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A Monte Carlo Study of the Half-Filled Two-Dimensional Hubbard Model

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Communications in Theoretical Physics 2001年第11期36卷 625-630页

作者： zhu xing LIU Chuan Department of Physics Peking UniversityBeijing 100871China Department of PhysicsPeking UniversityBeijing 100871China

Using the path integral representation,bulk thermodynamic properties of the two-dimensional Hubbard model on a square lattice are studied numerically using the hybrid Monte Carlo simulation *** for averaged energy,spin-spin correlation functions and Cooper pair correlation functions are *** these results suggest that the system exhibits an anti-ferromagnetic correlation at half-filling for a wide range of temperature.

关键词： strongly correlated electrons,bulk thermodynamic quantities,hybrid Monte Carlo

Nonliner Analysis of a Synthesized Optimal Velocity Model for Traffic Flow

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Communications in Theoretical Physics 2008年第8期50卷 505-510页

作者： zhu Wen-xing JIA Lei School of Control Science and Engineering Shandong University Jinan 250061 China Department of Automation Shanghai Jiao Tong University Shanghai 200240 China

We analyze a new car-following model described by a differential-difference equation with a synthesized optimal velocity function (SOVF),which depends on the front interactions between every two adjacent vehicles instead of the weighted average *** model is analyzed with the use of the linear stability theory and nonlinear analysis *** stability and neutral stability condition are *** also derive the modified KdV (Korteweg-de Vries) equation and the kink-antikink soliton solution near the critical point.A simulation is conducted with integrating the differential-difference equation by the Euler *** results of the numerical simulation verify the validity of the new model.

关键词： multi-interaction nonlinear analysis modified KdV equation SOVF

A distribution-based LASSO for a general single-index model

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Science China Mathematics 2015年第1期58卷 109-130页

作者： WANG Tao zhu Li xing Department of Mathematics Hong Kong Baptist University

A general single-index model with high-dimensional predictors is considered. Additive structure of the unknown link function and the error is not assumed in this model. The consistency of predictor selection and estimation is investigated in this model. The index is formulated in the sufficient dimension reduction framework. A distribution-based LASSO estimation is then suggested. When the dimension of predictors can diverge at a polynomial rate of the sample size, the consistency holds under an irrepresentable condition and mild conditions on the predictors. The new method has no requirement, other than independence from the predictors, for the distrlLbution of the error. This property results in robustness of the new method against outliers in the response variable. The conventional consistency of index estimation is provided after the dimension is brought down to a value smaller than the sample size. The importance of the irrepresentable condition for the consistency, and the robustness are examined by a simulation study and two real-data examples.

关键词： high dimensionality irrepresentable condition single-index models

Modeling the heterogeneous traffic flow considering the effect of self-stabilizing and autonomous vehicles

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Chinese Physics B 2022年第2期31卷 434-443页

作者： Yuan Gong Wen-xing zhu School of Control Science and Engineering Shandong UniversityJinan 250061China

With the increasing maturity of automatic driving technology,the homogeneous traffic flow will gradually evolve into the heterogeneous traffic flow,which consists of human-driving and autonomous *** better study the characteristics of the heterogeneous traffic system,this paper proposes a new car-following model for autonomous vehicles and heterogeneous traffic flow,which considers the self-stabilizing effect of *** linear and nonlinear methods,this paper deduces and analyzes the stability of such a car-following model with the self-stabilizing ***,the model is verified by numerical *** results show that the self-stabilizing effect can make the heterogeneous traffic flow more stable,and that increasing the self-stabilizing coefficient or historical time length can strengthen the stability of heterogeneous traffic flow and alleviate traffic congestion *** addition,the heterogeneous traffic flow can also be stabilized with a higher proportion of autonomous vehicles.

