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The Similarity for Nominal Variables Based on F-Divergence
Zhao Liang,Liu Jianhui 보안공학연구지원센터 2016 International Journal of Database Theory and Appli Vol.9 No.3
Measuring the similarity between nominal variables is an important problem in data mining. It's the base to measure the similarity of data objects which contain nominal variables. There are two kinds of traditional methods for this task, the first one simply distinguish variables by same or not same while the second one measures the similarity based on co-occurrence with variables of other attributes. Though they perform well in some conditions, but are still not enough in accuracy. This paper proposes an algorithm to measure the similarity between nominal variables of the same attribute based on the fact that the similarity between nominal variables depends on the relationship between subsets which hold them in the same dataset. This algorithm use the difference of the distribution which is quantified by f-divergence to form feature vector of nominal variables. The theoretical analysis helps to choose the best metric from four most common used forms of f-divergence. Time complexity of the method is linear with the size of dataset and it makes this method suitable for processing the large-scale data. The experiments which use the derived similarity metrics with K-modes on extensive UCI datasets demonstrate the effectiveness of our proposed method.
Zhao Liang,Hao Ding,Guangming Wang,Xiaohui Zhang 한국전기전자재료학회 2020 Transactions on Electrical and Electronic Material Vol.21 No.2
In order to explore the optimal spraying effect of diff erent electrostatic spraying parameters on droplet deposition on the back of target, the application height, angle, charging voltage, and nozzle water pressure had been applied as spraying variables for the test designed to investigate on droplet density, deposition and coverage in diff erent depth areas of the target. The results of the study showed that the height and angle of the spatial parameters of the application had a significant effect on the application effect. The droplet deposition effect decreased by 94.71%, 89.09% and 94.17% at diff erent depths on the back of the target as the height increased from 20 to 50 cm. The deposition effects of droplets at diff erent depths on the back of the target at 60° tilt angle are 5.91%, 9.81% and 51.97% of them at 0° tilt angle respectively. The results of orthogonal experiment showed that the optimal parameters of diff erent depth areas on the back of different targets were inconsistent. The height and angle of application are the main influencing factors, when the target is warped up. The depth range of the target (5–7.5 cm) is greatly affected by the nozzle water pressure. In the actual spraying pesticides application, the appropriate operating parameters can be selected according to the size and attitude of the leaf surface to improve the spraying effect.
HARNACK INEQUALITY FOR A NONLINEAR PARABOLIC EQUATION UNDER GEOMETRIC FLOW
Zhao, Liang Korean Mathematical Society 2013 대한수학회보 Vol.50 No.5
In this paper, we obtain some gradient estimates for positive solutions to the following nonlinear parabolic equation $$\frac{{\partial}u}{{\partial}t}={\triangle}u-b(x,t)u^{\sigma}$$ under general geometric flow on complete noncompact manifolds, where 0 < ${\sigma}$ < 1 is a real constant and $b(x,t)$ is a function which is $C^2$ in the $x$-variable and $C^1$ in the$t$-variable. As an application, we get an interesting Harnack inequality.
Avian Influenza: Should China Be Alarmed?
Zhaoliang Su,Huaxi Xu,Jianguo Chen 연세대학교의과대학 2007 Yonsei medical journal Vol.48 No.4
Avian influenza has emerged as one of the primary public health concern of the 21st century. Influenza strain H5N1 is capable of incidentally infecting humans and other mammals. Since their reemergence in 2003, highly pathogenic avian influenza A (H5N1) viruses have been transmitted from poultry to humans (by direct or indirect contact with infected birds) in several provinces of Mainland China, which has resulted in 22 cases of human infection and has created repercussions for the Chinese economy. People have been concerned whether a new pandemic will occur in the future. The eradication of pathogenic avian influenza viruses appears to be the most effective way to prevent an influenza pandemic. This paper will examine the features of H5N1, including incidence, infection, immunity, clinical management, prevention and control, and therapy in Mainland China.
