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REDUCTIONS OF ADJOINT REPRESENTATIONS TO LAX REPRESENTATIONS FOR CONSTRAINED FLOWS

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Chinese Annals of mathematics,Series B 1996年第2期17卷 187-198页

作者： ZENG YUNBO department of applied mathematics, tsinghua university, beijing 100084, china. TSING HUA UNIV DEPT APPL MATHBEIJING 100084PEOPLES R CHINA

Within framework of zero-curvature representation theory, the Lax representations for x- andtn-constrained flows of soliton hierarchy are obtained from reductions of adjoint representationsof the auxiliary linear problems. This method is applied to the third order spectral problem bytaking modified Boussinesq hierarchy as an illustrative example.

关键词： Constrained flow Lax representation Adjoint representation Soliton hierarchy

THE APPROXIMATIONS OF THE EXACT BOUNDARY CONDITION AT AN ARTIFICIAL BOUNDARY FOR LINEARIZED INCOMPRESSIBLE VISCOUS FLOWS

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Journal of Computational mathematics 1998年第3期16卷 239-256页

作者： Wei-zhu Bao (department of applied mathematics, tsinghua university, beijing 100084, P.R. china) 清华大学应用数学系北京

We consider the linearized incompressible Navier-Stokes (Oseen) equations in a flat channel. A sequence of approximations to the exact boundary condition at an artificial boundary is derived. Then the original problem is reduced to a boundary value problem in a bounded domain, which is well-posed. A finite element approximation on the bounded domain is given, furthermore the error estimate of the finite element approximation is obtained. Numerical example shows that our artificial boundary conditions are very effective.

关键词： Oseen equations artificial boundary artificial boundary condition finite element approximation error estimate

Median cross-validation criterion

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Chinese Science Bulletin 1997年第23期42卷 1956-1959页

作者： YANG Yingdepartment of applied mathematics, tsinghua university, beijing 100084, china department of applied mathematics Tsinghua University Beijing China

CONSIDER the nonparametric median regression model Yni = g (xni) + εni, 1≤i≤n （1）where g: [0, 1]|→R is an unknown function of interest; {xni, 1≤i≤n} is the fixed design pointsin the interval [0, 1]; {εni, 1≤i≤n} is a triangular array of row iid random variables having medi-an zero, and {Yni, 1≤i≤n} is the observation. For each x∈[0, 1], n≥1, let Dnj（x） denotethe jth nearest neighber of x, j=1, 2,…, n, i. e. {Dn1（x）, Dn2（x）,…, Dnn（x）} is a trans-position of {xn1, xn2,…, xnn} satisfying |Dn1（x）-x|≤|Dn2（x）-x|≤…≤|Dnn（x）-x|.The tie is broken by the chronological order. The

关键词： median cross validation Bahadur’s representation asymptotic oplimality.

Formulae of type Ankeny-Artin-Chowla for class numbers of general cyclic sextic fields

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Chinese Science Bulletin 1998年第10期43卷 824-826页

作者： LIU Tong department of applied mathematics, tsinghua university, beijing 100084, china department of applied mathematics Tsinghua University Beijing China

Let K 6 be a real cyclic sextic number fields, and K 2, K 3 be its quadratic and cubic subfields. Let h(L) denote the ideal class number of field L. Seven congruences for h -=h(K 6)/h(K 2)h(K 3) are obtained. In particular, when conductor f\-6 of K 6 is prime p, then Ch -≡B p-16B 5(p-1)6 (mod p), where C is an explicitly given constant, and B n is the Bernoulli number. These results for real cyclic sextic fields are an extension of results for quadratic and cyclic quartic fields obtained by Ankeny_Artin_Chowla, Kiselev, Carlitz, Lu Hongwen, Zhang Xianke from 1948 to 1988.

关键词： real cyclic sextic number fields class number fundamental relative unit.

THE EXISTENCE OF J-HOLOMORPHIC CURVES AND APPLICATIONS TO THE WEINSTEIN CONJECTURE

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Chinese Annals of mathematics,Series B 1999年第4期20卷 425-434页

作者： MA RENYI(department of applied Mathmatics, tsinghua university, beijing 100084, china) tsinghua Univ Dept Appl Math Beijing 100084 Peoples R China

The author first proves the existences of J-holomorphic curves in the symplectizations of Legendre fibrations and then as an application confirms the Weinstein conjectures on contact manifolds of Legendre fibrations. As a corollary a new proof on the theorem due to Hofer,Viterbo, Gluck, Ziller, Weinstein and Ljusternik-Fet Theorem is provided, which is quite different from their original proofs.

