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The “Dead Universe” Theory: Natural Separation of Galaxies Driven by the Remnants of a Supermassive Dead Universe
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作者 Joel Almeida 《Natural Science》 2024年第6期65-101,共37页
This article explores the dead universe theory as a novel interpretation for the origin and evolution of the universe, suggesting that our cosmos may have originated from the remnants of a preceding universe. This per... This article explores the dead universe theory as a novel interpretation for the origin and evolution of the universe, suggesting that our cosmos may have originated from the remnants of a preceding universe. This perspective challenges the conventional Big Bang theory, particularly concerning dark matter, the expansion of the universe, and the interpretation of phenomena such as gravitational waves. 展开更多
关键词 Dead Universe theory Heat Death of the Universe Big Bang theory Universe’s Ultimate Fate Universe Expansion Big Freeze Universe Cosmological Models End of Universe Theories Natural Galaxy Drift Future of the Universe Universe Cooling Down Cosmology and Entropy
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Research on Anthropomorphic Obstacle Avoidance Trajectory Planning for Adaptive Driving Scenarios Based on Inverse Reinforcement Learning Theory
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作者 Jian Wu Yang Yan +1 位作者 Yulong Liu Yahui Liu 《Engineering》 SCIE EI CAS CSCD 2024年第2期133-145,共13页
The forward design of trajectory planning strategies requires preset trajectory optimization functions,resulting in poor adaptability of the strategy and an inability to accurately generate obstacle avoidance trajecto... The forward design of trajectory planning strategies requires preset trajectory optimization functions,resulting in poor adaptability of the strategy and an inability to accurately generate obstacle avoidance trajectories that conform to real driver behavior habits.In addition,owing to the strong time-varying dynamic characteristics of obstacle avoidance scenarios,it is necessary to design numerous trajectory optimization functions and adjust the corresponding parameters.Therefore,an anthropomorphic obstacle-avoidance trajectory planning strategy for adaptive driving scenarios is proposed.First,numerous expert-demonstrated trajectories are extracted from the HighD natural driving dataset.Subsequently,a trajectory expectation feature-matching algorithm is proposed that uses maximum entropy inverse reinforcement learning theory to learn the extracted expert-demonstrated trajectories and achieve automatic acquisition of the optimization function of the expert-demonstrated trajectory.Furthermore,a mapping model is constructed by combining the key driving scenario information that affects vehicle obstacle avoidance with the weight of the optimization function,and an anthropomorphic obstacle avoidance trajectory planning strategy for adaptive driving scenarios is proposed.Finally,the proposed strategy is verified based on real driving scenarios.The results show that the strategy can adjust the weight distribution of the trajectory optimization function in real time according to the“emergency degree”of obstacle avoidance and the state of the vehicle.Moreover,this strategy can generate anthropomorphic trajectories that are similar to expert-demonstrated trajectories,effectively improving the adaptability and acceptability of trajectories in driving scenarios. 展开更多
关键词 Obstacle avoidance trajectory planning Inverse reinforcement theory anthropomorphic Adaptive driving scenarios
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Design of a Metasurface Antenna Based on Characteristic Mode Theory
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作者 HE Huan 《电讯技术》 北大核心 2024年第10期1561-1568,共8页
A novel metasurface antenna consisting of 5×5 rectangular patch elements is presented.Thestructure with and without the central element are both analyzed by the Characteristic Mode Theory(CMT).The developed mutua... A novel metasurface antenna consisting of 5×5 rectangular patch elements is presented.Thestructure with and without the central element are both analyzed by the Characteristic Mode Theory(CMT).The developed mutually orthogonal principal modes of the optimized periodic patch structure areexcited by a center-feed dipole.A differential feeding network is employed to realize impedance matching.Prototype with profile height of 0.07λ_(0)(λ_(0)is the wavelength in free space at the lowest operatingfrequency)is fabricated and assembled to verify the simulation results.The measured results show that thereflectance coefficient of proposed matesurface antenna is less than-10 dB in the whole operating bandrange from 4.2 GHz to 5.5 GHz,a relative bandwidth of 26.8%is achieved,and the maximummeasured realized gain is more than 9 dBi with a maximum radiation efficiency of 90%.The designprovides a guideline on the application of characteristic modes(CMs)to radiation problems. 展开更多