THE REPRESENTATION AND PERTURBATIONOF THE W-WEIGHTED DRAZIN INVERSE
ZHAOLIANG XU,GUORONG WANG 한국전산응용수학회 2007 Journal of applied mathematics & informatics Vol.23 No.1
Let A and E be m×n matrices and W an n×m matrix, and let Ad,W denote the W-weighted Drazin inverse of A . In this paper, a new representation of the W-weighted Drazin inverse of A is given. Some new properties for the W-weighted Drazin inverse Ad,W and Bd,W are investigated, where B = A+E. In addition, the Banach-type perturbation theorem for the W-weighted Drazin inverse of A and B are established, and the perturbation bounds for kBd,W k and kBd,W −Ad,W k/kAd,W k are also presented. When A and B are square matrices and W is identity matrix, some known results in the literature related to the Drazin inverse and the group inverse are directly reduced by the results in this paper as special cases.
THE REPRESENTATION AND PERTURBATION OF THE W-WEIGHTED DRAZIN INVERSE
Xu, Zhaoliang,Wang, Guorong 한국전산응용수학회 2007 Journal of applied mathematics & informatics Vol.23 No.1
Let A and E be $m{\times}n$ matrices and W an $n{\times}m$ matrix, and let $A_{d,w}$ denote the W-weighted Drazin inverse of A. In this paper, a new representation of the W-weighted Drazin inverse of A is given. Some new properties for the W-weighted Drazin inverse $A_{d,w}\;and\;B_{d,w}$ are investigated, where B=A+E. In addition, the Banach-type perturbation theorem for the W-weighted Drazin inverse of A and B are established, and the perturbation bounds for ${\parallel}B_{d,w}{\parallel}\;and\;{\parallel}B_{d,w}-A_{d,w}{\parallel}/{\parallel}A_{d,w}{\parallel}$ are also presented. When A and B are square matrices and W is identity matrix, some known results in the literature related to the Drazin inverse and the group inverse are directly reduced by the results in this paper as special cases.
Convergence analysis of a family of 14-node brick elements
Meng, Zhaoliang,Luo, Zhongxuan,Sheen, Dongwoo,Kim, Sihwan Elsevier 2016 Journal of computational and applied mathematics Vol.301 No.-
<P><B>Abstract</B></P> <P>In this paper, we will give convergence analysis for a family of 14-node elements which was proposed by Smith and Kidger (1992). The 14 DOFs are taken as the values at the eight vertices and the six face-centroids. For second-order elliptic problems, we will show that among all the Smith–Kidger 14-node elements, Type 1, Type 2 and Type 5 elements provide optimal-order convergent solutions while Type 6 element gives one-order lower convergent solutions. Motivated by our proof, we also find that the order of convergence of the Type 6 14-node nonconforming element improves to be optimal if we change the DOFs into the values at the eight vertices and the integration values on the six faces. We also show that Type 1, Type 2 and Type 5 keep the optimal-order convergence if the integral DOFs on the six faces are adopted.</P>
Songhua Ma,Zhaoliang Jiang,Wenping Liu 한국정밀공학회 2019 International Journal of Precision Engineering and Vol.6 No.2
By taking energy awareness and efficiency into consideration, this research applies multiple linear regression (MLR) models and artificial neural networks (ANNs) for predicting the real-time heating energy demand and natural gas consumption in the drying chamber of an automotive painting line. With the estimation of the correlation and randomness during the painting process, a total of six fundamental variables that integrate energy, product and process data are considered in order to cover the impact factors of the natural gas consumption. The independent variable value, used to calibrate and evaluate the model, is obtained from our constructed energy consumption monitoring system. In the prediction cases, the ANN-based model, which offers a well performance, provides great precision in the determination of the natural gas demand with an R2 coefficient and other error measurements of over 90%. Based on the MLR model, the process temperature and the corresponding variation are found to be two decisive factors for the natural gas consumption. It is foreseen that the ANN model, which can effectively perform input/output mapping, is reliable and powerful for predicting the natural gas consumption and estimating the energy demand. Being a general data-driven method, our method is convenient for application to other heating process lines and even other energy-consuming plants.