A sequential sorting network analogous to the batcher merge

We present a network of delay log₂N, whose comparators have only log₂N different lengths with maximum length N/2. This network is log-sequential in that it will sort N data items when they are passed through it log₂Ntimes. The design, which is related to the Batcher odd-even merge, is distinctly different from the first known example of a log-delay log-sequential network, due to Dowd, Perl, Rudolf, and Saks. It is quite probably the best possible sorting network.     

The two basic linear time Planarity algorithms: Are they the same?

We compare the two most widely known planarity testing algorithms, the one due to Hoperoft and Tarjan, and the other to Lempel. Even, and Cederbaum. These two algorithms are generally viewed as very different approaches to the problems of planarity testing and graph embedding. In this paper, however, by utilizing previously unnoticed freedoms of choice in the order in which the operations of the Hoperoft-Tarjan algorithm can be performed, we create a variation of this algorithm which, in terms of the order in which vertices are processed, is indistinguishable on all planar graph inputs from the Lempel -Even-Cederbaum algorithm. This allows one to create hybridized algorithms which, when interpreted as embedding algorithms, combine all of the features of both procedures.     

High-resolution infrared spectra of water vapor ν2 band of H2O

The ν₂ band of H₂¹⁸O occurring in the region 5–7.5 μ was recorded with a high-resolution vacuum infrared spectrograph and an analysis was presented of the rotational structure observed; comparison of the ground state (000) energy levels determined from the ν₂ band with those derived earlier by Fraley, Rao, and Jones from the ν₁ and ν₂ bands at 2.7 μ was of assistance in this analysis. Values for the energy levels of the first excited state (010) were evaluated.     

Menus of kuratowski subgraphs

Motivated by heuristic embedding algorithms, this paper is concerned with the organization of potentially large lists of Kuratowski subgraphs of an arbitrary nonpianar graph. A graphical structure called a "nearly Hamiltonian" graph is defined. It is shown that lists of Kuralowski subgraphs can be lexicographically organized in such structures. It is shown that any nonpianar graph contains such structures and at least one such structure with a nonempty list of Kuratowski subgraphs can be located in linear time in ihe edges of the graph.     

Kinetic and NMR spectroscopic studies of chiral mixed sodium/lithium amides used for the deprotonation of cyclohexene oxide

The mixed-metal complex formed from n-butylsodium, n-butyllithium, and a chiral amino ether has been studied by NMR spectroscopy. Three different mixed-metal amides were used as chiral bases for the deprotonation of cyclohexene oxide. The selectivity and initial rate of reaction were compared for sodium-amido ethers, lithium-amido ethers, and mixtures of sodium and lithiumamido ethers in diethyl ether and tetrahydrofuran, respectively. The mixed sodium/lithium amides are more reactive than the single sodium and lithium amides, whereas the stereoselectivities are higher when lithium amides are used. The alkali-metal/gamma-amido ethers exhibit both higher initial reaction rates and stereoselectivities than their beta-amido ether analogues. NMR spectroscopic studies of mixtures of n-butylsodium (nBuNa), n-butyllithium (nBuLi), and the gamma-amino ethers in diethyl ether show the exclusive formation of dimeric mixed-metal amides. In diethyl ether, the lithium atom of the mixed-metal amide is internally coordinated and the sodium atom is exposed to solvent; however, in tetrahydrofuran, both metals are internally coordinated.     

Magnetic circular dichroism and absorption spectra of phosphinidene in noble-gas matrices

Electronic magnetic circular dichroism and absorption spectra are reported for the A 3pi(i) <-- X 3sigma- transitions of phosphinidene (PH) isolated in Ar, Kr, and Xe matrices at cryogenic temperatures (approximately 1.4-20 K) and over a range of magnetic field strengths (0-5 T). The results are analyzed by the method of moments, and parameters are extracted by fitting the experimental data to a model in which the A 3pi(i) term is split by spin-orbit (SO) coupling interactions, while the X 3sigma- term is split by spin-spin and higher-order SO coupling. The analysis indicates that, unlike the equivalent imidogen (NH) systems, ground-state PH radicals isolated in noble-gas matrices do not behave as free rotors. Trends in excited-state SO coupling constants are attributed to the external heavy-atom effect and guest-host orbital mixing. It is tentatively concluded that librational amplitudes of the guest radical decrease in the order Ar > Xe > Kr, probably as a consequence of competition between stronger guest-host interactions and larger matrix sites in heavier hosts.