For a positive integer k,the total{k}-dominating function(T{k}DF)of a graph G without isolated vertices is a function f from the vertex set V(G)to the set{0,1,2,…,k}such that for each vertex v∈V(G),the sum of the va...For a positive integer k,the total{k}-dominating function(T{k}DF)of a graph G without isolated vertices is a function f from the vertex set V(G)to the set{0,1,2,…,k}such that for each vertex v∈V(G),the sum of the values of all its neighbors assigned by f is at least k.A set{f_(1),f_(2),…,f_(d)}of pairwise different T{k}DF s of G with the property that∑d i=1 f_(i)(v)≤k for each v∈V(G),is called a total{k}-dominating family(T{k}D family)of G.The total{k}-domatic number of a graph G,denoted by d^({k})_(t)(G),is the maximum number of functions in T{k}D family.In 2013,Aram et al.proposed a problem that whether or not d^({k})_(t)(C_(m)□C_(n))=3 when 4 nmk,and d^({k})_(t)(C m□C n)=4 when 4|nmk.It was shown that d^({k})_(t)(C_(m)□C_(n))=3 if 4 nmk and k≥2 or 4|nmk and 2 nk,which partially answered the above problem.In addition,the total{k}-domatic number of the direct product of a cycle and a path,two paths,and two cycles was studied,respectively.展开更多
This paper investigates outer synchronization of complex networks,especially,outer complete synchronizationand outer anti-synchronization between the driving network and the response network.Employing the impulsivecon...This paper investigates outer synchronization of complex networks,especially,outer complete synchronizationand outer anti-synchronization between the driving network and the response network.Employing the impulsivecontrol method which is uncontinuous,simple,efficient,low-cost and easy to implement in practical applications,weobtain some sufficient conditions of outer complete synchronization and outer anti-synchronization between two complexnetworks.Numerical simulations demonstrate the effectiveness of the proposed impulsive control scheme.展开更多
The study presents possibilities for reconstruction of electric power supply systems in Bulgarian Black Sea resorts and possibilities to use statistical methods in energy planning. The paper shows the use of classic s...The study presents possibilities for reconstruction of electric power supply systems in Bulgarian Black Sea resorts and possibilities to use statistical methods in energy planning. The paper shows the use of classic statistical methods in combination with advanced digital measurement systems in order to obtain the correlation dependencies, nature of energy consumption and opportunities for energy forecasting. The main purpose of the study is to obtain statistical dependencies of the nature of power consumption and correlations between electricity consumption and ambient temperature in order to improve the accuracy of energy planning. The analysis includes application of energy management systems for proper energy planning, improving economical efficiency and reducing power and energy losses.展开更多
基金Supported by NNSF of China(11671376,11401004)Anhui Provincial Natural Science Foundation(1708085MA18)
文摘For a positive integer k,the total{k}-dominating function(T{k}DF)of a graph G without isolated vertices is a function f from the vertex set V(G)to the set{0,1,2,…,k}such that for each vertex v∈V(G),the sum of the values of all its neighbors assigned by f is at least k.A set{f_(1),f_(2),…,f_(d)}of pairwise different T{k}DF s of G with the property that∑d i=1 f_(i)(v)≤k for each v∈V(G),is called a total{k}-dominating family(T{k}D family)of G.The total{k}-domatic number of a graph G,denoted by d^({k})_(t)(G),is the maximum number of functions in T{k}D family.In 2013,Aram et al.proposed a problem that whether or not d^({k})_(t)(C_(m)□C_(n))=3 when 4 nmk,and d^({k})_(t)(C m□C n)=4 when 4|nmk.It was shown that d^({k})_(t)(C_(m)□C_(n))=3 if 4 nmk and k≥2 or 4|nmk and 2 nk,which partially answered the above problem.In addition,the total{k}-domatic number of the direct product of a cycle and a path,two paths,and two cycles was studied,respectively.
基金Supported by the National Nature Science Foundation of China under Grant No. 70571059Young Project under Grant No. Q20111309Key Program under Grant No. D20111305 of Hubei Provincial Department of Education
文摘This paper investigates outer synchronization of complex networks,especially,outer complete synchronizationand outer anti-synchronization between the driving network and the response network.Employing the impulsivecontrol method which is uncontinuous,simple,efficient,low-cost and easy to implement in practical applications,weobtain some sufficient conditions of outer complete synchronization and outer anti-synchronization between two complexnetworks.Numerical simulations demonstrate the effectiveness of the proposed impulsive control scheme.
文摘The study presents possibilities for reconstruction of electric power supply systems in Bulgarian Black Sea resorts and possibilities to use statistical methods in energy planning. The paper shows the use of classic statistical methods in combination with advanced digital measurement systems in order to obtain the correlation dependencies, nature of energy consumption and opportunities for energy forecasting. The main purpose of the study is to obtain statistical dependencies of the nature of power consumption and correlations between electricity consumption and ambient temperature in order to improve the accuracy of energy planning. The analysis includes application of energy management systems for proper energy planning, improving economical efficiency and reducing power and energy losses.
