Lipschitz continuity and duality for dynamic oligopolistic market equilibrium problem with memory term

We are concerned with an infinite dimensional variational inequality which is connected with the dynamic oligopolistic market equilibrium problem. We will provide existence theorems and show, under minimal assumptions on the data, the Lipschitz continuity of the solution. Moreover a general duality theory is provided overcoming the difficulty of the voidness of the interior of the ordering cone which defines the cone constraints.     

Sub-wavelength probing and modification of photonic crystal nano-cavities

In this work we present a sizeable and reversible spectral tuning of the resonances of a two-dimensional photonic crystal nano-cavity by exploiting the introduction of a sub-wavelength size glass tip. The comparison between experimental near-field data and results of numerical calculations shows that the spectral shift induced by the tip is proportional to the local electric field intensity of the cavity mode. This observation proves that the electromagnetic local density of states in a microcavity can be directly measured by mapping the tip-induced spectral shift with a scanning near-field optical microscope. Moreover, a non-linear control on the cavity resonance is obtained by exploiting the local heating induced by near-field laser excitation at different excitation powers. The temperature gradient due to the optical absorption results in an index of refraction gradient which modifies the dielectric surroundings of the cavity and shifts the optical modes.     

The normal approximation rate for the drift estimator of multidimensional diffusions

We consider the problem of the density and drift estimation by the observation of a trajectory of an \mathbbR^d{\mathbb{R}^{d}}-dimensional homogeneous diffusion process with a unique invariant density. We construct estimators of the kernel type based on discretely sampled observations and study their asymptotic distribution. An estimate of the rate of normal approximation is given.     

Assessing the cost of capital for longevity risk

The cost of capital is a key element of the embedded value methodology for the valuation of a life business. Further, under some solvency approaches (in particular, the Swiss Solvency Test and the developing Solvency 2 project) assessing the cost of capital constitutes a step in determining the required capital allocation.Whilst the cost of capital is usually meant as a reward for the risks encumbering a given life portfolio, in actuarial practice the relevant parameter has been traditionally chosen, at least to some extent, inconsistently with such risks. The adoption of market-consistent valuations has then been advocated to reach a common standard.A market-consistent value usually acknowledges a reward to shareholders’ capital as long as the market does, namely if the risk is systematic or undiversifiable. When dealing with a life annuity portfolio (or a pension plan), an important example of systematic risk is provided by the longevity risk, i.e. the risk of systematic deviations from the forecasted mortality trend. Hence, a market-consistent approach should provide appropriate valuation tools.In this paper we refer to a portfolio of immediate life annuities and we focus on longevity risk. Our purpose is to design a framework for a valuation of the portfolio which is market-consistent, and therefore based on a risk-neutral argument, while involving some of the basic items of a traditional valuation, viz best estimate future flows and allocated capital. This way, we try to reconcile the traditional with a market-consistent (or risk-neutral) approach. This allows us, in particular, to translate the results obtained under the risk-neutral approach in terms of a properly redefined embedded value.     

Click chemistry on a ruthenium polypyridine complex. An efficient and versatile synthetic route for the synthesis of photoactive modular assemblies

In this Communication, we present the synthesis and use of [Ru(bpy)(2)(bpy-CCH)](2+), a versatile synthon for the construction of more sophisticated dyads by means of click chemistry. The resulting chromophore-acceptor or -donor complexes have been studied by flash photolysis and are shown to undergo efficient electron transfer to/from the chromophore. Additionally, the photophysical and chemical properties of the original chromophore remain intact, making it a very useful component for the preparation of visible-light-active dyads.     

New enantioselective entry to cycloheptane amino acid polyols

[reaction: see text] A diversity-oriented protocol has been developed for the assembly of densely hydroxylated cycloheptane amino acids via succession of a vinylogous Mukaiyama aldol reaction (VMAR), a Morita-Baylis-Hillman reaction (MBHR), and an intramolecular pinacol coupling reaction (IPCR). The plan utilizes D- or L-configured glyceraldehyde derivatives as "chiral" surrogates of glyoxal and N-[(tert-butoxycarbonyl)-2-(tert-butyldimethylsilyl)oxy]pyrrole as the synthetic equivalent of the alpha,gamma-dianion of gamma-aminobutanoic acid. The parallel, asymmetric syntheses of four cycloheptane representatives proceed with high diastereocontrol and virtually complete enantioselectivity in ten steps and overall yields of 15-37%.     

Inner cladding influence on mode interaction in symmetry-free photonic crystal fibers under heat load

A further output power scaling of Yb-doped double-cladding photonic crystal fiber lasers, required for practical applications in many industrial fields, is currently prevented by thermal effects, which significantly worsen the beam quality. In this work the mode interaction and, consequently, the single-mode regime of Yb-doped air-silica symmetry-free photonic crystal fibers have been numerically investigated in different heat load conditions using simulation tools based on the finite element method. The effect of the main inner cladding geometric parameters, in particular of the inner cladding dimension, on the guided-mode delocalization has been analyzed, with the aim to identify a design of the large mode area active fiber providing single-mode operation despite the presence of thermal effects. Simulation results have demonstrated that the inner cladding enlargement causes a stronger coupling between core-guided and cladding modes, as well as an increase of the differential overlap between fundamental and first higher-order mode for moderate heat load values. However, the inner cladding influence becomes less important under severe heat load, being the fiber behaviour mainly affected by the thermally-induced refractive index change in the doped core.     

Synthesis of Weinreb amides via Pd-catalyzed aminocarbonylation of heterocyclic-derived triflates

The direct transformation of lactam-, lactone-, and thiolactone-derived triflates into N-methoxy-N-methyl or morpholine Weinreb amides has been realized using Pd-catalyzed aminocarbonylation under CO atmospheric pressure and at room temperature. The carbonylative coupling can be efficiently carried out with 2% of catalyst in the presence of Xantphos as a ligand. The amides smoothly react with nucleophiles to afford acylated aza-, oxa-, and thio-heterocycles. The proposed methodology could be advantageously exploited for the synthesis of dienones in which one of the double bonds is embedded in a heterocyclic moiety, as useful substrates for Nazarov cyclization.