关键词 metasurface antenna characteristic mode theory dipole antenna realized gain
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Robustness of the octupole collectivity in 144Ba within the cranking covariant density functional theory in 3D lattice
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作者 Ze‑Kai Li Yuan‑Yuan Wang 《Nuclear Science and Techniques》 SCIE EI CAS CSCD 2024年第8期124-131,共8页
The octupole deformation and collectivity in octupole double-magic nucleus 144Ba are investigated using the Cranking covariant density functional theory in a three-dimensional lattice space.The reduced B(E3)transition... The octupole deformation and collectivity in octupole double-magic nucleus 144Ba are investigated using the Cranking covariant density functional theory in a three-dimensional lattice space.The reduced B(E3)transition probability is implemented for the first time in semiclassical approximation based on the microscopically calculated electric octupole moments.The available data,including the I-ωrelation and electric transitional probabilities B(E2)and B(E3)are well reproduced.Furthermore,it is shown that the ground state of 144Ba exhibits axial octupole and quadrupole deformations that persist up to high spins(I≈24h). 展开更多
关键词 Octupole collectivity Cranking covariant density functional theory Rotational spectrum Electric transitional probabilities
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Complex adaptive system theory,agent-based modeling,and simulation in dominant technology formation
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作者 ZHANG Ruihan SUN Bing 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2024年第1期130-153,共24页
Dominant technology formation is the key for the hightech industry to“cross the chasm”and gain an established foothold in the market(and hence disrupt the regime).Therefore,a stimulus-response model is proposed to i... Dominant technology formation is the key for the hightech industry to“cross the chasm”and gain an established foothold in the market(and hence disrupt the regime).Therefore,a stimulus-response model is proposed to investigate the dominant technology by exploring its formation process and mechanism.Specifically,based on complex adaptive system theory and the basic stimulus-response model,we use a combination of agent-based modeling and system dynamics modeling to capture the interactions between dominant technology and the socio-technical landscape.The results indicate the following:(i)The dynamic interaction is“stimulus-reaction-selection”,which promotes the dominant technology’s formation.(ii)The dominant technology’s formation can be described as a dynamic process in which the adaptation intensity of technology standards increases continuously until it becomes the leading technology under the dual action of internal and external mechanisms.(iii)The dominant technology’s formation in the high-tech industry is influenced by learning ability,the number of adopting users and adaptability.Therein,a“critical scale”of learning ability exists to promote the formation of leading technology:a large number of adopting users can promote the dominant technology’s formation by influencing the adaptive response of technology standards to the socio-technical landscape and the choice of technology standards by the socio-technical landscape.There is a minimum threshold and a maximum threshold for the role of adaptability in the dominant technology’s formation.(iv)The socio-technical landscape can promote the leading technology’s shaping in the high-tech industry,and different elements have different effects.This study promotes research on the formation mechanism of dominant technology in the high-tech industry,presents new perspectives and methods for researchers,and provides essential enlightenment for managers to formulate technology strategies. 展开更多
关键词 complex adaptive system theory agent-based modeling and simulation dominant technology socio-technical landscape adaptation-choice
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Bound State Description of Particles from a Quantum Field Theory of Fermions and Bosons, Compatible with Relativity
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作者 Hans-Peter Morsch 《Journal of High Energy Physics, Gravitation and Cosmology》 CAS 2024年第2期562-573,共12页
