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SOME PROPERTIES OF LSQR FOR LARGE SPARSE LINEAR LEAST SQUARES PROBLEMS

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Journal of Systems Science & Complexity 2010年第4期23卷 815-821页

作者： Zhongxiao JIA Department of Mathematical Sciences,Tsinghua University,beijing 100084,China. Department of Mathematical Sciences Tsinghua University Beijing China

It is well-known that many Krylov solvers for linear systems,eigenvalue problems,andsingular value decomposition problems have very simple and elegant formulas for residual *** not only allow us to further understand the methods theoretically but also can be usedas cheap stopping criteria without forming approximate solutions and residuals at each step beforeconvergence takes *** for large sparse linear least squares problems is based on the Lanczosbidiagonalization process and is a Krylov ***,there has not yet been an analogouslyelegant formula for residual *** paper derives such kind of *** addition,the authorgets some other properties of LSQR and its mathematically equivalent CGLS.

关键词： CGLS krylov subspace lanczos bidiagonalization least squares lsqr normal equations.

THE NAGUMO EQUATION ON SELF-SIMILAR FRACTAL SETS

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Chinese Annals of Mathematics,Series B 2002年第4期23卷 519-530页

作者： HU JIAXINDepartment of Mathematics, Tsinghua University, beijing 100084, China. Department of Mathematics Tsinghua University Beijing 100084 China

The Nagumo equation ut = △u+ bu(u-a)(1-u), t＞0is investigated with initial data and zero Neumann boundary conditions on post-critically finite (p.c.f.) self-similar fractals that have regular harmonic structures and satisfy the separation condition. Such a nonlinear diffusion equation has no travelling wave solutions because of the 'pathological' property of the fractal. However, it is shown that a global Holder continuous solution in spatial variables exists on the fractal considered. The Sobolev-type inequality plays a crucial role, which holds on such a class of p.c.f self-similar fractals. The heat kernel has an eigenfunction expansion and is well-defined due to a Weyl's formula. The large time asymptotic behavior of the solution is discussed, and the solution tends exponentially to the equilibrium state of the Nagumo equation as time tends to infinity if b is small.

关键词： Fractal set Spectral dimension Sobolev-type inequality Strong (Weak) solution

Closed and endoreversible chemical oscillation

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Chinese Journal of Chemistry 1994年第3期12卷 199-205页

作者： LI, Ru-ShengDepartment of Chemistry, Tsinghua University, beijing 100084, China Department of Chemistry Tsinghua University Beijing 100084 China

Based on a simple nonideal chemical reaction model, the closed system with reversible nonideal reactions and illumination is shown to be able to exhibit sustained oscillation. The essential points in the occurrence of such oscillations are the nonideality of reacting media, which gives rise to multiple chemical equilibria, and the energy flow through illumination and heat conduction, which gives rise to spontaneous transitions repeatedly between the multiple equilibrium states. During the oscillation, reacting media undergo only reversible chemical transformation and all irreversibilities are restricted to the coupling of the system to external world. This oscillation provides an example of the so-called endoreversible machine and a possible way to convert radiation energy of the light directly into mechanical energy.

关键词： Chemical oscillation closed system nonideality endoreversible machine illumination.

Studies of the unsteady supersonic base flows around three afterbodies

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Acta Mechanica Sinica 2009年第4期25卷 471-479页

作者： Zhixiang Xiao Song Fu School of Aerospace Engineering,Tsinghua University, 100084 beijing, China School of Aerospace Engineering Tsinghua University Beijing China

Unsteady supersonic base flows around three afterbodies, cylindrical （Cy）, boattailed （BT） and three-step （MS）, are investigated in this paper. Reynolds-averaged Navier-Stokes （RANS） and two RANS/LES （large-eddy simulation） hybrid methods, detached eddy simulation （DES） and delayed-DES （DDES）, are used to predict the base flow characteristics around the baseline Cy afterbody. All the RANS and hybrid methods are based on the two-equation SST （shear-stress transport） model with compressible corrections （CC）. According to the comparison of measurements, both DES and DDES can produce more satisfactory results than RANS. RANS can only present the ＂stable＂ flow pat- terns, while the hybrid methods can demonstrate unsteady flow structures. DDES and DES results are little different from one another although the latter exhibits better agreement with the experiment. DES is taken to investigate the 5° BT and three-step afterbodies. The mean flow data and the instantaneous turbulent coherent structures are compared against available measurements.

