一类f鞅的极大值不等式(英文)

本文研究了f框架下有关f-鞅的不等式性质.利用构造停时的方法和带跳的倒向随机微分方程的比较定理,得到了一类f-鞅的极大值不等式,推广了经典鞅论中的极大值不等式.     

Spiking patterns of a minimal neuron to ELF sinusoidal electric field

Neuron as the main information carrier in neural systems is able to generate diverse spiking trains in response to different stimuli. Neuronal spiking patterns are related to the information processing in neural system. This paper investigates the dynamical behaviors of a two-dimensional minimal neuron model exposed to externally-applied extremely low frequency (ELF) sinusoidal electric field (EF). By numerical stimulation, it is found that neuron can exhibit different spiking patterns such as p:q mode-locking (i.e. a periodic oscillation defined as p action potentials generated by q cycle stimulations) and chaotic behaviors, depending on the values of stimulus frequencies. Transitions between different spiking patterns during exposure to the external EF are explored by interspike intervals (ISIs) and average firing rate. It is found that frequencies of the external EF can act as a bifurcation parameter, whose small change can cause the transition in neuronal behaviors. It is shown that a rich bifurcation structure including period-adding without chaos and mode-locking alternated with chaos suggests frequency discrimination of the neuronal firing patterns. Our results can provide a useful insight into the organization of similar bifurcation structures in excitable systems such as neurons under periodic forcing. Through detail analysis of the spiking patterns, we have explained how neuron’s information (spiking patterns) encodes the stimulus information (frequency), and vice versa.     

含有五个反馈权值的二维细胞神经网络可实现Mosaic模式

研究一类含有五个反馈权值二维细胞神经网络系统,以系统的输出反馈权值及阈值为参数构成参数空间,引入几何方法,将此空间分解分块成有限个区域,当输出反馈权值及阈值在某一区域上时,给出系统具有M osaic解所有可能的输出函数M osaic模式的充要条件.     

2IV^m-p设计的弱最小低阶混杂与纯净效应准则等价的条件

该文给出了2IVm-p设计包含最多纯净两因子交互效应与该设计具有弱最小低阶混杂等价的几个条件．并在文章的末尾给出了一组既具有弱最小低阶混杂又包含最多纯净两因子交互效应的2IVm-p设计．     

Hypercyclic subspaces in Fréchet spaces

In this note, we show that every infinite-dimensional separable Fréchet space admitting a continuous norm supports an operator for which there is an infinite-dimensional closed subspace consisting, except for zero, of hypercyclic vectors. The family of such operators is even dense in the space of bounded operators when endowed with the strong operator topology. This completes the earlier work of several authors.

     

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??We study the linear quadratic optimal stochastic control problem which is jointly driven by Brownian motion and L\'{e}vy processes. We prove that the new affine stochastic differential adjoint equation exists an inverse process by applying the profound section theorem. Applying for the Bellman's principle of quasilinearization and a monotone iterative convergence method, we prove the existence and uniqueness of the solution of the backward Riccati differential equation. Finally, we prove that the optimal feedback control exists, and the value function is composed of the initial value of the solution of the related backward Riccati differential equation and the related adjoint equation.     

Modified Equations for Stochastic Differential Equations

We describe a backward error analysis for stochastic differential equations with respect to weak convergence. Modified equations are provided for forward and backward Euler approximations to Itô SDEs with additive noise, and extensions to other types of equation and approximation are discussed.     

± sign pattern matrices that allow orthogonality

A sign pattern A is a ± sign pattern if A has no zero entries. A allows orthogonality if there exists a real orthogonal matrix B whose sign pattern equals A. Some sufficient conditions are given for a sign pattern matrix to allow orthogonality, and a complete characterization is given for ± sign patterns with n − 1 ⩽ N₋(A) ⩽ n + 1 to allow orthogonality.     

一类反应扩散系统的分歧与斑图

本文研究了一类发生在密闭容器中的不可激活的高次自催化反应扩散系统．在适当的条件下,用渐进近似的方法讨论了系统平衡态的稳定范围;用多重尺度的方法证明了当扩散系数λ充分小时,系统出现两种类型的斑图,一类是由Hopf分歧引出的驻波斑图;另一类是由 Pitchfork分歧引出的定波斑图．进一步还讨论了,在分歧点附近,对于大于空间或等于空间波数的小扰动,斑图是局部稳定的,而小于自身空间波数的小扰动,斑图是不稳定的．