A Darling-Erdos-Type Theorem for Standardized Random Walk Summation

In this paper we consider the random walk summation method whichincludes, for example, the Borel, Euler, Meyer-König andValiron methods, and obtain a Darling-Erds-type limit theoremfor the maximum of normalized sums defined by random walk summation.     

INVESTIGATIONS ON BIOLOGICAL EFFECT OF POLARIZED LIGHT

Abstract— The biological effects of single and 4-time irradiation of primary human embryo fibroblasts with 4 J/cm² polarized light emitted by a halogen light source were investigated. The functional state of the plasma membrane was examined by means of lectin-binding and polycationized ferritin-binding techniques. It was established that the Con A binding of the cells did not change, whereas the number of negatively charged binding sites increased to a significant degree in relation to the untreated (control) samples and cell cultures exposed to diffuse (non-polarized) light. The micromorphological examinations showed no ultrastructural deviations. The quantitative increase of negative surface charges may be regarded as an indication of the biological effect of polarized light exerted on the cell membrane. The modifying effect of polarized light on the survival of E. coli exposed to the ionizing radiation was manifested in decreased anoxic radiation response.     

Cationization of simple organic molecules by singly-charged Ag<Stack><Subscript>3</Subscript><Superscript>+</Superscript></Stack> cluster ions in matrix-assisted laser desorption/ionization mass spectrometry: Metal cluster-molecule interactions

It was found earlier that under matrix-assisted laser desorption/ionization (MALDI) conditions several organic compounds which produce adduct with silver ions, are also capable of forming adducts with Ag(3)(+) cluster ions under appropriate conditions. The Ag(3)(+) cluster ion can be in situ generated under the MALDI analysis conditions from silver trifluoroacetate cationization agent in the presence of organic MALDI matrices. In this article the fragmentation of a commercial plasticizer, a peracetylated isoflavone glycoside and a pyrazolylphenyl disulfide derivative cationized with silver ions and Ag(3)(+) cluster ions are compared. It was observed that the complexes of Ag(3)(+) are less fragmented than the corresponding adduct ions with Ag(+). The presumable fragmentation channel of [M + Ag(3)(+)] is the elimination of Ag(2) units from these complexes. No significant dissociation of [M + Ag(3)(+)], into M and Ag(3)(+) takes place, indicating a tight connection between the corresponding molecule and Ag(3)(+) cluster ion. However, with a compound carrying very labile groups, such as the pyrazolylphenyl disulfide derivative, intramolecular cleavages can occur prior to significant dissociation of the Ag(3)(+) cluster ion.     

Electron impact and ammonia chemical ionization mass spectra of n-azabicyclo[m.2.0]alkan-(n + 1)-ones (m = 3–6, n = 6–9)

Electron impact induced fragmentation of the title compounds obeys a route where the lactam moiety, OCNH, is cleaved first, with the accompanying formation of a cycloalkene ion. This can be verified by low-resolution, high-resolution, B/E and B²/E spectra as well as by collisional activation spectra of, for example, the ions m/z 82 and 67 from 7-azabicyclo[4.2.0]octan-8-one and from cyclohexene. The only, and fairly weak, fragment ions including O and N are [C₃H₃O]+, [C_kH_2k-2N]⁺ (k = 5–8) and [C₃H₆N]⁺. The ammonia chemical ionization spectra are also characteristic for all four lactams and show the same dominant ions in all cases, namely [M + 1]⁺, [M + 1 + NH₃]⁺˙ and [2 M + 1]⁺˙.     

Über extrem entwässerte Gelatinefolien und ihre elektrische Leitfähigkeit

Zusammenfassung Die Entwässerung der Gelatinefolien wurde bei Vakuum-Behandlung und bei Erhitzung untersucht. Man kann feststellen, daß die Gelatine mindestens zwei verschiedene Arten von Wasser enthält. Das eine sei als Kapillarwasser, das andere als Kolloidwasser bezeichnet. Von diesen ist das erstere sehr locker, das andere stärker gebunden. Der Prozeß der Entwässerung ist in bezug auf die Vakuum-Behandlung reversibel, in bezug auf die Erhitzung aber irreversibel.Die Leitfähigkeit der Gelatinefolien vermindert sich mit der Entwässerung sehr stark. Wenn durch die vom Kapillarwasser befreite Gelatine Strom fließt, entsteht eine Aufladung in den Gelatinefolien, die in einem charakteristischen Polarisationsstrom sich sehr schnell wieder rückgängig macht.Vorliegende Arbeit wurde in der Kolloidabteilung des Physikalisch-chemischen Instituts der Universität Leipzig vollendet. Für die vielseitige Beihilfe und für die vielen wertvollen Ratschläge möchte ich auch an dieser Stelle Herrn Professor Ostwald herzlichst danken. Auch Herrn Professor Pál Fröhlich, Direktor des Instituts für Experimentalphysik an der Horthy-Miklös-Universität zu Szeged, spreche ich für die freundliche Anregung, sein ständiges Interesse und seine wertvollen Ratschläge meinen besten Dank aus.     

On Some Automorphisms of the Set of Effects on Hilbert Space

The set of all effects on a Hilbert space has an affine structure (it is a convex set) as well as a multiplicative structure (it can be equipped with the so-called Jordan triple product). In this paper we describe the corresponding automorphisms of that set.     

Optimal systems of fundamental S-units for LLL-reduction

We show that a particular parameter plays a vital role in the resolution of S-unit equations, at the stage where LLL-reduction is applied. We define the notion of optimal system of fundamental S-units (with respect to this parameter), and prove that such a system exists and can be effectively constructed. Applying our results and methods, one can obtain much better bounds for the solutions of S-unit equations after the reduction step, than earlier. We also briefly discuss some effects of our results on the method of Wildanger and Smart for the resolution of S-unit equations.     

Quasi-kernels and quasi-sinks in infinite graphs

Given a directed graph G=(V,E) an independent set A⊂V is called quasi-kernel (quasi-sink) iff for each point v there is a path of length at most 2 from some point of A to v (from v to some point of A). Every finite directed graph has a quasi-kernel. The plain generalization for infinite graphs fails, even for tournaments. We study the following conjecture: for any digraph G=(V,E) there is a a partition (V₀,V₁) of the vertex set such that the induced subgraph G[V₀] has a quasi-kernel and the induced subgraph G[V₁] has a quasi-sink.     

How To Split Antichains In Infinite Posets*

A maximal antichain A of poset P splits if and only if there is a set B ⊂ A such that for each p ∈ P either b ≤ p for some b ∈ B or p ≤ c for some c ∈ A\B. The poset P is cut-free if and only if there are no x < y < z in P such that [x,z]_P = [x,y]_P ∪ [y,z]_P . By [1] every maximal antichain in a finite cut-free poset splits. Although this statement for infinite posets fails (see [2])) we prove here that if a maximal antichain in a cut-free poset “resembles” to a finite set then it splits. We also show that a version of this theorem is just equivalent to Axiom of Choice. We also investigate possible strengthening of the statements that “A does not split” and we could find a maximal strengthening. * This work was supported, in part, by Hungarian NSF, under contract Nos. T37846, T34702, T37758, AT 048 826, NK 62321. The second author was also supported by Bolyai Grant.