Both, the dilemma to find a quantum field theory consistent with Einstein’s law of relativity and the problem to describe existing particles as bound states of matter has been solved by calculating bound state matrix... Both, the dilemma to find a quantum field theory consistent with Einstein’s law of relativity and the problem to describe existing particles as bound states of matter has been solved by calculating bound state matrix elements from a dual fermion-boson Lagrangian. In this formalism, the fermion binding energies are compensated by boson energies, indicating that particles can be generated out of the vacuum. This yields quantitative solutions for various mesons ω (0.78 GeV) - Υ (9.46 GeV) and all leptons e, μ and τ, with uncertainties in the extracted properties of less than 1‰. For transparency, a Web-page with the address htpps://h2909473.stratoserver.net has been constructed, where all calculations can be run on line and also the underlying fortran source code can be inspected. 展开更多
关键词 Quantum Field theory of Fermion and Boson Fields Hadrons and Leptons Described as Bound States of Relativistic Fermions and Bosons Leading to a Total Energy Equal to Zero
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规划设计学中的调查分析法14—数量化Ⅰ类(Quantification Theory Type Ⅰ) 被引量:1
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作者 章俊华 《中国园林》 2003年第9期47-50,共4页
回归及重回归分析和预测,被广泛地应用于各个行业中。但是,有些相当于回归分析中的说明变数,不是数量数据,而是非数量数据,例如:影响入园人数的因素有星期(平日、休日)、天气状况(晴天、阴天、雨雪天等)、季节(春、夏、秋、冬)等。这些... 回归及重回归分析和预测,被广泛地应用于各个行业中。但是,有些相当于回归分析中的说明变数,不是数量数据,而是非数量数据,例如:影响入园人数的因素有星期(平日、休日)、天气状况(晴天、阴天、雨雪天等)、季节(春、夏、秋、冬)等。这些因素因为不是“量”的数据,所以不能用回归或重回归等方法进行分析和预测,但这种情况在规划设计的调查中经常出现,所以数量化Ⅰ类,可以帮助人们进行与回归分析和预测相同的分析,这是十分有效的一种分析方法。 展开更多
关键词 风景园林 规划设计学 调查 数量化I类
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Blackboard Mechanism Based Ant Colony Theory for Dynamic Deployment of Mobile Sensor Networks 被引量:5
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作者 Guang-ping Qi Ping Song Ke-jie Li 《Journal of Bionic Engineering》 SCIE EI CSCD 2008年第3期197-203,共7页
A novel bionic swarm intelligence algorithm, called ant colony algorithm based on a blackboard mechanism, is proposed to solve the autonomy and dynamic deployment of mobiles sensor networks effectively. A blackboard m... A novel bionic swarm intelligence algorithm, called ant colony algorithm based on a blackboard mechanism, is proposed to solve the autonomy and dynamic deployment of mobiles sensor networks effectively. A blackboard mechanism is introduced into the system for making pheromone and completing the algorithm. Every node, which can be looked as an ant, makes one information zone in its memory for communicating with other nodes and leaves pheromone, which is created by ant itself in naalre. Then ant colony theory is used to find the optimization scheme for path planning and deployment of mobile Wireless Sensor Network (WSN). We test the algorithm in a dynamic and unconfigurable environment. The results indicate that the algorithm can reduce the power consumption by 13% averagely, enhance the efficiency of path planning and deployment of mobile WSN by 15% averagely. 展开更多
关键词 ant colony algorithm wireless sensor network blackboard mechanism bionic swarm intelligence algorithm
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问题与回答——Theorizing A New Agenda for Architecture,An Anthology of Architectural Theory,1965~1995一书引起的思考
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作者 张巍 王一平 《华中建筑》 2010年第3期4-6,共3页
内斯比特(KateNesbitt)在她的Theorizing A New Agenda for Architecture,An Anthology of Architectural Theory,1965~1995一书中较为全面地介绍了当代西方建筑理论界所关心的主要问题及其相关的思考。对于这些问题,国内建筑理论界也... 内斯比特(KateNesbitt)在她的Theorizing A New Agenda for Architecture,An Anthology of Architectural Theory,1965~1995一书中较为全面地介绍了当代西方建筑理论界所关心的主要问题及其相关的思考。对于这些问题,国内建筑理论界也有自己的认识。该文通过对两者的比较,试图理清建筑理论的基本意义,那就是提出问题并引起思考。 展开更多
关键词 问题 回答 理论的意义
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Longwall mining “cutting cantilever beam theory” and 110 mining method in China——The third mining science innovation 被引量:65
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作者 Manchao He Guolong Zhu Zhibiao Guo 《Journal of Rock Mechanics and Geotechnical Engineering》 SCIE CSCD 2015年第5期483-492,共10页
