In order to reveal the complex network characteristics and evolution principle of China aviation network,the relationship between the average degree and the average path length of edge vertices of China aviation netwo...In order to reveal the complex network characteristics and evolution principle of China aviation network,the relationship between the average degree and the average path length of edge vertices of China aviation network in 1988,1994,2001,2008 and 2015 was studied.According to the theory and method of complex network,the network system was constructed with the city where the airport was located as the network node and the airline as the edge of the network.On the basis of the statistical data,the average degree and average path length of edge vertices of China aviation network in 1988,1994,2001,2008 and 2015 were calculated.Through regression analysis,it was found that the average degree had a logarithmic relationship with the average path length of edge vertices and the two parameters of the logarithmic relationship had linear evolutionary trace.展开更多
Factors for determining the spindle size are the shaft diameter, positions of bearing and motor, and entire length of the spindle. Then, it is important to find the assembling of the optimal design variables, which sa...Factors for determining the spindle size are the shaft diameter, positions of bearing and motor, and entire length of the spindle. Then, it is important to find the assembling of the optimal design variables, which satisfy the stiffimss and rotational speed required to the spindle. A general full factorial design method was used to verify some factors that affect the natural frequency of a spindle. It is verified that the shorter shaft length and bearing span length represent the higher natural frequency, and there are some effects according to the change in the levels of factors. The detailed spindle dimension is determined by applying an EVD method, which can define the optimal bearing position through considering the limiting condition. Based on the estimated regression model, the optimal spindle size and bearing distance that can improve the primary natural frequency are obtained, and the influence of design factors on the natural frequency is also analyzed.展开更多
This paper mainly gives a sufficient and necessary condition for an order of hyperplanes of a graphic arrangement being supersolvable. In addition, we give the relations between the set of supersolvable orders of hype...This paper mainly gives a sufficient and necessary condition for an order of hyperplanes of a graphic arrangement being supersolvable. In addition, we give the relations between the set of supersolvable orders of hyperplanes and the set of quadratic orders of hyperplanes for a supersolvable arrangement.展开更多
Let G be a connected graph of order n and m_(RD)^(L)_(G)I denote the number of reciprocal distance Laplacian eigenvaluesof G in an interval I.For a given interval I,we mainly present several bounds on m_(RD)^(L)_(G)I ...Let G be a connected graph of order n and m_(RD)^(L)_(G)I denote the number of reciprocal distance Laplacian eigenvaluesof G in an interval I.For a given interval I,we mainly present several bounds on m_(RD)^(L)_(G)I in terms of various structuralparameters of the graph G,including vertex-connectivity,independence number and pendant vertices.展开更多
In the present study,a response optimization method using Extreme Vertices Mixer Design(EVMD)approach is proposed for stress optimization in a thermomechanically processed Mg-Li-Al alloy.Experimentation was planned as...In the present study,a response optimization method using Extreme Vertices Mixer Design(EVMD)approach is proposed for stress optimization in a thermomechanically processed Mg-Li-Al alloy.Experimentation was planned as per mixed design proportions of Mg,Li and Al and process variables(i.e.temperature and strain rate).Each experiment has been performed under different conditions of factors proportions and process variables.The response,particularly stress has been considered for each experiment.The response is optimized to find an optimum condition when the contributing factors influence material characteristics in such a way,to achieve better strength,ductility and corrosion resistance.Estimated regression coefficient table for response has been observed to identify the important factors in this process and significantly high variance inflation factor has been observed.Most importantly,an optimum condition is achieved from this analysis which fulfills the experimental observations and theoretical assumptions.展开更多
In order to reveal the complex network characteristics and evolution principle of China aviation network, the probability distribution and evolution trace of ratio of China aviation network edge vertices degree were s...In order to reveal the complex network characteristics and evolution principle of China aviation network, the probability distribution and evolution trace of ratio of China aviation network edge vertices degree were studied based on the statistics data of China civil aviation network in 1988, 1994, 2001, 2008 and 2015. According to the theory and method of complex network, the network system was constructed with the city where the airport was located as the network node and the route between cities as the edge of the network. Based on the statistical data, the ratio of edge vertices degree in China aviation network in 1988, 1994, 2001, 2008 and 2015 were calculated. Using the probability statistical analysis method and regression analysis approach, it was found that the ratio of edge vertices degree had linear probability distribution and the two parameters of the probability distribution had linear evolution trace.展开更多
In order to reveal the complex network characteristics and evolution principle of China aviation network, the probability distribution and evolution trace of average degree of edge vertices of China aviation network w...In order to reveal the complex network characteristics and evolution principle of China aviation network, the probability distribution and evolution trace of average degree of edge vertices of China aviation network were studied based on the statistics data of China civil aviation network in 1988, 1994, 2001, 2008 and 2015. According to the theory and method of complex network, the network system was constructed with the city where the airport was located as the network node and the route between cities as the edge of the network. Based on the statistical data, the average degrees of edge vertices in China aviation network in 1988, 1994, 2001, 2008 and 2015 were calculated. Using the probability statistical analysis method and regression analysis approach, it was found that the average degree of edge vertices had the probability distribution of normal function and the position parameters and scale parameters of the probability distribution had linear evolution trace.展开更多
