Form Invariance, Noether and Lie Symmetry of Non-conservative Hamiltonian Systems in Phase Space

For the non-conservative holonomic Hamiltonian systems in phase space, the definition and criteria of the form invariance of the generalized Hamilton canonical equations were given. The relations among the form invariance, Noether symmetry and Lie symmetry were studied. The theory of the form invariance for the conservative holonomical systems was worked out. An example was given to illustrate the results.     

Iris Localization Algorithm Based on Improved Generalized Symmetry Transform

Accuracy and fastness of iris localization are very important in automatic iris recognition. A new fast iris localization algorithm based on improved generalized symmetry transform (GST) was proposed by utilizing iris symmetry. GST was improved in three aspects: 1 ) A new distance weight function is defined. The new weight function, which is effective in iris localization, utilized the characteristic of irises that the iris is a circular object and it has one inner boundary and one outer boundary. 2) Each calculation of the symmetry measurement of a pair of symmetry points was performed by taking one point of a pair as the starting point of the transformation. This is the most important reason for fast iris localization, due to which, repetitious computation was largely excluded. 3) A new phase weight function was proposed to adjust GST to locate circle target much better because the inner part of iris is darker than the outer part. The edge map of iris image was acquired and GST was only implemented on the edge point, which decreased computation without loss of accuracy. The modification of distance weight function and phase weight function leads to the accuracy of localization, and other ideass peed up the localization. Experiments show that the average speed of new algorithm is about 7.0-8.5 times as high as traditional ones including integro-differential operator and Hough transform method.     

WVD的快速计算

The paper proposes a new method for computation of the Wigner-Ville distribution (WVD) taking account of the conjugate symmetry of the WVD kernel function and the periodicity and symmetry of the trigonometric function. The method transfers the computation of WVD into real field from complex field to remove the redundancies in the fast Fourier transform(FFT) computation. The realization of fast cosine operation and fast sine operation considerably reduces the computation cost. Theoretical analysis shows that     

Symmetry properties of tetraammine platinum(II) with C_(2v) and C_(4v) point groups

INTRODUCTION The simplicity and elegance of some of theapplications of graph theory to chemistry can perhapsonly be compared with the results from group theorydealing with symmetry as a basic quality of a system.In some problems connectivity and symmetry arecombined and the question of determining symmetryproperties of graph becomes important. Given here are some definitions and notations.An automorphism of a graph G is a permutation g ofthe vertex set of G with the property that, for an…     

An implicit symmetry constraint of the modified Korteweg-de Vries （mKdV） equation

In this paper, an implicit symmetry constraint is calculated and its associated binary nonlinearization of the Lax pairs and the adjoint Lax pairs is carried out for the modified Korteweg-de Vries （mKdV） equation. After introducing two new independent variables, we find that under the implicit symmetry constraint, the spatial part and the temporal part of the mKdV equation are decomposed into two finite-dimensional systems. Furthermore we prove that the obtained finite-dimensional systems are Hamiltonian systems and completely integrable in the Liouville sense.     

A Method of Image Symmetry Detection Based on Phase Information

Traditional methods for detecting symmetry in image suffer greatly from the contrast of im-age and noise, and they all require some preprocessing. This paper presents a new method of im-age symmetry detection. This method detects symmetry with phase information utilizing logGabor wavelets,because phase information is stable and significant, while symmetric points produce pat-terns easy to be recognised and confirmable in local phase. Phase method does not require any preprocessing. and its result is accurate or invariant to contrast, rotation and illumination conditions. This method can detect mirror symmetry, rotating symmetry and curve symmetry at one time. Results of experiment show that, compared with pivotal element algorithm based on intensity information, phase method is more accurate and robust.     

Mei symmetry and new conserved quantities of Tzénoff equations for higher-order nonholonomic system

In this paper,the Mei symmetry of Tzénoff equations for the higher-order nonholonomic system and the new conserved quantities derived from that are researched,and the function expression of new conserved quantities and criterion equation which deduces these conserved quantities are presented.This result establishes the theory basis for further researches on conservation laws of Tzénoff equations of the higher-order nonholonomic constraint system.     

Xian Xinghai—A Great Musician of the People

Xian Xinghai (冼星海) was one of the greatest musicians in China. He was a musician deeply loved by the people because he sang of the people and for the people from the bottom of his heart. He lived before the People's Republic of China was founded. It was a tragedy that he died at the age of only forty-five-in the prime of his most creative and productive years.     

Secondary cooling technology for high-efficiency continuous billet-casting

The mathematical model of high-efficiency continuous billet casting was developed, incorporating the effective spraying water coefficient and the effective specific spraying water flowrate of secondary cooling. To realize uniform cooling in secondary cooling zones, the spraying cooling structure and the arrangement of nozzles were redesigned and optimized, and an additional spraying cooling zone was used. A new secondary cooling model of spraying water was built. It was found that the required spraying water flowrate of a cooling zone was related with the casting speed, the casting temperature, the compositions of liquid steel and the cooling water temperature of secondary cooling. The operation of the reformed caster proved that the spraying cooling structure and the new secondary cooling model were suitable, and the casting speed was greatly enhanced. The highest casting speed was (3.8 to 4.0) m/min for billet with a section of 150×150 mm2. The quality and the output of the billet were improved, and the economical benefit was heightened.     

