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On the direct path problem of s-elementary frame wavelets

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Science china mathematics 2010年第12期53卷 3187-3196页

作者： DAI XingDe 1 , DIAO YuanAn 1 & GUO XunXiang 2,1 department of mathematics and Statistics, university of North Carolina at Charlotte, Charlotte, NC 28223, USA 2.department of mathematics, southwestern university of finance and economics, chengdu 611130, china 1. department of mathematics and Statistics University of North Carolina at Charlotte Charlotte NC 28223 USA2. Department of Mathematics Southwestern University of Finance and Economics Chengdu 611130 China

In this paper, we discuss the path-connectivity between two s-elementary normalized tight frame wavelets via the so-called direct paths. We show that the existence of such a direct path is equivalent to the non-existence of an atom of a σ-algebra defined over the defining sets of the corresponding frame wavelets, using a mapping defined by the natural translation and dilation operations between the sets. In particular, this gives an equivalent condition for the existence of a direct path between two s-elementary wavelets.

关键词： wavelets frame wavelets frame wavelet sets path-connectivity of wavelets direct path

Beurling's theorem and invariant subspaces for the shift on Hardy spaces

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Science china mathematics 2008年第1期51卷 131-142页

作者： QIU ZhiJian School of Economic mathematics, southwestern university of finance and economics, chengdu 610074, china 1. School of Economic mathematics Southwestern University of Finance and Economics Chengdu 610074 China

Let G be a bounded open subset in the complex plane and let H 2(G) denote the Hardy space on G. We call a bounded simply connected domain W perfectly connected if the boundary value function of the inverse of the Riemann map from W onto the unit disk D is almost 1–1 with respect to the Lebesgue measure on ?D and if the Riemann map belongs to the weak-star closure of the polynomials in H ∞(W). Our main theorem states: in order that for each M ∈ Lat (M z ), there exist u ∈ H ∞(G) such that M = ∨{uνH 2(G)}, it is necessary and sufficient that the following hold:each component of G is a perfectly connected domainthe harmonic measures of the components of G are mutually singularthe set of polynomials is weak-star dense in H ∞(G).Moreover, if G satisfies these conditions, then every M ∈ Lat (M z ) is of the form uH 2(G), where u ∈ H ∞(G) and the restriction of u to each of the components of G is either an inner function or zero.

关键词： Hardy space invariant subspace shift operator 47B20 30H05 30E10 46E15

Moving collocation methods for time fractional differential equations and simulation of blowup

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Science china mathematics 2011年第3期54卷 611-622页

作者： MA JingTang1 & JIANG YingJun2 1School of Economic mathematics, southwestern university of finance and economics, chengdu 611130, china 2department of mathematics and Scientific Computing, Changsha university of Science and Technology, Changsha 410076, china 1. School of Economic mathematics Southwestern University of Finance and Economics Chengdu 611130 China2. Department of Mathematics and Scientific Computing Changsha University of Science and Technology Changsha 410076 China

A moving collocation method is proposed and implemented to solve time fractional differential equations. The method is derived by writing the fractional differential equation into a form of time difference equation. The method is stable and has a third-order convergence in space and first-order convergence in time for either linear or nonlinear equations. In addition, the method is used to simulate the blowup in the nonlinear equations.

关键词： moving collocation methods time fractional differential equations blowup

Carleson Measures on Planar Sets

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Acta Mathematica Sinica,English Series 2009年第11期25卷 1881-1892页

作者： Zhijian QIU School of mathematics,southwestern university of finance and economics,chengdu 610074,P. R. china School of mathematics Southwestern University of Finance and Economics Chengdu 610074 P. R. China

In this paper, we investigate what are Carleson measures on open subsets in the complex plane. A circular domain is a connected open subset whose boundary consists of finitely many disjoint circles. We call a domain G multi-nicely connected if there exists a circular domain W and a conformal map ψ from W onto G such that ψ is almost univalent with respect the arclength on δW. We characterize all Carleson measures for those open subsets so that each of their components is multinicely connected and harmonic measures of the components are mutually singular. Our results suggest the extension of Carleson measures probably is up to this class of open subsets

关键词： Carleson measure circular domain harmonic measure multi-nicely connected domain

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金融多措并举支持经济高质量发展

中国金融 2024年第19期 9-15页

作者：本刊编辑部不详

2024年9月24日,国务院新闻办公室举行新闻发布会,中国人民银行行长潘功胜、国家金融监督管理总局局长李云泽、中国证券监督管理委员会主席吴清出席发布会并介绍金融支持经济高质量发展有关情况。“新政频出”成为此次发布会的亮点,这让... 详细信息

