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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 2.0433,{2. School of mathematics, Sichuan university, Chengdu 610064,{2. department of applied mathematics, shanghai university of finance & economics, shanghai 2.0433,{2. 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-

Saddlepoint approximations for studentized compound Poisson sums with no moment conditions in audit sampling

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Science china mathematics 2010年第12期53卷 3131-3138页

作者： ZHOU GuoLiang 1 & ZHOU Wang 2. 1 Institute of Accounting and finance, shanghai {2. of finance and economics, shanghai 2.0433, china 2.department of Statistics and applied Probability, National {2. of Singapore, Singapore 117546, Singapore 1. Institute of Accounting and finance Shanghai University of Finance and Economics Shanghai 200433 China2. Department of Statistics and Applied Probability National University of Singapore Singapore 117546 Singapore

Saddlepoint approximations for the studentized compound Poisson sums with no moment conditions in audit sampling are derived. This result not only provides a very accurate approximation for studentized compound Poisson sums, but also can be applied much more widely in statistical inference of the error amount in an audit population of accounts to check the validity of financial statements of a firm. Some numerical illustrations and comparison with the normal approximation method are presented.

关键词： saddlepoint approximation Laplace approximation self-normalized compound Poisson sum stu- dentized compound Poisson sum

Stability of Solution of a Class of Quasilinear Elliptic Equations

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Acta Mathematicae Applicatae Sinica 2002年第3期18卷 461-470页

作者： Qi-kang Ran, Ai-nong Fangdepartment of applied mathematics, shanghai {2. of finance and economics, shanghai 2.0433, chinadepartment of applied mathematics, shanghai Jiaotong {2., shanghai 2.0030, china department of applied mathematics Shanghai University of Finance and Economics Shanghai China department of applied mathematics Shanghai Jiaotong University Shanghai China

In this paper, using capacity theory and extension theorem of Lipschitz functions we first discuss the uniqueness of weak solution of nonhomogeneous quasilinear elliptic equationsin space W(θ,p)(Ω), which is bigger than W1,p(Ω). Next, using revise reverse Holder inequality we prove that if ωc is uniformly p-think, then there exists a neighborhood U of p, such that for all t ∈U, the weak solutions of equation corresponding t are bounded uniformly. Finally, we get the stability of weak solutions on exponent p.

关键词： Nonhoraogeneous quasilinear elliptic equations capacity stability

A Note on Twisted Hopf Algebras

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Journal of Mathematical Research with Applications 2012年第5期32卷 582-588页

作者： Yanhua WANG department of applied mathematics,shanghai {2. of finance and economics,shanghai 2.0433,P.R.china department of applied mathematics Shanghai University of Finance and Economics Shanghai 200433

In this paper,we get some properties of the antipode of a twisted Hopf *** proved that the graded global dimension of a twisted Hopf algebra coincides with the graded projective dimension of its trivial module k,which... 详细信息

关键词： Hopf algebras twisted Hopf algebras projective dimension global dimension.

ON THE LAPLACIAN SPECTRAL RADII OF TREES WITH NEARLY PERFECT MATCHINGS

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同方期刊数据库

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Journal of Systems Science & Complexity 2009年第3期22卷 533-540页

作者： Li ZHANG Jiayu SHAO department of applied mathematics Shanghai Finance University Shanghai 201209 China. department of mathematics Tongji University Shanghai 200092 China.

Let ：T2.＋1 be the set of trees on 2.＋ 1 vertices with nearly perfect matchings, and let S2.＋2.be the set of trees on 2. ＋ 2.vertices with perfect matchings. The largest Laplacian spectral radii of trees in ：T2.＋l and S2.＋2.and the corresponding trees were given by Guo （2.03）. In this paper, the authors determine the second to the sixth largest Laplacian spectral radii among all trees in T2.＋1 and give the corresponding trees.

关键词： Tree Laplacian eigenvalue nearly perfect matching perfect matching.

Checking for normality in linear mixed models

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Science china mathematics 2012年第4期55卷 787-804页

作者： WU Ping 1,,ZHU LiXing 2.3 & FANG Yun 4 1 School of finance and Statistics,East china Normal {2.,shanghai 2.02.1,china 2.School of Statistics and mathematics,Yunnan {2. of finance and economics,Yunnan 6502.1,china 3 The department of mathematics,Hong Kong Baptist {2.,Hong Kong 999077,china 4 mathematics and Science College,shanghai Normal {2.,shanghai 2.02.4,china 1. School of finance and Statistics East China Normal University Shanghai 200241 China2. School of Statistics and Mathematics Yunnan University of Finance and Economics Yunnan 650221 China3. The Department of Mathematics Hong Kong Baptist University Hong Kong 999077 China4. Mathematics and Science College Shanghai Normal University Shanghai 200234 China

Linear mixed models are popularly used to fit continuous longitudinal data, and the random effects are commonly assumed to have normal distribution. However, this assumption needs to be tested so that further analysis can be proceeded well. In this paper, we consider the Baringhaus-Henze-Epps-Pulley （BHEP） tests, which are based on an empirical characteristic function. Differing from their case, we consider the normality checking for the random effects which are unobservable and the test should be based on their predictors. The test is consistent against global alternatives, and is sensitive to the local alternatives converging to the null at a certain rate arbitrarily close to 1/V~ where n is sample size. ^-hlrthermore, to overcome the problem that the limiting null distribution of the test is not tractable, we suggest a new method： use a conditional Monte Carlo test （CMCT） to approximate the null distribution, and then to simulate p-values. The test is compared with existing methods, the power is examined, and several examples are applied to illustrate the usefulness of our test in the analysis of longitudinal data.

