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Adjoining Batch Markov Arrival Processes of a Markov Chain

Acta Mathematicae Applicatae Sinica 2018年第1期34卷 1-10页

作者： Xiao-yun MO Xu-yan xiang xiang-qun YANG College of Mathematics and Statistics Hunan University of Finance and Economics Changsha 410205 China College of Mathematics and Computational Science Hunan University of Arts and Science Changde 415000 China Key Laboratory of High performance Computing and Stochastic Information Processing Ministry of Education of China College of Mathematics and Computer Science Hunan Normal University Changsha 410081 China Hunan Province Cooperative Innovation Center for the Construction and Development of Dongting Lake Ecological Economic Zone Changde 415000 China

A batch Markov arrival process（BMAP） X^＊=（N, J） is a 2-dimensional Markov process with two components, one is the counting process N and the other one is the phase process J. It is proved that the phase process is a time-homogeneous Markov chain with a finite state-space, or for short, Markov chain. In this paper,a new and inverse problem is proposed firstly： given a Markov chain J, can we deploy a process N such that the 2-dimensional process X^＊=（N, J） is a BMAP？ The process X^＊=（N, J） is said to be an adjoining BMAP for the Markov chain J. For a given Markov chain the adjoining processes exist and they are not unique. Two kinds of adjoining BMAPs have been constructed. One is the BMAPs with fixed constant batches, the other one is the BMAPs with independent and identically distributed（i.i.d） random batches. The method we used in this paper is not the usual matrix-analytic method of studying BMAP, it is a path-analytic method. We constructed directly sample paths of adjoining BMAPs. The expressions of characteristic（D_k, k = 0, 1, 2· · ·）and transition probabilities of the adjoining BMAP are obtained by the density matrix Q of the given Markov chain J. Moreover, we obtained two frontal Theorems. We present these expressions in the first time.

关键词： Markov chain batch Markov arrival process (BMAP) adjoining BMAP fixed constant batch independent identically distributed (i.i.d) random batch

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Automatic generation of optical initial configuration based on Delano diagram

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Research in Astronomy and Astrophysics 2016年第1期16卷 59-66页

作者： Kai-Yuan Zhang xiang-Yan Yuan xiang-qun Cui National Astronomical Observatories/Nanjing Institute of Astronomical Optics & Technology Nanjing 210042 China Key Laboratory of Astronomical Optics & Technology Nanjing Institute of Astronomical Optics & Technology Chinese Academy of Sciences Nanjing 210042 China University of Chinese Academy of Sciences Beijing 100049 China

This paper presents a method to automatically initialize an optical system based on the Delano diagram. The process to generate the optical initial configuration is constrained by the control points, which are deduced from parameters related to basic design requirements. We present the theory and method to generate the optical initial configuration automatically when the basic design requirements are known. Two optical systems are taken as examples to demonstrate the proposed method.

关键词： telescopes -- methods: analytical

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Multipartite Entanglement of a Tetrahedron Lattice

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Communications in Theoretical Physics 2006年第5X期46卷 863-872页

作者： ZHANG Rong ZHU Shi-qun HAO xiang School of Physical Science and Technology Suzhou University Suzhou 215006 China

Three-dimensional Heisenberg model in the form of a tetrahedron lattice is investigated. The concurrence and multipartite entanglement are calculated through 2-concurrence C and 4-concurrence C4. The concurrence C and multipartite entanglement G4 depend on different coupling strengths Ji and are decreased when the temperature T is increased. For a symmetric tetrahedron lattice, the concurrence C is symmetric about J1 when J~ is negative while the multipartite entanglement G4 is symmetric about J1 when J2 〈 2. For a regular tetrahedron lattice, the concurrence G of ground state is 1/3 for ferromagnetic case while G = 0 for antiferromagnetic ***. However, there is no multipartitc entanglement since C4=0 in a regular tetrahedron lattice. The external magnetic field 13 can increase the maximum value of the concurrence GB and induce two or three peaks in Cn. There is a peak in the multipartite entanglement G4 B when G4B is varied as a function of the temperature T. This peak is mainly induced by the magnetic field B.