Graph neural networks have been shown to be very effective in utilizing pairwise relationships across samples.Recently,there have been several successful proposals to generalize graph neural networks to hypergraph neu...Graph neural networks have been shown to be very effective in utilizing pairwise relationships across samples.Recently,there have been several successful proposals to generalize graph neural networks to hypergraph neural networks to exploit more com-plex relationships.In particular,the hypergraph collaborative networks yield superior results compared to other hypergraph neural net-works for various semi-supervised learning tasks.The collaborative network can provide high quality vertex embeddings and hyperedge embeddings together by formulating them as a joint optimization problem and by using their consistency in reconstructing the given hy-pergraph.In this paper,we aim to establish the algorithmic stability of the core layer of the collaborative network and provide generaliz--ation guarantees.The analysis sheds light on the design of hypergraph filters in collaborative networks,for instance,how the data and hypergraph filters should be scaled to achieve uniform stability of the learning process.Some experimental results on real-world datasets are presented to illustrate the theory.展开更多
In order to reveal the complex network characteristics and evolution principle of China aviation network,the probability distribution and evolution trace of arithmetic average of edge vertices nearest neighbor average...In order to reveal the complex network characteristics and evolution principle of China aviation network,the probability distribution and evolution trace of arithmetic average of edge vertices nearest neighbor average degree values of China aviation network were studied based on the statistics data of China civil aviation network in 1988,1994,2001,2008 and 2015.According to the theory and method of complex network,the network system was constructed with the city where the airport was located as the network node and the route between cities as the edge of the network.Based on the statistical data,the arithmetic averages of edge vertices nearest neighbor average degree values of China aviation network in 1988,1994,2001,2008 and 2015 were calculated.Using the probability statistical analysis method,it was found that the arithmetic average of edge vertices nearest neighbor average degree values had the probability distribution of normal function and the position parameters and scale parameters of the probability distribution had linear evolution trace.展开更多
The augmented Zagreb index displays a good correlation with the formation heat of octanes and heptanes. The augmented Zagreb index of catacondensed hexagonal systems and molecular trees was discussed. By using the met...The augmented Zagreb index displays a good correlation with the formation heat of octanes and heptanes. The augmented Zagreb index of catacondensed hexagonal systems and molecular trees was discussed. By using the methods of analysis of graph structure and mathematical induction,the catacondensed hexagonal systems with extreme augmented Zagreb index were characterized.The lower bound for augmented Zagreb index of molecular trees with fixed numbers of pendent vertices was given,and the extremal trees were characterized. From these results,we can compare the formation heat of catacondensed hexagonal systems and molecular trees.展开更多
The main purpose of this paper is to develop and simplify the general conditions for an s-stage explicit canonical difference scheme of q-th order, while the simplified order conditions for canonical RKN methods which...The main purpose of this paper is to develop and simplify the general conditions for an s-stage explicit canonical difference scheme of q-th order, while the simplified order conditions for canonical RKN methods which are applied to a special kind of second order ordinary differential equations are also obtained here.展开更多
Let G be a graph of order n with vertex set V(G) = {v1, v2,…, vn}. the adjacency matrix of G is an n × n matrix A(G) = (aij)n×n, where aij is the number edges joining vi and vj in G. The eigenvalues λ1, λ...Let G be a graph of order n with vertex set V(G) = {v1, v2,…, vn}. the adjacency matrix of G is an n × n matrix A(G) = (aij)n×n, where aij is the number edges joining vi and vj in G. The eigenvalues λ1, λ2, λ3,…, λn, of A(G) are said to be the eigenvalues of the graph G and to form the spectrum of this graph. The number of nonzero eigenvalues and zero eigenvalues in the spectrum of G are called rank and nullity of the graph G, and are denoted by r(G) and η(G), respectively. It follows from the definitions that r(G) + η(G) = n. In this paper, by using the operation of multiplication of vertices, a characterization for graph G with pendant vertices and r(G) = 7 is shown, and then a characterization for graph G with pendant vertices and r(G) less than or equal to 7 is shown.展开更多
Coloring the nodes of a graph is a commonly used technique to speed up clique search algorithms. Coloring the edges of the graph as a preconditioning method can also be used to speed up computations. In this paper we ...Coloring the nodes of a graph is a commonly used technique to speed up clique search algorithms. Coloring the edges of the graph as a preconditioning method can also be used to speed up computations. In this paper we will show that an unconventional coloring scheme of the edges leads to an NP-complete problem when one intends to determine the optimal number of colors.展开更多
文摘In order to reveal the complex network characteristics and evolution principle of China aviation network,the relationship between the average degree and the average path length of edge vertices of China aviation network in 1988,1994,2001,2008 and 2015 was studied.According to the theory and method of complex network,the network system was constructed with the city where the airport was located as the network node and the airline as the edge of the network.On the basis of the statistical data,the average degree and average path length of edge vertices of China aviation network in 1988,1994,2001,2008 and 2015 were calculated.Through regression analysis,it was found that the average degree had a logarithmic relationship with the average path length of edge vertices and the two parameters of the logarithmic relationship had linear evolutionary trace.
