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Quasiperiodic Solutions for Nonlinear Differential Equations of Second Order with Symmetry

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Acta Mathematica Sinica,English Series 1994年第3期10卷 231-242页

作者： Liu Bin department of Mathematics peking university beijing,100871 china You Jiangong department of Mathematics Nanjing university Nanjing,210008 china department of Mathematics Peking University Beijing China department of Mathematics Nanjing University Nanjing China

In this paper,we study the existence of quasi-periodic solutions and the bound- edness of solutions for a wide class nonlinear differential equations of second *** the KAM theorem of reversible systems and the theory of transformations,we obtain the existence of quasi-periodic solutions and the boundedness of solutions under some reasonable conditions.

关键词： Th Quasiperiodic Solutions for Nonlinear Differential Equations of Second Order with Symmetry Math

Composition of sandstone and heavy minerals implies the provenance of Kuqa Depression in Jurassic, Tarim basin, china

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Progress in Natural Science:Materials International 2005年第7期15卷 633-640页

作者： WU Chaodong, LIN Changsong, SHEN Yanping and FENG Xue ( Key Laboratory of Orogenic Belts and Crustal Evolution, Ministry of Education, peking university, beijing 100871, china department of Resources, china university of Geosciences, beijing 100083, china) Key Laboratory of Orogenic Belts and Crustal Evolution Ministry of Education Peking University Beijing 100871 China. department of Resources China University of Geosciences Beijing 100083 China

The petrological characteristics and heavy mineral assembly of the Jurassic System in Kuqa Basin are consistent with the tectonic evolution, which is the major factor controlling the filling process of Kuqa Basin. Controlled by the source areas at the both sides of the Basin, the matrixes are dominated by sedimentary rock, high-grade metamorphic rock, acid magmatic rock, and the highest heavy mineral assemblage of zircon-garnet-magnetite in the content. According to heavy mineral indexes, the Jurassic strata can be classified into three rhythmic units of heavy mineral. The lower sequence contains abundant heavy minerals and relatively high content of detritus and its matrixes primarily came form the recycling orogen. The assemblage of "zircon-garnet-magnetite" indicates that the sedimentary area in the early evolution period of the basin is relatively near the provenance. The middle sequence is different from the lower sequence in the heavy mineral assemblage and has the different characteristics from that of source rock. The heavy mineral assemblage is "garnet-zircon" with the highest content of garnet and its main matrices are the high-grade metamorphic rock, acid magmatic rock and hydrothermal vein at the northeastern edge of the basin. The middle and upper sequences are characterized by the clast provenance, which is primarily from the recycling orogen at the northern edge of the basin and secondarily from the southern uplift. As a result of the two provenances, the strata with apparent changes of heavy mineral assemblage and index better coincides with the interfaces of the secondary strata sequences, which reflects the denudation history and the filling process of the orogen at the northern edge of the basin.

关键词： sandstone components provenance analysis filling sequence tectonic evolution.

Cloud point phenomenon in aqueous mixtures of cationic-anionic surfactants

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Chinese Journal of Chemistry 1994年第6期12卷 552-554页

作者： XIAO, Jin-Xin ZHAO, Guo-Xidepartment of Chemistry, peking university, beijing 100871, china department of Chemistry Peking University Beijing 100871 China Keywords Cloud point cation‐anionic surfactants.

It used to be held that the cloud point phenomenon was only a characteris-tic of nonionic surfactants alone. Such phenomenon is rarely observed in ionicsurfactants. The present study shows that the mixture of cationic-anionic surfac-tants not only has a krafft point which is the characteristic of an ionic surfactant,but also exhibits the cloud point phenomenon obviously at certain concentrations.

关键词： Cloud point cation-anionic surfactants.

Some Results on the Multiplier Conjecture for the Case n=5n_1

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Acta Mathematica Sinica,English Series 1998年第4期14卷 535-540页

作者： Wan Zhaoze, department of Mathematics, peking university, beijing 100871, china peking university Department of Mathematics Beijing China (GRID:grid.11135.37) (ISNI:***)

Using the method presented in [1], we obtain some new results which improve on the result of MacFarland’s theorem (see [2]) in this case.

关键词： Difference sets Multiplier CH-equations

Soluble protein and acid phosphatase exuded by ectomycorrhizal fungi and seedlings in response to excessive Cu and Cd

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Journal of Environmental Sciences 2009年第12期21卷 1667-1672页

作者： ZHENG Weishuang, FEI Yingheng, HUANG Yi College of Environmental Sciences and Engineering, peking university, beijing 100871, china. College of Environmental Sciences and Engineering Peking University

