Isolation and structure of [HC[CH(SiMe(3))(SnMe(3))](2)](+): a remarkably stable sec-alkyl cation

The reaction of the tin-substituted propene Me3Sn(R)CHCH=CHR (R = SiMe3) with MCl4 in dichloromethane in the presence of Me3SnCl gives the first examples of isolable sec-alkyl carbocation salts, [HC{CH(R)SnMe3}2]+M2Cl9- (M = Zr, Hf). The compounds are thermally stable and, unlike previously isolated trialkyl carbocations, do not require superacidic media or weakly coordinating anions for stability. The crystal structure and DFT calculations suggest polarization of the Sn substituents and hyperconjugation as the reason for the unexpected stability. The stabilizing effect of tin is significantly stronger than that of Si. The carbocations are effective initiators for the polymerization of isobutene, isoprene, and alpha-methylstyrene.     

The synthesis, structure and ethene polymerisation catalysis of mono(salicylaldiminato) titanium and zirconium complexes

The silyl ethers 3-But-2-(OSiMe3)C6H3CH=NR (2a-e) have been prepared by deprotonation of the known iminophenols (1a-e) and treatment with SiClMe3 (a, R = C6H5; b, R = 2,6-Pri2C6H3; c, R = 2,4,6-Me3C6H2; d, R = 2-C6H5C6H4; e, R = C6F5). 2a-c react with TiCl4 in hydrocarbon solvents to give the binuclear complexes [Ti{3-But-2-(O)C6H3CH=N(R)}Cl(mu-Cl3)TiCl3] (3a-c). The pentafluorophenyl species 2e reacts with TiCl4 to give the known complex Ti{3-But-2-(O)C6H3CH=N(R)}2Cl2. The mononuclear five-coordinate complex, Ti{3-But-2-(O)C6H3CH=N(2,4,6-Me3C6H2)}Cl3 (4c), was isolated after repeated recrystallisation of 3c. Performing the dehalosilylation reaction in the presence of tetrahydrofuran yields the octahedral, mononuclear complexes Ti{3-But-2-(O)C6H3CH=N(R)}Cl3(THF) (5a-e). The reaction with ZrCl4(THF)2 proceeds similarly to give complexes Zr{3-But-2-(O)C6H3CH=N(R)}Cl3(THF) (6b-e). The crystal structures of 3b, 4c, 5a, 5c, 5e, 6b, 6d, 6e and the salicylaldehyde titanium complex Ti{3-But-2-(O)C6H3CH=O}Cl3(THF) (7) have been determined. Activation of complexes 5a-e and 6b-e with MAO in an ethene saturated toluene solution gives polyethylene with at best high activity depending on the imine substituent.     

Parameter Inequalities for Orthogonal Arrays with Mixed Levels

An important question in the construction of orthogonal arrays is what the minimal size of an array is when all other parameters are fixed. In this paper, we will provide a generalization of an inequality developed by Bierbrauer for symmetric orthogonal arrays. We will utilize his algebraic approach to provide an analogous inequality for orthogonal arrays having mixed levels and show that the bound obtained in this fashion is often sharper than Raos bounds. We will also provide a new proof of Raos inequalities for arbitrary orthogonal arrays with mixed levels based on the same method.     

Sequencing and scheduling for filling lines in dairy production

We consider an integrated sequencing and scheduling problem arising at filling lines in dairy industry. Even when a processing sequence is decided, still a scheduling problem has to be solved for the sequence. This incorporates typical side constraints as they occur also in other sequencing problems in practice. Previously, we proposed a framework for general sequencing and scheduling problems: A genetic algorithm is utilized for the sequencing, incorporating a problem specific algorithm for the fixed-sequence scheduling. In this paper, we investigate how this approach performs for filling lines. Based on insights into structural properties of the problem, we propose different scheduling algorithms. In cooperation with Sachsenmilch GmbH, the algorithm was implemented for their bottleneck filling line, and evaluated in an extensive computational study. For the real data from production, our algorithm computes almost optimal solutions. However, as a surprising result, our simple greedy algorithms outperform the more elaborate ones in many aspects, showing interesting directions for future research.