With the third innovation in science and technology worldwide, China has also experienced thismarvelous progress. Concerning the longwall mining in China, the "masonry beam theory" (MBT) wasfirst proposed in the 1... With the third innovation in science and technology worldwide, China has also experienced thismarvelous progress. Concerning the longwall mining in China, the "masonry beam theory" (MBT) wasfirst proposed in the 1960s, illustrating that the transmission and equilibrium method of overburdenpressure using reserved coal pillar in mined-out areas can be realized. This forms the so-called "121mining method", which lays a solid foundation for development of mining science and technology inChina. The "transfer rock beam theory" (TRBT) proposed in the 1980s gives a further understanding forthe transmission path of stope overburden pressure and pressure distribution in high-stress areas. In thisregard, the advanced 121 mining method was proposed with smaller coal pillar for excavation design,making significant contributions to improvement of the coal recovery rate in that era. In the 21st century,the traditional mining technologies faced great challenges and, under the theoretical developmentspioneered by Profs. Minggao Qian and Zhenqi Song, the "cutting cantilever beam theory" (CCBT) wasproposed in 2008. After that the 110 mining method is formulated subsequently, namely one stope face,after the first mining cycle, needs one advanced gateway excavation, while the other one is automaticallyformed during the last mining cycle without coal pillars left in the mining area. This method can beimplemented using the CCBT by incorporating the key technologies, including the directional presplittingroof cutting, constant resistance and large deformation (CRLD) bolt/anchor supporting systemwith negative Poisson's ratio (NPR) effect material, and remote real-time monitoring technology. TheCCBT and 110 mining method will provide the theoretical and technical basis for the development ofmining industry in China. 展开更多
关键词 Mining innovation 121 mining method Cutting cantilever beam theory (CCBT) Non-pillar mining 110 mining method
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Optimal Power Management for Antagonizing Between Radar and Jamming Based on Continuous Game Theory 被引量:4
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作者 万开方 高晓光 +1 位作者 李波 梅军峰 《Transactions of Nanjing University of Aeronautics and Astronautics》 EI 2014年第4期386-393,共8页
To solve the problem of dynamic power resource allocation for cooperative penetration combat,the continuous game theory is introduced and a two-person general-sum continuous-game-based model is put forward with a comm... To solve the problem of dynamic power resource allocation for cooperative penetration combat,the continuous game theory is introduced and a two-person general-sum continuous-game-based model is put forward with a common payoff function named collaborative detection probability of netted radar countermeasures.Comparing with traditional optimization methods,an obvious advantage of game-based model is an adequate consideration of the opposite potential strategy.This model guarantees a more effective allocation of the both sides′power resource and a higher combat efficiency during a combat.Furthermore,an analysis of the complexity of the proposed model is given and a hierarchical processing method is presented to simplify the calculating process.Simulation results show the validity of the proposed scheme. 展开更多
关键词 game theory radar countermeasures power management detection probability penetration combat
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Theory of Quantum Dissipation in a Class of Non-Gaussian Environments
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作者 徐瑞雪 刘阳 +1 位作者 张厚道 严以京 《Chinese Journal of Chemical Physics》 SCIE CAS CSCD 2017年第4期395-403,I0001,共10页
In this work we construct a novel dissipaton-equation-of-motion (DEOM) theory in quadratic bath coupling environment, based on an extended algebraic statistical quasi-particle approach. To validate the new ingredien... In this work we construct a novel dissipaton-equation-of-motion (DEOM) theory in quadratic bath coupling environment, based on an extended algebraic statistical quasi-particle approach. To validate the new ingredient of the underlying dissipaton algebra, we derive an extended Zusman equation via a totally different approach. We prove that the new theory, if it starts with the identical setup, constitutes the dynamical resolutions to the extended Zusman equation. Thus, we verify the generalized (non-Gaussian) Wick's theorem with dissipatons-pair added. This new algebraic ingredient enables the dissipaton approach being naturally extended to nonlinear coupling environments. Moreover, it is noticed that, unlike the linear bath coupling case, the influence of a non-Gaussian environment cannot be completely characterized with the linear response theory. The new theory has to take this fact into account. The developed DEOM theory manifests the dynamical interplay between dissipatons and nonlinear bath coupling descriptors that will be specified. Numerical demonstrations will be given with the optical line shapes in quadratic coupling environment. 展开更多
