A stable convergence theorem for infinite products of nonexpansive mappings in Banach spaces

We use the concept of porosity in order to establish a generic stable convergence theorem for infinite products of nonexpansive mappings in Banach spaces.     

Physiological aspects involved in production of xylanolytic enzymes by deep-sea hyperthermophilic archaeon Pyrodictium abyssi

Xylanases (EC3.2.1.8) catalyze the hydrolysis of xylan, the major constituent of hemicellulose. The use of these enzymes could greatly improve the overall economics of processing lignocellulosic materials for the generation of liquid fuels and chemicals. The hyperthermophilic archaeon Pyrodictium abyssi, which was originally isolated from marine hot abyssal sites, grows optimally at 97°C and is a prospective source of highly thermostable xylanase. Its endoxylanase was shown to be highly thermostable (over 100 m in at 105°C) and active even at 110°C. The growth of the deep-sea archaeon P. abyssi was investigated using different culture techniques. Among the carbohydrates used, beech wood xylan, birch wood glucuronoxylan and the arabinoxylan from oats pelt appeared to be good inducers for endoxylanase and β-xylosidase production. The highest production of arabinofuranosidase, however, was detected in the cell extracts after growth on xylose and pyruvate, indicating that the intermediate of the tricarboxylic acid cycle acted as a nonrepressing carbon source for the production of thi enzyme. Electron microscopic studies did not show a significant difference in the cell surface (e.g., xylanosomes) when P. abyssi cells were grown on different carbohydrates. The main kinetic parameters of the organism have been determined. The cell yield was shown to be very low owing to incomplete substrate utilization, but a very high maximal specific growth rate was determined (μ_max=0.0195) at 90°C and pH 6.0. We also give information on the problems that arise during the fermentation of this hyperthermophilic archaeon at elevated temperatures.     

Restricted rotations and stereodynamics of aziridine-2-methanol derivatives

‘Gear-like’ rotations of simple C-C bonds have been observed in some aziridine methanol derivatives. These restricted rotations have been studied by dynamic and multinuclear magnetic resonance experiments, and the barrier for rotations of Csp³-Csp³ and Csp³-Csp² bonds have been calculated. The role of an intramolecular hydrogen bond on the stereodynamics has also been demonstrated.     

Semitotal Domination in Claw-Free Cubic Graphs

In this paper, we continue the study of semitotal domination in graphs in [Discrete Math. 324, 13–18 (2014)]. A set \({S}\) of vertices in \({G}\) is a semitotal dominating set of \({G}\) if it is a dominating set of \({G}\) and every vertex in \({S}\) is within distance 2 of another vertex of \({S}\). The semitotal domination number, \({{\gamma_{t2}}(G)}\), is the minimum cardinality of a semitotal dominating set of \({G}\). This domination parameter is squeezed between arguably the two most important domination parameters; namely, the domination number, \({\gamma (G)}\), and the total domination number, \({{\gamma_{t}}(G)}\). We observe that \({\gamma (G) \leq {\gamma_{t2}}(G) \leq {\gamma_{t}}(G)}\). A claw-free graph is a graph that does not contain \({K_{1, \, 3}}\) as an induced subgraph. We prove that if \({G}\) is a connected, claw-free, cubic graph of order \({n \geq 10}\), then \({{\gamma_{t2}}(G) \leq 4n/11}\).     

Indium

Analytical and Bioanalytical Chemistry -