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Low order nonconforming mixed finite element method for nonstationary incompressible Navier-Stokes equations

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Applied Mathematics and Mechanics(English Edition) 2016年第8期37卷 1095-1112页

作者： Chao XU Dongyang SHI xin liao Faculty of Mathematics and Physics Education Luoyang Institute of Science and Technology School of Mathematics and Statistics Zhengzhou University

This paper studies a low order mixed finite element method （FEM） for nonstationary incompressible Navier-Stokes equations. The velocity and pressure are approximated by the nonconforming constrained Q1^4ot element and the piecewise constant, respectively. The superconvergent error estimates of the velocity in the broken H^1-norm and the pressure in the L^2-norm are obtained respectively when the exact solutions are reasonably smooth. A numerical experiment is carried out to confirm the theoretical results.

关键词： nonstationary incompressible Navier-Stokes equation constrained Q1^rot nonconforming finite element (FE) superconvergent error estimate

Experimental model of Fusarium solani keratitis in rats

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International Journal of Ophthalmology(English edition) 2011年第4期4卷 371-376页

作者： Jiang-Li Zhu, xin liao People's Hospital Affiliated to Tongji University School of Medicine Shanghai 200072 China People's Hospital Affiliated to Shanghai Jiaotong University School of Medicine Shanghai 200011 China Department of Ophthalmology Shanghai East Hospital Affiliated to Tongji University School of Medicine Shanghai 200120 China

AIM: To establish a repeatable rat model of Fusarium solani keratitis (F. solani keratitis) that mimicked fungal keratitis in humans. METHODS: Wistar rats' corneas were scratched on the superficial stroma after scraping the unilateral corneal epithelia. Then, the corneal surface was inoculated with different inoculum dose of E solanispore suspension. Doses ranged from 10(6) to 10(9) colony-forming unit per milliliter (CFU/mL). The treated corneas were covered by contact lenses that were made of Parafilm M membrane. Negative controls were inoculated with sterile phosphate-buffered saline (PBS). For statistical analysis, corneas were evaluated daily on a 12-point scale to check the state of corneal inflammation. Furthermore, the pathological characteristics of this model were investigated. RESULTS: The rat model of F solani keratitis was established by the combination methods of corneal trauma and parafilm-made contact lens and inoculation of fungus spore suspension. 10(6) and 10(7)CFU/mL of F solani induced mild corneal infection, while 10(8)CFU/mL of F solani was sufficient to induce moderate infection that was consistent with human keratomycosis. Dose of 10(9)CFU/mL of E solani was excessive and led to perforated corneas. CONCLUSION: The rat model of E solani keratitis, established by the combinational methods of corneal trauma, parafilm-made contact lens and the appropriate dose of inoculum, that imitates the developing processes of F solani keratitis in human beings and provides a repeatable method of creating a rat model.

关键词： fungal keratitis Fusarium solani corneal trauma contact lens rat

Normal Mode Analysis on Three Different Structures of a Duplex DNA d(CGCGAATTCGCG)

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Chemical Research in Chinese Universities 1998年第3期14卷 67-71页

作者： LIN Dong-hai liao xin-li Department of Chemistry The Research Laboratory of SEDC of Analytical Science for Material and Life ChemistryXiamen UniversityXiamen361005

Normal mode analysis in dihedral angle space was carried out on two X ray crystal structures and one model structure responded to the same sequence of duplex DNA: d(CGCGAATTCGCG). Comparing these results indicates that it is reliable and meaningful to carry out normal mode analysis on model structures. The reliability is greater except for the ends of helix.

关键词： Normal mode analysis Duplex DNA Atomic fluctuation Molecular dynamics

Distributional expansion of maximum from logarithmic general error distribution

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Applied Mathematics(A Journal of Chinese Universities) 2016年第2期31卷 157-164页

作者： YANG Geng liao xin PENG Zuo-xiang School of Mathematics and Statistics Southwest University Business School University of Shanghai for Science and Technology

Logarithmic general error distribution is an extension of lognormal distribution. In this paper, with optimal norming constants the higher-order expansion of distribution of partial maximum of logarithmic general erro... 详细信息

关键词： Extreme value distribution Higher-order expansion Logarithmic general error distribution,Maximum

A deep reinforcement learning(DRL)based approach for well-testing interpretation to evaluate reservoir parameters

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Petroleum Science 2022年第1期19卷 264-278页

作者： Peng Dong Zhi-Ming Chen xin-Wei liao Wei Yu State Key Laboratory of Petroleum Resources and Prospecting China University of Petroleum Beijing(CUP)Beijing102249China University of Texas at Austin Austin78731TexasUSA

Parameter inversions in oil/gas reservoirs based on well test interpretations are of great significance in oil/gas *** well test interpretations based on artificial intelligence are the most promising to solve the problem of non-unique *** this work,a new deep reinforcement learning(DRL)based approach is proposed for automatic curve matching for well test interpretation,by using the double deep Q-network(DDQN).The DDQN algorithms are applied to train agents for automatic parameter tuning in three conventional well-testing *** addition,to alleviate the dimensional disaster problem of parameter space,an asynchronous parameter adjustment strategy is used to train the ***,field applications are carried out by using the new DRL *** show that step number required for the DDQN to complete the curve matching is the least among,when comparing the naive deep Q-network(naive DQN)and deep Q-network(DQN).We also show that DDQN can improve the robustness of curve matching in comparison with supervised machine learning *** DDQN algorithm to perform 100 curve matching tests on three traditional well test models,the results show that the mean relative error of the parameters is 7.58%for the homogeneous model,10.66%for the radial composite model,and 12.79%for the dual porosity *** the actual field application,it is found that a good curve fitting can be obtained with only 30 steps of parameter adjustment.

