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The X-ray emission from the knots in 3C 120

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Science China(Physics,Mechanics & Astronomy) 2010年第S1期53卷 212-215页

作者： ZHANG Jin1,2,3 & LI ShaoKun1,3 1 National Astronomical Observatories/Yunnan Observatory,Chinese Academy of Sciences,Kunming 650011,China 2 College of Physics and Electronic Engineering,Guangxi Teachers Education University,Nanning 530023,China 3 Graduate University of the Chinese Academy of Sciences,Beijing 100049,China National Astronomical Observatories/Yunnan Observatory Chinese Academy of Sciences Kunming China College of Physics and Electronic Engineering Guangxi Teachers Education University Nanning China Graduate University of the Chinese Academy of Sciences Beijing China

3C 120 is a Seyfert galaxy with a well detected X-ray *** investigate the X-ray emission of its five jet knots and fit their spectral energy distributions(SEDs) from the radio to the X-ray bands with a single-zone lepton *** find that the SEDs of knots k7,s2,and s3 can be explained by synchrotron radiation,and the X-rays are the simple extension of the radio-optical emission component,but that of the inner knot k4 requires the IC/CMB model,in which the X-rays are due to the inverse Compton scattering of the cosmic microwave background photons by relativistic electrons in the jet with a beaming factor δ-*** outer knot k25 is resolved into a three-part *** is shown that the fitting of the X-rays from this knot with the IC/CMB model needs an extraordinary beaming factor δ-15-25 for a jet at the kpc *** the X-rays of knot k25 are produced by synchrotron radiation similar to k7,s2,and s3,they may be contributed by a relativistic electron population whose radiations in other wavelengths are not detected.

关键词： 3C 120 knots X-rays non-thermal emission

Algorithms for Computing Some Invariants for Discrete knots

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Applied Mathematics 2013年第11期4卷 1526-1530页

作者： Gabriela Hinojosa David Torres Rogelio Valdez Facultad de Ciencias Universidad Autónoma del Estado de Morelos Cuernavaca México

Given a cubic knot K, there exists a projection? of the Euclidean space R3?onto a suitable plane ?such that p(K) is a knot diagram and it can be described in a discrete way as a cycle permutation. Using this fact, we develop an algorithm for computing some invariants for K: its fundamental group, the genus of its Seifert surface and its Jones polynomial.

关键词： Cubic knots Discrete knots Algorithms

Topological Properties of Spatial Coherence Function

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Chinese Physics Letters 2008年第2期25卷 367-370页

作者：任继荣朱涛段一士 Institute of Theoretical Physics Lanzhou University Lanzhou 730000

The topological properties of the spatial coherence function are investigated rigorously. The phase singular structures （coherence vortices） of coherence function can be naturally deduced from the topological current, which is an abstract mathematical object studied previously. We find that coherence vortices are characterized by the Hopf index and Brouwer degree in topology. The coherence flux quantization and the linking of the closed coherence vortices are also studied from the topological properties of the spatial coherence function.

关键词： WAVE DISLOCATION LINES PHASE SINGULARITIES BEAMS LIGHT knots

Cluster Partition Function and Invariants of 3-Manifolds

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Chinese Annals of Mathematics,Series B 2017年第4期38卷 937-962页

作者： Mauricio ROMO School of-Natural Sciences Institute for Advanced Study Princeton NJ 08540 USA.

The author reviews some recent developments in Chern-Simons theory on a hyperbolic 3-manifold M with complex gauge group G. The author focuses on the case of G = SL(N, C) and M being a knot complement: M = S^3\ K. The main result presented in this note is the cluster partition function, a computational tool that uses cluster algebra techniques to evaluate the Chern-Simons path integral for G = SL(N, C). He also reviews various applications and open questions regarding the cluster partition function and some of its relation with string theory.

关键词： Chern-Simons theory knots Cluster algebras

Topological Excitation in Skyrme Theory

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Communications in Theoretical Physics 2007年第1期47卷 85-88页

作者： DUAN Yi-Shi ZHANG Xin-Hui LIU Yu-Xiao Institute of Theoretical Physics Lanzhou University Lanzhou 730000 China

Based on the C-mapping topological current theory and the decomposition of gauge potential theory, we investigate knotted vortex lines and monopoles in Skyrme theory and simply discuss the branch processes （splitting... 详细信息

关键词： Skyrme theory knots monopoles

The Invariants θ_p(L(s, q)) of Lens Spaces

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Chinese Science Bulletin 1993年第13期38卷 1067-1070页

作者：李起升李邦河 Department of Mathematics Henan University Kaifeng 475001 PRC Institute of Systems Science Academia Sinica Beijing 100080 PRC

W. B. R. Lickorish constructed three-dimensional manifold invariants from the Kauffman brackets of links. Blanchet and Habegger et al. improved and simplified the result of Lickorish, which is based on the method of Kirby *** an example, the invariants θ_p(L(s, 1)) of lens spaces L(s, 1) are computed only by considering unknot. But there are no general methods for computing the invariants of general 3-dimensional manifolds. In this note, we first study Hopf link and compute the invariants of lens spaces L(s, 2). Secondly, we research string-like links of n-components, which enables

关键词： knots links invariants.

Predicting Financial Contagion and Crisis by Using Jones, Alexander Polynomial and Knot Theory

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Journal of Applied Mathematics and Physics 2015年第9期3卷 1073-1079页

作者： Ognjen Vukovic Department for Finance University of Liechtenstein Vaduz Liechtenstein

Topological methods are rapidly developing and are becoming more used in physics, biology and chemistry. One area of topology has showed its immense potential in explaining potential financial contagion and financial crisis in financial markets. The aforementioned method is knot theory. The movement of stock price has been marked and braids and knots have been noted. By analysing the knots and braids using Jones polynomial, it is tried to find if there exists an untrivial knot equal to unknot? After thorough analysis, possible financial contagion and financial crisis prediction are analysed by using instruments of knot theory pertaining in that sense to Jones, Laurent and Alexander polynomial. It is proved that it is possible to predict financial disruptions by observing possible knots in the graphs and finding appropriate polynomials. In order to analyse knot formation, the following approach is used: “Knot formation in three-dimensional space is considered and the equations about knot forming and its disentangling are considered”. After having defined the equations in three-dimensional space, the definition of Brownian bridge concerning formation of knots in three-dimensional space is defined. Using analogy method, the notion of Brownian bridge is translated into 2-dimensional space and the foundations for the application of knot theory in 2-dimensional space have been set up. At the same time, the aforementioned approach is innovative and it could be used in accordance with stochastic analysis and quantum finance.

关键词： Topology Knot Theory Financial Markets Stochastic Analysis Financial Disruption Financial Crisis knots Braids