Chinese Annals of Mathematics

The authors develop an algorithm to show that a class of self-affine sets with overlaps can be viewed as sofic affine-invariant sets without overlaps, thus by using the results of [11] and [10], the Hausdorff and Minkowski dimensions are determined.

The author obtains the theorems of Barth-Lefschetz type on Kähler manifolds with partially positive bisectional curvature without the assumption of nonnegative bisectional curvature. Some applications of the results to holomorphic mappings are given.

This paper considers the following Cauchy problem for semilinear wave equations in n space dimensions

The minimal value of s is determined such that the above Cauchy problem is locally well-posed in H^s. It turns out that for the general equation s must satisfy

For a continuous domain D, some characterization that the convex powerdomain CD is a domain hull of Max(CD) is given in terms of compact subsets of D. And in this case, it is proved that the set of the maximal points Max(CD) of CD with the relative Scott topology is homeomorphic to the set of all Scott compact subsets of Max(CD) with the topology induced by the Hausdorff metric derived from a metric on Max(CD) when Max(CD) is matrizable.

This paper gives some sufficient conditions for determining the simplicity of infinite dimensional Novikov algebras of characteristic 0, and also constructs a class simple Novikov algebras by extending the base field. At last, the deformation theory of Novikov algebras is introduced.

Ideal class groups H(K) of algebraic quadratic function fields K are studied. Necessary and sufficient condition is given for the class group H(K) to contain a cyclic subgroup of any order n, which holds true for both real and imaginary fields K. Then several series of function fields K, including real, inertia imaginary, and ramified imaginary quadratic function fields, are given, for which the class groups H(K) are proved to contain cyclic subgroups of order n.

This paper studies the tensor product of Jacobson radicals in nest algebras, and obtains that ; and based on the characterization of rank-one operators in , it is proved that if , are non-trivial then if and only if are continuous.

Consider the motion of immersed hypersurfaces driven by surface diffusion flow and give an lower bound on the life span of a smooth immersed solution, which depends only on how much the curvature of the initial surface is concentrated in space.

Let M be an approximately finite codimensional quasi-invariant subspace of the Fock space. This paper gives a formula to calculate the codimension of such spaces and uses this formula to study the structure of quasi-invariant subspaces of the Fock space. Especially, as one of applications, it is showed that the analogue of Beurling's theorem is not true for the Fock space in the case of n ≥ 2.

In order to construct estimating functions in some parametric models, this paper introduces two classes of information matrices. Some necessary and sufficient conditions for the information matrices achieving their upper bounds are given. For the problem of estimating the median, some optimum estimating functions based on the information matrices are acquired. Under some regularity conditions, an approach to carrying out the best basis function is introduced. In nonlinear regression models, an optimum estimating function based on the information matrices is obtained. Some examples are given to illustrate the results. Finally, the concept of optimum estimating function and the methods of constructing optimum estimating function are developed in more general statistical models.

In this paper, the authors obtain sharp upper and lower bounds for the heat kernel associated with jacobi transform, and get some analogues of Hardy's Theorem for Jacobi transform by using the sharp estimate of the heat kernel.

In this paper, the author at first develops a method to study convergence of the cascade algorithm in a Banach space without stable assumption on the initial (see Theorem 2.1), and then applies the previous result on the convergence to characterizing compactly supported refinable distributions in fractional Sobolev spaces and Hölder continuous spaces (see Theorems 3.1, 3.3, and 3.4). Finally the author applies the above characterization to choosing appropriate initial to guarantee the convergence of the cascade algorithm (see Theorem 4.2).

In [1], Shen Guangyu constructed several classes of new simple Lie algebras of characteristic 2, which are called the variations of G₂. In this paper, the authors investigate their derivation algebras. It is shown that G₂ and its variations all possess unique nondegenerate associative forms. The authors also find some nonsingular derivations of V_i G for i = 3, 4, 5, 6, and thereby construct some left-symmetric structures on V_i G for i = 3, 4, 5, 6. Some errors about the variations of in [1] are corrected.

This paper presents a geometrìc characterization of convex sets in locally convex spaces on which a strong optimization theorem of the Stegall-type holds, and gives Collier's theorem of ω* Asplund spaces a localized setting.