Enumeration of three kinds of rooted maps on the Klein bottle

Wenzhong Liu,Yanpei Liu 한국전산응용수학회 2007 Journal of applied mathematics & informatics Vol.24 No.1

In this paper, 2 essential rooted maps on the Klein bottle arecounted and an explicit expression with the size as a parameter is given.Further, the numbers of singular maps and the maps with one vertex onthe Klein bottle are derived.AMS Mathematics Subject Classication: 05C45.Key words and phrases : 2 essential map, singular map, enufunction.1. IntroductionEnumeration of non-planar maps has been initiated in the 1960s by Brown [3].On the object, some scholars did some inuential works such as Bender et al. [2],Arqu`es [1], Gao [4] and Liu [79], only name a few. In this paper, enumeratingformulae of three kinds of rooted maps on the Klein bottle are obtained byinvestigating g essential maps with the small genera which play an importantrole in the study of general maps on surfaces.The article begins with some denitions. Terms without description can beseen in [7-9].LetX = {x1,x2 · ,xn} be a set andK = {1,β,γ}, the Klein group,i.e.,α2 = β2 = γ2 = 1, where γ= = . F o rx ∈X, Kx = {x,αx,βx,γx}.Ifthe permutationP on X (X)=n.i=1Kxi = X satises the following conditions:for anyl ∈N and any x ∈ X, Plx .=αx, αP = P1 and the group ψτgenerated byτ= {α,β,γ} is transitive onX , and thenM =(X,P) is called amap.If a map M = (X,P) has an element, theroot denoted by r = r(M ), inXmarked beforehand, thenM is called arooted mapand the marked edge is calledthe root-edgeofM . Likewise theroot-vertexand the root-faceare clear. In thisReceived November 24, 2005.Corresponding author.1 Supported by NNSFC under Grant 603730308 and 10571013.c. 2007 Korean Society for Computational & Applied Mathematics and Korean SIGCAM .411412 Wenzhong Liu and Yanpei Liupaper, maps always mean rooted . ForM = (X,P), the root, the root-vertex,the root-edge and the root-face ofM are denoted by r(M ),vr(M ),er(M ) andfr(M ) respectively.A surfaceΣ here is a compact close 2 manifolds. Anorientable (nonori-

Enhanced Photoelectrochemical Water Splitting and Photocatalytic Water Oxidation of Cu2O Nanocube-Loaded BiVO4 Nanocrystal Heterostructures

Wenzhong Wang,Weiwei Zhang,Shan Meng,Lujie Jia,Miao Tan,Chenchun Hao,Yujie Liang,JUN WANG,Bin Zou 대한금속·재료학회 2016 ELECTRONIC MATERIALS LETTERS Vol.12 No.6

Reducing the fast recombination of photogenerated electron-hole pairsof semiconductor photocatalyst is very important to improve itsphotocatalysis. In this paper we fabricate Cu2O nanocube-decoratedBiVO4 nanocrystal (denoted as BiVO4@Cu2O nanocrystal@nanocube)heterostructure photocatalyst by coupling n-type BiVO4 with p-type Cu2O. The BiVO4@Cu2O nanocrystal@nanocube photocatalysts show superiorphotocatalytic activities in photoelectrochemical (PEC) activity andphotocatalytic water oxidation to BiVO4 photocatalysts under visible lightillumination. The BiVO4@Cu2O nanocrystal@nanocube heterostructureelectrode achieves the highest photocurrent density of ~ 10 μA cm−2 at 0 Vversus Ag/AgCl, 5 times higher than that of BiVO4 nanocrystal electrode (~ 2 μA cm−2). The light induced evolution rate of O2generation for BiVO4@Cu2O nanocrystal@nanocube heterostructures is as high as 150 μmol h−1100 mg cat−1, more than 3times higher than that (48 μmol h−1100 mg cat−1) of BiVO4 nanocrystals. The enhanced photocatalysis activities of theBiVO4@Cu2O nanocrystal@nanocube photocatalysts are attributed to the efficient separation of the photoexcited electron-holepairs caused by inner electronic field (IEF) of p-n junction. This study opens up new opportunities in designing photoactivematerials with highly enhanced performance for solar energy conversion.

