Size distribution characteristics of intercity bus hubs in China from 1997 to 2（104 were analyzed regarding highway passenger volume as a size index of intercity bus hubs. Yearly fractal dimensions of intercity bus h...Size distribution characteristics of intercity bus hubs in China from 1997 to 2（104 were analyzed regarding highway passenger volume as a size index of intercity bus hubs. Yearly fractal dimensions of intercity bus hub sizes were exactly calculated by a novel model. Fractal dimensions of the 200 biggest intercity bus hubs from 2000 to 2004 were 1. 486 2 to 1. 511 8, and that is consistent with fractal dimensions of Chinese urban system sizes. It showed that the size distribution of intercity bus hubs had fractal structure. Fractal dimensions from 1997 to 2004 indicated that intercity bus hub size distribution grew from bi-fractal to single fractal. It is concluded that the intercity bus hub system is in evolutionary progress, and the Central Government should support large intercity bus hubs more to optimize system structure.展开更多
It is proved that the coefficients of conway polynomial in z0,z1 and z2 and all ambient isotopic invariants. In particular,the coefficient in z2 of conway polynomial for link L with two components is only depend on sw...It is proved that the coefficients of conway polynomial in z0,z1 and z2 and all ambient isotopic invariants. In particular,the coefficient in z2 of conway polynomial for link L with two components is only depend on switch crossings in pairs.展开更多
City regions often have great diversity in form and function. To better understand the role of each region, the relations between city regions need to be carefully studied. In this work, the human mobility relations b...City regions often have great diversity in form and function. To better understand the role of each region, the relations between city regions need to be carefully studied. In this work, the human mobility relations between regions of Shanghai based on mobile phone data is explored. By formulating the regions as nodes in a network and the commuting between each pair of regions as link weights, the distribution of nodes degree, and spatial structures of communities in this relation network are studied. Statistics show that regions locate in urban centers and traffic hubs have significantly larger degrees. Moreover, two kinds of spatial structures of communities are found. In most communities, nodes are spatially neighboring. However, in the communities that cover traffic hubs, nodes often locate along corridors.展开更多
A conformal structure of a prion protein is thought to cause a prion disease by S.B. Prusiner＇s theory. Knot theory in mathematics is useful in studying a topological difference of topological objects. In this articl...A conformal structure of a prion protein is thought to cause a prion disease by S.B. Prusiner＇s theory. Knot theory in mathematics is useful in studying a topological difference of topological objects. In this article, concerning this conjecture, a topological model of prion proteins （PrPc, PrPsc） called a prion-tangle is introduced to discuss a question of whether or not the prion proteins are easily entangled by an approach from the mathematical knot theory. It is noted that any prion-string with trivial loop which is a topological model of a prion protein can not be entangled topologically unless a certain restriction such as ＂Rotaxsane Property＂ is imposed on it. Nevertheless, it is shown that any two split prion-tangles can be changed by a one-crossing change into a non-split prion-tangle with the given prion-tangles contained while some attentions are paid to the loop systems. The proof is made by a mathematical argument on knot theory of spatial graphs. This means that the question above is answered affirmatively in this topological model of prion-tangles. Next, a question of what is the simplest topological situation of the non-split prion-tangles is considered. By a mathematical argument, it is determined for every n 〉 1 that the minimal crossing number of n-string non-split prion-tangles is 2n or 2n-2, respectively, according to whether or not the assumption that the loop system is a trivial link is counted.展开更多
An equivalent description for the torus knot is given in this paper, and the classification theorem of the torus knot is proved in an elementary method. Using the circular presentation of torus knot , we showed that t...An equivalent description for the torus knot is given in this paper, and the classification theorem of the torus knot is proved in an elementary method. Using the circular presentation of torus knot , we showed that the genus of the torus knot Kp,q is 1/2（p-1）（q-1） A knot called as bitorus knot is defined in the paper and showed . special that bitorus knot are all the connected sum of two torus knots.展开更多
基金The Ph.D.Programs Foundation of Ministry of Edu-cation of China(No20050710006)
文摘Size distribution characteristics of intercity bus hubs in China from 1997 to 2（104 were analyzed regarding highway passenger volume as a size index of intercity bus hubs. Yearly fractal dimensions of intercity bus hub sizes were exactly calculated by a novel model. Fractal dimensions of the 200 biggest intercity bus hubs from 2000 to 2004 were 1. 486 2 to 1. 511 8, and that is consistent with fractal dimensions of Chinese urban system sizes. It showed that the size distribution of intercity bus hubs had fractal structure. Fractal dimensions from 1997 to 2004 indicated that intercity bus hub size distribution grew from bi-fractal to single fractal. It is concluded that the intercity bus hub system is in evolutionary progress, and the Central Government should support large intercity bus hubs more to optimize system structure.
文摘It is proved that the coefficients of conway polynomial in z0,z1 and z2 and all ambient isotopic invariants. In particular,the coefficient in z2 of conway polynomial for link L with two components is only depend on switch crossings in pairs.
基金Project(71303269)supported by the National Natural Science Foundation of ChinaProject(14ZZD006)supported by the Economics Major Research Task of Fostering,China
文摘City regions often have great diversity in form and function. To better understand the role of each region, the relations between city regions need to be carefully studied. In this work, the human mobility relations between regions of Shanghai based on mobile phone data is explored. By formulating the regions as nodes in a network and the commuting between each pair of regions as link weights, the distribution of nodes degree, and spatial structures of communities in this relation network are studied. Statistics show that regions locate in urban centers and traffic hubs have significantly larger degrees. Moreover, two kinds of spatial structures of communities are found. In most communities, nodes are spatially neighboring. However, in the communities that cover traffic hubs, nodes often locate along corridors.
文摘A conformal structure of a prion protein is thought to cause a prion disease by S.B. Prusiner＇s theory. Knot theory in mathematics is useful in studying a topological difference of topological objects. In this article, concerning this conjecture, a topological model of prion proteins （PrPc, PrPsc） called a prion-tangle is introduced to discuss a question of whether or not the prion proteins are easily entangled by an approach from the mathematical knot theory. It is noted that any prion-string with trivial loop which is a topological model of a prion protein can not be entangled topologically unless a certain restriction such as ＂Rotaxsane Property＂ is imposed on it. Nevertheless, it is shown that any two split prion-tangles can be changed by a one-crossing change into a non-split prion-tangle with the given prion-tangles contained while some attentions are paid to the loop systems. The proof is made by a mathematical argument on knot theory of spatial graphs. This means that the question above is answered affirmatively in this topological model of prion-tangles. Next, a question of what is the simplest topological situation of the non-split prion-tangles is considered. By a mathematical argument, it is determined for every n 〉 1 that the minimal crossing number of n-string non-split prion-tangles is 2n or 2n-2, respectively, according to whether or not the assumption that the loop system is a trivial link is counted.
文摘An equivalent description for the torus knot is given in this paper, and the classification theorem of the torus knot is proved in an elementary method. Using the circular presentation of torus knot , we showed that the genus of the torus knot Kp,q is 1/2（p-1）（q-1） A knot called as bitorus knot is defined in the paper and showed . special that bitorus knot are all the connected sum of two torus knots.
