(MeLi)4(dem)1.5]infinity] and [(thf)3Li3M3[(NtBu)3S--how to reduce aggregation of parent methyllithium

Organolithium compounds play the leading role among the organometallic reagents in synthesis and in industrial processes. Up to date industrial application of methyllithium is limited because it is only soluble in diethyl ether, which amplifies various hazards in large-scale processes. However, most reactions require polar solvents like diethyl ether or THF to disassemble parent organolithium oligomers. If classical bidentate donor solvents like TMEDA (TMEDA= N,N,N',N'tetramethyl-1,2-ethanediamine) or DME (DME=1,2-dimethoxyethane) are added to methyllithium, tetrameric units are linked to form polymeric arrays that suffer from reduced reactivity and/or solubility. In this paper we present two different approaches to tune methyllithium aggregation. In [[(MeLi)4(dem)1,5)infinity] (1; DEM = EtOCH2OEt, diethoxymethane) a polymeric architecture is maintained that forms microporous soluble aggregates as a result of the rigid bite of the methylene-bridged bidentate donor base DEM. Wide channels of 720 pm in diameter in the structure maintain full solubility as they are coated with lipophilic ethyl groups and filled with solvent. In compound 1 the long-range Li3CH3...Li interactions found in solid [[(MeLi)4]infinity] are maintained. A different approach was successful in the disassembly of the tetrameric architecture of [((MeLi)4]infinity]. In the reaction of dilithium triazasulfite both the parent [(MeLi)4] tetramer and the [[Li2[(NtBu)3S]]2] dimer disintegrate and recombine to give an MeLi monomer stabilized in the adduct complex [(thf)3Li3Me-[(NtBu)3S]] (2). One side of the Li3 triangle, often found in organolithium chemistry, is shielded by the tripodal triazasulfite, while the other face is mu3-capped by the methanide anion. This Li3 structural motif is also present in organolithium tetramers and hexamers. All single-crystal structures have been confirmed through solid-state NMR experiments to be the same as in the bulk powder material.     

Hydroxylamido(1-)-O,N-Komplexe des Molybdäns(VI) mit terminalen Oxo-, Sulfido- und Selenido-Liganden Die Kristallstrukturen von [MoO2(C5H10NO)2] und von [MoS2(C5H10NO)2]

Hydroxylamido(1-)-O,N Complexes of Molybdenum(VI) Containing Terminal Oxo, Sulfido, and Selenido Ligands. Crystal Structures of [MoO₂(C₅H₁₀NO)₂] and of [MoS₂(C₅H₁₀NO)₂] Molecular complexes of cis-dioxo-bis(hydroxylamido(1-)-O,N)molybdenum(VI) containing O,N-coordinated, N,N-substituted hydroxylamine ligands react with H₂S in toluene substituting one or both terminal oxo groups yielding cis-oxosulfido- and cis-disulfido-bis (hydroxylamido(1-)-O,N) molybdenum complexes, respectively. With H₂Se the corresponding cis-oxoselenido complexes are formed. The crystal structures of the two title compounds containing piperidine-N-oxide as ligands are described: The cis-disulfido complex crystallizes tetragonal in the space group D—I 4 2 m with four formula units per unit cell; the corresponding cis-dioxo complex crystallizes orthorhombic (D—P 2₁2₁2₁; Z = 4). The ¹H—nmr spectra and the UV-visible absorption spectra are reported.     

Constraints on the fundamental topological parameters of spatial tessellations

Tessellations of that use convex polyhedral cells to fill the space can be extremely complicated, especially if they are not “facet‐to‐facet”, that is, if the facets of a cell do not necessarily coincide with the facets of that cell's neighbours. In a recent paper 15 , we have developed a theory which covers these complicated cases, at least with respect to their combinatorial topology. The theory required seven parameters, three of which suffice for facet‐to‐facet cases; the remaining four parameters are needed for the awkward adjacency concepts that arise in the general case. This current paper establishes constraints that apply to these seven parameters and so defines a permissible region within their seven‐dimensional space, a region which we discover is not bounded. Our constraints in the relatively simple facet‐to‐facet case are also new.     

Coarse equivalences of Euclidean buildings

We prove the following rigidity results. Coarse equivalences between metrically complete Euclidean buildings preserve spherical buildings at infinity. If all irreducible factors have dimension at least two, then coarsely equivalent Euclidean buildings are isometric (up to scaling factors); if in addition none of the irreducible factors is a Euclidean cone, then the isometry is unique and has finite distance from the coarse equivalence.     

Polynomial time solutions for scheduling problems on a proportionate flowshop with two competing agents

In scheduling problems with two competing agents, each one of the agents has his own set of jobs and his own objective function, but both share the same processor. The goal is to minimize the value of the objective function of one agent, subject to an upper bound on the value of the objective function of the second agent. In this paper we study two-agent scheduling problems on a proportionate flowshop. Three objective functions of the first agent are considered: minimum maximum cost of all the jobs, minimum total completion time, and minimum number of tardy jobs. For the second agent, an upper bound on the maximum allowable cost is assumed. We introduce efficient polynomial time solution algorithms for all cases.     

More on cancellative semigroups on manifolds

Communicated by D.R.Brown     

Limits of chromatic zeros of some families of maps

Two families of maps are considered, one consisting of maps with two pentagons separated by n 5-rings, the other of maps with two n-gons separated by two n-rings. For each family, a homogeneous linear recursion is derived for the corresponding family of chromatic polynomials. It is shown that B₅, B₇, and B₁₀ are limits of sequences of zeros from one or another of the families, where $\text{B}{}_{\mathrm{n}}\text{= 2(1+}\text{cos}\text{2π}\text{n}\text{)}$.