Sonoelectrochemical hydrogenation of safrole: A reactor design,statistical analysis and computational fluid dynamic approach

In this work, ultrasound-assisted electrocatalytic hydrogenation (US-ECHSA) of safrole was carried out in water medium, using sacrificial anode of nickel. The ultrasonic irradiation was carried out at frequency of 20 kHz ± 500 Hz with a titanium cylindrical horn (MS 73 microtip; Ti-6AI-4V alloy; 3.0 mm diameter). The optimal conditions were analyzed by statistical experimental design (fractional factorial). The influence of the sonoelectrochemical reactor design was also investigated by using computational fluid dynamics as simulation tool. Among the five parameters studied: catalyst type, use of β-cyclodextrin as inverse phase transfer catalyst, sonoelectrochemical reactor design, ultrasound mode and the temperature of the solution, only the last three were significant. The hydrogenation product, dihydrosafrole, reached 94% yield, depending on the experimental conditions applied. Data of computational fluid dynamics showed that a wing shape tube added to the sonoelectrochemical reactor can work as a cooling apparatus, during the electrochemical process. The reactional solution temperature diminishes 14 °C when compared to the four-way-type reactor. Cooper cathode, absence of β-cyclodextrin, four-way-type reactor, ultrasound continuous mode (14 W) and absence of temperature control were the most effective reaction parameters for the safrole hydrogenation using US-ECHSA method. The proposed approach represents an important contribution for understanding the hydrodynamic behavior of sonoelectrochemical reactors designs and, consequently, for the reducing of the experimental costs inherent to the sonoelectrochemical process.     

Convergence of solutions for the fractional Cahn–Hilliard system

This paper deals with the Cauchy–Dirichlet problem for the fractional Cahn–Hilliard equation. The main results consist of global (in time) existence of weak solutions, characterization of parabolic smoothing effects (implying under proper condition eventual boundedness of trajectories), and convergence of each solution to a (single) equilibrium. In particular, to prove the convergence result, a variant of the so-called ?ojasiewicz–Simon inequality is provided for the fractional Dirichlet Laplacian and (possibly) non-analytic (but $C^1$) nonlinearities.     

Asymptotic expansion for vector-valued sequences of random variables with focus on Wiener chaos

We develop the asymptotic expansion theory for vector-valued sequences ${\left(F_N\right)}_{N\ge 1}$ of random variables in terms of the convergence of the Stein–Malliavin matrix associated with the sequence $F_N$. Our approach combines the classical Fourier approach and the recent Stein–Malliavin theory. We find the second order term of the asymptotic expansion of the density of $F_N$ and we illustrate our results by several examples.     

Representations for conditional expectations and applications to pricing and hedging of financial products in Lévy and jump-diffusion setting

In this article, we derive expressions for conditional expectations in terms of regular expectations without conditioning but involving some weights. For this purpose, we apply two approaches: the conditional density method and the Malliavin method. We use these expressions for the numerical estimation of the price of American options and their deltas in a Lévy and jump-diffusion setting. Several examples of applications to financial and energy markets are given including numerical examples.     

Multiplicity results of nonlinear fractional magnetic Schrödinger equation with steep potential

In this article, we prove the existence and multiplicity of non-trivial solutions for an indefinite fractional elliptic equation with magnetic field and concave–convex nonlinearities. Our multiplicity results are based on studying the decomposition of the Nehari manifold.     

Model selection based on Lorenz and concentration curves,Gini indices and convex order

In order to determine an appropriate amount of premium, statistical goodness-of-fit criteria must be supplemented with actuarial ones when assessing performance of a given candidate pure premium. In this paper, concentration curves and Lorenz curves are shown to provide actuaries with effective tools to evaluate whether a premium is appropriate or to compare two competing alternatives. The idea is to compare the premium income for sub-portfolios gathering low risks (identified as low by means of the premiums under consideration) to the true one, or equivalently, to the actual losses. Numerical illustrations performed on hypothetical data and real ones demonstrate the usefulness of the proposed approach.     

Statistical inference for Vasicek-type model driven by Hermite processes

Let $Z$ denote a Hermite process of order $q\ge 1$ and self-similarity parameter $H\in (\frac{1}{2},1)$. This process is $H$-self-similar, has stationary increments and exhibits long-range dependence. When $q=1$, it corresponds to the fractional Brownian motion, whereas it is not Gaussian as soon as $q?2$. In this paper, we deal with a Vasicek-type model driven by $Z$, of the form $d{X}_t=a(b?X_t)dt+d{Z}_t$. Here, $a>0$ and $b\in \mathbb{R}$ are considered as unknown drift parameters. We provide estimators for $a$ and $b$ based on continuous-time observations. For all possible values of $H$ and $q$, we prove strong consistency and we analyze the asymptotic fluctuations.