Cup product structure for symplectic K2

For a field F with trivial involution we have the Karoubi L-groups ±1^Ln(F). For 0≤n≤2 these groups are intimately related to subgroups of the classical Witt ring of quadratic forms. -1^L ₂(F) also has a presentation by symbols due to Matsumoto. In terms of this data we make explicit calculations for two cup product maps that appear in the L-theory of fields.     

Dependence and the asymptotic behavior of large claims reinsurance

We consider an extension of the classical compound Poisson risk model, where the waiting time between two consecutive claims and the forthcoming claim are no longer independent. Asymptotic tail probabilities of the reinsurance amount under ECOMOR and LCR treaties are obtained. Simulation results are provided in order to illustrate this.     

实际气体分子间吸引相互作用对Cp,m-CV,m的影响

在考虑温度对分子间吸引相互作用影响的前提下,对Cp,m-CV,m的值做了理论分析,并与实验值和引力项中没有考虑温度因子时的范德瓦耳斯方程的修正值做了比较.     

Weak Convergence of the Empirical Mean Excess Process with Application to Estimate the Negative Tail Index

Let Y _i , 1 ≤ i ≤ n be i.i.d. random variables with the generalized Pareto distribution W _γ,σ with γ < 0. We define the empirical mean excess process with respect to {Y _i , 1 ≤ i ≤ n} as in Eq. 2.1 (see below) and investigate its weak convergence. As an application, two new estimators of the negative tail index γ are constructed based on the linear regression to the empirical mean excess function and their consistency and asymptotic normality are obtained.      

Two-Sided Optimal Bounds for Green Functions of Half-Spaces for Relativistic <Emphasis Type="Italic">α</Emphasis>-Stable Process

The purpose of this paper is to find optimal estimates for the Green function of a half-space of the relativistic α -stable process with parameter m on ℝ ^d space. This process has an infinitesimal generator of the form mI–(m ^2/α I–Δ) ^α/2, where 0<α<2, m>0, and reduces to the isotropic α-stable process for m=0. Its potential theory for open bounded sets has been well developed throughout the recent years however almost nothing was known about the behaviour of the process on unbounded sets. The present paper is intended to fill this gap and we provide two-sided sharp estimates for the Green function for a half-space. As a byproduct we obtain some improvements of the estimates known for bounded sets. Our approach combines the recent results obtained in Byczkowski et al. (Bessel Potentials, Hitting Distributions and Green Functions (2006) (preprint). ), where an explicit integral formula for the m-resolvent of a half-space was found, with estimates of the transition densities for the killed process on exiting a half-space. The main result states that the Green function is comparable with the Green function for the Brownian motion if the points are away from the boundary of a half-space and their distance is greater than one. On the other hand for the remaining points the Green function is somehow related the Green function for the isotropic α-stable process. For example, for d≥3, it is comparable with the Green function for the isotropic α-stable process, provided that the points are close enough. Research supported by KBN Grants.     

Finite generation of canonical ring by analytic method

An overview of the analytic proof of the theorem on the finite generation of the canonical ring for the projective algebraic manifold of general type is given.     

关于Locale Wallman紧化的一点注记

本文证明了在正规locale范畴中,Banaschewski-Mulvey形式的紧正则反射与Johnstone形式的Wallman紧化一致,从而推广了Johnstone在文献[4]中的主要结果.     

关于强正则环的刻画

通过单边理想是广义弱理想来刻画强正则环,证明了下列条件是等价的:①R是强正则环;②R是半素的左GP-V′-环,且每一个极大的左理想是广义弱理想;③R是半素的左GP-V′-环,且每一个极大的右理想是广义弱理想.     

Finiteness of polyhedral decompositions of cusped hyperbolic manifolds obtained by the Epstein-Penner's method

Epstein and Penner give a canonical method of decomposing a cusped hyperbolic manifold into ideal polyhedra. The decomposition depends on arbitrarily specified weights for the cusps. From the construction, it is rather obvious that there appear at most a finite number of decompositions if the given weights are slightly changed. However, since the space of weights is not compact, it is not clear whether the total number of such decompositions is finite. In this paper we prove that the number of polyhedral decompositions of a cusped hyperbolic manifold obtained by the Epstein-Penner's method is finite.

     

The LIL for <Emphasis Type="Italic">U</Emphasis>-Statistics in Hilbert Spaces

We give necessary and sufficient conditions for the (bounded) law of the iterated logarithm for U-statistics in Hilbert spaces. As a tool we also develop moment and tail estimates for canonical Hilbert-space valued U-statistics of arbitrary order, which are of independent interest. R. Adamczak’s research partially supported by MEiN Grant 2 PO3A 019 30. R. Latała’s research partially supported by MEiN Grant 1 PO3A 012 29.