L 2 -discrete hedging in a continuous-time model

In the setting of the Black-Scholes option pricing market model, the seller of a European option must trade continuously in time. This is, of course, unrealistic from the practical viewpoint. He must then follow a discrete trading strategy. However, it does not seem natural to hedge at deterministic times regardless of moves of the spot price. In this paper, it is supposed that the hedger trades at a fixed number N of rebalancing (stopping) times. The problem (P^N) of selecting the optimal hedging times and ratios which allow one to minimize the variance of replication error is considered. For given N rebalancing, the discrete optimal hedging strategy is identified for this criterion. The problem (P^N) is then transformed into a multidimensional optimal stopping problem with boundary constraints. The restrictive problem (P^N _BS) of selecting the optimal rebalancing for the same criterion is also considered when the ratios are given by Black-Scholes. Using the vector-valued optimal stopping theory, the existence is shown of an optimal sequence of rebalancing for each one of the problems (P^N) and (P^N _BS). It also shown BS that they are asymptotically equivalent when the number of rebalances becomes large and an optimality criterion is stated for the problem (P^N). The same study is made when more realistic restrictions are imposed on the hedging times. In the special case of two rebalances, the problem (P² _BS) is solved and the problems (P² _BS) and (P²) are transformed into two optimal stopping problems. This transformation is useful for numerical purposes.     

Enantiopure Sulfinyl Aniline as a Removable and Recyclable Chiral Auxiliary for Asymmetric C(sp3)−H Bond Activation

An original and recyclable chiral bidentate aniline‐sulfoxide‐based directing group has been developed. This auxiliary allows challenging stereoselective Pd‐catalyzed direct functionalization of small cycloalkanes through C–aryl and C–alkyl bond formation. Although moderate diastereoselectivities are observed, both optically pure enantiomers of the highly functionalized products can be obtained separately by simple silica gel chromatography and cleavage of the chiral auxiliary. This strategy was further applied to the preparation of enantiomerically pure 1,2,3‐trisubstituted cyclopropane carboxylic acid derivatives, with three stereogenic centers and bearing both alkyl and aromatic substituents. These molecular scaffolds are not yet reported in the literature. The synthetic utility of this approach is validated by the chiral auxiliary being readily cleaved and recovered posteriori to the C?H activation step, without deterioration of its optical purity. Finally, an unprecedented palladacycle intermediate generated through C?H activation of the cyclopropane moiety has been isolated and fully characterized. Initial DFT calculations shed additional light on the reactivity of this original intermediate.     

Small perturbations of an interface for elastostatic problems

We consider the Lamé system for an elastic medium consisting of an inclusion embedded in a homogeneous background medium. Based on the field expansion method and layer potential techniques, we rigorously derived the asymptotic expansion of the perturbed displacement field because of small perturbations in the interface of the inclusion. We extend these techniques to determine a relationship between traction‐displacement measurements and the shape of the object and derive an asymptotic expansion for the perturbation in the elastic moment tensors because of the presence of small changes in the interface of the inclusion. Copyright © 2016 John Wiley & Sons, Ltd.     

Suppression of pull-in in a microstructure actuated by mechanical shocks and electrostatic forces

This work investigates the effect of a high-frequency voltage (HFV) on the pull-in instability in a microstructure actuated by mechanical shocks and electrostatic forces. The microstructure is modelled as a single-degree-of-freedom mass-spring-damper system. The method of direct partition of motion is used to split the fast and slow dynamics. Analysis of steady-state solutions of the slow dynamic allows the investigation of the influence of the HFV on the pull-in. The results show that adding HFV rigidifies the system, creates new stable equilibria and suppresses the pull-in instability for adequate high-frequency voltages. To illustrate the applicability of the result, a specific capacitive microelectromechanical system consisting of a clamped-clamped microbeam is considered.     

Application of the lattice Boltzmann method to transient conduction and radiation heat transfer in cylindrical media

In this paper, the lattice Boltzmann method (LBM) is applied to solve the energy equation of a transient conduction-radiation heat transfer problem in a two-dimensional cylindrical enclosure filled with an emitting, absorbing and scattering media. The control volume finite element method (CVFEM) is used to obtain the radiative information. To demonstrate the workability of the LBM in conjunction with the CVFEM to conduction-radiation problems in cylindrical media, the energy equation of the same problem is also solved using the finite difference method (FDM). The effects of different parameters, such as the grid size, the scattering albedo, the extinction coefficient and the conduction-radiation parameter on temperature distribution within the medium are studied. Results of the present work are compared with those available in the literature. LBM-CVFEM results are also compared with those given by the FDM-CVFEM. In all cases, good agreement has been obtained.     

Splitting of resonant and scattering frequencies under shape deformation

It is well known that the main difficulty in solving eigenvalue problems under shape deformation relates to the continuation of multiple eigenvalues of the unperturbed configuration. These eigenvalues may evolve, under shape deformation, as separated, distinct eigenvalues, and the splitting may only become apparent at high orders in their Taylor expansion. In this paper, we address the splitting problem in the evaluation of resonant and scattering frequencies of the two-dimensional Laplacian operator under boundary variations of the domain. By using surface potentials we show that the eigenvalues are the characteristic values of meromorphic operator-valued functions that are of Fredholm type with index 0. We then proceed from the generalized Rouché's theorem to investigate the splitting problem.     

Reynolds stress and vorticity in turbulent wall flows

Experimental measurements in a boundary layer and a large-eddy simulation of plane channel flow have been used to study the dynamics of vorticity and mass transport in the nearwall region. It was found that Reynolds stress generation occurs in the vicinity of quasi-streamwise vortices, and that smoke particles tend to be ejected from the wall near these vortical structures.     

Homoclinic Connections in Strongly Self-Excited Nonlinear Oscillators: The Melnikov Function and the Elliptic Lindstedt–Poincaré Method

A criterion to predict bifurcation of homoclinic orbits instrongly nonlinear self-excited one-degree-of-freedom oscillator

Impedance spectroscopy study of Pb<Subscript>2</Subscript>P<Subscript>2</Subscript>O<Subscript>7</Subscript> compound

The lead pyrophosphate, Pb₂P₂O₇, compound was prepared by conventional solid-state reaction and identified by X-ray powder diffractometer. Pb₂P₂O₇ has a triclinic structure whose electrical properties were studied using impedance spectroscopy technique. Both impedance and modulus analysis exhibit the grain and grain boundary contribution to the electrical response of the sample. The temperature dependence of the bulk and grain boundary conductivity were found to obey the Arrhenius law with activation energies E _g = 0.66 eV and E _gb = 0.67 eV, respectively. The scaling behavior of the imaginary part of the complex impedance suggests that the relaxation describes the same mechanism at various temperatures.