Saddlepoint Approximations to the Probability of Ruin in Finite Time for the Compound Poisson Risk Process Perturbed by Diffusion

A large deviations type approximation to the probability of ruin within a finite time for the compound Poisson risk process perturbed by diffusion is derived. This approximation is based on the saddlepoint method and generalizes the approximation for the non-perturbed risk process by Barndorff-Nielsen and Schmidli (Scand Actuar J 1995(2):169–186, 1995). An importance sampling approximation to this probability of ruin is also provided. Numerical illustrations assess the accuracy of the saddlepoint approximation using importance sampling as a benchmark. The relative deviations between saddlepoint approximation and importance sampling are very small, even for extremely small probabilities of ruin. The saddlepoint approximation is however substantially faster to compute.     

A unifying approach to solve a class of rank-three programs involving linear and quadratic functions

The aim of this paper is two-fold. First, the so-called ‘optimal level solutions’ method is described in a new unifying framework with the aim to provide an algorithmic scheme able to approach various different classes of problems. Then, the ‘optimal level solutions’ method is used to solve a class of low-rank programmes involving linear and quadratic functions and having a polyhedral feasible region. In particular, the considered class of programmes covers, among all, rank-three d.c., multiplicative and fractional programmes. Some optimality conditions are used to improve the performance of the proposed algorithm.     

A variational model for fracture mechanics: Numerical experiments

In the variational model for brittle fracture proposed in Francfort and Marigo [1998. Revisiting brittle fracture as an energy minimization problem. J. Mech. Phys. Solids 46, 1319-1342], the minimum problem is formulated as a free discontinuity problem for the energy functional of a linear elastic body. A family of approximating regularized problems is then defined, each of which can be solved numerically by a finite element procedure. Here we re-formulate the minimum problem within the context of finite elasticity. The main change is the introduction of the dependence of the strain energy density on the determinant of the deformation gradient. This change requires new, more general existence and Γ-convergence results. The results of some two-dimensional numerical simulations are presented, and compared with corresponding simulations made in Bourdin et al. [2000. Numerical experiments in revisited brittle fracture. J. Mech. Phys. Solids 48, 797-826] for the linear elastic model.     

Theoretical and experimental determination of the aerodynamic characteristics of a helicopter rotor

Summary A fairly simple theory which can determine the aerodynamic characteristics of a freely hinged rotor in any condition of forward flight is discussed in the present work.Theoretical results are compared with NASA experimental data and with data from tests on a helicopter model in the wind tunnel of Istituto di Meccanica Applicata alle Macchine, Aerodinamica e Gasdinamica (Politecnico of Torino).The agreement between theoretical and experimental results is well suited for practical purpose.

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Sommario Nella nota viene presentata una teoria relativamente semplice per la determinazione delle caratteristiche aerodinamiche di un rotore di elicottero completamente incernierato o basculante nelle condizioni di volo in avanti a regime. I risultati numerici vengono confrontati con dati sperimentali ottenuti dalla NASA e con misure sperimentali effettuate su di un modello di elicottero nella galleria del vento dell'Istituto di Meccanica Applicata alle Macchine, Aerodinamica e Gasdinamica (Politecnico di Torino).L'accordo tra i risultati teorici e i risultati sperimentali è giudicato valido nelle applicazioni pratiche.

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Research supported by the National Research Council (C.N.R.) of Italy.     

Zoology of condensed matter: framids,ordinary stuff,extra-ordinary stuff

Journal of High Energy Physics - We discuss some properties of recently proposed models of a ghost-free gravity. For this purpose we study solutions of linearized gravitational equations in the...     

New poly(phenylenevinylene)‐methyl methacrylate‐based photonic crystals

Monodisperse colloids have been prepared efficiently by copolymerization of methyl methacrylate and fluorescent first‐ and second‐generation poly(phenylenevinylene) dendrons under surfactant‐free emulsion polymerization conditions. The copolymers were characterized by UV–vis and fluorescence spectroscopy and size exclusion chromatography. Transmission electron microscopy revealed that the copolymers were microspheres with smooth surfaces and narrow dispersity. The bead diameter could be varied by changing the monomer/water ratio. The materials could be crystallized to give polymer opal photonic crystals. The emission was not affected by the periodic structure because of the large spectral distance between the emission and the pseudogap position. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 2659–2665, 2010     

Notes on a paper of Mess

These notes are a companion to the preceding paper by Geoffrey Mess, “Lorentz spacetimes of constant curvature”. Mess’ paper was written nearly 20 years ago and so we hope these notes will be useful as a guide to the literature that has appeared in the intervening years. Lars Andersson was supported in part by the NSF, contract no. DMS 0407732 and Thierry Barbot was supported by CNRS, ACI “Structures géométriques et Trous Noirs”.     

Principal parts bundles on projective spaces and quiver representations

We study the principal parts bundles \(\mathcal {P}^{k}\mathcal {O}_{\mathbb {P}^{n}}(d)\) as homogeneous bundles and we describe their associated quiver representations. With this technique we show that if n≥2 and 0≤d<k then there exists an invariant decomposition \(\mathcal {P}^{k}\mathcal {O}_{\mathbb {P}^{n}}(d)=Q_{k,d}\oplus(S^{d}V\otimes \mathcal {O}_{\mathbb {P}^{n}})\) with Q _k,d a stable homogeneous vector bundle. The decomposition properties of such bundles were previously known only for n=1 or k≤d or d<0. Moreover we show that the Taylor truncation maps \(H^{0}\mathcal {P}^{k}\mathcal {O}_{\mathbb {P}^{n}}(d)\to H^{0}\mathcal {P}^{h}\mathcal {O}_{\mathbb {P}^{n}}(d)\), defined for any h≤k and any d, have maximal rank.     

Acid mediated tunability of stimulated laser emission from dye doped chiral microdroplets

Abstract

In the last decade, the possibility to use liquid crystal droplets as optical micro-cavities and lasers has attracted much attention since it paves the way for many applications in the field of sensors or tunable photonics. Several techniques can be used to obtain small micro-resonators as, for example, dispersing a cholesteric liquid crystal inside an immiscible isotropic fluid to create an emulsion. Since liquid crystals are extremely sensitive to external factors as temperature or external fields, laser tuning can be easily achieved. Here, we report on the possibility to tune the laser emission from dye doped cholesteric liquid crystals microdroplets dispersed in a glycerol matrix in presence of nitric acid molecules in the emulsion. Using a fluorescent dye with pH dependent optical properties, the emitted laser wavelength can be tuned in a range of 60?nm. This effect could find applications for the development of spectroscopy based sensors.