关键词 Non-Gaussian environment Quantum dissipation Dissipaton theory
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Evaluation method and optimization strategies of resilience for air&space defense system of systems based on kill network theory and improved self-information quantity 被引量:6
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作者 Qi Han Bo Pang +4 位作者 Sen Li Ning Li Peng-song Guo Cheng-li Fan Wei-min Li 《Defence Technology(防务技术)》 SCIE EI CAS CSCD 2023年第3期219-239,共21页
Resilience of air&space defense system of systems(SoSs)is critical to national air defense security.However,the research on it is still scarce.In this study,the resilience of air&space defense SoSs is firstly ... Resilience of air&space defense system of systems(SoSs)is critical to national air defense security.However,the research on it is still scarce.In this study,the resilience of air&space defense SoSs is firstly defined and the kill network theory is established by combining super network and kill chain theory.Two cases of the SoSs are considered:(a)The kill chains are relatively homogenous;(b)The kill chains are relatively heterogenous.Meanwhile,two capability assessment methods,which are based on the number of kill chains and improved self-information quantity,respectively,are proposed.The improved self-information quantity modeled based on nodes and edges can achieve qualitative and quantitative assessment of the combat capability by using linguistic Pythagorean fuzzy sets.Then,a resilient evaluation index consisting of risk response,survivability,and quick recovery is proposed accordingly.Finally,network models for regional air defense and anti-missile SoSs are established respectively,and the resilience measurement results are verified and analyzed under different attack and recovery strategies,and the optimization strategies are also proposed.The proposed theory and method can meet different demands to evaluate combat capability and optimize resilience of various types of air&space defense and similar SoSs. 展开更多
关键词 network optimization theory
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Semantic Theory and The Teaching of English Vocabulary 被引量:1
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作者 葛欢 《海外英语》 2012年第8X期237-241,共5页
In this essay,the lexical competence in communication is discussed first of all,then semantic fields theory is elaborated followedby its implication for vocabulary teaching.From this paper,some information could be ac... In this essay,the lexical competence in communication is discussed first of all,then semantic fields theory is elaborated followedby its implication for vocabulary teaching.From this paper,some information could be acquired. 展开更多
关键词 TEACHING ENGLISH VOCABULARY SEMantIC theory
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Computational intelligence approach for uncertainty quantification using evidence theory 被引量:4
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作者 Bin Suo Yongsheng Cheng +1 位作者 Chao Zeng Jun Li 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2013年第2期250-260,共11页
As an alternative or complementary approach to the classical probability theory,the ability of the evidence theory in uncertainty quantification(UQ) analyses is subject of intense research in recent years.Two state-... As an alternative or complementary approach to the classical probability theory,the ability of the evidence theory in uncertainty quantification(UQ) analyses is subject of intense research in recent years.Two state-of-the-art numerical methods,the vertex method and the sampling method,are commonly used to calculate the resulting uncertainty based on the evidence theory.The vertex method is very effective for the monotonous system,but not for the non-monotonous one due to its high computational errors.The sampling method is applicable for both systems.But it always requires a high computational cost in UQ analyses,which makes it inefficient in most complex engineering systems.In this work,a computational intelligence approach is developed to reduce the computational cost and improve the practical utility of the evidence theory in UQ analyses.The method is demonstrated on two challenging problems proposed by Sandia National Laboratory.Simulation results show that the computational efficiency of the proposed method outperforms both the vertex method and the sampling method without decreasing the degree of accuracy.Especially,when the numbers of uncertain parameters and focal elements are large,and the system model is non-monotonic,the computational cost is five times less than that of the sampling method. 展开更多
关键词 uncertainty quantification(UQ) evidence theory hybrid algorithm interval algorithm genetic algorithm(GA).
