Let G be a finite group. A nonempty subset X of G is said to be noncommuting if xy≠yx for any x, y ∈ X with x≠y. If ｜X｜ ≥ ｜Y｜ for any other non-commuting set Y in G, then X is said to be a maximal non-commutin...Let G be a finite group. A nonempty subset X of G is said to be noncommuting if xy≠yx for any x, y ∈ X with x≠y. If ｜X｜ ≥ ｜Y｜ for any other non-commuting set Y in G, then X is said to be a maximal non-commuting set. In this paper, we determine upper and lower bounds on the cardinality of a maximal non-commuting set in a finite p-group with derived subgroup of prime order.展开更多
Let G be a group. A subset X of G is said to be non-commuting if xy ≠ yx for any x, y ∈ X with x ≠ y. If {X}≥ IYI for any other non-commuting set Y in G, then X is said to be a maximal non-commuting set. In this p...Let G be a group. A subset X of G is said to be non-commuting if xy ≠ yx for any x, y ∈ X with x ≠ y. If {X}≥ IYI for any other non-commuting set Y in G, then X is said to be a maximal non-commuting set. In this paper, the bound for the cardinality of a maximal non-commuting set in a finite p-group G is determined, where G is a non-abelian p-group given by a central extension as1 → Zp→ G →Zp ×→ × Zp →1 and its derivedsubgroup has order p.展开更多
The conditional version of sandwiched Tsallis relative entropy (CSTRE) is employed to study the bipartite separability of one parameter family of N-qudit Werner-Popescu states in their 1:N-1 partition. For all N, the ...The conditional version of sandwiched Tsallis relative entropy (CSTRE) is employed to study the bipartite separability of one parameter family of N-qudit Werner-Popescu states in their 1:N-1 partition. For all N, the strongest limitation on bipartite separability is realized in the limit and is found to match exactly with the separability range obtained using an algebraic method which is both necessary and sufficient. The theoretical superiority of using CSTRE criterion to find the bipartite separability range over the one using Abe-Rajagopal (AR) q-conditional entropy is illustrated by comparing the convergence of the parameter x with respect to q, in the implicit plots of AR q-conditional entropy and CSTRE.展开更多
The Sylow graph of a finite group originates from recent investigations on certain classes of groups, defined in terms of normalizers of Sylow subgroups. The connectivity of this graph has been proved only last year w...The Sylow graph of a finite group originates from recent investigations on certain classes of groups, defined in terms of normalizers of Sylow subgroups. The connectivity of this graph has been proved only last year with the use of the classification of finite simple groups (CFSG). A series of interesting questions arise naturally. First of all, it is not clear whether it is possible to avoid CFSG or not. On the other hand, what happens for infinite groups? Since the status of knowledge of the non-commuting graph and of the prime graph is satisfactory, is it possible to find relations between these two graphs and the Sylow graph? In the present note we make the point of the situation and formulate the above questions in appropriate way.展开更多
Let S and K be two subrings of a finite ring R. Then the generalized non- commuting graph of subrings S, K of R, denoted by [＇S,K, is a simple graph whose vertex set is （S U K）／（CK（S） U Cs（K））, and where two...Let S and K be two subrings of a finite ring R. Then the generalized non- commuting graph of subrings S, K of R, denoted by [＇S,K, is a simple graph whose vertex set is （S U K）／（CK（S） U Cs（K））, and where two distinct vertices a, b are adjacent if and only if a E S or b E S and ab ≠ ba. We determine the diameter, girth and some dominating sets for FS, K. Some connections between Fs,K and Pr（S, K） are also obtained. Further, Z-isoclinism between two pairs of finite rings is defined, and we show that the generalized non-commuting graphs of two Y_~isoclinic pairs are isomorphic under some conditions.展开更多
The characterization of non-stationary signal requires joint time and frequency information. However, time and frequency are a pair of non-commuting variables that cannot constitute a joint probability density in the ...The characterization of non-stationary signal requires joint time and frequency information. However, time and frequency are a pair of non-commuting variables that cannot constitute a joint probability density in the time-frequency plane. The time-frequency distributions have difficult interpretation problems arising from negative and complex values or spurious components. In this paper, we get time-frequency information from the marginal distributions in rotated directions in the time-frequency plane. The rigorous probability interpretation of the marginal distributions is without any ambiguities. This time-frequency transformation is similar to the computerized axial tomography (CT or CAT) and is applied to signal analysis and signal detection and reveals a lot of advantages especially in the signal detection of the low signal/noise (S/N).展开更多
城市节律可为观察和理解城市提供一种新的模式,为当代城市问题提供新的研究视角。城市居民出行时空行为呈现明显的节律特征,其一定程度反映出城市运行的复杂性,是城市地理和行为地理研究的重要问题之一。本研究引入城市节律这一概念,关...城市节律可为观察和理解城市提供一种新的模式,为当代城市问题提供新的研究视角。城市居民出行时空行为呈现明显的节律特征,其一定程度反映出城市运行的复杂性,是城市地理和行为地理研究的重要问题之一。本研究引入城市节律这一概念,关注居民非通勤出行时空行为,以交通小区为空间单元,利用手机信令数据和POI(Point of interest)数据,基于模糊C均值(Fuzzy C-Means Clustering,FCM)的时间序列软聚类方法和空间分析有机结合,探索居民非通勤出行活动节律模式;同时利用空间滞后模型揭示了出行节律模式隶属度的影响因素。结果表明:北京居民非通勤出行节律存在7种模式,根据不同模式区域的POI的频数密度和富集指数差异,可以将7种模式描述为:“居住导向型”“商业活动型”“商务导向型”“混合偏居住型”“混合偏商务型”“科教文化型”和“休闲娱乐型”。研究发现,不同模式的平均隶属度差异较大,影响因子也存在较大差异。在北京六环内非通勤出行节律模式混合度高,且不同模式的出行节律周期、功能特征和空间分布存在较大差异。此外,出行节律存在显著的空间依赖,并与城市商业、就业、居住等城市功能结构具有较强的相关性。本研究从时空融合视角对北京居民非通勤出行节律模式进行了深入探索,研究结果有助于进一步提高人群出行节律与城市功能结构关系的科学理解,从而能够为城市规划与建设提供重要的决策支撑。展开更多
基金The NSF(11301150,11371124)of Chinathe NSF(142300410134)of Henan ProvincePlan for Scientific Innovation Talent(11CXRC19)of Henan University of Technology
文摘Let G be a finite group. A nonempty subset X of G is said to be noncommuting if xy≠yx for any x, y ∈ X with x≠y. If ｜X｜ ≥ ｜Y｜ for any other non-commuting set Y in G, then X is said to be a maximal non-commuting set. In this paper, we determine upper and lower bounds on the cardinality of a maximal non-commuting set in a finite p-group with derived subgroup of prime order.
