Two General Extension Theorems

Suppose {Mn} is a sequence of pairwise disjoint, nowhere dense closed subsets of [0, 1] and {Fn} is a sequence of continuous functions. We show that there exists a continuous function F which has the same derivate structure as Fn at each point of Mn. In addition, F can be made BV if n=1 V(Fn, Mn), the sum of the variation of Fn|Mn, is finite. A well-known and very useful theorem of Laczkovich and Petruska as well as many classical examples follow readily from our results.     

Absolute Summability Factors and Absolute Tauberian Theorems for Double Series and Sequences

Let A and B be the linear methods of the summability of double series with fields of bounded summability MA _b ^' and B _b ^' , respectively. Let T be certain set of double series. The condition x T is called B _b-Tauberian for A if A _b ^' B _b ^' .Some theorems about summability factors enable one to find new B _b-Tauberian conditions for A from the already known B _b-Tauberian conditions for A.     

Proving Theorems in Elementary Geometry with Clifford Algebraic Method

本文结合吴方法及平面几何的Ｃｌｉｆｏｒｄ代数表示，提出了几何定理机器证明的一种完备的方法．用这种方法证明定理时，三角化的过程及证明的过程通常较以前的方法更简短而且它们是可以几何解释的．     

Liouville Theorems for a General Class of Nonlocal Operators

In this paper, we study the equation \(\mathcal {L} u=0\) in \(\mathbb {R}^{N}\), where \(\mathcal {L}\) belongs to a general class of nonlocal linear operators which may be anisotropic and nonsymmetric. We classify distributional solutions of this equation, thereby extending and generalizing recent Liouville type theorems in the case where \(\mathcal {L}= (-{\Delta })^{s}\), s ∈ (0, 1) is the classical fractional Laplacian.     

On Angles and The Fundamental Theorems of Metric Geometry

In this paper we investigate the abstract angle measure for affine metric spaces. Common features and differences between orthogonal angles and angles with measure ≠ 0 are examined. It turns out that an affine collineation which maps angles with a certain fixed measure α ≠ 0,4 to angles with another fixed measure β is already a metric collineation in nearly all cases (fundamental theorem). An analogous result is stated for projective metric spaces. Some applications concerning minimal conditions for metric collineations are given.     

Limit Theorems for General Markov Chains

Siberian Mathematical Journal -     

Embedding Theorems for General Multianisotropic Spaces

An integral representation and embedding theorems for functions in multianisotropic Sobolev spaces are proved. Unlike in previous works, the general case where the characteristic Newton polyhedron in ?ⁿ has an arbitrary number of vertices is considered.     

Minkowski空间的等价性定理及在Finsler几何的应用

首先利用中心仿射几何中的结果建立了Minkowski空间的等价性定理.作为在Finsler几何中的应用,我们证明满足一定条件的Landsberg空间为Berwald空间,这些条件可以是具有闭的Cartan型形式,S曲率为零或平均Berwald曲率为零.     

模糊矩阵三种广义逆的判定定理

给出模糊矩阵存在广义{1,3}逆,广义{1,4}逆和Moore-Penrose广义逆的判定定理.     

一类初等微分几何定理机器证明的算法与实现

空间曲面上的曲线论是初等微分几何的重要部分．作者提出了一种以外微分运算和向量计算为主要工具,可以进行有关曲面上曲线局部性质的定理机器证明的算法．该算法结合了曲面上的活动标架,曲面上曲线的测地标架和曲线自身的Frenet标架,在Maple 9下得到实现．对20个例子进行的测试表明,由该算法生成的自动证明简短可读．     

General Voronovskaya and Asymptotic Theorems in Simultaneous Approximation

In the present note we prove general asymptotic and Voronovskaya theorems for simultaneous approximation. These generalize the Voronovskaya type theorems obtained recently by Floater for the Bernstein operators, and previously by Heilmann and Müller for the Durrmeyer operators.     

一般拓扑空间上的KKM定理,匹配定理,重合点定理

引进没有任何凸结构的拓扑空间上的广义R-KKM映射的定义,并利用古典的KKM原理得到一般拓扑空间上的KKM型定理,然后利用该结果得到Lassonde型匹配定理和Klee型相交定理,最后作为应用给出非紧的拓扑空间上不动点定理和重合点存在定理.推广和改进了文献中的相应结果.     

Liouville-Type Theorems and Applications to Geometry on Complete Riemannian Manifolds

On a complete Riemannian manifold M with Ricci curvature satisfying $$\mathrm{Ric}(\nabla r,\nabla r) \geq -Ar^2(\log r)^2(\log(\log r))^2\cdots (\log^{k}r)^2$$ for r?1, where A>0 is a constant, and r is the distance from an arbitrarily fixed point in M, we prove some Liouville-type theorems for a C ² function f:M→? satisfying Δf≥F(f) for a function F:?→?. As an application, we obtain a C ⁰ estimate of a spinor satisfying the Seiberg–Witten equations on such a manifold of dimension 4. We also give applications to the conformal transformation of the scalar curvature and isometric immersions of such a manifold.     

次线性期望下的一般中心极限定理

受Peng-中心极限定理的启发,本文主要应用G-正态分布的概念,放宽Peng-中心极限定理的条件,在次线性期望下得到形式更为一般的中心极限定理.首先,将均值条件E[X_n]=ε[X_n]=0放宽为|E[X_n]|+|ε[X_n]|=O(1/n);其次,应用随机变量截断的方法,放宽随机变量的2阶矩与2+δ阶矩条件;最后,将该定理的Peng-独立性条件进行放宽,得到卷积独立随机变量的中心极限定理.     

An Asymptotic Version of General Commutator Theorems

An operator generalization of the asymptotic version of Fuglede's theorem is given for an arbitrary complex Banach algebra.