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Effective-mass theory for coupled quantum dots grown on (11N)-oriented substrates 被引量:2
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作者 李树深 夏建白 《Chinese Physics B》 SCIE EI CAS CSCD 2007年第1期1-5,共5页
The electronic structures of coupled quantum dots grown on (11N)-oriented substrates are studied in the framework of effective-mass envelope-function theory. The results show that the all-hole subbands have the smal... The electronic structures of coupled quantum dots grown on (11N)-oriented substrates are studied in the framework of effective-mass envelope-function theory. The results show that the all-hole subbands have the smallest widths and the optical properties are best for the (113), (114), and (115) growth directions. Our theoretical results agree with the available experimental data. Our calculated results are useful for the application of coupled quantum dots in photoelectric devices. 展开更多
关键词 coupled quantum dots effective-mass theory electronic structures
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Theory of nine elastic constants of biaxial nematics 被引量:2
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作者 刘红 《Chinese Physics B》 SCIE EI CAS CSCD 2008年第3期1060-1069,共10页
In this paper, a rotational invariant of interaction energy between two biaxial-shaped molecules is assumed and in the mean field approximation, nine elastic constants for simple distortion patterns in biaxial nematic... In this paper, a rotational invariant of interaction energy between two biaxial-shaped molecules is assumed and in the mean field approximation, nine elastic constants for simple distortion patterns in biaxial nematics are derived in terms of the thermal average (Dmn^(l)) (Dm'n'^(l')), where Dmn^(l) is the Wigner rotation matrix. In the lowest order terms, the elastic constants depend on coefficients Γ,Γ', λ, order parameters Q0 = Q0(D00^(2)) +Q2(D02^(2)+D0-2^(2)) and Q2 = Q0(D20^(2)) + Q2(D22^(2)+D2-2^(2)). Here Γ and Γ' depend on the function form of molecular interaction energy vj′j″j (τ12) and probability function fk′k″k (τ12), where r12 is the distance between two molecules, and λ is proportional to temperature. Q0 and Q2 are parameters related to multiple moments of molecules. Comparing these results with those obtained from Landau-de Gennes theory, we have obtained relationships between coefficients, order parameters used in both theories. In the special case of uniaxial nematics, both results are reduced to a degenerate case where K11=K33. 展开更多
关键词 biaxial nematic liquid crystal elastic theory
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INVESTIGATION OF THE SCATTERING OF ANTI-PLANE SHEAR WAVES BY TWO GRIFFITH CRACKS USING THE NON-LOCAL THEORY 被引量:2
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作者 Qu Guimin Zhou Zhengong Du Shanyi 《Acta Mechanica Solida Sinica》 SCIE EI 1999年第3期211-219,共9页
In this paper, the scattering of harmonic antiplane shear waves bytwo finite cracks is studied using the non-local theory. The Fouriertransform is applied and a mixed boundary value prob- lem isformulated. Then a set ... In this paper, the scattering of harmonic antiplane shear waves bytwo finite cracks is studied using the non-local theory. The Fouriertransform is applied and a mixed boundary value prob- lem isformulated. Then a set of triple integral equations is solved using anew method, namely Schimidt's method. This method is more exact andmore reasonable than Erigen's for solving this Kind of problem. Theresult of the stress near the crack tip was obtained. Contrary to theclassical elas- Ticity solution, it is found that no stresssingularity is present at the crack tip, which can explain theProblem of macroscopic and microscopic mechanics. 展开更多
关键词 antiplane shear wave the non-local theory Fourier transform
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Game Theory Model and Equilibrium Analysis of Peasant's Production Decision 被引量:2
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作者 Qi Xue-lian Zhang Ya-zhuo Meng Jun 《Journal of Northeast Agricultural University(English Edition)》 CAS 2012年第2期71-73,共3页
Unbalanced agricultural production decision becomes the great block that influences the effective distribution of social resources, national grain security, social stability and economic development. This paper took t... Unbalanced agricultural production decision becomes the great block that influences the effective distribution of social resources, national grain security, social stability and economic development. This paper took the game theory as an analyzed tool to describe the interactional processes among the peasants, and set up the game theory model of independent decision and joint decision by peasants. It was shown that the government's positive guide and the market environment macroscopically controlled by the government could effectively increased the peasants' income 展开更多
关键词 agricultural production decision game theory Nash equilibrium
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Quantization of light energy directly from classical electromagnetic theory in vacuum 被引量:2
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作者 佘卫龙 《Chinese Physics B》 SCIE EI CAS CSCD 2005年第12期2514-2521,共8页
It is currently believed that light quantum or the quantization of light energy is beyond classical physics, and the picture of wave-particle duality, which was criticized by Einstein but has attracted a number of exp... It is currently believed that light quantum or the quantization of light energy is beyond classical physics, and the picture of wave-particle duality, which was criticized by Einstein but has attracted a number of experimental researches, is necessary for the description of light. It is shown in this paper, however, that the quantization of light energy in vacuum, which is the same as that in quantum electrodynamics, can be derived directly from the classical electromagnetic theory through the consideration of statistics based on classical physics. Therefore, the quantization of energy is an intrinsic property of light as a classical electromagnetic wave and has no need of being related to particles. 展开更多
关键词 the nature of light quantization of light energy classical electromagnetic theory consideration of statistics
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