In this paper,the authors give some sufficient conditions for an amalgamated 3-manifold along a compact connected surface F with boundary to be ∂-irreducible in terms of distances between some kinds of vertex subsets ...In this paper,the authors give some sufficient conditions for an amalgamated 3-manifold along a compact connected surface F with boundary to be ∂-irreducible in terms of distances between some kinds of vertex subsets of the curve complex and the arc complex of F.展开更多
We show that every R-linear surjective isometry between the cotangent spaces to the Teichmüller space equipped with the Thurston norm is induced by some isometry between the underlying hyperbolic surfaces.This is...We show that every R-linear surjective isometry between the cotangent spaces to the Teichmüller space equipped with the Thurston norm is induced by some isometry between the underlying hyperbolic surfaces.This is an analogue of Royden's theorem concerning the Teichmüller norm.展开更多
For a handlebody H w ith dH = 5, let F belong S be an essential connected subsurface of S. Let C（S） be the curve complex of S, AC（F） be the arc and curve complex of F , D（H） belong C（S） be ...For a handlebody H w ith dH = 5, let F belong S be an essential connected subsurface of S. Let C（S） be the curve complex of S, AC（F） be the arc and curve complex of F , D（H） belong C（S） be the disk complex of H and πf（D （H ） ） belong AC（F） be the image of D （H） in AC （F）. We introduce the definition of subsurface 1-distance between the 1-simplices of AC（F） and show that under some hypothesis, πF（D（H） ） comes within subsurface 1-distance at most 4 of every 1-simplex of AC （F）.展开更多
In the study of complex networks almost all theoretical models have the property of infinite growth, but the size of actual networks is finite. According to statistics from the China Internet IPv4 （Internet Protocol ...In the study of complex networks almost all theoretical models have the property of infinite growth, but the size of actual networks is finite. According to statistics from the China Internet IPv4 （Internet Protocol version 4） addresses, this paper proposes a forecasting model by using S curve （logistic curve）. The growing trend of IPv4 addresses in China is forecasted. There are some reference values for optimizing the distribution of IPv4 address resource and the development of IPv6. Based on the laws of IPv4 growth, that is, the bulk growth and the finitely growing limit, it proposes a finite network model with a bulk growth. The model is said to be an S-curve network. Analysis demonstrates that the analytic method based on uniform distributions （i.e., Barabasi-Albert method） is not suitable for the network. It develops an approximate method to predict the growth dynamics of the individual nodes, and uses this to calculate analytically the degree distribution and the scaling exponents. The analytical result agrees with the simulation well, obeying an approximately power-law form. This method can overcome a shortcoming of Barabasi-Albert method commonly used in current network research.展开更多
In this article, it is proved that there doesn’t exist any nonsingular holomorphic sphere in complex Grassmann manifold G（2, 5） with constant curvature k = 4/7, 1/2, 4/9. Thus, from [7] it follows that if φ ： S2 ...In this article, it is proved that there doesn’t exist any nonsingular holomorphic sphere in complex Grassmann manifold G（2, 5） with constant curvature k = 4/7, 1/2, 4/9. Thus, from [7] it follows that if φ ： S2 → G（2, 5） is a nonsingular holomorphic curve with constant curvature K, then, K = 4, 2, 4/3, 1 or 4/5.展开更多
The results of accurate order of uniform approximation and simultaneous approximation in the early work ＂Jackson Type Theorems on Complex Curves＂ are improved from Fejer points to disturbed Fejer points in this arti...The results of accurate order of uniform approximation and simultaneous approximation in the early work ＂Jackson Type Theorems on Complex Curves＂ are improved from Fejer points to disturbed Fejer points in this article. Furthermore, the stability of convergence of Tn,∈（f,z） with disturbed sample values f（z^＊） ＋ Sk are also proved in this article.展开更多
We show that higher-dimensional integrable systems including the (2+1)-dimensional generalized sine-Gordon equation and the (2+1)-dimensional complex mKdV equation are associated with motions of surfaces inducedby end...We show that higher-dimensional integrable systems including the (2+1)-dimensional generalized sine-Gordon equation and the (2+1)-dimensional complex mKdV equation are associated with motions of surfaces inducedby endowing with an extra space variable to the motions of curves on S^2(R) and S^3(R).展开更多
Suppose V ∪S W is a strongly irreducible Heegaard splitting of a compact connected orientable 3-manifold M and F1 and F2 are pairwise disjoint homeomorphic essential subsurfaces in ?V. In this paper,we give a suffici...Suppose V ∪S W is a strongly irreducible Heegaard splitting of a compact connected orientable 3-manifold M and F1 and F2 are pairwise disjoint homeomorphic essential subsurfaces in ?V. In this paper,we give a sufficient condition such that the self-amalgamation of V ∪S W along F1 and F2 is unstabilized and uncritical.展开更多
