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science china mathematics 2007年第7期50卷 1055-1064页

作者： Bao-xing CHEN~(1+) Xie-bin CHEN~2 Ji-xiang MENG~3 Wen-jun XIAO~4.1 Department of Computer science,Zhangzhou Teachers college,Zhangzhou 363000,china 2 Department of mathematics and Information science,Zhangzhou Teachers college,Zhangzhou 363000,china 3 college of mathematics & system science,xinjiang University,urumqi 83004.,china 4.Department of Computer science,South china University of Technology,Guangzhou 51064.,china Department of Computer science Zhangzhou Teachers College Zhangzhou China Department of mathematics and Information science Zhangzhou Teachers College Zhangzhou China college of mathematics & system science Xinjiang University Urumqi China Department of Computer science South China University of Technology Guangzhou China

The double loop network(DLN)is a circulant digraph with n nodes and outdegree *** is an important topological structure of computer interconnection networks and has been widely used in the designing of local area networks and distributed *** the number n of nodes,how to construct a DLN which has minimum diameter?This problem has attracted great attention.A related and longtime unsolved problem is:for any given non-negative integer k,is there an infinite family of k-tight optimal DLN?In this paper,two main results are obtained:(1)for any k≥0,the infinite families of k-tight optimal DLN can be constructed,where the number n(k,e,c)of their nodes is a polynomial of degree 2 in e with integral coefficients containing a parameter c.(2)for any k≥0, an infinite family of singular k-tight optimal DLN can be constructed.

关键词： double loop network diameter k-tight optimal singular k-tight optimal 05C12 05C20 05C85

Optimal error bound of restricted Monte Carlo integration on anisotropic Sobolev classes

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Progress in Natural science:Materials International 2006年第6期16卷 588-593页

作者： GAO Wenhua, YE Peixin and WANG Hui (college of mathematics and system sciences, {4. University, urumqi 83004., china School of Mathematical sciences and LPMC, Nankai University, Tianjin 300071, china Department of mathematics, Ily Teachers' college, Yining 835000, china college of science, Hehai University, Nanjing 210098, china) college of mathematics and system sciences Xinjiang University Urumqi 830046 China School of Mathematical sciences and LPMC Nankai University Tianjin 300071 China Department of mathematics Ily Teachers'' College Yining 835000 China college of science Hehai University Nanjing 210098 China

We study the restricted Monte Carlo integration error for anisotropic Sobolev classes. Results prove that with O(log2 n) random bits we have the optimal order for the n-th minimal Monte Carlo integration error with ar... 详细信息

关键词： Monte Carlo integration random bits anisotropic Sobolev classes.

Identifying the geographical origin and processing technology of Moyao(Myrrh)on the basis of near-infrared spectroscopy combined with chemometrics

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Journal of Traditional Chinese Medicine 2024年第3期44卷 505-514页

作者： XU Ningning YAN Ganming XU Fengjie DENG Linfeng QIAO xinjiang LU Changzheng CHENG Shaomin TCM Diagnosis Institute College of Traditional Chinese MedicineJiangxi University of Chinese MedicineNanchang 330004China TCM Processing Institute Pharmaceutical CollegeJiangxi University of Chinese medicineNanchang 330004China School of Electronic Information and Artificial Intelligence Shaanxi University of Science and TechnologyXi'an 710021China Jiangzhong Pharmaceutical Co. Ltd.Nanchang 330096China Jiangxi Guhan Refined Chinese Herbal Pieces Co. Ltd.Nanchang330041.China

OBJECTIVE:To evaluate the quality of Moyao(Myrrh)in the identification of the geographical origin and processing of the ***:Raw Moyao(Myrrh)and two kinds of Moyao(Myrrh)processed with vinegar from three countries were identified using near-infrared(NIR)spectroscopy combined with chemometric *** component analysis(PCA)was used to reduce the dimensionality of the data and visualize the clustering of samples from different categories.A classical chemometric algorithm(PLS-DA)and two machine learning algorithms[K-nearest neighbor(KNN)and support vector machine]were used to conduct a classification analysis of the near-infrared spectra of the Moyao(Myrrh)samples,and their discriminative performance was ***:Based on the accuracy,precision,recall rate,and F1 value in each model,the results showed that the classical chemometric algorithm and the machine learning algorithm obtained positive *** all of the chemometric analyses,the NIR spectrum of Moyao(Myrrh)preprocessed by standard normal variation or Multivariate scattering correction combined with KNN achieved the highest accuracy in identifying the geographical origins,and the accuracy of identifying the processing technology established by the KNN method after first-order derivative pretreatment was the *** best accuracy of geographical origin discrimination and processing technology discrimination were 0.9853 and 0.9706 ***:NIR spectroscopy combined with chemometric technology can be an important tool for tracking the origin and processing technology of Moyao(Myrrh)and can also provide a reference for evaluations of its quality and the clinical use.

