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Assessment of Point and Nonpoint Sources Pollution in Songhua River Basin,Northeast China by Using Revised Water Quality Model 被引量:14
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作者 YANG Yuhong YAN Baixing SHEN Wanbin 《Chinese Geographical Science》 SCIE CSCD 2010年第1期30-36,共7页
Individual participation of pollutants in the pollution load should be estimated even if roughly for the appropriate environmental management of a river basin.It is difficult to identify the sources and to quantify th... Individual participation of pollutants in the pollution load should be estimated even if roughly for the appropriate environmental management of a river basin.It is difficult to identify the sources and to quantify the load, especially in modeling nonpoint source.In this study a revised model was established by integrating point and nonpoint sources into one-dimensional Streeter-Phelps(S-P) model on the basis of real-time hydrologic data and surface water quality monitoring data in the Jilin Reach of the Songhua River Basin.Chemical oxygen demand(COD) and ammonia nitrogen(NH 3-N) loads were estimated.Results showed that COD loads of point source and nonpoint source were 134 958 t/yr and 86 209 t/yr, accounting for 61.02% and 38.98% of total loads, respectively.NH 3-N loads of point source and nonpoint source were 16 739 t/yr and 14 272 t/yr, accounting for 53.98% and 46.02%, respectively.Point source pollution was stronger than nonpoint source pollution in the study area at present.The water quality of upstream was better than that of downstream of the rivers and cities.It is indispensable to treat industrial wastewater and municipal sewage out of point sources, to adopt the best management practices to control diffuse pollutants from agricultural land and urban surface runoff in improving water quality of the Songhua River Basin.The revised S-P model can be successfully used to identify pollution source and quantify point source and nonpoint source loads by calibrating and validating. 展开更多
关键词 ammonia nitrogen chemical oxygen demand nonpoint source pollution point source pollution revised water quality model Songhua River Basin
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Cross-Correlation Detection of Point Sources in the WMAP First Year Data
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作者 Jian-Yin Nie Shuang-Nan Zhang 《Chinese Journal of Astronomy and Astrophysics》 CSCD 2007年第2期199-208,共10页
We apply a Cross-Correlation (CC) method developed previously for detecting gamma-ray point sources to the WMAP first year data by using the Point-Spread Function of WMAP and obtain a full sky CC coefficient map. We... We apply a Cross-Correlation (CC) method developed previously for detecting gamma-ray point sources to the WMAP first year data by using the Point-Spread Function of WMAP and obtain a full sky CC coefficient map. We find that the CC method is a powerful tool to examine the WMAP foreground residuals which can be further cleaned accord- ingly. Evident foreground signals are found in the WMAP foreground cleaned maps and the Tegmark cleaned map. In this process 101 point sources are detected, and 26 of them are new sources additional to the originally listed WMAP 208 sources. We estimate the flux of these new sources and verify them by another method. As a result, a revised mask file based on the WMAP first year data is produced by including these new sources. 展开更多
关键词 cosmic microwave background: WMAP - cross-correlation - radio point source
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An updated search of steady TeV γ-ray point sources in northern hemisphere using the Tibet air shower array
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作者 汪越 毕效军 +45 位作者 崔树旺 丁林恺 丹增罗布 丁晓红 樊超 冯存峰 冯朝阳 冯振勇 高晓宇 耿庆喜 郭宏伟 何会海 何瑁 胡海冰 胡红波 黄庆 贾焕玉 拉巴次仁 乐贵明 李爱凤 李金玉 楼宇庆 卢红 陆穗苓 孟宪茹 木钧 任敬儒 谭有恒 王博 王辉 王永刚 吴含荣 薛良 杨先楚 叶宗海 余光策 袁爱芳 张慧敏 张吉龙 张乃健 张学尧 张勇 张毅 扎西桑珠 周勋秀 袁强 《Chinese Physics C》 SCIE CAS CSCD 北大核心 2008年第11期868-872,共5页
Using the data taken from Tibet II High Density (HD) Array (1997 February-1999 September) and Tibet-III array (1999 November--2005 November), our previous northern sky survey for TeV γ-ray point sources has now... Using the data taken from Tibet II High Density (HD) Array (1997 February-1999 September) and Tibet-III array (1999 November--2005 November), our previous northern sky survey for TeV γ-ray point sources has now been updated by a factor of 2.8 improved statistics. From 0.0° to 60.0° in declination (Dec) range, no new TeV T-ray point sources with sufficiently high significance were identified while the well-known Crab Nebula and Mrk421 remain to be the brightest TeV γ-ray sources within the field of view of the Tibet air shower array. Based on the currently available data and at the 90% confidence level (C.L.), the flux upper limits for different power law index assumption are re-derived, which are approximately improved by 1.7 times as compared with our previous reported limits. 展开更多
