Acta Mathematica Sinica, English Series

article

On the existence and uniqueness of solutions to an asymptotic equation of a variational wave equation

Ping Zhang, Yuxi Zheng

Acta Mathematica Sinica, English Series > 1999 > 15 > 1 > 115-129

We prove the global existence and uniqueness of admissible weak solutions to an asymptotic equation of a nonlinear hyperbolic variational wave equation with nonnegative L ²(ℝ) initial data.

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A formula for the non-integer powers of the laplacian

Zhengxu He

Acta Mathematica Sinica, English Series > 1999 > 15 > 1 > 21-24

We provide an elementary formula for the non-integer powers of the Laplace operator in the Euclidean spaces. Such formulas are helpful in establishing the elliptic nature of some pseudo-differential operators arising from the study of energies of knotted loops in space, and possibly of embedded submanifolds in a Riemannian manifold.

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Varieties for cohomology with twisted coefficients

Jon F. Carlson

Acta Mathematica Sinica, English Series > 1999 > 15 > 1 > 81-92

Let G be a finite group and k a field of characteristic p > 0. In this paper we consider the support variety for the cohomology module Ext _kG ^* (M, N) where M and N are kG-modules. It is the subvariety of the maximal ideal spectrum of H*(G, k) of the annihilator of the cohomology module. For modules in the principal block we show that that the variety is contained in the intersections of the varieties...

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Hermitian-einstein metrics on parabolic stable bundles

Jiayu Li, M. S. Narasimhan

Acta Mathematica Sinica, English Series > 1999 > 15 > 1 > 93-114

Let $$\overline M $$ be a compact complex manifold of complex dimension two with a smooth Kähler metric and D a smooth divisor on $$\overline M $$ . If E is a rank 2 holomorphic vector bundle on $$\overline M $$ with a stable parabolic structure along D, we prove the existence of a metric on $$E'{\text{ = }}E|_{\overline M \backslash D} $$ (compatible with the parabolic structure)...

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On the equivalence of multiplicative structures in floer homology and quantum homology

Gang Liu, Gang Tian

Acta Mathematica Sinica, English Series > 1999 > 15 > 1 > 53-80

In this paper, we will prove that Floer homology equipped with either the intrinsic or exterior product is isomorphic to quantum homology as a ring. We will also prove that GW-invariants in Floer homology and quantum homology are equivalent.

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Mapping problems, fundamental groups and defect measures

Fanghua Lin

Acta Mathematica Sinica, English Series > 1999 > 15 > 1 > 25-52

We study all the possible weak limits of a minimizing sequence, for p-energy functionals, consisting of continuous maps between Riemannian manifolds subject to a Dirichlet boundary condition or a homotopy condition. We show that if p is not an integer, then any such weak limit is a strong limit and, in particular, a stationary p-harmonic map which is C ^1,α continuous away from a closed subset of the...

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When closed graph manifolds are finitely covered by surface bundles over S ¹

Yan Wang, Fengchun Yu

Acta Mathematica Sinica, English Series > 1999 > 15 > 1 > 11-20

The problem of deciding whether a graph manifold is finitely covered by a surface bundle over the circle is discussed in this paper. A necessary and sufficient condition in term of the solutions of a certain matrix equation is obtained, as well as a necessary condition which is easy to compute. Our results sharpen and extend the earlier results of J. Leucke-Y. Wu, W. Neumann, and S. Wang-F. Yu in...

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The symplectic floer homology of the square knot and granny knots

Weiping Li

Acta Mathematica Sinica, English Series > 1999 > 15 > 1 > 1-10

Using a kind of Mayer-Vietoris principle for the symplectic Floer homology of knots, we compute the symplectic Floer homology of the square knot and granny knots.

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Finite groups acting 2-transitively on their sylow subgroups

Caiheng Li, Jie Wang

Acta Mathematica Sinica, English Series > 1999 > 15 > 1 > 131-144

In this paper we have completely determined: (1) all almost simple groups which act 2-transitively on one of their sets of Sylow p-subgroups. (2) all non-abelian simple groups T whose automorphism group acts 2-transitively on one of the sets of Sylow p-subgroups of T. (3) all finite groups which are 2-transitive on all their sets of Sylow subgroups.

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Linearized oscillations in nonlinear delay difference equations

Sanyi Tang, Yanni Xiao, Jufang Chen

Acta Mathematica Sinica, English Series > 1999 > 15 > 4 > 569-574

Consider the nonlinear delay difference equation $$x_{n + 1} - x_n + \sum\limits_{j = 1}^m {p_j f_j (x_n - x_j ) = 0.} $$ We establish a linearized oscillation result of this equation, which is the extension of the result in the paper [1].

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Decay rate of solutions to hyperbolic system of first order

Shuxing Chen, Yi Zhou

Acta Mathematica Sinica, English Series > 1999 > 15 > 4 > 471-484

In this paper we generalize the global Sobolev inequality introduced by Klainerman in studying wave equation to the hyperbolic system case. We obtain several decay estimates of solutions of a hyperbolic system of first order by different norms of initial data. In particular, the result mentioned in Theorem 1.5 offers an optimal decay rate of solutions, if the initial data belongs to the assigned weighted...

