Sub-Ramsey numbers for arithmetic progressions

Letm 3 andk 1 be two given integers. Asub-k-coloring of [n] = {1, 2,...,n} is an assignment of colors to the numbers of [n] in which each color is used at mostk times. Call an arainbow set if no two of its elements have the same color. Thesub-k-Ramsey number sr(m, k) is defined as the minimumn such that every sub-k-coloring of [n] contains a rainbow arithmetic progression ofm terms. We prove that((k – 1)m ²/logmk) sr(m, k) O((k – 1)m ² logmk) asm , and apply the same method to improve a previously known upper bound for a problem concerning mappings from [n] to [n] without fixed points.Research supported in part by Allon Fellowship and by a Bat Sheva de-Rothschild grant.Research supported in part by the AKA Research Fund of the Hungarian Academy of Sciences, grant No. 1-3-86-264.     

Localization of electronic excitation energy in Ru(2,2′-bipyridine)2(2,2′-bipyridine-4,4′-dicarboxylic acid)2+ and related complexes

The absorption spectra of Ru(2,2′-bipyridine)₂ (2,2′-bipyridine-4,4′-dicarboxylic acid)²⁺ (I) and its diethyl ester (II) are closely related and are both significantly different from the spectra of the mono-protonated (Ia) and deprotonated (Ib) complexes. Luminescence polarization measurements show that for I and II the luminescent states have the transferred electron in the bipy-4,4′(COOH)₂ and bipy-4,4′(COOEt)₂ ligands, respectively, rather than in the unsubstituted bipy ligands.     

A study of the mechanism of response of liquid ion exchanger calcium selective electrodes: Part III. Membrane behaviour under non-zero current conditions

The I-E response of the liquid membrane of the calcium selective electrode is studied under constant or linearly varying current and voltage. An increase in the membrane resistance, recorded when an electrical current crosses the membrane, is due to the outflow of Cl^? ions initially present in the membrane. When calcium ions are replaced by alkaline ions inside the membrane at constant current, the decrease of the membrane resistance due to an ion exchange is in agreement with the conductivity measurements (Part II). When the applied voltage is imposed besides the ion exchange one must take into account the interfacial overpotential to explain the important rectification effect observed. The interfacial transfer constant rate of alkaline ions seems greater than that of Ca²⁺ ion.     

The adsorption of endothelin 1 to phospholipids is governed by electrostatic interactions: A monolayer and fluorescence study

In order to elucidate the influence on the lipidic environment on the recognition process of its membrane associated receptor, the interactions of the vasoconstrictor peptide endothelin 1 with various phospholipids have been investigated using different lipidic model membranes: monolayers at constant surface pressure, vesicles and micelles. A monolayer study of ET1 adsorbed onto the water surface has shown that the C-terminus of the peptide points towards the aqueous phase. Penetration measurements into lipidic monolayers indicate that ET1 adsorbs to phospholipids with an orientation similar to that of the air–water interface and fluorescence measurements are in agreement with such an orientation of the peptide. This adsorption is selective for neutral phospholipids and indicates that the nature of the phospholipid headgroups is of major importance for the approach of the membrane associated receptor.     

Two combinatorial problems on posets

Bialostocki proposed the following problem: Let nk2 be integers such that k|n. Let p(n, k) denote the least positive integer having the property that for every poset P, |P|p(n, k) and every Z _k -coloring f: P Z _k there exists either a chain or an antichain A, |A|=n and _aA f(a) 0 (modk). Estimate p(n, k). We prove that there exists a constant c(k), depends only on k, such that (n+k–2)²–c(k) p(n, k) (n+k–2)²+1. Another problem considered here is a 2-dimensional form of the monotone sequence theorem of Erdös and Szekeres. We prove that there exists a least positive integer f(n) such that every integral square matrix A of order f(n) contains a square submatrix B of order n, with all rows monotone sequences in the same direction and all columns monotone sequences in the same direction (direction means increasing or decreasing).     

Determination of Trace Molybdenum in Biological Matrices by Neutron Activation Analysis

Based on consecutive extractions using bismuth diethyldithiocarbamate and thallium diethyldithiocarbamate as reagents, molybdenum was selectively and highly enriched from biological matrices, and then subjected to neutron activation analysis. Most of interfering elements, e.g., Na, K, Br, P, Fe, U, etc. were simultaneouly removed and the preconcentrated samples always showed only the r rays from molybdenum after neutron bombardment. Thus, molybdenum in the biological matrices could be accurately determined.     

Polyethylenimine-Containing Cotton Fabrics

Abstract

Polyethylenimine-containing cotton fabrics were prepared by reaction of 1-epoxyethyl-3, 4-epoxycyclohexane with cotton fabric impregnated with polyethylenimine of a moderately high molecular weight. Fabrics with a high unremovable polyethylenimine content and with a different degree of cross-linking were obtained. Adsorption of several heavy metal salts such as mercuric chloride and cupric sulfate by the fabrics was investigated. Adsorption was controlled by polyethylenimine content of the fabric, extent of cross-linking, and the pH of the solution.     

Reaction of Lithium Cellulosate with Episulfides

The reactions of propylene, ethylene, and styrene sulfide with cotton fabrics in the form of their lithium cellulosate derivative, obtained by metallation with lithium methoxide, were studied. Both graft and homo-polymerization took place and in the reaction with propylene and ethylene sulfide, cotton fabrics with high polysulfide content were obtained. With propylene sulfide 50% of the monomer polymerized was grafted. The effects of monomer concentration, cellulosate degree of substitution, reaction time, and solvent on the polymerization were investigated. In contrast with propylene and ethylene sulfide, only small conversions were obtained in the reaction with styrene sulfide. The results were attributed to steric effects.