关键词 ASγ experiment γ-ray point sources 90% C.L. flux upper limits
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Distributional Relations on Impulse Radiating Surface and Point Type Sources
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作者 Burak Polat 《Journal of Mathematics and System Science》 2012年第2期72-81,共10页
The electromagnetic field relations are demonstrated on impulse radiating surface and point type sources, which are characterized by first and second order singularities at rest in a Schwartz-Sobolev space setting. Th... The electromagnetic field relations are demonstrated on impulse radiating surface and point type sources, which are characterized by first and second order singularities at rest in a Schwartz-Sobolev space setting. The investigation starts with a general introduction to Schwartz-Sobolev distributions, the electromagnetic field equations and various modes of impulsive radiation. This is followed by an outline of temporal distributional relations in arbitrary media and distributional derivative operations on an arbitrary regular surface, all of which are employed in an investigation of impulse radiation mechanism on single and double layer sources. Similar steps are followed in a description of point distributions and investigation of impulse radiation mechanism on electric and magnetic point dipoles. 展开更多
关键词 Generalized functions electromagnetic phenomena single and double layers point sources impulse radiation.
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Point Sources Identification Problems for Heat Equations
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作者 Leevan Ling Tomoya Takeuchi 《Communications in Computational Physics》 SCIE 2009年第5期897-913,共17页
We considered the point source identification problems for heat equations from noisy observation data taken at the minimum number of spatially fixed measurement points.We aim to identify the unknown number of sources ... We considered the point source identification problems for heat equations from noisy observation data taken at the minimum number of spatially fixed measurement points.We aim to identify the unknown number of sources and their locations along with their strengths.In our previous work,we proved that minimum measurement points needed under the noise-free setting.In this paper,we extend the proof to cover the noisy cases over a border class of source functions.We show that if the regularization parameter is chosen properly,the problem can be transformed into a poles identification problem.A reconstruction scheme is proposed on the basis of the developed theoretical results.Numerical demonstrations in 2D and 3D conclude the paper. 展开更多
关键词 point source source identification heat equations noisy data CONVERGENCE
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Numerical Calculation of Seafloor Synthetic Seismograms Caused by Low Frequency Point Sound Source 被引量:4
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作者 LU Zaihua ZHANG Zhihong GU Jiannong 《Defence Technology(防务技术)》 SCIE EI CAS 2013年第2期125-132,共8页
Elastic wave on seafloor caused by low frequency noise radiated from ship is called ship seismic wave which can be used to identify ship target. In order to analyze the wave components and the propagating properties o... Elastic wave on seafloor caused by low frequency noise radiated from ship is called ship seismic wave which can be used to identify ship target. In order to analyze the wave components and the propagating properties of ship seismic wave, the numerical calculation of synthetic seismograms on seafloor aroused by a low frequency point sound source is carried out using a wave number integration technique combined with inverse Fourier transform. According to the numerical example of hard seafloor, the time series of seismic wave on seafloor are mostly composed of interface waves and normal mode waves. Each normal mode wave has a well defined low cut-off frequency, while the interface wave doesn't have. The frequency dispersion of normal mode wave is obvious when frequency is lower than 100Hz, while the interface wave is dispersive only in the infra-sound frequency range. The time series of seismic wave is dominated by the interface wave when the source frequency is less than the minimal cut-off frequency of normal mode wave. 展开更多
关键词 maritime engineering low frequency point sound source seismic wave synthetic seismogram numerical calculation
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Three-dimensional steady-state closed form solution for multilayered fluid-saturated anisotropic finite media due to surface/internal point source 被引量:1
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作者 Lianzhi YANG Fanmin HE +1 位作者 Yang LI Zhiyong SONG 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2021年第1期17-38,共22页