2024年9月24日,国务院新闻办公室举行新闻发布会,中国人民银行行长潘功胜、国家金融监督管理总局局长李云泽、中国证券监督管理委员会主席吴清出席发布会并介绍金融支持经济高质量发展有关情况。“新政频出”成为此次发布会的亮点,这让公众感受到了金融支持经济高质量发展的力度,支持实体经济发展的深度和提升老百姓生活幸福感、满足感的温度。

关键词：金融监督管理金融支持经济实体经济发展中国证券监督管理委员会高质量发展多措并举生活幸福感新闻发布会

RMB Exchange Market Pressure and Central Bank Exchange Market Intervention

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china & World Economy 2009年第3期17卷 75-92页

作者： Xiaohui Liu Jing Zhang Lecturer,Chinese finance Research Institute,southwestern university of finance and economics,chengdu,china. Lecturer,finance department,southwestern university of finance and economics,chengdu,china. Lecturer Chinese Finance Research Institute Southwestern University of Finance and Economics Chengdu China.

The present paper uses the model-dependent and the modeL independent approach to measure the RMB exchange market pressure （EMP） and the central bank＇s intervention using monthly data from January 1999 to June 2008. It is determined that the RMB has been under great appreciation pressure over the past decade. However, the pressure has been weakening since 2005. The two approaches provide significantly different results in terms of the estimated RMB EMP indices and the estimated central bank＇s interventions. The differences may lead to different predietions of potential currency crises. According to the estimation of the RMB EMP, and based on the model-independent approach, the paper shows that china has been under threat of an appreciation currency crisis since 2008. Therefore, china should adopt a moreflexible exchange rate regime to prevent a potential crisis.

关键词： exchange market intervention exchange market pressure model-dependent approach model-independent approach

Approximate solutions to infinite dimensional LQ problems over infinite time horizon

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Science china mathematics 2006年第7期49卷 865-876页

作者： PAN Liping, ZHANG Xu & CHEN Qihong School of Mathematical Sciences, Fudan university, Shanghai 200433, china School of mathematics, Sichuan university, chengdu 610064, china department of Applied mathematics, Shanghai university of finance & economics, Shanghai 200433, china School of Mathematical Sciences Fudan University Shanghai 200433 China School of mathematics Sichuan University Chengdu 610064 China department of Applied mathematics Shanghai University of Finance & Economics Shanghai 200433 China

This paper is addressed to develop an approximate method to solve a class of infinite dimensional LQ optimal regulator problems over infinite time horizon. Our algorithm is based on a construction of approximate solutions which solve some finite dimensional LQ optimal regulator problems over finite time horizon, and it is shown that these approximate solutions converge strongly to the desired solution in the double limit sense.

关键词： approximate solution LQ problem infinite dimensional infinite time hori-

Almost sure central limit theorems for random functions

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Science china mathematics 2006年第12期49卷 1788-1799页

作者： LU Chuanrong, QIU Jin & XU Jianjun School of mathematics and Statistics, Zhejiang university of finance and economics, Hangzhou 310018, china department of mathematics, Zhejiang university, Hangzhou 310028, china 1. School of mathematics and Statistics Zhejiang University of Finance and Economics Hangzhou 310018 China 2. department of mathematics Zhejiang University Hangzhou 310028 China

Let {Xn,-∞< n <∞} be a sequence of independent identically distributed random variables with EX1 = 0, EX12 = 1 and let Sn =∑k=1∞Xk, and Tn = Tn(X1,…,Xn) be a random function such that Tn = ASn + Rn, where supn E|... 详细信息

Let {Xn,-∞2 = 1 and let Sn =∑k=1∞Xk, and Tn = Tn(X1,…,Xn) be a random function such that Tn = ASn + Rn, where supn E|Rn| 2)) a.s., or Rn = O(n1/2-2γ) a.s., 0 <γ< 1/8. In this paper, we prove the almost sure central limit theorem (ASCLT) and the function-typed almost sure central limit theorem (FASCLT) for the random function Tn. As a consequence, it can be shown that ASCLT and FASCLT also hold for U-statistics, Von-Mises statistics, linear processes, moving average processes, error variance estimates in linear models, power sums, product-limit estimators of a continuous distribution, product-limit estimators of a quantile function, etc.

关键词： statistics,random function,almost sure central limit theorem,logarithm average.

Moderate deviation for super-Brownian motion with immigration

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Science china mathematics 2004年第3期47卷 440-452页

作者： ZHANG Mei department of mathematics, Beijing Normal university, Beijing 100875, china department of mathematics, The Central university of finance and economics, Beijing 100081, china 1. department of mathematics Beijing Normal University 100875 Beijing China 2. department of mathematics The Central University of Finance and Economics 100081 Beijing China

We prove a moderate deviation principle for a super-Brownian motion with immigration of all dimensions, and consequently fill the gap between the central limit theorem and large deviation principle.

关键词： moderate deviation principle super-Brownian motion with immigration large deviation principle evolution equation