A graph has exactly two main eigenvalues if and only if it is a 2-walk linear graph.In this paper,we show some necessary conditions that a 2-walk（a,b）-linear graph must obey.Using these conditions and some basic the...A graph has exactly two main eigenvalues if and only if it is a 2-walk linear graph.In this paper,we show some necessary conditions that a 2-walk（a,b）-linear graph must obey.Using these conditions and some basic theorems in graph theory,we characterize all 2-walk linear graphs with small cyclic graphs without pendants.The results are given in sort on unicyclic,bicyclic,tricyclic graphs.展开更多
A graph has exactly two main eigenvalues if and only if it is a 2-walk linear graph. In this paper, we show some structural properties that a 2-walk （a, b）-linear graph holds. According to these properties, we can e...A graph has exactly two main eigenvalues if and only if it is a 2-walk linear graph. In this paper, we show some structural properties that a 2-walk （a, b）-linear graph holds. According to these properties, we can estimate and characterize more 2-walk linear graphs that have exactly two main eigenvalues.展开更多
The idea of linear Diophantine fuzzy set(LDFS)theory with its control parameters is a strong model for machine learning and optimization under uncertainty.The activity times in the critical path method(CPM)representat...The idea of linear Diophantine fuzzy set(LDFS)theory with its control parameters is a strong model for machine learning and optimization under uncertainty.The activity times in the critical path method(CPM)representation procedures approach are initially static,but in the Project Evaluation and Review Technique(PERT)approach,they are probabilistic.This study proposes a novel way of project review and assessment methodology for a project network in a linear Diophantine fuzzy(LDF)environment.The LDF expected task time,LDF variance,LDF critical path,and LDF total expected time for determining the project network are all computed using LDF numbers as the time of each activity in the project network.The primary premise of the LDF-PERT approach is to address ambiguities in project network activity timesmore simply than other approaches such as conventional PERT,Fuzzy PERT,and so on.The LDF-PERT is an efficient approach to analyzing symmetries in fuzzy control systems to seek an optimal decision.We also present a new approach for locating LDF-CPM in a project network with uncertain and erroneous activity timings.When the available resources and activity times are imprecise and unpredictable,this strategy can help decision-makers make better judgments in a project.A comparison analysis of the proposed technique with the existing techniques has also been discussed.The suggested techniques are demonstrated with two suitable numerical examples.展开更多
An engineering system may consist of several different types of components,belonging to such physical"domains"as mechanical,electrical,fluid,and thermal.It is termed a multi-domain(or multi-physics)system.Th...An engineering system may consist of several different types of components,belonging to such physical"domains"as mechanical,electrical,fluid,and thermal.It is termed a multi-domain(or multi-physics)system.The present paper concerns the use of linear graphs(LGs)to generate a minimal model for a multi-physics system.A state-space model has to be a minimal realization.Specifically,the number of state variables in the model should be the minimum number that can completely represent the dynamic state of the system.This choice is not straightforward.Initially,state variables are assigned to all the energy-storage elements of the system.However,some of the energy storage elements may not be independent,and then some of the chosen state variables will be redundant.An approach is presented in the paper,with illustrative examples in the mixed fluid-mechanical domains,to illustrate a way to recognize dependent energy storage elements and thereby obtain a minimal state-space model.System analysis in the frequency domain is known to be more convenient than in the time domain,mainly because the relevant operations are algebraic rather than differential.For achieving this objective,the state space model has to be converted into a transfer function.The direct way is to first convert the state-space model into the input-output differential equation,and then substitute the time derivative by the Laplace variable.This approach is shown in the paper.The same result can be obtained through the transfer function linear graph(TF LG)of the system.In a multi-physics system,first the physical domains have to be converted into an equivalent single domain(preferably,the output domain of the system),when using the method of TFLG.This procedure is illustrated as well,in the present paper.展开更多