基金Project supported by the NSFC （11301150, 11371124）, Natural Science Foundation of Henan Province of China （142300410134）, Program for Innovation Talents of Science and Technology of Henan University of Technology （11CXRC19）.
文摘Let G be a group. A subset X of G is said to be non-commuting if xy ≠ yx for any x, y ∈ X with x ≠ y. If {X}≥ IYI for any other non-commuting set Y in G, then X is said to be a maximal non-commuting set. In this paper, the bound for the cardinality of a maximal non-commuting set in a finite p-group G is determined, where G is a non-abelian p-group given by a central extension as1 → Zp→ G →Zp ×→ × Zp →1 and its derivedsubgroup has order p.
文摘The conditional version of sandwiched Tsallis relative entropy (CSTRE) is employed to study the bipartite separability of one parameter family of N-qudit Werner-Popescu states in their 1:N-1 partition. For all N, the strongest limitation on bipartite separability is realized in the limit and is found to match exactly with the separability range obtained using an algebraic method which is both necessary and sufficient. The theoretical superiority of using CSTRE criterion to find the bipartite separability range over the one using Abe-Rajagopal (AR) q-conditional entropy is illustrated by comparing the convergence of the parameter x with respect to q, in the implicit plots of AR q-conditional entropy and CSTRE.
文摘The Sylow graph of a finite group originates from recent investigations on certain classes of groups, defined in terms of normalizers of Sylow subgroups. The connectivity of this graph has been proved only last year with the use of the classification of finite simple groups (CFSG). A series of interesting questions arise naturally. First of all, it is not clear whether it is possible to avoid CFSG or not. On the other hand, what happens for infinite groups? Since the status of knowledge of the non-commuting graph and of the prime graph is satisfactory, is it possible to find relations between these two graphs and the Sylow graph? In the present note we make the point of the situation and formulate the above questions in appropriate way.
文摘Let S and K be two subrings of a finite ring R. Then the generalized non- commuting graph of subrings S, K of R, denoted by [＇S,K, is a simple graph whose vertex set is （S U K）／（CK（S） U Cs（K））, and where two distinct vertices a, b are adjacent if and only if a E S or b E S and ab ≠ ba. We determine the diameter, girth and some dominating sets for FS, K. Some connections between Fs,K and Pr（S, K） are also obtained. Further, Z-isoclinism between two pairs of finite rings is defined, and we show that the generalized non-commuting graphs of two Y_~isoclinic pairs are isomorphic under some conditions.
基金Supported by the Open Project of the Key Laboratory of Jiangsu Province (Grant No. KJS03078)
文摘The characterization of non-stationary signal requires joint time and frequency information. However, time and frequency are a pair of non-commuting variables that cannot constitute a joint probability density in the time-frequency plane. The time-frequency distributions have difficult interpretation problems arising from negative and complex values or spurious components. In this paper, we get time-frequency information from the marginal distributions in rotated directions in the time-frequency plane. The rigorous probability interpretation of the marginal distributions is without any ambiguities. This time-frequency transformation is similar to the computerized axial tomography (CT or CAT) and is applied to signal analysis and signal detection and reveals a lot of advantages especially in the signal detection of the low signal/noise (S/N).
文摘城市节律可为观察和理解城市提供一种新的模式,为当代城市问题提供新的研究视角。城市居民出行时空行为呈现明显的节律特征,其一定程度反映出城市运行的复杂性,是城市地理和行为地理研究的重要问题之一。本研究引入城市节律这一概念,关注居民非通勤出行时空行为,以交通小区为空间单元,利用手机信令数据和POI(Point of interest)数据,基于模糊C均值(Fuzzy C-Means Clustering,FCM)的时间序列软聚类方法和空间分析有机结合,探索居民非通勤出行活动节律模式;同时利用空间滞后模型揭示了出行节律模式隶属度的影响因素。结果表明:北京居民非通勤出行节律存在7种模式,根据不同模式区域的POI的频数密度和富集指数差异,可以将7种模式描述为:“居住导向型”“商业活动型”“商务导向型”“混合偏居住型”“混合偏商务型”“科教文化型”和“休闲娱乐型”。研究发现,不同模式的平均隶属度差异较大,影响因子也存在较大差异。在北京六环内非通勤出行节律模式混合度高,且不同模式的出行节律周期、功能特征和空间分布存在较大差异。此外,出行节律存在显著的空间依赖,并与城市商业、就业、居住等城市功能结构具有较强的相关性。本研究从时空融合视角对北京居民非通勤出行节律模式进行了深入探索,研究结果有助于进一步提高人群出行节律与城市功能结构关系的科学理解,从而能够为城市规划与建设提供重要的决策支撑。
