Which new RSA-signatures can be computed from certain given RSA-signatures?

We consider the following problem. A signature authority issues RSA-signatures of certain types to an individual, and the individual tries, by using the signatures he received, to compute an RSA-signature of a type not issued by the authority. Is the individual able to do this? The RSA-signatures are products of rational powers of residue classes modulo the composite number N of the underlying RSA-system, and the residue classes are chosen at random by the signature authority. The rational exponents in the product determine the type of the signature. We prove that computing an RSA-signature of a particular type, from given RSA-signatures of other types, is polynomial time reducible to computing RSA-roots x ^1/d (mod N) for random x and some positive integer d. This extends results of Akl and Taylor [1] and Shamir [11] from one variable to arbitrarily many variables. As an application of this, under the assumption that for the individual it is infeasible to compute RSA-roots, we give necessary and sufficient conditions describing whether it is feasible for that individual to compute RSA-signatures of a prescribed type from signatures of other types that he received before from the authority.     

On‐line Determination of Aggregate Size and Morphology in Suspensions

Information concerning the aggregation state of fine solid particles is an important element for process control and monitoring of product quality in many applications of industrial slurries. This work deals with the application of different in‐line methods to the characterization of silica aggregate size and morphology. All of these methods exploit turbidity signals, obtained by various means including: from analysis of turbidity fluctuations in homogeneous suspension and from overall turbidity decrease during particle settling. This work also presents the opportunity to report progress in morphological and optical models of small aggregates. As a result of these models, the morphological characteristics of the aggregates along with the number of their constituting particles are derived from experimental results. Similarities between the different methods are examined and discussed.     

A Hamiltonian Model for Linear Friction in a Homogeneous Medium

 We introduce and study rigorously a Hamiltonian model of a classical particle moving through a homogeneous dissipative medium at zero temperature in such a way that it experiences an effective linear friction force proportional to its velocity (at small speeds). The medium consists at each point in a space of a vibration field modelling an obstacle with which the particle exchanges energy and momentum in such a way that total energy and momentum are conserved. We show that in the presence of a constant (not too large) external force, the particle reaches an asymptotic velocity proportional to this force. In a potential well, on the other hand, the particle comes exponentially fast to rest in the bottom of the well. The exponential rate is in both cases an explicit function of the model parameters and independent of the potential. Received: 18 July 2001 / Accepted: 20 April 2002 Published online: 12 August 2002     

Existence,unicité et homogénéité de certains immeubles hyperboliques

Résumé. Dans ce travail, nous introduisons une classe d'immeubles hyperboliques de dimension 2 à allure locale prescrite. Nous prouvons l'existence et l'unicité de ces immeubles. Nous montrons que leur groupe d'automorphismes est transitif sur les chambres. Ces résultats permettent d'identifier des immeubles hyperboliques construits par les diverses méthodes utilisées jusqu'ici: “blueprints” de Ronan-Tits et immeubles de Kac-Moody, revêtements ramifiés d'immeubles euclidiens, polygones de groupes etc... Nos méthodes s'appliquent en fait à des complexes polygonaux hyperboliques beaucoup plus généraux que les seuls immeubles. Received: 3 April 2000; in final form: 25 September 2000 / Published online: 23 July 2001     

Triangular finite elements of HCT type and classC ρ

Let τ be some triangulation of a planar polygonal domain Ω. Given a smooth functionu, we construct piecewise polynomial functionsv∈C ^ρ(Ω) of degreen=3 ρ for ρ odd, andn=3ρ+1 for ρ even on a subtriangulation τ₃ of τ. The latter is obtained by subdividing eachT∈ρ into three triangles, andv/T is a composite triangular finite element, generalizing the classicalC ¹ cubic Hsieh-Clough-Tocher (HCT) triangular scheme. The functionv interpolates the derivatives ofu up to order ρ at the vertices of τ. Polynomial degrees obtained in this way are minimal in the family of interpolation schemes based on finite elements of this type.     

On the Brownian motion of a massive sphere suspended in a hard-sphere fluid. I. Multiple-time-scale analysis and microscopic expression for the friction coefficient

The Fokker-Planck equation governing the evolution of the distribution function of a massive Brownian hard sphere suspended in a fluid of much lighter spheres is derived from the exact hierarchy of kinetic equations for the total system via a multiple-time-scale analysis akin to a uniform expansion in powers of the square root of the mass ratio. The derivation leads to an exact expression for the friction coefficient which naturally splits into an Enskog contribution and a dynamical correction. The latter, which accounts for correlated collisions events, reduces to the integral of a time-displaced correlation function of dynamical variables linked to the collisional transfer of momentum between the infinitively heavy (i.e., immobile) Brownian sphere and the fluid particles.     

Quadratic spline quasi-interpolants on Powell-Sabin partitions

In this paper we address the problem of constructing quasi-interpolants in the space of quadratic Powell-Sabin splines on nonuniform triangulations. Quasi-interpolants of optimal approximation order are proposed and numerical tests are presented. Dedicated to Prof. Mariano Gasca on the occasion of his 60th birthday.     

Lyapunov and Dynamical Spectra for Banach State-spaces

We study the Lyapunov exponents and exponential splittings for continuous linear skew-product flows acting on infinite dimensional Banach state-spaces.     

Linear and circular dichroism detection of magnetic torque on matrix isolated small manganese clusters

Matrix isolated atoms and small manganese clusters have been isolated in krypton matrices at concentrations lower than 10^?3. Absorption and polarized light measurements have been conducted simultaneously on these samples. Defined electronic transitions show distinct circular or linear dichroïsm signals only after the application of an external magnetic field. Clusters belonging to these bands have an axial structure with a plane of symmetry perpendicular to their magnetic moment. On the basis of previous ESR results we are concluding that three of the defined electronic transitions are due to Mn₅ cluster.