关键词： multipartite entanglement concurrence three dimensions tetrahedron lattice

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A V-shaped spectroscopic cell for FTIR measurements

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Chinese Chemical Letters 2011年第4期22卷 481-484页

作者： xiang Qin Lin Zhi xiang Zhang Wan qun Hu Department of Chemistry University of Science and Technology of China Hefei 230026 China

A V-shaped spacroscopic cell（V-cell） was constructed using two CaF2 optical plates for FTIR light transparent measurements in the range of 4000-1000 cm^（-1）.The spectrum of ethanol was characterized with the standard spectra,excellent fitting was achieved with a bottom-width correction *** principle of the V-cell was discussed,giving equations for the data *** shows that the V-cell is an auto-focus type spectroscopic cell,which can effectively avoid absorption saturation with amplifications for weak absorption *** V-cell design is simple and effective,easy to operate,suitable for applications in liquid samples with high absorption bands,willing to have broad application prospects.

关键词： V-shaped cell FTIR spectroscopy Light transparent Error correction Demountable Ethanol

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A Periodic Dividend Problem with Inconstant Barrier in Markovian Environment

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Acta Mathematica Sinica,English Series 2015年第2期31卷 281-294页

作者： Fang JIN Hui OU xiang qun YANG College of Mathematics and Computer Sciences Hu'nan Normal University

Periodic dividend problem is a meaningful issue. Based on a compound binomial model with periodic dividend, we use a homogeneous, ergodic and irreducible discrete-time Markov chain to express the evolution from one period to the subsequent of the economic or the environmental and climatic conditions. We derive some properties about the model. A system of integral equations for the expectation and the r-th moment of discounted dividends until ruin time are obtained respectively. Moreover, by using of Contraction Mapping Principle, we solve the equation system and obtain the explicit expression.

关键词： Periodic dividend Markovian environment inconstant barrier ruin time discounted dividends contraction mapping principle

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Simulation and analysis of co-phasing errors of the segmented primary mirror tiled by hexagonal segments in LOT

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Research in Astronomy and Astrophysics 2021年第10期21卷 37-45页

作者： Shi-Dong Shen xiang-qun Cui Yong Zhang National Astronomical Observatories/Nanjing Institute of Astronomical Optics&Technology Chinese Academy of SciencesNanjing 210042China CAS Key Laboratory of Astronomical Optics&Technology Nanjing Institute of Astronomical Optics&TechnologyNanjing 210042China University of the Chinese Academy of Sciences Beijing 100049China

In this paper,co-phasing errors of a segmented primary mirror tiled by hexagonal segments are successfully calculated for the 12-meter Large aperture Optical/infrared Telescope(LOT).Co-phasing errors including out-of-plane errors are simulated separately and comprehensively based on several software simulation *** simulation results show that the Strehl Ratio(SR)of LOT is larger than 0.8 when the RMS value of tip-tilt obeying a normal distribution is less than 0.018 arcsec,and the SR of LOT is larger than 0.8 when the RMS value of piston obeying a normal distribution is less than 40 ***,simulation results of Zemax show that the SR of LOT is larger than 0.8 when the RMS value of tip-tilt obeying a normal distribution is less than 0.02 arcsec,and the SR of LOT is larger than 0.8 when the RMS value of piston obeying a normal distribution is less than 40 *** simulation results successfully lay a solid foundation for LOT(especially the segmented primary mirror with active optics).

