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The proof of Ushio's conjecture concerning path factorization of complete bipartite graphs

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Science china Mathematics 2006年第3期49卷 289-299页

作者： DU Beiliang & WANG Jian Department of Mathematics, Suzhou University, Suzhou 215006, china Nantong Vocational college, Nantong 226007, china Department of Mathematics Suzhou University Suzhou 215006 China Nantong Vocational college Nantong 226007 China

Let Km,n be a complete bipartite graph with two partite sets having m and n vertices, respectively. A Pv-factorization of Km,n is a set of edge-disjoint Pv-factors of Km,n which partition the set of edges of Km,n. When v is an even number, Wang and Ushio gave a necessary and sufficient condition for existence of Pv-factorization of Km,n. When k is an odd number, Ushio in 1993 proposed a conjecture. Very recently, we have proved that Ushio's conjecture is true when v = 4k - 1. In this paper we shall show that Ushio Conjecture is true when v = 4k + 1, and then Ushio's conjecture is true. That is, we will prove that a necessary and sufficient condition for the existence of a P4k+1-factorization of Km,n is (i) 2km ≤ (2k + 1)n,(ii) 2kn ≤ (2k + 1)m, (iii) m + n ≡ 0 (mod 4k + 1), (iv) (4k + 1)mn/[4k(m + n)] is an integer.

关键词： complete bipartite graph, factorization, Ushio Conjecture.

Integrated intelligent control analysis on semi-active structures by using magnetorheological dampers

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Science china(Technological Sciences) 2008年第12期51卷 2270-2284页

作者： XU ZhaoDong1 & GUO YingQing2 1Civil Engineering college, Southeast University, Nanjing 210096, china 2 Automation college, Southeast University, Nanjing 210096, china Civil Engineering college Southeast University Nanjing 210096 China Automation college Southeast University Nanjing 210096 China

The control strategy is very important for semiactive control or active control systems. An integrated intelligent control strategy for building structures incorpo rated with magnetorheological (MR) dampers subjected to earthquake excitation is proposed. In this strategy, the time-delay problem is solved by a neural network and the control currents of the MR dampers are determined quickly by a fuzzy controller. Through a numerical example of a three-storey structure with one MR damper installed in the first floor, the seismic responses of the uncontrolled, the intelligently controlled, the passiveon controlled, and the passive-off controlled structures under different earthquake excitations are analyzed. Based on the numerical results, it can be found that the time domain and the frequency domain responses are reduced effectively when the MR damper is added in the structure, and the integrated intelligent control strategy has a better earthquake mitigation effect.

关键词： magnetorheological damper semi-active control intelligent

UNIFORM APPROXIMATION BY COMBINATIONS OF BERNSTEIN POLYNOMIALS

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Analysis in Theory and Applications 1995年第3期11卷 36-51页

作者： Xie Linsen (Lishui Teachers’ college, china) 1. Department of Mathematics Lishui Teacher's College 323000 Lishui Zhejiang P. R. China

We prove a pointwise characterization result for combinations of Bernstein polynomials. The main result of this paper includes an equivalence theorem of H. Berens and G. G. Lorentz as a special case.

关键词： II UNIFORM APPROXIMATION BY COMBINATIONS OF BERNSTEIN POLYNOMIALS

A CLASS OF NONLINEAR SINGULARLY PERTURBED NONLOCAL REACTION DIFFUSION SYSTEM

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Applied Mathematics(A Journal of Chinese Universities) 2003年第4期18卷 403-411页

作者： Mo JiaqiHuzhou Teachers college,Huzhou 313000,china. Huzhou Teachers college Huzhou China

In this paper the singularly perturbed initial boundary value problems for the nonlocal reaction diffusion system are *** the iteration method and the comparison theorem, the existence and its asymptotic behavior of s... 详细信息

关键词： reaction diffusion system singular perturbation,initial boundary value problem

Arbuscular mycorrhizal fungi associated with the clonal plants in Mu Us sandland of china

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Progress in Natural Science:Materials International 2007年第11期17卷 1296-1302页

作者： Zhao Jinli and He Xueli(college of Life Sciences, Hebei University, Baoding 071002, china) college of Life Sciences Hebei University Baoding 071002 China

