A note on scheduling to meet two min-sum objectives

We consider a single machine scheduling problem with two min-sum objective functions: the sum of completion times and the sum of weighted completion times. We propose a simple polynomial time (1+(1/γ),1+γ)-approximation algorithm, and show that for γ>1, there is no (x,y)-approximation with 1<x<1+(1/γ) and 1<y<1+(γ-1)/(2+γ).     

Ion Mobility,Phase Transitions,and Ion Conductivity in Alkali Metal Tetrafluoroantimonates(III) MSbF4 (M = Na,K, Rb,Cs)

The internal mobility of fluoride ions and electrophysical characteristics of alkali metal tetrafluoroantimonates(III) (M = Na, K, Rb, and Cs) are studied by ¹⁹F NMR and impedance spectroscopies. The types of ion motions in the anionic sublattice of these compounds are determined in the 180-510 K temperature range. The superionic conductivity of the MSbF₄ compounds is established above 480 K ( 2.9 × 10^-2 to 1.3 × 10^-4 S/cm).     

Infrared absorption and electron paramagnetic resonance studies of vinyl radical in noble-gas matrices

Vinyl radicals produced by annealing-induced reaction of mobilized hydrogen atoms with acetylene molecules in solid noble-gas matrices (Ar, Kr, and Xe) were characterized by Fourier transform infrared and electron paramagnetic resonance (EPR) spectroscopies. The hydrogen atoms were generated from acetylene by UV photolysis or fast electron irradiation. Two vibrational modes of the vinyl radical (nu7 and nu5) were assigned in IR absorption studies. The assignment is based on data for various isotopic substitutions (D and 13C) and confirmed by comparison with the EPR measurements and density-functional theory calculations. The data on the nu7 mode is in agreement with previous experimental and theoretical results whereas the nu5 frequency agrees well with the computational data but conflicts with the gas-phase IR emission results.     

Ionic Mobility, Phase Transitions, and Superionic Conduction in Solid Solutions (100 ? x)PbF2-xZrF4 and Crystals K2ZrF6, (NH4)2ZrF6, KSnZrF7, and M(NH4)6Zr4F23 (M = Li, Na)

Methods of (¹⁹F, ¹H) NMR and impedance spectroscopy are used to investigate the internal mobility and ionic conduction in solid solutions arising in the system PbF₂-ZrF₄ and polycrystals KSnZrF₇, Li(Na)(NH₄)₆Zr₄F₂₃, and M₂ZrF₆ (M = K, NH₄). Factors responsible for the form of ionic motions and their energetics at 170–550 K are considered. It is established that the phase transitions in these compounds are connected with the crystal transition to a superionic state and that the high ionic (superionic) conductivity of beta phases is due to the diffusion of fluoride ions, ammonium cations, and possibly alkali metal cations. The obtained data testify to a substantial role of chainlike aggregation of anionic groupings and a variableness of structural mechanisms of formation of such chains in fluorozirconates for the development of translational diffusion in these compounds.__________Translated from Elektrokhimiya, Vol. 41, No. 5, 2005, pp. 573–582.Original Russian Text Copyright © 2005 by Kavun, Uvarov, Slobodyuk, Goncharuk, Kotenkov, Tkachenko, Gerasimenko, Sergienko.     

19F NMR study of the influence of the nature of outer-spheric cations on the dynamics of the anion sublattice in compounds MM′AF6

Dynamics of octahedral ions in crystal compounds MM′AF₆ (M, M′=Li, Na, K, Rb, Cs; A=Ge, Ti) has been studied in the temperature range 115–500 K. Types of inner motions of complex ions have been established, and their activation energies have been estimated. First-order transition has been found in compound LiRbTiF₆. Institute of Chemistry, Far-East Branch, Russian Academy of Sciences. Translated fromZhurmal Strukturnoi Khimii, Vol. 36, No. 4, pp. 697–702, July–August, 1995. Translated by L. Smolina     

Ion mobility,phase transitions,and ion transport in potassium-ammonium hexafluorozirconates

The mobility of fluoride and ammonium ions (180–480 K) in compounds K_{2? n} (NH4)_nZrF₆ (0.2 ≤ n ≤ 1.70) was investigated by ¹⁹F and ¹H NMR. Correlations have been found between the composition of the cation sublattice, the character of ion motions, and phase transition temperature in these compounds. The hightemperature modifications with n ≥ 0.85 of the compounds are characterized by translational diffusion of fluoride and ammonium ions and by uniaxial anisotropy of the ¹⁹F magnetic shielding tensor. The electrophysical characteristics of these compounds were studied in the temperature range 300–480 K.