This paper provides several generalizations of Gauss theorem that counts points on special elliptic curves. It is demonstrated how to implement these generalizations for computation of complex primes, which are applic...This paper provides several generalizations of Gauss theorem that counts points on special elliptic curves. It is demonstrated how to implement these generalizations for computation of complex primes, which are applicable in several protocols providing security in communication networks. Numerical examples illustrate the ideas discussed in this paper.展开更多
This paper presents building one-parameter motion by complex numbers on a time scale. Firstly, we assumed that E and E′ were moving in a fixed time scale complex plane and {0, e1,e2} and {0', e'1,e'2} ?we...This paper presents building one-parameter motion by complex numbers on a time scale. Firstly, we assumed that E and E′ were moving in a fixed time scale complex plane and {0, e1,e2} and {0', e'1,e'2} ?were their orthonormal frames, respectively. By using complex numbers, we investigated the delta calculus equations of the motion on T. Secondly, we gave the velocities and their union rule on the time scale. Finally, by using the delta-derivative, we got interesting results and theorems for the instantaneous rotation pole and the pole curves (trajectory). In kinematics, investigating one-parameter motion by complex numbers is important for simplifying motion calculation. In this study, our aim is to obtain an equation of motion by using complex numbers on the time scale.展开更多
This paper considers a decomposition framework as a mechanism for information hiding for secure communication via open network channels. Two varieties of this framework are provided: one is based on Gaussian arithmeti...This paper considers a decomposition framework as a mechanism for information hiding for secure communication via open network channels. Two varieties of this framework are provided: one is based on Gaussian arithmetic with complex modulus and another on an elliptic curve modular equation. The proposed algorithm is illustrated in a numerical example.展开更多
Let S be a closed orientable surface of genus g ≥ 2,and C（S）the curve complex of S.In the paper,we introduce the concepts of 2-path between edges in C（S）,which can be regarded as an analogue to the edge path betw...Let S be a closed orientable surface of genus g ≥ 2,and C（S）the curve complex of S.In the paper,we introduce the concepts of 2-path between edges in C（S）,which can be regarded as an analogue to the edge path between vertices in C（S）.We show that C（S）is 2P-connected,and the 2-diameter of C（S）is infinite.展开更多
Let V be a nontrivial compression body which is not simple. An essential simple closed curve J in ?;V is called weakly disk-busting if ?;V-J has only one compressing disk up to isotopy. In this paper, we give an upper...Let V be a nontrivial compression body which is not simple. An essential simple closed curve J in ?;V is called weakly disk-busting if ?;V-J has only one compressing disk up to isotopy. In this paper, we give an upper bound of the diameter of the image of boundaries of essential disks in V under any projection determined by a weakly disk-busting curve. Moreover, we give a sufficient condition for the handle additions to be boundary irreducible.展开更多
A properly embedded essential planar surface P（not a disk） in a compression body V is called a spanning pre-disk with respect to J, if one boundary component of P is lying in ?;V and all other boundary components of...A properly embedded essential planar surface P（not a disk） in a compression body V is called a spanning pre-disk with respect to J, if one boundary component of P is lying in ?;V and all other boundary components of P are lying in?;V and coplanar with J. In this paper, we show that the number of boundary components of spanning pre-disks in a compression body is unbounded. But the number of a maximal collection of spanning pre-disks is bounded.展开更多
This paper discusses the problem that constructing a curve to satisfy the given endpoint constraints and chord-length parameters. Based on the research of Lu, the curve construction method for the entire tangent angle...This paper discusses the problem that constructing a curve to satisfy the given endpoint constraints and chord-length parameters. Based on the research of Lu, the curve construction method for the entire tangent angles region （α0, α1）∈（-r, r）×（-r, r） is given. Firstly, to ensure the weights are always positive, the three characteristics of cubic rational Bezier curve is proved, then the segment construction idea for the other tangent angles are presented in view of the three characteristics. The curve constructed with the new method satisfies the endpoint constraint and chord-length parameters, it＇s G1 continuous in every segment curve, and the shapes of the curve are well.展开更多
文摘为了明确山区公路曲线路段上的汽车轨迹形态和驾驶风格,使用小客车在山区复杂线形公路上开展了实车驾驶实验.记录了自然驾驶状态下男性驾驶人的行驶轨迹,分析了行驶轨迹相对于行车道中线的横向偏移特性,运用聚类方法识别了曲线路段的轨迹行为模式.结果发现:根据轨迹横向偏移率的聚类结果,山区公路曲线路段有6种轨迹模式,具有明显的多样性特征;切弯是曲线路段占主导的过弯方式,按照切弯点位置以及前后的轨迹形态,切弯又可进一步细分为多种类型;行驶轨迹的横向偏移导致了车道偏离,其中非预期偏离由于存在较高的事故风险,应进行防范和控制;平曲线半径越小,切弯效应越大,事故风险可控,驾驶人越倾向于采用切弯方式来通过弯道,曲线路段是否发生切弯行为的临界半径值为200 m.