基金Project(RTI04-01-03) supported by the Regional Technology Innovation Program of the Ministry of Knowledge Economy (MKE) of Korea
文摘Factors for determining the spindle size are the shaft diameter, positions of bearing and motor, and entire length of the spindle. Then, it is important to find the assembling of the optimal design variables, which satisfy the stiffimss and rotational speed required to the spindle. A general full factorial design method was used to verify some factors that affect the natural frequency of a spindle. It is verified that the shorter shaft length and bearing span length represent the higher natural frequency, and there are some effects according to the change in the levels of factors. The detailed spindle dimension is determined by applying an EVD method, which can define the optimal bearing position through considering the limiting condition. Based on the estimated regression model, the optimal spindle size and bearing distance that can improve the primary natural frequency are obtained, and the influence of design factors on the natural frequency is also analyzed.
文摘This paper mainly gives a sufficient and necessary condition for an order of hyperplanes of a graphic arrangement being supersolvable. In addition, we give the relations between the set of supersolvable orders of hyperplanes and the set of quadratic orders of hyperplanes for a supersolvable arrangement.
基金supported by the Natural Science Foundation of Xinjiang Uygur Autonomous Region of China“Graph problems of topological parameters based on the spectra of graph matrices”(2021D01C069)the National Natural Science Foundation of the People's Republic of China“The investigation of spectral properties of graph operations and their related problems”(12161085)。
文摘Let G be a connected graph of order n and m_(RD)^(L)_(G)I denote the number of reciprocal distance Laplacian eigenvaluesof G in an interval I.For a given interval I,we mainly present several bounds on m_(RD)^(L)_(G)I in terms of various structuralparameters of the graph G,including vertex-connectivity,independence number and pendant vertices.
文摘In the present study,a response optimization method using Extreme Vertices Mixer Design(EVMD)approach is proposed for stress optimization in a thermomechanically processed Mg-Li-Al alloy.Experimentation was planned as per mixed design proportions of Mg,Li and Al and process variables(i.e.temperature and strain rate).Each experiment has been performed under different conditions of factors proportions and process variables.The response,particularly stress has been considered for each experiment.The response is optimized to find an optimum condition when the contributing factors influence material characteristics in such a way,to achieve better strength,ductility and corrosion resistance.Estimated regression coefficient table for response has been observed to identify the important factors in this process and significantly high variance inflation factor has been observed.Most importantly,an optimum condition is achieved from this analysis which fulfills the experimental observations and theoretical assumptions.
文摘In order to reveal the complex network characteristics and evolution principle of China aviation network, the probability distribution and evolution trace of ratio of China aviation network edge vertices degree were studied based on the statistics data of China civil aviation network in 1988, 1994, 2001, 2008 and 2015. According to the theory and method of complex network, the network system was constructed with the city where the airport was located as the network node and the route between cities as the edge of the network. Based on the statistical data, the ratio of edge vertices degree in China aviation network in 1988, 1994, 2001, 2008 and 2015 were calculated. Using the probability statistical analysis method and regression analysis approach, it was found that the ratio of edge vertices degree had linear probability distribution and the two parameters of the probability distribution had linear evolution trace.
