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

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%.     

Zur Erh?hung der Empfindlichkeit wechselstrompolarographischer Analysenverfahren

Zusammenfassung Die Verwendung eines selektiven Verstärkers zur Messung des Oberwellenanteils in der Wechselstrompolarographie wird beschrieben. Durch die Verminderung des Kapazitätsstromes wird eine 10–20 fach höhere Empfindlichkeit erzielt.Mit einer pseudostationären Hg-Elektrode läßt sich eine weitere 3–5fache Empfindlichkeitssteigerung erreichen.Die vorliegende Arbeit wurde in dankenswerter Weise durch Mittel der Deutschen Forschungsgemeinschaft und des Verbandes der Chemie ermöglicht.Herrn Prof. Dr. F. Strassmann danke ich für die Bereitstellung von Institutsmitteln.Herrn Prof. Dr. Dr. W. Herzog (Institut für Elektrotechnik der Universität Mainz), der den Bau des selektiven Verstärkers in seinem Institut unterstützte, sei an dieser Stelle ebenfalls besonders herzlich gedankt.