关键词： Moyao(Myrrh) near-infrared spectroscopy geographical origin processing technology

A relative local variational principle for topological pressure

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science china mathematics 2010年第6期53卷 1491-1506页

作者： MA XianFeng1,CHEN ErCai2,3,& ZHANG AiHua2,4.1Department of mathematics,East china University of science and Technology,Shanghai 200237,china 2School of mathematics and Computer science,Nanjing Normal University,Nanjing 210097,china 3Center of Nonlinear science,Nanjing University,Nanjing 210093,china 4.9} of mathematics and Physics,Nanjing University of Posts and Telecommunications,Nanjing 21004.,china Department of mathematics East China University of Science and Technology School of mathematics and Computer science Nanjing Normal University Center of Nonlinear science Nanjing University college of mathematics and Physics Nanjing University of P

We define the relative local topological pressure for any given factor map and open cover,and prove the relative local variational principle of this *** precisely,for a given factor map π:(X,T)→(Y,S) between two topological dynamical systems,an open cover U of X,a continuous,real-valued function f on X and an S-invariant measure ν on Y,we show that the corresponding relative local pressure P(T,f,U,y) satisfies sup μ∈M(X,T){ hμ(T,U|Y)+∫X f(x)dμ(x) :πμ=ν}=∫Y P(T,f,U,y)dν(y),where M(X,T) denotes the family of all T-invariant measures on ***,the supremum can be attained by a T-invariant measure.

关键词： pressure conditional entropy relative local variational principle

Semigroup Method for a Mathematical Model in Reliability Analysis

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Journal of systems science and systems Engineering 2001年第2期13卷 137-147页

作者： Geni Gupur 1,3 , LI Xue-zhi 2,3 1.Department of mathematics, xinjiang University, urumqi 83004.,china2. Department of mathematics, Xinyang Teachers college, Henan 4.4.00, china3. Academy of mathematics and system sciences, Chinese Academy of Sci Department of mathematics Xinjiang University Urumqi 830046 China Academy of mathematics and system sciences Chinese Academy of Sciences Beijing 100080 China Department of mathematics Xinyang Teachers College Henan 464000 China Academy of mathematics and system sciences Chinese Academy of Sciences Beijing 100080 China

The system which consists of a reliable machine, an unreliable machine and a storage buffer with infinite many workpieces has been studied. The existence of a unique positive time-dependent solution of the model corre... 详细信息

关键词： steady-state solution time-dependent solution C 0-semigroup dispersive operator

Global asymptotic stability of a two species competitive system with stage structure and harvesting

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Communications in Nonlinear science and Numerical Simulation 2001年第2期6卷 81-87页

作者： Xinyu SONG and Lansun CHEN Department of mathematics, Xinyang Teachers college, Henan 4.4.00, china Institute of mathematics, Academy of mathematics and system sciences, Chinese Academy of sciences, Beijing 100080, china Department of mathematics Xinyang Teachers College Henan 464000 China Institute of mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing 100080 China

The dynamics of a two species competitive system, where the species one has two stages, a immature stage and a mature stage with harvesting, and the growth of the species two is of Lotka-Volterra nature, is modelled by a system of retarded functional differential equations. We obtain the conditions for global asymptotic stability of three nonnegative equilibria and the threshold of harvesting mature population. The effect of the delay on the population at equilibrium and the optimal harvesting of mature population are also considered.

关键词： optimal harvesting stage structure competitive system global asymptotic stability.

Checking for normality in linear mixed models

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science china mathematics 2012年第4期55卷 787-804页

作者： WU Ping 1,,ZHU LiXing 2,3 & FANG Yun 4.1 School of Finance and Statistics,East china Normal University,Shanghai 20024.,china 2 School of Statistics and mathematics,Yunnan University of Finance and Economics,Yunnan 650221,china 3 The Department of mathematics,Hong Kong Baptist University,Hong Kong 999077,china 4.mathematics and science college,Shanghai Normal University,Shanghai 200234.china School of Finance and Statistics East China Normal University Shanghai China School of Statistics and mathematics Yunnan University of Finance and Economics Yunnan China The Department of mathematics Hong Kong Baptist University Hong Kong China mathematics and science college Shanghai Normal University Shanghai China

