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Four-Dimensional Mathematics Creates the Super Universe
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作者 Ahti Rahikainen 《World Journal of Mechanics》 2023年第7期135-148,共14页
In the common theory of the Universe, the redshift of the light wavelength from distant stars indicates the speed of the star. In this study, the model of the Universe is the surface volume of the four-dimensional sph... In the common theory of the Universe, the redshift of the light wavelength from distant stars indicates the speed of the star. In this study, the model of the Universe is the surface volume of the four-dimensional sphere, and the shape of the Universe results in the most of the redshift of light wavelength. Therefore, there is no dark energy accelerating the Universe. The surface of the four-dimensional sphere is a volume, and this volume is a good model for the Universe. The surface volume of the four-dimensional sphere has been explained by a model of four-dimensional cube, within which the forming of surface volume can be easily shown. The model of four-dimensional cube containing six side cubes is ingenious for explaining the structure of the four-dimensional Universe, but it is not enough because the four-dimensional cube has not six side cubes, but eight side cubes. Therefore, in this study a better method has been created to construct the four-dimensional cube. Our three-dimensional Universe is the surface of the four-dimensional sphere Universe. The volume of our three-dimensional Universe is finite, and beneath it is the infinite volume four-dimensional Super Universe. Two important basic formulae have been derived: The surface volume of the four-dimensional sphere is π<sup>3</sup>R<sup>3</sup> in which R is the radius of the sphere, and the fourth-power volume of the four-dimensional sphere is 1/4 π<sup>3</sup>R<sup>4</sup>. The volume of the Universe has been calculated π<sup>3</sup>R<sup>3</sup> = 62 × 10<sup>30</sup> ly<sup>3</sup>. Time as the fourth dimension of the space takes effect only near the speed of light, and therefore it has been ignored in this study. 展开更多
关键词 Mathematics of the four-Dimensional Space Structure of the Universe Dark Matter Dark Energy Expansion of the Universe Big Bang four-Dimensional Sphere four-Dimensional Matter Atom Theory
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Research on Vehicle Control Technology Using Four-Wheel Independent Steering System 被引量:5
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作者 陈思忠 舒进 杨林 《Journal of Beijing Institute of Technology》 EI CAS 2006年第1期22-26,共5页
The enhancement of vehicle handling stability and maneuverability through active and independent rear wheels control is presented. Firstly, the configuration of four-wheel independent steering prototype vehide is intr... The enhancement of vehicle handling stability and maneuverability through active and independent rear wheels control is presented. Firstly, the configuration of four-wheel independent steering prototype vehide is introduced briefly. Then the concrete overall design of the electronic controllers of four wheel independent steering system (4WIS) is formulated in details. Under the control strategy of zero sideslip angle at mass center, the mathematical model of 4WIS is established to deduce the equations of separated rear wheel steering angles. According to these equations, simulation analysis for 4WIS vehicle performances is finished to show that 4WIS vehicle can improve the maneuverability greatly at low speed and increase the handling stability at high speed. Finally, the road test of 4WIS vehide has performed to verify the correctness of simulation and show that compared with the conventional four wheel steering (4WS) vehicle, the 4WIS vehicle not only improves the kinematical harmony but also decreases steering resistance and lighten abrasion of tires. 展开更多
关键词 four-wheel independent steering system (4WIS) control strategy four-wheel steering system (4WS)
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Anti-synchronization of Four-wing Chaotic Systems via Sliding Mode Control 被引量:4
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作者 Sundarapandian Vaidyanathan Sivaperumal Sampath 《International Journal of Automation and computing》 EI 2012年第3期274-279,共6页
