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A new DNA algorithm to solve graph coloring problem

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Progress in Natural science:Materials International 2007年第6期17卷 733-738页

作者： Jiang Xingpeng1, Li Yin2, Meng Ya3.and Meng Dazhi2(1. National Laboratory of Pattern Recognition,Institute of Automation, chinese academy of sciences, Beijing 100080, china 2. College of Applied {3., Beijing University of Technology, Beijing 100022, china 3. School of science, Beijing Institute of Technology, Beijing 100081, china) National Laboratory of Pattern Recognition Institute of Automation Chinese Academy of Sciences Beijing 100080 China College of Applied sciences Beijing University of Technology Beijing 100022 China School of science Beijing Institute of Technology Beijing 100081 China

Using a small quantity of DNA molecules and little experimental time to solve complex problems successfully is a goal of DNA computing. Some NP-hard problems have been solved by DNA computing with lower time complexity than conventional computing. However, this advantage often brings higher space complexity and needs a large number of DNA encoding molecules. One example is graph coloring problem. Current DNA algorithms need exponentially increasing DNA encoding strands with the growing of problem size. Here we propose a new DNA algorithm of graph coloring problem based on the proof of four-color theorem. This algorithm has good properties of needing a relatively small number of operations in polynomial time and needing a small number of DNA encoding molecules (we need only 6R DNA encoding molecules if the number of regions in a graph is R).

关键词： DNA computing NP-hard problem graph coloring problem.

Existence of SURU estimators in SURE model with special covariance structures

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chinese science Bulletin 1997年第14期42卷 1149-1151页

作者： WU QiguangInstitute of Systems science, chinese academy of sciences, Beijing 100080,{3. Institute of Systems science Chinese Academy of Sciences Beijing China

THROUGHOUT this note, the following notations are used: For a matrix A, A>0 means thatA is positive definite symmetric; R （A）, A′and A- stand for the column space, transposeand any g-inverse of A respectively; PA = A （A′A）- A′and PA = Ik - PA, where Ik is theidentity matrix of order k that is the number of rows in A. Rm×n is the totality of m×n realmatrices.

关键词： seemingly unrelated regression equations (SURE) model uniformly minimum risk unbiased (UMRU) estimator uniform covariance structure serial covariance structure.

Transformations and non-degenerate maps

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science china Mathematics 2005年第z1期48卷 195-205页

作者： LI Baokui & WANG Yuefei Institute of Mathematics, academy of Mathematics and System sciences, chinese academy of sciences, Beijing {3., china Graduate School, chinese academy of sciences, Beijing {3., china 1. Institute of Mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences 100080 Beijing China 2. Graduate School Chinese Academy of Sciences 100080 Beijing China

We shall prove the equivalences of a non-degenerate circle-preserving map and a M(o)bius transformation in ^Rn, of a non-degenerate geodesic-preserving map and an isometry in Hn of a non-degenerate line-preserving map and an affine transformation in Rn. That a map is non-degenerate means that the image of the whole space under the map is not a circle, or geodesic or line respectively. These results hold without either injective or surjective, or even continuous assumptions, which are new and of a fundamental nature in geometry.

关键词： M(o)bius transformation, circle-preserving map, non-degenerate map.

Hyperbolic geometry with geometric algebra

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chinese science Bulletin 1997年第3期42卷 262-263页

作者： LI Hong boInstitute of Systems science, chinese academy of sciences, Beijing 100080,{3. Institute of Systems science Chinese Academy of Sciences Beijing China

WE use the geometric algebra in refs. [1, 2] to study hyperbolic geometry. The n-dimensional hyperbolic space Hn is taken to be the unit sphere of G1 (I-n,1) with antipodal points identified. We study typically H2: the dualities between generalized point and generalized line, between generalized triangle and imaginary triangle; convex generalized triangles; Lorentz transformations; generalized circles and double-cycles, etc. Below we list some of the results.

关键词： line Hyperbolic geometry with geometric algebra

BOUNDARY FEEDBACK STABILIZATION OF NONUNIFORM TIMOSHENKO BEAM WITH A TIPLOAD

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chinese Annals of Mathematics,Series B 2001年第4期22卷 485-494页

作者： YAN QINGXU, FENG DEXING Institute of Systems science, academy of Mathematics and Systems science,{3., Beijing 100080, china. Institute of Systems science, academy of Mathematics and Systems science,{3., Be Institute of Systems science Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100080 China

The boundary stabilization problem of a Timoshenko beam attached with a mass at one end is studied. First, with linear boundary force feedback and moment control simultaneously at the end attached with the load, the energy corresponding to the closed loop system is proven to be exponentially convergent to zero as time t →∞. Then, some counterexamples are given to show that, in other casest the corresponding closed loop system is, in general, not stable asymtotically, let alone exponentially.

关键词： Timoshenko beam Boundary feedback control C0 semigroups Exponential stability Multiplier method

A quasi-local mass for 2-spheres with negative Gauss curvature

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science china Mathematics 2008年第9期51卷 1644-1650页

作者： ZHANG Xiao Institute of Mathematics, academy of Mathematics and Systems science, chinese academy of sciences, Beijing {3., china 1. Institute of Mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100080 China

We extend our previous definition of quasi-local mass to 2-spheres whose Gauss curvature is negative, and prove its positivity.