基金supported by the National Natural Science Foundation of China(No.12071051)。
文摘In this paper,the authors give some sufficient conditions for an amalgamated 3-manifold along a compact connected surface F with boundary to be ∂-irreducible in terms of distances between some kinds of vertex subsets of the curve complex and the arc complex of F.
基金supported by National Natural Science Foundation of China (Grant No.11901241).
文摘We show that every R-linear surjective isometry between the cotangent spaces to the Teichmüller space equipped with the Thurston norm is induced by some isometry between the underlying hyperbolic surfaces.This is an analogue of Royden's theorem concerning the Teichmüller norm.
文摘For a handlebody H w ith dH = 5, let F belong S be an essential connected subsurface of S. Let C（S） be the curve complex of S, AC（F） be the arc and curve complex of F , D（H） belong C（S） be the disk complex of H and πf（D （H ） ） belong AC（F） be the image of D （H） in AC （F）. We introduce the definition of subsurface 1-distance between the 1-simplices of AC（F） and show that under some hypothesis, πF（D（H） ） comes within subsurface 1-distance at most 4 of every 1-simplex of AC （F）.
基金Project supported by the National Natural Science Foundation of China (Grant No. 70871082)the Shanghai Leading Academic Discipline Project (Grant No. S30504)
文摘In the study of complex networks almost all theoretical models have the property of infinite growth, but the size of actual networks is finite. According to statistics from the China Internet IPv4 （Internet Protocol version 4） addresses, this paper proposes a forecasting model by using S curve （logistic curve）. The growing trend of IPv4 addresses in China is forecasted. There are some reference values for optimizing the distribution of IPv4 address resource and the development of IPv6. Based on the laws of IPv4 growth, that is, the bulk growth and the finitely growing limit, it proposes a finite network model with a bulk growth. The model is said to be an S-curve network. Analysis demonstrates that the analytic method based on uniform distributions （i.e., Barabasi-Albert method） is not suitable for the network. It develops an approximate method to predict the growth dynamics of the individual nodes, and uses this to calculate analytically the degree distribution and the scaling exponents. The analytical result agrees with the simulation well, obeying an approximately power-law form. This method can overcome a shortcoming of Barabasi-Albert method commonly used in current network research.
基金Supported by the National Natural Science Foundation of China (10531090)Knowledge Innovation Funds of CAS (KJCX3-SYW-S03)
文摘In this article, it is proved that there doesn’t exist any nonsingular holomorphic sphere in complex Grassmann manifold G（2, 5） with constant curvature k = 4/7, 1/2, 4/9. Thus, from [7] it follows that if φ ： S2 → G（2, 5） is a nonsingular holomorphic curve with constant curvature K, then, K = 4, 2, 4/3, 1 or 4/5.
基金Supported by NSF of Henan Province of China(20001110001)
文摘The results of accurate order of uniform approximation and simultaneous approximation in the early work ＂Jackson Type Theorems on Complex Curves＂ are improved from Fejer points to disturbed Fejer points in this article. Furthermore, the stability of convergence of Tn,∈（f,z） with disturbed sample values f（z^＊） ＋ Sk are also proved in this article.
基金National Natural Science Foundation of China under Grant No.10671156the Program for New Century Excellent Talents in Universities under Grant No.NCET-04-0968
文摘We show that higher-dimensional integrable systems including the (2+1)-dimensional generalized sine-Gordon equation and the (2+1)-dimensional complex mKdV equation are associated with motions of surfaces inducedby endowing with an extra space variable to the motions of curves on S^2(R) and S^3(R).
