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Monotone projected gradient methods for large-scale box-constrained quadratic programming

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Science China Mathematics 2006年第5期49卷 688-702页

作者： ZHOU Bin, GAO Li & DAI Yuhong school of mathematical sciences and lmam, {2., beijing 100871, China State Key Laboratory of Scientific and Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of sciences, beijing 100080, China school of mathematical sciences lmam Peking University Beijing 100871 China State Key Laboratory of Scientific Engineering Computing Institute of Computational Mathematics Scientific/Engineering Computing Academy of Mathematics Systems Science Chinese Academy of Sciences Beijing 100080 China

Inspired by the success of the projected Barzilai-Borwein (PBB) method for largescale box-constrained quadratic programming, we propose and analyze the monotone projected gradient methods in this paper. We show by experiments and analyses that for the new methods,it is generally a bad option to compute steplengths based on the negative gradients. Thus in our algorithms, some continuous or discontinuous projected gradients are used instead to compute the steplengths. Numerical experiments on a wide variety of test problems are presented, indicating that the new methods usually outperform the PBB method.

关键词： projected gradients, monotone gradient methods, box-constrained quadratic programming, large-scale problems.

CONVERGENCE OF VORTEX METHODS FOR 3-D EULER EQUATIONS

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Journal of Computational Mathematics 2000年第3期18卷 239-250页

作者： Jia-fu Lin (Institute of System Science, Academy of Mathematics and System sciences, Chinese Academy of sciences, {2., 100080, China school of mathematical sciences, peking university, beijing 100871, China) 中科院系统科学所北京 100080

Presents a study on the convergence of vortex methods for the three-dimensional Euler equations in bounded domains. Related studies on the convergence of vortex methods; Formulation of vortex methods; Convergence for ... 详细信息

关键词： Euler equations vortex methods convergence initial-boundary value problem

Kinematics and dynamics of the Mesozoic orogeny and late-orogenic extensional collapse in the Sino-Mongolian border areas

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Science China Earth sciences 2005年第7期48卷 849-862页

作者： ZHENG Yadong 1 & WANG Tao2.1. Key Laboratory of Orogenic Belts and Crustal Evolution (peking university), Ministry of Education, beijing 100871, China 2. Institute of Geology, Chinese Academy of Geological {2., beijing 100037, China Key Laboratory of Orogenic Belts and Crustal Evolution (peking university) Ministry of Education Beijing 100871 China Institute of Geology Chinese Academy of Geological Sciences Beijinq 100037 China

The Sino-Mongolian border areas underwent two important tectonic events during Mesozoic time after late Paleozoic orogeny: a late Triassic to earlier Jurassic contractional event that resulted in a large-scale south-vergent thrust during the orogeny and a late Jurassic-earlier Cretaceous extensional event in a north-south direction that formed a metamorphic core complex. The kinematic and dynamic analyses show that the thrust sheet moved southwards with a kinematic vorticity number of ca. -0.10 and sub-horizontal maximum compressive stress axis that belongs to a contraction-thickening shear. The upper plate of the late-orogenic detachment relatively moved in a 165°direction. The average kinematic vorticity in its earlier stage was 0.74 that belongs to simple shear dominated shearing and related to the maximum compressive stress axes dipping at ～66°, while the later average kinematic vorticity was ～0.55°that belongs to pure shear dominated shearing with sub-vertical maximum compressive stress axes. This suggests that the thrusting led to the crust thickened and the lower plate rocks that were originally located in the upper crust depressed through a brittle-ductile transition zone into the lower crust and became warmer. The heated rocks trended to uplift since their increasing volume and decreasing density while the loading of the upper-plate rocks increased due to the structural thickening. Under the combined effect of the loading and the thermal-uplifting, the ductile shear zone in between increased in its component of vertical pure shear. Once its pure-shear component exceeded its simple-shear one the ductile shear zone became an extension-thinned shear zone. This progressive transitional process reflects internal and essential temporal and spatial relationships: the extensional factor nucleated during the crust thickening by thrusting and increase of the extensional factor finally led to late-orogenic collapse.

关键词： Mesozoic thrusting,late-orogenic collapse,kinematic vorticity number,stress state.

The attenuation anisotropy of mudstones and shales in subsurface formations

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Science China Earth sciences 2005年第11期48卷 1882-1890页

作者： SHI Ge1 & DENG Jixin1,2.1. The Key Labratory of Orogenic Belts and Crustal Evolution, school of Earth and Space sciences, {2., beijing 100871, China 2. Geophysical Prospecting Key Lab (CNPC), university of Petroleum, beijing 102.49, China 1. The Key Labratory of Orogenic Belts and Crustal Evolution School of Earth and Space Sciences Peking University 100871 Beijing China 2. Geophysical Prospecting Key Lab (CNPC) University of Petroleum 102249 Beijing China

We have measured the relationships in the laboratorial condition between the at-tenuation in three samples of mudstones and shales as well as two samples of layered sand-stones and the alteration in direction, confining pressure and pore fluid. The relative contributions of different attenuation mechanisms are also discussed. Studies show that the attenuation in dry and saturated samples is strongly related to pressure and direction. The attenuation coefficient of P-wave propagating parallel to bedding (PH ) is less than that of P-wave propagating vertical to bedding (PV ), while the attenuation coefficient of S-wave both propagating and vibrating parallel to bedding (SH ) and that of S-wave propagating vertical to bedding while vibrating parallel to bedding (SV1) are less than that of S-wave propagating parallel to bedding while vibrating verti-cal to bedding (SV ). Under oil saturated conditions, the Biot flow attenuation acts as the domi-nant mechanism for waves propagating parallel to bedding, while the frame anelastic attenuation and squirt flow attenuation seem to play important roles in condition of propagation vertical to bedding.

