Synthesis of new Fe(II) and Ru(II) eta(5)-monocyclopentadienyl compounds showing significant second order NLO properties

A series of new ruthenium(II) complexes of the general formula [Ru(eta(5)-C5H5)(PP)(L)][PF6] (PP = DPPE or 2PPh(3), L = 4-butoxybenzonitrile or N-(3-cyanophenyl)formamide) and the binuclear iron(II) complex [Fe(eta(5)-C5H5)(PP)(mu-L)(PP)(eta(5)-C5H5)Fe][PF6](2) (L = (E)-2-(3-(4-nitrophenyl)allylidene)malononitrile, that has been also newly synthesized) have been prepared and studied to evaluate their potential in the second harmonic generation property. All the new compounds were fully characterized by NMR, IR and UV-Vis spectroscopies and their electrochemistry behaviour was studied by cyclic voltammetry. Quadratic hyperpolarizabilities (beta) of three of the complexes have been determined by hyper-Rayleigh scattering (HRS) measurements at fundamental wavelength of 1500 nm and the calculated static beta(0) values are found to fall in the range 65-212 x 10(-30) esu. Compound presenting beta(0) = 212 x 10(-30) esu has revealed to be 1.2 times more efficient than urea standard in the second harmonic generation (SHG) property, measured in the solid state by Kurtz powder technique, using a Nd:YAG laser (1064 nm). (C) 2013 Elsevier B.V. All rights reserved.

Fractional order describing functions

This paper addresses limit cycles and signal propagation in dynamical systems with backlash. The study follows the describing function (DF) method for approximate analysis of nonlinearities and generalizes it in the perspective of the fractional calculus. The concept of fractional order describing function (FDF) is illustrated and the results for several numerical experiments are analysed. FDF leads to a novel viewpoint for limit cycle signal propagation as time-space waves within system structure.

Quadratic programming versus second order con programming in portfolio optimization

Despite the extensive literature in finding new models to replace the Markowitz model or trying to increase the accuracy of its input estimations, there is less studies about the impact on the results of using different optimization algorithms. This paper aims to add some research to this field by comparing the performance of two optimization algorithms in drawing the Markowitz Efficient Frontier and in real world investment strategies. Second order cone programming is a faster algorithm, appears to be more efficient, but is impossible to assert which algorithm is better. Quadratic Programming often shows superior performance in real investment strategies.

Periodic solutions of second-order differential inclusions systems with p-Laplacian

Some existence results are obtained for periodic solutions of nonautonomous second-order differential inclusions systems with p-Laplacian

Periodic solutions for nonautonomous second order differential inclusions systems with p- Laplacian

Using the nonsmooth variant of minimax point theorems, some existence results are obtained for periodic solutions of nonautonomous second-order differential inclusions systems with p-Laplacian.

On the upper bound of the number of limit cycles obtained by the second order averaging method I

"Vegeu el resum a l'inici del document del fitxer adjunt."

On the upper bound of the number of limit cycles obtained by the second order averaging method II

"Vegeu el resum a l'inici del document del fitxer adjunt."

Second-Order Approximation to the Rotemberg Model around a Distorted Steady State

Less is known about social welfare objectives when it is costly to change prices, as in Rotemberg (1982), compared with Calvo-type models. We derive a quadratic approximate welfare function around a distorted steady state for the costly price adjustment model. We highlight the similarities and differences to the Calvo setup. Both models imply inflation and output stabilization goals. It is explained why the degree of distortion in the economy influences inflation aversion in the Rotemberg framework in a way that differs from the Calvo setup.

Theoretical study of the second-order vibrational Stark effect

The behaviour of the harmonic infrared frequency of diatomic molecules subjected to moderate static uniform electric fields is analysed. The potential energy expression has been developed as a function of a static uniform electric field, which brings about a formulation describing the frequency versus field strength curve. With the help of the first and second derivatives of the expressions obtained, which correspond to the first- and second-order Stark effects, it was possible to find the maxima of the frequency versus field strength curves for a series of molecules using a Newton-Raphson search. A method is proposed which requires only the calculation of a few energy derivatives at a particular value of the field strength. At the same time, the expression for the dependence of the interatomic distance on the electric field strength is derived and the minimum of this curve is found for the same species. Derived expressions and numerical results are discussed and compared with other studi

The curvature of the conical intersection seam: an approximate second-order analysis

We present a method for analyzing the curvature (second derivatives) of the conical intersection hyperline at an optimized critical point. Our method uses the projected Hessians of the degenerate states after elimination of the two branching space coordinates, and is equivalent to a frequency calculation on a single Born-Oppenheimer potential-energy surface. Based on the projected Hessians, we develop an equation for the energy as a function of a set of curvilinear coordinates where the degeneracy is preserved to second order (i.e., the conical intersection hyperline). The curvature of the potential-energy surface in these coordinates is the curvature of the conical intersection hyperline itself, and thus determines whether one has a minimum or saddle point on the hyperline. The equation used to classify optimized conical intersection points depends in a simple way on the first- and second-order degeneracy splittings calculated at these points. As an example, for fulvene, we show that the two optimized conical intersection points of C2v symmetry are saddle points on the intersection hyperline. Accordingly, there are further intersection points of lower energy, and one of C2 symmetry - presented here for the first time - is found to be the global minimum in the intersection space

Second-order Møller-Plesset perturbation theory without basis set superposition error : II : open-shell systems

The basis set superposition error-free second-order MØller-Plesset perturbation theory of intermolecular interactions was studied. The difficulties of the counterpoise (CP) correction in open-shell systems were also discussed. The calculations were performed by a program which was used for testing the new variants of the theory. It was shown that the CP correction for the diabatic surfaces should be preferred to the adiabatic ones

Calibration of stochastic volatility models via second order approximation: the Heston model case

Using a suitable Hull and White type formula we develop a methodology to obtain asecond order approximation to the implied volatility for very short maturities. Using thisapproximation we accurately calibrate the full set of parameters of the Heston model. Oneof the reasons that makes our calibration for short maturities so accurate is that we alsotake into account the term-structure for large maturities. We may say that calibration isnot "memoryless", in the sense that the option's behavior far away from maturity doesinfluence calibration when the option gets close to expiration. Our results provide a wayto perform a quick calibration of a closed-form approximation to vanilla options that canthen be used to price exotic derivatives. The methodology is simple, accurate, fast, andit requires a minimal computational cost.