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Symmetries and exact solutions of discrete nonconservative systems

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Science China(Physics,Mechanics & Astronomy) 2010年第9期53卷 1699-1706页

作者： FU JingLi1,LI XiaoWei2.LI ChaoRong1,ZHAO WeiJia3 & CHEN BenYong4 1 Institute of Mathematical Physics,zhejiang Sci-Tech university,{2. 310018,China 2.department of Physics,Shangqiu Normal university,Shangqiu 476000,China 3 department of mathematics,Qingdao university,Qingdao 2.6071,China 4 Faculty of Mechanical Engineering & Automation,zhejiang Sci-Tech university,{2. 310018,China 1. Institute of Mathematical Physics Zhejiang Sci-Tech University Hangzhou 310018 China2. Department of Physics Shangqiu Normal University Shangqiu 476000 China3. Department of Mathematics Qingdao University Qingdao 266071 China4. Faculty of Mechanical Engineering & Automation Zhejiang Sci-Tech University Hangzhou 310018 China

Based on the property of the discrete model entirely inheriting the symmetry of the continuous system,we present a method to construct exact solutions with continuous groups of transformations in discrete nonconservative *** Noether's identity of the discrete nonconservative system is *** symmetric discrete Lagrangian and symmetric discrete nonconservative forces are defined for the *** quasi-extremal equations of discrete nonconservative systems are *** conserved quantities are derived with symmetries associated with the continuous *** have also found that the existence of the one-parameter symmetry group provides a reduction to a conserved quantity;but the existence of a two-parameter symmetry group makes it possible to obtain an exact solution for a discrete nonconservative *** examples are discussed to illustrate these results.

关键词： discrete nonconservative system symmetry conserved quantity quasi-extremal equation exact solution

Perturbations of the Yang-Mills field in the universe

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Research in Astronomy and Astrophysics 2009年第8期9卷 874-882页

作者： Wen Zhao1,2.1 department of Physics, zhejiang university of Technology, {2. 310014, China W 2.School of Physics and Astronomy, Cardiff university, Cardiff, CF2. 3AA, United Kingdom department of Physics Zhejiang University of Technology Hangzhou 310014 China School of Physics and Astronomy Cardiff University Cardiff CF24 3AA United Kingdom

It has been suggested that the Yang-Mills （YM） field can be a kind of candidate for the inflationary field at high energy scales or dark energy at very low energy scales, which can naturally give the equation of state - 1 〈 ω 〈 0 or ω 〈 - 1. We discuss the zero order and first order Einstein equations and YM field kinetic energy equations of the free YM field models. From the zero order equations, we find that w ＋ 1 ω α^-2. from which it follows that the equation of state of the YM field always goes to - 1, independent of the initial conditions. By solving the first order Einstein equations and the YM field equations, we find that in the YM field inflationary models, the scale-invariant primordial perturbation power spectrum cannot be generated. Therefore, only using this kind of YM field is not enough to account for inflationary sources. However, as a kind of candidate for dark energy, the YM field has the ＇sound speed＇ c^2. = -1/3 〈 0, which makes the perturbation Ф have a damping behavior at large scales. This provides a way to distinguish the YM field dark energy models from other kinds of models.

关键词： cosmology theory- gravitation- methods analytical

NONTRIVIAL SOLUTION OF A NONLINEAR SECOND-ORDER THREE-POINT BOUNDARY VALUE PROBLEM

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Applied mathematics(A Journal of Chinese Universities) 2007年第1期22卷 37-47页

作者： Li Shuhong Sun Yongping department of mathematics, Lishui {2., Lishui 32.000,China department of Applied mathematics, zhejiang Sci-Tec {2., hangzhou 310018, China department of Electron and Information, zhejiang university of Media and Communications, hangzhou 310018, China. department of mathematics Lishui University Lishui China department of Applied mathematics Zhejiang Sci-Tec University Hangzhou China department of Electron and Information Zhejiang University of Media and Communications Hangzhou China

In this paper, for a second-order three-point boundary value problem u″＋f（t,u）=0,0〈t〈1,au（0）-bu′（0）=0,u（1）-au（η）=0,where η∈ （0, 1）, a, b, α ∈R with a^2.＋ b^2.〉 0, the existence of its nontrivial solution is studied. The＇conditions on f which guarantee the existence of nontrivial solution are formulated. As an application, some examples to demonstrate the results are given.

