研究K4-同胚图K4(α,1,1,δ,ε,η)色性的一个引理

主要介绍了一个引理，这个引理奠定了K4－同胚图K4（α，1，1，δ，ε，η）色性研究的基础。     

Application of Hilbert＇s Projective Metric on Symmetric Cones

Let Ω be a symmetric cone. In this note, we introduce Hilbert＇s projective metric on Ω in terms of Jordan algebras and we apply it to prove that, given a linear invertible transformation g such that g（Ω） = Ω and a real number p, ｜p｜ 〉 1, there exists a unique element x ∈ Ω satisfying g（x） = x^p.     

Projection of Markov Measures May Be Gibbsian

We study the induced measure obtained from a 1-step Markov measure, supported by a topological Markov chain, after the mapping of the original alphabet onto another one. We give sufficient conditions for the induced measure to be a Gibbs measure (in the sense of Bowen) when the factor system is again a topological Markov chain. This amounts to constructing, when it does exist, the induced potential and proving its Hölder continuity. This is achieved through a matrix method. We provide examples and counterexamples to illustrate our results.     

Construction algorithms for polynomial lattice rules for multivariate integration

We introduce a new construction algorithm for digital nets for integration in certain weighted tensor product Hilbert spaces. The first weighted Hilbert space we consider is based on Walsh functions. Dick and Pillichshammer calculated the worst-case error for integration using digital nets for this space. Here we extend this result to a special construction method for digital nets based on polynomials over finite fields. This result allows us to find polynomials which yield a small worst-case error by computer search. We prove an upper bound on the worst-case error for digital nets obtained by such a search algorithm which shows that the convergence rate is best possible and that strong tractability holds under some condition on the weights.

We extend the results for the weighted Hilbert space based on Walsh functions to weighted Sobolev spaces. In this case we use randomly digitally shifted digital nets. The construction principle is the same as before, only the worst-case error is slightly different. Again digital nets obtained from our search algorithm yield a worst-case error achieving the optimal rate of convergence and as before strong tractability holds under some condition on the weights. These results show that such a construction of digital nets yields the until now best known results of this kind and that our construction methods are comparable to the construction methods known for lattice rules.

We conclude the article with numerical results comparing the expected worst-case error for randomly digitally shifted digital nets with those for randomly shifted lattice rules.

     

Polynomial Reproduction in Subdivision

We study conditions on the matrix mask of a vector subdivision scheme ensuring that certain polynomial input vectors yield polynomial output again. The conditions are in terms of a recurrence formula for the vectors which determine the structure of polynomial input with this property. From this recurrence, we obtain an algorithm to determine polynomial input of maximal degree. The algorithm can be used in the design of masks to achieve a high order of polynomial reproduction.     

Gauss Algebras

A special class of associative algebras is introduced and studied. A criteria of semisimplicity for suitable category of modules is obtained.     

一类新的插值结点

有界单连通区域Ｇ，其边界θＧ＝Г∈（１，α），α〉０。本计算节以广义Ｆａｂｅｒ多项式φｎ（ｚ）的零点为插值结点的Ｌａｇｒａｎｇｅ插值多项式的逼近性质，得到了它对Ａ（Ｇ↑－）中的函数的一致逼近阶和平均逼近阶的估计，并且得到了它对Ｅ＾ｐ（Ｇ）中函数的平均逼近阶的估计，还指出关于平均逼近阶的估计是不可改进的。     

Hyers–Ulam–Rassias stability of Cauchy equation in the space of Schwartz distributions

We reformulate and prove the Hyers–Ulam–Rassias stability of Cauchy equation in the space of Schwartz tempered distributions and Fourier hyperfunctions.