On the non-occurrence of the coxeter graphs β<SUB>2n+1</SUB>, D<SUB>2n+1</SUB> and E<SUB>7</SUB> as the principal graph of an inclusion of II<SUB>1</SUB> factors

After discussing some preliminaries on the notion of an action of a hypergroup on a set, we present elementary proofs of the fact that the coxeter graphs β2n+1 D2n+1 and E7 do not arise as Jones' principal graph invariant of an inclusion of II1 factors. (Here, we use the symbol an to denote the graph that is normally denoted by Bn, the reason for this changed terminology being spelt out in the text.

Performance Investigation of Genetic Algorithm Based LCL Resonant Converter in Marine Applications

1377-1388This manuscript presents steady state stability analysis of LCL RC using frequency plot. Careful analysis favours LCL RC has the fine stability region. Also this paper presents a comparative estimation of conventional Proportional Integral Derivative (PID) Controller and Genetic Algorithm (GA) based PID controller for a modified LCL RC. The above controllers are simulated using MATLAB and their performance is analyzed. Result of the analysis shows the supremacy of GA based PID controller over the conventional PID control method. Design, simulation and experimental results for a 133W, 50 KHz GA based LCL resonant converter is presented in this script. In this work, the applicability of the Philips ARM (Advanced RISC Machine) processor LPC 2148 is also investigated for implementing the GA based PID controller for marine applications

Trifluoromethylation of Secondary Nitroalkanes

Using a commercially available Umemoto’s reagent, the metal-free trifluoromethylation of nitroalkanes is now possible. This method provides a general, high-yielding synthesis of α-(trifluoromethyl)­nitroalkanes. The quaternary α-(trifluoromethyl)­nitroalkanes obtained from this transformation can be elaborated to a variety of complex nitrogen-containing molecules, including α-(trifluoromethyl)­amines