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一道未定式极限习题的解法研究

科技风 2025年第1期 124-127页

作者：油俊彦菏泽学院数学与统计学院山东菏泽274000

极限是高等数学学习中的一个重点,是学生后续学习的重要基础与理论工具,但基于极限问题的形式多样性,因此它也是学生学习中的一个难点,尤其是未定式极限的求解方法更是灵活多样。0/0型未定式极限常用的方法主要有洛必达法则、等价无穷... 详细信息

极限是高等数学学习中的一个重点,是学生后续学习的重要基础与理论工具,但基于极限问题的形式多样性,因此它也是学生学习中的一个难点,尤其是未定式极限的求解方法更是灵活多样。0/0型未定式极限常用的方法主要有洛必达法则、等价无穷小的代换等,∞/∞型未定式极限常用的方法除了洛必达法则外,还要考虑使用重要极限、无穷大与无穷小的转化、重要结论等。本文针对一道∞/∞型的未定式极限习题,利用洛必达法则及其与多种形式的三角恒等变换的结合给出了六种解法,并对每一种解法进行了详细的分析。最后,总结在该题中得到的结论,旨在提高学生的计算能力和发散思维。

关键词：未定式极限洛必达法则三角恒等变换发散思维

Phase evolution,hydrogen storage thermodynamics and kinetics of ternary Mg90Ce5Sm5 alloy

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Journal of Rare Earths 2020年第6期38卷 633-641页

作者： Hui Yong shihai Guo Zeming Yuan Wei Zhang Yan Qi Dongliang Zhao Yanghuan Zhang Department of Functional Material Research Central Iron and Steel Research InstituteBeijing 100081China Key Laboratory of Integrated Exploitation of Baiyun Obo Multi-Metal Resources Inner Mongolia University of Science and TechnologyBaotou 014010China

Greatly stable thermodynamics and sluggish kinetics impede the practical application of Mg-based hydrogen storage *** modifications of composition and structure are important strategies in turning these hydrogen storage *** this study,Mg-based Mg90Ce5 Sm5 ternary alloy fabricated by vacuum induction melting was investigated to explore the performance and the reaction mechanism as hydrogen storage material by X-ray diffraction(XRD),scanning electron microscope(SEM),transmission electron microscopy(TEM) and pressure-composition isotherms(PCI) *** results indicate that the Mg-based Mg90Ce5 Sm5 ternary alloy consists of two solid solution phases,including the major phases(Ce,Sm)5 Mg41 and the minor phases(Ce,Sm)*** hydrogen absorption,these phases transform into the MgH2 and(Ce,Sm)H2.73 phase,while after hydrogen desorption,the MgH2 transforms into the Mg phase,but the(Ce,Sm)H2.73 phases are not *** alloy has a reversible hydrogen capacity of about 5.5 wt% H2 and exhibits well isothermal hydrogen absorption *** energy of 106 kJ/mol was obtained from the hydrogen desorption data between 573 and 633 K,which also exhibits the enhanced kinetics compared with the pure MgH2 sample,as a result of bimetallic synergy catalysis function of(Ce,Sm)H2.73 *** rate of hydrogen desorption is controlled by the release and recombination of H2 from the Mg ***,the changes of enthalpy and entropy of hydrogen absorption/desorption were calculated to be-80.0 kJ/mol H2,-137.5 J/K/mol H2 and 81.2 kJ/mol H2,139.2 J/K/mol H2,respectively.

关键词： Hydrogen storage Reaction mechanism Kinetics Thermodynamics Activation energy Rare earths

An enhanced digital predistortion algorithm based on polynomial model identification

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Science China(Information Sciences) 2019年第2期62卷 160-168页

作者： Wanzhi MA Xin QUAN Bo ZHAO Ying LIU Wensheng PAN shihai SHAO youxi TANG National Key Laboratory of Science and Technology on Communication University of Electronic Science and Technology of China Military Delegate Office in Shijiazhuang Military Delegate Bureau of Equipment Development Department

To improve the accuracy of the nonlinear distortion correction for the radio frequency(RF)power amplifier(PA), it is necessary to precisely obtain the reverse function of the PA nonlinear ***, the direct inversion of the PA nonlinear model involves solving a high-order univariate polynomial,which is difficult to apply in engineering. In this study, based on the envelope memory polynomial(EMP)model, the high-order terms of the nonlinear model are approximated by their previously calculated values through iterations and considered as known constants in the polynomial solution finding process, thereby resulting in a significant reduction in computational complexity. Compared with the direct inversion method,model of a 9 th-order nonlinear, the proposed method reduces the calculation time in the coordinated rotation digital computer(CORDIC) algorithm by at least 80%. The simulation results show that for a long-term evolution(LTE) downlink signal, the results obtained by the proposed simplified method agree well with those obtained by direct inversion method.