Sliding mode control is an important method used in nonlinear control systems. In robust control systems, the sliding mode control is often adopted due to its inherent advantages of easy realization, fast response and... Sliding mode control is an important method used in nonlinear control systems. In robust control systems, the sliding mode control is often adopted due to its inherent advantages of easy realization, fast response and good transient performance as well as its insensitivity to parameter uncertainties and disturbances. In this paper, we derive new results based on the sliding mode control for the anti-synchronization of identical Qi three-dimensional (3D) four-wing chaotic systems (2008) and identical Liu 3D four-wing chaotic systems (2009). The stability results for the anti-synchronization schemes derived in this paper using sliding mode control (SMC) are established using Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the SMC method is very effective and convenient to achieve global chaos anti-synchronization of the identical Qi four-wing chaotic systems and identical Liu four-wing chaotic systems. Numerical simulations are shown to illustrate and validate the synchronization schemes derived in this paper. 展开更多
关键词 Hybrid synchronization chaos sliding control Qi four-wing chaotic system Liu four-wing chaotic system
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Influence of Waveguide Properties on Wave Prototypes Likely to Accompany the Dynamics of Four-Wave Mixing in Optical Fibers
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作者 Jean Roger Bogning Marcelle Nina Zambo Abou’ou +4 位作者 Christian Regis Ngouo Tchinda Mathurin Fomekong Oriel Loh Ndichia Stallone Mezezem Songna François Béceau Pelap 《Journal of Applied Mathematics and Physics》 2024年第7期2601-2633,共33页
In this article, we study the impacts of nonlinearity and dispersion on signals likely to propagate in the context of the dynamics of four-wave mixing. Thus, we use an indirect resolution technique based on the use of... In this article, we study the impacts of nonlinearity and dispersion on signals likely to propagate in the context of the dynamics of four-wave mixing. Thus, we use an indirect resolution technique based on the use of the iB-function to first decouple the nonlinear partial differential equations that govern the propagation dynamics in this case, and subsequently solve them to propose some prototype solutions. These analytical solutions have been obtained;we check the impact of nonlinearity and dispersion. The interest of this work lies not only in the resolution of the partial differential equations that govern the dynamics of wave propagation in this case since these equations not at all easy to integrate analytically and their analytical solutions are very rare, in other words, we propose analytically the solutions of the nonlinear coupled partial differential equations which govern the dynamics of four-wave mixing in optical fibers. Beyond the physical interest of this work, there is also an appreciable mathematical interest. 展开更多
关键词 Optical Fiber Four Waves Mixing Implicit Bogning Function Coupled Nonlinear Partial Differential Equations Nonlinear Coefficient Dispersive Coefficient Waveguide Properties
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Translation Compensation Methods under Skopostheorie:A Comparative Study on Four-character Chengyu Translation Compensation in Hong Lou Meng
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作者 邓雪玲 《海外英语》 2011年第6X期209-210,共2页
This article attempts to apply skopos theory and make a comparative study of the translation compensation methods of two English versions of Hong Lou Meng in terms of four-character chengyu from the linguistic perspec... This article attempts to apply skopos theory and make a comparative study of the translation compensation methods of two English versions of Hong Lou Meng in terms of four-character chengyu from the linguistic perspective. 展开更多
关键词 TRANSLATION of four-CHARACTER chengyu COMPENSATION METHODS skopotheories LINGUISTIC perspective
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4-Staining of “Staining Dilemma Configuration” in Four-Color Conjecture
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作者 Yudian Zhang Lichong Zhang 《Journal of Applied Mathematics and Physics》 2022年第3期915-929,共15页