A three-dimensional(3 D)steady-state solution of fluid saturated anisotropic finite media is presented.The eigenequation method and the pseudo-Stroh formalism are used to obtain the exact solution for homogeneous satu... A three-dimensional(3 D)steady-state solution of fluid saturated anisotropic finite media is presented.The eigenequation method and the pseudo-Stroh formalism are used to obtain the exact solution for homogeneous saturated finite media.The propagator matrix method is introduced to deal with the corresponding multilayered poroelastic media.The poroelastic solutions due to surface or internal point fluid source are obtained.The comparison of the results of the saturated isotropic media in a half space and those obtained by the finite element method is given to illustrate the accuracy of the solution in a finite domain.Numerical solutions of a sandwich poroelastic medium are presented to analyze its hydromechanical behaviors.Two ratios of the horizontal permeability to vertical permeability and different source positions are investigated.The results show that the fluid parameters and source positions have great influence on the hydromechanical behaviors of the layered media. 展开更多
关键词 POROELASTIC pseudo-Stroh formalism MULTILAYERED point fluid source
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Evaluation of Red Blood Cell Contribution to Platelet Activation in the Bulk Applying Red Blood Cell—Platelet Thrombus as a Point Source Model 被引量:1
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作者 Taha M. Alkhamis Bahieh M. Alma’atah 《Advances in Bioscience and Biotechnology》 2022年第2期92-111,共20页
In this study, a point source mathematical model is proposed to describe the diffusion of adenosine di-phosphate (ADP) from either damaged red blood cell (RBC) or activated platelet. The convective diffusion equation ... In this study, a point source mathematical model is proposed to describe the diffusion of adenosine di-phosphate (ADP) from either damaged red blood cell (RBC) or activated platelet. The convective diffusion equation is reduced to describe the suggested problem. The final differential equation is solved using Laplace transforms and ADP concentration profiles around the source are obtained. Thrombi of 5 to 20 μm<sup>3</sup> containing platelets and a range of red blood cells (RBCs) (0%, 25%, 50%, 75%, 100%) concentrations are used to apply the model. Reported ADP concentrations in the literature are used and its dynamic release from the point source is calculated. Results suggest that RBC chemical contribution to platelet aggregation in the bulk is much less than that of platelet (almost) negligible. However, the physical effect of RBCs is dominant in the bulk through augmentation of released ADP and platelets diffusivities. Moreover, the chemical contribution reported in previous studies is suggested to be as a result of interaction of RBC with the surface under the influence of shear stresses in the boundary region. 展开更多
关键词 PLATELET Red Blood Cell AGGREGATION Adhesion Diffusion ADP point Source Chemical Contribution Physical Contribution Shear Stresses HEMOLYSIS
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FLOW PROPERTIES OF A DUSTY-GAS POINT SOURCE IN A SUPERSONIC FREE STREAM
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作者 王柏懿 Alexander N.Osiptsov Misha A.Teverovshii 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2003年第8期928-935,共8页
By using Lagrangian method, the flow properties of a dusty-gas point source in a supersonic free stream were studied and the particle parameters in the near-symmetry-axis region were obtained . It is demonstrated that... By using Lagrangian method, the flow properties of a dusty-gas point source in a supersonic free stream were studied and the particle parameters in the near-symmetry-axis region were obtained . It is demonstrated that fairly inertial particles travel along oscillating and intersecting trajectories between the bow and termination shock waves . In this region, formation of ' mufti- layer structure' in panicle distribution with alternating low- and high density layers is revealed. Moreover, sharp accumulation of particles occurs near the envelopes of particle trajectories . 展开更多
关键词 dusty gas supersonic flow point source particle inertia trajectory intersection multi-layer structure
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CONCENTRATION DISTRIBUTION OF FRACTIONAL ANOMALOUS DIFFUSION CAUSED BY AN INSTANTANEOUS POINT SOURCE
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作者 段俊生 徐明瑜 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2003年第11期1302-1308,共7页
The Fox function expression and the analytic expression for the concentration distribution of fractional anomalous diffusion caused by an instantaneous point source in n-dimensional space (n= 1, 2 or 3) are derived by... The Fox function expression and the analytic expression for the concentration distribution of fractional anomalous diffusion caused by an instantaneous point source in n-dimensional space (n= 1, 2 or 3) are derived by means of the condition of mass conservation , the time-space similarity of the solution , Mellin transform and the properties of the Fox function . And the asymptotic behaviors for the solutions are also given . 展开更多
