A generalization of the Shapley–Ichiishi result

The Shapley–Ichiishi result states that a game is convex if and only if the convex hull of marginal vectors equals the core. In this paper, we generalize this result by distinguishing equivalence classes of balanced games that share the same core structure. We then associate a system of linear inequalities with each equivalence class, and we show that the system defines the class. Application of this general theorem to the class of convex games yields an alternative proof of the Shapley–Ichiishi result. Other applications range from computation of stable sets in non-cooperative game theory to determination of classes of TU games on which the core correspondence is additive (even linear). For the case of convex games we prove that the theorem provides the minimal defining system of linear inequalities. An example shows that this is not necessarily true for other equivalence classes of balanced games.     

Microreactors as Tools for Synthetic Chemists—The Chemists' Round‐Bottomed Flask of the 21st Century?

Will microreactors replace the round‐bottomed flask to perform chemical reactions in the near future? Recent developments in the construction of microstructured reaction devices and their wide‐ranging applications in many different areas of chemistry suggest that they can have a significant impact on the way chemists conduct their experiments. Miniaturizing reactions offers many advantages for the synthetic organic chemist: high‐throughput scanning of reaction conditions, precise control of reaction variables, the use of small quantities of reagents, increased safety parameters, and ready scale‐up of synthetic procedures. A wide range of single‐ and multiphase reactions have now been performed in microfluidic‐based devices. Certainly, microreactors cannot be applied to all chemistries yet and microfluidic systems also have disadvantages. Limited reaction‐time range, high sensitivity to precipitating products, and new physical, chemical, and analytical challenges have to be overcome. This concept article presents an overview of microfluidic devices available for chemical synthesis and evaluates the potential of microreactor technology in organic synthesis.     

Quantification of ultrasound-induced chain scission in PdII-phosphine coordination polymers

A kinetically inert, reversible coordination polymer (3) was obtained through complexation of dicyclohexylphosphine telechelic poly(tetrahydrofuran) with palladium(II) dichloride. This coordination polymer is unreactive towards palladium(II) dichloride bis(1-diphenylphosphino)dodecane (4), because ligand dissociation in the coordination polymer is slow. However, upon ultrasonication of solutions of 3 in toluene in the presence of 4, formation of palladium(II) heterocomplexes was observed with (31)P NMR spectroscopy. Heterocomplex formation, the consumption of 4, and changes in molecular weight were used to quantify the scission process. In the presence of 60 equivalents of the alkyldiphenylphosphine stopper complex, the reduction in molecular weight was strongly enhanced; over a period of eight hours the weight-averaged molecular weight was reduced from 1.1x10(5) to 2.3x10(4) g mol(-1) while 47 % of the palladium(II) complexes in the coordination polymer had been converted into heterocomplexes. These results show that the system of 3 in combination with scavenger 4 is a suitable system to study the efficiency of ultrasound-induced chain scission of coordination polymers.     

Multinuclear solid-state high-resolution and 13C -{27Al} double-resonance magic-angle spinning NMR studies on aluminum alkoxides

A combination of 27Al magic-angle spinning (MAS)/multiple quantum (MQ)-MAS, 13C-1H CPMAS, and 13C-{27Al} transfer of population in double-resonance (TRAPDOR) nuclear magnetic resonance (NMR) were used for the structural elucidation of the aluminum alkoxides aluminum ethoxide, aluminum isopropoxide, and aluminum tertiarybutoxide. Aluminum alkoxides exist as oligomers with aluminum in different coordinations. High-resolution 27Al MAS NMR experiments with high-spinning speed distinguished the aluminum atoms in different environments. The 27Al MAS NMR spectrum gave well-resolved powder patterns with different coordinations. Z-filter MQ-MAS was performed to obtain the number and types of aluminum environments in the oligomeric structure. 13C-1H CPMAS chemical shifts resolved the different carbon species (-CH3, =CH2, =CH-, and =C=) in the structures. 13C-{27Al} TRAPDOR experiments were employed to obtain relative Al-C dipolar interactions and to distinguish between terminal and bridging alkoxides in the crystallographic structures. The complete characterization of selected aluminum alkoxides using advanced NMR methods has evidenced the tetrameric structure for aluminum isopropoxide and the dimeric structure for aluminum tertiary-butoxide, as reported in the literature, and proposed a polymeric structure for aluminum ethoxide.     

Amplification of chirality of the majority-rules type in helical supramolecular polymers: the impact of the presence of achiral monomers

We present a theoretical treatment describing the conformational state of helical supramolecular polymers that consist of three types of monomer: right-handed and left-handed chiral monomers and achiral ones. We find that chirality amplification of the majority-rules type, that is, a disproportionately large shift in the helix screw sense due to a small enantiomeric excess, can occur in these polymers. The strength of the chirality amplification depends on the free-energy penalty of a helix reversal along the self-assembled chain and on that of a mismatch between the conformation of a bond and the preferred conformation of the preceding monomer. It turns out that the impact of achiral monomers also depends on these two parameters. For high values of these free energies, the net helicity does not change much from the situation where no achiral material is present. However, if the free-energy penalties are not both large, the impact of the achiral monomers on the conformational state of the aggregates can be quite substantial.     

Rerouting and Improving Dauc-8-en-11-ol Synthase from Streptomyces venezuelae to a High Yielding Biocatalyst

The dauc-8-en-11-ol synthase from Streptomyces venezuelae was investigated for its catalytic activity towards alternative terpene precursors, specifically designed to enable new cyclisation pathways. Exchange of aromatic amino acid residues at the enzyme surface by site-directed mutagenesis led to a 4-fold increase of the yield in preparative scale incubations, which likely results from an increased enzyme stability instead of improved enzyme kinetics.     

Differences Between Individual ZSM‐5 Crystals in Forming Hollow Single Crystals and Mesopores During Base Leaching

After base treatment of ZSM‐5 crystals below 100 nm in size, TEM shows hollow single crystals with a 10 nm shell. SEM images confirm that the shell is well‐ preserved even after prolonged treatment. Determination of the Si/Al ratios with AAS and XPS in combination with argon sputtering reveals aluminum zoning of the parent zeolite, and the total pore volume increases in the first two hours of base treatment. In corresponding TEM images, the amount of hollow crystals are observed to increase during the first two hours of base treatment, and intact crystals are visible even after 10 h of leaching; these observations indicate different dissolution rates between individual crystals. TEM of large, commercially available ZSM‐5 crystals shows inhomogeneous distribution of mesopores among different crystals, which points to the existence of structural differences between individual crystals. Only tetrahedrally coordinated aluminum is detected with ²⁷Al MAS NMR after the base leaching of nano‐sized ZSM‐5.