文摘In order to reveal the complex network characteristics and evolution principle of China aviation network, the probability distribution and evolution trace of average degree of edge vertices of China aviation network were studied based on the statistics data of China civil aviation network in 1988, 1994, 2001, 2008 and 2015. According to the theory and method of complex network, the network system was constructed with the city where the airport was located as the network node and the route between cities as the edge of the network. Based on the statistical data, the average degrees of edge vertices in China aviation network in 1988, 1994, 2001, 2008 and 2015 were calculated. Using the probability statistical analysis method and regression analysis approach, it was found that the average degree of edge vertices had the probability distribution of normal function and the position parameters and scale parameters of the probability distribution had linear evolution trace.
基金Ng was supported in part by Hong Kong Research Grant Council General Research Fund(GRF),China(Nos.12300218,12300519,117201020,17300021,CRF C1013-21GF,C7004-21GF and Joint NSFC-RGC NHKU76921)Wu is supported by National Natural Science Foundation of China(No.62206111)+3 种基金Young Talent Support Project of Guangzhou Association for Science and Technology,China(No.QT-2023-017)Guangzhou Basic and Applied Basic Research Foundation,China(No.2023A04J1058)Fundamental Research Funds for the Central Universities,China(No.21622326)China Postdoctoral Science Foundation(No.2022M721343).
文摘Graph neural networks have been shown to be very effective in utilizing pairwise relationships across samples.Recently,there have been several successful proposals to generalize graph neural networks to hypergraph neural networks to exploit more com-plex relationships.In particular,the hypergraph collaborative networks yield superior results compared to other hypergraph neural net-works for various semi-supervised learning tasks.The collaborative network can provide high quality vertex embeddings and hyperedge embeddings together by formulating them as a joint optimization problem and by using their consistency in reconstructing the given hy-pergraph.In this paper,we aim to establish the algorithmic stability of the core layer of the collaborative network and provide generaliz--ation guarantees.The analysis sheds light on the design of hypergraph filters in collaborative networks,for instance,how the data and hypergraph filters should be scaled to achieve uniform stability of the learning process.Some experimental results on real-world datasets are presented to illustrate the theory.
文摘In order to reveal the complex network characteristics and evolution principle of China aviation network,the probability distribution and evolution trace of arithmetic average of edge vertices nearest neighbor average degree values of China aviation network were studied based on the statistics data of China civil aviation network in 1988,1994,2001,2008 and 2015.According to the theory and method of complex network,the network system was constructed with the city where the airport was located as the network node and the route between cities as the edge of the network.Based on the statistical data,the arithmetic averages of edge vertices nearest neighbor average degree values of China aviation network in 1988,1994,2001,2008 and 2015 were calculated.Using the probability statistical analysis method,it was found that the arithmetic average of edge vertices nearest neighbor average degree values had the probability distribution of normal function and the position parameters and scale parameters of the probability distribution had linear evolution trace.
基金National Natural Science Foundation of China(No.11071227)Shanxi Scholarship Council of China(No.2012-070)Foundation of North University of China(No.2013-12-1)
文摘The augmented Zagreb index displays a good correlation with the formation heat of octanes and heptanes. The augmented Zagreb index of catacondensed hexagonal systems and molecular trees was discussed. By using the methods of analysis of graph structure and mathematical induction,the catacondensed hexagonal systems with extreme augmented Zagreb index were characterized.The lower bound for augmented Zagreb index of molecular trees with fixed numbers of pendent vertices was given,and the extremal trees were characterized. From these results,we can compare the formation heat of catacondensed hexagonal systems and molecular trees.
文摘The main purpose of this paper is to develop and simplify the general conditions for an s-stage explicit canonical difference scheme of q-th order, while the simplified order conditions for canonical RKN methods which are applied to a special kind of second order ordinary differential equations are also obtained here.
文摘Let G be a graph of order n with vertex set V(G) = {v1, v2,…, vn}. the adjacency matrix of G is an n × n matrix A(G) = (aij)n×n, where aij is the number edges joining vi and vj in G. The eigenvalues λ1, λ2, λ3,…, λn, of A(G) are said to be the eigenvalues of the graph G and to form the spectrum of this graph. The number of nonzero eigenvalues and zero eigenvalues in the spectrum of G are called rank and nullity of the graph G, and are denoted by r(G) and η(G), respectively. It follows from the definitions that r(G) + η(G) = n. In this paper, by using the operation of multiplication of vertices, a characterization for graph G with pendant vertices and r(G) = 7 is shown, and then a characterization for graph G with pendant vertices and r(G) less than or equal to 7 is shown.
文摘Coloring the nodes of a graph is a commonly used technique to speed up clique search algorithms. Coloring the edges of the graph as a preconditioning method can also be used to speed up computations. In this paper we will show that an unconventional coloring scheme of the edges leads to an NP-complete problem when one intends to determine the optimal number of colors.