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On the isomorphic classes of hopf-galois extensions with normal bases over a commutative ring

Xiaolong Jiang, Yonghua Xu

Acta Mathematica Sinica, English Series > 1999 > 15 > 4 > 515-524

In this paper we consider the isomorphic classes of H-Galois extensions with the normal basis property over a fixed commutative ring B for a finite Hopf algebra H. The result is that when H is cocommutative, then the above isomorphic classes and the 2-nd cohomology group H ²(L*, U) are isomorphic as groups under the product defined in this paper, where L=B∝H, L*=Hom_B(L, B).

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C-wellposedness of the complete second order abstract cauchy problem and applications

Mingchu Gao

Acta Mathematica Sinica, English Series > 1999 > 15 > 4 > 535-548

In this paper, we first give a sufficient and necessary condition for $$M = \left( {\begin{array}{*{20}c} {A_1 } & I \\ {A_0 } & 0 \\ \end{array} } \right)$$ to generate an exponentially bounded $$\tilde C = \left( {\begin{array}{*{20}c} C & 0 \\ 0 & C \\ \end{array} } \right)$$ -semigroup and discuss its relations to the C-wellposedness of the complete second order abstract...

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On extending real functions to finite dimensional algebras

Bingren Li, Yimin Yang

Acta Mathematica Sinica, English Series > 1999 > 15 > 4 > 455-470

In a finite dimensional real algebra, we define functional calculus for real functions. The analytic hypothesis is replaced by a differentiable hypothesis. High order differentibility is essentially necessary and sufficient to our discussions. Moreover, we give some examples.

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On nonsingular modules over infinite-dimensional simple novikov algebra of characteristic 0

Hongji Chen

Acta Mathematica Sinica, English Series > 1999 > 15 > 4 > 561-568

In this paper we show that an A-module is a direct sum of a trivial module and a nosingular module, and we also give the structure of nonsingular module over infinite dimensional simple Novikov algebras of types (II) and (III) over a field F of Characteristic 0.

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On the isometric minimal immersion into a euclidean space

Qing Chen

Acta Mathematica Sinica, English Series > 1999 > 15 > 4 > 555-560

We study the volume growth of the geodesic balls of a minimal submanifold in a Euclidean space. A necessary condition for the isometric minimal immersion into a Euclidean space is obtained. A classification of non-positively curved minimal hypersurfaces in a Euclidean space is given.

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Algebraic independence of certain numbers

Yonggao Chen, Yaochen Zhu

Acta Mathematica Sinica, English Series > 1999 > 15 > 4 > 507-514

In this note the algebraic independence of values of general Mahler series with different parameters at algebraic points is established.

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Dynamic programming for multidimensional stochastic control problems

Jin Ma, Jiongmin Yong

Acta Mathematica Sinica, English Series > 1999 > 15 > 4 > 485-506

In this paper we study a general multidimensional diffusion-type stochastic control problem. Our model contains the usual regular control problem, singular control problem and impulse control problem as special cases. Using a unified treatment of dynamic programming, we show that the value function of the problem is a viscosity solution of certain Hamilton-Jacobi-Bellman (HJB) quasivariational inequality...

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Exponential growth solutions of elliptic equations

Fengbo Hang, Fanghua Lin

Acta Mathematica Sinica, English Series > 1999 > 15 > 4 > 525-534

We show that for a class of second order divergence form elliptic equations on an infinite strip with the Dirichlet boundary condition, the space of fixed order exponential growth solutions is of finite dimension. An optimal estimation of the dimension is given. Examples also show that the finiteness property may not be true if one drops some of the conditions we make in our result.

article

The blow-up rate for a system of heat equations with neumann boundary conditions

Zhigui Lin, Chunhong Xie

Acta Mathematica Sinica, English Series > 1999 > 15 > 4 > 549-554

This paper deals with the blow-up properties of solutions to a system of heat equations u _t=Δu, v _t=Δv in B _R×(0, T) with the Neumann boundary conditions εu/εη=e ^v, εv/εη=e ^u on S _R×[0, T). The exact blow-up rates are established. It is also proved that the blow-up will occur only on the boundary.

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Acta Mathematica Sinica, English Series

On the existence and uniqueness of solutions to an asymptotic equation of a variational wave equation

A formula for the non-integer powers of the laplacian

Varieties for cohomology with twisted coefficients

Hermitian-einstein metrics on parabolic stable bundles

On the equivalence of multiplicative structures in floer homology and quantum homology

Mapping problems, fundamental groups and defect measures

When closed graph manifolds are finitely covered by surface bundles over S ¹

The symplectic floer homology of the square knot and granny knots

Finite groups acting 2-transitively on their sylow subgroups

Linearized oscillations in nonlinear delay difference equations

Decay rate of solutions to hyperbolic system of first order

On the isomorphic classes of hopf-galois extensions with normal bases over a commutative ring

C-wellposedness of the complete second order abstract cauchy problem and applications

On extending real functions to finite dimensional algebras

On nonsingular modules over infinite-dimensional simple novikov algebra of characteristic 0

On the isometric minimal immersion into a euclidean space

Algebraic independence of certain numbers

Dynamic programming for multidimensional stochastic control problems

Exponential growth solutions of elliptic equations

The blow-up rate for a system of heat equations with neumann boundary conditions

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