A Low-Computation Indirect Model Predictive Control for Modular Multilevel Converters

Wenzhong Ma,Peng Sun,Guanyu Zhou,Gulipali Sailijiang,Ziang Zhang,Yong Liu 전력전자학회 2019 JOURNAL OF POWER ELECTRONICS Vol.19 No.2

The modular multilevel converter (MMC) has become a promising topology for high-voltage direct current (HVDC) transmission systems. To control a MMC system properly, the ac-side current, circulating current and submodule (SM) capacitor voltage are taken into consideration. This paper proposes a low-computation indirect model predictive control (IMPC) strategy that takes advantages of the conventional MPC and has no weighting factors. The cost function and duty cycle are introduced to minimize the tracking error of the ac-side current and to eliminate the circulating current. An optimized merge sort (OMS) algorithm is applied to keep the SM capacitor voltages balanced. The proposed IMPC strategy effectively reduces the controller complexity and computational burden. In this paper, a discrete-time mathematical model of a MMC system is developed and the duty ratio of switching state is designed. In addition, a simulation of an eleven-level MMC system based on MATLAB/Simulink and a five-level experimental setup are built to evaluate the feasibility and performance of the proposed low-computation IMPC strategy.

UNIVERSAL DISPERSION EQUATION FOR MAGNETOSTATIC WAVES (MSW)

Hu Wenzhong 한국자기학회 1995 韓國磁氣學會誌 Vol.5 No.5

A universal dispersion equation for magnetostatic waves(MSW) propagating in the film with arbitrary-multiple magnetic layers magnetized in an arbitrary direction was derived with a matching boundary condition method. The computing result curves of delay time were shown.

Estimation of Genetic and Phenotypic Covariance Functions for Body Weight as Longitudinal Data of SD-II Swine Line

Liu, Wenzhong,Cao, Guoqing,Zhou, Zhongxiao,Zhang, Guixian Asian Australasian Association of Animal Productio 2002 Animal Bioscience Vol.15 No.5

Growth records over six generations of 686 pigs in SD-II Swine Line were used to estimate the genetic and phenotypic covariance functions for body weight as longitudinal data. A random regression model with Legendre polynomials of age as independent variables was used to estimate the (co)variances among the regression coefficients, thus the coefficients of genetic and permanent environmental covariance functions by restricted maximum likelihood employing the average information algorithm. The results showed that, using litter effect as additional random effect, a reduced order of fit did not describe the data adequately. For all five orders of fit, however, the change trends of genetic and phenotypic (co)variances were very similar from ${\kappa}$=3 onwards.

Silver nanoparticle-induced degranulation observed with quantitative phase microscopy.

Yang, Wenzhong,Lee, Seungrag,Lee, Jiyong,Bae, Yoonsung,Kim, Dugyoung SPIE--the International Society for Optical Engine 2010 JOURNAL OF BIOMEDICAL OPTICS Vol.15 No.4

<P>Monitoring a degranulation process in a live mast cell is a quite important issue in immunology and pharmacology. Because the size of a granule is normally much smaller than the resolution limit of an optical microscope system, there is no direct real-time live cell imaging technique for observing degranulation processes except for fluorescence imaging techniques. In this research, we propose optical quantitative phase microscopy (QPM) as a new observation tool to study degranulation processes in a live mast cell without any fluorescence labeling. We measure the cell volumes and the cross sectional profiles (x-z plane) of an RBL-2H3 cell and a HeLa cell, before and after they are exposed to calcium ionophore A23187 and silver nanoparticles (AgNPs). We verify that the volume and the cross sectional line profile of the RBL-2H3 cell were changed significantly when it was exposed to A23187. When 50 microg/mL of AgNP is used instead of A23187, the measurements of cell volume and cross sectional profiles indicate that RBL-2H3 cells also follow degranulation processes. Degranulation processes for these cells are verified by monitoring the increase of intracellular calcium ([Ca(2+)](i)) and histamine with fluorescent methods.</P>

Estimation of Covariance Functions for Growth of Angora Goats

Liu, Wenzhong,Zhang, Yuan,Zhou, Zhongxiao Asian Australasian Association of Animal Productio 2009 Animal Bioscience Vol.22 No.7

