Abstract We first consider the group inverses of the block matrices（AB0C）over a weakly finite ring. Then we study the sufficient and necessary conditions for the existence and the representations of the group invers...Abstract We first consider the group inverses of the block matrices（AB0C）over a weakly finite ring. Then we study the sufficient and necessary conditions for the existence and the representations of the group inverses of the block matrices（ABCD）over a ring with unity 1 under the following conditions respectively： （i） B = C, D = 0,B#and（BπA0#both exist; （ii） B is invertible and m = n;（iii）A#and （D - CA#B）# both exist, C = CAA#, where A and D are m × m and n × n matrices, respectively.展开更多
Studies on the stability of the equilibrium points of continuous bidirectional associative memory (BAM) neural network have yielded many useful results. A novel neural network model called standard neural network mode...Studies on the stability of the equilibrium points of continuous bidirectional associative memory (BAM) neural network have yielded many useful results. A novel neural network model called standard neural network model (SNNM) is ad- vanced. By using state affine transformation, the BAM neural networks were converted to SNNMs. Some sufficient conditions for the global asymptotic stability of continuous BAM neural networks were derived from studies on the SNNMs’ stability. These conditions were formulated as easily verifiable linear matrix inequalities (LMIs), whose conservativeness is relatively low. The approach proposed extends the known stability results, and can also be applied to other forms of recurrent neural networks (RNNs).展开更多
To facilitate stability analysis of discrete-time bidirectional associative memory (BAM) neural networks, they were converted into novel neural network models, termed standard neural network models (SNNMs), which inte...To facilitate stability analysis of discrete-time bidirectional associative memory (BAM) neural networks, they were converted into novel neural network models, termed standard neural network models (SNNMs), which interconnect linear dynamic systems and bounded static nonlinear operators. By combining a number of different Lyapunov functionals with S-procedure, some useful criteria of global asymptotic stability and global exponential stability of the equilibrium points of SNNMs were derived. These stability conditions were formulated as linear matrix inequalities (LMIs). So global stability of the discrete-time BAM neural networks could be analyzed by using the stability results of the SNNMs. Compared to the existing stability analysis methods, the proposed approach is easy to implement, less conservative, and is applicable to other recurrent neural networks.展开更多
Regarding a single-layered PLN network with feedback connections as an associative memory network,the complexity of recognition is discussed.We have the main result:if the size of the network N is m,then the complexit...Regarding a single-layered PLN network with feedback connections as an associative memory network,the complexity of recognition is discussed.We have the main result:if the size of the network N is m,then the complexity of recognition is an exponential function of m.The necessary condition under which the complexity of recognition is polynomial is given.展开更多
基金Acknowledgements The authors were grateful to the referees for their constructive comments and suggestions. This work was supported by the National Natural Science Foundation of China （Grant No. 11371109） and the Education Department of Heilongjiang Province of China （No. 12541605）.
文摘Abstract We first consider the group inverses of the block matrices（AB0C）over a weakly finite ring. Then we study the sufficient and necessary conditions for the existence and the representations of the group inverses of the block matrices（ABCD）over a ring with unity 1 under the following conditions respectively： （i） B = C, D = 0,B#and（BπA0#both exist; （ii） B is invertible and m = n;（iii）A#and （D - CA#B）# both exist, C = CAA#, where A and D are m × m and n × n matrices, respectively.
基金Project (No. 60074008) supported by the National Natural Science Foundation of China
文摘Studies on the stability of the equilibrium points of continuous bidirectional associative memory (BAM) neural network have yielded many useful results. A novel neural network model called standard neural network model (SNNM) is ad- vanced. By using state affine transformation, the BAM neural networks were converted to SNNMs. Some sufficient conditions for the global asymptotic stability of continuous BAM neural networks were derived from studies on the SNNMs’ stability. These conditions were formulated as easily verifiable linear matrix inequalities (LMIs), whose conservativeness is relatively low. The approach proposed extends the known stability results, and can also be applied to other forms of recurrent neural networks (RNNs).
基金Project (No. 60074008) supported by the National Natural Science Foundation of China
文摘To facilitate stability analysis of discrete-time bidirectional associative memory (BAM) neural networks, they were converted into novel neural network models, termed standard neural network models (SNNMs), which interconnect linear dynamic systems and bounded static nonlinear operators. By combining a number of different Lyapunov functionals with S-procedure, some useful criteria of global asymptotic stability and global exponential stability of the equilibrium points of SNNMs were derived. These stability conditions were formulated as linear matrix inequalities (LMIs). So global stability of the discrete-time BAM neural networks could be analyzed by using the stability results of the SNNMs. Compared to the existing stability analysis methods, the proposed approach is easy to implement, less conservative, and is applicable to other recurrent neural networks.
文摘Regarding a single-layered PLN network with feedback connections as an associative memory network,the complexity of recognition is discussed.We have the main result:if the size of the network N is m,then the complexity of recognition is an exponential function of m.The necessary condition under which the complexity of recognition is polynomial is given.