Mn3+～甲苯非均相体系的氧化反应动力学

The reaction kinetics of the heterogeneous oxidation oftoluene with Mn^3 was studied by considering the effects of disproportionation of Mn^3 in reaction system,a “parallel”modulus was set up.And then the concentration of Mn^3 in disproportionation and the concentration of benzaldehyde in oxidation were respectively determined in turn.the rate constant,order and pseudo-activation energy of the heterogeneous oxidation were obtained by mathematical deduction and the kinetic equation was concluded.In addition,the reaction mechanism was analyzed.It shows that the results are completely consistent with modulus.     

对称原则:现代物理学研究的美学方法

在2 0世纪末(80年代初至90年代末)物理学界围绕“对称与物理学”这一中心议题,进行了一场影响深远的讨论,提出了一种新的研究方法———根据对称为美的原则进行理论研究。本文将这种从现代物理学理论研究中抽象分离出来的研究方法称为“对称原则”。认为该方法植根于现代美学,是一种美学研究方法。并阐述了它与现代美学及物理学传统实在论思想的关系。     

热力学中的平衡与非平衡、对称与对称破缺

平衡与非平衡,对称与对称破缺是自然界中普遍存在着的矛盾关系.平衡、对称是变化中的同一,反映不同物质形态在运动中的共性,非平衡,对称破缺是变化中的差异,反映不同物质形态在运动中各自的特性.自然界的物质(包括整个自然界在内)处于(平衡)对称→(非平衡)对称破缺→(新一级平衡)新一级对称……这样不断深化之中.     

教育质量提升的对称化教育路径——势科学视角

从势科学视角来看,提升教育质量的有效路径是有效地生产教育信息量、营造教育信息势。而对称化教育,即"感性与理性的对称"、"理论与实践的对称"、"直觉与逻辑的对称"、"知识与抽象的对称"、"学习与探索的对称"和"系统性学习与渗透式学习的对称"的教育,则是生产最大教育信息量、营造最大教育信息势的根本路径。     

积分对称性及其在简化积分计算中的应用

将各种积分统一划分为无方向积分和有方向积分两类,并以简洁的形式分别归纳出这两类积分的对称性结论,同时建立了交换对称性的相关理论;通过示例阐述了各种对称性在积分计算中的应用,并提供了创设对称性条件的方法,指出利用对称性简化积分计算时保证对称性匹配是其关键所在。     

对称性在物理学中的基本地位

对称性对人类的心智具有迷人的魅力,而在宇宙中的对称性——存在于支配物质世界运作的基本定律自身中的对称性更值得我们注意和研究。本文谈物理学中关于对称性的认识和从美学方法论角度探讨对称性的方法问题,介绍了对称性的原理,从物理对称性阐明了物理守恒定律的物理渊源,以强调对称性在物理学中的基本地位。     

有多余坐标完整系统的Hojman守恒量

研究有多余坐标完整系统的Hojman守恒量．给出系统Lie对称性与Noether对称性，Lie对称性与形式不变性间的关系．得到特殊Lie对称性、Noether对称性以及形式不变性导致的Hojman守恒量．举例说明结果的应用．     

因果关系和守恒律的对称性探讨

物理学中的对称性包括某件具体事物的对称性和物理规律的对称性两大类。对称性原理是凌驾于牛顿定律、麦克斯韦方程等基本规律之上的更高层次的法则。由时空对称性导出的能量、动量等守恒定律,是跨越物理学各个领域的普遍法则。     

能级简并与对称性

利用量子力学中的基本对称性理论,研究轴对称变形势和非轴对称变形势中能级的简并度与体系对称性的关系.在量子理论中,粒子能级的简并度往往与体系Hamiltonian量的某种对称性相联系.随着势的变化,体系的对称性也发生相应变化,能级的简并度可能增大,也可能被破坏或完全消除.通过理论分析,得出引起体系能级简并度发生变化的理论依据是对称性破缺.     

相空间中Hamilton系统的Noether对称性、Lie对称性和形式不变性

For the non-conservative holonomic Hamiltonian systems in phase space, the definition and criteria of the form invariance of the generalized Hamilton canonical equations were given. The relations among the form invariance, Noether symmetry and Lie symmetry were studied. The theory of the form invariance for the conservative holonomical systems was worked out. An example was given to illustrate the results.     

Form Invariance, Noether and Lie Symmetry of Non-conservative Hamiltonian Systems in Phase Space

1　Introduction　Thesymmetriesofmechanicalandphysicalsystemshavecloseconnectionwiththeassociatedconservedquantities.Therearetwomethodsforseekingtheconservedquantitiesofthemechanicaland physicalsystems:theNoethersymmetry ,aninvarianceoftheHamiltonactionundertheinfinitesimaltransformationofgroups ,leadingtomanyimportantresults[1 5] ;theLiesymmetry ,aninvarianceofthedifferentialequationsundertheinfinitesimaltransformationsofgroups ,extensivelystudiedintherecentyears[6 10 ] .　Since 2 0 0 0 ,Me…