A note on the radical of a Banach algebra

Relying on the results of the paper [5], we show that the Jacobson radical of a Banach algebra can be characterized as the set of exactly those elements perturbations by which leave the spectrum invariant. A number of corollaries are listed.     

UV Light-induced Crosslinking of the Complementary Strands of Plasmid pUC19 DNA Restriction Fragments

Restriction fragments of pUC19 DNA were irradiated by various doses of UV light and analyzed by denaturing (alkaline) agarose gel electrophoresis. The irradiation generated retarded species whose mobility indicated two crosslinked DNA strands. Quantitative analysis of the experimental data provided an empirical equation relating the fraction of crosslinked DNA molecules to their length and to the dose of their irradiation by UV light. This equation can be used to predict the crosslinking behavior of pUC19-like DNA molecules whose primary structures do not much differ from a random nucleotide sequence. The amount of interstrand crosslinks increased with the (A+T) content of the pUC19 DNA fragments but the dependence was not clear-cut to indicate that oligonucleotide composition of DNA played a significant role as well.     

One-phase supported titanium-based catalyst for polymerization of ethylene. IV. Effect of alkyl group at organoaluminium compound on catalyst performance

The effect of a basic layer (SiO₂—R₃Al intermediate) in the one-phase silica supported titanium-based catalyst was investigated using the simple model catalyst systems obtained by reacting the activated silica gel consecutively with R₃Al and TiCl₄. Mode of the interaction of SiO₂ with R₃Al—resulting in the formation of the basic layer—was observed via analysis of the concentration of the unreacted OH groups on the silica surface employing IR spectroscopy and via analysis of the concentration of aluminium in solvent using AA spectroscopy. It was found that nature of the alkyl group in R₃Al modified the structure of the basic layer, thus influencing the catalyst performance including the concentration of both the sum of Ti²⁺ and Ti³⁺ and the ESR-active Ti (III) centers. The sum of Ti²⁺ and Ti³⁺ ranged from 45 to 52 mol % and the amount of the ESR-active Ti (III) species ranged from 6 to 17 mol % of the all titanium content. A significant effect of alkyl group at organoaluminium compound on the molecular weight distribution of the resulting polymer was observed. © 1996 John Wiley & Sons, Inc.     

On bounded treewidth duality of graphs

For a graph H, the H-coloring problem is to decide whether or not an instance graph G is homomorphic to H. The H-coloring problem is said to have bounded treewidth duality if there is an integer k such that for any graph G which is not homomorphic to H, there is a graph F of treewidth k which is homomorphic to G but not homomorphic to H. It is known that if the H-coloring problem has bounded treewidth duality then it is polynomial time decidable. We shall prove in this paper that for any integers m, k, there is an integer n₀ such that if G is a graph of girth ≥ n₀ then any graph F of treewidth k homomorphic to G is also homomorphic to C_2m+1. It follows from this result that for non-bipartite graphs H, the H-coloring problems do not have bounded treewidth duality. We also present some classes of directed graphs H for which the H-coloring problems do not have bounded treewidth duality. In particular, there are oriented cycles H for which the H-coloring problems do not have bounded treewidth duality. This answers a question of Hell and Zhu (Siam J. Discrete Math., 8 (1995), 208–222). © 1996 John Wiley & Sons, Inc.     

Monte Carlo Simulation of Clustering in Solutions

A simple Monte Carlo simulation has been used for the study of clusters formation in solutions. The dependence of induction periods on supersaturation as well as the obtained clusters size distribution are in qualitative accord with the theoretical expectations.     

Correlation of Phase Equilibria in Systems with Double Salts

The method of expansion of the relative activity coefficients has been extended to systems with double salts formation. This use of resulting theoretical equations has been demonstrated on the systems NH₄Al(SO₄)₂ – (NH₄)₂SO₄ – H₂O and NH₄Al(SO₄)₂ – Al₂(SO₄)₃ – H₂O. The fit of the experimental data taken from the literature and of the calculated data is very good.     

Polymerization in inverse microemulsion

Homopolymerization of acrylamide as well as that of methyl methacrylate and the copolymerization of acrylamide with methyl methacrylate and/or styrene in inverse microemulsion toluene/water 10: 1 by weight have been studied. Water-soluble ammonium peroxodisulfate, partially water-soluble 2,2′-azobisisobutyronitrile, and oil-soluble dibenzoyl peroxide were used for initiation of these polymerizations at 60°C. Redox initiation system consisting of ammonium peroxodisulfate and tetramethylethylenediamine has been used for an effective initiation of the reactions studied at 30°C. Polymerizations in inverse microemulsions were found start in the interlayer oil macrophase/water microphase. The initial rates of copolymerizations reactions studied depended only on the comonomer mixture composition. The type of the initiator used affected only the exhibited inhibition period.     

Development of an Inhibition Enzyme-Linked Immunosorbent Assay (ELISA) Prototype for Detecting Cytotoxic Three-Finger Toxins (3FTxs) in African Spitting Cobra Venoms

The administration of toxin-specific therapy in snake envenoming is predicated on improved diagnostic techniques capable of detecting specific venom toxins. Various serological tests have been used in detecting snakebite envenoming. Comparatively, enzyme-linked immunosorbent assay (ELISA) has been shown to offer a wider practical application. We report an inhibition ELISA for detecting three-finger toxin (3FTx) proteins in venoms of African spitting cobras. The optimized assay detected 3FTxs in N. ashei (including other Naja sp.) venoms, spiked samples, and venom-challenged mice samples. In venoms of Naja sp., the assay showed inhibition, implying the detection of 3FTxs, but showed little or no inhibition in non-Naja sp. In mice-spiked samples, one-way ANOVA results showed that the observed inhibition was not statistically significant between spiked samples and negative control (p-value = 0.164). Similarly, the observed differences in inhibition between venom-challenged and negative control samples were not statistically significant (p-value = 0.9109). At an LOD of 0.01 µg/mL, the assay was able to confirm the presence of 3FTxs in the samples. Our results show a proof of concept for the use of an inhibition ELISA model as a tool for detecting 3FTxs in the venoms of African spitting cobra snakes.