Both independence and independence-separation problems on chessboard graphs have been studied in detail, with hundreds of papers in the broader independence category, and several on the independence-separation problem...Both independence and independence-separation problems on chessboard graphs have been studied in detail, with hundreds of papers in the broader independence category, and several on the independence-separation problem variant for chessboard graphs. In this paper, the inde-pendence-separation problem is considered on the d-dimensional rook’s graph. A lower bound of k, for , is found for the independence-separation number on the d-dimensional rook’s graph, denoted by . For the case where , it is found that when n is odd and , . Conjecture and discussion are added.展开更多
Background For the purpose of utilising hybrid vigour to produce possible hybrids with a suitable level of stability,the knowledge of gene activity and combining ability is a crucial prerequisite before choosing desir...Background For the purpose of utilising hybrid vigour to produce possible hybrids with a suitable level of stability,the knowledge of gene activity and combining ability is a crucial prerequisite before choosing desirable parents.The present study was carried out with six parents crossed in full diallel fashion and generated 30 F1 hybrids.These hybrids were evaluated in two replications in Randomized Block Design at Department of Cotton,TNAU for combining ability and gene action.Diallel analysis was carried out according to Griffing’s method-I(parents + F_(1) + reciprocals) and model-I and Hayman’s graphical approach by using INDOSTAT software.Results Analysis of variance for combining ability indicated that mean square values of GCA,SCA and reciprocals were highly significant for all the traits except for the uniformity index.RG763 and K12 showed highly positively significant GCA effects for most of the yield traits while PA838 and K12 for fibre quality traits,so they were found as best general combiners.PAIG379 × K12 and PDB29 × K12 for yield traits,and PDB29 × PA838,RG763 × PA838,and CNA1007 × RG763 cross combinations for fibre quality traits could be recommended for future breeding programms.Conclusion The results of both Griffing’s and Hayman’s approaches showed that non-additive gene action predominates as SCA variance was bigger than GCA variance,so heterosis breeding is thought to be a more fruitful option for enhancing GCA of many traits.展开更多
Dynamic modeling of a parallel manipulator（PM） is an important issue. A complete PM system is actually composed of multiple physical domains. As PMs are widely used in various fields, the importance of modeling the ...Dynamic modeling of a parallel manipulator（PM） is an important issue. A complete PM system is actually composed of multiple physical domains. As PMs are widely used in various fields, the importance of modeling the global dynamic model of the PM system becomes increasingly prominent. Currently there lacks further research in global dynamic modeling. A unified modeling approach for the multi-energy domains PM system is proposed based on bond graph and a global dynamic model of the 3-UPS/S parallel stabilized platform involving mechanical and electrical-hydraulic elements is built. Firstly, the screw bond graph theory is improved based on the screw theory, the modular joint model is modeled and the normalized dynamic model of the mechanism is established. Secondly, combined with the electro-hydraulic servo system model built by traditional bond graph, the global dynamic model of the system is obtained, and then the motion, force and power of any element can be obtained directly. Lastly, the experiments and simulations of the driving forces, pressure and flow are performed, and the results show that, the theoretical calculation results of the driving forces are in accord with the experimental ones, and the pressure and flow of the first limb and the third limb are symmetry with each other. The results are reasonable and verify the correctness and effectiveness of the model and the method. The proposed dynamic modeling method provides a reference for modeling of other multi-energy domains system which contains complex PM.展开更多
In this paper, both the roman domination number and the number of minimum roman dominating sets are found for any rectangular rook’s graph. In a similar fashion, the roman domination number and the number of minimum ...In this paper, both the roman domination number and the number of minimum roman dominating sets are found for any rectangular rook’s graph. In a similar fashion, the roman domination number and the number of minimum roman dominating sets are found on the square bishop’s graph for odd board sizes. Also found are the number of minimum total dominating sets associated with the light-colored squares when n?≡1(mod12)? (with n>1), and same for the dark-colored squares when n?≡7(mod12) .展开更多
