The job-shop problem and immediate selection

The job-shop problem is one of the most difficult NP-hard scheduling problems. A 10×10-problem published in 1963 has been solved only recently by Carlier and Pinson using a branch and bound method. Other branch and bound algorithms have been developed recently. The efficiency of all these branch and bound methods relies on the concept of immediate selection which allows to introduce order relations on the setI of all operations to be processed on the same machine before branching. We present new algorithms for immediate selection. Among them are

1. anO(max {n logn,f})-algorithm for fixing all disjunctions induced by cliques;
2. anO(n ²)-algorithm based on concepts which are different from those used by Carlier and Pinson.

Here,n is the number of operations inI andf is the number of induced order relations.     

The Lewis basicity of the [Pt3(μ-CO)3(PR3)3] clusters and the X-ray crystal structure of [{ZnI2}{Pt3(μ-CO)3(PPh(i-Pr)2)3}]

The cluster compounds [Pt₃(μ-CO)₃(PR₃)₃] act as Lewis bases towards the metal halides of Group XI, MX, Group XII, MX₂, and Group XIII, MX₃, to form cluster compounds of the composition [{MX_n}{Pt₃(μ-CO)₃(PR₃)₃}]. The X-ray crystal structure, NMR and IR data are given for the compound [{ZnI}{Pt₃(μ-CO)₃(PPh(i-Pr)₂)₃}].     

The Structures of Some Products from the Photodegradation of the Pluramycin Antibiotics Hedamycin and Kidamycin

The photolability of the antitumor antibiotic hedamycin ( 1 ) was investigated by irradiation in different solvents in the presence or in the absence of oxygen. The products formed were separated chromatographically and their structures determined by NMR spectroscopy. Photolysis of 1 in the presence of oxygen gave only one isolable product, photohedamycin A ( 3 ), where ring E of hedamycin had been transformed into an enol ether. The reaction in the absence of oxygen yielded the photohedamycins B, C, and D ( 5, 6 , and 7 , respectively). In these compounds, one of the epoxides of hedamycin had been opened reductively, and in photohedamycin D ( 7 ) the substituent at C(8) - originally ring E of hedamycin - was now acyclic. In addition to these compounds, the photolyses yielded a large number of unstable minor products, which could not be isolated.     

NMR spectra of a microcrystalline protein at 30 kHz MAS

Proteins are not always available in amounts desirable for solid-state magic-angle spinning (MAS) nuclear-magnetic resonance (NMR) spectroscopy. To maximize the signal-to-noise ratio achievable with small samples, the filling factor must be optimized by using small-diameter MAS rotors. These rotors have the added benefit of allowing higher radio frequency field amplitudes during polarization transfer steps and during decoupling periods as well as allowing higher spinning frequencies. We demonstrate the advantages of relatively fast MAS (30 kHz using a 2.5 mm rotor) compared to MAS at 12 kHz for the 10.4 kDa model protein Crh with 93 residues and show that the signal-to-noise ratio in two-dimensional correlation spectra can be significantly improved by taking advantage of optimized pulse sequences available with rapid MAS.     

Synthesis of Naturally Occurring Pyrazine and Imidazole Alkaloids from Botryllus LeachiRID=”a”ID=”a”?Dedicated to Prof. G. M?rkl on the occasion of his 75th birthday

The synthesis of the naturally occurring and biologically active alkaloids 1 and 2, first isolated from the red ascidian Botryllus leachi by Duran et al. [1], is described and the structure proposed for Botryllazine B (1) is confirmed. The analytical data for 2-(p-hydroxybenzoyl)-4-(p-hydroxyphenyl)imidazole (2) are discussed and compared with the literature. With special emphasis of ¹H NMR data the tautomerism of aroylimidazolemethanones is described.     