关键词： methods:analytical techniques:miscellaneous telescopes

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Undersea safety mining of the large gold deposit in Xinli District of Sanshandao Gold Mine

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International Journal of Minerals,Metallurgy and Materials 2012年第7期19卷 574-583页

作者： Zhi-xiang Liu Wen-gang Dang Xian-qun He School of Resources and Safety Engineering Central South University Changsha 410083 China

The exploration of undersea resources becomes popular as land resources decrease. Researches were conducted with emphasis on the safety and efficiency of undersea mining of the large gold deposit in Xinli District of Sanshandao Gold Mine. A series of tests for the physical and mechanical characteristics of rock mass were carried out, and the three-dimensional geo-stress distribution was tested in the mining area. Further, a similar experimental simulation platform, which revealed the mechanism of water inrush and ascertained the reason- able thickness of the safety isolate layer, was established for the undersea mining. Meanwhile, the feasibility of cancelling the ore pillars and the safety conditions was checked by numerical simulation. The simulation results show that it is safe to exploit the ore body below the -85 m level （presently, the exploitation level is below -160 m in Xinli District）, and the ore pillars can be cancelled below the -560 m level. Fur- thermore, a novel backfill method was designed to reduce the rock strata disturbance and settlement, and the settlement of roof strata was monitored during the mining process. Engineering practice shows that the settlement of roof strata was small and that no disaster happened. This indicates that the undersea safety mining technology of the large gold deposit is achieved in Xinli District.

关键词： undersea mining gold deposits rock mechanics mine roof control computer simulation

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Average Fidelity of Teleportation in Quantum Noise Channel

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Communications in Theoretical Physics 2006年第5期45卷 802-806页

作者： HAO xiang ZHANG Rong ZHU Shi-qun School of Physical Science and Technology Suzhou University Suzhou 215006 China

The effects of amplitude damping in quantum noise channels on average fidelity of quantum teleportation are analyzed in Bloeh sphere representation for every stage of teleportation. When the quantum channels are varied from maximally entangled states to non-maximally entangled states, it is found that the effects of noise channels on the fidelity are nearly equivalent to each other for strong quantum noise. The degree of damage on the fidelity of non-maximally entangled channels is smaller than that of maximally entangled channels. The average fidelity of values larger than 2/3 may be one representation indirectly showing how much the unavoidable quantum noise is.

关键词： average fidelity teleportation quantum noise channel Bloch sphere

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Application of Moore-Penrose Inverse in Deciding the Minimal Martingale Measure

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Acta Mathematicae Applicatae Sinica 2010年第4期26卷 653-660页

作者： Luo-gen Yao Gang Yang xiang-qun Yang Information Department of Hunan Business College Changsha 410205China College of Mathematics and Computer Science Hunan Normal UniversityChangsha 410081China

The Moore-Penrose inverse is an important tool in *** paper shows that the MoorePenrose inverse is also an effcient technique in determining the minimal martingale measure if a security price follows a semi-martingale which satisfies some structure *** extend a result of Dzhaparidze and Spreij concerning the Moore-Penrose inverse to the case that the Moore-Penrose inverse of any matrix-valued predictable process is still ***,we obtain an explicit formula of the minimal martingale measure by employing the Moore-Penrose ***,the minimal martingale measure in a generalized Black-Scholes model is found.

关键词： Moore-Penrose inverse minimal martingale measure semi-martingales structure condition

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Modeling dependence based on mixture copulas and its application in risk management

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Applied Mathematics(A Journal of Chinese Universities) 2009年第4期24卷 393-401页

作者： OUYANG Zi-sheng LIAO Hui YANG xiang-qun School of Information Hunan University of Commerce Changsha 410205 China School of Mathematics Hunan Normal University Changsha 410081 China

This paper is concerned with the statistical modeling of the dependence structure of multivariate financial data using the copula, and the application of copula functions in VaR valuation. After the introduction of the pure copula method and the maximum and minimum mixture copula method, authors present a new algorithm based on the more generalized mixture copula functions and the dependence measure, and apply the method to the portfolio of Shanghai stock composite index and Shenzhen stock component index. Comparing with the results from various methods, one can find that the mixture copula method is better than the pure Gaussian copula method and the maximum and minimum mixture copula method on different VaR level.

关键词： Gaussian mixture copula value-at-risk dependence back-test Spearman's rho

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