关键词： Symplectic geometry J-holomorphic curves Periodic orbit

Frequency-domain analysis of fluid-structure interaction in aircraft hydraulic pipeline systems: numerical and experimental studies

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Journal of Zhejiang university-Science A(applied Physics & Engineering) 2024年第8期25卷 605-617页

作者： Yang DENG zongxia JIAO Yuanzhi XU School of Automation Science and Electrical Engineering Beihang UniversityBeijing 100191China Research Institute for Frontier Science Beihang UniversityBeijing 100191China Key Laboratory of Advanced Airborne Systems Beihang UniversityBeijing 100191China Ningbo Institute of Technology Beihang UniversityNingbo 315800China Tianmushan Laboratory Hangzhou 310023China

The fluid-structure interaction(FSI)in aircraft hydraulic pipeline systems is of great concern because of the damage it *** accurately predict the vibration characteristic of long hydraulic pipelines with curved segments,we studied the frequency-domain modeling and solution method for FSI in these pipeline *** partial differential equations(PDEs)are utilized to model the pipeline FSI,considering both frequency-dependent friction and bending-flexibility *** address the numerical instability encountered by the traditional transfer matrix method(TMM)in solving relatively complex pipelines,an improved TMM is proposed for solving the PDEs in the frequency domain,based on the matrix-stacking strategy and matrix representation of boundary *** proposed FSI model and improved solution method are validated by numerical cases and *** experimental rig of a practical hydraulic system,consisting of an aircraft engine-driven pump,a Z-shaped aero-hydraulic pipeline,and a throttle valve,was constructed for *** magnitude ratio of acceleration to pressure is introduced to evaluate the theoretical and experimental results,which indicate that the proposed model and solution method are effective in practical *** methodology presented in this paper can be used as an efficient approach for the vibrational design of aircraft hydraulic pipeline systems.

关键词： Fluid-structure interaction(FSI) Frequency-domain analysis Aircraft hydraulic pipeline Pipeline vibration Transfer matrix method(TMM)

RECOGNITION AND CLASSIFICATION FOR O(n)-EQUIVARIANT BIFURCATIONS WITH O(n)-CODIMENSION LESS THAN 5

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Chinese Annals of mathematics,Series B 1998年第4期19卷 391-400页

作者： WANG XIAOFENG (department of applied mathematics, tsinghua university, beijing 100084, china.)TANG YUN (department of applied mathematics, tsinghua university, beijing 100084, china.)WANG DUO (School of Mathematical Science, Peking universityl Beliing 10 Tsing Hua Univ Dept Appl Math Beijing 100084 Peoples R China Peking Univ Sch Math Sci Beijing 100080 Peoples R China

Bifurcation problems equivariant under the standard action of the orthogonal group O(n) up to O(n)-codimension 4 are classified into 19 classes. For each class the normal form and one universal unfolding are calculate... 详细信息

关键词： O(n)-equivariant bifurcation Normal form Universal unfolding Recognition problem

Quantum and Non-Causal Stochastic Calculus

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Acta Mathematica Sinica,English Series 1998年第3期14卷 289-294页

作者： liang zongxia Zheng Mingli department of applied mathematics, tsinghua university, beijing 100084, china department of applied mathematics Tsinghua University 100084 Beijing China

In this paper, using the Guichardet space technique, the relationship between Fermion quantum stochastic calculus and non-causal calculus in Segal space L^2(H) is discussed, and an anticipating quantum stochastic calc... 详细信息

关键词： Non-causal stochastic analysis Quantum stochastic analysis Guichardet space

SERIES REPRESENTATION OF DAUBECHIES' WAVELETS

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Journal of Computational mathematics 1997年第1期15卷 81-96页

作者： X.G. Lu (department of applied mathematics, tsinghua university, beijing, china) 清华大学应用数学系北京

This paper gives a kind of series represeotation of the scaling functions φNand the associated wavelets . constructed by Daubechies. Based on Poission sununation formula, the functions gh. φN(x+N-1), φN (x+N),'''' φN (x+2N-2)(Ox 1) are linearly represented by φN(x), φN(x + 1),''', φN(x + 2N - 2) and some polynomials of order less than N, and φ0(x):= (φN (x), φN (x + 1),''', φN (x + N -2))t is translated into a solution of a nonhomogeneous vectorvalued functional equationwhere A0, A1 are (N - 1) x (N - 1)-dimensional matrices, the components of P0(x), P1 (x) are polynomials of order less than N. By iteration, .φ0(x) is eventualy represented as an (N - 1)-dimensional vector series with vector norm where and

关键词： Pro ER Math Si WAVELETS SERIES REPRESENTATION OF DAUBECHIES