On the Spectrum of the Poincaré Variational Problem for Two Close-to-Touching Inclusions in 2D

We study the spectrum of the Poincaré variational problem for two close to touching inclusions in R ². We derive the asymptotics of its eigenvalues as the distance between the inclusions tends to zero.     

Stochastic multi-site supply chain planning in textile and apparel industry under demand and price uncertainties with risk aversion

A multi-product, multi-period, multi-site supply chain production and transportation planning problem, in the textile and apparel industry, under demand and price uncertainties is considered in this paper. The problem is formulated using a two-stage stochastic programming model taking into account the production amount, the inventory and backorder levels as well as the amounts of products to be transported between the different plants and customers in each period. Risk management is addressed by incorporating a risk measure into the stochastic programming model as a second objective function, which leads to a multi-objective optimization model. The objectives aim to simultaneously maximize the expected net profit and minimize the financial risk measured. Two risk measures are compared: the conditional-value-at-risk and the downside risk. As the considered objective functions conflict with each other’s, the problem solution is a front of Pareto optimal robust alternatives, which represents the trade-off among the different objective functions. A case study using real data from textile and apparel industry in Tunisia is presented to illustrate the effectiveness of the proposed model and the robustness of the obtained solutions.     

ERROR ESTIMATES FOR THE RECURSIVE LINEARIZATION OF INVERSE MEDIUM PROBLEMS

This paper is devoted to the mathematical analysis of a general recursive linearization algorithm for solving inverse medium problems with multi-frequency measurements. Under some reasonable assumptions, it is shown that the algorithm is convergent with error estimates. The work is motivated by our effort to analyze recent significant numerical results for solving inverse medium problems. Based on the uncertainty principle, the recursive linearization allows the nonlinear inverse problems to be reduced to a set of linear problems and be solved recursively in a proper order according to the measurements. As an application, the convergence of the recursive linearization algorithm [Chen, Inverse Problems 13（1997）, pp.253-282] is established for solving the acoustic inverse scattering problem.     

Three-Period Quasi-Periodic Solutions in the Self-Excited Quasi-Periodic Mathieu Oscillator

In this work, we investigate three-period quasi-periodic (QP) oscillations in the vicinity of 2:2:1 resonance in a self-excited QP Mathieu equation using perturbation method. Two successive averaging are performed to reduce the original QP equation to an autonomous amplitude and phase system describing the modulation of the slow flow dynamic. Approximation of three-period QP solution is obtained via the study of limit cycle of the reduced autonomous system. The efficiency of the method is illustrated by comparison between analytical approximations and numerical integration. The double reduction procedure, applied in previous works to construct two-period QP solution, can be implemented to approximate excplicit analytical three-period QP solutions.     

Synthesis and characterization of new hexahelicene derivatives

The synthesis and structural characterization of a new hexahelicene derivative 2 is reported. This compound features a new type of structure bearing a bromine atom and a methoxy group. Suitable crystals of the latter indicate that its conformation closely resembles that of the unsubstituted [6]helicene, whose idealized symmetry is C2. This 3-bromo-14-methoxyhexahelicene was subjected to lithiation/phosphinilation and yielded the new 3-methoxy-14-(diphenylphosphino)hexahelicene 3.     

Characterizations of Six Pomegranate (Punica granatum L.) Varieties of Global Commercial Interest in Morocco: Pomological,Organoleptic, Chemical and Biochemical Studies

Pomegranate variety properties are important not only to demonstrate their diversity but also to satisfy the current market need for high-quality fruits. This study aims to characterize pomological and physico-chemical features as well as the antioxidant capacity of Moroccan local cultivars (Djeibi, Mersi, Sefri 1 and Sefri 2) compared to the imported ones (Mollar de Elche and Hicaz). The pomological characteristics of varieties were relatively diverse. The juice varieties (PJ) displayed a marketed variability in organoleptic and quality properties, such as the flavor, juice yield, and micro/macronutrients contents. Interrelationships among the analyzed properties and PJ varieties were investigated by principal component analysis (PCA). Dimension of the data set was reduced to two components by PCA accounting for 64.53% of the variability observed. The rinds varieties (PR) were studied for their total phenolics, flavonoids, and condensed tannins quantifications. PR varieties extracts exhibited different levels of free radical scavenging activity and local varieties revealed a greater potential with stability over time. The HPLC-DAD analyses of PR extracts revealed (+) catechin as the major compound, where the highest content was found for the local varieties. The SEC analysis showed the molecular weight distribution of phenolic compounds with a high size of condensed tannins formed by the polymerization of the catechin monomer. Given these properties, this research provides an easy selection of high-quality fruits as potential candidates for local market needs.     

Physicochemical Properties and Functional Characteristics of Ecologically Extracted Shrimp Chitosans with Different Organic Acids during Demineralization Step

The current study aims to develop eco-friendly and economical chitosans with a wide range of applications using organic acids for shrimp shells demineralization. Chitosan samples were extracted from shrimp (Parapenaeus longirostris) shells and the demineralization step was performed with three organic acids (citric, acetic, and lactic) and two mineral acids (hydrochloric and sulfuric). The chitosans were characterized by Fourier transform infrared (FTIR) spectroscopy, X-ray diffraction (XRD), and scanning electron microscopy (SEM). The chitosans’ physicochemical properties were also determined. The characteristic bands and functional groups of the chitosans were identified by FTIR spectra. The chitosans’ crystallinity order was as follows: Ch_HCl > Ch_Citric > Ch_H2SO4 > Ch_Lactic > Ch_Acetic. The chitosans’ morphological characteristics revealed a smooth surface and fibrous structures with pores. Chitosans extracted by organic acids showed the highest extraction yields. Ch_HCl and Ch_Citric had higher degrees of deacetylation values; 83.67% and 81.47%, respectively. The solubility was proportional to the degree of deacetylation. Furthermore, Ch_H2SO4 and Ch_Citric had lower molecular weight values; 149 kDa and 183 kDa, respectively. Organic acids are as effective as mineral acids for shrimp shells demineralization. The developed process opens up possibilities to produce chitin and chitosan in a more eco-friendly way and at a lower cost in many industrial sectors.     

Circularly Polarized Fluorescent Helicene-Boranils: Synthesis,Photophysical and Chiroptical Properties

Mono- and di-boranil-substituted helicenes were prepared by BF₂-borylation of the corresponding anils, readily synthesized by condensation of 2-amino- and 2,15-diamino-helicenes with 4-(diethylamino)salicylaldehyde. After enantiomeric resolution using HPLC, their chiroptical properties including circularly polarized fluorescence in solution and in PMMA films were investigated and rationalized with the help of NMR, X-ray and quantum-chemical calculations.     

Conductivity study by complex impedance spectroscopy of solid solution AgxK1 − xNb4AsO13 (x = 0.2 and 0.62): effect of the substitution of K+ by Ag+ cations on the ionic conduction properties

Journal of Solid State Electrochemistry - Crystals of Ag0.2K0.8Nb4AsO13 (I) and Ag0.62K0.38Nb4AsO13 (II) were synthesized by a solid-state reaction. Both of them crystallize in the orthorhombic...     

Synthesis and characterisation of a new helically chiral ruthenium complex

A new helically chiral hexacyclic phosphine, containing one thiophene ring was prepared in good yield via a five-step sequence involving a palladium-catalysed Mizoroki-Heck coupling reaction and classical oxidative photocyclisation. A mononuclear air stable ruthenium complex of this phosphine was also prepared and characterised.