Topological structure of the many vortices solution in Jackiw-Pi model

By using the gauge potential decomposition, we discuss the self-dual equation and its solution in Jackiw-Pi model. We obtain a new concrete self-dual equation and find relationship between Chern-Simons vortices solution and topological number which is determined by Hopf indices and Brouwer degrees of Psi-mapping. To show the meaning of topological number we give several figures with different topological numbers. In order to investigate the topological properties of many vortices, we use five parameters (two positions, one scale, one phase per vortex and one charge of each vortex) to describe each vortex in many vortices solutions in Jackiw-Pi model. For many vortices, we give three figures with different topological numbers to show the effect of the charge on the many vortices solutions. We also study the quantization of flux of those vortices related to the topological numbers in this case.

Topological structure of vortex solution in Jackiw-Pi model

By using phi-mapping method, we discuss the topological structure of the self-duality solution in Jackiw-Pi model in terms of gauge potential decomposition. We set up relationship between Chern-Simons vortex solution and topological number, which is determined by Hopf index and Brouwer degree. We also give the quantization of flux in this case. Then, we study the angular momentum of the vortex, which can be expressed in terms of the flux.

Topological structure of the solitons solution in SU(3) Dunne-Jackiw-Pi-Trugenberger model

By using phi-mapping topological current theory and gauge potential decomposition, we discuss the self-dual equation and its solution in the SU(N) Dunne-Jackiw-Pi-Trugenberger model and obtain a new concrete self-dual equation with a 6 function. For the SU(3) case, we obtain a new self-duality solution and find the relationship between the soliton solution and topological number which is determined by the Hopf index and Brouwer degree of phi-mapping. In our solution, the flux of this soliton is naturally quantized.