This article attempts to successfully fill Kempe proof loophole, namely 4-staining of “staining dilemma configuration”. Our method is as follows: 1) Discovered and proved the existence theorem of the quadrilateral w... This article attempts to successfully fill Kempe proof loophole, namely 4-staining of “staining dilemma configuration”. Our method is as follows: 1) Discovered and proved the existence theorem of the quadrilateral with four-color vertices and its properties theorems, namely theorems 1 and 2. From this, the non-10-fold symmetry transformation rule of the geometric structure of Errera configuration is generated, and using this rule, according to whether the “staining dilemma configuration” is 10-fold symmetry, they are divided into two categories;2) Using this rule, combining the different research results of several mathematicians on Errera graphs, and using four different classifications of propositional truth and falsehood, a new Theorem 3 is established;3) Using Theorem 3, the theoretical proof that the non-10-fold symmetric “ staining dilemma configuration” can be 4-staining;4) Through 4-staining of the four configurations of Errera, Obtained the Z-staining program (also called Theorem 4), and using this program and mathematical induction, gave the 10-fold symmetric “staining dilemma configuration” 4-staining proof. Completed the complete and concise manual proof of the four-color conjecture. 展开更多
关键词 four-Color Conjecture Kempe Proof Staining Dilemma Configuration four-Color Vertex Quadrilateral Non-10 Fold Symmetric Transformation
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A novel four-wing chaotic attractor generated from a three-dimensional quadratic autonomous system 被引量:12
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作者 董恩增 陈在平 +1 位作者 陈增强 袁著祉 《Chinese Physics B》 SCIE EI CAS CSCD 2009年第7期2680-2689,共10页
This paper presents a new 3D quadratic autonomous chaotic system which contains five system parameters and three quadratic cross-product terms,and the system can generate a single four-wing chaotic attractor with wide... This paper presents a new 3D quadratic autonomous chaotic system which contains five system parameters and three quadratic cross-product terms,and the system can generate a single four-wing chaotic attractor with wide parameter ranges. Through theoretical analysis,the Hopf bifurcation processes are proved to arise at certain equilibrium points.Numerical bifurcation analysis shows that the system has many interesting complex dynamical behaviours;the system trajectory can evolve to a chaotic attractor from a periodic orbit or a fixed point as the proper parameter varies. Finally,an analog electronic circuit is designed to physically realize the chaotic system;the existence of four-wing chaotic attractor is verified by the analog circuit realization. 展开更多
关键词 CHAOS four-wing chaotic attractor bifurcation analysis chaotic circuit
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Spatial Vibration and Its Numerical Analytical Method of Four-high Rolling Mills 被引量:11
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作者 Yong-jiang ZHENG Guang-xian SHEN +2 位作者 Yi-geng LI Ming LI Hong-min LIU 《Journal of Iron and Steel Research International》 SCIE EI CAS CSCD 2014年第9期837-843,共7页
The rolls in contemporary four-high mills cannot be maintained parallel during the rolling process. There- fore, four-high rolling mill vibrations take place in six degree of freedom (DOF) leading to spatial behavio... The rolls in contemporary four-high mills cannot be maintained parallel during the rolling process. There- fore, four-high rolling mill vibrations take place in six degree of freedom (DOF) leading to spatial behaviors invol- ving vertical, horizontal, axial, torsional, cross and swinging vibration modes resulting in complex relative motions between the rolls. Two numerical methods, modified Riccati-transfer matrix method (Riccati-TMM) and finite ele- ment method (FEM), are presented to analyze a spatial vibration characteristic of two four-high rolling mills with different stability. The natural frequency and mode shape of four-high rolling mills are obtained, and the clearance has a great effect on natural frequency and mode shape. In addition, field testing experiment is also conducted to measure natural frequency by power spectrum analysis of rolling mill vibration. Experimental results basically agree with those calculated by Riccati-TMM and FEM, which means that the Riccati-TMM and the FEM can be used for analysis of spatial vibration of four-high rolling mill. Meanwhile, the spatial vibration shows more compound vibra- tion behaviors and the negative effect of horizontal, vertical, cross and swinging vibration modes are effectively con- trolled after redesign of rolling mill. These advantages have a great significance for the rolling mill to be operated with a much higher rolling speed and improved yield of products. 展开更多
