Single machine group scheduling with ordered criteria

The single machine group scheduling problem is considered. Jobs are classified into several groups on the basis of group technology, i.e. jobs of the same group have to be processed jointly. A machine set-up time independent of the group sequence is needed between each two consecutive groups. A schedule specifies the sequence of groups and the sequence of jobs in each group. The quality of a schedule is measured by the criteriaF ₁, ...,F _m ordered by their relative importance. The objective is to minimize the least important criterionF _m subject to the schedule being optimal with respect to the more important criterionF _m–1 which is minimized on the set of schedules minimizing criterionF _m–2 and so on. The most important criterion isF ₁, which is minimized on the set of all feasible schedules. An approach to solve this multicriterion problem in polynomial time is presented if functionsF ₁, ...,F _m have special properties. The total weighted completion time and the total weighted exponential time are the examples of functionsF ₁, ...,F _m–1 and the maximum cost is an example of functionF _m for which our approach can be applied.The research of the authors was partially supported by a KBN Grant No. 3 P 406 003 05, the Fundamental Research Fund of Belarus, Project N 60-242, and the Deutsche Forschungsgemeinschaft, Project Schema, respectively. The paper was completed while the first author was visiting the University of Melbourne.     

Investigation of the extraction equilibria in the system hexachloridorhenate(IV)-neotetrazolium chloride-dichloroethane-water

The neotetrazolium hexachloridorhenate(IV) (NTReCl(6)) has been synthesized and its composition checked. The optimum conditions for the extraction of NTReCl(6) with dichloroethane have been established. The recovery factor for one-fold extraction is R = 74%. The distribution constant, K(D), extraction constant, K(ex), and ion-association constant, beta, have been determined. Neotetrazolium chloride was found to be suitable reagent for extraction-spectrophotometric determination of rhenium(IV) ((NTReCl(6)) = 3.42 +/- 0.20 x 10(4)M(-1) cm(-1)).     

Electron phonon systems from weak to strong coupling

Electron and phonon spectra are derived for an electron-phonon system coupled by the Fröhlich interaction. We cover the range from small coupling <1 to large coupling 1 for a commensurate filling of the bare band. The evolution of the Migdal solution into a charge density wave and finally into a regular lattice of small polarons is studied.     

Rossby solitary vortices,on giant planets and in the laboratory

This is a review of laboratory experiments with a layer of shallow water having a free surface and rotating together with a vessel of parabolic form. Such a (rather original) setup has allowed one to create Rossby solitary vortex for the first time. The latter is an anticyclonic Rossby vortex not subjected to dispersive spread owing to its compensation by the nonlinearity of KdV type. By its structural, collisional, and other properties, including clear-cut cyclonic-anticyclonic asymmetry, it may be considered as a physical prototype of the large-scale long-lived anticyclonic Rossby vortices like the Great Red Spot of Jupiter or the Great Dark Spot of Neptune (this remarkable vortex was discovered by the spacecraft Voyager-2 during its farewell to the Solar System) and other vortices dominating in the atmospheres of giant planets and created by the unstable zonal flows. It has been shown that the vortex under study is a long-lived entity provided it satisfies "antitwisting condition," i.e., it has rather large amplitude (at which it rotates more quickly than it propagates and thereby carries the trapped fluid). In this case, it is not subjected to the "twisting" deformation and may be ascribed by the generalized Charney-Obukhov equation for Rossby vortices on shallow water with a free surface. The results of creating the vortex under consideration by the different methods have been compared with the results obtained by other authors in the experiments on shear-flow generation of Rossby vortices.     

Some remarks on coherent structures out of chaos in planetary atmospheres and oceans

In the context of planetary atmospheres and oceans, it is natural to define "coherent structures" as "long-lived," or "solitary," Rossby vortices. These can be described by the generalized Charney-Obukhov equation (in fluid dynamics) or the analogous generalized Hasegawa-Mima equation (in plasma physics). These two equations contain KdV-type nonlinearities which (together with the compensating dispersive spreading) determine the formation of the coherent structures and explain the clear-cut cyclonic/anticyclonic asymmetry observed experimentally in long-lived planetary Rossby vortices. Examples are given of natural vortices which are (and which are not) coherent structures.     

Mechanism studies of the conversion of 13C-labeled n-butane on zeolite H-ZSM-5 by using 13C magic angle spinning NMR spectroscopy and GC-MS analysis

By using 13C MAS NMR spectroscopy (MAS = magic angle spinning), the conversion of selectively 13C-labeled n-butane on zeolite H-ZSM-5 at 430-470 K has been demonstrated to proceed through two pathways: 1) scrambling of the selective 13C-label in the n-butane molecule, and 2) oligomerization-cracking and conjunct polymerization. The latter processes (2) produce isobutane and propane simultaneously with alkyl-substituted cyclopentenyl cations and condensed aromatic compounds. In situ 13C MAS NMR and complementary ex situ GC-MS data provided evidence for a monomolecular mechanism of the 13C-label scrambling, whereas both isobutane and propane are formed through intermolecular pathways. According to 13C MAS NMR kinetic measurements, both pathways proceed with nearly the same activation energies (E(a) = 75 kJ mol(-1) for the scrambling and 71 kJ mol(-1) for isobutane and propane formation). This can be rationalized by considering the intermolecular hydride transfer between a primarily initiated carbenium ion and n-butane as being the rate-determining stage of the n-butane conversion on zeolite H-ZSM-5.     

Oxidation of bridging groups by carboxylate coordinated ligands in palladium clusters

Thermolysis of tetranuclear palladium clusters Pd₄(-Q)₄ Pd₄(-Q)₄(-O₂CR)₄ (Q=CPh₂ or CO;R=Me, CMe₃, Ph, CH₂Cl or CF₃) has been found to involve innersphere oxidation of carbene or carbonyl ligands during which an oxygen atom transfer occurs from the carboxylate group to the carbene or carbonyl ligand. The thermolysis of the carbonyl clusters gives rise to the products of CO₂ insertion into the C–H bond of benzene or toluene used as solvents forming benzoic acid from benzene and a mixture of phenylacetic and toluic acids from toluene. The reaction of [Pd(OAc)₂(PPh₃)]₂ with HCO₂H includes the transfer of an O atom from formate ligand to the P atom and cleavage of the P-Ph bond accompanied by transfer of the Ph group from PPh₃ ligand to the palladium atom. The structure of the complex formed, [Pd(-O₂PPh₂)(C₆H₅)(PPh₃)]₂, has been resolved by X-ray analysis.     

Synthesis, crystal structure, and nonlinear optical behavior of beta-unsubstituted meso-meso E-vinylene-linked porphyrin dimers

[structure: see text] A vinylene-linked porphyrin dimer, with no substituents at the beta-positions, has been synthesized by CuI/CsF promoted Stille coupling. In the crystal structure of this dimer, the C(2)H(2) bridge is twisted by 45 degrees relative to the plane of the porphyrins. The absorption, emission spectra, and electrochemistry reveal substantial porphyrin-porphyrin pi-conjugation. The triplet excited-state absorption spectrum of this dimer makes it suitable for reverse saturable absorption at 710-900 nm.