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THE PERSISTENCE OF SOLUTIONS IN A NONLOCAL PREDATOR-PREY SYSTEM WITH A SHIFTING HABITAT
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作者 赵敏 袁荣 《Acta Mathematica Scientia》 SCIE CSCD 2024年第3期1096-1114,共19页
In this paper,we mainly study the propagation properties of a nonlocal dispersal predator-prey system in a shifting environment.It is known that Choi et al.[J Differ Equ,2021,302:807-853]studied the persistence or ext... In this paper,we mainly study the propagation properties of a nonlocal dispersal predator-prey system in a shifting environment.It is known that Choi et al.[J Differ Equ,2021,302:807-853]studied the persistence or extinction of the prey and of the predator separately in various moving frames.In particular,they achieved a complete picture in the local diffusion case.However,the question of the persistence of the prey and of the predator in some intermediate moving frames in the nonlocal diffusion case was left open in Choi et al.'s paper.By using some a prior estimates,the Arzelà-Ascoli theorem and a diagonal extraction process,we can extend and improve the main results of Choi et al.to achieve a complete picture in the nonlocal diffusion case. 展开更多
关键词 predator-prey system PERSISTENCE nonlocal dispersal shifting environment
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The modern textile factory:Charting the impact of a shifting textile supply chain landscape
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《China Textile》 2024年第1期42-43,共2页
Smartex is at the forefront of transforming the textile industry through the integration of Artificial Intelligence,focusing specifically on achieving zero waste and traceability in Tier 2,the most impactful step of t... Smartex is at the forefront of transforming the textile industry through the integration of Artificial Intelligence,focusing specifically on achieving zero waste and traceability in Tier 2,the most impactful step of the textile supply chain.They are part of a larger movement involving dynamic technology companies,forward-thinking factories,pioneering brands,and influential policy-makers all actively addressing challenges within the supply chain. 展开更多
关键词 impact LANDSCAPE shifting
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Matching actions to needs: shifting policy responses to the changing health needs of Chinese children and adolescents
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作者 Tian-Jiao Chen 《四川生理科学杂志》 2024年第4期866-866,共1页
China is home to the second largest population of children and adolescents in the world.Yet demographic shifts mean that the government must manage the challenge of fewer children with the needs of an ageing populatio... China is home to the second largest population of children and adolescents in the world.Yet demographic shifts mean that the government must manage the challenge of fewer children with the needs of an ageing population,while considering the delicate tension between economic growth and environmental sustainability.We mapped the health problems and risks of contemporary school-aged children and adolescents in China against current national health policies.We involved multidisciplinary experts,including young people,with the aim of identifying actionable strategies and specific recommendations to promote child and adolescent health and wellbeing.Notwithstanding major improvements in their health over the past few decades,contemporary Chinese children and adolescents face distinct social challenges,including high academic pressures and youth unemployment,and new health concerns including obesity,mental health issues,and sexually transmitted infections.Inequality by gender,geography,and ethnicity remains a feature of health risks and outcomes.We identified a mismatch between current health determinants,risks and outcomes,and government policies. 展开更多
关键词 POLICY children shifting
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A Shifting Strategy for Electric Commercial Vehicles Considering Mass and Gradient Estimation 被引量:1
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作者 Weiguang Zheng Junzhu Zhang +3 位作者 Shanchao Wang Gaoshan Feng Xiaohong Xu Qiuxiang Ma 《Computer Modeling in Engineering & Sciences》 SCIE EI 2023年第10期489-508,共20页
The extended Kalman filter (EKF) algorithm and acceleration sensor measurements were used to identify vehiclemass and road gradient in the work. Four different states of fixed mass, variable mass, fixed slope and vari... The extended Kalman filter (EKF) algorithm and acceleration sensor measurements were used to identify vehiclemass and road gradient in the work. Four different states of fixed mass, variable mass, fixed slope and variableslope were set to simulate real-time working conditions, respectively. A comprehensive electric commercial vehicleshifting strategy was formulated according to the identification results. The co-simulation results showed that,compared with the recursive least square (RLS) algorithm, the proposed algorithm could identify the real-timevehicle mass and road gradient quickly and accurately. The comprehensive shifting strategy formulated had thefollowing advantages, e.g., avoiding frequent shifting of vehicles up the hill, making full use ofmotor braking downthe hill, and improving the overall performance of vehicles. 展开更多
