A Generalized Implicit Function Theorem

We prove a theorem generalizing the classical implicit function theorem to the case in which the derivative of the map is a surjective continuous linear operator. We do not assume that the kernel of the derivative is a complemented subspace.     

Whitney定理的一个推广形式

Whitney's theorem is a famous theorem in the local singularity theory. In this paper, as an application of Malgrange preparation theorem, a generalized form of Whitney's theorem will be derived.     

广义KKM定理的一个注记

本文对有限闭值的广义KKM映象建立了一个非空交定理。并给出了一个极大极小不等式的推广形式。     

关于广义对角占优的一条定理

本文给出了判定矩阵为广义对角占优的充分条件,这些条件是通过一系列三元线性严格不等式组的解集的存在性来描述的.     

A Generalized Form of Whitney's Theorem

Whitney's theorem is a famous theorem in the local singularity theory.In this paper,as an application of Malgrange preparation theorem,a generalized form of Whitney's theorem will be derived.     

A Generalized Form of Whitney＇s Theorem

Whitney's theorem is a famous theorem in the local singularity theory.In this paper,as an application of Malgrange preparation theorem,a generalized form of Whitney's theorem will be derived.     

Lusternik-Schnirelmann 定理的推广

本文根据Brouwer映射度的理论和微分拓扑的基本方法推广了Lusternik_Schnirelmann定理     

A KAM-type Theorem for Generalized Hamiltonian Systems

In this paper we mainly concern the persistence of invariant tori in generalized Hamiltonian systems. Here the generalized Hamiltonian systems refer to the systems which may admit a distinct number of action and angle variables. In particular, system under consideration can be odd dimensional. Under the Riissmann type non-degenerate condition, we proved that the majority of the lower-dimension invariant tori of the integrable systems in generalized Hamiltonian system are persistent under small perturbation. The surviving lower-dimensional tori might be elliptic, hyperbolic, or of mixed type.     

de Bruijn定理的推广

de Bruijn定理是一种重要的组合计数方法，本文以非常自然的方式推广了这种方法．p图是图G在其顶点上的置换群P作用下形成的轨道．文中引进了P-图，P-图的色容指标，P-图关于色置换群H的色权多项式以及色对称与全色对称图等概念，建立了色权多项式的计算公式和一系列的组合公式及性质．     

广义对策的一个新的平衡存在定理

在本文中，我们对具有不可数多个经纪人，具有非紧选择集和具有一般选择对应的广义对策证明了一个新的平衡存在定理。这用既不要求选择对应有开图也不要求它有开下截口。这个定理改进了Ｋｉｍ的一个最近结果。     

A Generalized Beurling Theorem for Some Lie Groups

Mathematical Notes - For any real numbers p,q ≥ 1, we present in this paper a (p, q)-generalized version of Beurling’s uncertainty principle for ?n, which largely extends the...     

A Support Theorem for a Generalized Burgers SPDE

When the initial condition u ₀ to a parabolic Burgers SPDE (containing a quadratic term) belongs to L ^q [0,1],2q, the trajectories of the solution u(t,x) a.s. belong to the space C([0,T],L ^q [0,1]). We characterize the support of the law of u in this space; the proof is based on an approximation of u by a sequence of stochastic processes obtained by replacing the Brownian sheet by linear adapted interpolations.     

“Katona-Kleitman定理的推广定理”的简短证明

本文给出“Katona-Kleitman定理的推广”的简短证明.设S是n元集合,S1,S2,…,Sk是S的k分划,f是S的子集系,使得没有A,B∈f,满足存在某个Si有A∩Si=B∩Si,而对所有Sj(1≤j≠i≤k)有A∩Sj∈B∩Sj,则     

广义路余代数和广义对偶Gabriel定理

通过将箭图的每个顶点放置一个k-余代数,首先引进了广义路余代数的概念,其次给出了广义路余代数的一些基本性质,还讨论了同构问题.证明了两个正规广义路余代数是同构的当且仅当他们的箭图及对应顶点上的单余代数是同构的.对于满足Codim C_0■1余代数C,证明了对偶Wedderburn-Malcev定理成立.作为广义路余代数的一个应用,推广了点余代数的对偶Gabriel定理.     

Stolz定理推广定理的推广

本文把孙本旺关于 Stolz定理的改进结果做了进一步拓广     

广义Cauchy中值定理及其逆定理

将C auchy中值定理的条件进行适当减弱,得到了广义C auchy中值定理,从而推广了C auchy中值定理,并在凸函数的条件下,证明了其逆定理亦成立.     

A Theorem for Generalized Extension ofOperators and Some Applications

In this note it is shown that every bounded linear operator T Э B(Y,Z)defined on a closed subspace Y of a Banach space X admits a generalized extension T Э B(X, V). Some examples of the applications are given; especially, a characterization of H.I. spaces is obtained.     

On the Equivalence and Generalized of Weyl Theorem Weyl Theorem

We know that an operator T acting on a Banach space satisfying generalized Weyl＇s theorem also satisfies Weyl＇s theorem. Conversely we show that if all isolated eigenvalues of T are poles of its resolvent and if T satisfies Weyl＇s theorem, then it also satisfies generalized Weyl＇s theorem. We give also a sinlilar result for the equivalence of a-Weyl＇s theorem and generalized a-Weyl＇s theorem. Using these results, we study the case of polaroid operators, and in particular paranormal operators.