Ultrasonic cleavage of thioethers

The rates of DPPH (diphenylpicrylhydrazyl) trapping and the sonolytical products obtained during the sonolysis of thioethers at normal and low temperature are reported. CS2, lower sulfides, thiophene, and sulfurized species are the common products during the ultrasonic irradiations. Hydrocarbons are also obtained during the sonolysis of diallyl sulfide, diethyl disulfide, and dipropyl disulfide. Furthermore, aldehydes are obtained as oxidized species; SO2 is found at 208 K. The principal sonochemical process appears to be the cleavage of C-S or S-S bond with secondary combinations and rearrangements. DPPH has been used to probe the sonolytical potential of thioethers. The results show a good correlation between the rates of DPPH trapping and the vapor pressures of thioethers. In conclusion, a lower vapor pressure results in a higher sonolytical rate. The sonochemical behaviors of thioethers have strong qualitative similarities to the pyrolysis.     

Elliptic Curves Suitable for Pairing Based Cryptography

For pairing based cryptography we need elliptic curves defined over finite fields whose group order is divisible by some prime with where k is relatively small. In Barreto et al. and Dupont et al. [Proceedings of the Third Workshop on Security in Communication Networks (SCN 2002), LNCS, 2576, 2003; Building curves with arbitrary small Mov degree over finite fields, Preprint, 2002], algorithms for the construction of ordinary elliptic curves over prime fields with arbitrary embedding degree k are given. Unfortunately, p is of size .We give a method to generate ordinary elliptic curves over prime fields with p significantly less than which also works for arbitrary k. For a fixed embedding degree k, the new algorithm yields curves with where or depending on k. For special values of k even better results are obtained.We present several examples. In particular, we found some curves where is a prime of small Hamming weight resp. with a small addition chain.AMS classification: 14H52, 14G50     

On minimal forbidden subgraph characterizations of balanced graphs

A graph is balanced if its clique-matrix contains no edge–vertex incidence matrix of an odd chordless cycle as a submatrix. While a forbidden induced subgraph characterization of balanced graphs is known, there is no such characterization by minimal forbidden induced subgraphs. In this work, we provide minimal forbidden induced subgraph characterizations of balanced graphs restricted to graphs that belong to one of the following graph classes: complements of bipartite graphs, line graphs of multigraphs, and complements of line graphs of multigraphs. These characterizations lead to linear-time recognition algorithms for balanced graphs within the same three graph classes.     

TMSCH(2)Li and TMSCH(2)Li-LiDMAE: efficient reagents for noncryogenic halogen-lithium exchange in bromopyridines

TMSCH(2)Li and TMSCH(2)Li-LiDMAE have been used efficiently for bromine-lithium exchange in 2-bromo-, 3-bromo-, and 2,5-dibromopyridines under noncryogenic conditions, while low temperatures (-78 to -100 degrees C) are always needed with n-BuLi. The aminoalkoxide LiDMAE induced a remarkable C-2 selectivity with 2,5-dibromopyridines in toluene at 0 degrees C, which was unprecedented at such a temperature. The lithiopyridines were successfully reacted with electrophiles also under noncryogenic conditions giving the expected adducts in good yields.