关键词 EKF algorithm electric commercial vehicle vehicle mass road gradient comprehensive shifting strategy
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Existence of Forced Waves and Their Asymptotic for Leslie-Gower Prey-Predator Model with Nonlocal Effects under Shifting Environment
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作者 Qingru Guo Hongmei Cheng 《Journal of Applied Mathematics and Physics》 2023年第6期1737-1754,共18页
In this paper, we prove the existence of forced waves for Leslie-Gower prey-predator model with nonlocal effects under shifting environment. By constructing a pair of upper and lower solutions with the method of monot... In this paper, we prove the existence of forced waves for Leslie-Gower prey-predator model with nonlocal effects under shifting environment. By constructing a pair of upper and lower solutions with the method of monotone iteration, we can obtain the existence of forced waves for any positive constant shifting speed. Finally, we show the asymptotical behavior of traveling wave fronts in two tails. 展开更多
关键词 Leslie-Gower Prey-Predator Model Nonlocal Effects shifting Environment Forced Waves
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Performance of bottleneck shifting for remanufacturing system considering returns' quality grading 被引量:1
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作者 郑玉巧 苏春 +1 位作者 曹白雪 施杨梅 《Journal of Southeast University(English Edition)》 EI CAS 2015年第4期516-521,共6页
Aimed at the remanufacturing system, the effect of the uncertainty of returns' quality on bottleneck shifting is investigated. A novel definition of bottleneck station is presented and the probability of a station be... Aimed at the remanufacturing system, the effect of the uncertainty of returns' quality on bottleneck shifting is investigated. A novel definition of bottleneck station is presented and the probability of a station becoming a bottleneck is also given. By calculating the effective output, the effective operation time (EOT) and the ratio of EOT of each station, the system's current bottleneck of effective output time is determined. By calculating the probability coefficient of variation and index of bottleneck shifting, the quantitative performance of bottleneck shifting is obtained. Discrete event simulation and the experiment design method are adopted to simulate the system, in which the proportion of quality grading, repair rates and process routes are considered. The case study shows that the uncertainty of returns' quality greatly increases the probability of bottleneck shifting, and with the increase of the discrete degree of the returns' repair rate, the bottleneck shifting phenomenon is more obvious. Furthermore, bottleneck shifting is closely related to the process route of the dominating returns' quality grade. 展开更多
关键词 bottleneck shifting REMANUFACTURING returns quality grading UNCERTAINTY
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Error-CompensatingFive-SamplePhase-Shifting Algorithm Based on Phase-Shift Error Estimation
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作者 黄文宇 龚建伟 陆际联 《Journal of Beijing Institute of Technology》 EI CAS 2001年第4期337-341,共5页
A new error compensating five sample phase shifting algorithm which is insensitive to phase shift error is proposed to retrieve the phase distribution of a fringe pattern. It includes two steps. First, the linear ... A new error compensating five sample phase shifting algorithm which is insensitive to phase shift error is proposed to retrieve the phase distribution of a fringe pattern. It includes two steps. First, the linear phase shift error is estimated using four sample images. Then, the phase distribution is calculated with error corrected by using the phase shift error estimated in the first step. As the equations of error estimation and phase calculation are simple, this new algorithm is practical as well as effective. Computer simulations were carried out to verify the effectiveness of the algorithm. Results of two other well known error compensating algorithms are also presented, which show the new algorithm is the least sensitive to phase shift error. 展开更多
关键词 phase shifting algorithm phase measuring profilometry optical measurement
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关于α-shifting环,α-sy环和α-sc环 被引量:1
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作者 张玖琳 王尧 任艳丽 《数学理论与应用》 2013年第3期15-21,共7页
本文讨论α-shifting环、α-sy环、α-sc环以及α-rigid环之间的关系.在α-compatible和Cα条件下,分别给出α-shifting环、α-sy环和α-sc环与相关环之间的等价关系,推广Pourtaherian-Rakhimov的一些研究结论.
