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Non-wandering points and the depth for graph maps

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Science china mathematics 2007年第12期50卷 1818-1824页

作者： Jie-hua MAI~1 Tai-xiang SUN~(2+) ~1 Institute of mathematics,Shantou university,Shantou 515063,china ~2 college of mathematics and information sciences,guangxi university,nanning 530004,china Institute of mathematics Shantou University Shantou China college of mathematics and information sciences Guangxi University Nanning China

Let G be a graph and f:G→G be *** by R(f) andΩ(f) the set of recurrent points and the set of non-wandering points of f ***Ω_0(f) = G andΩ_n(f)=Ω(f|_(Ω_(n-1)(f))) for all n∈*** minimal m∈NU {∞} such thatΩ_m(f)=Ω_(m+1)(f) is called the depth of *** this paper,we show thatΩ_2 (f)=(?) and the depth of f is at most ***,we obtain some properties of non-wandering points of f.

关键词： graph map, non-wandering point, the depth of a graph map

Quantum self-attention neural networks for text classification

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Science china(information sciences) 2024年第4期67卷 301-313页

作者： guangxi LI Xuanqiang ZHAO Xin WANG Institute for Quantum Computing Baidu Research Centre for Quantum Software and information University of Technology Sydney QICI Quantum information and Computation Initiative Department of Computer ScienceThe University of Hong Kong Thrust of Artificial Intelligence Information HubHong Kong University of Science and Technology(Guangzhou)

An emerging direction of quantum computing is to establish meaningful quantum applications in various fields of artificial intelligence, including natural language processing(NLP). Although some efforts based on syntactic analysis have opened the door to research in quantum NLP(QNLP), limitations such as heavy syntactic preprocessing and syntax-dependent network architecture make them impracticable on larger and real-world data sets. In this paper, we propose a new simple network architecture, called the quantum selfattention neural network(QSANN), which can compensate for these limitations. Specifically, we introduce the self-attention mechanism into quantum neural networks and then utilize a Gaussian projected quantum self-attention serving as a sensible quantum version of self-attention. As a result, QSANN is effective and scalable on larger data sets and has the desirable property of being implementable on near-term quantum devices. In particular, our QSANN outperforms the best existing QNLP model based on syntactic analysis as well as a simple classical self-attention neural network in numerical experiments of text classification tasks on public data sets. We further show that our method exhibits robustness to low-level quantum noises and showcases resilience to quantum neural network architectures.

关键词： quantum neural networks self-attention natural language processing text classification parameterized quantum circuits

Luminosity-peak energy relation in the decay phases of gamma-ray burst pulses

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Science china(Physics,Mechanics & Astronomy) 2010年第1期53卷 163-170页

作者： LU RuiJing & LIANG EnWei Physical Science & Technology college, guangxi university, nanning 530004, china Physical Science & Technology college Guangxi University Nanning China

Using time-resolved spectral data for a sample of 30 pulses in 27 bright GRBs detected with CGRO/BATSE, we investigate the luminosity-peak energy relation (L-E p relation) in the decay phases of these pulses. A tight L-E p relation is found for most of the pulses, but its power law index is various among pulses, which is normally distributed at 1.84±0.60(1σ) for the pulses in our sample, roughly consistent with the L-E p relation within a GRB and the isotropic gamma-ray energy-E p relation among GRBs. The large scatter of the power law index cannot be explained with both the statistical or observational effects and it may be an intrinsic feature, indicating that no universal L-E p relation would be expected among GRBs/pulses. This may strongly weaken the cosmological use of this relation.

关键词： gamma ray bursts observations statistical luminosity-peak energy relation

Asymptotic normality and strong consistency of maximum quasi-likelihood estimates in generalized linear models

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Science china mathematics 2006年第2期49卷 145-157页

作者： YIN Changming, ZHAO Lincheng & WEI Chengdong School of mathematics and information Science, guangxi university, Manning 530004, china Department of Statistics and Finance, university of Science and Technology of china, Hefei 230026, china Department of mathematics, guangxi Teacher college, Manning 530001, china School of mathematics and information Science Guangxi University Nanning China Department of Statistics and Finance University of Science and Technology of China Hefei China Department of mathematics Guangxi Teacher College Nanning China

In a generalized linear model with q x 1 responses, the bounded and fixed (or adaptive) p × q regressors Zi and the general link function, under the most general assumption on the minimum eigenvalue of ZiZ'i,the moment condition on responses as weak as possible and the other mild regular conditions, we prove that the maximum quasi-likelihood estimates for the regression parameter vector are asymptotically normal and strongly consistent.

关键词： generalized linear models quasi-likelihood estimates asymptotic normality strong consistency.