关键词： Cylindrical Boattailed and three-stepafterbodies DES and DDES Unsteady flow

A MESSAGE-DRIVING FORMALISM FOR MODELING AND SIMULATION OF MULTI-AGENT SUPPLY CHAIN SYSTEMS

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Journal of Systems Science and Systems Engineering 2011年第4期20卷 385-399页

作者： Wenzhe TAN1 Yueting CHAI2 Yi LIU3 1Department of Automation, Tsinghua University, beijing, 100084, China 2Department of Automation, Tsinghua University, beijing, 100084, China 3Department of Automation, Tsinghua University, beijing, 100084, China Department of Automation Tsinghua University Beijing China

To acquire a competitive advantage in the expanding market, manufacturing enterprises should be able to manage their supply chains as effectively as possible. It is now becoming popular to model supply chains as multi-agent systems and use discrete event simulation to learn more about their behaviors or investigate the implications of alternative configurations. In order to enhance the computational efficiency and keep the simulation credibility, this paper proposes a message-driving formalism for the simulation of multi-agent supply chain systems. Through the message-driving formalism, the problem of shared variables is addressed and the parallel operation of agents is implemented. Simulation experiments with a prototype implementation show that the message-driving formalism is able to provide credible results in significantly less simulation time.

关键词： Supply chain multi-agent system modeling and simulation parallel discrete event simulation message-driving formalism

Self-Organizing Tunnel Peers

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计算机工程 2002年第S1期28卷 7-12页

作者： CHEN Maoke , LI Xing (Department of Electronic Engineering, Tsinghua University, beijing 100084,China ) Department of Electronic Engineering Tsinghua University Beijing 100084China

Tunneling is an important approach in IPv6 transition techniques. The tunnel broker model provides a way to build virtual IPv6 networks without manual ***, neither it adapts performance variation on the IPv4 infrastructure, norit is a scalable solution for a wide-area IPv6 networking environment. In this paper, a self-organizing tunnel peer (SOTP) model is *** peers are clustered in the SOTP system so that optimization is scalable. Four primitive operations related to --cluster constructionarrest,release,division and deathendow the system with the nature of self-organization. Occurrence and behavior of the operations are decided by criteria on the IPv4 end-to-end performance; hence measurement is an indispensable component of the system. The metabolism of cluster relaxes the requirement to accuracy of measurement and optimization.

关键词： S elf-organizationTunnelingEnd-to-end measurementIPv6

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) Department of Applied Mathmatics Tsinghua University Beijing 100084 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

DIMENSIONS OF SELF-AFFINE SETS WITH OVERLAPS

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Chinese Annals of Mathematics,Series B 2003年第3期24卷 275-284页

作者： HUA Su Department of Mathematics, Tsinghua University, beijing 100084, China. Department of Mathematics Tsinghua University Beijing 100084 China

The authora develop an algorithm to show that a class of self-affine sets with overlaps can be viewed as sofic affine-invariant sets without overlaps,thus by using the results of [11] and [10],the hausdorff and minkow... 详细信息

关键词： self-affine set overlap hausdorff dimension minkowski dimension

Moran sets and Moran classes

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Chinese Science Bulletin 2001年第22期46卷 1849-1856页

作者： WEN ZhiyingDepartment of Mathematics, Tsinghua University, beijing 100084, China Department of Mathematics Tsinghua University Beijing China

The purpose of this survey is to present Moran sets and Moran classes which generalize the classical self-similar sets from the following points: (i) The placements of the basic sets at each step of the constructions can be arbitrary; (ii) the contraction ratios may be different at each step; and (iii) the lower limit of the contraction ratios permits zero. In this discussion we will present geometrical properties and results of dimensions of these sets and classes, and discuss conformal Moran sets and random Moran sets as well.

关键词： Moran set Moran classes dimension.