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MULTIPLICITY OF PERIODICSOLUTIONS OF DUFFING'S EQUATIONSWITH LIPSCHITZIAN CONDITIONMULTIPLICITY OF PERIODICSOLUTIONS OF DUFFING'S EQUATIONS WITH LIPSCHITZIAN CONDITION

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Chinese Annals of mathematics,Series B 2000年第4期21卷 479-488页

作者： WANG ZAIHONG (Department of mathematics, {2., beijing 100037, China.) Department of mathematics Capital Normal University Beijing 100037 China

This paper deals with the existence and multiplicity of periodic solutions of Duffing equations x + g(x) = p(t). The author proves an infinity of periodic solutions to the periodically forced nonlinear Duffing equations provided that g(x) satisfies the globally lipschitzian condition and the time-mapping satisfies the weaker oscillating property.

关键词： Periodic solution Time mapping Poincare-Birkhoff twist theorem

Sieve M-estimation for semiparametric varying-coefficient partially linear regression model

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Science China mathematics 2010年第8期53卷 1995-2010页

作者： HU Tao 1,2.& CUI HengJian 1,2.1 School of Mathematical Sciences,beijing normal {2.,Laboratory of mathematics and Complex Systems,Ministry of Education,beijing 100875,China 2.School of Mathematical Sciences,capital normal university,beijing 1.0048,China 1. School of Mathematical Sciences Beijing Normal University Laboratory of Mathematics and Complex Systems Ministry of Education Beijing 100875 China2. School of Mathematical Sciences Capital Normal University Beijing 100048 China

This article considers a semiparametric varying-coefficient partially linear regression *** semiparametric varying-coefficient partially linear regression model which is a generalization of the partially linear regression model and varying-coefficient regression model that allows one to explore the possibly nonlinear effect of a certain covariate on the response variable.A sieve M-estimation method is proposed and the asymptotic properties of the proposed estimators are *** main object is to estimate the nonparametric component and the unknown parameters *** is easier to compute and the required computation burden is much less than the existing two-stage estimation ***,the sieve M-estimation is robust in the presence of outliers if we choose appropriate ρ(·).Under some mild conditions,the estimators are shown to be strongly consistent;the convergence rate of the estimator for the unknown nonparametric component is obtained and the estimator for the unknown parameter is shown to be asymptotically normally *** experiments are carried out to investigate the performance of the proposed method.

关键词： partly linear model varying-coefficient robustness optimal convergence rate asymptotic normality

Study on Green Residential Space Design

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IJLAI Transactions on Science and Engineering

IJLAI Transactions on Science and Engineering 2024年第1期2卷 32-37页

作者： Yu Jiang Shenyang normal university No.2.3 Huanghe North Street Shenyang 110034China

With the ever-changing nature,green ecology has become an international trend of ***,the green ecological design of residential space has become the main melody of people’s *** always implement the concept of ecological and environmental protection in the design process,attach importance to the ecological effect of residential space,carry out reasonable budget and use of environmentally friendly decorative materials,reduce the waste of materials,save money and save resources at the same time,and protect the *** the same time,people began to put their hopes on the residential space design,which made the green residential space design began to *** the bold exploration and practice of designers,the design of green residential space will be endowed with more distinctive characteristics and unique *** from the concept of green design,this paper explores the method of green space design through typical analysis.

关键词： Green Residential space Haze

METHOD OF NONCONFORMING MIXED FINITE ELEMENT FOR SECOND ORDER ELLIPTIC PROBLEMS METHOD OF NONCONFORMING MIXED FINITE ELEMENT FOR SECOND ORDER ELLIPTIC PROBLEMS

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Journal of Computational mathematics 2000年第5期18卷 449-456页

作者： Zhen-dong Luo (Department of mathematics, {2., beijing 100057, China) 首都师范大学北京 100037

In this paper, the method of non-conforming mixed finite element for second order elliptic problems is discussed and a format of real optimal order for the lowest order error estimate.

关键词： Non-conforming mixed finite element Error estimate Second order elliptic problems.

Cu(Ⅱ) Potentiation of Alzheimer Aβ1-40 Cytotoxicity and Transition on its Secondary Structure

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Acta Biochimica et Biophysica Sinica 2006年第11期38卷 765-772页

作者： Xue-Ling DAI~1 Ya-Xuan SUN~2.Zhao-Feng JIANG~2. 1 College of Life Science,capital normal university,beijing 100037,China 2.College of Applied Sciences and Humanities,beijing Union university,beijing 100083,China College of Life Science Capital Normal UniversityBeijing 100037 China College of Applied Sciences and Humanities Beijing Union UniversityBeijing 100083 China

Mounting evidence has shown that dyshomeostasis of the redox-active biometals such as Cuand Fe can lead to oxidative stress,which plays a key role in the neuropathology of Alzheimer's disease（AD）.Here we demonstrate that with the formation of Cu（Ⅱ）·Aβ1-40 complexes,copper markedly potentiatesthe neurotoxicity exhibited by β-amyloid peptide （Aβ）.A greater amount of hydrogen peroxide was releasedwhen Cu（Ⅱ）·Aβ1-40 complexes was added to the xanthine oxidase/xanthine system detected by potassiumiodide *** bound to Aβ1-40 was observed by electron paramagnetic resonance（EPR） *** dichroism （CD） studies indicated that copper chelation could cause a structuraltransition of Aβ.The addition of copper to Aβ introduced an increase on β-sheet as well as α-helix,whichmay be responsible for the aggregation of Aβ.We hypothesized that Aβ aggregation induced by copper maybe responsible for local injury in *** interaction between Cu2.and Aβ also provides a possible mechanismfor the enrichment of metal ions in amyloid plaques in the AD brain.