关键词 instantaneous point source anomalous diffusion fractional calculus Fox function Mellin transform
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Simulation and analysis of point-source surface wave fields
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作者 Chengyu Sun Xingyao Yin Yunfei Xiao 《Earthquake Science》 CSCD 2011年第5期419-426,共8页
The complexity of near surface intensifies the diversity of seismic wave fields, which makes study on near surface wavefields important in many aspects. The strong absorption of low velocity layer can affect the resol... The complexity of near surface intensifies the diversity of seismic wave fields, which makes study on near surface wavefields important in many aspects. The strong absorption of low velocity layer can affect the resolution of seismic data, and free boundary can cause surface wave. Considering the above problems, we focus on the Rayleigh wavefields simulation using finite-difference wave equation of higher-order staggered grids and PML boundary conditions. Free boundary, buried source and overlying low velocity layer are taken into consideration and point explosion source is adopted. Through some numerical simulation with different parameters, we quantitatively analyze relationship between wave intensity and source depth, as well as the energy variation with propagation and obtain some practical knowledge and conclusions. 展开更多
关键词 near surface point source free boundary Rayleigh wave wave field simulation
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Development of point source method and its practical significance
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作者 Bidya Sagar PANI 《Water Science and Engineering》 EI CAS 2009年第2期19-31,共13页
The advantages of Reichardt's hypothesis in dealing with single and multiple circular jets in a stagnant environment are highlighted. The stages involved in the development of the point source method, an offshoot of ... The advantages of Reichardt's hypothesis in dealing with single and multiple circular jets in a stagnant environment are highlighted. The stages involved in the development of the point source method, an offshoot of the new hypothesis, are presented, Previous results of experiments on multiple circular jets in a stagnant environment justify the method of superposition. As a prelude to discussion of multiple jets in a co-flowing stream, results on the excess-velocity decay, the growth of the shear layer, and the dilutions for a single jet based on Reichardt's hypothesis are presented. The spreading hypothesis is generalized by introducing a link factor kl to account for the co-flowing stream. The distribution of excess-momentum flux uAu is shown to be Gaussian in nature. Based on the principle of superposition, the decay of the maximum excess velocity and the dilution are predicted for odd and even numbers of jets in an array. The predictions seem to be in good agreement with observed data. 展开更多
关键词 point source method method of superposition co-flowing jets Reiehardt'shypothesis multiple circular jets
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THEORETICAL ANALYSIS ON THE AUTOPLOIDY BETWEEN THE TWELVE YUAN (SOURCE) POINTS AND THEIR CORRESPONDING ZANGFU-ORGANS
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作者 成泽东 张立德 陈以国 《World Journal of Acupuncture-Moxibustion》 2006年第1期33-38,共6页
In the present paper, the authors make a theoretical analysis on the autoploidy between the twelve Yuan (source) points and their corresponding Zangfu-organs from 1 ) historical development, 2) correlation, 3) cl... In the present paper, the authors make a theoretical analysis on the autoploidy between the twelve Yuan (source) points and their corresponding Zangfu-organs from 1 ) historical development, 2) correlation, 3) clinical application, 4) experimental research results about the relationship between Yuan points and the Zangfu-organs, and between meridians and Zangfu-organs, and 5) literature description. The twelve Yuan points have an important role in clinical diagnosis and treatment of diseases, and a close association with the Zangfu-organs. 展开更多
关键词 Twelve Yuan (source) points Zangfu-organs Somato-visceral correlation
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Non point source ground water pollution trends in an urban area
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《Global Geology》 1998年第1期3-4,共2页
关键词 Non point source ground water pollution trends in an urban area
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Multivariate Analyses of Potentially Toxic Elements along an Industrialized Urban River in Northern Taiwan
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作者 Kuo-Yen Wei Li-Chuan Hsu Huang Chuen-Lan Yen 《Journal of Environmental Protection》 2021年第11期983-1000,共18页
