Acta Mathematica Sinica

Select

Classification of Homomorphisms from C(X) to Simple C^*-Algebras of Real Rank Zero

Guihua Gong, Huaxin Lin

Acta Mathematica Sinica. 2000, 16(2): 181-206. https://doi.org/10.1007/s101140000036

Abstract ( ) Download PDF ( )

Knowledge map

Save

Let A be a unital simple C^*-algebra of real zero, stable rank one, with weakly unperforated K₀(A) and unique normalized quasi-trace τ, and let X be a compact metric space. We show that two monomorphisms φ, ψ : C(X)→A are approximately unitarily equivalent if and only if φψ induce the same element in KL(C(X), A) and the two lineal functionals τοφ and τοψ are equal. We also show that, with an injectivity condition, an almost multiplicative morphism from C(X) into A with vanishing KK-obstacle is close to a homomorphism.

Select

Boundary Layer Theory and the Zero-Viscosity Limit of the Navier-Stokes Equation

Weinan E

Acta Mathematica Sinica. 2000, 16(2): 207-218. https://doi.org/10.1007/s101140000034

Abstract ( ) Download PDF ( )

Knowledge map

Save

A central problem in the mathematical analysis of fluid dynamics is the asymptotic limit of the fluid flow as viscosity goes to zero. This is particularly important when boundaries are present since vorticity is typically generated at the boundary as a result of boundary layer separation. The boundary layer theory, developed by Prandtl about a hundred years ago, has become a standard tool in addressing these questions. Yet at the mathematical level, there is still a lack of fundamental understanding of these questions and the validity of the boundary layer theory. In this article, we review recent progresses on the analysis of Prandtl's equation and the related issue of the zero-viscosity limit for the solutions of the Navier-Stokes equation. We also discuss some directions where progress is expected in the near future.

Select

Generalized Chow Forms and Reduction of Semi-Stable Varieties

Qingchun Tian

Acta Mathematica Sinica. 2000, 16(2): 219-228. https://doi.org/10.1007/s101140000047

Abstract ( ) Download PDF ( )

Knowledge map

Save

In this note, by using the method of S. Zhang[1], we obtain the local version of a theorem of BGS[2] which links Faltings heights of projective varieties with the Philippon heights for the corresponding generalized Chow points. By the stable reduction theorem of S. Zhang[1], we prove that Chow semistabilities and generalized Chow semistabilities are the same.

Select

On the Birch-Swinnerton-Dyer Conjecture of Elliptic Curves E_D : y² = x³-D²x

Delang Li, Ye Tian

Acta Mathematica Sinica. 2000, 16(2): 229-236. https://doi.org/10.1007/s101140000040

Abstract ( ) Download PDF ( )

Knowledge map

Save

We prove in this paper that the BSD conjecture holds for a certain kind of elliptic curves.

Select

Normal Forms of Symplectic Matrices

Yiming Long, Di Dong

Acta Mathematica Sinica. 2000, 16(2): 237-260. https://doi.org/10.1007/s101140000048

Abstract ( ) Download PDF ( )

Knowledge map

Save

In this paper, we prove that for every symplectic matrix M possessing eigenvalues on the unit circle, there exists a symplectic matrix PP^-1MP is a symplectic matrix of the normal forms defined in this paper.

Select

Existence and Application of Optimal Markovian Coupling with Respect to Non-Negative Lower Semi-Continuous Functions

Shaoyi Zhang

Acta Mathematica Sinica. 2000, 16(2): 261-270. https://doi.org/10.1007/s101140000049

Abstract ( ) Download PDF ( )

Knowledge map

Save

In this paper, for two given transition probabilities, the existence of the optimal Markovian coupling with respect to a non-negative lower semi-continuous function is proved. As an application of this result, the well-known Strassen's theorem is generalized. Moreover, it is proved that the existence of an order-preserving Markovian coupling of two given jump processes is equivalent to their stochastical comparability.

Select

Accuracy of Multivariable Refinable Functions and Two-Scale Similarity Transform

Qiuhui Sheng, Silong Peng

Acta Mathematica Sinica. 2000, 16(2): 271-276. https://doi.org/10.1007/s101140000050

Abstract ( ) Download PDF ( )

Knowledge map

Save

In this paper, we prove that if two multiresolutions satisfy a relation, then they have the same accuracy in the multivariate FSI case.

Select

Discrete Calderón-type Reproducing Formula

Youngsheng Han

Acta Mathematica Sinica. 2000, 16(2): 277-294. https://doi.org/10.1007/s101140000037

Abstract ( ) Download PDF ( )

Knowledge map

Save

In this paper we use the Calderón-Zygmund operator theory to provide a discrete Calderón-type reproducing formula. Since translation, dilation and, in particular, the Fourier transform are never used in the proofs, all results still hold on spaces of homogenous type introduced by Coifman and Weiss. As a consequence, we obtain a class of frames with the minimum regularity properties.

