Characterization of cores of assignment games

We consider the assignment game of Shapley and Shubik (1972). We prove that the class of possible cores of such games (expressed in terms of payoffs for players on one side of the market) is exactly the same as a special class of polytopes, called 45-lattices. These results parallel similar work done by Conway (in Knuth, 1976) and Blair (1984) for marriage markets.Research supported by the Office of Naval Technology.     

Synthesis and Characterization of Canola-Based Cholesteryl Ester and Nematic E7 Mixture

Abstract

The fatty acid of Canola Oil, 61% of which is Oleic acid, was extracted. Fourier Transform Infrared Spectrophotometry (FTIR) confirmed the fatty acid extraction. Canola-based Cholesteryl Ester (CANCE) was obtained through esterification. FTIR scans of the CANCE and the fatty acid were compared to verify the complete esterification. The resulting crude product is a yellow wax with some crystals embedded on it. Thin layer chromatography was then performed to determine the appropriate solvent for the column chromatography to purify the crude sample. The purified product was characterized using Optical Polarizing Microscopy and Differential Scanning Calorimetry. Mixtures of the Nematic E7 and CANCE in different ratios were prepared. Transition temperatures of each mixture were determined using differential scanning calorimetry and verified using optical polarizing microscopy.     

Synthesis of Densely Functionalised 5‐Halogen‐1,3‐oxazin‐2‐ones by Halogen‐Mediated Regioselective Cyclisation of N‐Cbz‐Protected Propargylic Amines: A Combined Experimental and Theoretical Study

A very efficient synthesis of 5‐halogen‐1,3‐oxazin‐2‐ones has been accomplished by the halocyclisation reaction of chiral nonracemic N‐carbobenzyloxy (N‐Cbz)‐protected propargylic amines by using I₂, Br₂ and Cl₂ as electrophile sources. The nature of the halogen influences the reaction time and yield. However, in all cases the reaction is totally regioselective taking place through a 6‐endo‐dig process regardless of the nature of the halogen and of the substituents in the starting material. To rationalise the experimental results, theoretical studies at the B3LYP/6‐311G* level have been performed.     

Structural Diversity from the Transannular Cyclizations of Natural Germacrone and Epoxy Derivatives: A Theoretical–Experimental Study

Treatment of germacrone ( 1 ) with different electrophiles, and of its epoxy derivatives germacrone‐4,5‐epoxide ( 2 ), germacrone‐1,10‐epoxide ( 3 ) and isogermacrone‐4,5‐epoxide ( 4 ) with Brönsted/Lewis acids and Ti^III, gives rise to a great structural diversity. Thus, by using a maximum of two steps, the production of more than 40 compounds corresponding to 14 skeletons is described. Computational calculations rationalizing the structural divergence produced are also described. Finally, since some of the compounds generated are bioactive natural sesquiterpenes, the mechanisms of formation of these substances will provide new insights in their biosynthesis.     

Access to Optically Active 3‐Substituted Piperidines by Ring Expansion of Prolinols and Derivatives

The ring expansion of prolinols via an aziridinium intermediate gives C3‐substituted piperidines in good yields and enantiomeric excess, the substituent at the C3 position being derived from the most reactive nucleophile in the reaction mixture. Depending on the nucleophile, the reaction proceeds under thermodynamic or kinetic control. The regioselectivity of attack of nucleophiles on the aziridinium intermediate depends on the nature of the substituents on the nitrogen atom and the C4 position of the starting prolinols.     

A Silver Bite: Crystalline Heterometallic Architectures Based on Ag–π Interactions with a Bis‐Dipyrrin Zinc Helicate

An unprecedented mode of assembly of helical motives and Ag^I ions in the crystalline state is described. The combination of a Zn^II helicate based on a 2,2′‐bisdpm bearing peripheral benzonitrile moieties with AgX salts, leads to the formation of a tetranuclear core containing Ag–π interactions. Depending on the coordinating ability of the X^? anion and the solvents used, the tetranuclear complex self‐assembles into coordination polymers of varying dimensionality. From the sequence of coordination events (Ag–π or Ag–peripheral site), one may envisage two possible construction scenarios. However, the Ag–π as primary event seems reasonable owing to the rather weak binding propensity of the nitrile group and the chelating nature of the π‐clefts.