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Behavior of the Solutions to an Othmer-Stevens Chemotaxis Model with Reproduction Term

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wuhan university Journal of Natural Sciences 2010年第4期15卷 277-282页

作者： CHEN Xueyong, liu weian school of mathematics and statistics, wuhan university, wuhan 430072, hubei, china school of mathematics and statistics Wuhan University Wuhan Hubei China

In this paper,we study a simplified Othmer-Stevens model with reproduction term. By making use of a smart function transformation,the comparative method and some special mathe-matical analysis,we prove the existence of global,blow-up or quenching solutions of the problem on different conditions. More interesting results are reached. The result of the paper not only verifies a real biological phenomenon,but also provides a theo-retical groundwork for numerical problems of the chemotaxis model.

关键词： chemotaxis global existence blow-up quenching solution

Necessary and sufficient conditions for moderate deviations of dependent random variables with heavy tails

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Science china mathematics 2010年第6期53卷 1421-1434页

作者： liu Li school of mathematics and statistics,wuhan university,wuhan 430072,china 1. school of mathematics and statistics Wuhan University Wuhan 430072 China

This paper studies the moderate deviations of real-valued extended negatively dependent(END) random variables with consistently varying *** moderate deviations of partial sums are first *** results are then used to establish the necessary and sufficient conditions for the moderate deviations of random sums under certain circumstances.

关键词： moderate deviation extended negative dependence consistently varying tail random sum

Some Index Classes of Singularity of Vector Fields on Manifolds with Boundary

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wuhan university Journal of Natural Sciences 2002年第4期7卷 388-390页

作者： Xu Xu, liu Heng-xing school of mathematics and statistics, wuhan university, wuhan 430072, hubei, china wuhan university School of Mathematics and Statistics Wuhan Hubei China (GRID:grid.49470.3e) (ISNI:***)

V. I. Arnold defined some particular classes of index for singularities of adapted fields. We generalize these index classes for general fields on manifolds with boundary and get some relations of these index classes.

关键词： adapted fields singularity index

Incorporation sodium ions into monodisperse lead-free double perovskite Cs_(2)AgBiCl_(6) nanocrystals to improve optical properties

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Chinese Chemical Letters 2024年第3期35卷 549-553页

作者： Song Wang Ying Xie Wenchao Jiang Binghang liu keying Shi Kai Pan Key Laboratory of Functional Inorganic Material Chemistry Ministry of EducationHeilongjiang UniversityHarbin 150080China school of Materials Science and Engineering Jiangsu Engineering Laboratory of Light-Electricity-Heat Energy-Converting Materials and ApplicationsChangzhou UniversityChangzhou 213164China State Key Laboratory of Catalysis Dalian National Laboratory for Clean EnergyDalian Institute of Chemical PhysicsChinese Academy of SciencesDalian 116023China

Lead-free double perovskite nanocrystals(NCs)have emerged as a promising candidate in the optical field,owing to their non-toxic,good moist heat and chemical ***,their poor optical properties limited their *** improve the optical properties of lead-free double perovskite NCs,metal ion doping or alloying had been suggested as a promising ***,we prepared monodisperse,uniformly sized,cubic morphology of Cs_(2)AgBiCl_(6)NCs with different Na^(+)incorporation amounts via a simple hot-injection *** Na^(+)incorporation broke the parity-forbidden transition by reducing the inversion symmetry of the electron wave function at the Ag site,which changed the parity of the self-trapped exciton wave function and thus allowed radiative *** a result,the photoluminescence quantum yield(PLQY)of Na^(+)-alloyed Cs_(2)AgBiCl_(6)NCs(12.1%)was higher than that of Cs_(2)AgBiCl_(6)NCs(2.4%),and the exciton lifetime of Na^(+)-alloyed Cs_(2)AgBiCl_(6)NCs increased to 36.98 ns from 17.58 ns for Cs_(2)AgBiCl_(6)*** adjusting the amount of Na^(+)incorporation,the band gap of Cs_(2)AgBiCl_(6)NCs can be significantly tuned from~2.90 eV to~3.50 ***,the temperature-dependent photoluminescence spectra indicated that the Na^(+)-alloyed Cs_(2)AgBiCl_(6)NCs possessed higher longitudinal optical phonon energy and exciton binding energy compared to Cs_(2)AgBiCl_(6)*** suggested that there were strong exciton-phonon interactions during exciton recombination,a reduced probability of non-radiative processes,and excellent thermal *** offers a promising strategy for improving the optical properties of lead-free double perovskite NCs,and have the potential to replace traditional lead halide perovskite NCs in future optoelectronic applications.