关键词： Well testing Deep reinforcement learning Automatic interpretation Parameter evaluation

Calculation of propellant gas pressure by simple extended corresponding state principle

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Defence Technology（防务技术） 2016年第2期12卷 86-89页

作者： Bin XU San-jiu YING xin liao School of Chemistry Engineering Nanjing University of Science and Technology

The virial equation can well describe gas state at high temperature and pressure, but the difficulties in virial coefficient calculation limit the use of virial equation. Simple extended corresponding state principle(SE-CSP) is introduced in virial equation. Based on a corresponding state equation, including three characteristic parameters, an extended parameter is introduced to describe the second virial coefficient expressions of main products of propellant gas. The modified SE-CSP second virial coefficient expression was extrapolated based on the virial coefficients experimental temperature, and the second virial coefficients obtained are in good agreement with the experimental data at a low temperature and the theoretical values at high temperature. The maximum pressure in the closed bomb test was calculated with modified SE-CSP virial coefficient expressions with the calculated error of less than 2%, and the error was smaller than the result calculated with the reported values under the same calculation conditions. The modified SE-CSP virial coefficient expression provides a convenient and efficient method for practical virial coefficient calculation without resorting to complicated molecular model design and integral calculation.

关键词：计算结果气体压力对应状态原理第二维里系数推进剂密闭爆发器试验维里方程高温高压

Dynamic bivariate normal copula

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Science China Mathematics 2016年第5期59卷 955-976页

作者： liao xin PENG Liang PENG ZuoXiang ZHENG YanTing School of Mathematics and Statistics Southwest University Department of Risk Management and Insurance Georgia State University Department of Finance Beijing Technology and Business University

Normal copula with a correlation coefficient between-1 and 1 is tail independent and so it severely underestimates extreme probabilities. By letting the correlation coefficient in a normal copula depend on the sample size, H¨usler and Reiss(1989) showed that the tail can become asymptotically dependent. We extend this result by deriving the limit of the normalized maximum of n independent observations, where the i-th observation follows from a normal copula with its correlation coefficient being either a parametric or a nonparametric function of i/n. Furthermore, both parametric and nonparametric inference for this unknown function are studied, which can be employed to test the condition by H¨usler and Reiss(1989). A simulation study and real data analysis are presented too.

关键词： estimation normal copula tail dependence/independence

Second-order Asymptotics on Distributions of Maxima of Bivariate Elliptical Arrays

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Acta Mathematica Sinica,English Series 2018年第7期34卷 1159-1178页

作者： xin liao Zhi Chao WENG Zuo Xiang PENG Business School University of Shanghai for Science and Technology Shanghai 200093 P. R. China School of Economics and Management Fuzhou University Fujian 350116 P. R. China School of Mathematics and Statistics Southwest University Chongqing 400715 P. R. China

Let {（ξni, ηni）, 1 ≤ i ≤ n, n ≥ 1} be a triangular array of independent bivariate elliptical random vectors with the same distribution function as （S1,ρnS1 ＋ √1- ρ2nS2）, ρn ∈（0, 1）, where （S1,S2） is a bivariate spherical random vector. For the distribution function of radius√S12 ＋ S22 belonging to the max-domain of attraction of the Weibull distribution, the limiting distribution of maximum of this triangular array is known as the convergence rate of p~ to 1 is given. In this paper, under the refinement of the rate of convergence of p~ to 1 and the second-order regular variation of the distributional tail of radius, precise second-order distributional expansions of the normalized maxima of bivariate elliptical triangular arrays are established.

关键词： Bivariate elliptical triangular array maximum second-order expansion second-order regular variation

Data embedding based on pixel value differencing and modulus function using indeterminate equation

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The Journal of China Universities of Posts and Telecommunications 2015年第1期22卷 95-100页

作者： Wang Zhao Zhang Jie liao xin Wen Qiaoyan School of Science Beijing University of Posts and Telecommunications College of Computer Science and Electronic Engineering Hunan University State Key Laboratory of Networking and Switching Technology Beijing University of Posts and Telecommunications

An effective data hiding method based on pixel value differencing （PVD） and modulus function （MF） PVD （MF-PVD） was proposed. MF-PVD method was derived by Wang et al in which the MF was employed to adjust the remainder of two pixels for data embedding and extraction. In the proposed method, a new remainder function in a more general form is defined by selecting proper parameters, in which an indeterminate equation is constructed and an optimal solution is applied to revise the pixels. This strategy leads to a significant image distortion reduction compared with the original method. The experiment reveals that, by preserving the original embedding capacity, the method provides better embedding efficiency than both MF-PVD and PVD methods.

关键词： pixel value differencing modulus function indeterminate equation data embedding