New chiral imino- and amino-sulfoxides as activators of allyl trichlorosilane in the asymmetric allylation of aldehydes

Chiral 2-methylsulfinyl benzaldehyde proved to be a valuable starting material for a convenient approach towards a variety of imino- and amino-sulfoxides. The catalytic properties of these new ligands, as potential activators of allyl trichlorosilane, have been exploited in new catalytic procedures for the synthesis of enantioenriched homoallylic alcohols.     

On the enumerative nature of Gomory’s dual cutting plane method

For 30 years after their invention half a century ago, cutting planes for integer programs have been an object of theoretical investigations that had no apparent practical use. When they finally proved their practical usefulness in the late eighties, that happened in the framework of branch and bound procedures, as an auxiliary tool meant to reduce the number of enumerated nodes. To this day, pure cutting plane methods alone have poor convergence properties and are typically not used in practice. Our reason for studying them is our belief that these negative properties can be understood and thus remedied only based on a thorough investigation of such procedures in their pure form. In this paper, the second in a sequence, we address some important issues arising when designing a computationally sound pure cutting plane method. We analyze the dual cutting plane procedure proposed by Gomory in 1958, which is the first (and most famous) convergent cutting plane method for integer linear programming. We focus on the enumerative nature of this method as evidenced by the relative computational success of its lexicographic version (as documented in our previous paper on the subject), and we propose new versions of Gomory’s cutting plane procedure with an improved performance. In particular, the new versions are based on enumerative schemes that treat the objective function implicitly, and redefine the lexicographic order on the fly to mimic a sound branching strategy. Preliminary computational results are reported.     

The classical problem of the calculus of variations in the autonomous case: Relaxation and Lipschitzianity of solutions

We consider the problem of minimizing

Under the assumption that the Lagrangian is continuous and satisfies a growth assumption that does not imply superlinear growth, we provide a result on the relaxation of the functional and show that a solution to the minimum problem is Lipschitzian.

     

On resolvable finite Minkowski planes

Among the known finite Minkowski planes we determine an infinite family of examples admitting a partition of the set of blocks into equivalence classes, each of which in turn partitions the point set; in particular non-miquelian finite Minkowski planes with this property exist.work done within the activity of GNSAGA of CNR and supported by the Italian Ministry of Public Education     

Biological surfactants stabilizing natural microbubbles in aqueous media

Recent experimental work, using carbohydrate (agarose) gels derived from marine algae, has provided much evidence that largely hydrophobic surfactants surround and stabilize the long-lived gas microbubbles present in such aqueous gels. Later work involving three different types of protein-specific chemical tests further revealed that these biological surfactants, which were also found to be present (in much higher concentrations) in forest soils, are proteinaceous compounds whose surface activity depend upon aromatic amino acid residues. These proteinaceous surfactants have now been successfully isolated from both agarose and aqueous soil extracts and found to-have extremely similar total amino acid compositions. Electrophoresis showed that the microbubble surfactants from both natural sources migrated as a single (but somewhat diffuse) band with or without sulfhydryl-reducing reagent present, and the same apparent molecular weight (< 6,000 daltons), were stained by both peptide- and carbohydrate- specific reagents and, in effect, were essentially indistinguishable. Further electrophoresis experiments, involving enzymatic degradation of the isolated microbubble glycopeptide surfactant, verified the present of covalently bound carbohydrate in the microbubble surfactant. Thereafter, the glycopeptide surfactant was dansylated and chromatographed on Sephadex G-25 and LH-20 columns and, thereby, separated into five major fractions; it was calculated that the $\text{average}$ molecular weight of the microbubble glycopeptide surfactant (as a whole) was very close to 4,000 daltons. Moreover, the same dansyl NH₂-terminal amino acid, specifically alanine, was identified for all five major fractions. It is concluded that microbubble glycopeptide surfactant actually represents a small distribution of structurally similar surface-active glycopeptides, rather than a single molecular species. In addition, a selected review of the biochemical and natural-product organochemical literature further suggests that the microbubble surfactant is essentially a partial degradation product of larger, precursor glycoproteins, which are probably of biological exudate origin and are widely distributed in the environment.     

Photochemical behaviour of 5-bromo-2-furyl ketones : Synthesis of 5-aryl-2-furyl ketones

The photochemical behaviour of the compound 8 was studied. The irradiation of a 10^-3M solution of 8 in aromatic solvents gave high yields of 9 The irradiation of 8 in ethereal or amine solution quantitatively gave 10 The comparison of reaction rates and quantum yields in different solvents gave results in agreement with the hypothesis of an exciplex formation.