Gamma-ray bursts in the Swift-Fermi era:Confronting data with theory

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Science china(Physics,Mechanics & Astronomy) 2010年第S1期53卷 14-23页

作者： LIANG EnWei Physical Science & Technology college,guangxi university,nanning 530004,china Physical Science & Technology college Guangxi University Nanning China

With the prompt slewing capability of the X-ray and UV-optical telescopes onboard the Swift mission and with the gamma-ray large area telescope onboard the Fermi mission,gamma-ray bursts(GRBs) are now accessible in a full time window and in all electromagnetic wavelengths for the *** observational breakthroughs have been made in recent years.I present here a brief review of some observational breakthroughs with the two missions,focusing on how these breakthroughs have revolutionized our understanding of the nature of this phenomenon and puzzles as well as challenges of confronting the conventional models with data.

关键词： radiation mechanism gamma rays bursts high energy phenomenon

A Superlinearly Convergent Combined PhaseⅠ-PhaseⅡ Subfeasible Method

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Systems Science and Systems Engineering 1994年第2期4卷 104-111页

作者： JIAN Jinbao(mathematics and information Science Department of guangxi university,nanning 530004, guangxi)

This paper presents a new algorithm for optimization problems with nonlinear inequality constricts. At each iteration, the algorithm generates the search direction by solving only one quadratic programming (QP), and then making a simple correction for the solution of the QP, moreover this new algorithm needn’t to do searching. The other advantage is that it may not only choose any point in En as a starting point, but also escape from the complex penalty function and diameter. moreover the iteration point will be a feasible descent sequence whenever some iteration point gets into the feasible region. So we call it subfeasible *** mild assumptions,the new algorithm is shown to possess global and two step superlinear convergence.

关键词： constrained optimization quadratic programming phase Ⅰ-hase Ⅱ global and superlinear convergence arbitrary starting point subfeasible method.

THE CONVERGENCE OF A NEW MODIFIED BFGS METHOD WITHOUT LINE SEARCHES FOR UNCONSTRAINED OPTIMIZATION OR COMPLEXITY SYSTEMS

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Journal of Systems Science & Complexity 2010年第4期23卷 861-872页

作者： Liying LIU Zengxin WEI Xiaoping WU college of mathematics Science Liaocheng University Liaocheng 252059 China college of mathematics and information Science Guangxi University Nanning 530004 China School of Management Xi'an Jiaotong University Xi'an 710049 China

In this paper,a new modified BFGS method without line searches is *** traditionalBFGS method,this modified BFGS method is proposed based on the so-called fixed steplengthstrategy introduced by Sun and *** some suitable assumptions,the global convergence andthe superlinear convergence of the new algorithm are established,*** some preliminarynumerical experiments,which shows that the new Algorithm is feasible,is also reported.

关键词： BFGS method complexity systems global convergence superlinear convergence unconstrained optimization.

A NEWε-GENERALIZED PROJECTION METHOD OF STRONGLY SUB-FEASIBLE DIRECTIONS FOR INEQUALITY CONSTRAINED OPTIMIZATION

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Journal of Systems Science & Complexity 2011年第3期24卷 604-618页

作者： Jinbao JIAN Guodong MA Chuanhao GUO college of mathematics and information Science Guangxi University Nanning 530004 China Department of mathematics and Computer Science Yulin Normal University Yulin 537000 China college of Science Shanghai University Shanghai 200444 China.

In this paper, the nonlinear optimization problems with inequality constraints are discussed. Combining the ideas of the strongly sub-feasible directions method and the s-generalized projection technique, a new algorithm starting with an arbitrary initial iteration point for the discussed problems is presented. At each iteration, the search direction is generated by a new s-generalized projection explicit formula, and the step length is yielded by a new Armijo line search. Under some necessary assumptions, not only the algorithm possesses global and strong convergence, but also the iterative points always get into the feasible set after finite iterations. Finally, some preliminary numerical results are reported.

关键词： E-generalized projection global and strong convergence inequality constraints method of strongly sub-feasible directions optimization.

On a problem of Skiba from the Kourovka Notebook

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Science china mathematics 2004年第1期47卷 96-103页

作者： WANG Yanming & WEI HuaquanLingnan college and School of mathematics, Zhongshan university, Guangzhou 510275, china School of mathematics, Zhongshan university, Guangzhou 510275, china Department of mathematics, guangxi Teacher’s college, nanning 530001, china Lingnan college and School of mathematics Zhongshan University Guangzhou China School of mathematics Zhongshan University Guangzhou China Department of mathematics Guangxi Teacher’s College Nanning China

In this paper, we give a positive answer to a recent open problem of Skiba in Kourovka Notebook without using the odd order theorem and other deep theorems. Some of the techniques are improved.

关键词： supersolvable group c-supple merited subgroup complemented subgroup generalized fitting subgroup saturated formation