Randomized UMD Banach spaces and decoupling inequalities for stochastic integrals

In this paper we prove the equivalence of decoupling inequalities for stochastic integrals and one-sided randomized versions of the UMD property of a Banach space as introduced by Garling.

     

Sub-Riemannian geometry of the coefficients of univalent functions

We consider coefficient bodies Mn for univalent functions. Based on the Löwner-Kufarev parametric representation we get a partially integrable Hamiltonian system in which the first integrals are Kirillov's operators for a representation of the Virasoro algebra. Then Mn are defined as sub-Riemannian manifolds. Given a Lie-Poisson bracket they form a grading of subspaces with the first subspace as a bracket-generating distribution of complex dimension two. With this sub-Riemannian structure we construct a new Hamiltonian system to calculate regular geodesics which turn to be horizontal. Lagrangian formulation is also given in the particular case M₃.     

Adaptive Constrained Control of Unknown Strict Feedback Nonlinear Systems With Dead Zone Input北大核心CSCD

研究了具有死区输入的预设约束未知高阶严格反馈非线性系统的控制问题,提出了一种基于免疫函数的自抗扰预设漏斗约束自适应控制策略。首先,针对系统内部的未知问题,采用免疫函数与扩张状态观测器结合对系统内部未知项进行观测;其次,通过Lyapunov方法与漏斗控制相结合设计控制器,使得跟踪误差能够维持在预先设定的漏斗约束范围内;同时,利用双曲正切函数速率变化快这一特性设计自适应控制律,引入指令滤波器避免反步法中重复求导问题,分析证明了闭环系统所有信号的有界性。仿真实例表明了控制方法的有效性。     

A five-channel grating spectrometer for millimeter-waves

A five-channel grating spectrometer for use in millimeter wave band (25100GHz) is described with its design theory of optical path, and measured results of insertion loss and resolving power.     

对甲烷氧化偶联W－Mn／SiO＿2催化剂Na＿2WO＿4的流失及其影响的考察

用ＸＲＤ、ＦＴ－ＩＲ、ＥＳＲ、Ｈ２－ＴＰＲ和ＴＰＯ等方法，对Ｎａ２ＷＯ４－Ｍｎ２Ｏ３／ＳｉＯ２催化剂和其经水煮处理的一系列样品进行了表征．实验发现该催化剂中的结晶态Ｎａ２ＷＯ４易于流失，单层分布的Ｎａ２ＷＯ４在苛刻的处理条件下也有可能流失．依此，探讨了上述流失现象与Ｎａ２ＷＯ４－Ｍｎ２Ｏ３／ＳｉＯ２催化剂的催化活性及该催化剂在长时间反应中发生的ＳｉＯ２相变之间的关系，证明了结晶态Ｎａ２ＷＯ４的流失对该催化剂甲烷氧化偶联反应的催化活性只有轻微的影响，单层分布Ｎａ２ＷＯ４的流失可造成催化剂中Ｍｎ从Ｍｎ３＋转变为Ｍｎ２＋，并使催化剂的催化活性明显降低．但在水煮条件下，无论是结晶态的还是单层分布，Ｎａ２ＷＯ４的流失都没有对ＳｉＯ２的α－方石英结构产生影响     

Dielectric properties of beryllia ceramics in the near-millimeter wavelength range

We report the refractive indices and absorption coefficients for four beryllia (BeO) ceramic samples. These dielectric properties have been measured over the range from 4 to 18 cm^–1 by use of a Michelson interferometer. The index n, follows the linear relationship n=0.6517 cm³/g×+0.7130 with density, , over the range 2.8<<3.0 g/cm³.     

Generalized nets in neurology: an example of mathematical modelling

The purpose of this paper is to explain the basic theory of generalized nets (GNs) and their applications in the context of the differential diagnosis of neurological diseases. We define formally the concepts of a GN and transitions of a GN and also outline some remarks on their theory. The work here constructs an example which aims to trace the process of diagnosing different signs and symptoms in neurology. This will enable the interested reader to see the scope of nets in general as tools for the modelling, simulation, optimization and control of real processes.     

The construction and approximation of feedforward neural network with hyp erb olic tangent function

In this paper, we discuss some analytic properties of hyperbolic tangent function and estimate some approximation errors of neural network operators with the hyperbolic tangent activation functionFirstly, an equation of partitions of unity for the hyperbolic tangent function is givenThen, two kinds of quasi-interpolation type neural network operators are constructed to approximate univariate and bivariate functions, respectivelyAlso, the errors of the approximation are estimated by means of the modulus of continuity of functionMoreover, for approximated functions with high order derivatives, the approximation errors of the constructed operators are estimated.