过程延缓了,并且两个坐标系中的观察者都认为对方的时钟变慢,是“动钟变慢”而非“动钟变快”,不会导致“矛盾方程”,不能混淆同一事件的变换规律与两个事件的变换结果．     

车载红外告警系统中目标航迹管理及DSP实现

介绍了车载红外告警系统中多目标的航迹建立及目标从图像坐标到载体坐标的转换方法。系统在方位360°视场内均匀布置了6个红外传感器，天顶方向布置1个红外传感器，形成360°全半球视场。每个传感器对应1个目标检测板，系统设计有1个系统控制板，用于对目标进行坐标转换、航迹管理以及向各个检测板发送控制命令。当目标检测板完成目标检测后，便向控制板发送7个传感器中的目标信息，控制板对目标进行坐标转换使之统一于载体坐标系，在载体坐标系建立目标航迹并对航迹进行预测管理，最后通过串口向上位机输出目标在载体坐标系的位置信息并报警。实验证明，转换后的目标位置完全正确，且误差小于1°，满足系统指标要求。     

Semifolded Localized Structures in Three-Dimensional Soliton Systems

By means ofa Painlev6 Backlund transformation and a multi-linear variable separation approach, abundant localized coherent excitations of the three-dimensional Broer Kaup Kupershmidt system with variable coeft~cients are derived. There are possible phase shifts for the interactions of the three-dimensional novel localized structures discussed in this paper.     

机载光电平台目标交会定位

根据直线交会测量原理,构建了机载光电平台目标定位数学模型。首先建立5个坐标系,确定了坐标系之间的变换关系,在地心直角坐标系下,根据光电平台观测目标的方位和俯仰角度参数,结合飞机的位置和姿态测量参数,通过坐标变换确定从光电平台到目标之间的观测直线方程。选择一组目标观测直线建立目标交会测量目标函数,根据最小二乘原理,建立关于直线交会点坐标的线性方程组。解出直线交会点的三维坐标并根据从地心直角坐标系到大地地理坐标系的变换关系,计算目标的大地经纬度和高程坐标,通过样本数据进行交会定位精度实验。实验结果表明,本文方法定位结果和实际测量数据接近,经度误差为0.65",纬度误差为0.82",高程误差为5 m,验证了本文方法的准确性。本文方法有效可行,对机载光电平台目标定位具有实用价值。     

Painlev property of the modified C-KdV equation and its exact solutions

In this paper,the Painlev’e properties of the modified C-KdV equation are verified by using the W-K algorithm.Then some exact soliton solutions are obtained by applying the standard truncated expansion method and the nonstandard truncated expansion method with the help of Maple software,respectively.     

Presentation of Molecular Force Fields in Terms of Dimensionless Coordinates

It is suggested that force fields calculated for polyatomic molecules may be presented in dimensionless coordinates, ξ (=R/R_e, where R is internal coordinate and Re is the equilibrium value of corresponding bond distance or angle). Stretching force constants when presented in dimensionless coordinates show interesting trends. It is found that whereas the force constants in terms of internal coordinates, F_ii vary widely for bonds with different atoms in the series Z-H (Z:C, Si, Ge), Y-H (Y:N, P, As, Sb, O, S), X-H (X:F, Cl, Br, I), X-C etc, the corresponding force constants in dimensionless coordinates, Φ_ii are same within the limits of experimental errors. It is felt that such force constants may have better prospects of transferability between related molecules and may be helpful in making the normal coordinate analysis easier to some extent.