A star forest is a forest whose components are stars. The star arboricity of a graph G,denoted by sa（ G）,is the minimum number of star forests needed to decompose G. Let k be a positive integer. A k-star forest is a...A star forest is a forest whose components are stars. The star arboricity of a graph G,denoted by sa（ G）,is the minimum number of star forests needed to decompose G. Let k be a positive integer. A k-star forest is a forest whose components are stars of order at most k ＋ 1. The k-star arboricity of a graph G,denoted by sak（ G）,is the minimum number of k-star forests needed to decompose G. In this paper,it is proved that if any two vertices of degree 3 are nonadjacent in a subcubic graph G then sa2（ G） ≤2.For general subcubic graphs G, a polynomial-time algorithm is described to decompose G into three 2-star forests. For a tree T and[Δ k, T）/k]t≤ sak（ T） ≤[Δ（ T）- 1/K]＋1,where Δ（ T） is the maximum degree of T.kMoreover,a linear-time algorithm is designed to determine whether sak（ T） ≤m for any tree T and any positive integers m and k.展开更多
In order to effectively derive the inverse kinematic solution of the Delta robot and realize actuator control a description of the linear graph principle for automatically generating kinematic equations in a mechanica...In order to effectively derive the inverse kinematic solution of the Delta robot and realize actuator control a description of the linear graph principle for automatically generating kinematic equations in a mechanical system as well as the symbolic computation implementation of this procedure is reviewed and projected into the Delta robot. Based on the established linear graph representation the explicit symbolic expression of constraint equations and inverse kinematic solutions are obtained successfully using a symbolic computation engine Maple so that actuator control and trajectory tracking can be directly realized.Two practical motions the circular path and Adept motion are simulated for the validation of symbolic solutions respectively.Results indicate that the simulation satisfies the requirement of the quick motion within an acceptable threshold. Thus the precision of kinematic response can be confirmed and the correctness of inverse solution is verified.展开更多
The enhanced definition of Mechatronics involves the four underlying characteristics of integrated,unified,unique,and systematic approaches.In this realm,Mechatronics is not limited to electro-mechanical systems,in th...The enhanced definition of Mechatronics involves the four underlying characteristics of integrated,unified,unique,and systematic approaches.In this realm,Mechatronics is not limited to electro-mechanical systems,in the multi-physics sense,but involves other physical domains such as fluid and thermal.This paper summarizes the mechatronic approach to modeling.Linear graphs facilitate the development of state-space models of mechatronic systems,through this approach.The use of linear graphs in mechatronic modeling is outlined and an illustrative example of sound system modeling is given.Both time-domain and frequency-domain approaches are presented for the use of linear graphs.A mechatronic model of a multi-physics system may be simplified by converting all the physical domains into an equivalent single-domain system that is entirely in the output domain of the system.This approach of converting(transforming)physical domains is presented.An illustrative example of a pressure-controlled hydraulic actuator system that operates a mechanical load is given.展开更多
We consider the real three-dimensional Euclidean Jordan algebra associated to a strongly regular graph. Then, the Krein parameters of a strongly regular graph are generalized and some generalized Krein admissibility c...We consider the real three-dimensional Euclidean Jordan algebra associated to a strongly regular graph. Then, the Krein parameters of a strongly regular graph are generalized and some generalized Krein admissibility conditions are deduced. Furthermore, we establish some relations between the classical Krein parameters and the generalized Krein parameters.展开更多
This paper presents a method of constructing a mixed graph which can be used to analyze the causality for multivariate time series.We construct a partial correlation graph at first which is an undirected graph.For eve...This paper presents a method of constructing a mixed graph which can be used to analyze the causality for multivariate time series.We construct a partial correlation graph at first which is an undirected graph.For every undirected edge in the partial correlation graph,the measures of linear feedback between two time series can help us decide its direction,then we obtain the mixed graph.Using this method,we construct a mixed graph for futures sugar prices in Zhengzhou（ZF）,spot sugar prices in Zhengzhou（ZS） and futures sugar prices in New York（NF）.The result shows that there is a bi-directional causality between ZF and ZS,an unidirectional causality from NF to ZF,but no causality between NF and ZS.展开更多
基金Supported by the National Natural Science Foundation of China (10671081)
文摘A graph has exactly two main eigenvalues if and only if it is a 2-walk linear graph.In this paper,we show some necessary conditions that a 2-walk（a,b）-linear graph must obey.Using these conditions and some basic theorems in graph theory,we characterize all 2-walk linear graphs with small cyclic graphs without pendants.The results are given in sort on unicyclic,bicyclic,tricyclic graphs.