关键词： mudstone, shale, attenuation, anisotropy, attenuation mechanism

Source time-function as discriminant using empirical Green's function

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Science China Earth sciences 2005年第12期48卷 2118-2122页

作者： HE Yongfeng1,2.& CHEN Xiaofei1 1. Department of Geophysics, school of Earth & Space sciences, {2., beijing 100871, China 2. North-West Institute of Nuclear Technology, Xi’an 71002., China 1. Department of Geophysics School of Earth & Space Sciences Peking University 100871 Beijing China 2. North-West Institute of Nuclear Technology 710024 Xi’an China

The source mechanism of underground nuclear explosions is remarkably different from that of earthquakes in both spatial radiation pattern and source time-function (STF). Small underground nuclear explosions can be used as empirical Green’s functions (EGF) to isolate the source-time spectrum of a large suspected earthquake occurred in a Nuclear Test Site (target area) by the spectral division method. As this study shows, with high-quality data, the quotient spectrum can be transformed to the time domain, yielding the apparent far-field source-time function of the large suspected event. The relative source time-function (RSTF) of a nuclear ex-plosion is usually a simple pulse with a duration of about 1 s., while an earthquake’s is more complicated with a series of pulses and a longer duration. The RSTF can be used as a nice dis-criminant to distinguish the nature earthquakes from underground nuclear explosions in target areas.

关键词： target-area, empirical Green's function, RSTF.

Finite time extinction of super-Brownian motions with deterministic catalyst

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Science China Mathematics 2003年第4期46卷 538-551页

作者：任艳霞王永进 lmam School of Mathematical Sciences Peking University Beijing 100871China school of Mathematics Nankai UniversityTianjin 300071 China

In this paper we consider a super-Brownian motion X with branching mechanism k(x)z α, where k(x) > 0 is a bounded H?lder continuous function on ?d and ${}_{{}_x \in \mathbb{R}^d }k(x) = 0$ . We prove that ifk(x)?‖x‖?l (0?l2.and d ≥ 3: it isO(‖x‖?(α+1)) in one dimension,O(‖x‖?2.log ‖x‖))?(α+1)) in two dimensions, andO(‖x‖2. in higher dimensions. These growth orders also turn out to be the maximum order for the nonexistence of a positive solution for 1/2.u=k(x)u α.

关键词： super-Brownian motion, compact support property, finite time extinction, positive solutions to nonlinear pde's.

A new Early Cretaceous lizard with well-preserved scale impressions from western Liaoning, China

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Progress in Natural Science:Materials International 2005年第2期15卷 67-73页

作者： JI Shu’an*(school of Earth and Space sciences, {2., beijing 100871, China) school of Earth and Space sciences Peking University Beijing 100871 China

A new small lizard, Liaoningolacerta brevirostra gen. et sp. nov., from the Early Cretaceous Yixian Formation of western Liaoning is described in detail. The new specimen was preserved not only by the skeleton, but also by the exceptionally clear scale impressions. This lizard can be included within the taxon Scleroglossa based on its 2. or more presacrals, cruciform interclavicle with a large anterior process, moderately elongated pubis, and slightly notched distal end of tibia. The scales vary evidently in size and shape at different parts of body: small and rhomboid ventral scales, tiny and round limb scales, and large and longitudinally rectangular caudal scales that constitute the caudal whorls. This new finding provides us with more information on the lepidosis of the Mesozoic lizards.

关键词： new genus Squamata skeleton lepidosis Early Cretaceous western Liaoning

CONVERGENCE OF CHORIN-MARSDEN FOR MULA FOR THENAVIER-STOKES EQUATIONS ON CONVEX DOMAINS

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Journal of Computational Mathematics 1999年第1期17卷 73-88页

作者： Lung-an Ying(Research institute for mathematical sciences, Kyoto {2., Japan Department of Mathematics, peking university, beijing 100871, China) peking Univ Dept Math Beijing 100871 Peoples R China Kyoto Univ Math Sci Res Inst Kyoto Japan

We prove the convergence of the Chorin-Marsden product formula for solving the initial-boundary value problems of the Navier-Stokes equations on convex domains. As a particular case we consider the case of the half pl... 详细信息

关键词： Navier Stokes equation vortex method fractional step method convergence

Theory of optimal blocking for fractional factorial split-plot designs

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Science China Mathematics 2005年第5期48卷 649-656页

作者： Al Mingyao & HE Shuyuan Key Laborartory of Pure and Applied Mathematics, school of mathematical sciences, peking university, {2., China 1. Key Laborartory of Pure and Applied Mathematics School of Mathematical Sciences Peking University 100871 Beijing China

The issue of optimal blocking for fractional factorial split-plot (FFSP) designs is considered under the two criteria of minimum aberration and maximum estimation capacity. The criteria of minimum secondary aberration (MSA) and maximum secondary estimation capacity (MSEC) are developed for discriminating among rival nonisomorphic blcoked FFSP designs. A general rule for identifying MSA or MSEC blocked FFSP designs through their blocked consulting designs is established.

关键词： blocking consulting design estimation capacity minimum secondary aberration fractional factorial split-plot design.