关键词 α—shifting α—sy环 α—sc环 α—rigid环 α—compatible环
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ANALYSIS OF TIPOVER STABILITY FOR NOVEL SHAPE SHIFTING MODULAR ROBOT 被引量:10
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作者 LIU Jinguo WANG Yuechao +1 位作者 MA Shugen LI Bin 《Chinese Journal of Mechanical Engineering》 SCIE EI CAS CSCD 2006年第2期181-186,共6页
A novel three-module robot has been introduced. It can change its configuration to adapt to the uneven terrain and to improve its tipover stability. This three-module tracked robot has three kinds of symmetry configur... A novel three-module robot has been introduced. It can change its configuration to adapt to the uneven terrain and to improve its tipover stability. This three-module tracked robot has three kinds of symmetry configuration. They are line type, triangle type, and row type. After the factors and the countermeasures of mobile robot's tipover problem are analyzed, stability pyramid and tipover stabil-ity index are proposed to globally determinate the mobile robot's static stability and dynamic stability. The shape shifting robot is tested by this technique under the combined disturbance of pitch, roll and yaw in simulation. The simulation result shows that this technique is effective for the analysis of mobile robot's tipover stability, especially for the reconfigurable or shape shifting modular robot. Experiments on three symmetry configurations are made under unstructured environments. The environment experiment shows the same result as that of the simulation that the triangle type configuration has the best stability. Both simulation and experiment provide a valid reference for the reconfigurable robot's potential application. 展开更多
关键词 Reconfigurable modular robot Shape shifting robot Stability pyramid Tipover stability index Unstructured environment
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Reliability-based multidisciplinary design optimization using incremental shifting vector strategy and its application in electronic product design 被引量:9
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作者 Z.L.Huang Y.S.Zhou +2 位作者 C.Jiang J.Zheng X.Han 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2018年第2期285-302,共18页
Use of multidisciplinary analysis in reliabilitybased design optimization(RBDO) results in the emergence of the important method of reliability-based multidisciplinary design optimization(RBMDO). To enhance the effici... Use of multidisciplinary analysis in reliabilitybased design optimization(RBDO) results in the emergence of the important method of reliability-based multidisciplinary design optimization(RBMDO). To enhance the efficiency and convergence of the overall solution process,a decoupling algorithm for RBMDO is proposed herein.Firstly, to decouple the multidisciplinary analysis using the individual disciplinary feasible(IDF) approach, the RBMDO is converted into a conventional form of RBDO. Secondly,the incremental shifting vector(ISV) strategy is adopted to decouple the nested optimization of RBDO into a sequential iteration process composed of design optimization and reliability analysis, thereby improving the efficiency significantly. Finally, the proposed RBMDO method is applied to the design of two actual electronic products: an aerial camera and a car pad. For these two applications, two RBMDO models are created, each containing several finite element models(FEMs) and relatively strong coupling between the involved disciplines. The computational results demonstrate the effectiveness of the proposed method. 展开更多
关键词 Reliability-based design optimization(RBDO) Multidisciplinary design optimization(MDO) Incremental shifting vector(ISV) Decoupling algorithm Electronic product
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A Preliminary Study of the Dynamics of Eastward Shifting Cyclonic Vortices 被引量:5
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作者 陈联寿 罗哲贤 《Advances in Atmospheric Sciences》 SCIE CAS CSCD 2003年第3期323-332,共10页
The dynamics of eastward shifting cyclonic vortices are investigated in terms of a barotropic primitive equation model, and six experiments are performed. Both the interaction of a cyclonic vortex with vorticity lumps... The dynamics of eastward shifting cyclonic vortices are investigated in terms of a barotropic primitive equation model, and six experiments are performed. Both the interaction of a cyclonic vortex with vorticity lumps and the interaction of the vortex with the shearing basic flow may induce the strengthening of the vortex in a short period, however, the vortex intensity still shows a general decreasing tendency over the whole integration time period. The interaction among the shearing basic flow, cyclonic vortex, and multiple vorticity lumps can change the tendency. The merging of the cyclonic vortex with vorticity lumps in the shearing basic flow of positive vorticity is directly responsible for the maintenance and development of the cyclonic vortex. 展开更多
关键词 eastward shifting cyclonic vortex shearing basic flow vorticity lump merging of vortex with lumps intensification of vortex
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Study on soils under shifting cultivation and other land use categories in Chittagong Hill Tracts, Bangladesh 被引量:3
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作者 Alake Biswas M.Alamgir +1 位作者 S.M.S.Haque K.T.Osman 《Journal of Forestry Research》 CAS CSCD 2012年第2期261-265,共5页
