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The evolution and morphological stability of a spherical crystal

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Science china(Technological Sciences) 2008年第3期51卷 225-243页

作者： CHEN MingWen1,2, WANG ZiDong2 & XU JianJun3,4.1 school of Applied Sciences, university of Science and Technology Beijing, Beijing 100083, china 2 school of Materials Science and Engineering, university of Science and Technology Beijing, Beijing 100083, china 3 school of Mathematical Sciences, Nankai university, Tianjin 300071, china 4.Department of mathematics and statistics, McGill university, Montreal H3A 2K6, Canada 1. school of Applied Sciences University of Science and Technology Beijing Beijing 100083 China 2. school of Materials Science and Engineering University of Science and Technology Beijing Beijing 100083 China 3. school of Mathematical Sciences Nankai University Tianjin 300071 China 4. Department of mathematics and statistics McGill University Montreal H3A 2K6 Canada

The growth model of a spherical crystal in the undercooled melt including the surface energy, interfacial kinetics and convective flow is established. The effect of the convective flow induced by a small far field flow on the evolution and morphological stability of the interface of the spherical crystal is studied. The interface shape of the spherical crystal, which is affected by the far field flow, and the dispersion relation of the growth rate of amplitude of the perturbed interface are derived. It is shown that the convection induced by the far field flow makes the interface of the growing spherical crystal further grow in the upstream direction of the far field flow and inhibit growth in the downstream direction; the interface of the decaying spherical crystal further decays in the upstream direction and inhibits decay in the downstream direction. The theoretical result suggests that both the growth of the sphere in the upstream direction and the decay of the sphere in the downstream direction make the spherical crystal tend to evolve into an oval; the morphological stability of the interface depends on a certain radius R c such that the spherical crystal is unstable when its radius is greater than R c and stable when its radius is less than R c . The surface energy and interfacial kinetics have strong stabilizing effects on the growth of the spherical crystal. In the meantime interfacial kinetics is a table factor of the interface when the interface of the sphere is growing; it is an unstable factor of the interface when the interface is decaying.

关键词： solid-liquid interface spherical crystal convective flow crystal growth morphological stability

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 university, Jinan 250100, china Department of statistics and {4., Shandong finance Institute, Jinan 250014. china. school of Computer Science and Technology, Shandong university, Jinan 250100, china Department of {4., Qufu Normal university, Qufu 273165, 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 13/15 〈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

An isoperimetric deficit upper bound of the convex domain in a surface of constant curvature

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Science china mathematics 2010年第8期53卷 1941-1946页

作者： LI Ming & ZHOU JiaZu school of mathematics and statistics,Southwest university,Chongqing 4.0715,{4. 1. school of mathematics and statistics Southwest University Chongqing 400715 China

In this paper,we give a reverse analog of the Bonnesen-style inequality of a convex domain in the surface X of constant curvature,that is,an isoperimetric deficit upper bound of the convex domain in *** result is an a... 详细信息

关键词： Kinematic formula the surface of constant curvature isoperimetric deficit convex set

Carleson Measures on Planar Sets

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Acta Mathematica Sinica,English Series 2009年第11期25卷 1881-1892页

作者： Zhijian QIU school of mathematics,Southwestern university of finance and Economics,Chengdu 610074.P. R. {4. school of mathematics Southwestern University of Finance and Economics Chengdu 610074 P. R. China

In this paper, we investigate what are Carleson measures on open subsets in the complex plane. A circular domain is a connected open subset whose boundary consists of finitely many disjoint circles. We call a domain G multi-nicely connected if there exists a circular domain W and a conformal map ψ from W onto G such that ψ is almost univalent with respect the arclength on δW. We characterize all Carleson measures for those open subsets so that each of their components is multinicely connected and harmonic measures of the components are mutually singular. Our results suggest the extension of Carleson measures probably is up to this class of open subsets

关键词： Carleson measure circular domain harmonic measure multi-nicely connected domain

Non-Homogeneous Riemann Boundary Value Problem with Radicals

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Wuhan university Journal of Natural Sciences 2002年第4期7卷 379-382页

作者： Lu Jian-ke school of mathematics and statistics,Wuhan university,Wuhan 4.0072, Hubei,{4. Wuhan university School of Mathematics and Statistics Wuhan Hubei China (GRID:grid.49470.3e) (ISNI:***)