关键词： Nanocrystals Alloy Double perovskites Optical properties Exciton binding energy

Weighted Inequalities in Martingale Spaces

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wuhan university Journal of Natural Sciences 2010年第1期15卷 1-6页

作者： CHEN Wei,liu Peide school of mathematics and statistics,wuhan university,wuhan 430072,hubei,china school of mathematics and statistics Wuhan University Wuhan China

We give a condition on the couple of weights（u,v） for Doob＇s operator to be a bounded one from martingale space Lp（u） to function space Lp（v） .Moreover,we also obtain necessary and sufficient conditions in order that the maximal geometric mean operator is bounded from martingale space Lp（u） to function space Lp（v） or Lp,∞（v） .

关键词： martingale maximal operator maximal geometric mean operator weight

Weak Orlicz space and its applications to the martingale theory

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Science china mathematics 2010年第4期53卷 905-916页

作者： liu PeiDe,HOU YouLiang & WANG MaoFa school of mathematics and statistics,wuhan university,wuhan 430072,china 1. school of mathematics and statistics Wuhan University Wuhan 430072 China

In this paper,the weak Orlicz space wL Φ is introduced and its applications to the martingale theory are *** particular,a series of martingale inequalities including the maximal function inequality in weak Orlicz spaces are established;the relationships between these spaces are ***,the boundedness of several sublinear operators from one weak Orlicz space to another is proved;their vector-valued analogues are also considered.

关键词： weak Orlicz space maximal function martingale space martingale inequality

Consistency of the Estimator of Cumulative Hazard Function in Estimated Pseudo-Partial-Likelihood Approach

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wuhan university Journal of Natural Sciences 2009年第5期14卷 373-377页

作者： liu Yanyan,YUAN Zhongshang school of mathematics and statistics,wuhan university,wuhan 430072,hubei,china school of mathematics and statistics Wuhan University Wuhan 430072 Hubei China

For multivariate failure time with auxiliary covariate information, an estimated pseudo-partial-likelihood estimator under the marginal hazard model with distinguishable baseline hazard has been proposed. However, the asymptotic properties of the corresponding estimated cumulative hazard function have not been studied. In this paper, based on counting process martingale, we use the continuous mapping theorem and Lenglart inequality and prove the consistency of the estimated cumulative hazard function in estimated pseudo-partial-likelihood approach.

关键词： cumulative hazard function pseudo-partial-likeli- hood consistency auxiliary covariate multivariate data validation sample

Atomic Decompositions of Weak Hardy Spaces of B-Valued Martingales

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wuhan university Journal of Natural Sciences 2006年第3期11卷 456-460页

作者： MA Tao liu Peide school of mathematics and statistics Wuhan UniversityWuhan 430072 Hubei China

The atomic decompositions of weak Hardy spaces of Banach-space-valued martingales are given. With the help of the atomic decompositions, some inequalities for B-valued martingales are established in the case 0〈r≤1. Here the results are connected closely with the p-uniform smoothness and q-uniform convexity of Banach spaces which the martingales take values in.

关键词： atomic decomposition weak Hardy space B-valued martingale

Exponential Convergence of Fisher Entropy for Diffusion Processes

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wuhan university Journal of Natural Sciences 2011年第2期16卷 130-132页

作者： liu Wei school of mathematics and statistics Wuhan UniversityWuhan 430072 Hubei China

In this paper, we introduce the definition of Γ-Fisher entropy. For the stochastic differential equation in Rd and the unique invariant probability measure μ, we obtain the exponential convergence of Γ-Fisher entropy with respect to μ under some condition about Γ and the drift b. Moreover, we revisit the exponential convergence of the usual Fisher entropy under the Bakry Emery condition.

关键词： Fisher entropy diffusion processes exponential convergence