关键词： digital predistortion power amplifier nonlinear distortion memory effects radio frequency

Holographic QSAR of environmental estrogens

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Science China Chemistry 2005年第2期48卷 156-161页

作者： WANG Xiaodong XIAO Qianfen CUI shihai LIU Shushen YIN Daqiang WANG Liansheng State Key Laboratory of Pollution Control and Resources Reuse School of the Environment Nanjing University Nanjing 210093 China State Key Laboratory of Pollution Control and Resources ReuseSchool of the Environment Nanjing University Nanjing 210093 China State Key Laboratory of Pollution Control and Resources ReuseSchool of the Environment Nanjing University Nanjing 210093 China State Key Laboratory of Pollution Control and Resources ReuseSchool of the Environment Nanjing University Nanjing 210093 China State Key Laboratory of Pollution Control and Resources ReuseSchool of the Environment Nanjing University Nanjing 210093 China State Key Laboratory of Pollution Control and Resources ReuseSchool of the Environment Nanjing University Nanjing 210093 China

Experimental and epidemiological studies suggest that some man-made and natu- rally occurring chemicals related to the environment have the potential to interrupt normal func- tioning of the endocrine systems of humans and wildlife. These chemicals, termed EDCs (Endo- crine disrupting Chemicals), pose serious threats to the reproductive capability of humans and wildlife. Because of the structural diversity and various types, development of structure-based rapid screening methodologies is important and necessary for the assessment of the environ- mental pollutants. In this paper molecular hologram based QSAR models were developed with the combinatory application of partial least square (PLS) regression for a large diverse set of 105 environmental estrogens. Quantitatively predictive models were developed based on only mo- lecular structures, which can be used for the accurate prediction of estrogenicity to rapidly screen potential environmental endocrine disrupting chemicals.

关键词： EDCs, RBA, molecular hologram, QSAR, CoMFA.

A semi-spring and semi-edge combined contact model in CDEM and its application to analysis of Jiweishan landslide

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Journal of Rock Mechanics and Geotechnical Engineering 2014年第1期6卷 26-35页

作者： Chun Feng shihai Li Xiaoyu Liu Yanan Zhang Institute of Mechanics Chinese Academy of Sciences

Continuum-based discrete element method(CDEM)is an explicit numerical method used for simulation of progressive failure of geological *** improve the efficiency of contact detection and simplify the calculation steps for contact forces,semi-spring and semi-edge are introduced in *** is derived from block vertex,and formed by indenting the block vertex into each face(24semisprings for a hexahedral element).The formation process of semi-edge is the same as that of semi-spring(24semi-edges for a hexahedral element).Based on the semi-springs and semi-edges,a new type of combined contact model is *** to this model,six contact types could be reduced to two,*** semi-spring target face contact and semi-edge target edge *** the combined model,the contact force could be calculated directly(the information of contact type is not necessary),and the failure judgment could be executed in a straightforward way(each semi-spring and semi-edge own their characteristic areas).The algorithm has been successfully programmed in C++*** simple numerical cases are presented to show the validity and accuracy of this ***,the failure mode,sliding distance and critical friction angle of Jiweishan landslide are studied with the combined model.

关键词： Continuum-based discrete element method (CDEM) Contact detection method Semi-spring Semi-edge Landslide

Effect of anisotropic characteristics on the mechanical behavior of asphalt concrete overlay

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Frontiers of Structural and Civil Engineering 2019年第1期13卷 110-122页

作者： Lingyun you Zhanping you Kezhen YAN Department of Civil and Environmental Engineering Michigan Technological UniversityHoughtonMI 49931USA College of Civil Engineering Hunan UniversityChangsha 410082China