Fungi and their symbionts can alleviate heavy metal stress by exuding soluble proteins and enzymes. This study examined the role of soluble protein and acid phosphatase （APase） exuded by Xerocomus chrysenteron, an ectomycorrhizal fungus, and the seedlings of its symbiont, Chinese pine （Pinus tabulaeformis）, under conditions of excessive Cu and Cd. The growth type showed that this poorly studied ectomycorrhizal fungus was capable of tolerating high concentrations of Cu, and may be useful in phytoremediation. X. chrysenteron grew well at 80 mg/L Cu, and the EC50 for Cd was 17.82 mg/L. X. chrysenteron also showed enhanced exudation of soluble protein in both isolated and inoculated cultivations under the influence of Cu and Cd. Soluble protein exudation, however, differed under Cu and Cd stress in isolates. In mediums containing Cu, soluble protein exudation increased with concentration, but in mediums containing Cd the content of soluble protein increased to a comparable level at all concentrations. This study demonstrated that soluble protein was related to heavy metal tolerance, although the different ions played different roles. While APase activity in exudates of fungi and seedlings decreased under Cu and Cd stress in comparison to the control, the APase activity in seedlings was maintained by inoculation. Thus, X. chrysenteron facilitated the ability of plant to maintain a normal nutrient uptake, and therefore to protect it from heavy metal toxicity.

关键词： soluble protein acid phosphatase exudate Cu, Cd Xerocomus chrysenteron

EFFECTS OF L-PHENYLALANINE ON THE RADIATION SYNTHESIS OF POLY(N,N'-METHYLENEBISACRYLAMIDE-co-4-VINYLPYRIDINE)(MICRO)GELS

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Chinese Journal of Polymer Science 2005年第6期23卷 643-650页

作者： Qing-de Chen Xing-hai Shen and Hong-cheng Gao department of Applied Chemistry,College of Chemistry and Molecular Engineering,peking university,beijing 100871,china department of Applied Chemistry College of Chemistry and Molecular Engineering Peking University Beijing 100871 China

The effects of L-phenylalanine （L-Phe） on the synthesis ofpoly（N,N＇-methylenebisacrylamide-co-4-vinylpyridine）（poly（Bis-co-4-VP））（micro）gels by γ-ray irradiation were studied. The addition of L-Phe could not only decrease the gelation dose （Dg） of the synthesis obviously, but also transform the morphology of copolymer from microgel to gel. In addition, the swelling ability of the （micro）gels was also affected in the presence of L-Phe. The decrease of Dg was ascribed to the effect of pH, while the transformation of the morphology was ascribed to the effect of L-Phe on the stability of the poly（Bis-co-4-VP） microgel. Such an effect was confirmed further as compared with the effects of L-alanine, L-glutamic acid, L-arginine, sulfuric acid and aqueous ammonia.

关键词： L-Phenylalanine γ-Ray irradiation Gelation dose Morphology transformation (Micro)gel

Estimates of solutions of initial-irregular oblique derivative problems for fully nonlinear parabolic equations

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Communications in Nonlinear Science and Numerical Simulation 2000年第4期5卷 174-178页

作者： Guochun WEN (Departmet of Mathematics, peking university, beijing 100871, china e-mail: wengc@***) (Received October 24, 2000) Departmet of Mathematics Peking University Beijing 100871 China

In this paper the initial-irregular oblique derivative problems for fully nonlinear parabolic equations of second order are proposed, and then some a priori estimates of solutions for the above problems are given.

关键词： initial-irregular oblique derivative problems fully nonlinear parabolic equatit

STABILITY OF POLY(N,N'-METHYLENEBISACRYLAMIDE-co-4-VINYLPYRIDINE)MICROGEL DISPERSION AND ADJUSTMENT OF THE HYDROPHOBICITY IN THE MICROGELS

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Chinese Journal of Polymer Science 2005年第6期23卷 635-642页

In the UV-Vis spectra of pure light-scattering systems, there is an exponential relationship between absorbance and wavelength （A = Kλ^-n）. Here, the exponent n is named as flocculation-coagulation parameter. In the present paper, the effects of different additives on the stability of poly（N,N＇-methylenebisacrylamide-co-4-vinylpyridine）（poly（Bis-co-4-VP）） microgel dispersion were studied in detail via this parameter. The results showed that the stability of the dispersion mainly comes from the ionization of pyridine groups, making the microgel positively charged on its surface. This was confirmed by the measurement of Zeta potential and the result of conductometric titration. The result of fluorescence analysis indicated that the hydrophobicity in the microgels is enhanced with the increase in total 4-VP unit content.

关键词： Microgel dispersion(s) 4-Vinylpyridine Flocculation-coagulation parameter Zeta potential

Maslov-type index and brake orbits in nonlinear Hamiltonian systems

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Science china Mathematics 2007年第6期50卷 761-772页

作者： Duan-zhi ZHANG School of Mathematical Sciences, peking university, beijing 100871, china School of Mathematical Sciences Peking University Beijing China

In this paper, we study the Maslov-type index theory for linear Hamiltonian systems with brake orbits boundary value conditions and its applications to the existence of multiple brake orbits of nonlinear Hamiltonian s... 详细信息

关键词： brake orbit Maslov-type index relative Morse index dual variational method 58E05 70H05 34C25