On Haar measurable additive maps on Β(N)

Let Β(N) be the power set of the set of natural numbers endowed with the usual structure of a compact abelian group and let Μ be the normed Haar measure on it. The paper studies the properties of Μ-measurable additive maps of Β(N) into Hausdorff abelian groups.     

Remark on generalized Markov processes

It is shown that a multidimensional Markov process which is Euclidean invariant and so that the translation group acts ergodically is a constant. This is a (Euclidean) counterpart of a theorem by Wightman [6] and is inspired by the work of Nelson [1].     

Nontriviality of the scattering matrix for weakly coupled Φ34 models

It is shown that the weakly coupled, three space-time dimensions, boson quantumfield-theory model with Φ⁴ self-interaction has a scattering matrix which is different from $\text{1}$.     

Über die Klassifikation der Riemannschen Flächen

Ohne Zusammenfassung     

On the luminescence of luminol in DMSO in the presence of potassium superoxide-18-crown-6-ether and fluorescein

Luminol solution in DMSO in the presence of [18C6…K]⁺ O₂⁻ supramolecular complex (achieved from KO₂ and 18-Crown-6 (18C6)-ether) is chemiluminescent, and its intensity depends on the complex concentration. Using fluorescein (Fl) as an energy acceptor in this system, the luminescence energy transfer process from chemically excited species, aminophtalate dianion, to Fl could be evidenced. On the basis of Förster theory, the critical energy transfer distance, for both fluorescence and chemiluminescence, has been determined. The values are comparable: 22.41 Å (for chemiluminescence) and 20.88 Å (for fluorescence).     

On a conjecture by Kalai

We show that monomial ideals generated in degree two satisfy a conjecture by Eisenbud, Green and Harris. In particular, we give a partial answer to a conjecture of Kalai by proving that h-vectors of flag Cohen-Macaulay simplicial complexes are h-vectors of Cohen-Macaulay balanced simplicial complexes.     

On the concept of code-isomorphy

LetF be a finite set of cardinality ¦F¦ =q 2,n 1 an integer and :F ⁿ×Fⁿ₀ theHamming metric. Acode isomorphism C D between two block codesC,D Fⁿ is defined as an isometry which can be extended to an isometry of the whole space Fⁿ. Any permutation S _n of the positions canonically induces a so-calledequivalence map Aut Fⁿ; any system (₁,₂,...,_n) ofn permutations of the character setF induces a so-calledconfiguration Aat Fⁿ. The group Aut Fⁿ of all isometries of Fⁿ turns out to be semidirect product of the configuration group with the symmetric group of degreen. The codeword estimating failure probability of a maximum likelihood codeword estimator for aq-nary symmetric channel does not depend on the transmitted codeword, if the automorphism group of the code acts transitively on the set of codewords. When using a systematic (n, k)-encoder, the symbol decoding failure probability does not depend on the transmitted symbol or on the time of transmission if the configuration group and the automorphism group act transitively on the set of codewords resp. on the set of thek information positions.In memoriam Giuseppe Tallini