Select

Boundedness of Multilinear Operators in Herz-type Hardy Space

Lin Tang, Dachun Yang

Acta Mathematica Sinica. 2000, 16(2): 295-306. https://doi.org/10.1007/s101140000035

Abstract ( ) Download PDF ( )

Knowledge map

Save

Let κ∈N. We prove that the multilinear operators of finite sums of products of singular integrals on R_n are bounded from $HK}^{{\alpha _{1},p_{1} }}_{{q1}} {\left( {\mathbb{R}^{n} } \right)}\times \cdots \times{\kern 1pt} HK}^{{\alpha,p}}_{q} {\left( {\mathbb{R}^{n} } \right)}$ into $HK}^{{\alpha,p}}_{q} {\left( {\mathbb{R}^{n} } \right)}$ if they have vanishing moments up to a certain order dictated by the target spaces. These conditions on vanishing moments satisfied by the multilinear operators are also necessary when α_j≥ 0 and the singular integrals considered here include the Calderón-Zygmund singular integrals and the fractional integrals of any orders.

Select

Classification of Wavelet Bases by Translation Subgroups and Nonharmonic Wavelet Bases

Qiao Wang

Acta Mathematica Sinica. 2000, 16(2): 307-312. https://doi.org/10.1007/s101140000051

Abstract ( ) Download PDF ( )

Knowledge map

Save

The structure of the set S of shiftable points of wavelet subspaces is researched in this paper. We prove that S = R or S = 1/qZ where q∈N. The spectral and functional characterizations for the shiftability are given. Furthermore, the nonharmonic wavelet bases are discussed.

Select

On the Solvability of Degenerate Quasilinear Parabolic Equations of Second Order

Zhenhai Liu

Acta Mathematica Sinica. 2000, 16(2): 313-324. https://doi.org/10.1007/s101140000052

Abstract ( ) Download PDF ( )

Knowledge map

Save

In this paper, we consider nonlinear degenerate quasilinear parabolic initial boundary value problems of second order. Using results from the theory of pseudomonotone operators, we show that there exists at least one weak solution in a suitable weighted Sobolev space.

Select

Quasi-Homeomorphisms and Measures of Finite Energy Integrals of Generalized Dirichlet Forms

Wei Sun

Acta Mathematica Sinica. 2000, 16(2): 325-336. https://doi.org/10.1007/s101140000038

Abstract ( ) Download PDF ( )

Knowledge map

Save

We introduce the quasi-homeomorphisms of generalized Dirichlet forms and prove that any quasi-regular generalized Dirichlet form is quasi-homeomorphic to a semi-regular generalized Dirichlet form. Moreover, we apply this quasi-homeomorphism method to study the measures of finite energy integrals of generalized Dirichlet forms. We show that any 1-coexcessive function which is dominated by a function in ${\hat\cal F}}$ is associated with a measure of finite energy integral. Consequently, we prove that a Borel set B is ε-exceptional if and only if μ(B) = 0 for any measure μ of finite energy integral.

Select

Oseen Coupling Method for the Exterior Flow Part Ⅰ: Oseen Coupling Approximation

Yinnian He, Kaitai Li

Acta Mathematica Sinica. 2000, 16(2): 337-348. https://doi.org/10.1007/s101140000053

Abstract ( ) Download PDF ( )

Knowledge map

Save

In this paper, we consider the bidimensional exterior unsteady Navier-Stokes equations with nonhomogeneous boundary conditions and present an Oseen coupling problem which approximates the Navier-Stokes problem, obtained by coupling the Navier-Stokes equations in the inner region and the Oseen equations in the outer region. Moreover, we prove the existence, uniqueness and the approximate accuracy of the weak solution of the Oseen coupling equations.

Select

Solvability of Elliptic Boundary Value Problems without Standard Landesman-Lazer Condition

Zhiqing Han

Acta Mathematica Sinica. 2000, 16(2): 349-360. https://doi.org/10.1007/s101140000054

Abstract ( ) Download PDF ( )

Knowledge map

Save

In this paper we prove a very general result concerning solvability of the resonant problem: Δu + λ_k u + g(x, u) = h(x); u = 0, x ∈∂Ω, which immediately gives three generalized Landesman-Lazer conditions. The most interesting application of the general result is concerned with the problem when λ_k = λ₁, in which case we prove solvability results for it under conditions which are not the standard Landesman-Lazer condition or only partly enjoy it. Furthermore, we propose a new sign condition and give a comprehensive extension of a main result of Figueiredo and Ni.

Please choose a citation manager

Content to export

15 June 2000, Volume 16 Issue 2

Share

模态框（Modal）标题

Please choose a citation manager

Content to export

15 June 2000, Volume 16 Issue 2