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On characterizations of isometries on function spaces

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Science China mathematics 2008年第4期51卷 620-631页

作者： LI SongYing~(1+) RUAN YingBin~2 1 department of mathematics university of California Irvine CA 92697 usa 2 school of mathematics and Computer Science Fujian Normal university Fuzhou 350007 China 1. department of mathematics University of California Irvine CA 92697 USA 2. school of mathematics and Computer Science Fujian Normal University Fuzhou 350007 China

The paper gives characterization for an isometric isomorphism on little Bloch space, VMOA and holomorphic Besov space over the unit ball B n in ? n .

关键词： ismometry Besov spaces 32A17 47A15

A note on certain square functions on product spaces

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Science China mathematics 2006年第1期49卷 98-108页

作者： WANG Meng, CHEN Jiecheng2 & FAN Dashan department of mathematics, Zhejiang university (at Yuquan campus), Hangzhou 310027, China department of mathematics, Zhejiang university (at Xixi campus), Hangzhou 310028, China department of mathematics, university of Wisconsin-Milwaukee, Milwaukee, WI53201, usa department of mathematics Zhejiang University [at Yuquan campus] Hangzhou 310027 China department of mathematics Zhejiang University [at Xixi campus] Hangzhou 310028 China department of mathematics University of Wisconsin-Milwaukee Milwaukee WI53201 USA

We study certain square functions on product spaces Rn × Rm, whose integral kernels are obtained from kernels which are homogeneous in each factor Rn and Rm and locally in L(log+ L) away from Rn × {0} and {0} × Rm by means of polynomial distortions in the radial variable. As a model case, we obtain that the Marcinkiewicz integral operator is bounded on Lp(Rn × Rm)(P > 1) for Ω∈ e Llog+ L(Sn-1 × Sm-1) satisfying the cancellation condition.

关键词： square function, Marcinkiewicz integral, product space.

ESTIMATING MERIDIONAL ENERGY TRANSPORTS BY THE ATMOSPHERIC AND OCEANIC GENERAL CIRCULATIONS USING BOUNDARY FLUX DATA~1

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ESTIMATING MERIDIONAL ENERGY TRANSPORTS BY THE ATMOSPHERIC A...

ON THE FORMATION OF THE BULGE IN A SPILLING BREAKING WATER WAVE

理论与应用地球物理研讨会

作者： Yuanchong Zhang department of Applied Physics and Applied mathematics, Columbia university at NASA Goddard Institute for Space Studies, new york, ny, usa and William B. Rossow NASA Goddard Institute for Space Studies, new york, ny, usa

＜正＞ The annual-mean meridional energy transport in the atmosphere-ocean system （total transport） is estimated using 4-year mean net radiative fluxes at the top of the atmosphere （TOA） calculated from the International Satellite Cloud Climatology Project （ISCCP） cloud datasets. In addition, the net atmospheric and surface radiative fluxes are calculated. When supplemented by a climatology of the surface latent and sensible heat fluxes, these radiative fluxes are used to derive the separate atmospheric and oceanic energy transports using a surface and planetary energy-balance （SPEB） method. Most previous results are based on direct calculations of the atmospheric energy transport from in situ measurements of horizontal wind velocity, temperature and humidity in the atmosphere and on inference of oceanic heat transports as the difference between the atmospheric transports and the total energy transport [the planetary energy-balance （PEB） method]. The total, atmospheric and oceanic energy transports from this study are in good agreement with more recent results （within mutual uncertainties）. A detailed assessment is made of the uncertainties in the atmosphere and ocean energy transports that arise from uncertainties in the TOA and surface energy fluxes: the largest uncertainties are associated with the surface radiative and latent heat fluxes. Since the errors in the present SPEB method are from different sources and have different geographic distributions, the results of this study complement previous estimates of the atmospheric and oceanic energy transports. Assessment of error sources also suggests that improvement of this type of results is more likely in the near future than for the other methods. Because the radiative fluxes are calculated from physical quantities, the authors can characterize the mean effects of clouds on the atmospheric and oceanic energy transports: （1） cloud effects on the TOA radiation budget reduce hemispheric differences introduced by hemi

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来源： cnki会议评论

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Journal of Hydrodynamics 1997年第3期9卷 41-48页

作者： Wang, Zhongyuan Nadine, Aubry Jim, H.Duncan Nanjing Univ of Science and Technology Nanjing China

The early stages of a spilling breaking water wave leading to the formation of a bulge on the forward face of the wave are investigated. In this study, simultaneous space-time measurements of the free-surface elevation of a spilling breaking water wave are recorded and analyzed. The analysis, carried out in the frame of reference moving with the crest of the wave,reveals that the formation of the bulge is due to the presence of a shock-like mode. In the previous frame of reference, the shock itself is unsteady but its (spatial) location is time independent and coincides with the 'toe' of the bulge. As time increases, the shock undergoes a flip (a reflection symmetry) with respect to the midpoint of our time interval. Such a flip is responsible for an abrupt increase of the wave steepe-ness, which will lead to wave breaking at later times. Following these observations, we present a two-dimensional quantitative model which reproduces both the formation of the bulge and the sudden increase of the wave steepeness.

