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Electroosmotic Flow of MHD Power Law Al_2O_3-PVC Nanofluid in a Horizontal Channel: Couette-Poiseuille Flow Model

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Communications in Theoretical Physics 2018年第6期69卷 655-666页

作者： N.Shehzad A.Zeeshan R.Ellahi department of Mathematics and statistics FBAS IIUI

The current manuscript is reported about the eiectro-osmotic Couette-Poiseuille ftow of power law Al2O3- PVC nanofluid through a channel, in which upper wall is moving with constant velocity. The influences of magnetic field, mixed convection, joule heating, and viscous dissipation are also incorporated. The flow is generated because of constant pressure gradient in axial direction. The resulting flow problem is coupled nonlinear ordinary differential equations, which are at first modeled and then transform into dimensionless form through appropriate transformation. Analytical solution of the governing is carried out. The impact of modified Brinkman number, modified Magnetic field, electro-osmotic parameters on velocity and temperature are examined graphically. From the results, it is concluded that the Skin friction at moving isolated wail decreases with the increase of electro-osmotic parameter and reverse behavior for Nusselt number at heated stationary wall occur.

关键词： Couette-Poiseuille flow power law nanofluid electro-osmotic flow MHD PVC Alumina

Guidance on the Choice of Threshold for Binary Forecast Modeling

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Advances in Atmospheric Sciences 2008年第1期25卷 83-88页

作者： Keon Tae SOHN Sun Min PARK department of statistics Pusan National University

This paper proposes useful guidance on the choice of threshold for binary forecasts. In weather forecast systems, the probabilistic forecast cannot be used directly when estimated too smoothly. In this case, the binary forecast, whether a meteorological event will occur or not, is preferable to the probabilistic forecast. A threshold is needed to generate a binary forecast, and the guidance in this paper encompasses the use of skill scores for the choice of threshold according to the forecast pattern. The forecast pattern consists of distribution modes of estimated probabilities, occurrence rates of observations, and variation modes. This study is performed via Monte-Carlo simulation, with 48 forecast patterns considered. Estimated probabilities are generated by random variate sampling from five distributions separately. Varying the threshold from 0 to 1, binary forecasts are generated by threshold. For the assessment of binary forecast models, a 2×2 contingency table is used and four skill scores （Heidke skill score, hit rate, true skill statistic, and threat score） are compared for each forecast pattern. As a result, guidance on the choice of skill score to find the optimal threshold is proposed.

关键词： binary forecast Monte-Carlo simulation threshold skill score

The Support of the Solution for Stochastic Differential Equations Driven by G-Brownian Motion

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Acta Mathematica Sinica,English Series 2012年第12期28卷 2417-2430页

作者： Fu Qing GAO Ming Zhou XU department of Mathematics and statistics Wuhan University

By a linear interpolation approximation method, we obtain a characterization of the support of the solution for stochastic differential equations driven by G-Brownian motion.

关键词： G-Brownian motion G-stochastic differential equation support theorem

Control charts for the Pareto distribution

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Applied Mathematics(A Journal of Chinese Universities) 2015年第4期30卷 379-396页

作者： GUO Bao-cai WANG Bing-xing department of statistics Zhejiang Gongshang University

The Pareto distribution plays an important role in various areas of research. In this paper, the average run length （ARL） unbiased control charts, which monitor the shape and threshold parameters of the Pareto distribution respectively, are proposed when the incontrol parameters are known. The effects of parameter estimation on the performance of the proposed control charts are also studied. Results show that the control charts with the estimated parameters are not suitable to be used in the known parameter case, thus the ARL-unbiased control charts for the shape and threshold parameters with the desired ARLo, which consider the variability of the parameter estimates, are further developed. The performance of the proposed control charts is investigated in terms of the ARL. Finally, an example is given to illustrate the proposed control charts.

关键词： Pareto distribution average run length process control unbiased control chart.

