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Riemann-Hilbert problem for first order complex equations of mixed type with degenerate curve

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Applied Mathematics(A Journal of Chinese Universities) 2010年第3期25卷 253-263页

作者： WEN guo-chun School of Mathematical Sciences Peking University Beijing 100871 China

This paper considers the Riemann-Hilbert problem for linear mixed（elliptichyperbolic） complex equations of first order with degenerate curve in a simply connected domain. We first give the representation theorem and uniqueness of solutions for such boundary value problem. Then by using the methods of successive iteration and parameter extension, the existence of solutions for this problem is proved.

关键词： Riemann-Hilbert problem mixed complex equations of first order degenerate curve.

The Tricomi and Frankl Problems for Generalized Chaplygin Equations in Multiply Connected Domains

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Acta Mathematica Sinica,English Series 2008年第11期24卷 1759-1774页

作者： guo chun WEN LMAM School of Mathematical Sciences Peking University Beijing 100871 P. R. China

The present paper deals with Tricomi and Frankl problems for generalized Chaplygin equations in multiply connected domains. We first give the representation of solutions of the Tricomi problem for the equations, and then prove the uniqueness and existence of solutions for the problem by a new method, i.e. the complex functions in the elliptic domain and the hyperbolic complex functions in hyperbolic domain are used. Finally we discuss the Frankl problem for generalized Chaplygin equations in multiply connected domains.

关键词： Tricomi and Frankl problems generalized Chaplygin equations multiply connected domains

The Exterior Tricomi Problem for Generalized Mixed Equations with Parabolic Degeneracy

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Acta Mathematica Sinica,English Series 2006年第5期22卷 1385-1398页

作者： guo chun WEN LMAM School of Mathematical Sciences Peking University Beijing 100871 P. R. China

This paper deals with the exterior Tricomi problem for generalized mixed equations with parabolic degeneracy. Firstly the representation of solutions of the problem for the equations is given, and then the uniqueness ... 详细信息

关键词： Exterior Tricomi problem Equations of mixed type Doubly connected domain

Oblique Derivative Problems for Second Order Nonlinear Equations of Mixed Type with Degenerate Hyperbolic Curve

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Acta Mathematica Sinica,English Series 2011年第10期27卷 2051-2064页

作者： guo chun WEN LMAM School of Mathematical Sciences Peking University Beijing 100871 P. R. China

The present paper deals with oblique derivative problems for second order nonlinear equa- tions of mixed type with degenerate hyperbolic curve, which include the Tricomi problem as a special case. Firstly the formulation of the problems for the equations is given, next the representation and estimates of solutions for the above problems are obtained, finally the existence of solutions for the problems is proved by the successive iteration of solutions of the equations and the fixed-point princi- ple. In this paper, we use the complex analytic method, namely the new partial derivative notations, elliptic complex functions in the elliptic domain and hyperbolic complex functions in the hyperbolic domain are introduced, such that the second order equations of mixed type with degenerate curve are reduced to the first order mixed complex equations with singular coefficients, and then the advantage of complex analytic method can be applied.

关键词： Oblique derivative problems nonlinear mixed equations degenerate hyperbolic curve

The Riemann-Hilbert Problem for Mixed Complex Equations of First Order with Degenerate Rank 0

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Acta Mathematicae Applicatae Sinica 2015年第1期31卷 31-42页

作者： guo-chun WEN LMAM School of Mathematical Sciences Peking University

This article deals with the Riemann-Hilbert boundary value problem for quasilinear mixed （elliptic- hyperbolic） complex equations of first order with degenerate rank 0. Firstly, we give the representation theorem and prove the uniqueness of solutions for the boundary value problem. Afterwards, by using the method of successive iteration, the existence and estimates of solutions for the boundary value problem are verified. The above problem possesses the important applications to the Tricomi problem of mixed type equations of second order. In this article, the proof of HSlder continuity of a singular double integer is very difficult and interesting as in this Section 4 below.

