Slodkowski定理的Chirka证明的一些注解(英文)

通过在一个积分算子上运用Schauder不动点定理,Chirka对Slokowski的全纯运动扩张定理提供了一个优美的简单证明.本文中,作者对构造此证明的启发提供一个参考同时用此方法通过不同方式来构造全纯扩张.一个自然的问题是研究这些用不同方式得到的全纯扩张是否相同.因此对全纯扩张唯一性已有的判断法提供一个简单的综述.最后介绍在全纯扩张唯一性存在时的一个应用.     

拟对称的有界度圆填充逼近

拟对称集和拟圆周集是万有Teichm(u|¨)er空间中两个常用模型.对于任一个由K-拟圆周诱导的拟对称,应用有界度圆填充的方法,构造了其近似映射,并证明了这些近似映射一致收敛于该拟对称.     

Exceptional sets in Waring-Goldbach problem for fifth powers

We consider exceptional sets in the Waring-Goldbach problem for fifth powers.For example,we prove that all but O(N^131/132)integers satisfying the necessary local conditions can be represented as the sum of 11 fifth powers of primes,which improves the previous results due to A.V.Kumchev[Canad.J.Math.,2005,57:298–327]and Z.X.Liu[Int.J.Number Theory,2012,8:1247–1256].     

Spectral gap of Boltzmann measures on unit circle

We give a two sided estimate on the spectral gap for the Boltzmann measures μ_h on the circle. We prove that the spectral gap is greater than 1 for any h\in ℝ and the spectral gap tends to the positive infinity as h\to \infty with speed \left|h\right|.     

数值积分求解均匀带电圆环平面上的电场分布

本文用数值积分的方法计算椭圆积分，求出在均匀带电圆环平面上的场强与电势．     

Infinite type homeomorphisms of the circle and convergence of Fourier series

We consider the problem of convergence of Fourier series when we make a change of variable. Under a certain reasonable hypothesis, we give a necessary and sufficient condition for a homeomorphism of the circle to transform absolutely convergent Fourier series into uniformly convergent Fourier series.

     

On Minimal Annuli with a Straight Line Boundary

Shiffman proved that if a minimal annulus A in a slab is bounded by two convex Jordan curves contained respectively in the two boundary planes P and Q of the slab, then A intersects all parallel planes between P and Q in strictly convex curves. We generalize Shiffman's result to the case that A is bounded by a strictly convex C² Jordan curve and a straight line. We show that in this case Shiffman's result is still true.     

Rotation Numbers of Discontinuous Orientation-Preserving Circle Maps

We extend a few well-known results about orientation preserving homeomorphisms of the circle to orientation preserving circle maps, allowing even an infinite number of discontinuities. We define a set-valued map associated to the lift by filling the gaps in the graph, that shares many properties with continuous functions. Using elementary set-valued analysis, we prove existence and uniqueness of the rotation number, periodic limit orbit in the case when the latter is rational, and Cantor structure of the unique limit set when the rotation number is irrational. Moreover, the rotation number is found to be continuous with respect to the set-valued extension if we endow the space of such maps with the Haussdorff topology on the graph. For increasing continuous families of such maps, the set of parameter values where the rotation number is irrational is a Cantor set (up to a countable number of points).     

On foliated circle bundles over closed orientable 3-manifolds

We show that there exists a family of smooth orientable circle bundles over closed orientable 3-manifolds each of which has a codimension-one foliation transverse to the fibres of class C ⁰ but has none of class C ³ . There arises a necessary condition induced from the Milnor-Wood inequality for the existence of a foliation transverse to the fibres of an orientable circle bundle over a closed orientable 3-manifold. We show that with some exceptions this necessary condition is also sufficient for the existence of a smooth transverse foliation if the base space is a closed Seifert fibred manifold. Received: May 13, 1996