关键词： heterogeneous traffic flow self-stabilizing effect car-following model autonomous vehicle

A Note on Parameter Estimations of Panel Vector Autoregressive Models with Intercorrelation

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Acta Mathematicae Applicatae Sinica 2009年第2期25卷 177-182页

作者： Jian-hong Wu Li-xing zhu Zai-xing Li College of Statistics and Mathematics Zhejiang Gongshang University Hangzhou 310018 China Department of Mathematics Hong Kong Baptist University Hong Kong China Department of Statistics East China Normal University Shanghai 200062 China Department of Mathematics China University of Mining and Technology Beijing 100083 China

This note considers parameter estimation for panel vector autoregressive models with intercorrelation. Conditional least squares estimators are derived and the asymptotic normality is established. A simulation is carr... 详细信息

关键词： Estimation intercorrelation panel Vector autoregression time series

On Corepresentations of Multiplier Hopf Algebras

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Acta Mathematica Sinica,English Series 2010年第6期26卷 1087-1114页

作者： Shuan-hong WANG Hai-xing zhu Department of Mathematics Southeast University Nanjing 210096 P. R. China

We present a general construction producing a unitary corepresentation of a multiplier Hopf algebra in itself and study RR-corepresentations of twisted tensor coproduct multiplier Hopf algebra. Then we investigate some properties of functors, integrals and morphisms related to the categories of the crossed modules and covariant modules over multiplier Hopf algebras. By doing so, we can apply our theory to the case of group-cograded multiplier Hopf algebras, in particular, the case of Hopf group-coalgebras.

关键词： (group-cograded) multiplier Hopf algebra copresentation crossed module covariant module Hopf group-coalgebra twisted tensor coproduct

Empirical Likelihood Based Goodness-of-fit Testing for Generalized Linear Mixed Models

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Acta Mathematicae Applicatae Sinica 2014年第1期30卷 37-48页

作者： Song-qiao WEN Li-xing zhu College of Mathematics and Computational Science Shenzhen University School of Statistics Renmin University of China

In this paper, we propose a bias-corrected empirical likelihood （BCEL） ratio to construct a goodness- of-fit test for generalized linear mixed models. BCEL test maintains the advantage of empirical likelihood that is self scale invariant and then does not involve estimating limiting variance of the test statistic to avoid deteri- orating power of test. Furthermore, the bias correction makes the limit to be a process in which every variable is standard chi-squared. This simple structure of the process enables us to construct a Monte Carlo test proce- dure to approximate the null distribution. Thus, it overcomes a problem we encounter when classical empirical likelihood test is used, as it is asymptotically a functional of Gaussian process plus a normal shift function. The complicated covariance function makes it difficult to employ any approximation for the null distribution. The test is omnibus and power study shows that the test can detect local alternatives approaching the null at parametric rate. Simulations are carried out for illustration and for a comparison with existing method.

关键词： Empirical likelihood bias correction monte carlo test generalized linear mixed model

A Berry-Essen Inequality for the Kaplan-Meier L-Estimator

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Acta Mathematica Sinica,English Series 2001年第1期17卷 169-180页

作者： Qi Hua WANG Li xing zhu Institute of Applied Mathematics. Academy of Mathematics and Systems Sciences Chinese Academy of Sciences Institute of Applied Mathematics Academy of Mathematics and Systems Sciences Chinese Academy of Sciences Department of Statistice and Actuarial Science The University of Hong Kong

Let F_n be the Kaplan-Meier estimator of distribution function F. Let J(·) be a measureable real-valued function. In this paper, a U-statistic representation for the Kaplan-Meier L-estimator, T(F_n)=∫xJ( _n(x))d _n(... 详细信息

关键词： Kaplan-Meier L-estimator U-statistic representation Berry-Essen Inequality

A Score Type Test for General Autoregressive Models in Time Series

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Acta Mathematicae Applicatae Sinica 2007年第3期23卷 439-450页

作者： Jian-hong Wu Li-xing zhu College of Statistics and Mathematics Zhejiang Gongshang University Hangzhou 310018 China Hong Kong Baptist University Hong Kong China East China Normal University Shanghai 200062 China

This paper is devoted to the goodness-of-fit test for the general autoregressive models in time series. By averaging for the weighted residuals, we construct a score type test which is asymptotically standard chi-squared under the null and has some desirable power properties under the alternatives. Specifically, the test is sensitive to alternatives and can detect the alternatives approaching, along a direction, the null at a rate that is arbitrarily close to n-1/2. Furthermore, when the alternatives are not directional, we construct asymptotically distribution-free maximin tests for a large class of alternatives. The performance of the tests is evaluated through simulation studies.

关键词： Autoregressive model goodness-of-fit maximin test model checking score type test time series