关键词 four-high roiling mill spatial vibration transfer matrix method FEM SIMULATION
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Coupling Ensemble Kalman Filter with Four-dimensional Variational Data Assimilation 被引量:26
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作者 Fuqing ZHANG Meng ZHANG James A. HANSEN 《Advances in Atmospheric Sciences》 SCIE CAS CSCD 2009年第1期1-8,共8页
This study examines the performance of coupling the deterministic four-dimensional variational assimilation system (4DVAR) with an ensemble Kalman filter (EnKF) to produce a superior hybrid approach for data assim... This study examines the performance of coupling the deterministic four-dimensional variational assimilation system (4DVAR) with an ensemble Kalman filter (EnKF) to produce a superior hybrid approach for data assimilation. The coupled assimilation scheme (E4DVAR) benefits from using the state-dependent uncertainty provided by EnKF while taking advantage of 4DVAR in preventing filter divergence: the 4DVAR analysis produces posterior maximum likelihood solutions through minimization of a cost function about which the ensemble perturbations are transformed, and the resulting ensemble analysis can be propagated forward both for the next assimilation cycle and as a basis for ensemble forecasting. The feasibility and effectiveness of this coupled approach are demonstrated in an idealized model with simulated observations. It is found that the E4DVAR is capable of outperforming both 4DVAR and the EnKF under both perfect- and imperfect-model scenarios. The performance of the coupled scheme is also less sensitive to either the ensemble size or the assimilation window length than those for standard EnKF or 4DVAR implementations. 展开更多
关键词 data assimilation four-dimensional variational data assimilation ensemble Kalman filter Lorenz model hybrid method
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Hopf bifurcation analysis and circuit implementation for a novel four-wing hyper-chaotic system 被引量:11
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作者 薛薇 齐国元 +2 位作者 沐晶晶 贾红艳 郭彦岭 《Chinese Physics B》 SCIE EI CAS CSCD 2013年第8期325-332,共8页
In the paper, a novel four-wing hyper-chaotic system is proposed and analyzed. A rare dynamic phenomenon is found that this new system with one equilibrium generates a four-wing-hyper-chaotic attractor as parameter va... In the paper, a novel four-wing hyper-chaotic system is proposed and analyzed. A rare dynamic phenomenon is found that this new system with one equilibrium generates a four-wing-hyper-chaotic attractor as parameter varies. The system has rich and complex dynamical behaviors, and it is investigated in terms of Lyapunov exponents, bifurcation diagrams, Poincare maps, frequency spectrum, and numerical simulations. In addition, the theoretical analysis shows that the system undergoes a Hopf bifurcation as one parameter varies, which is illustrated by the numerical simulation. Finally, an analog circuit is designed to implement this hyper-chaotic system. 展开更多
关键词 HYPER-CHAOS four-wing chaotic system one equilibrium Hopf bifurcation circuit implementation
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Testing a Four-Dimensional Variational Data Assimilation Method Using an Improved Intermediate Coupled Model for ENSO Analysis and Prediction 被引量:13
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作者 Chuan GAO Xinrong WU Rong-Hua ZHANG 《Advances in Atmospheric Sciences》 SCIE CAS CSCD 2016年第7期875-888,共14页
A four-dimensional variational (4D-Var) data assimilation method is implemented in an improved intermediate coupled model (ICM) of the tropical Pacific. A twin experiment is designed to evaluate the impact of the ... A four-dimensional variational (4D-Var) data assimilation method is implemented in an improved intermediate coupled model (ICM) of the tropical Pacific. A twin experiment is designed to evaluate the impact of the 4D-Var data assimilation algorithm on ENSO analysis and prediction based on the ICM. The model error is assumed to arise only from the parameter uncertainty. The "observation" of the SST anomaly, which is sampled from a "truth" model simulation that takes default parameter values and has Gaussian noise added, is directly assimilated into the assimilation model with its parameters set erroneously. Results show that 4D-Var effectively reduces the error of ENSO analysis and therefore improves the prediction skill of ENSO events compared with the non-assimilation case. These results provide a promising way for the ICM to achieve better real-time ENSO prediction. 展开更多
