Lower bound for the ratios of eigenvalues of Schrödinger with nonpositive single‐barrier potentials

Horváth and Kiss (Proc. Amer. Math. Soc., 2005) proved the upper bound estimate for Dirichlet eigenvalue ratios of the Schrödinger problem ?y^′′ + q(x)y = λy with nonnegative and single‐well potential q. In this paper, we prove that if q(x) is a nonpositive, continuous, and single‐barrier potential, then for λ_n > λ_m≥ ? 2q^?, where . In particular, if q(x) satisfies the additional condition , then λ₁ > 0 and for n > m ≥ 1. For this result, we develop a new approach to study the monotonicity of the modified Prüfer angle function.     

Characterization of polyoxometalate/polymer photo-composites: A toolbox for the photodegradation of organic pollutants

Different inorganic/organic photocomposites based on polyoxometalate (POM) nanoparticles have been developed for photocatalytic applications. Currently, polyoxometalate nanoparticles have been successfully in-situ embedded into an acrylate polymer network by photopolymerization upon mild visible light irradiation at 405 nm. The proposed POM/polymer photocomposites have been characterized using complementary techniques for a better understanding of their photocatalytic activity. Interestingly, the obtained photocomposites exhibit high rigidity, excellent thermal stability, a non-negligible porosity and new functionalities such as light reactivity and redox properties. Moreover, developed composites showed efficient catalytic activity for the color removal of aqueous solutions of erythrosine and rose Bengal under Light Emitting Diodes LED@375 nm irradiation reaching 80 and 90% as a final color removal, respectively.     

Rheological studies of the gelation of aqueous solutions of acrylamide-acrylic acid copolymers in the presence of chromium chloride

The gelation kinetics of aqueous solutions of acrylamideacrylic acid copolymers in the presence of chromium ions was studied with different rheometers. The gel time is found to vary with the principle of the apparatus because of a low shear dependence of the elongation of the macromolecules. The variations of the gel time with the experimental conditions of the gel preparation were investigated and we conclude that the gelation is governed by the oligornerization kinetics of the chromium ions which are instantaneously, complexated by the carboxylate groups of the polymer. The variation laws of the gel time and of the elastic modulus with chromium and polymer concentrations, temperature and ionic strength are in qualitative agreement with the structure of the temporary network of the semi-dilute solutions of these copolymers.     

Influence of the formulation of catalysts deposited on cordierite monoliths for acetic acid oxidation

Monolithic catalysts are prepared by washcoating cordierite monoliths with different sols (Pt/Al₂O₃, Pt/CeO₂, Pt/ZrO₂, Pt/Al₂O₃CeO₂, Pt/Al₂O₃ZrO₂, and Pt/CeO₂ZrO₂). These sols are prepared by a sol–gel process and characterized by specific surface area (S_BET), inductively coupled plasma, hydrogen chemisorption, high-resolution transmission electron microscopy, field emission scanning electron microscopy, oxygen storage capacity, X-ray diffraction, temperature-programmed reduction, CO₂ chemisorption, and the model reaction of 3,3-dimethylbutene isomerization. The catalytic performances of the monolithic catalysts are then evaluated for the acetic acid oxidation. The nature of catalyst coating has been found to influence the adherence with the cordierite monolith and the presence of cerium in the catalyst appears to increase the adherence of the latter. Pt/CeO₂, Pt/Al₂O₃CeO₂, and Pt/CeO₂ZrO₂ are found to be the most reducible catalysts (oxygen storage capacity and temperature-programmed reduction) and to have the lowest acidities (3,3-dimethylbutene isomerization). CO₂ chemisorption shows that these catalysts possess a good basicity. From the relation established between the catalytic activity and the redox and acid–base properties it has been concluded that the reducibility is the key factor for a good catalytic activity although the basicity has a significant influence on the catalytic performance.     

