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Pair-wise error probability and its Chernoff upper bound for unitary space-time code

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Science china(Information Sciences) 2010年第8期53卷 1613-1621页

作者： ZHANG DaPeng 1.2 , LIU Ju 1., XU HongJi 1.& JI Hui 1.1.school of Information Science and Engineering, Shandong {1., jinan 2501.0, china 2 State Key Laboratory of Integrated Services Networks, Xidian {1., Xi’an 71.071. china 1. school of Information Science and Engineering Shandong University Jinan 250100 China2. State Key Laboratory of Integrated Services Networks Xidian University Xi’an 710071 China

Unitary space-time code is ideally suited for rapid fading scenarios as it can operate well without channel state information (CSI), which is of vital significance for improving the effectivity and reliability of wireless communication systems. Pair-wise error probability (PEP) is an important factor for studying the reliability of a communication system. However, the existing scheme only gives the final result of PEP and the corresponding Chernoff upper bound (CUB) is obtained through magnification, which is not of universal significance for this kind of problems. In this paper, we employ the log-likelihood ratio of probability density functions of the received signals conditioned on the two possibly transmitted signals and by virtue of moment generating function we give the details in deriving the final precise residue expression for PEP and its CUB. At last, we verify the above results by simulations.

关键词： multiple-input multiple-output space-time code unitary space-time code pair-wise error probability Chernoff upper bound

A first-principles study of dihydroazulene as a possible optical molecular switch

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Science china(Physics,Mechanics & Astronomy) 2011年第3期Mechanics & Astronomy) .卷 437-441页

作者： XIA CaiJuan1. LIU DeSheng2,3 & LIU HanChen1.1.school of Science, Xi’an Polytechnic {1., Xi’an 71.048, china 2 school of Physics, State Key Laboratory of Crystal Materials, Shandong {1., jinan 2501.0, china 3 Department of Physics, Jining {1., Qufu 2731.5, china 1. school of Science Xi’an Polytechnic University Xi’an 710048 China2. School of Physics State Key Laboratory of Crystal Materials Shandong University Jinan 250100 China3. Department of Physics Jining University Qufu 273155 China

By applying nonequilibrium Green's function formalism combined with first-principles density functional theory, we investigate the electronic transport properties of the dihydroazulene optical molecular switch. Three kinds of adsorption sites including the hollow, bridge and top sites are studied. The two forms of this molecule, namely the open form and the closed form, can reversibly switch from each other upon photoexcitation. Their transmission spectra are remarkably distinctive. Theoretical results show that the current of the closed form is always significantly larger than that of the open form for all three adsorption sites, which promises this system as possibly one of the good candidates for optical switches due to its unique advantage, and which may have some potential applications in the future molecular circuit.

关键词： molecular switch nonequilibrium Green’s function electronic transport density functional theory

Construction of convex solutions for the second type of Feigenbaum's functional equations

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Science china Mathematics 2009年第8期52卷 1617-1638页

作者： SI JianGuo & ZHANG Min school of Mathematics, Shandong {1., jinan 2501.0, china school of Mathematics Shandong University Jinan 250100 China

In this paper, convex solutions for the second type of Feigenbaum's equation f (x) = λ1.f (f (λx)), 0 < λ < 1. f (0) = 1. 0 f (x) 1. x ∈ [0, 1. are investigated. Using constructive methods, we discuss the existenc... 详细信息

In this paper, convex solutions for the second type of Feigenbaum's equation f (x) = λ1.f (f (λx)), 0 1. f (0) = 1. 0 f (x) 1. x ∈ [0, 1. are investigated. Using constructive methods, we discuss the existence and uniqueness of continuous convex solutions, C1.convex solutions and C2-convex solutions of the above equation.

关键词： the second type of Feigenbaum’s functional equations constructive method initial function convex solutions

A Hybrid of Theorems of Goldbach and Piatetski-Shapiro

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Chinese Annals of Mathematics,Series B 2006年第3期27卷 341-352页

作者： Xianmeng MENG Mingqiang WANG school of Computer Science and Technology, Shandong {1., jinan 2501.0, china Department of Statistics and Mathematics, Shandong Finance Institute, jinan 25001., china. school of Computer Science and Technology, Shandong {1., jinan 2501.0, china Department of Mathematics, Qufu Normal {1., Qufu 2731.5, Shandong, china. school of Computer Science and Technology Shandong University Jinan 250100 China Department of Statistics and Mathematics Shandong Finance Institute Jinan 250014 China Department of Mathematics Qufu Normal University Qufu 273165 Shandong China

It is proved that for almost all sufficiently large even integers n, the prime variable equation n = p1.＋ p2, p1.∈ Pγ is solvable, with 1./1. 〈γ≤ 1. where Pγ = {p ｜p = [m^1.γ], for integer m and prime p} is t... 详细信息

