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An Alternating Iterative Method and Its Application in Statistical Inference

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Acta Mathematica Sinica,English Series 2008年第5期24卷 843-856页

作者： ning zhong shi Guo Rong HU Qing CUI Key Laboratory for Applied Statistics of MOE and School of Mathematics and Statistics Northeast No~nal University Changchun 130024 P. R. China Department of Basic Courses Shijiazhuang Railway Institute Shijiazhuang 050043 P. R. China

This paper studies non-convex programming problems. It is known that, in statistical inference, many constrained estimation problems may be expressed as convex programming problems. However, in many practical problems, the objective functions are not convex. In this paper, we give a definition of a semi-convex objective function and discuss the corresponding non-convex programming problems. A two-step iterative algorithm called the alternating iterative method is proposed for finding solutions for such problems. The method is illustrated by three examples in constrained estimation problems given in Sasabuchi et al. （Biometrika, 72, 465472 （1983））, shi N. Z. （J. Multivariate Anal., 50, 282-293 （1994）） and El Barmi H. and Dykstra R. （Ann. Statist., 26, 1878 1893 （1998））.

关键词： semi-convex function alternating iterative method accumulation point maximum likelihood estimation order restriction

Two-group SIR Epidemic Model with Stochastic Perturbation

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Acta Mathematica Sinica,English Series 2012年第12期28卷 2545-2560页

作者： Chun Yan JI Da Qing JIANG ning zhong shi School of Mathematics and Statistics Changshu Institute of Technology School of Mathematics and Statistics Northeast Normal University

A stochastic two-group SIR model is presented in this paper. The existence and uniqueness of its nonnegative solution is obtained, and the solution belongs to a positively invariant set. Further- more, the globally asymptotical stability of the disease-free equilibrium is deduced by the stochastic Lyapunov functional method if R0 〈 1, which means the disease will die out. While if R0 〉 1, we show that the solution is fluctuating around a point which is the endemic equilibrium of the deterministic model in time average. In addition, the intensity of the fluctuation is proportional to the intensity of the white noise. When the white noise is small, we consider the disease will prevail. At last, we illustrate the dynamic behavior of the model and their approximations via a range of numerical experiments.

关键词： Stochastic two-group SIR model disease-free equilibrium endemic equilibrium stochastic Lyapunov function asymptotically stable in the large

Nonparametric Estimation of Interval-censored Failure Time Data in the Presence of Informative Censoring

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Acta Mathematicae Applicatae Sinica 2017年第1期33卷 107-114页

作者： Chun-jie WANG Jian-guo SUN De-hui WANG ning-zhong shi The College of Basic Science Changchun University of Technology Changchun 130012 China Mathematics School and Institute of Jilin University Changchun 130012 China Department of Statistics University of Missouri 146 Middlebush Hall MO 65211. USA Key Laboratory of Applied Statistics of MOE School of Mathematics and Statistics Northeast Normal University Changchun 130024 China

Nonparametric estimation of a survival function is one of the most commonly asked questions in the analysis of failure time data and for this, a number of procedures have been developed under various types of censoring structures （Kalbfleisch and Prentice, 2002）. In particular, several algorithms are available for interval-censored failure time data with independent censoring mechanism （Sun, 2006; Turnbull, 1976）. In this paper, we consider the interval-censored data where the censoring mechanism may be related to the failure time of interest, for which there does not seem to exist a nonparametric estimation procedure. It is well-known that with informative censoring, the estimation is possible only under some assumptions. To attack the problem, we take a copula model approach to model the relationship between the failure time of interest and censoring variables and present a simple nonparametric estimation procedure. The method allows one to conduct a sensitivity analysis among others.

关键词： copula models interval censored data dependent censoring nonparametric estimation

Existence,uniqueness,and global attractivity of positive solutions and MLE of the parameters to the Logistic equation with random perturbation

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Science China Mathematics 2007年第7期50卷 977-986页

作者： Da-qing JIANG Bao-xue ZHANG De-hui WANG ning-zhong shi School of Mathematics and Statistics Northeast Normal UniversityChangchun 130024China School of Mathematics Jilin UniversityChangchun 130012China

This paper discusses a randomized Logistic equation $\dot N(t) = (r + \alpha \dot B(t))N(t)[1 - \frac{{N(t)}}{K}]$ with an initial value N(0) = N 0, and N 0 is a random variable satisfying 0 < N 0 < K. The existence, uniqueness and global attractivity of positive solutions and maximum likelihood estimate (MLE) of the parameters of the equation are studied.

