Lower semicontinuity of quasi-convex integrals in BV

Some boundedness properties for an extension operator are proved and used together with techniques of Maly [24], Meyers [29], Fonseca and Müller [13] and Fonseca and Marcellini [12] to obtain lower semicontinuity results in BV for quasiconvex integrals of super-linear growth. Received January 25, 1997 / Accepted October 3, 1997     

Algebraic representation of the linear problem as a method to construct the Darboux-Bäcklund transformation

An effective algorithm to construct the Darboux matrix based on the dressing method is proposed. Our approach consists in representing the linear problem as a system of algebraic constraints on two matrices. The Darboux matrix is determined from the requirement that the Darboux-Bäcklund transformation preserves these constraints. A non-isospectral deformation of the derivative nonlinear Schrödinger equation is discussed as an example.     

Polyèdre de Newton et distributionf + s . II

Sans résumé

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RANDOM EDGE can be exponential on abstract cubes

We prove that RANDOM EDGE, the simplex algorithm that always chooses a random improving edge to proceed on, can take a mildly exponential number of steps in the model of abstract objective functions (introduced by Williamson Hoke [Completely unimodal numberings of a simple polytope, Discrete Appl. Math. 20 (1988) 69-81.] and by Kalai [A simple way to tell a simple polytope from its graph, J. Combin. Theory Ser. A 49(2) (1988) 381-383.] under different names). We define an abstract objective function on the n-dimensional cube for which the algorithm, started at a random vertex, needs at least exp(const·n^1/3) steps with high probability. The best previous lower bound was quadratic. So in order for RANDOM EDGE to succeed in polynomial time, geometry must help.     

A new insight into the understanding of the collapsed form of poly(N-isopropylacrylamide) molecules

Possible collapsed forms of poly(N-isopropylacrylamide) molecules are reviewed on the basis of first principle calculations. Various configurations and associated conformations are detailed. The calculated optimized structures exhibit different possibilities of creating networks of intra-molecular bonds of the hydrogen type. We show that the most remarkable one is able to form a local, self-saturated and well ordered helix. We also indicate in which direction the synthesis of the molecule should be oriented to improve its global behavior in term of hydrophobic/hydrophilic behavior.     

Semigroups of matrices of intermediate growth

Finitely generated linear semigroups over a field K that have intermediate growth are considered. New classes of such semigroups are found and a conjecture on the equivalence of the subexponential growth of a finitely generated linear semigroup S and the nonexistence of free noncommutative subsemigroups in S, or equivalently the existence of a nontrivial identity satisfied in S, is stated. This ‘growth alternative’ conjecture is proved for linear semigroups of degree 2, 3 or 4. Certain results supporting the general conjecture are obtained. As the main tool, a new combinatorial property of groups is introduced and studied.     

Two crystals of doubly protonated melaminium salts: melaminium bis­(trifluoro­acetate) trihydrate and melaminium bis­(trichloro­acetate) dihydrate

Crystals of 2,4,6‐triamino‐1,3,5‐triazine‐1,3‐dium bis­(trifluoro­acetate) trihydrate, C₃H₈N₆²⁺·2CF₃COO⁻·3H₂O, and 2,4,6‐triamino‐1,3,5‐triazine‐1,3‐dium bis­(trichloro­acetate) dihydrate, C₃H₈N₆²⁺·2CCl₃COO⁻·2H₂O, both contain doubly protonated melamine rings that lie on crystallographic twofold axes. In the former structure, one water mol­ecule also lies on a twofold axis. While the trifluoro­acetate compound crystallizes in a centrosymmetric space group, the trichloro­acetate is non‐centrosymmetric, so it is useful as a material for non‐linear optics. The efficiency of second harmonic generation is about three times greater than that of KDP (KH₂PO₄). A combination of ionic and donor–acceptor hydrogen‐bond inter­actions link the melaminium(2+) residues with trifluoro­acetate or trichloro­acetate ions and water mol­ecules to form a three‐dimensional network.     

The Matsumoto-Yor property and the structure of the Wishart distribution

This paper establishes a link between a generalized matrix Matsumoto-Yor (MY) property and the Wishart distribution. This link highlights certain conditional independence properties within blocks of the Wishart and leads to a new characterization of the Wishart distribution similar to the one recently obtained by Geiger and Heckerman but involving independences for only three pairs of block partitionings of the random matrix.In the process, we obtain two other main results. The first one is an extension of the MY independence property to random matrices of different dimensions. The second result is its converse. It extends previous characterizations of the matrix generalized inverse Gaussian and Wishart seen as a couple of distributions.We present two proofs for the generalized MY property. The first proof relies on a new version of Herz's identity for Bessel functions of matrix arguments. The second proof uses a representation of the MY property through the structure of the Wishart.