关键词： three-point boundary value problem nonlinear alternative of Leray-Schauder, nontrivial solution.

Interaction mechanisms of organic contaminants with burned straw ash charcoal

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Journal of Environmental Sciences 2010年第10期22卷 1586-1594页

作者： Wenhai Huang,Baoliang Chen department of Environmental Science,zhejiang {2.,hangzhou 31002.,China [a] department of Environmental Science Zhejiang University Hangzhou 310028 China

Black carbons （e.g., charcoal） have a great impact on the transport of organic contaminants in soil and water because of its strong affinity and ubiquity in the environment. To further elucidate their interaction mechanism, sorption of polar （p-nitrotoluene, m-dinitrobenzene and nitrobenzene） and nonpolar （naphthalene） aromatic contaminants to burned straw ash charcoal under different de-ashed treatments were investigated. The sorption isotherms fitted well with Freundlich equation, and the Freundlich N values were all around 0.31-0.38, being independent of the sorbate properties and sorbent types. After sequential removal of ashes by acid treatments （HCl and HCl-HF）, both adsorption and partition were enhanced due to the enrichment of charcoal component. The separated contribution of adsorption and partition to total sorption were quantified. The effective carbon content in ash charcoal functioned as adsorption sites, partition phases, and hybrid regions with adsorption and partition were conceptualized and calculated. The hybrid regions increased obviously after de-ashed treatment. The linear relationships of Freundlich N values with the charring-temperature of charcoal or biochar （the charred byproduct in biomass pyrolysis） were observed based on the current study and the cited publications which included 15 different temperatures （100-850℃）, 10 kinds of precursors of charcoal/biochar, and 10 organic sorbates.

关键词： ash charcoal organic pollutant adsorption partition effective carbon

Bloch constant of holomorphic mappings on the unit polydisk of C^n

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Science China mathematics 2008年第4期51卷 652-659页

作者： WANG JianFei~(1+) LIU TaiShun~2.1 College of mathematics and Physics Information Engineering zhejiang Normal {2. Jinhua 32.004,China 2.department of mathematics Huzhou Teachers College Huzhou 313000 China College of mathematics and Physics Information Engineering Zhejiang Normal University Jinhua China department of mathematics Huzhou Teachers College Huzhou China

In this paper,we give a definition of Bloch mappings defined in the unit polydisk D^n, which generalizes the concept of Bloch functions defined in the unit disk *** is known that Bloch theorem fails unless we have some restrictive assumption on holomorphic mappings in several complex *** shall establish the corresponding distortion theorems for subfamiliesβ(K)andβ_(loc)(K) of Bloch mappings defined in the polydisk D^n,which extend the distortion theorems of Liu and Minda to higher *** an application,we obtain lower and upper bounds of Bloch constants for various subfamilies of Bloeh mappings defined in D^*** particular,our results reduce to the classical results of Ahlfors and Landau when n=1.

关键词： Bloch constant Bloch mapping univalent ball critical point Julia lemma locally biholomorphic mapping Landau constant

Analytical solution and semi-analytical solution for anisotropic functionally graded beam subject to arbitrary loading

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Science China(Physics,Mechanics & Astronomy) 2009年第8期52卷 1244-1256页

作者： HUANG DeJin1,2.DING HaoJiang1 & CHEN WeiQiu3 1 Key Laboratory of Soft Soils and Geoenvironmental Engineering,Ministry of Education,zhejiang university,{2. 31002.,China 2.Faculty of Engineering,Ningbo university,Ningbo 3152.1,China 3 department of Engineering Mechanics,zhejiang university,{2. 31002.,China Key Laboratory of Soft Soils and Geoenvironmental Engineering Ministry of Education Zhejiang University Hangzhou 310027 China Faculty of Engineering Ningbo University Ningbo 315211 China department of Engineering Mechanics Zhejiang University Hangzhou 310027 China