Neutral and ionic aluminum,gallium, and indium compounds carrying two or three terminal ethynyl groups

The syntheses of the ionic compounds [Li(+).2 dioxane (2,6-iPr(2)C(6)H(3)N(SiMe(3))Al(C triplebond CSiMe(3))(3))(-)].0.75 dioxane (1), [(Li(+))(2).(dioxane)(7)](0.5) [2,6-iPr(2)C(6)H(3)N(SiMe(3))Ga(C triplebond CSiMe(3))(3)(-)].1.5 dioxane (2), and [(Li(+))(2).(dioxane)(7)](0.5) [2,6-iPr(2)C(6)H(3)N(SiMe(3))In(C triplebond CSiMe(3))(3)(-)].1.5 dioxane (3) by the reaction of the corresponding organo metal chloride with LiC triplebond CSiMe(3) are reported. The neutral ethynyl compounds Br-Al(C triplebond CtBu)(2).2 THF (4), Cl-Ga(C triplebond CtBu)(2).THF (5), Cl-In(C triplebond CtBu)(2).2 THF (6), Al(C triplebond CtBu)(3).C[N(Me)CMe](2) (7), Ga(C triplebond CtBu)(3).dioxane (8), and In(C triplebond CtBu)(3).NEt(3) (9) have been obtained in good yields from the reaction of AlBr(3), GaCl(3), and InCl(3) with LiC triplebond CtBu in the presence of a Lewis base. Compound 7 is the first heterocyclic carbene substituted ethynyl derivative. Aluminum and gallium compounds with three terminal ethynyl groups Al(C triplebond CPh)(3).NMe(3) (10) and Ga(C triplebond CPh)(3).NMe(3) (11) have been prepared by the reaction of AlH(3).NMe(3) or GaH(3).NMe(3) with three equivalents of phenylethyne. All the above-mentioned compounds have been structurally studied. In compound 1 the lithium ion is coordinated to the three terminal ethynyl groups, whereas in compounds 2 and 3 the lithium is coordinated to the solvent (dioxane). Compound 8 crystallizes as a coordination polymer with dioxane molecules bridging the individual gallium units.     

A Quantitative Assessment of „Through-space”︁ and „Through-bond”︁ Interactions. Application to Semi-empirical SCF Models

The scheme of ‘through-space’ and ‘through-bond’ interaction of (semi)localized orbitals, originally proposed by Hoffmann, is reexamined in terms of SCF many-electron treatments. It is shown that the two types of interaction can be characterized by examining the corresponding off-diagonal matrix elements of the Hartree-Fock matrices of the localized or the symmetry adapted localized orbitals and of the partially diagonalized Hartree-Fock matrices referring to ‘precanonical orbitals’. The procedure outlined is applied to three practical examples using the semiempirical many-electron treatments SPINDO, MINDO/2 and CNDO/2:

• a A reassessment of ‘through-space’ and ‘through-bond’ interaction in norbornadiene indicates, that the latter type of interaction is also of importance for the orbital based mainly on the antisymmetric combination of the localized x-orbitals. The differences in the predictions derived from the three models are critically examined.
• b The competition between ‘through-space’ and ‘through-bond’ interaction in the series of bicyclic dienes from norbornadiene to bicyclo[4.2.2]-dcca-7,9-diene and in cyclohexa-1,4-diene, i. e. their dependence on the dihedral angle UI is reexamined. It is found that the rationalization for the orbital crossing near ω = 130° deduccd from PE. spectroscopic data can not be as simple as originally suggested and that the relay’ orbitals responsible for ‘through-bond interaction affecting both the symmetric and the antisymmetric combination of the π-orbitals extend over the whole CC-σ-system of the six membered ring.
• c ‘Through-bond’ interaction of the two lone pair orbitals in 1,4-diazabicyclo[2.2.2]octane is found to be large for their symmetric and the antisymmetric linear combination.

The analysis quoted, draws attention to some of the dangers involved in using semiempirical treatments for the interpretation of PE. data in terms of Koopmans′ theorem, without due caution.