The Advanced Encryption Standard(AES)is the most widely used symmetric cipher today.AES has an important place in cryptology.Finite field,also known as Galois Fields,are cornerstones for understanding any cryptography...The Advanced Encryption Standard(AES)is the most widely used symmetric cipher today.AES has an important place in cryptology.Finite field,also known as Galois Fields,are cornerstones for understanding any cryptography.This encryption method on AES is a method that uses polynomials on Galois fields.In this paper,we generalize the AES-like cryptology on 2×2 matrices.We redefine the elements of k-order Fibonacci polynomials sequences using a certain irreducible polynomial in our cryptology algorithm.So,this cryptology algorithm is called AES-like cryptology on the k-order Fibonacci polynomial matrix.展开更多
Two k-hyperconnection expressions of a general k-order cofactor Y<sub>（i,j）</sub> are presentedfor the indefinite parameter matrix Y of a linear system by applying directed hypergraph theory,and based on...Two k-hyperconnection expressions of a general k-order cofactor Y<sub>（i,j）</sub> are presentedfor the indefinite parameter matrix Y of a linear system by applying directed hypergraph theory,and based on it a decomposition theorem of Y<sub>（i,j）</sub> is derived.By this theorem,the multi-leveltearing and analysis can be carried out easily for any linear large system.This is a new mul-tilevel topological analysis method.Using proposed method the scale of systems which can betopologically analysed by a computer will be enlarged.展开更多
Two sharp Chernoff type inequalities are derived for star bodies in R2,one is an extension of the dual Chernoff-Ou-Pan inequality,and the other is the reverse Chernoff type inequality.Furthermore,we establish a genera...Two sharp Chernoff type inequalities are derived for star bodies in R2,one is an extension of the dual Chernoff-Ou-Pan inequality,and the other is the reverse Chernoff type inequality.Furthermore,we establish a generalized dual symmetric mixed Chernoff inequality for two planar star bodies.As a direct consequence,a new proof of the dual symmetric mixed isoperimetric inequality is presented.展开更多
针对城市重要公交线路识别与优化问题,以西安市公交系统作为研究对象,利用高阶网络模型甄别和优化西安市公交系统的重要公交线路.首先,考虑到城市公交系统具有典型的路径依赖特征,基于高阶网络模型方法构建高阶公交网络.其次,基于公交...针对城市重要公交线路识别与优化问题,以西安市公交系统作为研究对象,利用高阶网络模型甄别和优化西安市公交系统的重要公交线路.首先,考虑到城市公交系统具有典型的路径依赖特征,基于高阶网络模型方法构建高阶公交网络.其次,基于公交站点道路等级、站点与轨道交通接驳情况、站点服务范围内兴趣点(Point of Interest,POI)、站点所在区域的人口密度4项位置属性指标,提出改进的加权k核分解算法,将高阶公交网络分为核心层、桥层和外围层.最后,以西安市为例进行实证分析,以各层中连边承担的平均线路数为依据甄别重要公交线路,并根据路段在重要连边中出现的次数识别出最重要的公交路段,针对存在的问题提出优化建议.研究结果表明:西安市公交系统中存在234条重要的公交路段以及经过6条最重要路段的55条公交线路;西安市存在城市新区及近郊区域与中心城区连接不畅的问题,桥层中有524个公交站点与核心层中的任意一个站点都没有直达的公交线路;通过对13条非直达线路进行优化,站点直达率提高4.72%,增加了13条线路中247个站点与核心层站点的直达路线选择,改善了城市居民的出行便利性.展开更多
A digraph D is k-ordered if for every sequence S：v 1,v 2,…,v k of k distinct vertices,there exists a cycle C such that C encounters the vertices of S in the specified order.In particular,we say that D is k-ordered h...A digraph D is k-ordered if for every sequence S：v 1,v 2,…,v k of k distinct vertices,there exists a cycle C such that C encounters the vertices of S in the specified order.In particular,we say that D is k-ordered hamiltonian if for every sequence S：v 1,v 2,…,v k of k distinct vertices,there exists a hamiltonian cycle C such that the vertices of S are encountered on C in the specified order.In this paper,sufficient conditions for digraphs to be ordered and ordered hamiltonian have been given.展开更多
基金This work is supported by the Scientific Research Project(BAP)2020FEBE009,Pamukkale University,Denizli,Turkey.
