Γ-Limit of Periodic Obstacles

We compute the -limit of a sequence obstacle functionals in the case of periodic obstacles.     

Numerical Representations of Interval Orders

In the framework of the analysis of orderings whose associated indifference relation is not necessarily transitive, we study the structure of an interval order and its representability through a pair of real-valued functions. We obtain a list of characterizations of the existence of a representation, showing that the three main techniques that have been used in the literature to achieve numerical representations of interval orders are indeed equivalent.     

A free boundary problem in an absorbing porous material with saturation dependent permeability

We prove a well posedness result for a free boundary problem describing the filtration of an incompressible viscous fluid in a porous medium containing water absorbing granules.?The location of the wetting front (the free boundary) is described by a Stefan like problem for a parabolic equation which is coupled with an hyperbolic equation describing the absorption kinetic of the granules. Received December 1999     

Enantiopure α-imino glyoxylate: a versatile substrate for the spontaneous asymmetric synthesis of unnatural hydroxyaryl glycinates

A novel synthesis of useful enantiomerically pure arylglycinates via spontaneous reaction between phenol or naphthol derivatives and enantiopure α-imino glyoxylate in the absence of an acid catalyst is reported. A library of enantiopure substituted phenol or naphthol glycinates was obtained in good yields and high diastereoselectivities. Diastereoisomerically pure aryl glycinates were obtained by direct flash chromatography separation of the crude reaction mixture. The free OH moiety of the phenols or naphthols contributed to the activation of the imino group to form an intermolecular hydrogen bond and promoted the reaction in the absence of an acid catalyst, as shown in the transition state reported. The diastereoselectivity is due to thermodynamic control in the addition step.     

Gradient bounds for minimizers of free discontinuity problems related to cohesive zone models in fracture mechanics

In this note we consider a free discontinuity problem for a scalar function, whose energy depends also on the size of the jump. We prove that the gradient of every smooth local minimizer never exceeds a constant, determined only by the data of the problem.     

A highly efficient stereocontrolled synthesis of (S)-2′,6′-dimethyltyrosine [(S)-DMT]

A new, practical and very convenient stereocontrolled synthesis of (S)-2′,6′-dimethyltyrosine [(S)-Dmt] 4 was accomplished in a good yield, starting from the chiral synthon 1,4-N,N-[(S)-phenylethyl]-piperazine-2,5-dione 1. The procedure, which is an extension of our original strategy and occurs with a high level of stereoselectivity (>98%), is simple and inexpensive allowing us to prepare the unnatural α-aminoacid (S)-Dmt also on a multi-gram scale.     

Continuous Utility Representation Theorems in Arbitrary Concrete Categories

In this paper the continuous utility representation problem will be discussed in arbitrary concrete categories. In particular, generalizations of the utility representation theorems of Eilenberg, Debreu and Estévez and Hervés will be presented that also hold if the codomain of a utility function is an arbitrary totally ordered set and not just the real line. In addition, we shall prove and apply a general result on the characterization of structures that have the property that every continuous total preorder has a continuous utility representation. Finally, generalizations of the utility representation theorems of Debreu and Eilenberg will be discussed that are valid if we consider arbitrary binary relations and allow a utility function to have values in an arbitrary totally ordered set.      

Excess Gibbs energies and volumes of the ternary system chloroform + tetrahydrofuran + cyclohexane at 298.15 K

Vapour–liquid equilibria and densities for the ternary system chloroform + tetrahydrofuran + cyclohexane and for the binary mixtures containing chloroform have been determined at 298.15 K. Vapour–liquid equilibrium data have been collected by head-space gas-chromatographic analysis of the vapour phase directly withdrawn from an equilibration apparatus. Density measurements have been carried out by means of a vibrating tube densimeter. Molar excess Gibbs energies G^E and volumes V^E, as well as activity coefficients and apparent molar volumes of the components, have been obtained from the measured quantities and discussed. The binary chloroform + tetrahydrofuran displays negative deviations from ideality, while chloroform + cyclohexane positive deviations, for both volume and Gibbs energy. The G^E's and V^E's for the ternary system are positive in the region rich in cyclohexane while negative in the region rich in chloroform + tetrahydrofuran. This indicates that hydrogen bonding between chloroform and tetrahydrofuran molecules produces negative values of G^E and V^E and strongly influences the behaviour of the ternary system.     

Finding the maximum suffix with fewer comparisons

It is shown how to compute the lexicographically maximum suffix of a string of n?2 characters over a totally ordered alphabet using at most (4/3)n−5/3 three-way character comparisons. The best previous bound, which has stood unchallenged for more than 25 years, is (3/2)n−O(1) comparisons. We also prove an interesting property of an algorithm for computing the maximum suffix both with respect to a total order < and with respect to its inverse order >.