Clonal plants in Mu Us sandland change the sandy enviroment. The clonal plant is a kind of resource in restoration of the Mu Us sandy landscape. Soil samples at depth of 50 cm in the rhizosphere of the clonal plants were collected in 4 replicates at each location and divided into sections corresponding to 0—10, 10—20, 20—30, 30—40 and 40—50 cm depths in two representative sites from north to south in Mu Us sandland, northwestern china, in July 2005. Clonal plants included Psammochloa villosa and Hedysarum laeve. The colonization and ecological distribution of arbuscular mycorrhizal (AM) fungi were investigated in the rhizosphere of clonal plants in Mu Us sandland. The results showed that the clonal plants established well symbiosis with AM fungi; AM fungal species and spatial distribution were significantly related with the host plants and soil factors. Of 16 AM fungal taxa in three genera isolated and identified, Glomus multicaule was only observed in the rhizosphere of Psammochloa villosa; Glomus aggregatum, Glomus hydembadensis, Glomus constrictum and Acaulospora rehmii only appeared in the rhizosphere of Hedysarum leave. The depth of soil layers observably affected the spore density and the frequency of colonization (%F). The maximal %F and spore density occurred in the 10—20 cm layer at the site of Ordos Sandy Land Ecological Station, but which occurred in the 0—10 cm layer in Shanxi Yulin Rare Sandy-plants Conversation Field. AM fungal status and colonization might be used to monitor desertification and soil degradation.

关键词： AM fungi clonal plants Mu Us sandland

Solutions and solvabilities of general binary quadric indefinite equations

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Chinese Science Bulletin 1997年第7期42卷 541-545页

作者： LiU LiAnhui Traditional Chinese Medical college, Hefei 230038, china Anhui Traditional Chinese Medical college Hefei China

To this day for special m and small |c|, solvable, c are obtained about general equations x^2-my^2=c with positive squarefree integer m and integer c by Ankeny, Mollin et al. Afterwards, Zhang in ref. [1] greatly developed their correspondent results and gave all proper integer solutions and solvable c about the equations for general m. Then Lu in ref. [2] gave results for small |q| about general binary quadric indefinite

关键词： general binary quadric indefinite equation proper integer solution solvability.

Continuous embedding between harmonic Hardy spaces and mixed-norm spaces

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Chinese Science Bulletin 1997年第2期42卷 106-108页

作者： HU ZhangjianDepartment of Mathematics, Huzhou Teachers college, Zhejiang 313000, china Department of Mathematics Huzhou Teachers College Zhejiang China

LET D Rn be a bounded domain with C∞ boundary, and λ （x） be a defining function. This means that λ（x） is in C∞（Rn）, is bounded and |▽λ|≠0 in some neighborhood of aD （see ref. [1]）. For r positive and sufficiently small, set Dr = {x∈Rn; λ（x） r,and dσ be the （n-1）-dimensional Hausdorff measures on aD,={x∈Rn; λ（x） = -Υ} and on αD = {x∈Rn; λ（x） = 0} respectively, and dm be the Lebesgue volume element on Rn.By h（D） we will denote the space of all complex valued harmonic functions on D. For a multi-index α= （α1,α2…,αn）, aj being a non-negative integer, and x = （x1,x2,…,xn）∈D, write |α| = α1 + α2 + … + αn

关键词： harmonic Hardy space integral mean gradient.

Noether-Form Invariance of Nonholonomic Controllable Mechanical Systems in Phase Space

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Communications in Theoretical Physics 2007年第7期48卷 23-26页

作者： XIA Li-Li LI Yuan-Cheng college of Physics Science and Technology,china University of Petroleum,Dongying 257061,china college of Physics Science and Technology China University of Petroleum

In this paper,we study the Noether-form invariance of nonholonomic mechanical controllable systems inphase *** of motion of the controllable mechanical systems in phase space are *** definitionand the criterion for this system are presented.A new conserved quantity and the Noether conserved quantity deducedfrom the Noether-form invariance are *** example is given to illustrate the application of the results.

关键词： nonholonomic controllable mechanical system phase space Noether-form invariance conserved quantity

Instability of forced flow in a rotating cylindrical pool with a differentially rotating disk on the free surface

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Science china(Technological Sciences) 2010年第9期53卷 2477-2488页

作者： WU ChunMei & LI YouRong college of Power Engineering,Chongqing University,Chongqing 400044,china 1. college of Power Engineering Chongqing University Chongqing 400044 China

The instability of forced flow in a rotating cylindrical pool with a differentially rotating disk on the free surface is investigated through a series of unsteady three-dimensional numerical *** results show that the basic flow state of this system is axisymmetric and steady,but has rich structures at the meridian ***,when the rotation Reynolds number exceeds a critical value,the flow will undergo a transition to three-dimensional oscillatory flow,characterized by the velocity fluctuation waves traveling in the azimuthal *** main characteristics of the flow patterns are presented,including the propagating direction,velocity,amplitude and wave number,which depend on the rotation rates and directions of the disk and the cylindrical pool,and the critical conditions for the onset of oscillatory flow are also *** the case of disk-only rotation,the centrifugal instability is responsible for the flow transition,and when the disk isoand counter-rotates with the cylindrical pool,the mechanisms for the transition are elliptic and of circular shear instabilities,respectively.

关键词： rotation flow transition flow instability