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Integrability of the general product Hardy operators on the product Hardy spaces

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Applied Mathematics(A Journal of Chinese Universities) 2012年第2期27卷 225-233页

作者： zhu xiang-rong CHEN Jie-cheng Department of Mathematics Zhejiang Normal UniversityJinhua 321004China

In this paper,we prove that the general product Hardy operators are bounded from the product Hardy space H1n（Rm1×···×Rmn） to L1（R（∑ni=1mi）.

关键词： product Hardy operator product Hardy space atom decomposition.

Some remarks on Wente's inequality and the Lorentz-Sobolev space

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Applied Mathematics(A Journal of Chinese Universities) 2016年第3期31卷 355-361页

作者： zhu xiang-rong CHEN Jie-cheng Department of Mathematica Zhejiang Normal University

In this note we consider Wente＇s type inequality on the Lorentz-Sobolev space. If f∈L^p1,q1（Rn）,G∈L^p2,q2 （Rn） and div G ≡ 0 in the sense of distribution where 1/p1＋1/p2=1/q ＋1/q2=1,1〈p1,p2〈∞, it is known that G. f belongs to the Hardy space H1 and furthermore ‖G· f‖N1≤C‖ f‖Lp1,q1（R2）‖G‖Lp2,q2（R2）Reader can see [9] Section 4 Here we give a new proof of this result. Our proof depends on an estimate of a maximal operator on the Lorentz space which is of some independent interest. Finally, we use this inequality to get a generalisation of Bethuel＇s inequality.

关键词： Lorentz space Wente type inequality Hardy space

Expansion of spherical cavity of strain-softening materials with different elastic moduli of tension and compression

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Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2007年第9期8卷 1380-1387页

作者： LUO Zhan-you zhu xiang-rong GONG Xiao-nan Ningbo Institute of Technology. Zhejiang University Ningbo 315100 China Geotechnical Engineering Institute Zhejiang University of Science and Technology Hangzhou 310012 China Geotechnical Engineering Institute Zhejiang University Hangzhou 310027 China

An expansion theory of spherical cavities in strain-softening materials with different moduli of tension and com-pression was presented. For geomaterials,two controlling parameters were introduced to take into account the different moduli and strain-softening properties. By means of elastic theory with different moduli and stress-softening models,general solutions cal-culating Tresca and Mohr-Coulomb materials' stress and displacement fields of expansion of spherical cavity were derived. The effects caused by different elastic moduli in tensile and compression and strain-softening rates on stress and displacement fields and development of plastic zone of expansion of cavity were analyzed. The results show that the ultimate expansion pressure,stress and displacement fields and development of plastic zone vary with the different elastic moduli and strain-softening prop-erties. If classical elastic theory is adopted and strain-softening properties are neglected,rather large errors may be the result.

关键词： Expansion of spherical cavity Tresca material Mohr-Coulomb material Elastic theory with different moduli of tension and compression Stress-dropping softening model

Static load test and load transfer mechanism study of squeezed branch and plate pile in collapsible loess foundation

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Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2007年第7期8卷 1110-1117页

作者： GAO Xiao-juan WANG Jin-chang zhu xiang-rong College of Civil Engineering and Architecture Zhejiang University Hangzhou 310027 China Institute of Architecture Engineering Henan University of Science and Technology Luoyang 471003 China Ningbo Institute of Technology Zhejiang University Ningbo 315005 China

As a special geological phenomenon, the character of collapsible loess foundation is collapsible when penetrated by water. This character leads to the soil losing load bearing capacity largely and may lead to foundation failure. Pile is a popular foundation used in collapsible loess. The squeezed branch and plate pile is a new type of pile developed in recent years and has not be used in a project before. In this paper three squeezed branch and plate piles are tested in collapsible loess after immersion processing. The results may be used for reference in similar construction project, and to provide theoretical references for de- signing of the squeezed branch and plate piles in engineering practice.

关键词： Collapsible loess foundation Squeezed branch and plate pile Immersion processing Full-scale static load test

Rearrangement and the weighted logarithmic Sobolev inequality

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Applied Mathematics(A Journal of Chinese Universities) 2021年第2期36卷 207-217页

作者： JIANG Ming-hong RUAN Jian-miao zhu xiang-rong Department of Mathematics Zhejiang Normal UniversityJinhua 321004China Department of Mathematics Zhejiang International Studies UniversityHangzhou 310014China

Here we consider some weighted logarithmic Sobolev inequalities which can be used in the theory of singular Riemanian *** give the necessary and sufficient conditions such that the 1-dimension weighted logarithmic Sob... 详细信息

关键词： rearrangement singular Riemannian manifold weighted logarithmic Sobolev inequality