关键词： linear mixed models estimated best linear unbiased predictors BHEP tests conditional MonteCarlo test

DISTRIBUTION FREE LAWS OF THEITERATED LOGARITHM FOR KERNELESTIMATOR OF REGRESSION FUNCTIONBASED ON DIRECTIONAL DATADISTRIBUTION FREE LAWS OF THEITERATED LOGARITHM FOR KERNELESTIMATOR OF REGRESSION FUNCTIONBASED ON DIRECTIONAL DATA

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Chinese Annals of mathematics,Series B 2000年第4期21卷 489-498页

作者： WANGXIAOMING ZHAOLINCHENG WUYAOHUA departmentofstatistics ShanghaiUniversityofFinanceandEconomicsShanghai200433China. departmentofstatisticsandfinance UniversityofScienceandTechnologyofChinaHefei230026China.

The authors derive laws of the iterated logarithm for kernel estimator of regression function based on directional data. The results are distribution free in the sense that they are true for all distributions of desig... 详细信息

关键词： Directional data Laws of the iterated logrithm Regression function kernel estimator Strong convergence rates

Weighted Profile Least Squares Estimation for a Panel Data Varying-Coefficient Partially Linear Model

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Chinese Annals of mathematics,Series B 2010年第2期31卷 247-272页

作者： Bin ZHOU Jinhong YOU Qinfeng XU Gemai CHEN School of finance and Statistics East China Normal University Shanghai 200241 China. department of Statistics Shanghai University of Finance and Economics Shanghai 200433 China. Corresponding Author. School of Management Fudan University Shanghai 200433 China. department of mathematics and Statistics University of Calgary Calgary Alberta T2N 1N4 Canada.

This paper is concerned with inference of panel data varying-coefficient partially linear models with a one-way error structure. The model is a natural extension of the well-known panel data linear model （due to Baltagi 1995） to the setting of semiparametric regressions. The authors propose a weighted profile least squares estimator （WPLSE） and a weighted local polynomial estimator （WLPE） for the parametric and nonparametric components, respectively. It is shown that the WPLSE is asymptotically more efficient than the usual profile least squares estimator （PLSE）, and that the WLPE is also asymptotically more efficient than the usual local polynomial estimator （LPE）. The latter is an interesting result. According to Ruckstuhl, Welsh and Carroll （2.00） and Lin and Carroll （2.00）, ignoring the correlation structure entirely and ＂pretending＂ that the data are really independent will result in more efficient estimators when estimating nonparametric regression with longitudinal or panel data. The result in this paper shows that this is not true when the design points of the nonparametric component have a closeness property within groups. The asymptotic properties of the proposed weighted estimators are derived. In addition, a block bootstrap test is proposed for the goodness of fit of models, which can accommodate the correlations within groups illustrate the finite sample performances of the Some simulation studies are conducted to proposed procedures.

关键词： Semiparametric Panel data Local polynomial Weighted estimation Block bootstrap

VISCOSITY EFFECTS ON THE BEHAVIOR OF A RISING BUBBLE

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Journal of Hydrodynamics 2010年第1期22卷 81-89页

作者： WANG Han ZHANG Zhen-yu YANG Yong-ming ZHANG Hui-sheng department of Mechanics and Engineering Science Fudan University Shanghai 200433 China department of mathematics Shanghai University of Finance and Economics Shanghai 200433 China

In the incompressible fluid flow regime, without taking consideration of surface tension effects, the viscosity effects on the behavior of an initially spherical buoyancy-driven bubble rising in an infinite and initially stationary liquid are investigated numerically by the Volume Of Fluid （VOF） method. The ratio of the gas density to the liquid density is taken as 0.001, and the gas viscosity to the liquid viscosity is 0.01, which is close to the case of an air bubble rising in water. It is found by numerical experiments that there exist two critical Reynolds numbers Re1 and Re2., which are in between 30 and 50 and in between 10 and 2., respectively. As Re 〉 Re1 the bubble will have the transition to toroidal form, and the toroidal bubble will break down into two toroidal bubbles. In this case viscosity will damp the development of the liquid jet and delay the formation of the toroidal bubble. As Re〈Re1 the transition will not happen. As Re2.〈 Re 〈 Re1, the bubble will split from its rim into a toroidal bubble and a spherical cap-like bubble, and as Re〈Re2.the splitting will not occur and the bubble can finally reach a stationary shape. With the decrease of the Reynolds number, the stationary shape changes from spherical-cap bubble with skirt to dimpled peach-like bubble. Before the bubble reaches its stationary shape the vortex structure in the flow field varies with time. The vortex structure corresponding to bubble stationary shape varies with the Reynolds number. It is also found that there exists another critical Reynolds number Re^＊ which is in between Re1 and Re2., and as Re 〈 Re^＊, after the bubble rises in an accelerating manner for a moment, it will rise with an almost constant speed, and the speed increases with increasing Reynolds number. As Re 〉 Re^＊, it will not rise with a constant speed. The mechanism of the above phenomena has been analyzed theoretically and numerically.

关键词： rising bubble viscosity effects buoyancy force Volume Of Fluid (VOF) method