关键词： Alzheimer’s disease Cu(Ⅱ)·Aβ1-40 complex neuron injury Aβ secondary structure

Fuzzy controllers based on some fuzzy implication operators and their response functions

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Progress in Natural Science:Materials International 2004年第1期14卷 16-21页

作者： LI Hongxing 1*, YOU Fei 1 and PENG Jiayin 2.1. Department of mathematics, {2. normal university, {2. 100875, China 2. Department of mathematics, Neijiang Teacher's College, Neijiang 641112. China) beijing normal Univ Dept Math Beijing 100875 Peoples R China

The fuzzy controllers constructed by 2. fuzzy implication operators based on CRI algorithm and their response functions are discussed. The conclusions show that the fuzzy controllers constructed by 9 fuzzy implication operators are universal approximators to continuous functions and can be used in practical fuzzy control systems. And these 9 fuzzy implication operators except for Einstein operator intersection are all the adjoint pairs of some fuzzy implication operators. Besides, there are 3 other fuzzy controllers formed by fuzzy implication operators being regarded approximately as fitted functions.

关键词： fuzzy implication operators CRI algorithm fuzzy controllers response functions universal approximators

Note on the number of integral ideals in Galois extensions

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Science China mathematics 2010年第9期53卷 2417-2424页

作者： L GuangShi1,& WANG YongHui2.1School of mathematics,Shandong university,Jinan 2.0100,China {2.,capital normal university,beijing 1.0048,China 1. School of mathematics Shandong University Jinan 250100 China2. Department of Mathematics Capital Normal University Beijing 100048 China

Let K be an algebraic number field of finite degree over the rational filed *** ak be the number of integral ideals in K with norm *** this paper we study the l-th integral power sum of ak,i.e.,∑k≤ x akl(l = 2.3,...).We are able to improve the classical result of Chandrasekharan and *** an application we consider the number of solutions of polynomial congruences.

关键词： Dedekind zeta-function integral ideal congruences

Progress of Lyman-alpha-based beam emission spectroscopy(Ly BES)diagnostic on the HL-2. tokamak

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Plasma Science and Technology 2024年第3期26卷 118-125页

作者：周艺轩余羿许敏柯锐聂林徐皓赵光义刘灏袁子豪肖晨雨李继全肖池阶 the HL-2. Team Southwestern Institute of Physics Chengdu 610041People's Republic of China Sino-French Institute of Nuclear Engineering and Technology Sun Yat-sen UniversityZhuhai 519082People's Republic of China State Key Laboratory of Nuclear Physics and Technology School of PhysicsPeking UniversityBeijing 100871People's Republic of China

An edge Lyman-alpha-based beam emission spectroscopy(LyBES)diagnostic,using a heating NBI(neutral beam injection)system,is currently under development on the HL-2. *** 2.-channel edge LyBES,which is intended to measure the density fluctuation in plasma edge(from R=1960 mm to R=2.2. mm)with an improved spatial resolution of 3.3 mm,is a complement to the existing conventional beam emission spectroscopy(BES)*** this article,we introduce the progress of LyBES diagnostic,including the collection optics,the monochromator,and the detector *** reflectance of the collection mirrors is measured to be~82.at 12. nm,and the aberration geometrical radius of the collection optics is tested to be~150μm in the aimed *** linear dispersion of the LyBES monochromator is designed to be~0.09 nm mm^(-1).The bandwidth of the detector system with the 5×10^(7)V A^(-1)preamplifier gain is measured to be~2.0 kHz,and the peak-to-peak noise of the detector system is tested to be~16 *** finalized design,components development and testing of the LyBES diagnostic have been completed at present,and an overall performance of the LyBES diagnostic is to be confirmed in the next HL-2. campaign.

关键词： density fluctuation Ly BES BES vacuum ultraviolet

Integral spinor norms in dyadic local fields Ⅲ

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Science China mathematics 2010年第9期53卷 2425-2446页

作者： L JianRui1 & XU Fei2.1Department of mathematics,Jinan {2.,Guangzhou 510632.China 2.chool of mathematics,capital normal university,beijing 1.0048,China Department of mathematics Jinan University Guangzhou China School of mathematics Capital Normal University Beijing China

In this paper we give an alternative computation of integral spinor norms over dyadic local fields by using the Jordan decomposition of *** particular,we emphasize the striking similarity between the theory over dyadi... 详细信息

关键词： integral lattice spinor norm Jordan decomposition