关键词： general relativity quasi-local mass positivity 53.27 53.50 83.60

Thermal analysis of the baffle structure of the Solar space Telescope

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science china(Physics,Mechanics & Astronomy) 2010年第9期53卷 1755-1764页

作者： LI Rong1,2,3.& WANG Sen1,3.1 National Astronomical Observatories,chinese academy of sciences,Beijing 100012,{3. 2 Graduate University of chinese academy of sciences,Beijing 100049,{3. 3.Key Laboratory of Solar Activity,National Astronomical Observatories of chinese academy of sciences,Beijing 100012,{3. 1. National Astronomical Observatories Chinese Academy of Sciences Beijing 100012 China2. Graduate University of Chinese Academy of Sciences Beijing 100049 China3. Key Laboratory of Solar Activity National Astronomical Observatories of Chinese Academy of Sciences Beijing 100012 China

The SST(space Solar Telescope) is an astronomical telescope with a primary mirror of 1 m in *** observes the sun with a small view field to ensure that its high spatial resolution imaging has 0.1″-0.15″ and high SNR(signal to noise ratio).Surrounding the small view field is still the sun,which is an intense source of both heat and stray *** baffles(the main baffle,the aperture,and the outer baffle),which are used to eliminate the stray light,will change the thermal flux in the SST and will weaken the effect of the thermal control *** this study,the compatibility analysis of the thermal effect of baffle structures in SST is *** GCF(Geometry Composing Function) and BRDF(Bidirectional Reflectance Distribution Function),which are two inherent related parameters in the compatibility analysis,are *** objective and method of the compatibility analysis are *** the thermal analysis software,the temperature fields are calculated for different lengths of the main baffle,different radii of apertures,different lengths of the outer baffle with a 3. tilt angle and 16' tilt angle,and different tilt angles of the outer baffle with a 200 mm length.A series of configurations and sizes of the baffles are studied with the goals of both thermal control and elimination of stray *** design of the baffle structure of SST is achieved:the main baffle of length 4100 mm,the internal shield of radius 494 mm,the outer baffle of length 200 mm,and the outer baffle of tilt angle 3. are successfully *** paper presents the relationship between the thermal control design and stray light elimination plan in the *** aims of the optimal design of the baffle structure of SST are *** thoughts and methods of the optimal analysis are also useful for similar optical telescopes designed for solar observation.

关键词： baffle the main baffle the outer baffle GCF BRDF

Nonlinear interactions between gravity waves and background winds

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Progress in Natural science:Materials International 2007年第6期17卷 639-644页

作者： Liu Xiao1,2 and Xu Jiyao1(1. State Key Laboratory for space Weather, Center for space science and Applied Research,{3., Beijing 100080, china 2. Graduate University of{3., Beijing 10003., china) [a]State Key Laboratory for space Weather Center for Space Science and Applied Research Chinese Academy of Sciences Beijing China [b]Graduate University of chinese academy of sciences Beijing China

Using the nonlinear propagating gravity waves (GW) model in the two-dimensional compressible atmosphere and the linear GW theory, the process of GW propagation in different background winds, e.g. the direction of the background wind is opposite to (dead wind) or the same as (tail wind) the direction of the horizontal phase velocity of GW, is studied. The results show that the dead wind prolongs the vertical wavelength and accelerates GW propagation. Therefore, GW propagates up to a higher height becomes instable in a short time and eventually induces an inverse jet flow. Then, the vertical wavelength is becoming short due to the nonlinear interactions between GW and the inverse jet flow. The vertical wavelength and group velocity decrease after GW propagates into the tail wind. The initial instable time is delayed. Although most of GW is trapped in the instable region, some of GW propagates above the instable region. Compared with GW propagation in the tail wind, the nonlinear interactions between GW and the dead wind are also strong. In contrast, the linear GW theory predicts that GW can propagate freely in the dead wind. The vertical wavelength simulated by the nonlinear numerical model is different from that predicted by the linear theory greatly after GW propagates into the dead wind.

关键词： gravity waves background winds vertical group velocity vertical wavelength nonlinear interactions.

Re-Os(ICP-MS)dating of the massive sulfide ores from the Jinchuan Ni-Cu-PGE deposit

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science china Earth sciences 2005年第10期48卷 1672-1677页

作者： YANG Gang1,2, DU Andao1, LU Jiren3. QU Wenjun1 & CHEN Jiangfeng2 1. National Research Center of Geoanalysis, Beijing 10003., china 2. Laboratory for Earth Material Cycling, School of Earth and space sciences, University of {3. and Technology of china, Hefei 23.026, china 3. Institute of Mineral Resource, chinese academy of Geological sciences, Beijing 10003., china National Research Center of Geoanalysis Beijing china Laboratory for Earth Material Cycling School of Earth and Space Sciences University of Science and Technology of China Hefei China Institute of Mineral Resource chinese academy of Geological sciences Beijing{3.

Massive sulfide ore from the Jinchuan Ni-Cu-PGE deposit was dated by Re-Os technique using Carius Tube digestion, Os distillation, Re extraction by acetone and ICP-MS measurement. An isochron giving an age of 83. ± 3. Ma, initial 187Os/188Os ratio of 0.279 ± 0.018 (MSWD = 1.7) and γOs = 13. ± 15 is obtained. The Re-Os age obtained agrees, within analytical uncertainties, with previous SHRIMP zircon U-Pb age of 827 ± 8 Ma (n=5, MSWD = 4.3.. The result suggests that the deposit was formed at Neoproterozoic and that the formation of the Jinchuan Ni-Cu-PGE sulfide deposit may be closely related to the plume activity, which were attributed to the breakup of the Rodinia supercontinent. The high γOs of the massive ores sug-gests that crustal material was involved in the formation of the Jinchuan deposit, however, the quantity of the added crustal material is less than 10%.

关键词： Jinchuan Ni-Cu-PGE deposit, Re-Os dating, ICP-MS.