关键词 four-dimensional variational data assimilation intermediate coupled model twin experiment ENSO prediction
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A novel four-way combining catalysts for simultaneous removal of exhaust pollutants from diesel engine 被引量:11
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作者 Jian Liu,Jie Xu,Zhen Zhao,Aijun Duan,Guiyuan Jiang,Yanni Jing State Key Laboratory of Heavy Oil Processing,China University of Petroleum,Beijing 102249,China. 《Journal of Environmental Sciences》 SCIE EI CAS CSCD 2010年第7期1104-1109,共6页
A novel four-way combining catalysts containing double layers was applied to simultaneously remove four kinds of exhaust pollutants (NOx, CO, HC and PM) emitted from diesel engine. The four-way catalysts were charac... A novel four-way combining catalysts containing double layers was applied to simultaneously remove four kinds of exhaust pollutants (NOx, CO, HC and PM) emitted from diesel engine. The four-way catalysts were characterized using scanning electron microscope (SEM) and Ultraviolet visible diffuse reflectance spectroscopy (UV-Vis DRS). Their catalytic performances were evaluated by temperature-programmed reaction technology. The double layer catalysts could effectively remove the four main pollutants. The highest catalytic activity was given by the two-layered catalysts of La0.6 K0.4CoO3/Al2O3 and W/HZSM-5. Under the simulated exhaust gases conditions, the peak temperature of the soot combustion was 421℃, the maximal conversion of NO to N2 was 74%, the temperature of the HC total conversion was 357℃, and the maximum conversion ratio of CO was 99%. 展开更多
关键词 four-way combining catalyst diesel engine exhaust double layers perovskite oxides zeolite catalysts
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Automatic three-dimensional reconstruction based on four-view stereo vision using checkerboard pattern 被引量:5
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作者 XIONG Jie ZHONG Si-dong +1 位作者 LIU Yong TU Li-fen 《Journal of Central South University》 SCIE EI CAS CSCD 2017年第5期1063-1072,共10页
An automatic three-dimensional(3D) reconstruction method based on four-view stereo vision using checkerboard pattern is presented. Mismatches easily exist in traditional binocular stereo matching due to the repeatable... An automatic three-dimensional(3D) reconstruction method based on four-view stereo vision using checkerboard pattern is presented. Mismatches easily exist in traditional binocular stereo matching due to the repeatable or similar features of binocular images. In order to reduce the probability of mismatching and improve the measure precision, a four-camera measurement system which can add extra matching constraints and offer multiple measurements is applied in this work. Moreover, a series of different checkerboard patterns are projected onto the object to obtain dense feature points and remove mismatched points. Finally, the 3D model is generated by performing Delaunay triangulation and texture mapping on the point cloud obtained by four-view matching. This method was tested on the 3D reconstruction of a terracotta soldier sculpture and the Buddhas in the Mogao Grottoes. Their point clouds without mismatched points were obtained and less processing time was consumed in most cases relative to binocular matching. These good reconstructed models show the effectiveness of the method. 展开更多
关键词 three-dimensional reconstruction four-view STEREO VISION CHECKERBOARD pattern DENSE point
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Linkage analysis and integrated software GAPL for pure-line populations derived from four-way and eight-way crosses 被引量:7
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作者 Luyan Zhang Lei Meng Jiankang Wang 《The Crop Journal》 SCIE CAS CSCD 2019年第3期283-293,共11页