香港地区湍蛙遗传多样性研究

依据线粒体上ND2和CO1两个变异较大的基因序列分析了香港地区香港湍蛙7种群、华南湍蛙1种群，以及大陆其他地区华南湍蛙7种群，戴云湍蛙1种群，武夷湍蛙1种群的系统发育关系，进而探讨香港湍蛙的遗传多样性、香港湍蛙特有性、如何确定香港湍蛙最佳保护单元以及这四种湍蛙的物种分类地位。 1． 香港湍蛙保护遗传学研究 香港湍蛙核苷酸传多样性较低，从其遗传多样性信息、单倍型网络分析、中性检验值以及岐点分布结果一致显示香港湍蛙很可能经历了瓶颈后的扩张，种群正在由一个较小的有效种群大小迅速增长, 有足够的时间通过变异用于积累单倍型的多态性, 而对于提高核苷酸多样化而言, 时间尚短（Nei M et al，1975，Avise J C，2000；李明等，2003）。 分子变异分析结果显示香港湍蛙种群间存在较多的基因交流，且系统发育树上各种群间交叉在一起，没有形成与地理单元相关的分支，而从其单倍型网络看，他们源于共同的祖先，是一个单系群，与地理单元间没有形成显著的遗传分化。因此应作为一个进化显著单元（ESU）。结合其与其他湍蛙发育关系及遗传距离以及野外采集信息认为香港湍蛙只在香港地区有分布，属于香港特有种。该物种内遗传多样性较低，又属于世界自然保护联盟红皮书中的近危种，同时也是《野生动物保护条例》中的受保护野生动物，且由于香港城市建设等使得其栖息环境受到威胁，因此在香港特别行政区应该受到重点保护。 从单倍型分布和核苷酸多样性可以看出大榄涌种群和城门种群具有较高的单倍型多样性和核苷酸多样性，应该作为保护的重点区域。 2. 华南湍蛙东、南沿海种群间系统关系 华南湍蛙分布广，各种群存在着丰富的遗传多样性信息且中部种群广西龙胜和湖南张家界种群核苷酸多样性明显高于其他边缘种群华南湍蛙。种群间几乎没有基因交流，且各种群间无共享单倍型，可见已形成了显著的遗传分化。各种群间遗传距离都较远，其中广东南昆山种群以及福建三港种群与其他种群距离最远，因此可以推测其他种群（广东深圳、香港大屿山、广西龙胜和防城以及湖南张家界种群）可能为独立进化的种群。但是否是一新种或一隐存种，还需要结合形态学进行更深入的研究。 本研究中无论从系统关系看还是从遗传距离看，大屿山种群与深圳种群最近，支持陈坚峰等将其定为华南湍蛙，即华南湍蛙新增一个分布点：香港大屿山。 系统树上广西防城种群（支B）与龙胜和湖南种群（支A）形成姐妹群。香港大屿山种群与深圳种群先形成姐妹群（支C），但却没有与其距离很近的广东南岭及南昆山种群（支D）形成姐妹群，可能粤北和粤中的环境及气候较复杂因此与粤南其他种群形成了明显的隔离。同时可以看出华南湍蛙种群遗传分化与地理距离没有显著的相关性。 3. 四种湍蛙间的系统关系 根据线粒体CO1基因建立四种湍蛙间的系统关系及其遗传距离，很清楚地看到，香港湍蛙与戴云湍蛙关系很近，而华南湍蛙则与武夷湍蛙较近。然而，戴云湍蛙同一个种群内部共有两个单倍型DY1和DY2，且两个单倍型间遗传距离大于DY1与香港湍蛙间遗传距离，更远远大于香港湍蛙种群内部的距离，即戴云湍蛙内部两个单倍型间遗传距离达到了种级水平，同样在系统发育树上这两个单倍型与香港湍蛙形成并系。但是，戴云湍蛙种内在形态上差异不显著。因此，其是否属于萌芽物种分化形成（budding speciation）或已经完全分化为两个不同的种值得进一步研究？ 与戴云湍蛙香港湍蛙关系类似，从系统树上看华南湍蛙不形成单系，而是分成两个大支，与武夷湍蛙形成并系，且福建和南昆山的华南湍蛙与武夷湍蛙遗传距离远大于武夷湍蛙种内福建种群与浙江种群的遗传距离，达到了种级分化水平。由此，可以推断武夷湍蛙是有效种。系统树上广东深圳、香港大屿山、广西防城和龙胜以及湖南张家界种群与华南湍蛙福建及南昆山各种群间遗传距离已超出了种内各种群间的遗传距离，但是至于这一支是否应为另外一个种，有必要扩大采样，并结合核基因及形态信息进行进一步研究。 MtDNA of ND2 and CO1 gene were used to investigate genetic diversity of Amolops in Hongkong .We collected seven populations of A. hongkongensis,，one population of A.ricketti from Hong Kong and other seven populations of A.ricketti from East and South of Chinese mainland. As well as one population of A. daiyunensis and one population of A.wuyiensis Phylogenetic relationship were analyzed of four species. Discussed whether A.hongkongensis is an endemic species and how can we make the conservation and management decisions. 1. Conservation Genetics of A. hongkongensis A. hongkongensis has a low nucleotide diversity, the results of genetic diversity, haplotype network, neutrality test and the mismatch distributions indicate that A. hongkongensis experienced a recent expansion after a bottle neck. They had enough time to accumulated haplotype diversity, but it’s too short to have a high nucleotide diversity（Nei M et al，1975，Avise J C，2000；Li et al，2003）. The result of AMOVA reveals that it has much gene exchange among the populations of A. hongkongensis. The clades of the phylogenetic tree were mixed together, no significant genetic differentiation among 8 populations and they share the same ancestor from the network analysis, these indicate that they are monophyly and should be protected as one ESU. Combined with the information of relationships of interspecies, genetic distance and distribution investigate, We conclude that A. hongkongensis is an endemic species of Hong Kong. Considering on the status of low genetic diversity in A.hongkongensis, and this species was listed in the IUCN red list as near threatened, as well as listed in the . Furthermore, it’s habitat loss and degradation more rapidly as the human activity got higher and higher. So it’s urgent to protect them in Hong Kong. Our results suggest that Tai Lam Wu and TAI MO Shan -Shing Mun populations have the higher priority to be protected because their higher genetic diversity. 2．Phylogenetic relationships among populations of Amolops ricketti from the Southern and eastern China A. ricketti has the considerable genetic diversity of mitochondrial haplotypes within and among populations, and Mitochondrial DNA diversity was higher in populations at the central area of the present distribution range of the frog，i. e. the Longsheng population and Zhangjiajie population, than at the edges of their distribution range. They have no share haplotype among populations, and have a significant genetic differentiation. Genetic distance is high among the populations, especially the distance of Nankun and Sangang group with others, which suggested that they evolved independently. May be there is a cryptic species or a new species, a further study is needed. The results of gene tree and the genetic distance clearly demonstrate that the population from LanTau island is A. ricketti, so we agree with Chen et al(2005) . That means A.ricketti have a new distribution site: LanTau island, HongKong. Phylogenetic relationships were analyzed through NJ and Mrbayes methods and got a consistent topological structure, the structure indicated that the ingroup were comprised four groups. Populations Longsheng and Zhangjiajie were first clustered as clade A; Populations Fangcheng was clustered together (clade B) as a sister group to clade A；Populations Shenzhen and Lantau island were sister groups and clustered as clade C；Then the clade D included populations Nankunshan and Nanling in Guangdong province and Sangang in Fujian province. 3. Phylogenetic Relationships among these four specises Phylogenetic relationships based on 1503bp CO1 gene and the genetic distance show that A. hongkongensis close to A. daiyunensis whereas A.ricketti near to A.wuyiensis. Nevertheless, there are two haplotypes in A.daiyunensis and the genetic distance between them higher than the distance between DY1 with A. hongkongensis. A. hongkongensis is nested in the paraphyletic ancestral species A. daiyunensis. Without significant difference in the morphological characters, So, we considered both A.daiyunensis and A.hongkongensis are valid species, may be this represents a case of ‘budding speciation’ like Batrachuperus pinchonii(Fu and Zeng,2008) in the population of A. daiyunensis. Just like two species above A. wuyiensis and A. ricketti are not monophyly, instead, A.wuyiensis is nested in the paraphyletic ancestral species A.ricketti. We need do more research to make sure whether they are new species.

