多线性Littlewood-paley算子在一类Block-hardy空间上的加权有界性

定义一类与L ittlewood-paley算子相关的多线性算子,它是L ittlewood-paley算子的交换子的推广.然后利用Hardy空间的原子分解和B lock空间的块分解方法引入一类B lock-hardy空间,并由此证明这类与L ittlewood-paley算子相关联的多线性算子在上述B lock-hardy空间上的加权有界性.     

一类次线性算子在Morrey空间的加权有界性

设 T 为次线性算子 ,如果 T 在Lebesgue空间Lp 上有界 ,则证明了T也在Morrey空间上有界 .该算子T包含许多重要例子 .     

H~p空间上Toeplitz算子的联合谱包含定理

本文研究了多变量H~p空间上Toeplitz算子的联合谱,得到了联合近似点谱的包含定理.     

多线性Marcinkiewicz算子在一类Hardy空间上的加权有界性

证明了多线性Marcinkiewicz算子在一类Hardy空间和Hardy-Block空间上的加权有界性．     

具有不连续非线性项的抛物型方程组解的存在性

本文研究具有不连续非线性项的抛物型方程组解的存在性.我们利用上下解方法和单调算子的不动点定理,证明了解的存在性.     

向量值加权Sobolev空间

数值Sobolev空间已有较完善的理论,本文的目的在于推广其到向量值加权情形。首先通过讨论拟微分算子在向量值加权L~p空间L~p(l~q,w)的有界性,引入了向量值加权Sobolev空间,讨论了该空间的基本性质,得到了其加权嵌入定理等结论。     

集值L-A-Proper映射的广义拓扑度理论

本文考虑 Hilbert 空间中一类半线性方程Z∈(L+N)u,其中L是闭稠定线性算子.1≤dimkerL≤+∞、R(L)=KerL~⊥、N 是一集值映射,定义了 N 为所谓集值 L-A-Proper 映射,对半线性映射 L+N 建立了广义拓扑度理论,用此度理论给出若干该类方程解的存在定理。     

关于p-凸泛函族的共鸣定理

共鸣定理是泛函分析中重要的基础定理之一,其形式也有多种变化。在[1]——[5]中讨论了一类共鸣定理,即所谓凸泛函族的共鸣定理。由于凸分析的广泛运用性,凸性的概念有必要进一步推广。本文首先给出p-凸性的概念,p-凸集和p-凸泛函具有完全类似于凸集和凸泛函的性质,然后导出了在拓扑向量空间及赋范空间中p-凸泛函族的几个共鸣定理,推广了文[1]——[5]中的相应结果。     

Littlewood-Paley算子的多线性交换子的加权H^1-Block有界性

证明了Littlewood-Paley算子的多线性交换子的在加权H^1-Block空间上的有界性．     

多线性Littlewood—Paley算子在Block—H^1空间的加权有界性

证明了多线性Littlewood-Paley算子在一类Block-H^1空间上的加权有界性。     

Conservation of quasi-energy in electrodynamics

We establish a general theorem of quasi-energy conservation for the electromagnetic scattering problem in the time-dependent and time-harmonic cases. This theorem expresses two bilinear relationships between two distinct electromagnetic states, which can be chosen independently one from the other and thus exhibit no causality link between them. The terminology used is borrowed from Tellegen's theorem in the electrical network theory. The Maxwell equations are shown to be equivalent to the theorem of quasi-energy conservation.     

高阶中立型时滞微分方程正解的存在性

利用Ｂａｎａｃｈ空间的压缩映射原理，建立了偶数阶线性中立型时滞微分方程正解的存在性定理。     

参数型非空交定理及其在变分不等式理论中的应用

在已经证明的广义区间空间中几个参数型非空交定理的基础上，利用这些结果得到了广义区间空间中变分不等式解的存在性定理。这一研究成果推广了ＹｅｎＣＬ１９８１年所发表的“极大极小定理及其在变分不等式中的应用”一文中的定理３。     

On the almost sure central limit theorem for ARX processes in adaptive tracking

The goal of this paper is to highlight the almost sure central limit theorem (ASCLT) for martingales to the control community. We shall establish the ASCLT for the least squares estimator of the unknown parameter of a controllable ARX(p,q) process in adaptive tracking. The usual notion of controllability for ARX(p,q) processes allows us to avoid the use of a persistent excitation in the adaptive tracking control. We shall also provide strongly consistent estimators of the even moments of the driven noise as well as two quadratic strong laws for the average costs and the estimation errors sequences. Our theoretical results are illustrated by numerical experiments.     