The solution of the non-homogeneous Riemann boundary value problem with radicals (1. 2) together with its condition of solvability is obtained for arbitrary positive integersp andq, which generalizes the results for t... 详细信息

关键词： Riemann boundary value problem branch points of radicals index order at infinity sectionally holomorphic functions

Criteria for Regularity of Elliptic Diffusion Processes and It’s Application

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Wuhan university Journal of Natural Sciences 2005年第2期10卷 347-350页

作者： LI Bo 1,2 , ZHANG Xiao-min 3 1.school of mathematics and statistics,Huazhong Normal university,Wuhan 4.0079,Hubei,{4. 2.school of mathematics and statistics, Wuhan university, Wuhan 4.0072, Hubei, {4. 3.Faculty of Science,Ningbo university,Ningbo 315211,Zhejiang, {4. Huazhong Normal university School of Mathematics and Statistics Wuhan Hubei China (GRID:grid.411407.7) (ISNI:***) Wuhan university School of Mathematics and Statistics Wuhan Hubei China (GRID:grid.49470.3e) (ISNI:***) Ningbo university Faculty of Science Ningbo Zhejiang China (GRID:grid.203507.3) (ISNI:***)

The cone condition for x to be tegular for B under the elliptic diffusionprocess was proved. We also gave a necessary and sufficient condition for 0 to be regular for thornunder the elliptic diffusion process.

关键词： regular capacity thorn diffusion process

The construction of Markov processes in random environments and the equivalence theorems

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Science china mathematics 2004年第4期47卷 481-496页

作者： HU Diheschool of mathematics and statistics, Wuhan university, Wuhan 4.0072, {4. 1. school of mathematics and statistics Wuhan University 430072 Wuhan China

In sec.1, we introduce several basic concepts such as random transition function, p-m process and Markov process in random environment and give some examples to construct a random transition function from a non-homogeneous density function. In sec.2, we construct the Markov process in random enviromment and skew product Markov process by p - m process and investigate the properties of Markov process in random environment and the original process and environment process and skew product process. In sec. 3, we give several equivalence theorems on Markov process in random environment.

关键词： radom transition function, p -m process, Markov process in random environment, skew product Markov process, density function.

Adaptive quasi-likelihood estimate in generalized linear models

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Science china mathematics 2005年第6期48卷 829-846页

作者： CHEN Xia & CHEN Xiru school of mathematics and statistics, Wuhan university, Wuhan 4.0072, {4. Graduate school, Chinese Academy of Science, Beijing 10004., {4. 1. school of mathematics and statistics Wuhan University 430072 Wuhan China 2. Graduate school Chinese Academy of Science 100049 Beijing China

This paper gives a thorough theoretical treatment on the adaptive quasilikelihood estimate of the parameters in the generalized linear models. The unknown covariance matrix of the response variable is estimated by the sample. It is shown that the adaptive estimator defined in this paper is asymptotically most efficient in the sense that it is asymptotic normal, and the covariance matrix of the limit distribution coincides with the one for the quasi-likelihood estimator for the case that the covariance matrix of the response variable is completely known.

关键词： generalized linear models, quasi likelihood estimate, adaptive estimate.

Commission Strategy of the Auction House

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Wuhan university Journal of Natural Sciences 2006年第3期11卷 507-510页

作者： WANG Yan~ 1,2 1. College of Economics, Fudan university, Shanghai 2004.3, china 2. school of mathematics and {4., Wuhan university , Wuhan 4.0072, Hubei, china College of Economics Fudan University 200433 Shanghai China school of mathematics statistics Wuhan University 430072 Wuhan Hubei China

In a SIPV model, when the commission proportion is not certain, but related with bargain price, generally, it is a linear function of the bargain price, this paper gives bidders＇ equilibrium bidding strategies in the first-and secondprice auctions. We find that the equilibrium strategies in second-price auction are dominant strategies. For seller or auction house, whether the fixed proportion or the unfixed proportion is good is not only related with constant item and the linear coefficient of the linear function, the size of the fixed commission proportion, but also related with the value of the item auctioned. So, in the practical auctions, the seller and the auction house negotiated with each other to decide the commission rules for their own advantage.

关键词： auction commission proportion Bayesian equilibrium bidding strategy