Soil samples were collected and analyzed from 25 sites of three hilly regions (Rangamati, Banderban and Khagrachari) for an understanding of the impact of denudation and land use on soils in Chittagong Hill Tracts, ... Soil samples were collected and analyzed from 25 sites of three hilly regions (Rangamati, Banderban and Khagrachari) for an understanding of the impact of denudation and land use on soils in Chittagong Hill Tracts, Bangladesh. There were natural forests, bushy land, slashed sites, slashed and burnt sites, and the sites prepared for shifting cultivation, one year after shifting cultivation and two years after shifting cultivation. The soils were generally yellowish brown to reddish brown, sandy to sandy clay loam, strongly acid, and well to excessively drained on steep slopes with considerable variation among the sites and land use categories. Bulk density was the highest in sites of one year after shifting cultivation (1.52 g·cm^-3) and the lowest in forested sites (1.38 g·cm^-3). Water holding capacities were, however, statistically similar in all sites. Organic carbon varied from 0.54% (slashed and burnt sites) to 1.55% (forested sites) and total N ranged from 0.05% (shifting cultivation for one year) to 0.13% (forested sites). Available phosphorus (Bray & Kurtz-2 P) was the maximum in forested sites (12.32 mg·kg^-l), and it did not differ significantly in other sites. Contents of available Ca, Mg and K were also higher in the bushy lands and forested sites than cleared and shifting cultivated sites. 展开更多
关键词 Chittagong Hill Tracts BANGLADESH DENUDATION shifting cultivation soil degradation
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Shifting Rule Modification Strategy of Automatic Transmission Based on Driver-vehicle-road Environment 被引量:3
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作者 WU Guangqiang ZHANG Deming 《Chinese Journal of Mechanical Engineering》 SCIE EI CAS CSCD 2010年第3期346-352,共7页
Accidental or frequent shift often occurs when the shifting rule is built based on traditional two parameters (i.e., velocity and throttle), because the speed of engine varies slower than change of throttle opening.... Accidental or frequent shift often occurs when the shifting rule is built based on traditional two parameters (i.e., velocity and throttle), because the speed of engine varies slower than change of throttle opening. Currently, modifying shift point velocity value or throttle by throttle change rate is one of common methods, but the results are not so satisfactory in some working condition such as uphill. The reason is that these methods merely consider throttle change rate which is not enough for a car driving in driver-vehicle-road environment system. So a novel fuzzy control modification strategy is proposed to avoid or reduce those abnormal shift actions. It can adjust shifting rule by the change rate of throttle, current gear position and road environment information, while different gear position and driving environment get corresponding modification value. In order to compare the results of shifting actions, fuel consumption and braking distance, emergent braking in level road and extra-urban driving cycle(EUDC) working conditions with fuzzy shifting schedule modification strategy are simulated digitally. Furthermore, a hardware-in-the-loop simulation platform is introduced to verify its effect in slope road condition according to the ON/OFF numbers of solenoid valve in hydraulic system. The simulation results show that the problem of unexpected shift in those working conditions may be resolved by fuzzy modification strategy. At last, it is concluded that although there is some slight decline in power performance in uphill situation, this fuzzy modification strategy could correctly identify slope of road, decrease braking distance, improve vehicle comfort and fuel economy effectively and prolong the life of clutch system. So, this fuzzy logic shifting strategy provides important references for vehicle intelligent shifting schedule. 展开更多
关键词 shifting rule modification strategy fuzzy logic control simulation and hardware-in-the-loop experiments
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Effects of shifting time on pressure impact in hydraulic systems 被引量:5
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作者 ZHU Zhen-cai CHEN Guo-an 《Journal of Central South University of Technology》 2005年第z1期217-221,共5页
The limitations in existing measures for absorbing pressure impact in hydraulic systems were summarized in this paper. Based on the forming principle of the oil in a hydrostatic closed pressure chamber, the underlying... The limitations in existing measures for absorbing pressure impact in hydraulic systems were summarized in this paper. Based on the forming principle of the oil in a hydrostatic closed pressure chamber, the underlying reasons of the pressure impact were analyzed theoretically, the intrinsic laws that the extent of the pressure impact in hydraulic oil lines are affected by some factors, such as oil elastic modulus, oil line's geometrical volume, and changing rate of oil volume versus time etc, were discussed. Experimental investigations into pressure impact in all pressure chambers because of shifting were conducted under different working conditions by employing a special experimental system. The effects of shifting time on pressure impact were studied. A new concept with universal meaning, i.e. optimal shifting time, and its characterizing parameter and the methods of shifting at optimal shifting time were also proposed. The results show that shifting time lag △t is of rationality and maneuverablility. The higher the working pressure, the shorter the shifting time. 展开更多
