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Oscillatory integrals for phase functions having certain degenerate critical points

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Science China Mathematics 2008年第3期51卷 474-480页

作者： Jinmyong KIM Department of Mathematics.Huazhong University of Science and Technology

The paper is concerned with oscillatory integrals for phase functions having certain de- generate critical points. Under a finite type condition of phase functions we show the estimate of oscillatory integrals of the first kind. The decay of the oscillatory integral depends on indices of the finite type, the spatial dimension and the symbol.

关键词： oscillatory integral phase function finite type 42B10

Multiple scattering of light by water cloud droplets with external and internal mixing of black carbon aerosols

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Chinese Physics B 2012年第5期21卷 241-246页

作者：王海华孙贤明 School of Electrical and Electronic Engineering Shandong University of Technology

The mixture of water cloud droplets with black carbon impurities is modeled by external and internal mixing *** internal mixing model is modeled with a two-layered sphere（water cloud droplets containing black carbon（BC） inclusions）,and the single scattering and absorption characteristics are calculated at the visible wavelength of 0.55 μm by using the Lorenz-Mie *** external mixing model is developed assuming that the same amount of BC particles are mixed with the water droplets *** multiple scattering characteristics are computed by using the Monte Carlo *** results show that when the size of the BC aerosol is small,the reflection intensity of the internal mixing model is bigger than that of the external mixing ***,if the size of the BC aerosol is big,the absorption of the internal mixing model will be larger than that of the external mixing model.

关键词： aerosols multiple scattering Monte Carlo method phase function

Aerosol optical properties derived from simultaneous sunphotometer and aureolemeter measurements in Lhasa

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Journal of Environmental Sciences 2000年第4期12卷 439-443页

作者： BAI Yu-bo SHI Guang-yu Koichi Tamura Takashi Shibata Yasunobu Iwasaka Kaneta Shin′ichi Takamura Tamio State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics Inst itute of Atmospheric PhysicsChinese Academy of SciencesBeijing 100029China Solar Terrestrial Environment Laboratory Nagoya UniversityNagoyaJapan Center for Environmental Remote Sensing Chiba UniversityChibaJapan

In order to obtain some aerosol properties in Tibetan Plateau atmosphere, simultaneous measurements of aerosols by use of a sunphotometer and an aureolementer were performed in the summer of 1998 in Lhasa(29.65°N, 91.13°E). Optical depth, volume size distribution and phase\|function of aerosols were obtained from the measurements. Religious activities can have an effect on optical depth in Lhasa. The daily average aerosol optical depth( λ =500 nm) is less than 0.2. The diurnal variations of aerosol optical depth are relatively small during the period of summer. The maximal value of the mode radius in the volume size distribution are about 0.4, 2.0 and 4.0μm.

关键词： sunphotometer aureolemeter optical depth aerosol volume spectrum phase function

Real-Time Rendering of Dynamic Clouds Using Multi-Resolution Adaptive Grids

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Transactions of Nanjing University of Aeronautics and Astronautics 2015年第4期32卷 428-437页

作者：范晓磊张立民钟兆根 Department of Electronics and Information Engineering Naval Aeronautical and Astronautical University Noncommissioned Officers Vocational and Technical Education College the Second Artillery Engineering University Department of Scientific Research Naval Aeronautical and Astronautical University

The multi-resolution adaptive grids method is proposed to solve the problems of inefficiency in the previous grid-based methods,and it can be used in clouds simulation as well as the interactive simulation between objects and *** bounding box(OBB)hierarchical trees of objects are established,and the resolutions of global and local grids can be selected *** motion equations of fluid dynamics are *** difference is applied to ensure the stability of the simulation process during the discrete process of partial differential *** solve the speed problem of existed phase functions,the improved phase function is applied to the illumination calculation of *** results show that the proposed methods can promote the simulation efficiency and meet the need for the simulation of large-scale clouds ***-time rendering of clouds and the interaction between clouds and objects have been realized without preprocessing stage.

关键词： real-time rendering multi-resolution adaptive grids clouds simulation phase function

THE ENDPOINT ESTIMATE FOR FOURIER INTEGRAL OPERATORS

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Acta Mathematica Scientia 2021年第2期41卷 426-436页

作者： Guangqing WANG Jie YANG Wenyi CHEN School of Mathematics and Statistics Wuhan UniversityWuhan 430072China College of Mathematics and System Science Xinjiang UniversityXinjiang 830046China

Let T_(a,φ)be a Fourier integral operator defined by the oscillatory integral T_(a,φ)u(x)=1/(2π)^(n)∫_(R^(n))^e^(iφ(x,ξ))a(x,ξ)(u)(ξ)dξ,where a∈S_(e,δ)^(m)andφ∈Φ^(2),satisfying the strong non-degenerate *** is shown that if0<(e)≤1,0≤δ<1 and m≤e^(2)-n/2,thenT_(α,φ)is a bounded operator from L^(∞()R^(n))to BMO(R^(n)).

关键词： Fourier integral operators phase function BMO spaces

Three-Dimensional Radiation in Absorbing-Emitting Scattering Medium Using the Discrete-OrdinatesApproximation

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Journal of Thermal Science 1998年第4期7卷 255-263页

作者： Xiao-Lin Wei Tong-Mo Xu Shi-En Hui Institute of Mechanics Chinese Academy of Sciences Beijing China Department of Thermal Engineering Xi’an Jiaotong University China

The discrete-ordinates method is a simple, accurate and of little computational time solution to predict the radiative heat transfer in the combustion chambers. In this paperl three-dimension radiative problems for absorbing-emitting-scattering medium are modeled using this method in the rectangular enclosure. And in addition, new discrete-ordinates are developed to study the absorbing-emitting-scattering radiation processes for complex phase function. The reasonable results can be obtained through these new ordinates, yet the deviated results are only obtained through conventional Sn ordinates.

关键词： radiation discrete-ordinates method phase function

STABILITY STUDY OF AN UNSTEADY OSCILLATION FLOW

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Applied Mathematics and Mechanics(English Edition) 1996年第3期17卷 281-294页

作者：王发民赵烈于欣 Institute of Mechanics. Academia Sinica Beijing Peoples Republic of China

In ihis *** instability problem of an unsteady oscillationo flow is *** particultar,the *** of the disturbance *** is soived by using the charocteristic theory of partial differential equation and an expansion of Orysommerfeid eigenvalue *** of using the disturbance model which is given previously *** considered is a combination of plane *** with aflow oscillating periodically and its instability is found for a special initial value of a developing wave due to continuous oscillationg source.

关键词： Charpsits method phase function Pfaffian equation instability through flow