Decomposition of Noncommutative U(1) Gauge Potential

We investigate the decomposition of noncommutative gauge potential (A) over cap (i), and find that it has inner structure, namely, (A) over cap (i) can he decomposed in two parts, (b) over cap (i) and (a) over cap (i), where (b) over cap (i) satisfies gauge transformations while (a) over cap (i) satisfies adjoint transformations, so close the Seiberg-Witten mapping of noncommutative, U(1) gauge potential. By, means of Seiberg-Witten mapping, we construct a mapping of unit vector field between noncommutative space and ordinary space, and find the noncommutative U(1) gauge potential and its gauge field tensor can be expressed in terms of the unit vector field. When the unit vector field has no singularity point, noncommutative gauge potential and gauge field tensor will equal ordinary gauge potential and gauge field tensor

New vortex solutions of Jackiw-Pi model

Based on current phi-mapping topological theory, a kind of self-dual equations in Jackiw-Pi model are studied. We first obtain explicit, self-dual solutions that satisfy Liouville equation which contains delta-function. Then we get perfect vortex solutions which reflect the system's internal topological structure, and consequently the quantization of flux.

Knotlike chi disclinations in the cholesteric liquid crystals

We investigate the topological properties of N(N >= 1) disclination lines in cholesteric liquid crystals. The topological structure of N disclination lines is obtained with the Hopf index and Brouwer degree. Furthermore, the knotted x disclination loops is proposed with the Hopf invariant. And we consider the stability of such configuration based on the higher order interaction. At last, the evolution of the disclinations is discussed.

规范势分解与Chern-Simons场中涡旋解的拓扑结构

本论文主要包括两部分内容，一部分简述了规范势的可分解理论，第二部分研究了Chern-Simons涡旋解的拓扑结构。讨论了SU(2)规范势分解的几何意义。提出了非对易规范势的可分解性，求出了非对易 群规范势用单位矢量场的分解以及规范平行条件下的规范场强。利用规范势分解理论和Ф-映射拓扑流理论分别研究了Jackiw-Pi模型和SU(2)Dunne-Jackiw-Pi-Trugenberger模型涡旋的拓扑结构，得到一个新的自对偶方程，发现了Chern-Simons多涡旋解与拓扑数之间的联系。我们构造了一个新的静态的自对偶Chern-Simons多涡旋解，每个涡旋由5个实参数描述。为了研究拓扑数对涡旋形状的影响，给出了具有不同拓扑数的多涡旋解，并绘出了涡旋密度的分布图。我们还研究了该涡旋解的磁通量的拓扑量子化