Asphalt concrete (AC)overlays placed over old asphalt pavement have become an alternative to repairing and reinforcing *** strength contributed by the AC overlay is strongly influenced by the anisotropic properties of the pavement *** study was conducted to analyze the influence of anisotropy,modulus gradient properties,and the condition of the AC overlay and old pavement contact plane on the mechanical behaviors of AC overlays,as well as to quantify the influence of the degree of anisotropy on the mechanical behaviors of AC overlay by a sensitivity analysis (SA).The mechanical behaviors of the AC overlay were numerically obtained using the three- dimensional finite element method with the aid of ABAQUS,a commercial *** in the AC overlay's modulus as a function of temperature as well as the contact state between the AC overlay and AC layer were considered. The SA is based on standardized regression coefficients *** the mechanical behavior in terms of surface deflection,stress,and strain of the anisotropy model against those corresponding to the isotropic model under static loads show that the anisotropic properties had greater effects on the mechanical behavior of the AC *** addition,the maximum shear stress in the AC overlay was the most significant output parameter affected by the degree of anisotropy. Therefore,future research concerning the reinforcement and repair of pavements should consider the anisotropic properties of the pavement materials.

关键词： asphalt concrete overlay anisotropy temperature gradients modulus gradients finite element simulation sensitivity analysis

Mission-driven autonomous perception and fusion based on UAV swarm

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Chinese Journal of Aeronautics 2020年第11期33卷 2831-2834页

作者： you HE Research Institute of Information Fusion Naval Aviation UniversityYantai 264001China

Distributed autonomous situational awareness is one of the most important foundation for Unmanned Aerial Vehicle(UAV)swarm to implement various *** the application environment being usually characterized by strong confrontation,high dynamics,and deep uncertainty,the distributed situational awareness system based on UAV swarm needs to be driven by the mission requirements,while each node in the network can autonomously avoid collisions and perform detection mission through limited resource sharing as well as complementarity of respective *** efficiently solving the problems of self-avoidance,autonomous flocking and splitting,joint estimation and control,etc.,perception data from multi-platform multi-source should be extracted and fused reasonably,to generate refined,tailored target information and provide reliable support for decision-making.

关键词： Autonomous perception Consensus Distributed information fusion Situation awareness State estimation Swarm Unmanned aerial vehicle

AN IMPROVED AND EFFICIENT DETECTION SCHEME FOR V-BLAST SYSTEMS WITH QAM MODULATION

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Journal of Electronics(China) 2008年第5期25卷 588-594页

作者： Lin Huajiong Tang youxi Shao shihai National Anti-Jamming Communications Laboratory University of Electronic Science and Technology of China Chengdu 510054 China

The paper proposed an improved Ordered Successive Interference Cancellation(OSIC) detection scheme for V-BLAST systems with square/rectangular Quadrature Amplitude Modulation(QAM) *** utilizes an equivalent real-valued vector expression of relationship between transmit signals and received signals,exploits the constellation's product-form structure and can eventually make the order,in which components of the transmit signals vector are extracted,more "optimal" in some ***,it can offer an improved error probability as compared to the conventional OSIC detection *** addition,the paper also proposes an efficient projection al-gorithm to calculate nulling vectors in a simple recursive fashion in order to avoid the vast increase of complexity,which is due to the fact that the original complex N -dimensional data vector and M×N channel matrix are transformed into a real 2N -dimensional data vector and a real 2M ×2N channel matrix respectively.A scrutinous complexity analysis shows that the complexity increases by only 33% as compared to the conventional scheme.

关键词： Multiple-Input Multiple-Output (MIMO) Ordered Successive Interference Cancellation (OSIC) Quadrature Amplitude Modulation (QAM) Vertical Bell Labs Architecture of Layered Space-Time (V-BLAST)

Quantitative structure—activity relationship 0t estrogen activities of bisphenol A analogs

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Chinese Science Bulletin 2006年第3期51卷 287-292页

作者： CUI shihai LIU Shushen YANG Jing WANG Xiaodong WANG Liansheng State Key Laboratory of Pollution Control and Resource Reuse School of Environment Nanjing University. Nanjing 210093 China College of Chemistry and Environment Nanjing Normal University Nanjing 210093 China

The molecular electronegativity-distance vector (MEDV) is employed to describe the chemical structure of bisphenol A analogs and their correlated estrogen activities. The result shows that the constructed models have ... 详细信息

关键词：双酚A类似物内分泌紊乱化学制品分子负电性距离向量雌激素定量构效关系