Pure lines derived from multiple parents provide abundant variation for genetic study.However,efficient genetic analysis methods and user-friendly software are still lacking.In this study, we developed linkage analysi... Pure lines derived from multiple parents provide abundant variation for genetic study.However,efficient genetic analysis methods and user-friendly software are still lacking.In this study, we developed linkage analysis methods and integrated analysis software for pure-line populations derived from four-way and eight-way crosses.First, polymorphic markers are classified into different categories according to the number of identifiable alleles in the inbred parents.Expected genotypic probability is then derived for each pair of complete markers, and based on them a maximum likelihood estimate(MLE) of recombination frequency is calculated.An EM algorithm is proposed for calculating recombination frequencies in scenarios that at least one marker is incomplete.A linkage map can thus be constructed using estimated recombination frequencies.We describe a software package called GAPL for recombination frequency estimation and linkage map construction in multi-parental pure-line populations.Both simulation studies and results from a reported four-way cross recombinant inbred line population demonstrate that the proposed method and software can build more accurate linkage maps in shorter times than other published software packages.The GAPL software is freely available from www.isbreeding.net and can also be used for QTL mapping in multi-parental populations. 展开更多
关键词 Pure lines four-way CROSS Eight-way CROSS Recombination frequency estimation Integrated software
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Chatter stability prediction in four-axis milling of aero-engine casings with bull-nose end mill 被引量:10
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作者 Zhou Xu Zhang Dinghua +1 位作者 Luo Ming Wu Baohai 《Chinese Journal of Aeronautics》 SCIE EI CAS CSCD 2015年第6期1766-1773,共8页
An analytical model for chatter aero-engine casings is presented in this paper stability prediction in bull-nose end milling of And the mechanics and dynamics variations due to the complex cutter and workpiece geomet... An analytical model for chatter aero-engine casings is presented in this paper stability prediction in bull-nose end milling of And the mechanics and dynamics variations due to the complex cutter and workpiece geometry are considered by analyzing the effects of the lead angle on the milling process. Firstly, the tool-workpiece engagement region is obtained by using a previously developed method and divided into several disk elements along the tool-axis direction. Secondly, a 3D dynamic model for stability limit calculation is developed and simplified into a 1D model in normal direction considering only the dominant mode of the workpiece. Then the cutting force coefficients, the start and exit angles corresponding to each disk element are determined. And the total stability lobe diagram is calculated using an iterative algorithm. Finally, several experimental tests are carried out to validate the feasibility and effectiveness of the proposed ~rediction approach. 展开更多
关键词 Aero-engine casings Bull-nose end mill Chatter four-axis milling Stability lobe diagram
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Kinematics and Dynamics Analysis of Drive Mechanism of Parallel Four-Bar Energy-Saving Pumping Unit 被引量:5
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作者 ZHANG Xiangming YANG Xia GUO Zhao 《Wuhan University Journal of Natural Sciences》 CAS 2012年第1期73-78,共6页
The conventional beam pumping unh consumes a large amount of energy due to its unsmooth movement. In this work, we design a new energy-saving parallel four-bar pumping unit and derive the kinematic and dynamic law of ... The conventional beam pumping unh consumes a large amount of energy due to its unsmooth movement. In this work, we design a new energy-saving parallel four-bar pumping unit and derive the kinematic and dynamic law of the drive mechanism systematically by theoretical method. For the given target technical parameter, the theoretical results are verified by computer simulation, which shows that the simulation dynamic curves agree well with the theoretical ones and the calculated power consumption is low. Theoretical analysis shows that the newly designed pumping unit reduces average power by 28.8% compared with its conventional counterpart. The much lower theoretical energy consumption and the better dynamic performance indicate that the new energy-saving pumping unit is well designed and will have a significant application prospect. 展开更多