Boundedness of Hausdorff operators on the power weighted Hardy spaces

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Applied Mathematics(A Journal of Chinese Universities) 2017年第4期32卷 462-476页

作者： CHEN Jie-cheng HE Shao-yong zhu xiang-rong Department of Mathematics Zhejiang Normal University Jinhua 321004 China

In this paper, we consider the two-dimensional Hausdorff operators on the power weighted Hardy space H;（R;）（ -1 ≤α≤0）, defined by H;f（x）=∫R;Φ（u）f(A（u）x)du,where Φ∈L;oc;（R;）,A（u） = (α;（u）);is a 2×2 matrix, and each α;is a *** obtain that HΦ,A is bounded from H;（R;）（ -1≤α≤0） to itself, if∫R2|Φ（u）‖det A;（u）|‖A（u）‖;ln(1+‖A;（u）‖;/|det A;（u）|)du<∞.This result improves some known theorems, and in some sense it is sharp.

关键词： Hausdorff operator Hardy space power weight

Gibson土体内部作用沿深度分布简谐荷载的基本解

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浙江大学学报（工学版） 2006年第7期40卷 1234-1238页

作者：杜秦文朱向荣浙江大学岩土工程研究所

采用Hankel积分变换方法,研究了Gibson地基土体的Lamb问题,通过构造复平面上的积分围道技术,对解沿深度进行积分,利用对围道上奇点的处理方法,以消除驻波相来满足实际波的辐射条件,得到了沿深度不变、沿深度增加和沿深度减小等3种沿分... 详细信息

采用Hankel积分变换方法,研究了Gibson地基土体的Lamb问题,通过构造复平面上的积分围道技术,对解沿深度进行积分,利用对围道上奇点的处理方法,以消除驻波相来满足实际波的辐射条件,得到了沿深度不变、沿深度增加和沿深度减小等3种沿分布线荷载作用下,地基土体竖向位移的积分形式解.通过对沿深度均匀分布线荷载作用下的具体数值算例,分析了地基土体的非均质性、荷载频率以及分布深度等因素对地基土体表面竖向位移的影响.结果表明,在低频荷载作用下,地基土体的非均质性对其表面位移有较大影响.

关键词： Gibson地基简谐荷载动力响应

面层与基层层间摩擦系数对应力强度因子影响的研究

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岩石力学与工程学报 2005年第15期24卷 2757-2764页

作者：王金昌朱向荣浙江大学土木工程系浙江杭州310027

开裂为沥青混凝土路面中存在的主要问题。基于线弹性断裂力学理论,采用ABAQUS软件中的平面应变单元法,分别分析了变温作用下裂缝的长度、面层与基层层间摩擦系数态对含表面裂缝和含反射沥青混凝土路面的应力强度因子分布规律的影响。得... 详细信息

开裂为沥青混凝土路面中存在的主要问题。基于线弹性断裂力学理论,采用ABAQUS软件中的平面应变单元法,分别分析了变温作用下裂缝的长度、面层与基层层间摩擦系数态对含表面裂缝和含反射沥青混凝土路面的应力强度因子分布规律的影响。得出了含表面裂缝和反射裂缝路面体的应力强度因子均随着裂缝长度的增加逐渐增大。表面裂缝裂尖位于面层中时,应力强度因子随着摩擦系数的增加而逐渐减小;裂尖位于基层中时,应力强度因子随着摩擦系数的增加而逐渐增大。反射裂缝裂尖位于基层中时,应力强度因子随着摩擦系数的增加而减小;反射裂缝裂尖位于面层中且长度小于某一值时,应力强度因子随着摩擦系数的增加而增大;反射裂缝裂尖位于面层中且裂缝长度大于某一值时,应力强度因子随着摩擦系数的增加而减小。

关键词：道路工程沥青混凝土路面应力强度因子有限单元法表面裂缝反射裂缝变温摩擦

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应用简帛文献解读传世经典文献的三点思考

社会科学家 2008年第10期23卷 47-49页

作者：朱湘蓉陕西师范大学文学院陕西西安710062

本文对简帛文献在传世经典文献解读中的应用进行了思考,提出:一、简帛文献的作用不仅在于提供了版本对比研究,更在于丰富了文献类型,能够更清晰完整地勾勒出当时的历史文化背景,而许多问题在这样的历史文化背景之下可以得到解决。二、... 详细信息

本文对简帛文献在传世经典文献解读中的应用进行了思考,提出:一、简帛文献的作用不仅在于提供了版本对比研究,更在于丰富了文献类型,能够更清晰完整地勾勒出当时的历史文化背景,而许多问题在这样的历史文化背景之下可以得到解决。二、充分发挥简帛文献的作用,就要多学科、多角度、多重证据、多种方法相结合。三、对简帛文献的作用不可夸大。

关键词：简帛文献传世经典文献解读