基金Supported by the National Natural Science Foundation of China(11171129)
文摘A graph has exactly two main eigenvalues if and only if it is a 2-walk linear graph. In this paper, we show some structural properties that a 2-walk （a, b）-linear graph holds. According to these properties, we can estimate and characterize more 2-walk linear graphs that have exactly two main eigenvalues.
基金supported by the Deanship of Scientific Research,Vice Presidency for Graduate Studies and Scientific Research,King Faisal University,Saudi Arabia[Grant No.GRANT3862].
文摘The idea of linear Diophantine fuzzy set(LDFS)theory with its control parameters is a strong model for machine learning and optimization under uncertainty.The activity times in the critical path method(CPM)representation procedures approach are initially static,but in the Project Evaluation and Review Technique(PERT)approach,they are probabilistic.This study proposes a novel way of project review and assessment methodology for a project network in a linear Diophantine fuzzy(LDF)environment.The LDF expected task time,LDF variance,LDF critical path,and LDF total expected time for determining the project network are all computed using LDF numbers as the time of each activity in the project network.The primary premise of the LDF-PERT approach is to address ambiguities in project network activity timesmore simply than other approaches such as conventional PERT,Fuzzy PERT,and so on.The LDF-PERT is an efficient approach to analyzing symmetries in fuzzy control systems to seek an optimal decision.We also present a new approach for locating LDF-CPM in a project network with uncertain and erroneous activity timings.When the available resources and activity times are imprecise and unpredictable,this strategy can help decision-makers make better judgments in a project.A comparison analysis of the proposed technique with the existing techniques has also been discussed.The suggested techniques are demonstrated with two suitable numerical examples.
基金supported by research grants from the Natural Sciences and Engineering Research Council(NSERC)of Canada
文摘An engineering system may consist of several different types of components,belonging to such physical"domains"as mechanical,electrical,fluid,and thermal.It is termed a multi-domain(or multi-physics)system.The present paper concerns the use of linear graphs(LGs)to generate a minimal model for a multi-physics system.A state-space model has to be a minimal realization.Specifically,the number of state variables in the model should be the minimum number that can completely represent the dynamic state of the system.This choice is not straightforward.Initially,state variables are assigned to all the energy-storage elements of the system.However,some of the energy storage elements may not be independent,and then some of the chosen state variables will be redundant.An approach is presented in the paper,with illustrative examples in the mixed fluid-mechanical domains,to illustrate a way to recognize dependent energy storage elements and thereby obtain a minimal state-space model.System analysis in the frequency domain is known to be more convenient than in the time domain,mainly because the relevant operations are algebraic rather than differential.For achieving this objective,the state space model has to be converted into a transfer function.The direct way is to first convert the state-space model into the input-output differential equation,and then substitute the time derivative by the Laplace variable.This approach is shown in the paper.The same result can be obtained through the transfer function linear graph(TF LG)of the system.In a multi-physics system,first the physical domains have to be converted into an equivalent single domain(preferably,the output domain of the system),when using the method of TFLG.This procedure is illustrated as well,in the present paper.