<div style="text-align:justify;"> We know that functional and structural organization is altered in human brain network due to Alzheimer’s disease. In this paper we highlight how Graph Theory techniqu...<div style="text-align:justify;"> We know that functional and structural organization is altered in human brain network due to Alzheimer’s disease. In this paper we highlight how Graph Theory techniques, its structural parameters like connectivity, diameter, vertex centrality, betweenness centrality, clustering coefficient, degree distribution, cluster analysis and graph cores are involved to analyse magnetoencephalography data to explore functional network integrity in Alzheimer’s disease affected patients. We also record that both weighted and unweighted undirected/directed graphs depending on functional connectivity analysis with attention to connectivity of the network and vertex centrality, could model and provide explanation to loss of links, status of the hub in the region of parietal, derailed synchronization in network and centrality loss at the vital left temporal region that is clinically significant were found in cases carrying Alzheimer’s disease. We also notice that graph theory driven measures such as characteristic path length and clustering coefficient could be used to study and report a sudden electroencephalography effect in Alzheimer’s disease through entropy of the cross-sample. We also provide adequate literature survey to demonstrate the latest and advanced graphical tools for both graph layouts and graph visualization to understand the complex brain networks and to unravel the mysteries of Alzheimer’s disease. </div>展开更多
Solving for currents of an electrical circuit with resistances and batteries has always been the ultimate test of proper understanding of Kirchoff’s rules. Yet, it is hardly ever emphasized that a systematic solution...Solving for currents of an electrical circuit with resistances and batteries has always been the ultimate test of proper understanding of Kirchoff’s rules. Yet, it is hardly ever emphasized that a systematic solution of more complex cases requires good understanding of the relevant part of Graph theory. Even though this is usually not covered by Physics’ curriculum, it may still be of interest to some teachers and their mathematically inclined students, who may want to learn details of the rigorous approach. The purpose of this article is to provide a concise derivation of a linear set of equations leading to a unique solution of the problem at hand. We also present a simple computer program which builds such a solution for circuits of any textbook size.展开更多
By introducing the notions of L-spaces and L_r-spaces, a complete generalization of Kalton's closed graph theorem is obtained. It points out the class of L_r-spaces is the maximal class of range spaces for the clo...By introducing the notions of L-spaces and L_r-spaces, a complete generalization of Kalton's closed graph theorem is obtained. It points out the class of L_r-spaces is the maximal class of range spaces for the closed graph theorem when the class of domain spaces is the class of Mackey spaces with weakly * sequentially complete dual.Some examples are constructed showing that the class of L_r-spaces is strictly larger than the class of separable B_r-complete spaces.Some properties of L-spaces and L_r-spaces are discussed and the relations between B-complete (resp. B_r-complete) spaces and L-spaces (resp. L_r-spaces) are given.展开更多
文摘Both independence and independence-separation problems on chessboard graphs have been studied in detail, with hundreds of papers in the broader independence category, and several on the independence-separation problem variant for chessboard graphs. In this paper, the inde-pendence-separation problem is considered on the d-dimensional rook’s graph. A lower bound of k, for , is found for the independence-separation number on the d-dimensional rook’s graph, denoted by . For the case where , it is found that when n is odd and , . Conjecture and discussion are added.
文摘Background For the purpose of utilising hybrid vigour to produce possible hybrids with a suitable level of stability,the knowledge of gene activity and combining ability is a crucial prerequisite before choosing desirable parents.The present study was carried out with six parents crossed in full diallel fashion and generated 30 F1 hybrids.These hybrids were evaluated in two replications in Randomized Block Design at Department of Cotton,TNAU for combining ability and gene action.Diallel analysis was carried out according to Griffing’s method-I(parents + F_(1) + reciprocals) and model-I and Hayman’s graphical approach by using INDOSTAT software.Results Analysis of variance for combining ability indicated that mean square values of GCA,SCA and reciprocals were highly significant for all the traits except for the uniformity index.RG763 and K12 showed highly positively significant GCA effects for most of the yield traits while PA838 and K12 for fibre quality traits,so they were found as best general combiners.PAIG379 × K12 and PDB29 × K12 for yield traits,and PDB29 × PA838,RG763 × PA838,and CNA1007 × RG763 cross combinations for fibre quality traits could be recommended for future breeding programms.Conclusion The results of both Griffing’s and Hayman’s approaches showed that non-additive gene action predominates as SCA variance was bigger than GCA variance,so heterosis breeding is thought to be a more fruitful option for enhancing GCA of many traits.
