In this paper. a method to study the stability of nonholonomic systems withrespect to partial variables is given and several stability theorems of nonholonomicsystems with respect to partial variables are obtained. Mo...In this paper. a method to study the stability of nonholonomic systems withrespect to partial variables is given and several stability theorems of nonholonomicsystems with respect to partial variables are obtained. Moreover, a relationshipbetween the stability of a nonholonomic system with respect to all variables and thatto partial variables is obtained.展开更多
In this paper, we obtain the moment conditions for the supermun of normed sums of ρ^--mixing random variables by using the Rosenthal-type inequality for Maximum partial sums of ρ^--mixing random variables. The resul...In this paper, we obtain the moment conditions for the supermun of normed sums of ρ^--mixing random variables by using the Rosenthal-type inequality for Maximum partial sums of ρ^--mixing random variables. The result obtained generalize the results of Chen(2008) and extend those to negatively associated sequences and ρ^--mixing random variables.展开更多
By using the method developed in the paper [Georg. Inter. J. Sci. Tech., Volume 3, Issue 1 （2011）, 107-129], it is obtained a representation in an explicit form of the weak solution of a linear partial differential...By using the method developed in the paper [Georg. Inter. J. Sci. Tech., Volume 3, Issue 1 （2011）, 107-129], it is obtained a representation in an explicit form of the weak solution of a linear partial differential equation of the higher order in two variables with initial condition whose coefficients are real-valued simple step functions.展开更多
Partial epilepsy is characterized by recurrent seizures that arise from a localized pathological brain region. During the onset of partial epilepsy, the seizure evolution commonly exhibits typical timescale separation...Partial epilepsy is characterized by recurrent seizures that arise from a localized pathological brain region. During the onset of partial epilepsy, the seizure evolution commonly exhibits typical timescale separation phenomenon. This timescale separation behavior can be mimicked by a paradigmatic model termed as Epileptor, which consists of coupled fast-slow neural populations via a permittivity variable. By incorporating permittivity noise into the Epileptor model, we show here that stochastic fluctuations of permittivity coupling participate in the modulation of seizure dynamics in partial epilepsy. In particular, introducing a certain level of permittivity noise can make the model produce more comparable seizure-like events that capture the temporal variability in realistic partial seizures. Furthermore, we observe that with the help of permittivity noise our stochastic Epileptor model can trigger the seizure dynamics even when it operates in the theoretical nonepileptogenic regime. These findings establish a deep mechanistic understanding on how stochastic fluctuations of permittivity coupling shape the seizure dynamics in partial epilepsy,and provide insightful biological implications.展开更多
We propose a new method for finding the local optimal points of the constrained nonlinear programming by Ordinary Differential Equations (ODE) , and prove asymptotic stability of the singular points of partial vari...We propose a new method for finding the local optimal points of the constrained nonlinear programming by Ordinary Differential Equations (ODE) , and prove asymptotic stability of the singular points of partial variables in this paper. The condition of overall uniform, asymptotic stability is also given.展开更多
This paper addresses an ordinary differential equations (ODE) approach to constrained nonlinear optimization problem. First, it proposes a method of finding the local optimal points for the problem with equality and i...This paper addresses an ordinary differential equations (ODE) approach to constrained nonlinear optimization problem. First, it proposes a method of finding the local optimal points for the problem with equality and inequality constraints. We prove the asymptotical stability of the singular points about partial variables. The condition of overall uniform asymptotical stability is also given.展开更多
文摘In this paper. a method to study the stability of nonholonomic systems withrespect to partial variables is given and several stability theorems of nonholonomicsystems with respect to partial variables are obtained. Moreover, a relationshipbetween the stability of a nonholonomic system with respect to all variables and thatto partial variables is obtained.
基金Supported by the National Science Foundation of China(10661006)Supported by Innovation Project of Guangxi Graduate Education(2007105960812M18)
文摘In this paper, we obtain the moment conditions for the supermun of normed sums of ρ^--mixing random variables by using the Rosenthal-type inequality for Maximum partial sums of ρ^--mixing random variables. The result obtained generalize the results of Chen(2008) and extend those to negatively associated sequences and ρ^--mixing random variables.
文摘By using the method developed in the paper [Georg. Inter. J. Sci. Tech., Volume 3, Issue 1 （2011）, 107-129], it is obtained a representation in an explicit form of the weak solution of a linear partial differential equation of the higher order in two variables with initial condition whose coefficients are real-valued simple step functions.
基金supported by the National Natural Science Foundation of China(Grant Nos.81571770,61527815,81371636 and 81330032)
文摘Partial epilepsy is characterized by recurrent seizures that arise from a localized pathological brain region. During the onset of partial epilepsy, the seizure evolution commonly exhibits typical timescale separation phenomenon. This timescale separation behavior can be mimicked by a paradigmatic model termed as Epileptor, which consists of coupled fast-slow neural populations via a permittivity variable. By incorporating permittivity noise into the Epileptor model, we show here that stochastic fluctuations of permittivity coupling participate in the modulation of seizure dynamics in partial epilepsy. In particular, introducing a certain level of permittivity noise can make the model produce more comparable seizure-like events that capture the temporal variability in realistic partial seizures. Furthermore, we observe that with the help of permittivity noise our stochastic Epileptor model can trigger the seizure dynamics even when it operates in the theoretical nonepileptogenic regime. These findings establish a deep mechanistic understanding on how stochastic fluctuations of permittivity coupling shape the seizure dynamics in partial epilepsy,and provide insightful biological implications.
文摘We propose a new method for finding the local optimal points of the constrained nonlinear programming by Ordinary Differential Equations (ODE) , and prove asymptotic stability of the singular points of partial variables in this paper. The condition of overall uniform, asymptotic stability is also given.
基金This work is supported by Chongqing Application Basic Research Foundation of China
文摘This paper addresses an ordinary differential equations (ODE) approach to constrained nonlinear optimization problem. First, it proposes a method of finding the local optimal points for the problem with equality and inequality constraints. We prove the asymptotical stability of the singular points about partial variables. The condition of overall uniform asymptotical stability is also given.