关键词 HYDRAULIC system shifting TIME PRESSURE impact EXPERIMENT LAW
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Roll shifting strategy with varying stroke and step in hot strip mill 被引量:3
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作者 李维刚 刘相华 +1 位作者 郭朝晖 黄建平 《Journal of Central South University》 SCIE EI CAS 2012年第5期1226-1233,共8页
A new roll shifting strategy with varying stroke and varying step was investigated,Two characteristic parameters including cat ear height and gap contour smoothness were introduced to assess the effect of shifting str... A new roll shifting strategy with varying stroke and varying step was investigated,Two characteristic parameters including cat ear height and gap contour smoothness were introduced to assess the effect of shifting strategy on roll wear,and the relation between characteristic parameters and shifting strategy was established.Both varying stroke and varying step can reduce cat ear height and gap contour smoothness,so the shifting strategy with varying stroke and varying step is better than the one with either varying stroke or varying step,Based on the effect of shifting control parameters on characteristic parameters of roll wear,the selection principle of these shifting control parameters was gained.A case study was conducted to validate the proposed roll shifting strategy,reducing uncontrollable quartic loading gap contour,improving strip profile and extending rolling length of a rolling campaign. 展开更多
关键词 hot rolling work roll shifting varying step roll wear roll contour schedule free rolling
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Food Security of Shifting Cultivation Systems: Case Studies from Luang Prabang and Oudomxay Provinces, Lao PDR 被引量:3
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作者 Linkham Douangsavanh Anan Polthanee Roengsak Katawatin 《Journal of Mountain Science》 SCIE CSCD 2006年第1期48-57,共10页
The Government of the Lao PDR’s policy is to eliminate the cultivation of upland rice by means of ‘slash-and-burn’ cultivation and to replace it with more ecologically stable systems based on sustainable land use a... The Government of the Lao PDR’s policy is to eliminate the cultivation of upland rice by means of ‘slash-and-burn’ cultivation and to replace it with more ecologically stable systems based on sustainable land use at the village and household level. The objectives of this policy are to alleviate poverty and to introduce more sustainable management of agricultural resources. In order to achieve these objectives, the government has initiated a program of relocation to upland ‘focal areas’ from which marketing, distribution and other services can be supplied, these being essential preconditions for effective agricultural development in these regions. This diagnostic study has examined communal and household strategies for addressing food security issues, and has highlighted the main problems encountered in the pursuit of food security on the local level. The specific objective was to conduct a broadly focused participatory problem diagnosis of the study areas in two districts Phonsay and Namo, in order to understand farmers’ problems, livelihood goals and how their perspectives on food security have changed, and to investigate food security in shifting cultivation systems in Luang Prabang andOudomxay provinces. Within these two provinces Phonsay and Namo districts were selected as the research areas. The two districts are the poorest districts in the Luang Prabang and Oudomxay provinces and two of ten priority poorest districts in the whole country. Semi-structured interviews were conducted for the study. The results of this study were reviewed against the sustainable land use systems strategy formulated from the Lao PDR policy. The study highlights both the benefits and stresses on household welfare, food insecurity conditions in the study areas, and interrelated problems of insufficient rice for household consumption. Finally based on these results the authors propose recommendations and future research indications. 展开更多
关键词 shifting cultivation food security RICE sustainable land management Lao PDR
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Simulation-based multi-objective optimization for roll shifting strategy in hot strip mill 被引量:2
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作者 李维刚 《Journal of Central South University》 SCIE EI CAS 2013年第5期1226-1234,共9页