基金Supported by National Natural Science Foundation of China(Grant Nos.51275438,51405421)Hebei Provincial Natural Science Foundation of China(Grant No.E2015203101)
文摘Dynamic modeling of a parallel manipulator（PM） is an important issue. A complete PM system is actually composed of multiple physical domains. As PMs are widely used in various fields, the importance of modeling the global dynamic model of the PM system becomes increasingly prominent. Currently there lacks further research in global dynamic modeling. A unified modeling approach for the multi-energy domains PM system is proposed based on bond graph and a global dynamic model of the 3-UPS/S parallel stabilized platform involving mechanical and electrical-hydraulic elements is built. Firstly, the screw bond graph theory is improved based on the screw theory, the modular joint model is modeled and the normalized dynamic model of the mechanism is established. Secondly, combined with the electro-hydraulic servo system model built by traditional bond graph, the global dynamic model of the system is obtained, and then the motion, force and power of any element can be obtained directly. Lastly, the experiments and simulations of the driving forces, pressure and flow are performed, and the results show that, the theoretical calculation results of the driving forces are in accord with the experimental ones, and the pressure and flow of the first limb and the third limb are symmetry with each other. The results are reasonable and verify the correctness and effectiveness of the model and the method. The proposed dynamic modeling method provides a reference for modeling of other multi-energy domains system which contains complex PM.
文摘In this paper, both the roman domination number and the number of minimum roman dominating sets are found for any rectangular rook’s graph. In a similar fashion, the roman domination number and the number of minimum roman dominating sets are found on the square bishop’s graph for odd board sizes. Also found are the number of minimum total dominating sets associated with the light-colored squares when n?≡1(mod12)? (with n>1), and same for the dark-colored squares when n?≡7(mod12) .
文摘<div style="text-align:justify;"> We know that functional and structural organization is altered in human brain network due to Alzheimer’s disease. In this paper we highlight how Graph Theory techniques, its structural parameters like connectivity, diameter, vertex centrality, betweenness centrality, clustering coefficient, degree distribution, cluster analysis and graph cores are involved to analyse magnetoencephalography data to explore functional network integrity in Alzheimer’s disease affected patients. We also record that both weighted and unweighted undirected/directed graphs depending on functional connectivity analysis with attention to connectivity of the network and vertex centrality, could model and provide explanation to loss of links, status of the hub in the region of parietal, derailed synchronization in network and centrality loss at the vital left temporal region that is clinically significant were found in cases carrying Alzheimer’s disease. We also notice that graph theory driven measures such as characteristic path length and clustering coefficient could be used to study and report a sudden electroencephalography effect in Alzheimer’s disease through entropy of the cross-sample. We also provide adequate literature survey to demonstrate the latest and advanced graphical tools for both graph layouts and graph visualization to understand the complex brain networks and to unravel the mysteries of Alzheimer’s disease. </div>
文摘Solving for currents of an electrical circuit with resistances and batteries has always been the ultimate test of proper understanding of Kirchoff’s rules. Yet, it is hardly ever emphasized that a systematic solution of more complex cases requires good understanding of the relevant part of Graph theory. Even though this is usually not covered by Physics’ curriculum, it may still be of interest to some teachers and their mathematically inclined students, who may want to learn details of the rigorous approach. The purpose of this article is to provide a concise derivation of a linear set of equations leading to a unique solution of the problem at hand. We also present a simple computer program which builds such a solution for circuits of any textbook size.
文摘By introducing the notions of L-spaces and L_r-spaces, a complete generalization of Kalton's closed graph theorem is obtained. It points out the class of L_r-spaces is the maximal class of range spaces for the closed graph theorem when the class of domain spaces is the class of Mackey spaces with weakly * sequentially complete dual.Some examples are constructed showing that the class of L_r-spaces is strictly larger than the class of separable B_r-complete spaces.Some properties of L-spaces and L_r-spaces are discussed and the relations between B-complete (resp. B_r-complete) spaces and L-spaces (resp. L_r-spaces) are given.