Body weights of 862 Angora goats between birth and 36 months of age, recorded on a semiyearly basis from 1988 to 2000, were used to estimate genetic, permanent environmental and phenotypic covariance functions. These functions were estimated by fitting a random regression model with 6th order polynomial for direct additive genetic and animal permanent environmental effects and 4th and 5th order polynomial for maternal genetic and permanent environmental effects, respectively. A phenotypic covariance function was estimated by modelling overall animal and maternal effects. The results showed that the most variable coefficient was the intercept for both direct and maternal additive genetic effects. The direct additive genetic (co)variances increased with age and reached a maximum at about 30 months, whereas the maternal additive genetic (co)variances increased rapidly from birth and reached a maximum at weaning, and then decreased with age. Animal permanent environmental (co)variances increased with age from birth to 30 months with lower rate before 12 months and higher rate between 12 and 30 months. Maternal permanent environmental (co)variances changed little before 6 months but then increased slowly and reached a maximum at about 30 months. These results suggested that the contribution of maternal additive genetic and permanent environmental effects to growth variation differed from those of direct additive genetic and animal permanent environmental effects not only in expression time, but also in action magnitude. The phenotypic (co)variance estimates increased with age from birth to 36 months of age.

A Low-Computation Indirect Model Predictive Control for Modular Multilevel Converters

Ma, Wenzhong,Sun, Peng,Zhou, Guanyu,Sailijiang, Gulipali,Zhang, Ziang,Liu, Yong The Korean Institute of Power Electronics 2019 JOURNAL OF POWER ELECTRONICS Vol.19 No.2

The modular multilevel converter (MMC) has become a promising topology for high-voltage direct current (HVDC) transmission systems. To control a MMC system properly, the ac-side current, circulating current and submodule (SM) capacitor voltage are taken into consideration. This paper proposes a low-computation indirect model predictive control (IMPC) strategy that takes advantages of the conventional MPC and has no weighting factors. The cost function and duty cycle are introduced to minimize the tracking error of the ac-side current and to eliminate the circulating current. An optimized merge sort (OMS) algorithm is applied to keep the SM capacitor voltages balanced. The proposed IMPC strategy effectively reduces the controller complexity and computational burden. In this paper, a discrete-time mathematical model of a MMC system is developed and the duty ratio of switching state is designed. In addition, a simulation of an eleven-level MMC system based on MATLAB/Simulink and a five-level experimental setup are built to evaluate the feasibility and performance of the proposed low-computation IMPC strategy.

ENUMERATION OF THREE KINDS OF ROOTED MAPS ON THE KLEIN BOTTLE

Liu, Wenzhong,Liu, Yanpei 한국전산응용수학회 2007 Journal of applied mathematics & informatics Vol.24 No.1

In this paper, $\tilde{2}$-essential rooted maps on the Klein bottle are counted and an explicit expression with the size as a parameter is given. Further, the numbers of singular maps and the maps with one vertex on the Klein bottle are derived.

宗教與國家:代中韓憲政化中的宗教問題

杜文忠(Du wenzhong) 경북대학교 인문학술원 2008 동서사상 Vol.5 No.-

Religion, coming from the West of Christianity in modern times especially, has important significance for China and South Korea from the Confucian tradition to the road of the Western modern constitutional government. Historically, these two countries have not appeared the factor of politics and religion, which as the legitimacy church of west feudalism of the common customs regime completely depended on admits. Based on this information, from the angle of legal history, there has been religion of Confucianism, the relationship between religion and politics. Christianity in China is different from the fate in South Korea, the relationship between religion and the State is a comparative study with a view of modern China and South Korea. All of study expects to reveal in the process of constitutional, religion, and law. The text contains three parts: Firstly, religion and traditional politics; secondly, Confucianism and traditional Chinese religion of the church; thirdly, Christianity and South Korea's modern politics and laws; the reform of Christianity, Confucianism and modern Chinese constitutional. The article holds that the tradition of Confucianism surpasses the sacred nature of religious. Although legitimacy political includes such a nature, political and religious separation is still the traditional political characteristics in East Asia. Owning to South Korea in modern times has been a long history of annexation by Japan, Christianity and Confucianism in South Korea have been able to exist and to the development of the situation today. During the pain of the Japanese colonial period, west religion has been big space in Korea Republic’s propagation and development. Such as South Korea, the spread of Christianity in China has been resisted at the beginning by the same Confucian culture. In the later it hasn’t ruled out such an effect. The difference between South Korea and Chinese is that South Korea in modern times by the non Christian culture of Japan's annexation and oppression. China has been aggressed by Christian cultural background of Western countries. Thanks to the Christian West is accompanied by a Western invasion force within a wide range of transmission in modern time in China, the culture of the West of Christianity not only has been resisted by traditional Confucian , but also has been impacted by national salvation during the process of constitutional government in China.