A simulation-based multi-objective optimization approach for roll shifting strategy in hot strip mills was presented. Firstly, the effect of roll shifting strategy on wear contour was investigated by mtmerical simulat... A simulation-based multi-objective optimization approach for roll shifting strategy in hot strip mills was presented. Firstly, the effect of roll shifting strategy on wear contour was investigated by mtmerical simulation, and two evaluation indexes including edge smoothness and body smoothness of wear contours were introduced. Secondly, the edge smoothness average and body smoothness average of all the strips in a rolling campaign were selected as objective functions, and shifting control parameters as decision variables, the multi-objective method of MODE/D as the optimizer, and then a simulation-based multi-objective optimization model for roll shifting strategy was built. The experimental result shows that MODE/D can obtain a good Pareto-optimal front, which suggests a series of alternative solutions to roll shifting strategy. Moreover, the conflicting relationship between two objectives can also be found, which indicates another advantage of multi-objective optimization. Finally, industrial test confirms the feasibility of the multi-objective approach for roll shifting strategy, and it can improve strip profile and extend same width rolling miles of a rolling campaign from 35 km to 70 km. 展开更多
关键词 hot rolling roll shifting strategy roll wear multi-objective optimization Pareto-optimal front
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Effects of shifting cultivation on biological and biochemical characteristics of soil microorganisms in Khagrachari hill district, Bangladesh 被引量:2
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作者 Sohag Miah S.M. Sirajul Haque +1 位作者 Wahida Sumi Mohammad Mosharraf Hossain 《Journal of Forestry Research》 SCIE CAS CSCD 2014年第3期689-694,共6页
We collected soil samples from two representative sites at Aatmile of Khagarachari hill district in Chittagong Hill Tracts. One of the sites was under shifting cultivation and the other an adjacent 13-year old teak pl... We collected soil samples from two representative sites at Aatmile of Khagarachari hill district in Chittagong Hill Tracts. One of the sites was under shifting cultivation and the other an adjacent 13-year old teak plantation. Both sites were in the same physiographic condition and same aspect with parable soil type, which enabled us to measure the effects of shifting cultivation on soil micro-flora. We studied soil phys-ico-chemical properties and the biochemical and biological properties of soil microbes. Moisture and organic matter content as well as fungi and bacterial populations, both in surface and subsurface soils, were signifi-cantly (p≤0.001) lower in shifting cultivated soils compared to soils not under shifting cultivation, i.e. the teak plantation site. The most abundant bacteria in surface (0-10 cm) and sub-surface (10-20 cm) soils under shifting cultivation were Pseudomonas diminuta and Shigella, respec-tively, while in corresponding soil layers of teak plantation, predominant microbes were Bacillus firmus (0-10 cm) and Xanthomonas (10-20 cm). The microbial population differences cannot be explained by soil texture differences because of the textural similarity in soils from the two sites but could be related to the significantly lower moisture and organic mat-ter contents in soils under shifting cultivation. 展开更多
关键词 shifting cultivation soil biological properties soil biochemical properties soil microflora Chittagong Hill Tracts
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Comparative analysis of phase extraction methods based on phase-stepping and shifting curve in grating interferometry 被引量:2
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作者 刘小松 李恩荣 +8 位作者 朱佩平 刘宜晋 张凯 王志立 洪友丽 张慧滔 袁清习 黄万霞 吴自玉 《Chinese Physics B》 SCIE EI CAS CSCD 2010年第4期173-179,共7页
Two phase extraction methods which are based separately on phase-stepping and shifting curve are mainly used in phase-sensitive imaging in gating interferometry to determine the x-ray phase shift induced by an object ... Two phase extraction methods which are based separately on phase-stepping and shifting curve are mainly used in phase-sensitive imaging in gating interferometry to determine the x-ray phase shift induced by an object in the beam. In this paper, the authors perform a full comparative analysis and present the main virtues and limitations of these two methods according to the theoretical analysis of the grating interferometry. 展开更多
关键词 x-ray phase sensitive imaging grating interferometer phase-stepping shifting curve
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New representation of the multimode phase shifting operator and its application 被引量:2
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作者 王帅 蒋继建 +1 位作者 徐世民 李洪奇 《Chinese Physics B》 SCIE EI CAS CSCD 2010年第1期332-336,共5页
Based on the rotation transformation in phase space and the technique of integration within an ordered product of operators, the coherent state representation of the multimode phase shifting operator and one of its ne... Based on the rotation transformation in phase space and the technique of integration within an ordered product of operators, the coherent state representation of the multimode phase shifting operator and one of its new applications in quantum mechanics are given. It is proved that the coherent state is a natural language for describing the phase shifting operator or multimode phase shifting operator. The multimode phase shifting operator is also a useful tool to solve the dynamic problems of the mnltimode coordinate-momentum coupled harmonic oscillators. The exact energy spectra and eigenstates of such multimode coupled harmonic oscillators can be easily obtained by using the rnultimode phase shifting operator. 展开更多
关键词 phase shifting operator coupled harmonic oscillators energy spectrums energy eigenstates
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