The Ker-Ya River flows through the high-tech industrial park and urban residential areas of Hsin-Chu in northern Taiwan. Major and trace element concentrations of waste effluents, river water, and sediment samples col... The Ker-Ya River flows through the high-tech industrial park and urban residential areas of Hsin-Chu in northern Taiwan. Major and trace element concentrations of waste effluents, river water, and sediment samples collected during 2017 along the Ker-Ya River were analyzed to elucidate the distribution pattern of potential pollutants. Principal component analyses were applied, and four major contaminant associations were recognized: 1) Ce, Co, Fe, La, V, and Cr;2) Cu and Ni associated with Hg, Ni, P, Ga, W, In, and Ti;3) B, Li, Ba, Ca, and Ag;and 4) Sn with Zn, In, and Cd. All associations are considered to be mainly anthropogenic. Although the element associations recognized from the water samples are not exactly the same as those from the sediment samples but nevertheless, they are similar, suggesting that the short-term and long-term distribution patterns are consistent. The A association accounts for the most variance in the data and exhibits the widest distribution, suggesting the existence of contaminant sources in the upper and lower reaches, respectively. The sediments near the outlet of the city sewage plant also contain association A elements, signaling incomplete processing of the diverged waters sent to the plant at the river mouth. The B association (mainly Cu and Ni) appeared mainly in the upper and middle reaches, indicative of sources from industries in the upper reaches and the tributary Nan-Men Creek. The C association (B, Ba, Ca, and Li) was limited to the center part of the river, probably attributable to a nearby paper mill. The D association (primarily Sn, In, and Zn) was present in the top point of the middle reaches, suggesting the presence of other contaminant sources in the upper reaches. Although a total of four concomitant associations were recognized, none of the elements exceeded the drinking water standard, suggesting that there was no severe pollution present. 展开更多
关键词 Toxic Elements Spatial Distribution Principal Component Analysis point sources
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Direct Analytical Method to Calculate Photopeak Efficiency and Photopeak Attenuation Coefficient of NaI(Tl) Well-Type Detector
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作者 K. S. Al-Mugren Mahmoud I. Abbas +1 位作者 Eman M. El-Bayoumi N. S. Aly 《World Journal of Nuclear Science and Technology》 2016年第2期115-124,共10页
In this paper full-energy peak (photopeak) efficiency and photopeak attenuation coefficient of 3'' × 3'' NaI(Tl) well-type scintillation detector were calculated using gamma-rayisotropic radiating... In this paper full-energy peak (photopeak) efficiency and photopeak attenuation coefficient of 3'' × 3'' NaI(Tl) well-type scintillation detector were calculated using gamma-rayisotropic radiating point sources (with photon energy: 0.245, 0.344, 0.662, 0.779, 0.964, 1.1732, 1.333 and 1.408 MeV) placed outside the detector well. These energies were obtained from <sup>152</sup>Eu, <sup>137</sup>Cs and <sup>60</sup>Co. The relations between the full energy peak efficiency and photopeak attenuation coefficients, were plotted vs. photon energy at different sources to detector distance, and it found that the full energy peak efficiency decreased by increasing the distance between the source and the detector. 展开更多
关键词 NaI(Tl) Well-Type Scintillation Detector Full-Energy Peak Efficiency Photopeak Attenuation Coefficient Gamma-Ray point sources
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Focal mechanism caused by fracture or burst of a coal pillar 被引量:8
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作者 CAO An-ye DOU Lin-ming CHEN Guo-xiang GONG Si-yuan WANG Yu-gang LI Zhi-hua 《Journal of China University of Mining and Technology》 EI 2008年第2期153-158,共6页
As a regional, real-time and dynamic method, microseismic monitoring technology is quite an appropriate technology for forecasting geological hazards, such as rock bursts, mine tremors, coal and gas outbursts and can ... As a regional, real-time and dynamic method, microseismic monitoring technology is quite an appropriate technology for forecasting geological hazards, such as rock bursts, mine tremors, coal and gas outbursts and can even be used to prevent or at least reduce these disasters. The study of the focal mechanisms of different seismic sources is the prerequisite and basis for forecasting rock burst by microseismic monitoring technology. Based on the analysis on the mechanism and fracture course of coal pillars where rock bursts occur mostly, the equivalent point source model of the seismicity caused by a coal pillar was created. Given the model, the seismic displacement equation of a coal pillar was analyzed and the seismic mechanism was pointed out by seismic wave theory. The course of the fracture of the coal pillar was simulated closely in the laboratory and the equivalent microseismic signals of the fractures of the coal pillar were acquired using a TDS-6 experimental system. The results show that, by the pressure and friction of a medium near the seismic source, both a compression wave and a shear wave will be emitted and shear fracture will be induced at the moment of breakage. The results can be used to provide an academic basis to forecast and prevent rock bursts or tremors in a coal pillar. 展开更多
