Online C-benevolent job scheduling on multiple machines

We consider scheduling a sequence of C-benevolent jobs on multiple homogeneous machines. For two machines, we propose a 2-competitive Cooperative Greedy algorithm and provide a lower bound of 2 for the competitive ratio of any deterministic online scheduling algorithms on two machines. For multiple machines, we propose a Pairing-m Greedy algorithm, which is deterministic 2-competitive for even number of machines and randomized \((2+2/{\hbox {m}})\)-competitive for odd number of machines. We provide a lower bound of 1.436 for the competitive ratio of any deterministic online scheduling algorithms on three machines, which is the best known lower bound for competitive ratios of deterministic scheduling algorithms on three machines.     

Isothiazoles I: 4-isothiazolin-3-ones. A general synthesis from 3,3′-dithiodipropionamides

The syntheses of 3-hydroxyisothiazole, 4-methyl-3-hydroxyisothiazole, and a eomprehensive series of the respective 2-substituted-4-isothiazoIin-3-ones have been achieved by the one-step chlorination-cyclization of the corresponding 3,3 -dithiodipropionamides. In several instances, 5-chloro-4-isothiazolin-3-ones were isolated as side products; however, no 4-chloro-4-isothiazo-lin-3-ones were evident in the reaction mixtures. These observations, coupled with the exclusive 4- or 4,5-halogenation of several preformed 4-isothiazoIin-3-ones, support a proposed reaction pathway involving introduction of chlorine α to the sulfur atom in intermediate reaction products.     

On the equivalence between KMS-states and equilibrium states for classical systems

It is shown that for any KMS-state of a classical system of non-coincident particles, the distribution functions are absolutely continuous with respect to Lebesgue measure; the equivalence between KMS states and Canonical Gibbs States is then established.Supported in part by NSF Grant MCS 75-21684Supported in part by NSF Grant MPS 72-04534Supported in part by NSF Grant MPS 75-20638     

Spin and parity assignments for 23Na levels from the 19F(α, p)22Ne reaction

Resonances were found in the 120° and 160° excitation functions for the ¹⁹F(α, p_o)²²Ne reaction between E = 2.5 and 5.0 MeV corresponding to ²³Na levels at excitation energies between 12.56 and 14.51 MeV. Twenty-one on-resonance angular distributions were analysed with single-level and two-level theory to extract ²³Na spin and parity information. The results of an earlier experiment were analysed by the same procedure, extending the diagnostics down to a ²³Na excitation energy of 11.55 MeV. The analysis incorporated an optical potential for the α-particle consistent with previous channel-spin-$\text{1}\text{2}$ reaction studies and α-induced reaction data.     

Two connected inverse spectral transforms

We establish a transformation which connects the potentials of the one-dimensional Dirac and Klein-Gordon operators. This transformation links the solutions of the nonlinear evolution equations solvable by means of the two inverse spectral transforms which use the Dirac and Klein-Gordon direct and inverse spectral problems.