关键词： Circle method Sieve method Goldbach problem

A 1./1.-approximation algorithm for sorting by short block-moves

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Science china(Information Sciences) 2011年第2期54卷 279-292页

作者： JIANG HaiTao & ZHU DaMing school of Computer Science and Technology, Shandong {1., jinan 2501.1. china 1. school of Computer Science and Technology Shandong University Jinan 250101 China

Block-move is one of the popular operations for genome rearrangement. A short block-move is an operation on a permutation that moves an element at most two positions away from its original position. Heath and Vergara investigated the problem of finding a minimum-length sorting sequence of short block-moves for a given permutation and devised a 4/3-approximation algorithm. In this paper, we present a new 1./1.-approximation algorithm for this problem. Firstly, we devise an exact polynomial time algorithm for sorting a special kind of sub permutations called umbrella; then we split the permutation into a series of related umbrellas and sort them greedily. We obtain a new lower bound of the short block-move distance by exploiting the properties of five kinds of sub-permutations. After some complicated analysis, we prove that the approximation ratio of the new algorithm is at most 1./1..

关键词： short block-move approximation algorithm

On the error term in Weyl’s law for the Heisenberg manifolds (Ⅱ)

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Science china Mathematics 2009年第5期52卷 857-874页

作者： ZHAI WenGuang school of Mathematical Sciences, Shandong Normal {1., jinan 25001., china 1. school of Mathematical Sciences Shandong Normal University Jinan 250014 China

In this paper we study the mean square of the error term in the Weyl's law of an irrational (2l + 1.-dimensional Heisenberg manifold. An asymptotic formula is established.

关键词： Heisenberg manifold Weyl’s law error term mean square

S-rough sets and knowledge separation

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Journal of Systems Engineering and Electronics 2005年第2期16卷 403-410页

作者： Shi Kaiquan 1.21. school of Mathematics and System Sciences, Liaocheng {1., Liaocheng 252059, P. R. china 2. school of Mathematics and System Sciences, Shandong {1., jinan 2501.0, P. R. china school of Mathematics and System Sciences Liaocheng University Liaocheng 252059 P. R. China school of Mathematics and System Sciences Shandong University Jinan 250100 P. R. China

The conceptions of the knowledge screen generated by S-rough sets are given: f- screen and - screen , and then puts forward - filter theorem, - filter theorem of knowledge. At last, the applications of knowledge separ... 详细信息

关键词： S- rough sets f- screen - screen f-filter theorem - filter theorem knowledge separation.

A general central limit theorem under sublinear expectations

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Science china Mathematics 2010年第8期53卷 1989-1994页

作者： LI Min & SHI YuFeng school of Mathematics,Shandong {1.,jinan 2501.0,china 1. school of Mathematics Shandong University Jinan 250100 China

Under some weaker conditions,we give a central limit theorem under sublinear expectations,which extends Peng's central limit theorem.

关键词： central limit theorem sublinear expectation G-normal distribution

The dynamical properties of Rydberg hydrogen atom near a metal surface

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Science china(Physics,Mechanics & Astronomy) 2005年第6期48卷 667-675页

作者： GE Meihua1. ZHANG Yanhui1. WANG Dehua2, DU Mengli3 & LIN Shenglu1.1. College of Physics and Electronics, Shandong Normal university, {1. 25001., china 2. Department of Mathematics and Physics, Shandong Institute of Architecture and Engineering, {1. 25001., china 3. Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 1.0080, china 1. College of Physics and Electronics Shandong Normal University 250014 Jinan China 2. Department of Mathematics and Physics Shandong Institute of Architecture and Engineering 250014 Jinan China 3. Institute of Theoretical Physics Chinese Academy of Sciences 100080 Beijing China

The dynamical properties of Rydberg hydrogen atom near a metal surface are presented by using the methods of phase space analysis and closed orbit theory. Transforming the coordinates of the Hamiltonian, we find that the phase space of the system is divided into vibrational and rotational region. Both the Poincaré surface of section and the closed orbit theory verify the same conclusion clearly. In this paper we choose the atomic principal quantum number as n = 20. The dynamical character of the exited hydrogen atom depends sensitively on the atom-surface distance d. When d is sufficiently large, the atom-surface potential can be expressed by the traditional van der Waals force and the system is integrable. When d becomes smaller, there exists a critical value dc. For d > dc, the system is near-integrable and the motion is regular. While chaotic motion appears for d < dc, and the system tends to be non-integrable. The trajectories become unstable and the electron might be captured onto the metal surface.

关键词： Rydberg hydrogen atom, van der Waals interaction, Poincaré surface of section, closed orbit theory, chaos.