关键词： Riemann-Hilbert problem quasilinear mixed complex equations degenerate rank 0 unique solv-ability of the problem HSlder continuity of singulax double integer

HSM strategy study for hardened die and mold steels manufacturing based on the mechanical and thermal load reduction strategy

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Journal of University of Science and Technology Beijing 2008年第6期15卷 723-728页

作者： ying Tang Hongsheng guo School of Mechanical Engineering University of Science and Technology Beijing Beijing 100083 China Research Institute Beijing No.1 Machine Tool Plant Beijing 101300 China

The paper discussed cutter-work engagement situation hidden behind the mechanical and thermal load effect on cutting edges during high speed hard machining process. The engagement situation was investigated in great detail using experimental and geometrical analytic measures. Experiments were conducted using A1TiN-coated micro-grain carbide end mill cutters to cut hardened die steel. On the basis, a general high speed hard machining strategy, which aimed at eliminating excessive engagement situation during high-speed machining （HSM） hard machining, was proposed. The strategy includes the procedures to identify prone-to-overload areas where excessive engagement situation occurs and then to create a reliable tool path, which has the effect of cutting load reduction to remove the prone-to-overload areas.

关键词： high-speed machining (HSM) hard machining die/mold manufacturing tool path generation load reduction

杉木目测等级规格材足尺抗弯强度的设计值研究

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西部林业科学 2017年第3期46卷 23-27页

作者：龚迎春武国芳王朝辉骆秀琴任海青中国林业科学研究院木材工业研究所北京100091

依据国标GB 50329-2002对杉木规格材进行足尺的抗弯测试,选取正态分布对测试数据进行拟合,利用K-S检验对正态分布进行拟合优度检验,参照极限状态设计法和ASTM D2915-2010标准计算杉木规格材设计值。结果表明,No.1等级规格材的抗弯强度最... 详细信息

依据国标GB 50329-2002对杉木规格材进行足尺的抗弯测试,选取正态分布对测试数据进行拟合,利用K-S检验对正态分布进行拟合优度检验,参照极限状态设计法和ASTM D2915-2010标准计算杉木规格材设计值。结果表明,No.1等级规格材的抗弯强度最小;SS、No.1和No.2等级规格材抗弯强度的测试数据均能与正态分布拟合;SS、No.1和No.2等级抗弯强度设计参考值分别为11.01MPa、9.36MPa和9.03MPa。

关键词：杉木规格材抗弯强度设计值

Lateral growth rate of δ phase during solidification of Fe-0.15wt%C-0.8wt%Mn steel

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International Journal of Minerals,Metallurgy and Materials 2012年第4期19卷 312-316页

作者： guo-wei Chang Shu-ying Chen Qing-chun Li Xu-dong Yue Guang-can Jin School of Materials Science and Engineering Liaoning University of Technology Jinzhou 121001 China

Taking Fe-0.15wt%C-0.8wt%Mn steel as the research object, in situ observations of the 8 phase growth process during solidifica- tion were conducted by using a high-temperature confocal scanning laser microscope （HTCSLM）. The effects of the solid/liquid （S/L） inter- face＇s shape, temperature, and curvature radius on the lateral growth rate of 6 phase were investigated in detail, and the relational expression among the lateral growth rate of 5 phase, temperature, and curvature radius of column-shaped ~ phase was deduced for the carbon steel dur- ing solidificatiorL The results indicate the growth rate of the concave-shaped S/L interface is larger than that of the convex-shaped S/L inter- face during the beginning growth of ~ phase, but these two kinds of growth rates gradually approach with proceeding in solidification. The calculated lateral growth rate of 6 phase is consistent with the experimental result at a cooling rate of 0.045℃/s.

关键词： carbon steel solidification ferrite growth rate interfaces

Research of {0001} crystal orientation for magnesium alloys solidified in a fashion of cellular crystals

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International Journal of Minerals,Metallurgy and Materials 2012年第2期19卷 136-140页

作者： guo-wei Chang Shu-ying Chen Qing-chun Li Xu-dong Yue Yi-hui Qi School of Materials Science and Engineering Liaoning University of TechnologyJinzhou 121001China

The magnesium alloy grew in a fashion of cellular crystals during the process of unidirectional solidification, and the {0001} crystal face orientation in the cast ingot of the magnesium alloy was studied. The theoretical model and methodology were set up, and a cor-responding experiment was carried out to verify the theoretical analysis results. The experimental results indicate that the {0001} crystal face of magnesium crystals parallels to the width direction for the thin-plate cast ingot when the magnesium grows in a manner of cellular crystals. The separation angle between the {0001} crystal face of magnesium crystals and the vertical axis line of the cast ingot is about 62° for the circular column cast ingot, which distributes in cone-type. The theoretical analysis results are basically in agreement with the experimental ones of previous literatures and this paper.

关键词： magnesium alloys solidification crystal growth crystal faces