UNIQUENESS OF VISCOSITY SOLUTIONS OF STOCHASTIC HAMILTON-JACOBI EQUATIONS

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Acta Mathematica Scientia 2019年第3期39卷 857-873页

作者： Jinniao QIU Wenning WEI department of Mathematics & statistics University of Calgary

This article is devoted to the study of fully nonlinear stochastic Hamilton-Jacobi (HJ) equations for the optimal stochastic control problem of ordinary differential equations with random coefficients. Under the standard Lipschitz continuity assumptions on the coefficients, the value function is proved to be the unique viscosity solution of the associated stochastic HJ equation.

关键词： Stochastic Hamilton-Jacobi equation optimal stochastic control backward stochastic partial differential equation viscosity solution

Rate of Convergence of Euler's Approximations for SDEs with Non-Lipschitz Coefficients

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Acta Mathematica Sinica,English Series 2013年第8期29卷 1555-1568页

作者： Ji Cheng LIU School of Mathematics and statistics Huazhong University of Science and Technology department of statistics Purdue University

We prove that Euler＇s approximations for stochastic differential equations driven by infinite many Brownian motions and with non-Lipschitz coefficients converge almost surely. Moreover, the rate of convergence is obt... 详细信息

关键词： Stochastic differential equations non-Lipschitz Euler's approximations

Degrees of freedom in low rank matrix estimation

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Science China Mathematics 2016年第12期59卷 2485-2502页

作者： YUAN Ming department of statistics University of Wisconsin-Madison

The objective of this paper is to quantify the complexity of rank and nuclear norm constrained methods for low rank matrix estimation problems. Specifically, we derive analytic forms of the degrees of freedom for these types of estimators in several common settings. These results provide efficient ways of comparing different estimators and eliciting tuning parameters. Moreover, our analyses reveal new insights on the behavior of these low rank matrix estimators. These observations are of great theoretical and practical importance. In particular, they suggest that, contrary to conventional wisdom, for rank constrained estimators the total number of free parameters underestimates the degrees of freedom, whereas for nuclear norm penalization, it overestimates the degrees of freedom. In addition, when using most model selection criteria to choose the tuning parameter for nuclear norm penalization, it oftentimes suffices to entertain a finite number of candidates as opposed to a continuum of choices. Numerical examples are also presented to illustrate the practical implications of our results.

关键词： degrees of freedom low rank matrix approximation model selection nuclear norm penalization reduced rank regression Stein's unbiased risk estimator

Quantitative Properties on the Steady States to a Schr?dinger-Poisson-Slater System

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Acta Mathematica Sinica,English Series 2015年第12期31卷 1845-1856页

作者： Chang-Lin XIANG University of Jyvaskyla Department of Mathematics and Statistics

In this paper,we obtain the existence,uniqueness and asymptotic behavior of steady states to a class of Schr？dinger-Poisson-Slater System.

关键词： Schrodinger-Poisson-Slater system existence uniqueness asymptotic behavior

Momentum Effect Differs Across Stock Performances:Chinese Evidence

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Acta Mathematicae Applicatae Sinica 2014年第2期30卷 279-288页

作者： Zhao-yuan LI Si-bo LIU Mao-zai TIAN department of statistics and Actuarial Science The University of Hong Kong department of Finance and Insurance Lingnan University Center for Applied statistics School of StatisticsRenmin University of China School of statistics Lanzhou University of Finance and Economics

Prior empirical studies find positive and negative momentum effect across the global nations, but few focus on explaining the mixed results. In order to address this issue, we apply the quantile regression approach to analyze the momentum effect in the context of Chinese stock market in this paper. The evidence suggests that the momentum effect in Chinese stock is not stable across firms with different levels of performance. We find that negative momentum effect in the short and medium horizon （3 months and 9 months） increases with the quantile of stock returns. And the positive momentum effect is observed in the long horizon （12 months）, which also intensifies for the high performing stocks. According to our study, momentum effect needs to be examined on the basis of stock returns. OLS estimation, which gives an exclusive and biased result, provides misguiding intuitions for momentum effect across the global nations. Based on the empirical results of quantile regression, effective risk control strategies can also be inspired by adjusting the proportion of assets with past performances.

关键词： chinese stock market investment strategy momentum effect quantile regression