This paper studies the topological properties of knotted solitons in the （3 ＋1）-dimensional Aratyn-Ferreira- Zimerman （AFZ） model. Topologically, these solitons are characterized by the Hopf invariant I, which is...This paper studies the topological properties of knotted solitons in the （3 ＋1）-dimensional Aratyn-Ferreira- Zimerman （AFZ） model. Topologically, these solitons are characterized by the Hopf invariant I, which is an integral class in the homotopy group π3（S3） = Z. By making use of the decomposition of U（1） gauge potential theory and Duan＇s topological current theory, it is shown that the invariazat is just the total sum of all the self-linking and linking numbers of the knot family while only linking numbers are considered in other papers. Furthermore, it is pointed out that this invariant is preserved in the branch processes （splitting, merging and intersection） of these knot vortex lines.展开更多
By means of the method of torus knot theory, this paper gives the complete processes of obtaining the knotted pictures of four Bell b^es from the knotted pictures of four basic two qubit states.
By means of the torus knot theory method, this paper presents the complete process of obtaining the knotted pictures of eight GHZ states on the surface of a trivial torus from the knotted pictures of eight basic three...By means of the torus knot theory method, this paper presents the complete process of obtaining the knotted pictures of eight GHZ states on the surface of a trivial torus from the knotted pictures of eight basic three-qubit states on the surface of a trivial torus. Thus, we obtain eight knotted pictures 121 linkage on the ordinary plane.展开更多
Knot theory is a branch of topology in pure mathematics, however, it has been increasingly used in different sciences such as chemistry. Mathematically, a knot is a subset of three-dimensional space which is homeomorp...Knot theory is a branch of topology in pure mathematics, however, it has been increasingly used in different sciences such as chemistry. Mathematically, a knot is a subset of three-dimensional space which is homeomorphic to a circle and it is only defined in a closed loop. In chemistry, knots have been applied to synthetic molecular design. Mathematics and chemistry together can work to determine, characterize and create knots which help to understand different molecular designs and then forecast their physical features. In this study, we provide an introduction to the knot theory and its topological concepts, and then we extend it to the context of chemistry. We present parametric representations for several synthetic knots. The main goal of this paper is to develop a geometric and topological intuition for molecular knots using parametric equations. Since parameterizations are non-unique;there is more than one set of parametric equations to specify the same molecular knots. This parametric representation can be used easily to express geometrically molecular knots and would be helpful to find out more complicated molecular models.展开更多
Based on the knot theory and researching of network structures of glucomannan molecules, the polysaccharides were analyzed. The link prediction analysis is to further reveal the interactions between polysaccharides, t...Based on the knot theory and researching of network structures of glucomannan molecules, the polysaccharides were analyzed. The link prediction analysis is to further reveal the interactions between polysaccharides, to elaborate QSAR of polysaccharides, and to analyze the network conformation relationships among polysaccharides. We made a classification for glucomannan molecules based on the related domestic and international theories, and investigated their network structures and application prospects. The knot theory and the link predictions not only simplify the glucomannan microscopic descriptions but also play a guiding role in predicting and regulating the structures.展开更多
基金supported by the National Natural Science Foundation of China(Grant No 10275030)the Cuiying Program of Lanzhou University,China(Grant No 22500-582404)
文摘This paper studies the topological properties of knotted solitons in the （3 ＋1）-dimensional Aratyn-Ferreira- Zimerman （AFZ） model. Topologically, these solitons are characterized by the Hopf invariant I, which is an integral class in the homotopy group π3（S3） = Z. By making use of the decomposition of U（1） gauge potential theory and Duan＇s topological current theory, it is shown that the invariazat is just the total sum of all the self-linking and linking numbers of the knot family while only linking numbers are considered in other papers. Furthermore, it is pointed out that this invariant is preserved in the branch processes （splitting, merging and intersection） of these knot vortex lines.
文摘By means of the method of torus knot theory, this paper gives the complete processes of obtaining the knotted pictures of four Bell b^es from the knotted pictures of four basic two qubit states.
文摘By means of the torus knot theory method, this paper presents the complete process of obtaining the knotted pictures of eight GHZ states on the surface of a trivial torus from the knotted pictures of eight basic three-qubit states on the surface of a trivial torus. Thus, we obtain eight knotted pictures 121 linkage on the ordinary plane.
文摘Knot theory is a branch of topology in pure mathematics, however, it has been increasingly used in different sciences such as chemistry. Mathematically, a knot is a subset of three-dimensional space which is homeomorphic to a circle and it is only defined in a closed loop. In chemistry, knots have been applied to synthetic molecular design. Mathematics and chemistry together can work to determine, characterize and create knots which help to understand different molecular designs and then forecast their physical features. In this study, we provide an introduction to the knot theory and its topological concepts, and then we extend it to the context of chemistry. We present parametric representations for several synthetic knots. The main goal of this paper is to develop a geometric and topological intuition for molecular knots using parametric equations. Since parameterizations are non-unique;there is more than one set of parametric equations to specify the same molecular knots. This parametric representation can be used easily to express geometrically molecular knots and would be helpful to find out more complicated molecular models.
基金Supported by the National Natural Science Foundation of China(31271837 and 31071518)Specialized Research Fund for the Doctoral Program of Higher Education jointly funded by Ministry of Education(20113515110010)+2 种基金Special Research Funds from Ministry of Science and Technology(2012GA7200022)Major projects of industries,universities and research in Fujian Province(2013N5003)Natural Science Foundation of Fujian Province(2011J0101)
文摘Based on the knot theory and researching of network structures of glucomannan molecules, the polysaccharides were analyzed. The link prediction analysis is to further reveal the interactions between polysaccharides, to elaborate QSAR of polysaccharides, and to analyze the network conformation relationships among polysaccharides. We made a classification for glucomannan molecules based on the related domestic and international theories, and investigated their network structures and application prospects. The knot theory and the link predictions not only simplify the glucomannan microscopic descriptions but also play a guiding role in predicting and regulating the structures.