文摘The Advanced Encryption Standard(AES)is the most widely used symmetric cipher today.AES has an important place in cryptology.Finite field,also known as Galois Fields,are cornerstones for understanding any cryptography.This encryption method on AES is a method that uses polynomials on Galois fields.In this paper,we generalize the AES-like cryptology on 2×2 matrices.We redefine the elements of k-order Fibonacci polynomials sequences using a certain irreducible polynomial in our cryptology algorithm.So,this cryptology algorithm is called AES-like cryptology on the k-order Fibonacci polynomial matrix.
文摘Two k-hyperconnection expressions of a general k-order cofactor Y<sub>（i,j）</sub> are presentedfor the indefinite parameter matrix Y of a linear system by applying directed hypergraph theory,and based on it a decomposition theorem of Y<sub>（i,j）</sub> is derived.By this theorem,the multi-leveltearing and analysis can be carried out easily for any linear large system.This is a new mul-tilevel topological analysis method.Using proposed method the scale of systems which can betopologically analysed by a computer will be enlarged.
基金supported by the Postgraduate Scientic Research Innovation Project of Chongqing Normal University(YKC24010)Chunna Zeng's research was supported by the Major Special Project of the National Natural Science Foundation of China(12141101)+2 种基金the Young Top-Talent program of Chongqing(CQYC2021059145)the Technology Research Foundation of Chongqing Educational committee(KJZD-K202200509)the Natural Science Foundation Project of Chongqing(CSTB2024NSCQ-MSX0937)。
文摘Two sharp Chernoff type inequalities are derived for star bodies in R2,one is an extension of the dual Chernoff-Ou-Pan inequality,and the other is the reverse Chernoff type inequality.Furthermore,we establish a generalized dual symmetric mixed Chernoff inequality for two planar star bodies.As a direct consequence,a new proof of the dual symmetric mixed isoperimetric inequality is presented.
文摘针对城市重要公交线路识别与优化问题,以西安市公交系统作为研究对象,利用高阶网络模型甄别和优化西安市公交系统的重要公交线路.首先,考虑到城市公交系统具有典型的路径依赖特征,基于高阶网络模型方法构建高阶公交网络.其次,基于公交站点道路等级、站点与轨道交通接驳情况、站点服务范围内兴趣点(Point of Interest,POI)、站点所在区域的人口密度4项位置属性指标,提出改进的加权k核分解算法,将高阶公交网络分为核心层、桥层和外围层.最后,以西安市为例进行实证分析,以各层中连边承担的平均线路数为依据甄别重要公交线路,并根据路段在重要连边中出现的次数识别出最重要的公交路段,针对存在的问题提出优化建议.研究结果表明:西安市公交系统中存在234条重要的公交路段以及经过6条最重要路段的55条公交线路;西安市存在城市新区及近郊区域与中心城区连接不畅的问题,桥层中有524个公交站点与核心层中的任意一个站点都没有直达的公交线路;通过对13条非直达线路进行优化,站点直达率提高4.72%,增加了13条线路中247个站点与核心层站点的直达路线选择,改善了城市居民的出行便利性.
基金Foundation item： Supported by the National Natural Science Foundation of China（61070229） Supported by the Natural Science Foundation of Shanxi Province（2008011010）
文摘A digraph D is k-ordered if for every sequence S：v 1,v 2,…,v k of k distinct vertices,there exists a cycle C such that C encounters the vertices of S in the specified order.In particular,we say that D is k-ordered hamiltonian if for every sequence S：v 1,v 2,…,v k of k distinct vertices,there exists a hamiltonian cycle C such that the vertices of S are encountered on C in the specified order.In this paper,sufficient conditions for digraphs to be ordered and ordered hamiltonian have been given.