考虑省间经济差异的区域电力市场调节分析

我国区域电力市场中,普遍存在各省经济发展不平衡和省间电价差异较大的问题,这是区域电力市场建设需要有效解决的一个重要问题。运用庇古定理,采取“税收-补贴”的市场调节措施,向低成本省的发电商征税,建立区域电力平等基金,并利用基金向低购买力省的供电公司提供补贴,以省为节点,建立区域电力市场单时段市场交易模型。算例分析表明,通过市场调节能够提高高成本省的发电商出力和市场占有率,提高低购买力省的供电公司购电功率和市场占有率,在一定程度上保护了高成本省的发电商和低购买力省的供电公司的市场竞争力,解决了存在省间经济差异的区域电力市场失灵问题。     

计及时滞影响的广域附加阻尼控制

针对广域测量信号的时滞对系统动态性能的不利影响,提出了一种电力系统广域附加区间阻尼控制器设计的直接迭代方法。由已知的线性矩阵不等式定理,推得一种作为时滞系统渐近稳定性判据的基于状态反馈的矩阵不等式定理。利用变量替换法,将定理中的非线性矩阵不等式转变为线性矩阵不等式,进而将阻尼控制器设计转化为隶属于线性矩阵不等式的锥补问题并进行迭代求解。该方法可直接获得状态反馈控制矩阵,并具有良好的收敛性。测试系统的仿真结果表明,广域附加区间阻尼控制器,具有一定的时滞不敏感性,能够较好地抑制区间振荡。     

Adaptive recurrent Chebyshev neural network control for PM synchronous motor servo‐drive electric scooter with V‐belt continuously variable transmission

Because of unknown nonlinearity and time‐varying characteristics of electric scooter with V‐belt continuously variable transmission (CVT) driven by permanent magnet synchronous motor (PMSM), its accurate dynamic model is difficult to establish for the design of the linear controller in whole system. In order to conquer this difficulty and raise robustness, an adaptive recurrent Chebyshev neural network (NN) control system is proposed to control for PMSM servo‐drive electric scooter with V‐belt CVT under lumped nonlinear external disturbances in this study. The adaptive recurrent Chebyshev NN control system consists of a recurrent Chebyshev NN control and a compensated control with estimation law. In addition, the online parameters tuning methodology of the recurrent Chebyshev NN and the estimation law of the compensated controller can be derived by using the Lyapunov stability theorem. Moreover, the two optimal learning rates of the recurrent Chebyshev NN based on a discrete‐type Lyapunov function are proposed to guarantee the convergence of tracking error. Finally, comparative studies are demonstrated by experimental results in order to show the effectiveness of the proposed control scheme. Copyright © 2014 John Wiley & Sons, Ltd.     

Comments on `A network theorem dual to Miller's theorem' by M.K.Kazimierczuk

The above-named work (ibid., vol.31, p.265-9, Nov. 1988) introduces a network theorem which is dual to Miller's theorem, and it is applied to the analysis of the common-emitter (CE) amplifier with emitter resistor. The same material can be found in earlier textbooks, specifically in the 1972 book by J. Millman and C.C. Halkias. It is noted that section 8-11 of that book bears the heading `Miller's theorem and its dual'. Fig. 8-19 and its related discussion are identical to the paper's Fig.1 and equations (1)-(8). Fig. 8-28, applying the concept to the CE amplifier stage, is equivalent to the paper's Fig. 2. In addition, it is argued that the usefulness of the theorem in electronic circuit analysis is questionable     

关于映象面积为有界的解析函数的几个问题(Ⅱ)

本文是文 [1] 的继续,在本文中,我们首先改进了文 [1]中的定理4,并证明了本文中,关于平均模的定理1与定理2。在文(2)中有如下关于|z|o,那么W=f(z)的反函数在圆域 |w|≤(aR)~2/(6M)内有单值解析的分支z=g(w),满足g(o)=o.本文将对S_m类函数进行研究,得到相应的两个定理。     

Lossless chain scattering matrices and optimum linear prediction: The vector case

In this paper we give a systematic treatment of the exact and approximate realization of a positive real matrix-valued function on the open unit disc by means of a lossless circuit connected to a passive load. We discuss the mathematical properties of the chain scattering matrix which describes the lossless circuit and rederive a form of the classical Darlington synthesis theorem generalized to roomy matrix-valued transmission functions. We then develop a matrix version of an algorithm due to Schur for the construction of approximate realizations which produces (minimal degree) Nevanlinna–Pick approximants to the original positive real matrix. We further identify the normalized inverse of one of the outer factors of the approximant to the positive real matrix as the orthogonal projection of the identity onto a suitably defined subspace, give its interpretation as a reproducing kernel, and establish strong convergence under mild conditions on the growth of the order of the approximation. Finally we interpret and apply the mathematical theory developed in the body of the paper to the theory of prediction for vector-valued second order stationary stochastic sequences and briefly discuss connections with the theory of maximum entropy extensions and of inverse scattering.