Orientations of chain groups

We prove generalizations to chain groups, of Minty's Arc Colouring Lemma and its extension, the well-known Farkas Lemma. In these the orientation of the edges is replaced by an arbitrary chain.A function on a chain groupN isrepresentable if there exists a chainR such that (X)=R·X for allXN. Anorientation is a chain with values ±1. We prove that for a regular chain group a linear function that is representable by an orientation for each chainXN locally, is representable by an orientation globally.     

A note on theΠ 2 0 -induction rule

It is well-known (due to C. Parsons) that the extension of primitive recursive arithmeticPRA by first-order predicate logic and the rule of ₂ ⁰ -induction ₂ ⁰ -IR is ₂ ⁰ -conservative overPRA. We show that this is no longer true in the presence of function quantifiers and quantifier-free choice for numbersAC ^0,0-qf. More precisely we show that :=PRA ² + ₂ ⁰ -IR+AC ^0,0-qf proves the totality of the Ackermann function, wherePRA ² is the extension ofPRA by number and function quantifiers and ₂ ⁰ -IR may contain function parameters.This is true even forPRA ² + ₁ ⁰ -IR+ ₂ ⁰ -IR ^–+AC ^0,0-qf, where ₂ ⁰ -IR ^– is the restriction of ₂ ⁰ -IR without function parameters.I am grateful to an anonymous referee whose suggestions led to an improved discussion of our results     

BV periodic solutions of an evolution problem associated with continuous moving convex sets

This paper is concerned with BV periodic solutions for multivalued perturbations of an evolution equation governed by the sweeping process (or Moreau's process). The perturbed equation has the form –DuN _C (t)(u(t))+F(t,u(t)), whereC is a closed convex valued continuousT-periodic multifunction from [0,T] to ^d ,N ^C (t)(u(t)) is the normal cone ofC(t) atu(t),F: [0,T]× ^{d d} is a compact convex valued multifunction and Du is the differential measure of the periodic BV solutionu. Several existence results for this differential inclusion are stated under various assumptions on the perturbationF.     

Fractal dimension,attractors, and the boussinesq approximation in three dimensions

The Boussinesq approximation, where the viscosity depends polynomially on the shear rate, finds more and more frequent use in geological practice. In the paper, this modified Boussinesq approximation is investigated as a dynamical system for which the existence of a global attractor is proved. Finally, a new criterion for estimating the fractal dimension of invariant sets is formulated and its application to the problem under consideration is illustrated.     

On the two-gap elliptic potentials

The-parametrized family of two-gap elliptic potentials is constructed so that (i) 0<<1, (ii) for rational values of such potentials are elliptic (i.e., double-periodic), (iii) within the limit0 this family degenerates to the soliton potential, (iv) within the limit1 this family degenerates to the one-gap Lamé potential.Dedicated to the memory of J.-L. Verdier     

Shock fluctuations in the asymmetric simple exclusion process

Summary We consider the one dimensional nearest neighbors asymmetric simple exclusion process with ratesq andp for left and right jumps respectively;q<p. Ferrari et al. (1991) have shown that if the initial measure isv _, , a product measure with densities and to the left and right of the origin respectively, <, then there exists a (microscopic) shock for the system. A shock is a random positionX _t such that the system as seen from this position at timet has asymptotic product distributions with densities and to the left and right of the origin respectively, uniformly int. We compute the diffusion coefficient of the shockD=lim _t t ^–1(E(X _t )²–(EX _t )²) and findD=(p–q)(–)^–1((1–)+(1–)) as conjectured by Spohn (1991). We show that in the scale the position ofX _t is determined by the initial distribution of particles in a region of length proportional tot. We prove that the distribution of the process at the average position of the shock converges to a fair mixture of the product measures with densities and . This is the so called dynamical phase transition. Under shock initial conditions we show how the density fluctuation fields depend on the initial configuration.     

The drift of a one-dimensional self-repellent random walk with bounded increments

Summary Consider a one-dimensional walk (S _k ) _k having steps of bounded size, and weight the probability of the path with some factor 1–(0,1) for every single self-intersection up to timen. We prove thatS _n /S S converges towards some deterministic number called the effective drift of the self-repellent walk. Furthermore, this drift is shown to tend to the basic drift as tends to 0 and, as tends to 1, to the self-avoiding walk's drift which is introduced in [10]. The main tool of the present paper is a representation of the sequence of the local times as a functional of a certain Markov process.Partially supported by Swiss National Sciences Foundation Grant 20-36305.92     

A transmission problem in the calculus of variations

We study hölder regularity of minimizers of the functional , wherep(x) takes only two values and jumps across a Lipschitz surface. No restriction on the two values is imposed.This article was processed by the author using the Springer-Verlag T_EX PJourlg macro package 1991.     

The invertibility of the product of unbounded Toeplitz operators

In this note I give necessary and sufficient conditions on outer functionsf andg for the operator to be bounded and invertible on H². I also discuss the relationship of this question to two open questions in operator theory and weighted norm inequalities.     

Spectroscopic properties of the photoproducts of pyridoxal-5′-P irradiation: Catalytic site recognition of ribonuclease A

Photoproducts of pyridoxal-5-P, i.e., 4-pyridoxic-5-P and bis-pyridoxal-5-P, have been studied by spectroscopic methods. The spectroscopic properties of bis-pyridoxal-5-P (bis-PLP) resemble those of pyridoxal-5-P (PLP) under similar experimental conditions. The coupling of methylen hydrogens to the phosphorus atom has been shown by NMR spectroscopy. The singlet in the³¹P-NMR spectra and the triplet in¹H-undecoupled experiments confirm the presence of the phosphate group in the 5 position of the structure of the vitamin. The effect of pH and solvent composition on the relative distribution of species of bis-pyridoxine-5-P (bis-PNP) has been investigated by absorption and fluorescence spectroscopy. The acid-base dissociation of the phosphate group is easily detected by emission spectroscopy. Bis-PNP and bis-PLP bind to the enzyme RNase A and they behave as competitive inhibitors with respect to the substrate cytidine-2-3-cyclic phosphate. The natural forms of vitamin B₆, pyridoxine, and pyridoxine-5-P have no effect on the catalytic activity of the protein. Experimental evidence derived from fluorescence and inhibition experiments is consistent with the hypothesis that bis-PNP recognizes the catalytic site of RNase A.