Strict Monotonicity of Eigenvalues and Unique Continuation

In this paper, we show that the strict mononicity of the eigen-values of an uniformly elliptic operator of second order is equivalent to a unique continuation property.     

Surfaces in {\mathbb{R}^4} with constant principal angles with respect to a plane

We study surfaces in ${\mathbb{R}^4}$ whose tangent spaces have constant principal angles with respect to a plane. Using a PDE we prove the existence of surfaces with arbitrary constant principal angles. The existence of such surfaces turns out to be equivalent to the existence of a special local symplectomorphism of ${\mathbb{R}^2}$ . We classify all surfaces with one principal angle equal to 0 and observe that they can be constructed as the union of normal holonomy tubes. We also classify the complete constant angles surfaces in ${\mathbb{R}^4}$ with respect to a plane. They turn out to be extrinsic products. We characterize which surfaces with constant principal angles are compositions in the sense of Dajczer-Do Carmo. Finally, we classify surfaces with constant principal angles contained in a sphere and those with parallel mean curvature vector field.     

Sequential Monte Carlo Methods for Option Pricing

In this article, we provide a review and development of sequential Monte Carlo (SMC) methods for option pricing. SMC are a class of Monte Carlo-based algorithms, that are designed to approximate expectations w.r.t a sequence of related probability measures. These approaches have been used successfully for a wide class of applications in engineering, statistics, physics, and operations research. SMC methods are highly suited to many option pricing problems and sensitivity/Greek calculations due to the nature of the sequential simulation. However, it is seldom the case that such ideas are explicitly used in the option pricing literature. This article provides an up-to-date review of SMC methods, which are appropriate for option pricing. In addition, it is illustrated how a number of existing approaches for option pricing can be enhanced via SMC. Specifically, when pricing the arithmetic Asian option w.r.t a complex stochastic volatility model, it is shown that SMC methods provide additional strategies to improve estimation.     

Long-Range Lateral Correlation between Self-Assembled Domains of Fluorocarbon-Hydrocarbon Tetrablocks by Quantitative GISAXS

The structure and lateral correlation of fluorocarbon-hydrocarbon tetrablock di(F10Hm) domains at the air/water interface have been determined by quantitative analysis of grazing incidence small-angle X-ray scattering (GISAXS) data. The measured GISAXS signals can be well represented by the full calculation of the form and structure factors. The form factor suggests that di(F10Hm) domains take a hemiellipsoid shape. Both major and minor axes of the hemiellipsoids monotonically increased in response to the elongation of the hydrocarbon blocks, which can be explained by the concominant increase in van der Waals interaction. The structure factor calculated from the GISAXS signals suggests that the domains take an orthorhombic lattice. Remarkably, the lateral correlation can reach over a distance that is more than 14 times longer than the distance to the nearest neighbors. Our data suggest that quantitative GISAXS enables the optimal design of mesoscopic self-assemblies at the air/water interface by fine-tuning of the structures of molecular building blocks.     

Ultrabroadband conical emission generated from the ultraviolet up to the far-infrared during the optical filamentation in air

Ultraviolet and infrared conical emissions were observed during the filamentation in air of powerful femtosecond laser pulses produced by a portable terawatt laser system. The broadband spectrum was measured from 200 nm up to 14 microm and covered the complete optical transmission window of the atmosphere. The angularly resolved spectrum showed some X-wave structure across the frequency range analyzed. However, we demonstrated that the strong conical emission observed in the mid- and far-infrared is mainly owing to the four-wave mixing between the pump pulse and its blueshifted conical emission.     

Onset of itinerant ferromagnetism associated with semiconductor-metal transition in Ti<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>Nb<Subscript>1 − <Emphasis Type="Italic">x</Emphasis></Subscript>CoSn half Heusler solid solution compounds

In this paper, the magnetic and transport properties of the Ti _x Nb_{1 − x} CoSn solid solution compounds with half Heusler cubic MgAgAs-type structure have been studied. This work shows the onset of ferromagnetism associated with a semiconductor to metal transition. The transition occurs directly from ferromagnetic metal to semiconducting state as it is the case in the TiCo _x Ni_{1 − x} Sn series studied previously. A weak quantity of Ti in NbCoSn is suffcient to allow the appearance of ferromagnetic order and metallic state. The variations of the Curie temperature as a function of saturation and effective paramagnetic moments are related to the itinerant ferromagnetism model. A comparison is made with the TiCoSn _x Sb_{1 − x} series (also studied previously), where the transition from TiCoSn ferromagnetic metal to non-magnetic semiconductor TiCoSb occurs through an intermediate metallic Pauli-like state.      

Theory and experiment of large numerical aperture objective Raman microscopy: application to the stress‐tensor determination in strained cubic materials

We present the theory underlying the large numerical aperture objective micro‐Raman backscattering experiment and apply it to the elaboration of a characterization methodology for the determination of the stress tensor in strained cubic semiconductor structures. The presented stress characterization technique consists in monitoring the variations of the stress‐sensitive optical phonon peak position and linewidth while rotating stepwise the sample about its normal. The practical application of the technique is illustrated on a silicon‐on‐insulator (SOI) microelectronic structure demonstrating a plane stress‐tensor determination. Copyright © 2008 John Wiley & Sons, Ltd.     

Small-scale seismic inversion using surface waves extracted from noise cross correlation

Green's functions can be retrieved between receivers from the correlation of ambient seismic noise or with an appropriate set of randomly distributed sources. This principle is demonstrated in small-scale geophysics using noise sources generated by human steps during a 10-min walk in the alignment of a 14-m-long accelerometer line array. The time-domain correlation of the records yields two surface wave modes extracted from the Green's function between each pair of accelerometers. A frequency-wave-number Fourier analysis yields each mode contribution and their dispersion curve. These dispersion curves are then inverted to provide the one-dimensional shear velocity of the near surface.     

Rational Topological Design for Fluorescence Enhancement upon Aggregation of Distyrylfuran Derivatives

A series of 2,5‐distyrylfuran derivatives bearing pentafluorophenyl‐ and cyanovinyl units have been synthesized for aggregation‐induced emission (AIE). The effect of the type and extent of the supramolecular connections on the AIE of the furan derivatives were examined and correlated with their X‐ray crystal structures. It was found that the simultaneous presence of cyano and perfluorophenyl units strongly enhances the fluorescence upon aggregation. Single‐crystal X‐ray diffraction analysis confirmed that C?H???F, F???F, C?H???nitrile, Ar???Ar_F (Ar=aryl, Ar_F=fluoroaryl), and nitrile???Ar_F intra‐ and intermolecular interactions drive the topology of the molecule and that solid‐state supramolecular contacts favor AIE of the furan derivatives.     

Some Expressions of a Generalized Version of the Expected Time in the Red and the Expected Area in Red

Methodology and Computing in Applied Probability - In this paper, we study a generalized version of the expected time in the red and the expected area in red introduced in Loisel (2005). We derive...