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Cavitation bubbles collapse characteristics behind a convex body

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Journal of Hydrodynamics 2013年第6期25卷 886-894页

作者：李瑶许唯临张亚磊张敬威陈春祺阿蓉 State Key Laboratory of Hydraulics and Mountain River Engineering Sichuan University

Cavitation bubbles behind a convex body were experimentally studied by a high speed camera and a hydrophone synchronously. The experiments were conducted in a circulating water tunnel with five various contraction ratios： β = 0.497, β= 0.6, β= 0.697, β= 0.751, and β= 0.799. The distributions of the cavitation bubble collapse positions behind the five different convex bodies were obtained by combining the images taken by the high speed camera. According to the collapse positions, it was found that no cavitation bubble was collapsed in the region near the wall until the ratio of the water head loss over the convex body height was larger than 20, which can be used to predict if the cavitation damage would occur in the tunnel with orifice energy dissipaters.

关键词： convex body cavitation bubble collapse high speed camera cavitation noise

ON MEAN CURVATURES OF A PARALLEL convex body

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Acta Mathematica Scientia 2008年第3期28卷 489-494页

作者：周家足姜德烁 School of Mathematics and Statistics Southwest University School of Mathematics and Statistics Wuhan University

In this article, we obtain some results about the mean curvature integrals of the parallel body of a convex set in R^n. These mean curvature integrals are generalizations of the Santalo＇s results.

关键词： convex body parallel body mean curvature quermassintegrale

Measure of Segments which Intersect a convex body from Rotational Formulae

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Acta Mathematica Sinica,English Series 2015年第2期31卷 345-352页

作者： Ximo GUAL-ARNAU Silena HEROLD-GARCA Departament de Matemàtiques-INIT Universitat Jaume I. 12071-CastellSpain Departamento de Computacin Universidad de Oriente. 90900-Santiago de CubaCuba

Classical problems in integral geometry and geometric probability involve the kinematic measure of congruent segments of fixed length within a convex body in R3. We give this measure from rotational formulae; that is, from isotropic plane sections through a fixed point. From this result we also obtain a new rotational formula for the volume of a convex body; which is proved to be equivalent to the wedge formula for the volume.

关键词： convex body flower integral geometry stereology rotational formulae segment supportset

Continuity of the Solution to the L_(p) Minkowski Problem in Gaussian Probability Space

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Acta Mathematica Sinica,English Series 2022年第12期38卷 2253-2264页

作者： He Jun WANG School of Mathematics and Statistics Shandong Normal UniversityJi'nan 250358P.R.China

In this paper,it is proved that the weak convergence of the L_(p) Gaussian surface area measures implies the convergence of the corresponding convex bodies in the Hausdorff metric for p≥1.Moreover,continuity of the s... 详细信息

关键词： L_(p)Gaussian Minkowski problem L_(p)Gaussian surface area measure continuity convex body

Complex-Valued Valuations on L^(p) Spaces

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Wuhan University Journal of Natural Sciences 2022年第1期27卷 35-41页

作者： LIU Lijuan School of Mathematics and Computational Science Hunan University of Science and TechnologyXiangtan 411201HunanChina

All continuous translation invariant complex-valued valuations on Lebesgue measurable functions are completely classified.And all continuous rotation invariant complex-valued valuations on spherical Lebesgue measurabl... 详细信息

关键词： convex body valuation translation invariance rotation invariance

The Non-Convergence of Steiner Symmetrizations

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Wuhan University Journal of Natural Sciences 2023年第3期28卷 217-220页

作者： WANG Tian LIN Youjiang School of Mathematics and Statistics Chongqing Technology and Business UniversityChongqing 400067China

In this paper,we demonstrate the existence of iterated Steiner symmetrizations of K that does not converge,even if the sequence of directions is dense in the unit sphere.

关键词： convex body compact set Steiner symmetrization non-convergence

RECONSTRUCTING TRIANGLES INSCRIBED IN convex BODIES FROM X-RAY FUNCTIONS

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Acta Mathematica Scientia 2004年第4期24卷 608-612页

作者：熊革李德宜 Department of Mathematics Shanghai University Shanghai 200436 China Department of Mathematics Wuhan University of Science and Technology Wuhan 430081 Chinahis paper provides a method using fixed-point theory for the reconstruction of the triangle inscribed in convex bodies from X-ray functions in three arbitrary mutual directions.

This paper provides a method using fixed-point theory for the reconstruction of the triangle inscribed in convex bodies from X-ray functions in three arbitrary mutual directions.

关键词： convex body X-ray reconstruction

Quasi-Shephard's Problem on Projections of convex Bodies

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Wuhan University Journal of Natural Sciences 2014年第1期19卷 55-61页

作者： MA Tongyi ZHANG Lili College of Mathematics and Statistics Hexi University College of Mathematics and Statistics Northwest Normal University

In this paper, we develop a Fourier analytic approach to study the problem in the Brunn-Minkowski-Firey theory of convex bodies. We formulate and solve a quasi-Shephard＇s problem on projections of convex bodies.

关键词： convex body projection body the Shephard＇s problem Fourier transform

Asymptotic properties of two affine invariants for 1-unconditional convex bodies

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Journal of Shanghai University(English Edition) 2010年第3期14卷 223-227页

作者：谢富生何斌吾易军 Department of Mathematics College of SciencesShanghai University Basic Education Department Tianhua College of Shanghai Normal University

Let K be a 1-unconditional convex bodies in Euclidean spaces.We study the asymptotic properties of two affine invariants m2（K） and S2（K） for a random simplex inside K.As an application,we discuss the asymptotic pr... 详细信息

关键词： convex body 1-unconditional convex body isotropic constant Sylvester’s problem random simplex