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.     

THERMODYNAMICS OF PORPHYRIN BINDING TO SERUM ALBUMIN: EFFECTS OF TEMPERATURE, OF PORPHYRIN SPECIES and OF ALBUMIN-CARRIED FATTY ACIDS

Abstract Porphyrin binding to serum albumin was studied at the molecular level probing the effects of: porphyrin self-aggregation, porphyrin species, temperature and protein-bound fatty acids. Human serum albumin was found to have a single high-affinity site for porphyrin monomers, with binding constants of 2 x 10⁶, 5 x 10⁷ and 3 x 10⁸ (37^o C, neutral pH, M ⁻¹), for hemato-, deutero- and protoporphyrins, respectively. Three equilibria models for the dimer binding were developed and tested. The data were found to fit best with a model proposing a single high-affinity binding site for the dimer, independent of and different than the monomer site. The binding constants of the hematoporphyrin and deuteroporphyrin dimers to human serum albumin (37^o C, neutral pH, M^−l) being 4 x 10* and 5 x 10⁸ respectively. The temperature dependence (Dp and HSA, 22-37^o C) of the monomer binding showed the process to be entropy-driven (δG^o= -45 kJ mol⁻¹; δS^o=+146 kJ mol⁻¹; δH^o= 0 kJ mol⁻¹). For the dimer binding, the enthalpy change was found to be highly temperature-dependent implying continuous changes in the heat capacity of the system over the entire temperature range, the trend at the 37^o C region fitting an entropy-driven process. The monomer vs dimer differences in temperature dependence strongly support separate and independent binding sites for these species. Similar thermodynamics were determined for fatty-acid carrying as well as for fatty-acid free HSA, with mild quantitative (but not qualitative) shifts.     

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).     

Phase-locked InGaAsP laser array with diffraction coupling

A phase-locked array of InGaAsP lasers has been fabricated for the first time. The array utilized diffraction coupling between 10 adjacent lasers to achieve phase locking. Threshold current as low as 200 mA is obtained for arrays with 250 m cavity length. Smooth single-lobe far field patterns with beam divergence as narrow as 3° have been achieved.     

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.     

Adsorption of Silver Nitrate by Cotton Fabrics Containing Polyethylene Sulfide

The adsorption of silver nitrate from aqueous solution by polyethylene sulfide-containing cotton fabrics was investigated. The adsorption could be described by a Freundlich-type isotherm with n= 1. δH^os was calculated from adsorption isotherms and from the equilibrium constant of complex formation and similar results of-5.6 and -5.4 kcal/mole were obtained, respectively. At low silver nitrate concentrations most of the silver nitrate present in solution could be adsorbed. It was found that adsorption by polyethylene sulfide in the fabric was much higher than that of homo-polyethylene sulfide.     

This electrode is best served cold—a reversible electrochemical lithiation of a gray cubic tin

Journal of Solid State Electrochemistry - The behavior of a cubic allotropic modification of tin (α-Sn) towards lithium electrochemical alloying/de-alloying is reported for the first time. The...     

Tuning Chemical and Physical Properties of Phosphorus Corroles for Advanced Applications

Although the affinity of metallocorroles to axial ligands is quite low, this is not the case when the chelated element is phosphorus. This work is hence focused on the mechanism of ligand exchange of six-coordinate phosphorus corroles as a tool for affecting their chemical and physical properties. These fundamental investigations allowed for the development of facile methodologies for the synthesis of a large series of complexes and the establishment of several new structure/activity profiles that may be used to understand and predict spectroscopic features and for tailor-made modification of photophysical and electrochemical properties. This is exemplified by the facile access to complexes with terminal groups that are of large potential for practical applications based on click chemistry, optical imaging, and surface science.