Analytical and semi-analytical solutions are presented for anisotropic functionally graded beams subject to an arbitrary load,which can be expanded in terms of sinusoidal *** plane stress problems,the stress function is assumed to consist of two parts,one being a product of a trigonometric function of the longitudinal coordinate(x) and an undetermined function of the thickness coordinate(y),and the other a linear polynomial of x with unknown coefficients depending on *** governing equations satisfied by these y-dependent functions are *** expressions for stresses,resultant forces and displacements are then deduced,with integral constants determinable from the boundary *** the analytical solution is derived for the beam with material coefficients varying exponentially or in a power law along the thickness,the semi-analytical solution is sought by making use of the sub-layer approximation for the beam with an arbitrary variation of material parameters along the *** present analysis is applicable to beams with various boundary conditions at the two *** numerical examples are presented for validation of the theory and illustration of the effects of certain parameters.

关键词： anisotropic material functionally graded arbitrary loading stress function analytical solution semi-analytical solution

Treatment of turtle-breeding wastewater and domestic fecal sewage with soil cultivating system

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Journal of Environmental Sciences 2001年第3期13卷 342-345页

作者： LAO Shan\|gen(department of Environmental Engineering, zhejiang university,{2. 31002., China) department of Environmental Engineering Zhejiang University Hangzhou 310029 China.

Turtle-breeding wastewater and domestic fecal sewage were treated by means of soil cultivating system. Results indicated that more than 50% CODCr and BOD5, of wastewaters were removed, removal rates of NH4+ -N could reach about 70%-80%, but PO43- could not be removed. The thesis analyzed functional mechanisms for pollutants and put forward main elements affecting treatment efficiencies, thus provided conditions for further research.

关键词： turtle-breeding wastewater fecal sewage soil CODCr BOD5 N P

Physically-based approach to analyze rainfall-triggered landslide using hydraulic gradient as slide direction

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Journal of zhejiang university-Science A(Applied Physics & Engineering) 2012年第12期13卷 943-957页

作者： Qi-hua RAN1,Dan-yang SU1,Qun QIAN1,Xu-dong FU2.Guang-qian WANG1,2.Zhi-guo HE3 (1department of Hydraulic Engineering,zhejiang {2.,hangzhou 310058,China) (2.tate Key Laboratory of Hydroscience and Engineering,Tsinghua {2.,Beijing 100084,China) (3department of Ocean Science and Engineering,zhejiang {2.,hangzhou 310058,China) 1. department of Hydraulic Engineering Zhejiang University Hangzhou 310058 China 2. State Key Laboratory of Hydroscience and Engineering Tsinghua University Beijing 100084 China 3. department of Ocean Science and Engineering Zhejiang University Hangzhou 310058 China

An infinite slope stability numerical model driven by the comprehensive physically-based integrated hydrology model(InHM) is *** this approach,the failure plane is assumed to be parallel to the hydraulic gradient instead of the slope *** method helps with irregularities in complex terrain since depressions and flat areas are allowed in the *** present model has been tested for two synthetic single slopes and a small catchment in the Mettman Ridge study area in Oregon,United States,to estimate the shallow landslide *** results show that the present approach can reduce the simulation error of hydrological factors caused by the rolling topography and depressions,and is capable of estimating spatial-temporal variations for landslide susceptibilities at simple slopes as well as at catchment scale,providing a valuable tool for the prediction of shallow landslides.

关键词： Shallow landslide Infinite slope stability model Hydraulic gradient Physically-based hydrology model Integrated hydrology model(InHM)

(s,t,d)-bi-Koszul algebras

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Science China mathematics 2009年第11期52卷 2419-2431页

作者： SI JunRu department of mathematics,{2. Dianzi university,{2. 310018,China 1. department of mathematics Hangzhou Dianzi University Hangzhou 310018 China

The paper focuses on the 1-generated positively graded algebras with non-pure resolutions and mainly discusses a new kind of algebras called(s,t,d)-bi-Koszul algebras as the generalization of bi-Koszul algebras. An(s,t,d)-bi-Koszul algebra can be obtained from two periodic algebras with pure resolutions. The generation of the Koszul dual of an(s,t,d)-bi-Koszul algebra is discussed. Based on it,the notion of strongly(s,t,d)-bi-Koszul algebras is raised and their homological properties are further discussed.

关键词： bi-Koszul algebra periodic algebra pure resolution 16E05 16E40 16S37 16W50