关键词： hydrodynamics,turbulence water wave,data analysis

On hypothesis testing with a partitioned random alternative

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Science China mathematics 2010年第4期53卷 927-938页

作者： WANG WeiZhen department of mathematics and Statistics,Wright State university,Dayton,OH 45435,usa 1. department of mathematics and Statistics Wright State University Dayton OH 45435 USA

It is common in statistical practice that one needs to make a choice among m + 1 mutually exclusive claims on *** m=1,it is done by the (traditional) hypothesis *** this paper,a generalization to the case m > 1 is *** fundamental difference with the case m=1 is that the new alternative hypothesis is a partition of m multiple claims and is *** is used to decide which claim in the partition is to be tested as the ***,a random alternative is *** conditional and overall type I errors of the proposed test are controlled at a given level,and this test can be used as a new solution for the general multiple test *** classical problems,including the one-sample problem,model selection in multiple linear regression,and multi-factor analysis,are revisited,and new tests are provided ***,the famous two-sided t-test should be replaced by the proposed.

关键词： analysis of variance conditional probability multiple linear regression one-sample problem

A spectral interpretation for the explicit formula in the theory of prime numbers

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Science China mathematics 2010年第3期53卷 791-812页

作者： LI Xian-Jin department of mathematics, Brigham Young university, Provo, Utah 84602, usa 1. department of mathematics Brigham Young University Provo Utah 84602 USA

A spectral interpretation for the poles and zeros of the L-function of algebraic number fields is given by Meyer. As Meyer works with Schwartz spaces which are not Hilbert spaces, the information on the location of zeros of the L-function is lost. In 1999, A. Connes gave a spectral interpretation for the critical zeros the Riemann zeta function. He works with Hilbert spaces. In this paper, we show that a variant of Connes’ trace formula is essentially equal to the explicit formula of A. Weil.

关键词： explicit formula fourier analysis Riemann hypothesis trace formula

CONVERGENCE RATES OF MARKOV CHAIN APPROXIMATION METHODS FOR CONTROLLED DIFFUSIONS WITH STOPPING

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Journal of Systems Science & Complexity 2010年第3期23卷 600-621页

作者： Qingshuo SONG Gang George YIN department of mathematics City University of Hong Kong 83 Tat Chee Avenue Kowloon Tong Hong Kong China department of mathematics Wayne State University Detroit Michigan 48202 USA

This work is concerned with rates of convergence of numerical methods using Markov chainapproximation for controlled diffusions with stopping (the first exit time from a bounded region).In lieuof considering the associated finite difference schemes for Hamilton-Jacobi-Bellman (HJB) equations,a purely probabilistic approach is *** is an added difficulty due to the boundary condition,which requires the continuity of the first exit time with respect to the discrete *** prove theconvergence of the algorithm by Markov chain approximation method,a tangency problem might arise.A common approach uses certain conditions to avoid the tangency ***,by modifying thevalue function,it is demonstrated that the tangency problem will not arise in the sense of convergencein probability and in L^*** addition,controlled diffusions with a discount factor is also treated.

关键词： Controlled diffusion dynamic programming equation Markov chain approximation rate of convergence.

A QUANTIFIER-ELIMINATION BASED HEURISTIC FOR AUTOMATICALLY GENERATING INDUCTIVE ASSERTIONS FOR PROGRAMS

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Journal of Systems Science & Complexity 2006年第3期19卷 307-330页

作者： Deepak KAPUR department of Computer Science University of New MexicoAlbuquerqueUSA

A method using quantifier-elimination is proposed for automatically generating program invariants/inductive assertions. Given a program, inductive assertions, hypothesized as parameterized formulas in a theory, are associated with program locations. Parameters in inductive assertions are discovered by generating constraints on parameters by ensuring that an inductive assertion is indeed preserved by all execution paths leading to the associated location of the program. The method can be used to discover loop invariants-properties of variables that remain invariant at the entry of a loop. The parameterized formula can be successively refined by considering execution paths one by one; heuristics can be developed for determining the order in which the paths are considered. Initialization of program variables as well as the precondition and postcondition, if available, can also be used to further refine the hypothesized invariant. The method does not depend on the availability of the precondition and postcondition of a program. Constraints on parameters generated in this way are solved for possible values of parameters. If no solution is possible, this means that an invariant of the hypothesized form is not likely to exist for the loop under the assumptions/approximations made to generate the associated verification condition. Otherwise, if the parametric constraints are solvable, then under certain conditions on methods for generating these constraints, the strongest possible invariant of the hypothesized form can be generated from most general solutions of the parametric constraints. The approach is illustrated using the logical languages of conjunction of polynomial equations as well as Presburger arithmetic for expressing assertions.

关键词： Automated software analysis and verification inductive assertion loop invariant quantifier elimination.

On interpolation for Hormander’s algebras

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Science China mathematics 2010年第3期53卷 763-770页

作者： LI Bao Qin department of mathematics, Florida International university, Miami, FL 33199, usa 1. department of mathematics Florida International University Miami FL 33199 USA

We discuss some recent results on interpolation problems for weighted Hrmander’s algebras of holomorphic functions in several complex variables, and also give a sharp estimate on counting functions of interpolating... 详细信息

关键词： weight pseudoconvex set Hrmander’s algebra interpolating variety plurisubharmonic function holomorphic function entire function