Stochastic Heat and Wave Equations on a Lie Group

We study nonlinear heat and wave equations on a Lie group. The noise is assumed to be a spatially homogeneous Wiener process. We give necessary and sufficient conditions for the existence of a function-valued solution in terms of the covariance kernel of the noise.     

Study and modelling of two apple quality attributes: the soluble solids content and the firmness

Recently, the basic dynamics of fruit characteristics have been modelled using a stochastic approach. The time evolution of apple quality attributes was represented by means of a system of differential equations in which the initial conditions and model parameters are both random. In this work, a complete study of two apple quality attributes, the soluble solids content and the firmness, is carried out. For each of these characteristics, the system of differential equations is linear and the state variables and the parameters are represented as random variables with their statistical properties (mean values, variances, covariances, joint probability density function) known at the initial time. The dynamic behaviour of these statistical properties is analysed. The variance propagation algorithm is used to obtain an analytical expression of the dynamic behaviour of the mean value, the variance, the covariance and the probability density function. A Monte Carlo method and the Latin hypercube method were developed to obtain a numerical expression of the dynamic behaviour of these statistical quantities and particularly to follow the time evolution of joint probability density function which represents one but the best mean to characterize random phenomena linked with fruit quality attributes.     

Effect of Medium Acidity and Photostability of 3‐(4‐Dimethylamino‐phenyl)‐1‐(2,5‐dimethyl‐thiophen‐3‐yl)‐propenone (DDTP): A New Green Emitting Laser Dye

On the line of a previous work on the spectral properties of some of heteroaryl chalcone, the effect of medium acidity and photoreactivity of 3‐(4‐dimethylamino‐phenyl)‐1‐(2,5‐dimethyl‐thiophen‐3‐yl)‐propenone (DDTP) has been investigated in dimethylformamide and in chloromethane solvents such as methylenechloride, chloroform and carbon tetrachloride. The dye solution (ca. 5×10⁻⁴ mol·L⁻¹ in DMF) gives a good laser emission in the range 470–560 nm with emission maximum at 515 nm upon pumping by nitrogen laser (λ_ex=337.1 nm). The laser parameters such as gain coefficient (α), emission cross section (δ_e) and half life energy (E_1/2) at maximum laser emission are also determined.     

Formation mechanisms of gold-zinc oxide hexagonal nanopyramids by heterogeneous nucleation using microwave synthesis

This work reports the development of a fast and simple "one-pot" route for the synthesis of hybrid Au-ZnO hexagonal nanopyramids by sequential homogeneous-heterogeneous nucleation steps involving both Au and Zn ions using microwave irradiation (MWI). The rapid decomposition of zinc acetate by MWI in the presence of a mixture of oleic acid (OAc) and oleylamine (OAm) results in the formation of hexagonal ZnO nanopyramids. In the presence of Au ions, the initially formed Au nanocrystals act as heterogeneous nuclei for the nucleation and growth of the ZnO nanopyramids. The Au nanoparticles promote the heterogeneous nucleation of ZnO and the formation of the hexagonal base of the ZnO nanopyramids. Using preformed Au nanoparticles instead of Au ions results in a narrow size distribution of uniform Au-ZnO nanopyramids, each consisting of a gold nanoparticle embedded in the center of the hexagonal base of the ZnO nanopyramid. We study the factors that control the nucleation and growth of these complex structures, and provide new insights into the stepwise homogeneous-heterogeneous mechanism and the conventional heterogeneous nucleation on preformed Au nanoparticles. The formation of the hetero nanostructures Au-ZnO nanopyramids is strongly dependent on the molar ratios of OAc to OAm. The presence of OAc with a considerable dipole moment results in strong electrostatic interaction with the polar surfaces of the growing ZnO nanocrystals thus resulting in slowing the growth rate of the polar planes and allowing the formation of well-developed facets. In the absence of Au nanoparticles, a high concentration of zinc acetate and longer MWI times are required for the production of the nanopyramids. The gold nanoparticles could provide the metallic contact points within the hybrid nanopyramids which could facilitate the bottom-up assembly of Au-ZnO devices. Furthermore, the Au-ZnO nanopyramids could have improved performance in solar energy conversion and photocatalysis.     

Inclusion of Paracetamol into β-cyclodextrin nanocavities in solution and in the solid state

We report on steady-state UV-visible absorption and emission characteristics of Paracetamol, drug used as antipyretic agent, in water and within cyclodextrins (CDs): β-CD, 2-hydroxypropyl-β-CD (HP-β-CD) and 2,6-dimethyl-β-CD (Me-β-CD). The results reveal that Paracetamol forms a 1:1 inclusion complex with CD. Upon encapsulation, the emission intensity enhances, indicating a confinement effect of the nanocages on the photophysical behavior of the drug. Due to its methyl groups, the Me-β-CD shows the largest effect for the drug. The observed binding constant showing the following trend: Me-β-CD>HP-β-CD>β-CD. The less complexing effectiveness of HP-β-CD is due to the steric effect of the hydroxypropyl-substituents, which can hamper the inclusion of the guest molecules. The solid state inclusion complex was prepared by co-precipitation method and its characterization was investigated by Fourier transform infrared spectroscopy, 1H NMR and X-ray diffractometry. These approaches indicated that Paracetamol was able to form an inclusion complex with CDs, and the inclusion compounds exhibited different spectroscopic features and properties from Paracetamol.     

The complexation of a novel squaric bis(thiosemicarbazone); 3,4-bis{[(aminothioxomethyl)amino]azamethylene}cyclobut-ene-1,2-diol

A novel chelating agent (Sqtsc; H(4)L) bearing both hard and soft donor atoms was synthesized by the condensation of squaric acid with thiosemicarbazide. The ligand has two symmetrical sets of donor atoms (SNO), therefore, it was allowed to react with the metal ions at the mole ratio 2:1 (M:L). Mono- and bi-nuclear chelates were obtained in which the ligand showed a variety of modes of bonding viz. (OO)(2-), (SNNS)(2-) and (SNO)(2-) per each metal ion supporting the ambidentate and flexidentate characters of the ligand. The mode of bonding and basicity of the ligand depend mainly on the type of the metal cation and its counter anion. All the obtained complexes have the preferable O(h)-geometry except the VO(II)-complex (7) which has also the preferable square pyramid geometry. Structural elucidation was achieved via elemental and spectral data.     

Explicit mapping of acoustic regimes for wind instruments

This paper proposes a methodology to map the various acoustic regimes of wind instruments. The maps can be generated in a multidimensional space consisting of design, control parameters, and initial conditions. The boundaries of the maps are obtained explicitly in terms of the parameters using a Support Vector Machine (SVM) classifier as well as a dedicated adaptive sampling scheme. The approach is demonstrated on a simplified clarinet model for which several maps are generated based on different criteria. Examples of computation of the probability of occurrence of a specific acoustic regime are also provided. In addition, the approach is demonstrated on a design optimization example for optimal intonation.     

Approximation of stationary solutions to SDEs driven by multiplicative fractional noise

In a previous paper, we studied the ergodic properties of an Euler scheme of a stochastic differential equation with a Gaussian additive noise in order to approximate the stationary regime of such an equation. We now consider the case of multiplicative noise when the Gaussian process is a fractional Brownian motion with Hurst parameter H>1/2$H>1/2$ and obtain some (functional) convergence properties of some empirical measures of the Euler scheme to the stationary solutions of such SDEs.