基金National Natural Science Foundation of China(No.10971025)
文摘A star forest is a forest whose components are stars. The star arboricity of a graph G,denoted by sa（ G）,is the minimum number of star forests needed to decompose G. Let k be a positive integer. A k-star forest is a forest whose components are stars of order at most k ＋ 1. The k-star arboricity of a graph G,denoted by sak（ G）,is the minimum number of k-star forests needed to decompose G. In this paper,it is proved that if any two vertices of degree 3 are nonadjacent in a subcubic graph G then sa2（ G） ≤2.For general subcubic graphs G, a polynomial-time algorithm is described to decompose G into three 2-star forests. For a tree T and[Δ k, T）/k]t≤ sak（ T） ≤[Δ（ T）- 1/K]＋1,where Δ（ T） is the maximum degree of T.kMoreover,a linear-time algorithm is designed to determine whether sak（ T） ≤m for any tree T and any positive integers m and k.
基金The National Natural Science Foundation of China(No.51205208)
文摘In order to effectively derive the inverse kinematic solution of the Delta robot and realize actuator control a description of the linear graph principle for automatically generating kinematic equations in a mechanical system as well as the symbolic computation implementation of this procedure is reviewed and projected into the Delta robot. Based on the established linear graph representation the explicit symbolic expression of constraint equations and inverse kinematic solutions are obtained successfully using a symbolic computation engine Maple so that actuator control and trajectory tracking can be directly realized.Two practical motions the circular path and Adept motion are simulated for the validation of symbolic solutions respectively.Results indicate that the simulation satisfies the requirement of the quick motion within an acceptable threshold. Thus the precision of kinematic response can be confirmed and the correctness of inverse solution is verified.
基金supported by research grants from the Natural Sciences and Engineering Research Council(NSERC)of Canada
文摘The enhanced definition of Mechatronics involves the four underlying characteristics of integrated,unified,unique,and systematic approaches.In this realm,Mechatronics is not limited to electro-mechanical systems,in the multi-physics sense,but involves other physical domains such as fluid and thermal.This paper summarizes the mechatronic approach to modeling.Linear graphs facilitate the development of state-space models of mechatronic systems,through this approach.The use of linear graphs in mechatronic modeling is outlined and an illustrative example of sound system modeling is given.Both time-domain and frequency-domain approaches are presented for the use of linear graphs.A mechatronic model of a multi-physics system may be simplified by converting all the physical domains into an equivalent single-domain system that is entirely in the output domain of the system.This approach of converting(transforming)physical domains is presented.An illustrative example of a pressure-controlled hydraulic actuator system that operates a mechanical load is given.
基金supported by the European Regional Development Fund through the program COMPETEby the Portuguese Government through the FCT—Fundacao para a Ciencia e a Tecnologia under the project PEst—C/MAT/UI0144/2013+1 种基金partially supported by Portuguese Funds trough CIDMA—Center for Research and development in Mathematics and Applications,Department of Mathematics,University of Aveiro,3810-193,Aveiro,Portugalthe Portuguese Foundation for Science and Technology(FCT-Fundacao para a Ciencia e Tecnologia),within Project PEst-OE/MAT/UI4106/2014
文摘We consider the real three-dimensional Euclidean Jordan algebra associated to a strongly regular graph. Then, the Krein parameters of a strongly regular graph are generalized and some generalized Krein admissibility conditions are deduced. Furthermore, we establish some relations between the classical Krein parameters and the generalized Krein parameters.
基金supported by Program for Innovative Research Team in UIBE(No.CXTD5-05)UIBE Networking and Collaboration Center for China's Multinational Business(No.201504YY006A)+1 种基金supported by the BCMIS,NSF China Zhongdian Project(No.11131002)NSFC(No.11371062)
文摘This paper presents a method of constructing a mixed graph which can be used to analyze the causality for multivariate time series.We construct a partial correlation graph at first which is an undirected graph.For every undirected edge in the partial correlation graph,the measures of linear feedback between two time series can help us decide its direction,then we obtain the mixed graph.Using this method,we construct a mixed graph for futures sugar prices in Zhengzhou（ZF）,spot sugar prices in Zhengzhou（ZS） and futures sugar prices in New York（NF）.The result shows that there is a bi-directional causality between ZF and ZS,an unidirectional causality from NF to ZF,but no causality between NF and ZS.