Linear mixed models are popularly used to fit continuous longitudinal data, and the random effects are commonly assumed to have normal distribution. However, this assumption needs to be tested so that further analysis can be proceeded well. In this paper, we consider the Baringhaus-Henze-Epps-Pulley （BHEP） tests, which are based on an empirical characteristic function. Differing from their case, we consider the normality checking for the random effects which are unobservable and the test should be based on their predictors. The test is consistent against global alternatives, and is sensitive to the local alternatives converging to the null at a certain rate arbitrarily close to 1/V~ where n is sample size. ^-hlrthermore, to overcome the problem that the limiting null distribution of the test is not tractable, we suggest a new method： use a conditional Monte Carlo test （CMCT） to approximate the null distribution, and then to simulate p-values. The test is compared with existing methods, the power is examined, and several examples are applied to illustrate the usefulness of our test in the analysis of longitudinal data.

关键词： linear mixed models estimated best linear unbiased predictors BHEP tests conditional MonteCarlo test

Weighted Estimates for Marcinkiewicz Integrals with Non-Doubling Measures

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Journal of Mathematical Research with Applications 2012年第2期32卷 223-234页

作者： Songbai WANG,Yinsheng JIANG,Baode LI college of mathematics and system sciences,{4. University,{4. 83004.,P.R.china college of mathematics and system sciences Xinjiang University Xinjiang 830046

Let μ be a nonnegative Radon measure on R d which satisfies the growth condition μ(B(x,r)) ≤ C0rn for all x ∈Rd and r >0,where C0 is a fixed constant and 0 详细信息

Let μ be a nonnegative Radon measure on R d which satisfies the growth condition μ(B(x,r)) ≤ C0rn for all x ∈Rd and r >0,where C0 is a fixed constant and 0

关键词： maximal singular integrals Muckenhoupt type weights sharp maximal operators non-doubling measures.

Weighted estimation of single index models with right censored responses

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science china mathematics 2011年第3期54卷 479-514页

作者： WANG YanHua1, LI XiaYan2, WANG QiHua3 & HE ShuYuan4.1School of sciences, Beijing Institute of Technology, Beijing 100081, china 2Department of mathematics, University of science and Technology of china, Hefei 230026, china 3Chinese Academy of mathematics and system science, Beijing 100080, china 4.chool of Mathematical sciences, Capital Normal University, Beijing 10004., china School of sciences Beijing Institute of Technology Department of mathematics University of Science and Technology of China Chinese Academy of mathematics and system science

In this paper, the unknown link function, the direction parameter, and the heteroscedastic variance in single index models are estimated by the random weight method under the random censorship, respectively. The central limit theory and the convergence rate of the law of the iterated logarithm for the estimator of the direction parameter are derived, respectively. The optimal convergence rates for the estimators of the link function and the heteroscedastic variance are obtained. Simulation results support the theoretical results of the paper.

关键词： single index models random censorship central limit theorem law of the iterated logarithm weighted least squares unknown link function

Minimal regular 2-graphs and applications

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science china mathematics 2006年第2期49卷 158-172页

作者： FAN Hongbing, LIU Guizhen & LIU Jiping Department of Physics and Computer science, Wilfrid Laurier University, Waterloo, ON., N2L 3C5 Canada School of mathematics and system science, Shandong University, Jinan 250100, {4. Department of mathematics and Computer science, University of Lethbridge, Lethbridge, AB., T1K 3M4. Canada Department of Physics and Computer science Wilfrid Laurier University Waterloo Canada School of mathematics and system science Shandong University Jinan China Department of mathematics and Computer science University of Lethbridge Lethbridge Canada

A 2-graph is a hypergraph with edge sizes of at most two. A regular 2-graph is said to be minimal if it does not contain a proper regular factor. Let f2(n) be the maximum value of degrees over all minimal regular 2-graphs of n vertices. In this paper, we provide a structure property of minimal regular 2-graphs, and consequently, prove that f2(n) = n+3-i/3, where 1 ≤ i ≤ 6, i ≡ n (mod 6) and n ≥ 7, which solves a conjecture posed by Fan, Liu, Wu and Wong. As applications in graph theory, we are able to characterize unfactorable regular graphs and provide the best possible factor existence theorem on degree conditions. Moreover, fa(n) and the minimal 2-graphs can be used in the universal switch box designs, which originally motivated this study.

关键词： graph regular factor 2-graph switch box design.