Structural, vibrational study and conductivity investigation of a new cesium–bismuth polyphosphate CsBi(PO3)4

Synthesis, a complete structural characterization by X-ray diffraction, IR-Raman, and conductivity investigation are given for cesium–bismuth polyphosphate CsBi(PO₃)₄. This compound crystallizes in the monoclinic system with a space group P2₁/n (structural type IV). The structure consists of a three-dimensional framework made up of spiral (PO₃)_n chains linked by BiO₈ polyhedra. Two infinite (PO₃)_n chains with a period of eight tetrahedra run along the [101] direction. The infrared and the Raman spectra show clearly some characteristic bands of infinite chain structures of PO₄ tetrahedra linked by bridge oxygen. The thermo-differential analysis shows two endothermic peaks at T₁?=?448 and T₂?=?919 K. No weight loss was observed in the (TGA) until the temperature 800 K. The conductivity measurements confirm the presence of a phase transition at 448 K accompanied by an important increasing of the conductivity of Cs⁺ cations and a significant decreasing of the activation energy.     

On local existence and blowup of solutions for a time‐space fractional diffusion equation with exponential nonlinearity

In this paper, we are concerned with local existence and blowup of a unique solution to a time‐space fractional evolution equation with a time nonlocal nonlinearity of exponential growth. At first, we prove the existence and uniqueness of the local solution by the Banach contraction mapping principle. Then, the blowup result of the solution in finite time is established by the test function method with a judicious choice of the test function.     

On the class of weak^{\star } Dunford–Pettis operators

We give a characterization of weak\(^{\star }\) Dunford–Pettis operators and we study its relation with limited completely continuous operators.     

Kinetics of hydrolysis and self condensation reactions of silanes by NMR spectroscopy

The hydrolysis of four alkoxy-silane coupling agents, 3-methacryloxypropyl trimethoxy silane (MPMS), 3-mercaptopropyl trimethoxy silane (MRPMS), octyl triethoxy silane (OES) and 3-aminopropyl triethoxy silane (APES) was carried out in an ethanol/water 80/20 (w/w) solution under acidic, alkaline and neutral conditions and followed by ¹H, ¹³C and ²⁹Si NMR spectroscopy. It was found that the kinetic rate of the hydrolysis of the silanes under neutral conditions was very low, except for APES, which displayed the fastest reaction speed. The addition of TEA catalyzed both silane hydrolysis and self condensation reactions. Acidic conditions enhanced the hydrolysis and the ensuing silanol entities were quite stable. In fact, these conditions slowed down the rate of the self condensation reactions, as deduced from in situ ¹H and ¹³C NMR. Thanks to in situ ²⁹Si NMR spectroscopy, the nature of the intermediary species versus reaction time was established.     

Different strategies for obtaining high opacity films of MFC with TiO2 pigments

The present study examines the production and characterization of opaque solid films made with microfibrillated cellulose (MFC) suspension and titanium dioxide (TiO₂) nanoparticles. Three different strategies were investigated: a blend of (1) MFC and TiO₂ (2) a premix in which TiO₂ particles are used to favor the fibrillation step of MFC and (3) a sol–gel strategy in which TiO₂ particles were directly generated onto the surface of MFC. The different process parameters have been optimized both for the production of MFC and the sol–gel reaction. Gel suspensions containing different ratios of TiO₂ were morphologically and chemically characterized. In order to characterize the size and the nature of the particles, diffraction laser scattering, atomic force microscopy were used while the thermo gravimetric analysis and X-ray diffraction were used to investigate the degradation of MFC for all the three strategies. To highlight the level of dispersion of TiO₂ within the MFC network, scanning electron microscopy in BSE mode has been employed. Finally, the transparence and the mechanical properties of solid films were measured by UV spectrophotometry and tensile tests, respectively. Very good TiO₂ dispersion and high opacity MFC films have been achieved with a very low amount of TiO₂. Thus, the best strategy that takes into account the easiest process for making the hybrids and leading to the high level of opacity with the lowest ratio of TiO₂ is the premix strategy.     

Synthesis of a new flocculant based on poly(acrylamide-co-(N-octyl-4-vinylpyridinium bromide)) [AM5/VP5C8Br]-application for the turbidity removal from clay suspension

The interactions between poly(acrylamide-co-(N-octyl-4-vinylpyridinium bromide)) [AM5/VP5C8Br] cationic polyelectrolyte, and clay particles in dilute aqueous suspensions are studied in the aim of adsorption and flocculation. The extents of both phenomena are significantly influenced by the ionic strength of the medium. The adsorption of the clay particles on the copolymer chains occurs initially by the hydrophobic interaction. As flocculation mechanisms, the hydrophobic interaction between copolymer chains and the clay particles appears to be principal. In this work, we have prepared a copolymer which has been characterized by conductivity, viscosity, ¹H NMR, and FT-IR spectroscopies. The copolymer dosage and pH are two of the most important experimental parameters in the coagulation/flocculation operations used for study and optimization of the wastewater treatment operations. Under optimized conditions, 97% efficiency of the turbidity elimination, with a very low flocculant concentration of 3?ppm have been achieved in order to produce drinking water with standard limits around the world (< 1 NTU). The conclusion drawn on the basis of these results is that wastewater treatment using this new copolymer [AM5/VP5C8Br] has proved to be a good flocculant in overseeing of wastewater turbidity problems.     

Hankel Determinants of a Linear Combination of Three Successive Catalan Numbers

We evaluate the determinants of Hankel matrices, whose elements are a linear combination of three successive shifted Catalan numbers. This is done by finding a Jacobi linear functional, such that their moments are, up to a multiplicative constant, the Catalan numbers. The values of such determinants are then expressed in terms of Jacobi polynomials.     

Local and blowing‐up solutions for a space‐time fractional evolution system with nonlinearities of exponential growth

Local and blowing‐up solutions for the Cauchy problem for a system of space and time fractional evolution equations with time‐nonlocal nonlinearities of exponential growth are considered. The existence and uniqueness of the local mild solution is assured by the Banach fixed point principle. Then, we establish a blow‐up result by Pokhozhaev capacity method. Finally, under some suitable conditions, an estimate of the life span of blowing‐up solutions is established.     

Quadratic finite element approximation of the Signorini problem

Applying high order finite elements to unilateral contact variational inequalities may provide more accurate computed solutions, compared with linear finite elements. Up to now, there was no significant progress in the mathematical study of their performances. The main question is involved with the modeling of the nonpenetration Signorini condition on the discrete solution along the contact region. In this work we describe two nonconforming quadratic finite element approximations of the Poisson-Signorini problem, responding to the crucial practical concern of easy implementation, and we present the numerical analysis of their efficiency. By means of Falk's Lemma we prove optimal and quasi-optimal convergence rates according to the regularity of the exact solution.

     

Error bounds in high-order Sobolev norms for POD expansions of parameterized transient temperatures

In this work, we analyze the convergence of the POD expansion for the solution to the heat conduction parameterized with respect to the thermal conductivity coefficient. We obtain error bounds for the POD approximation in high-order norms in space that assure an exponential rate of convergence, uniformly with respect to the parameter whenever it remains within a compact set of positive numbers. We present some numerical tests that confirm this theoretical accuracy.