基金supported by National Natural Science Foundation of China(Grant Nos.11601209,11671064,11471151,11401069,11329101 and 11431009)Scientific Research Foundation for Doctors of Liaoning Province(Grant No.201601239)+1 种基金Scientific Research Fund of Liaoning Provincial Education Department(Grant No.L201683660)the Fundamental Research Funds for the Central Universities(Grant No.DUT16LK40)
文摘Suppose V ∪S W is a strongly irreducible Heegaard splitting of a compact connected orientable 3-manifold M and F1 and F2 are pairwise disjoint homeomorphic essential subsurfaces in ?V. In this paper,we give a sufficient condition such that the self-amalgamation of V ∪S W along F1 and F2 is unstabilized and uncritical.
文摘This paper provides several generalizations of Gauss theorem that counts points on special elliptic curves. It is demonstrated how to implement these generalizations for computation of complex primes, which are applicable in several protocols providing security in communication networks. Numerical examples illustrate the ideas discussed in this paper.
文摘This paper presents building one-parameter motion by complex numbers on a time scale. Firstly, we assumed that E and E′ were moving in a fixed time scale complex plane and {0, e1,e2} and {0', e'1,e'2} ?were their orthonormal frames, respectively. By using complex numbers, we investigated the delta calculus equations of the motion on T. Secondly, we gave the velocities and their union rule on the time scale. Finally, by using the delta-derivative, we got interesting results and theorems for the instantaneous rotation pole and the pole curves (trajectory). In kinematics, investigating one-parameter motion by complex numbers is important for simplifying motion calculation. In this study, our aim is to obtain an equation of motion by using complex numbers on the time scale.
文摘This paper considers a decomposition framework as a mechanism for information hiding for secure communication via open network channels. Two varieties of this framework are provided: one is based on Gaussian arithmetic with complex modulus and another on an elliptic curve modular equation. The proposed algorithm is illustrated in a numerical example.
基金Supported by the National Natural Science Foundation of China (Grant No.10931005)
文摘Let S be a closed orientable surface of genus g ≥ 2,and C（S）the curve complex of S.In the paper,we introduce the concepts of 2-path between edges in C（S）,which can be regarded as an analogue to the edge path between vertices in C（S）.We show that C（S）is 2P-connected,and the 2-diameter of C（S）is infinite.
基金The NSF(11601209)of ChinaResearch Foundation(201601239)for Doctor of Liaoning Province+1 种基金Scientific Research Fund(L201683660)of Liaoning Provincial Education DepartmentYouth Foundation(LS2015L002)of Liaoning Normal University
文摘Let V be a nontrivial compression body which is not simple. An essential simple closed curve J in ?;V is called weakly disk-busting if ?;V-J has only one compressing disk up to isotopy. In this paper, we give an upper bound of the diameter of the image of boundaries of essential disks in V under any projection determined by a weakly disk-busting curve. Moreover, we give a sufficient condition for the handle additions to be boundary irreducible.
基金The NSF(11601209,11471151,11401069 and 11671064)of Chinathe Research Foundation (201601239)for Doctor of Liaoning Province+2 种基金the Scientific Research Fund(L201683660)of Liaoning Provincial Education Departmentthe Youth Foundation(LS2015L002)of Liaoning Normal Universitya grant of the Fundamental Research Funds(DUT16LK40)for the Central Universities
文摘A properly embedded essential planar surface P（not a disk） in a compression body V is called a spanning pre-disk with respect to J, if one boundary component of P is lying in ?;V and all other boundary components of P are lying in?;V and coplanar with J. In this paper, we show that the number of boundary components of spanning pre-disks in a compression body is unbounded. But the number of a maximal collection of spanning pre-disks is bounded.
基金Supported by Shandong Province Higher Educational Science and Technology Program(No.J12LN34)Shandong Ji'nan College and Institute Independent Innovation Project(No.201303011,No.201303021,No.201303016)
文摘This paper discusses the problem that constructing a curve to satisfy the given endpoint constraints and chord-length parameters. Based on the research of Lu, the curve construction method for the entire tangent angles region （α0, α1）∈（-r, r）×（-r, r） is given. Firstly, to ensure the weights are always positive, the three characteristics of cubic rational Bezier curve is proved, then the segment construction idea for the other tangent angles are presented in view of the three characteristics. The curve constructed with the new method satisfies the endpoint constraint and chord-length parameters, it＇s G1 continuous in every segment curve, and the shapes of the curve are well.