关键词 coal pillar rock burst MICROSEISMICITY FRACTURE focal mechanism point source model
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Sedimentation retention basin utilization for best management practice 被引量:2
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作者 Zaheer Iqbal 《Journal of Environmental Sciences》 SCIE EI CAS CSCD 2003年第5期662-668,共7页
Approaches to the artificial impoundment and theoretical design of sedimentation retention basin are reviewed with particular attention to best management practice(BMP) to control agriculture and surface runoff. Sedim... Approaches to the artificial impoundment and theoretical design of sedimentation retention basin are reviewed with particular attention to best management practice(BMP) to control agriculture and surface runoff. Sediments retention basins are the small version of farm pond used where a criteria of farm pond is not met. Such basin traps the pollutants and suspended solids prior to entry into streams and lakes. The study is focused with special reference to the assessment and control of non point source pollution(NPSP) from the sub basin area of Tai Lake in the Xishan County of Wuxi City of China. The author suggested two different approaches to conduct this study including theoretical design for sedimentation retention basin and computation of flow, sediment transport and deposition during the artificial impoundment of retention basin for BMP's utilization. Theoretical design will provide a useful function as a first line defense against the movement of sediments and transport of pollutants into the Tai Lake while the assessment of sediments deposition will help to make its proper use and periodic cleanup. 展开更多
关键词 agriculture runoff artificial impoundment best management practice sediment retention basin Tai Lake sub basin non point source pollution
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Optical Design and Stray Light Analysis of the Space Infrared Optical System 被引量:1
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作者 Yuchen Zhao Yanjun Xu +2 位作者 Changzheng Chen Fan Zhang Jianyue Ren 《Journal of Harbin Institute of Technology(New Series)》 EI CAS 2017年第1期32-36,共5页
This article describes a novel configuration design for a re-imaging off-axis catadioptric space infrared optical system,and in order to satisfy the signal noise ratio requirements of the system,the stray light of the... This article describes a novel configuration design for a re-imaging off-axis catadioptric space infrared optical system,and in order to satisfy the signal noise ratio requirements of the system,the stray light of the system is necessary to analyze and restrain. The optical system with a focal length of 1 200 mm,an entrance pupil diameter of 600 mm,an F-number of 2,a field of view of 3°× 0. 15°,a working wave band of 8 μm-10 μm,and the image quality of the optical system almost approach to diffraction limits in all field of view.Then the mathematical models of stray light are built,and the suppressive structure is established to eliminate the effect of stray light. Finally,TraceP ro is used to analyze and simulate stray light with and without the suppressive structure,and also get the results of the PST curves. The results indicate that appropriate optical system and suppressive structure can highly reduce the stray light of the space infrared optical system. 展开更多
关键词 space infrared optical system off-axis optical system stray light point Source Transmission(PST)
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General Solutions of Thermoelastic Plane Problems of Two-Dimensional Quasicrystals 被引量:1
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作者 张亮亮 杨连枝 +1 位作者 余莲英 高阳 《Transactions of Nanjing University of Aeronautics and Astronautics》 EI 2014年第2期132-136,共5页
The thermoelastic plane problems of two-dimensional decagonal quasicrystals(QCs)are systematically investigated.By introducing a displacement function,the problem of thermoelastic plane problems can be simplified to a... The thermoelastic plane problems of two-dimensional decagonal quasicrystals(QCs)are systematically investigated.By introducing a displacement function,the problem of thermoelastic plane problems can be simplified to an eighth-order partial differential governing equation,and then general solutions are presented through an operator method.By virtue of the Almansi′s theorem,the general solutions are further established,and all expressions for the phonon,phason and thermal fields are described in terms of the potential functions.As an application of the general solution,for a steady point heat source in a semi-infinite quasicrystal plane,the closed form solutions are presented by four newly induced harmonic functions. 展开更多
关键词 two-dimensional quasicrystals THERMOELASTICITY general solutions point heat source
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