Higher order radiative corrections to the QED Compton events at HERA

We estimate the higher order QED corrections to the QED Compton events at HERA employing the leading logarithmic approximation to all orders in α. The Compton events are events of the typee+p→e′+γ+ Hadrons, wheree′ and γ have nearly balancedp _T .     

The photon two-point function in unitary approximation

The photon two-point function is calculated using the exponential representation for the time-evolution operator taking into account terms up to second order ine in the exponent. The limiting case of vanishing electron mass is examined and it is shown that mass singularities cancel by means of unitarity. Near mass shell the causal Green function exhibits in the limit of vanishing electron mass the expected cut behaviour, off mass shell we recover the result of the usual perturbation theory.     

Adaptive application of operators in standard representation

Recently adaptive wavelet methods have been developed which can be shown to exhibit an asymptotically optimal accuracy/work balance for a wide class of variational problems including classical elliptic boundary value problems, boundary integral equations as well as certain classes of noncoercive problems such as saddle point problems. A core ingredient of these schemes is the approximate application of the involved operators in standard wavelet representation. Optimal computational complexity could be shown under the assumption that the entries in properly compressed standard representations are known or computable in average at unit cost. In this paper we propose concrete computational strategies and show under which circumstances this assumption is justified in the context of elliptic boundary value problems. Dedicated to Charles A. Micchelli on the occasion of his 60th birthday Mathematics subject classifications (2000) 41A25, 41A46, 65F99, 65N12, 65N55. This work has been supported in part by the Deutsche Forschungsgemeinschaft SFB 401, the first and third author are supported in part by the European Community's Human Potential Programme under contract HPRN-CT-202-00286 (BREAKING COMPLEXITY). The second author acknowledges the financial support provided through the European Union's Human Potential Programme, under contract HPRN-CT-2002-00285 (HASSIP) and through DFG grant DA 360/4–1.     

Algebraic properties of discrete box splines

The central objective of this paper is to discuss linear independence of translates of discrete box splines which we introduced earlier as a device for the fast computation of multivariate splines. The results obtained here allow us to draw conclusions about the structure of such discrete splines which have, in particular, applications to counting the number of nonnegative integer solutions of linear diophantine equations.     

Surface characterization of fluorinated polymers (PTFE, PVDF, PFA) for use in ultratrace analysis

Surface characterization of new unused PTFE, PFA and PVDF labware has been carried out by light microscopy, scanning electron microscopy, profilometry and atomic force microscopy. It has been found that in spite of higher micro-roughness, PFA exhibits the lowest nano-roughness and hence seems best suited as vessel material for relatively mild pressureless chemical operations for sample preparation of ultrapure substances, as container material for storage of ultrapure liquids, and for transport of such liquids, e.g., from the producer in the chemical to the end user in the microelectronics industry. This suitability refers only to the surface quality of the investigated materials. PTFE-surfaces, due to the sintering process of production, exhibit the most unfavourable surface quality of the investigated fluorinated polymers.     

Adsorption of the halogens on cerium dioxide

Summary CeO₂, alone or mixed with La₂O₃, is used as halogen adsorbent in the determination of carbon and hydrogen. Quantitative data are given on the adsorption of the single halogens on various samples of pure CeO₂ and La₂O₃. Retention of CO₂ and the influence of several parameters of special interest in the carbon and hydrogen determination, have been examined. It has been found that the conditions for optimum adsorption of the halogens are a large surface and relatively low adsorption temperature. Unfortunately these conditions cannot be applied in the determination of carbon and hydrogen.

---

Zusammenfassung CeO₂ allein oder im Gemisch mit La₂O₃ wurde als Adsorbens für Halogen bei der CH-Bestimmung verwendet. Quantitative Angaben über die Adsorption der einzelnen Halogene an verschiedenen Mustern von reinem CeO₂ und La₂O₃ wurden gebracht. Die Retention von CO₂ und der Einfluß einzelner Parameter, die für die CH-Bestimmung von besonderem Interesse sind, wurden geprüft. Die besten Bedingungen für die Adsorption der Halogene sind große Oberfläche und relativ niedere Temperatur. Beide Bedingungen können leider bei der CH-Bestimmung nicht eingehalten werden.

     

Efficient synthesis of sulfonic,phosphoric, and phosphinic esters employing alkylating polymer-bound reagents

The efficient esterification of various sulfonic acids and sulfonates using polymer-bound triazenes based on the triazene T2 linker is described. Esterification of enantiopure alpha-substituted sodium sulfonates was performed in the presence of an alkylating resin without racemization. Racemization is a serious drawback in the esterification route via sulfonyl chlorides because of intermediate sulfene formation. To demonstrate the versatility of this protocol, phosphoric and phosphinic acids have been converted into the corresponding esters as well. All products were obtained in good yield and excellent purities without any further purification steps.     

Correction to: Preface

Foundations of Computational Mathematics -     

C-H Activation by dinuclear phosphine bridged complexes of rhodium,iridium, and ruthenium

The possibility of activation of the C-H bond by dinuclear phosphine bridged complexes of rhodium, iridium, and ruthenium is considered.This work was reported at the conference Modern Problems of Organometallic Chemistry (8–13 May, 1994, Moscow).Institut fer Technische Chemie und Petrolchemie der RWTH Aachen Worringerweg 1, 52074 Aachen, Deutschland.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 4, pp. 589–593, April, 1994.