The purpose of this paper is to introduce an unknown method for finding a real possible x value of any degree polynomial equation and to show how this can be applied to make computers which are at least x1000 （one th...The purpose of this paper is to introduce an unknown method for finding a real possible x value of any degree polynomial equation and to show how this can be applied to make computers which are at least x1000 （one thousand times） faster than today＇s existing highest speed computers. Since one of the Milennium Prize Problems offered by Claymath asks about whether P （Deterministic Polynomial） is equal to NP （Non-Deterministic Polynomial） （what that means informally is that whether we can design a computer which can quickly solve a certain complicated problem can also verify the solution quickly （and vice versa）. Fortunately, the answer to P vs. NP problem based on my findings in certain algebraic algorythms is yes although there have been many people who claimed the answer is no. What that means is that humans can make machines that work very fast and close to human intelligence in the identification of, say, certain proteins and amino acids, in case my theory is proven to be a fact. This paper is therefore an initial stage of planting the first seeds of the process, in terms of describing how exactly this can happen, theoretically of course, since everything in Science begins with a theory based on the outcome of a hypothesis.展开更多
This paper investigates a consensus design problem for continuous-time first-order multiagent systems with uniform constant communication delay.Provided that the agent dynamic is unstable and the diagraph is undirecte...This paper investigates a consensus design problem for continuous-time first-order multiagent systems with uniform constant communication delay.Provided that the agent dynamic is unstable and the diagraph is undirected,sufficient conditions are derived to guarantee consensus.The key technique is the adoption of historical input information in the protocol.Especially,when agent's own historical input information is used in the protocol design,the consensus condition is constructed in terms of agent dynamic,communication delay,and the eigenratio of the network topology.Simulation result is presented to validate the effectiveness of the theoretical result.展开更多
In this paper, the problem of consensus for continuous time singular systems of multi-agent networks is considered. The definition of r-consensus is introduced for singular systems of multi-agent networks. Firstly, li...In this paper, the problem of consensus for continuous time singular systems of multi-agent networks is considered. The definition of r-consensus is introduced for singular systems of multi-agent networks. Firstly, linear systems with algebraic constraints are considered, and the corresponding results about consensus and average-consensus are derived. Then r-consensus and consensus problems of singular systems are investigated. Sufficient conditions of r-consensus and consensus are obtained,respectively. Finally, an illustrative example is given to show the effectiveness of the proposed method.展开更多
文摘The purpose of this paper is to introduce an unknown method for finding a real possible x value of any degree polynomial equation and to show how this can be applied to make computers which are at least x1000 （one thousand times） faster than today＇s existing highest speed computers. Since one of the Milennium Prize Problems offered by Claymath asks about whether P （Deterministic Polynomial） is equal to NP （Non-Deterministic Polynomial） （what that means informally is that whether we can design a computer which can quickly solve a certain complicated problem can also verify the solution quickly （and vice versa）. Fortunately, the answer to P vs. NP problem based on my findings in certain algebraic algorythms is yes although there have been many people who claimed the answer is no. What that means is that humans can make machines that work very fast and close to human intelligence in the identification of, say, certain proteins and amino acids, in case my theory is proven to be a fact. This paper is therefore an initial stage of planting the first seeds of the process, in terms of describing how exactly this can happen, theoretically of course, since everything in Science begins with a theory based on the outcome of a hypothesis.
基金supported by the Taishan Scholar Construction Engineering by Shandong Government,the National Natural Science Foundation of China under Grant Nos.61120106011 and 61203029
文摘This paper investigates a consensus design problem for continuous-time first-order multiagent systems with uniform constant communication delay.Provided that the agent dynamic is unstable and the diagraph is undirected,sufficient conditions are derived to guarantee consensus.The key technique is the adoption of historical input information in the protocol.Especially,when agent's own historical input information is used in the protocol design,the consensus condition is constructed in terms of agent dynamic,communication delay,and the eigenratio of the network topology.Simulation result is presented to validate the effectiveness of the theoretical result.
基金supported by the National Natural Science Foundation of China under Grant Nos.61174141 and 61374025Research Awards Young and Middle-Aged Scientists of Shandong Province under Grant Nos.BS2011SF009 and BS2011DX019Excellent Youth Foundation of Shandong Province under Grant No.JQ201219
文摘In this paper, the problem of consensus for continuous time singular systems of multi-agent networks is considered. The definition of r-consensus is introduced for singular systems of multi-agent networks. Firstly, linear systems with algebraic constraints are considered, and the corresponding results about consensus and average-consensus are derived. Then r-consensus and consensus problems of singular systems are investigated. Sufficient conditions of r-consensus and consensus are obtained,respectively. Finally, an illustrative example is given to show the effectiveness of the proposed method.