关键词： randomized Logistic equation existence uniqueness global attractivity MLE of the parameter 34F05 34E10 62F10

Electrodeposition mechanism of ZnSe thin film in aqueous solution

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Rare Metals 2017年第10期36卷 816-820页

作者： Jun-Li Xu Wei-Ying Gong Wei Wang Hao Meng Xia Zhang zhong-ning shi Geir-Martin Haarberg School of Science Northeastern University Shenyang 110004 China School of Materials and Metallurgy Northeastern University Shenyang 110004 China Department of Materials Science and Engineering Norwegian University of Science and Technology 7491 Trondheim Norway

ZnSe is one of the important and excellent II-VI semiconductor materials, which has direct transition band structure. In this paper, ZnSe thin films were prepared by an electrochemical deposition method, and the formation mechanism of ZnSe was studied systematically. Voltammerry and chronoamperometry combined with X-ray diffraction （XRD） and Raman techniques were used to analyze the deposition processes. It is found that the substrate and deposition potentials have a great influence on the phase composition of deposited thin film, and Zn substrate is beneficial to the preparation ZnSe films. Strong selenium-substrate interaction results in the formation of selenimn compounds involving electrode materials. The addition of Zn（II） source can affect the reduction potential of Se, and results in the change of reducing mechanism of Se（0） from Se（IV）. Se（0） formed from H2Se because the formation of H2Se is more active than forming Se（0） directly from Se（IV）, and H2Se can recombine with the substrate material, forming selenium-substrate compounds more quickly.

关键词： ZnSe Thin film Electrodepostion Mechanism Raman spectra

Raman spectroscopy and quantum chemical calculation on YCl_(3)-KCl molten salt system

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Rare Metals 2023年第11期42卷 3886-3896页

作者： Can Xu Xian-Wei Hu Jiang-Yu Yu Peng-Wei Li Ai-Min Liu Shao-Hua Luo zhong-ning shi Zhao-Wen Wang Key Laboratory Ecological Metallurgy of Multimetallic Mineral‘Ministry of Education’ School of MetallurgyNortheastern UniversityShenyang110819China State Key Laboratory of Rolling and Automation Northeastern UniversityShenyang110819China School of Materials Science and Engineering Northeastern UniversityShenyang110819China Department of Chemistry and Bioscience Aalborg University9220AalborgDenmark

The knowledge on the ionic structure of YCl_(3)-KCl molten system is of guiding significance for the practical production of yttrium metals and yttrium alloys via molten salt electrolysis using this system as *** this paper,the theoretical Raman spectra of the ionic groups which may exist in YCl_(3)-KCl molten system are simulated by quantum chemical calculation using Gaussian09 and Gauss View 5.0 programs based on density functional theory(DFT).Then the ionic structures of 20 mol%-60 mol%YCl_(3)-KCl molten salt systems are studied by comparing the Raman shift values of the bands in the theoretical Raman spectra of different ionic groups with the experimental spectra of this ***_(6)^(3-),Y_(2)Cl_(7)^(-),Y_(2)Cl_(8)^(2-)and Y_(2)Cl_(9)^(3-)are thought to exist in the molten *** the increase of temperature,the relative content of YCl_(6)^(3-)ionic groups increases while those of Y_(2)Cl_(7)^(-),Y_(2)Cl_(8)^(2-)and Y_(2)Cl_(9)^(3-)ionic groups ***,the"lifetime"of all ionic groups decreases within the temperature range of 692-730℃.Meanwhile,the relative contents of Y_(2)Cl_(7)^(-),Y_(2)Cl_(8)^(2-)and Y_(2)Cl_(9)^(3-)increase with the increase of YCl_(3)content,while that of YCl_(6)^(3-)*** wave function analysis of the four ionic groups(YCl_(6)^(3-),Y_(2)Cl_(7)^(-),Y_(2)Cl_(8)^(2-),and Y_(2)Cl_(9)^(3-))is carried out by Multiwfn *** net charge in each group,the direction of electron migration during the formation of each group,the sites where electrophilic and nucleophilic reactions are most likely to occur in each ionic group,and the order of bond breaking during chemical reactions for the four groups are obtained.

关键词： YCl_(3)-KCl molten salt Ionic structure Raman spectroscopy Quantum chemical calculation Wave function analysis

A light-through-side cell and co-used furnace designed for micro-Raman spectra study on volatile melts

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Chinese Chemical Letters 2012年第11期23卷 1291-1294页

作者： Xian Wei Hu Huan Li Bing Liang Gao Jing Jing Liu zhong ning shi Jiang Yu Yu Zhao Wen Wang School of Materials and Metallurgy Northeastern UniversityShenyang 110004China

A new type of sample cell specially designed for micro-Raman spectra study on volatile melts is described. The cell is made of quartz. The lower section of the cell is circular ring-shaped and the one-end-closed hole in the cell is used for locating the heating body. The tube attached to the cell lid for placing the thermal couple is inserted into the sample, which ensures that the temperature measurement accuracy is good. The cell can be sealed for reducing the effect of the composition change caused by the in_homogeneous volatilization. During the Raman spectra scanning, the laser beam is transmitted into the cell through the side but not the top. Meanwhile, a furnace has been designed to match the cell. The heating body is closely coupled with the sample cell, and there is a hole on the side wall of the furnace for the entrance of the microlens. The assembly has performed well in the tested Raman spectrum measurement of molten NaNO3 at 602 ℃.

