Combinatorial Characterizations of Authentication Codes II

For any authentication code for k source states and v messages having minimum possible deception probabilities (namely, % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9qq-f0-yqaqVeLsFr0-vr% 0-vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGqbWaaS% baaSqaaiaadsgaaeqaaOWaaSbaaSqaaiaaicdaaeqaaOGaeyypa0Za% aSGbaeaacaWGRbaabaGaamODaaaaaaa!3F28!\[P_d _0 = {k \mathord{\left/ {\vphantom {k v}} \right. \kern-\nulldelimiterspace} v}\] and % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9qq-f0-yqaqVeLsFr0-vr% 0-vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGqbWaaS% baaSqaaiaadsgaaeqaaOWaaSbaaSqaaiaaigdaaeqaaOGaeyypa0Ze% xLMBb50ujbqeguuDJXwAKbacfaGae8hkaGIaam4AaiabgkHiTiaaig% dacqWFPaqkcqWFVaWlcqWFOaakcqWF2bGDcqGHsislcaaIXaGae8xk% aKIae8xkaKcaaa!4CD1!\[P_d _1 = (k - 1)/(v - 1))\], we show that there must be at least v encoding rules. (This can be thought of as an authentication-code analogue of Fisher's Inequality.) We derive several properties that an extremal code must satisfy, and we characterize the extremal codes for equiprobable source states as arising from symmetric balanced incomplete block designs. We also present an infinite class of extremal codes, in which the source states are not equiprobable, derived from affine planes.Dedicated to Gus Simmons     

A new proof of the Komlós-Révész-theorem

The Komlós-Révész theorem states: For r.v.s.X _n with X _{n 1}M there exists a subsequenceX _{k n} and a r.v.X with X₁M such that

Spin-resolved photoemission from epitaxial Au layers on Pt(111): Coverage dependence of the bandstructure and evidence of surface resonances

Au/Pt(111) has been studied by spin-, angle- and energy-resolved photoemission with normal incident circularly polarized synchrotron radiation of BESSY and normal photoelectron emission for different Au coverages. The prepared layers were characterized by LEED and Augerelectron spectroscopy and turned out to grow up two dimensional and epitaxially. In the photoemission experiments the development of the 3-dimensional bandstructure in the -direction could be observed. For a coverage of 2.6 layers the highest occupied spin-orbit split bands are located at about 0.6 eV lower binding energy than the corresponding bands for a 3D-Au crystal and show dispersion which is, however, weaker than in a 3D-Au crystal. A 5 layer Au adsorbate was found to have already the same dispersion and energetic location as a Au(111)-crystal. For thick gold layers, which behave in photoemission like Au(111)-crystals, we find structures that cannot be due to direct transitions into a free electron like final band. The coverage dependence and spin polarization of these structures show that some of them are due to surface resonances, while the origin of one strong peak could not yet be explained conclusively. In addition we find strong hybridization and two avoided crossings in the occupied part of the bandstructure.     

Meromorphic extensions of regular holonomic distributions

In this paper we consider distributions of the form 1/P and dy/P(x,y), whereP is a polynomial. Using results by Kashiwara and Kawai we give fairly accessible proofs that these expressions can be defined as regular holonomic distributions by utilising a meromorphic parameter. We also discuss distributions of the form /P and their direct image , when one knows that is a regular holonomic distribution. All these distributions are relevant to the study of renormalised Feynman integrals.     

Invers-voltammetrische Bestimmung von Chrom(III)

Solutions of Cr(III) salts containing ammonium hydroxide and ammonium salts can be determined after proper pretreatment by inverse voltammetry at carbon paste and glassy carbon electrodes. The determination may be performed, too, with organic solutions of the Cr(III) oxinate. Sensitivity is 5 × 10^?7 M (= 26 ng Cr/ml), standard deviation is in the range of 4–6%.