Regioselective C-H Functionalization of the Six-Membered Ring of the 6,5-Fused Heterocyclic Systems: An Overview

The regioselective C-H functionalization of the five-membered ring of the 6,5-fused heterocyclic systems is nowadays well documented due to its high reactivity compared to the six-membered ring. So, developing new procedures of C-H functionalization of the six-membered ring “by thinking out of the box” is extremely challenging, which explains the limited number of reports published to date. This review paper aims to highlight advances achieved in this emerging chemistry research and discusses recently reported methods.     

Symmetrical and unsymmetrical incorporation of active biological monomers on the surface of phosphorus dendrimers

Phosphorus-containing dendrimers are attractive carriers for the delivery of bioactive molecules due to their very particular architecture, globular shape and chemical and physical properties. Herein we report a simple synthetic approach of ethacrynic acid derivatives loaded-phosphorus dendrimers by symmetrical grafting of ethacrynic acid analogues by nucleophilic substitution of each chlorine of P(S)Cl₂ end groups. We report also for the first time an unsymmetrical grafting of two different phenol derivatives by a selective substitution of one chlorine of P(S)Cl₂ end group followed by the grafting of the second phenol.     

Synthesis and FT–IR study of the acido–basic properties of the V2O5 catalysts supported on zirconia

In this paper we describe the synthesis and characterization of the acido–basic properties of catalysts containing varied amounts of vanadium supported on ZrO₂. The preparation of the zirconia was carried out using a hydrolysis method and the vanadium was introduced by impregnation with a porous volume in several stages, followed by calcinations under air at a temperature of 723 K. The obtained samples are characterized by adsorption–desorption of nitrogen and infrared spectral analysis of different species formed by acidic and basic probes. This adsorption on the surface of these compounds has been studied in order, in the hand to investigate information on their surface acidity and in the other hand to know particularly the nature and strength of acidic and basic sites. Among the molecular probes, we used carbon monoxide, carbon dioxide, pyridine and 2,6-dimethylpyridine. The adsorption of CO has shown that contrary to pure zirconia and oxidized V₂O₅/ ZrO₂, the reduced V₂O₅/ ZrO₂ samples favour the formation of CO co-ordinated on Lewis acidic sites of reduced V₂O₅ species (CO on V⁴⁺ or V³⁺). We also observe the creation of Brønsted acidic sites by means of the incorporation of vanadium.     

Investigation of electrocoagulation reactor design parameters effect on the removal of cadmium from synthetic and phosphate industrial wastewater

This study investigates the effect of reactor design parameters on cadmium removal from industrial wastewater discharged by the Tunisian Chemical Group (TCG) to improve as much as possible efficiency and cost of electrocoagulation (EC) process. Based on an examination of the design parameters one by one, the best cadmium removal was achieved for an inter-electrode distance (d_ie) of 0.5 cm, monopolar connection mode, stirring speed of 300 rev min^?1, surface-area-to-volume ratio (S/V) of 13.6 m^?1, and an initial temperature of 50 °C. These operating conditions are allowed to achieve efficient removal in a relatively short operating time with the lowest energy consumption and cost possible. The present study proved that the parameters that have an effect on the operating cost are the electrode configuration, inter-electrode distance and S/V ratio. The energy consumption, the pH evolution, and the treatment cost were studied. The investigation of the effect of all the selected optimum EC design parameters together on the removal of cadmium from the TCG wastewater proved that the treatment was highly efficient; 100% of cadmium removal was reached in 5 min, with a very low power consumption (1.6 kW h m^?3) and very low cost (0.116 TND m^?3). Moreover, EC was found to be capable of removing cadmium as well as other pollutants at the same time from the case-study industrial wastewater. The investigation carried out in this work explores and proposes a very cost-effective treatment method to remove heavy metals from industrial wastewater if compared to results reported about cost of this treatment process through other widely used technologies such as coagulation (4.36 Tunisian National Dinar (TND) m^?3) and precipitation (9.96 TND m^?3) employed in previous studies.