中低纬度变化磁场的暴时特征研究

Magnetic storm is a kind of severe disturbances in the whole solar-earth electromagnetic space. It has significant effects on communication, electric power, oil transport pipe and human activities in space. Therefore, magnetic storms are worth for applications systems, not only being a favorable issue for scientists. In this paper, the spatial and temporal distributions of the magnetic fields produced by the magnetosphere-ionosphere current systems during storms are studied. Four parts are included in this paper decomposion of different disturbances with different origins, topological structure of the ring current, the asymmetric characteristics of the ring current, and the statistic peculiarities of the day-to-day variability (DTD) of Sq. 1 The decomposition of magnetic disturbances at mid-low latitudes and its evolutions during storms Transient variations in the geomagnetic field recorded at mid-low latitudes mainly include the storm-time variation (Dst), solar quiet daily variation (Sq) and disturbance daily variation (SD). With the data of the geomagnetic meridian chain observatories in China, 25 storms during the period of 1997 to 1999 have been analyzed. According to the features of different variations, a method of “three-steps decomposition” is developed by using the method of Natural Orthogonal Components (NOC), Correlation Analysis and Fourier Analysis to separate those three components in turn. The results show that, the first eigenmode by the MNOC clearly describing the special distribution and temporal evolution of storm-time variation, in addition, Correlation Analysis and Fourier Analysis offer a useful method to extract the Sq and SD variations. The latitudinal shift of the Sq current focus seems to be the principal reason of the day-to-day variaitons in the daily range of Sq. The magnitude of SD reaches a maximum during the main phase, and then gradually decreases. 2 The topology structure of the ring current during storms Both the mechanism of the ring current and the geomagnetic data suggest that the central plane of the ring current is declining to the geomagnetic equator plane with a tilt angle δ. Using the H and Z component data at two stations in a meridian chain, we deduce a new parameter describing the invariable peculiarity of different storms. Then the δ angle is calculated by using the data from a meridian chain and tested with the ERC model. Finally the deduced tilt angles are used to modify Dst index. 3 The asymmetric characteristics of the ring current during storms The variations of the geomagnetic field at mid-low latitudes show a significant dawn-dusk asymmetry, resulting from the superposition of the fields from the symmetric ring current and the partial ring current. On the basis of the data from the 20°E, 30°E meridian chains and 30°N latitudinal chain, the dawn-dusk asymmetry is investigated by using three methods, namely, statistic analysis, ring current model calculation and typical event analysis. This characteristic implies the asymmetry of the spatial distribution of the ring current. In addition, during the main phase after the sudden commencement (SC), H field increases and reaches maximum around noontime, implying the effect of the Chapman-Ferraro current. 4 The statistic characteristics of the day-to-day variability and its mechanism The day-to-day variability of the geomagnetic Sq field is studied by using the magnetic data from a meridian chain of magnetometers along 120° E longitude. The method of NOC is applied to separate the Sq variation from complicated disturbances. The first eigenmode with the largest eigenvalue represents fairly well the Sq variation with a conspicuous day-to-day variability in the daily range. For the stations on the same north- or south-side of the Sq current system focus, the day-to-day variations show a positive correlation. In contrast, for the stations on the different sides of the Sq focus, they show a negative correlation, suggesting an important role of latitudinal shift of the Sq current system focus to the day-to-day variability of the Sq daily range. The Sq daily range is correlated with the magnetic indices Ap and Dst in a peculiar way: on some severe disturbed days, noticeably enhancements of the Sq are observed, implying increases of the ionospheric conductivities and/or tidal wind velocities; on other severe disturbed days, however, dramatically reduced Sq variations occur, suggesting dominant effects of the ‘disturbance dynamo’ process.

Low temperature specific heat and thermal stability of Fe-B ultrafine amorphous alloy particles

Fe-B ultrafine amorphous alloy particles (UFAAP) were prepared by chemical reduction of Fe3+ with NaBHO4 and confirmed to be ultrafine amorphous particles by transmission electron microscopy and X-ray diffraction. The specific heat of the sample was measured by a high precision adiabatic calorimeter, and a differential scanning calorimeter was used for thermal stability analysis. A topological structure of Fe-B atoms is proposed to explain two crystallization peaks and a melting peak observed at T=600, 868 and 1645 K, respectively.

Study on structure-property relationships between color reagents and sensitivity of color reactions with yttrium by topological indices

In this paper, three topological indices, Am-1, Am-2, and Am-3, multivariate analysis in structure-property studies. The topological indices of twenty asymmetrical phosphosphono bisazo derivatives of chromotropic acid have been calculated. The structure-property relationships between color reagents and molar absorptivity of color reactions with yttrium have been studied by A(m) indices and structure selective factors. Good results have been obtained by using correlation equation to predict the molar absorptivity of new color reagents.

Studies on structure-property relationship between color reagents and contrast of their color reactions with cerium by topological indices

In this paper, three topological indices A(m1), A(m2) and A(m3) have been applied to multivariate analysis in structure property relationship studies. The topological indices oi fourty-three asymmetrical phosphono bisazo derivatives of chromotropic acid have been calculated, The structure-property relationship between color reagents and contrast of color reactions with cerium has been studied by A, indices and structure selective factors, Good results have been obtained.

STUDIES ON STRUCTURE-PROPERTY RELATIONSHIP BETWEEN COLOR REAGENTS AND SENSITIVITY OF THEIR COLOR-REACTIONS WITH YTTERBIUM BY TOPOLOGICAL INDEXES

In this paper A, topological indices and molecular connectivity inidces have been applied to multivariate analysis in structure-property studies. The topological indices of twenty asymmetrical phosphone bisazo derivatives of chromotropic acid have been calculated. The structure-property relationships between color reagents and molar absorptivity of color reactions with ytterbium have been studied by A(m) indices and molecular connectivity indices. Good results have been obtained.

STUDY ON STRUCTURE-ACTIVITY-RELATIONSHIPS OF ORGANIC-COMPOUNDS - 3 NEW TOPOLOGICAL INDEXES AND THEIR APPLICATIONS

In this paper, three new topological indices, A(x1), A(x2), and A(x3), have been developed for use in multivariate analysis in structure-property relationship (SPR) and structure-activity relationship (SAR) studies. Good results have been obtained by using them to predict the physical and chemical properties and biological activities of some organic compounds.