UNIFORM CONVERGENCE OF CESARO MEANS OF NEGATIVE ORDER OF DOUBLE TRIGONOMETRIC FOURIER SERIES

In this paper we prove that iff ∈ C([-π,π]2) and the function f is bounded partial p-variation for some p ∈ [1, ∞), then the double trigonometric Fourier series of a function f is uniformly (C;-α,-β) summable (α β＜ 1/p,α,β＞ 0) in the sense of Pringsheim. If α β≥ 1/p, then there exists a continuous function f0 of bounded partial double trigonometric Fourier series of fo diverge over cubes.     

ON THE UNIFORM DISSIPATIVITY OF SOME FIFTH-ORDER NON-LINEAR DIFFERENTIAL EQUATIONS

This paper studies the problem of uniformly dissipative solutions of somefifth order non-linear differential equations by the use of frequency domaintechnique. We use the generalized theorem of Yacubovich on dissipativity toobtain some new sufficient conditions of the existence of solutions that aredissipative for (1.1) and (1.2).     

全变差有界函数列的一致(R)可积性

给出了一致有界单调函数列一致可积性定理 ,由此得出全变差序列有界的收敛函数列的一致可积性 .说明了该结论可判断一些非一致收敛函数列的逐项积分性质 .     

The Ends of Manifolds with Bounded Geometry, Linear Growth and Finite Filling Area

We prove that simply connected open manifolds of bounded geometry, linear growth and sublinear filling growth (e.g. finite filling area) are simply connected at infinity.     

On the use of the Galerkin method for 3D numerical modelling of the general circulation: the South Atlantic eperiment

A linear three‐dimensional hydrodynamical numerical model, with the application of the Galerkin Method for the vertical dependence, is here presented. The spherical coordinate system is used, in order to allow large‐scale simulations. The equations and mathematical development of the model are shown in detail, together with the boundary and initial conditions, and the sequence of equations' solution. The model is applied to the South Atlantic Ocean, for estimating typical seasonal circulations, and the results are summarized in maps of currents at surface and 1000 m depth, and in transport values of the Brazil Current between 30°S and 40°S. Copyright © 2002 John Wiley & Sons, Ltd.     

Carleson测度与Bloch的刻画

在文中，对于C^n中有界强拟凸域。我们得到Carleson测度，消没Carleson测度的刻画。利用Carleson测度，我们还得到Bloch，小Bloch的刻画。     

ALTERNATION THEORY IN APPROXIMATION BY POLYNOMIALS HAVING BOUNDED COEFFICIENTS

ＡＬＴＥＲＮＡＴＩＯＮＴＨＥＯＲＹＩＮＡＰＰＲＯＸＩＭＡＴＩＯＮＢＹＰＯＬＹＮＯＭＩＡＬＳＨＡＶＩＮＧＢＯＵＮＤＥＤＣＯＥＦＦＩＣＩＥＮＴＳＸＵＳＨＵＳＨＥＮＧ（许树声）（ＪｉａｎｇｎａｎＵｎｉｖｅｒｓｉｔｙ,Ｗｕｘｉ２１４０６３,Ｃｈｉｎａ）Ａｂｓ...     

Bounded sets structure of CpX and quasi‐(DF)‐spaces

For wide classes of locally convex spaces, in particular, for the space $C_p(X)$ of continuous real‐valued functions on a Tychonoff space X equipped with the pointwise topology, we characterize the existence of a fundamental bounded resolution (i.e., an increasing family of bounded sets indexed by the irrationals which swallows the bounded sets). These facts together with some results from Grothendieck's theory of $(DF)$‐spaces have led us to introduce quasi‐ $(DF)$‐spaces, a class of locally convex spaces containing $(DF)$‐spaces that preserves subspaces, countable direct sums and countable products. Regular $(LM)$‐spaces as well as their strong duals are quasi‐ $(DF)$‐spaces. Hence the space of distributions $D^{\prime }(\mathrm{\Omega })$ provides a concrete example of a quasi‐ $(DF)$‐space not being a $(DF)$‐space. We show that $C_p(X)$ has a fundamental bounded resolution if and only if $C_p(X)$ is a quasi‐ $(DF)$‐space if and only if the strong dual of $C_p(X)$ is a quasi‐ $(DF)$‐space if and only if X is countable. If X is metrizable, then $C_k(X)$ is a quasi‐ $(DF)$‐space if and only if X is a σ‐compact Polish space.     

Existence of strong minimizers for the Griffith static fracture model in dimension two

We consider the Griffith fracture model in two spatial dimensions, and prove existence of strong minimizers, with closed jump set and continuously differentiable deformation fields. One key ingredient, which is the object of the present paper, is a generalization to the vectorial situation of the decay estimate by De Giorgi, Carriero, and Leaci. This is based on replacing the coarea formula by a method to approximate $SB{D}^p$ functions with small jump set by Sobolev functions, and is restricted to two dimensions. The other two ingredients will appear in companion papers and consist respectively in regularity results for vectorial elliptic problems of the elasticity type and in a method to approximate in energy $GSB{D}^p$ functions by $SB{V}^p$ ones.     

NESTED GRID METHODS FOR AN OCEAN MODEL: A COMPARATIVE STUDY

In this paper a comparison is carried out between three correction methods for multigrid local mesh refinement in oceanic applications: FIC, LDC and the direct method (DM) proposed by Spall and Holland. This study is based on a nested primitive equation model developed by Laugier on the basis of the code OPA (LODYC). The external barotropic problem is solved using any of the three local grid correction algorithms yielding an interactive nested grid model. The non-linear elliptic equation for the barotropic streamfunction tendency is solved on two nested grids, called the global and the zoom grid, that interact between themselves. The zoom grid is entirely embedded within the global domain with a horizontal grid step ratio of 3:1. The computation on the global grid supplies the boundary conditions for the zoom grid region and the fine grid fields are used to correct the global coarse solution. The three local correction methods are tested on two problems relevant to oceanic circulation phenomena proposed by Spall and Holland: a barotropic modon and an anticyclonic vortex. The results show that the nesting technique is a very efficient way to solve these problems in terms of a gain in precision compared with the required CPU time. The two-domain model with local mesh refinement allows one both to manage effectively the open boundary conditions for the local grid and to correct the global solution thanks to the zoom solution. In the case of the modon propagation the three local correction methods provide approximately the same results. For the baroclinic vortex it appears that the two iterative methods are more efficient than the direct one.