Homographic Solutions of the N-body Generalized Lennard-Jones System

In this paper,we obtain the existence of non-planar circular homographic solutions and non-circular homographic solutions of the(2+N)-and(3+N)-body problems of the Lennard-Jones system.These results show the essential difference between the Lennard-Jones potential and the Newton's potential of universal gravitation.

Macroscopic Equation and Its Application for Free Ways

Effective transportation systems lead to the efficient movement of goods and people, which significantly contribute to the quality of life in every society. In the heart of every economic and social development, there is always a transportation system. Mathematically the problem of modeling vehicle traffic flow can be solved at two main observation scales: The microscopic and the macroscopic levels. In the microscopic level, every vehicle is considered individually, and therefore, for every vehicle, we have an equation that is usually an ordinary differential equation (ODE). At a macroscopic level, we use from the dynamics models, where we have a system of partial differential equation, which involves variables such as density, speed, and flow rate of traffic stream with respect to time and space. Therefore, considering above content, this study has tried to compare solution of equation of macroscopic flow considering linear form (speed-density) and applying boundary condition that resulting to form solved is non-linear one-order partial differential equation (sharpy method) with non-linear assuming (speed and density) and consequently homographic nonlinear relation (speed-density). The recent case clearly gives more significant speeds than linear case of speed and density that can be a good scientific basis. In terms of safety for accidents and traffic signal, just as a reminder, but it is resulted of the reality that generally solutions of partial differential equations can have different forms. Therefore, the solution of partial differential equation (macroscopic flow) can have different answers and solutions so that all of these solutions apply in PDE (equation of macroscopic flow). Thus, under this condition, we can have solution of linear equation similar to greenberg or greenshield & android that are explained in logarithm and exponential function, but this article is based mostly on nonlinear solution of macroscopic equation, provided that existing nonlinear relationship between speed and density (homographic the second degree function). As mentioned above, as it gives more reliable and reasonable speeds than greenshield case, it will have more safety. This article has been provided in this field.

浅析homograph,homonym,homophone的应用及产生的效果

在英语学习过程中 ,对同形异义词、同音同形异义词、同音异形异义词的运用很容易造成混淆。正确掌握它们之间的区别 ,能起到良好的修辞效果 ,达到预期目的 ,从而激发英语学习者对英语学习的极大兴趣。

A New Method of Recognizing Polygons under Perspective Transformation

Existing methods for recognizing polygons can be improved. A new concept ＂homograph＂ and then a new method for recognizing polygons based on the principle of homograph are proposed. First, five topological characteristics and geometrical characteristics are introduced that are invariant to describe polygon under perspective transformation. Then, the new concept of homograph is defined in terms of five topological characteristics and geometrical characteristics. Based on this definition, a new algorithm is proposed for recognizing that two polygons are homograph. The topological structure is introduced to analyze homograph qualitatively and the algorithm is insensitive to noises; and the geometrical structure is introduced to analyze homograph quantitatively, thus the algorithms can show tiny differences between polygons. It can not only recognize the objects with different shapes but also distinguish between objects with same shape but with different sizes and scales. Comparing with other recognition algorithms, the algorithm presented showed apparent improvement. The effectiveness of the algorithm is demonstrated by experiments.

A Contrastive Analysis of Chinese and Japanese Homographs and a Study on the Causes of Differences

Since ancient times,China and Japan have had a close relationship in cultural exchanges,and there are words borrowed and influenced by each other in terms of words.Therefore,there are a large number of words in the languages of China and Japan that are identical or similar in appearance,but differ in meaning or usage.As Learners of Japanese,it is necessary for us to make a comparative study of homomorphic words.This paper tries to analyze and discuss the characteristics and causes of homomorphic words based on the classification of homomorphic words from the perspective of lexicology.

Geometric characterization for the least Lagrangian action of n-body problems

For n-body problems with quasihomogeneous potentials in Rk (2［n/2］≤k) we prove that the minimum of the Lagrangian action integral defined on the zero mean loop space is exactly the circles with center at the origin and the configuration of the n-bodies is always a regular n-1 simplex with fixed side length.

Estimation of Vehicle Pose and Position with Monocular Camera at Urban Road Intersections

With the rapid development of urban, the scale of the city is expanding day by day. The road environment is becoming more and more complicated. The vehicle ego-localization in complex road environment puts forward imperative requirements for intelligent driving technology. The reliable vehicle ego-localization, including the lane recognition and the vehicle position and attitude estimation, at the complex traffic intersection is significant for the intelligent driving of the vehicle. In this article, we focus on the complex road environment of the city, and propose a pose and position estimation method based on the road sign using only a monocular camera and a common GPS （global positioning system）. Associated with the multi-sensor cascade system, this method can be a stable and reliable alternative when the precision of multi-sensor cascade system decreases. The experimental results show that, within 100 meters distance to the road signs, the pose error is less than 2 degrees, and the position error is less than one meter, which can reach the lane-level positioning accuracy. Through the comparison with the Beidou high-precision positioning system L202, our method is more accurate for detecting which lane the vehicle is driving on.