关键词： Light-through-side cell Raman spectroscopy Volatile melts Comer microlens Cell-around-heating body furnace

High-resolution remote thermometry based on Bi^(3+)-doped 0D zinc halide hybrids

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Science China Chemistry 2024年第8期67卷 2599-2605页

作者： Cui-Mi shi Shu-Hua Xue Jin-Yun Wang Liang-Jin Xu zhong-ning Chen State Key Laboratory of Structural Chemistry Fujian Institute of Research on the Structure of MatterChinese Academy of SciencesFuzhou 350002China Fujian Science Technology Innovation Laboratory for Optoelectronic Information of ChinaFuzhou 350108China University of Chinese Academy of Sciences Beijing 100049China

Developing highly sensitive optical thermometers is of great significance due to their capability to enable remote and non-contact temperature measurements, rendering them highly applicable in diverse and harsh environments. Herein we report a temperature-dependent phosphor of 0D metal halide hybrid by incorporating Bi^(3+)into the(MePPh_(3))_(2)ZnCl_(4) matrix. Through Bi^(3+)doping,the initially non-luminescent(MePPh_(3))_(2) ZnCl_(4) matrix exhibits a deep-blue emission centered at 453 nm, with a photoluminescence quantum yield(PLQY) of 5.71% and a Stokes shift of 75 nm at room temperature. Experimental characterization demonstrates that exciton-like luminescence of Bi^(3+)is mainly responsible for the blue emission. Single crystals of Bi^(3+)-doped(MePPh_(3))_(2)ZnCl_(4) show an unusual correlation between photoluminescence(PL) lifetime and temperature. Particularly, the dependence of luminescence lifetime on temperature is most remarkable in the temperature range of 80 to 100 K with an exceptional sensitivity up to 0.09 K^(-1), representing one of the best levels for thermometry based on PL decay lifetime. Our work not only provides a viable strategy for designing a novel, environmentally friendly, and stable blue emitter, but also paves the way for precise thermometric application at low temperature.

关键词： lead-free hybrids Bi^(3+)doping blue emission temperature sensing

Chiral multiple-resonance thermally activated delayed fluorescence materials based on chiral spiro-axis skeleton for efficient circularly polarized electroluminescence

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Science China Chemistry 2024年第7期67卷 2257-2264页

作者： shi-Quan Song Xiao Han zhong-zhong Huo Ching-Fai Yip Xian-Fang Hong Meng-ning Ding You-Xuan Zheng State Key Laboratory of Coordination Chemistry Jiangsu Key Laboratory of Advanced Organic MaterialsSchool of Chemistry and Chemical EngineeringNanjing UniversityNanjing 210023China Key Laboratory of Mesoscopic Chemistry of Ministry of Education School of Chemistry and Chemical EngineeringNanjing UniversityNanjing 210023China

Chiral luminescence materials have potential applications in the field of three-dimensional displays due to their circularly polarized luminescence(CPL)***,the further development of circularly polarized organic light-emitting diodes(CP-OLEDs)needs to meet the requirements of high efficiency,high color purity,low cost,and high dissymmetry factor(gPLor gEL),chiral multiple resonance thermally activated delayed fluorescence(MR-TADF)materials are considered as candidates in these ***,based on a pair of chiral spirofluorene precursors,two pairs of high-performance chiral MR-TADF emitters((R/S)-p-Spiro-DtBuCzB and(R/S)-m-Spiro-DtBuCzB)are developed,which exhibit strong emissions peaking at 491 and 502 nm in toluene with full-width at half-maximum values of 25 and 33 nm,*** addition,small singlet–triplet energy gaps of 0.15 and 0.10 eV with high absolute photoluminescence efficiencies of 95.0%and 96.7%are observed for p-Spiro-DtBuCzB and m-Spiro-DtBuCzB molecules,*** based on p-Spiro-DtBuCzB and m-Spiro-DtBuCzB display high maximum external quantum efficiencies of 29.6%and 33.8%,*** importantly,CP-OLEDs present symmetric circularly polarized electroluminescence spectra with|gEL|factors of 3.36×10^(-4)and 7.66×10^(-4)for devices based on(R/S)-p-Spiro-DtBuCzB and(R/S)-m-Spiro-DtBuCzB enantiomers,respectively.

关键词： chiral spiro-axis skeleton-based material multiple resonance thermally activated delayed fluorescence circularly polarized electroluminescence dissymmetry factor external quantum efficiency