关键词 parallel four-bar pumping unit drive mechanism KINEMATICS dynamics energy consumption
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Four-Dimensional Variational Data Assimilation Experiments for a Heavy Rain Case During the 2002 IOP in China 被引量:5
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作者 张林 倪允琪 《Advances in Atmospheric Sciences》 SCIE CAS CSCD 2005年第2期300-312,共13页
A heavy rainfall event along the mei-yu front during 22-23 June 2002 was chosen for this study. To assess the impact of the routine and additional IOP (intensive observation period) radiosonde observations on the meso... A heavy rainfall event along the mei-yu front during 22-23 June 2002 was chosen for this study. To assess the impact of the routine and additional IOP (intensive observation period) radiosonde observations on the mesoscale heavy rainfall forecast, a series of four-dimensional variational (4DVAR) data assimilation and model simulation experiments was conducted using nonhydrostatic mesoscale model MM5 and the MM5 4DVAR system. The effects of the intensive observations in the different areas on the heavy rainfall forecast were also investigated. The results showed that improvement of the forecast skill for mesoscale heavy rainfall intensity was possible from the assimilation of the IOP radiosonde observations. However, the impact of the IOP observations on the forecast of the rainfall pattern was not significant. Initial conditions obtained through the 4DVAR experiments with a 12-h assimilation window were capable of improving the 24-h forecast. The simulated results after the assimilation showed that it would be best to perform the intensive radiosonde observations in the upstream of the rainfall area and in the moisture passageway area at the same time. Initial conditions created by the 4DVAR led to the low-level moisture convergence over the rainfall area, enhanced frontogenesis and upward motion within the mei-yu front, and intensified middle- and high-level unstable stratification in front of the mei-yu front. Consequently, the heavy rainfall forecast was improved. 展开更多
关键词 intensive radiosonde observations four-dimensional variational assimilation
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基于“Four-hot”编码和Transformer-LSTM模型的船型识别方法 被引量:1
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作者 王哲 张静 +1 位作者 李磊 蒋俊 《信息工程大学学报》 2021年第6期756-763,共8页
为克服依靠图像数据进行识别的局限,使用航迹数据和深度学习方法是当前船型识别的热门方案。针对船型识别任务中常用的长短时记忆(Long Short Term Memory,LSTM)网络对航迹数据特征提取的性能饱和问题,提出了一种基于“Four-hot”编码和... 为克服依靠图像数据进行识别的局限,使用航迹数据和深度学习方法是当前船型识别的热门方案。针对船型识别任务中常用的长短时记忆(Long Short Term Memory,LSTM)网络对航迹数据特征提取的性能饱和问题,提出了一种基于“Four-hot”编码和Transformer-LSTM神经网络模型的船型识别方法。首先将航迹数据编码为“Four-hot”向量形式;然后构建由Transformer编码模块和LSTM网络级联的Transformer-LSTM神经网络模型,用LSTM网络对Transformer输出的高层表示进行二次学习。在船舶自动识别系统(Automatic Identification System,AIS)数据集上的实验结果显示,所提出的方法在测试集上的加权平均F1分数(Weighted Average F1,WAF1)比未编码航迹数据经5类实验模型直接训练和测试得到的值高3.09百分点以上。 展开更多
关键词 four-hot”编码 船型识别 Transformer模型 长短时记忆(LSTM)
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Multiple positive solutions for a class of nonlinear four-point boundary value problem with p-Laplacian 被引量:10
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作者 LI Xiang-feng 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2008年第2期143-150,共8页
This paper deals with the existence of multiple positive solutions for a class of nonlinear singular four-point boundary value problem with p-Laplacian:{(φ(u′))′+a(t)f(u(t))=0, 0〈t〈1, αφ(u(... This paper deals with the existence of multiple positive solutions for a class of nonlinear singular four-point boundary value problem with p-Laplacian:{(φ(u′))′+a(t)f(u(t))=0, 0〈t〈1, αφ(u(0))-βφ(u′(ξ))=0,γφ(u(1))+δφ(u′(η))0,where φ(x) = |x|^p-2x,p 〉 1, a(t) may be singular at t = 0 and/or t = 1. By applying Leggett-Williams fixed point theorem and Schauder fixed point theorem, the sufficient conditions for the existence of multiple (at least three) positive solutions to the above four-point boundary value problem are provided. An example to illustrate the importance of the results obtained is also given. 展开更多
关键词 p-Laplacian operator multiple positive solution four-point singular boundary value problem fixed-point theorem.
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