Gaussian quadrature formulas and Laguerre-Perron's equation

LetI(f) be the integral defined by:I(f) = ∫ _a ^b f(x)w(x)dx withf a given function,w a nonclassical weight function and [a, b] an interval of IR (of finite or infinite length). We propose to calculate the approximate value ofI(f) by using a new scheme for deriving a non-linear system, satisfied by the three-term recurrence coefficients of semi-classical orthogonal polynomials. Finally we studies the Stability and complexity of this scheme.     

Schur operators and domination problem

In this paper we are concerned with developing generalizing concepts of Dunford–Pettis operators analogous to the generalization of compact operators by strictly singular operators. Also, we give some new results concerning the domination problem in the setting of positive operators between Banach lattices.     

Mathematical Modeling to Simulate the Movement of Contaminants in Groundwater

The objectives of this paper are twofold. Firstly, we formulate a system of partial differential equations that models the contamination of groundwater due to migration of dissolved contaminants through unsaturated to saturated zone. A closed form solution using the singular perturbation techniques for the flow and solute transport equations in the unsaturated zone is obtained. Indeed, the solution can be used as a tool to verify the accuracy of numerical models of water flow and solute transport. The second part of this paper, deals with how the water level in a water reserve drops due to pumping water out of a well that is some distance away.     

Experimental and theoretical DFT study of the reaction of 3-amino-1,2-diols with dichloromethane and paraformaldehyde

The reactions of 3-phenyl-3-methylamino-1,2-propanediol 1a and 3-[(tert-butyldimethylsilyl)oxy]-1-methylamino-1-phenyl-2-propanol 1b with (CH₂O)n and CH₂Cl₂ are appropriate procedures for the preparation of 1,3-oxazines or 1,3-oxazolidines under proper selection of kinetic or thermodynamic reaction conditions. The reaction of 1b with (CH₂O)n or CH₂Cl₂, affords the oxazolidine 2b under kinetic conditions and then this compound can be slowly converted into 5-[(tert-butyldimethylsilyl)oxy]-3-methyl-4-phenyl-3,4,5,6-tetrahydro-2H-1,3-oxazine 3b under thermodynamic control. The mechanism proposed for this transformation and the effect of polar solvents on the acceleration of the reaction has been studied theoretically (DFT level).     

Direct carbamation of cellulose fiber sheets

The paper is on introducing carbamate groups in sheets of cellulose fiber assemblies by pad-dry-cure treatments with aqueous solutions of polyethylene glycol, amide and salt. The effects of process variables—on carbamation levels and on mechanical properties of the substrate—are reported. Depending on treatment conditions, the nitrogen contents in substrates are in the range 0.668–2.252 wt%, corresponding to nominal degrees of carbamate group substitution of 0.08–0.28. The carbamation is initiated at 140 °C curing, and the levels rise with temperature up to 220 °C, but decrease at higher temperatures. The duration of curing also exerts an influence. There is a catalytic effect of sodium acetate on the carbamation, but the salt also induces a brown coloration in samples, which is likely a result of Maillard-type reactions. The treatments cause hydrolytic degradation in substrates, but there are options to adjust treatment conditions and minimize damage. Pad-dry-cure treatments are a common operation in the textile and paper industries, and the process may be adopted in commercial-scale operations to create derivatized paper or fabrics (woven, knitted or non-woven) for utilization in applications such as adsorbents for heavy metals from waste water, in hygiene products, in the creation of flame retardant products, or in creating all-cellulose composites by further treatment with alkali.     

Synthesis,structure, and morphology of polymer–silica hybrid nanocomposites based on hydroxyethyl methacrylate

Two types of polymer–silica nanocomposites have been prepared by undergoing free radical polymerization of 2-hydroxyethyl methacrylate (HEMA) either in the presence of HEMA-functionalized SiO₂ nanoparticles (Type 1) or during the simultaneous in situ growing of the silica phase through the acid-catalyzed sol–gel polymerization of tetraethoxysilane (TEOS) (Type 2). Relationships between synthesis conditions, chemical structure, and resulting morphology have been studied. Type 1 systems exhibit a classical particle-matrix morphology, but where particles tend to form aggregates. Type 2 systems possess a finer morphology characterized by a very open mass-fractal silicate structure, which is believed to be bicontinuous with the organic phase at a molecular level. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 3172–3187, 1999     

Structural and optical properties of TiO2 thin films prepared by spin coating

Transparent semiconducting thin films of titanium oxide (TiO₂) were deposited on glass substrates by the sol–gel method and spin-coating technique. The physical properties of the prepared films were studied as a function of the number of spun-cast layers. The microstructure and surface morphology of the TiO₂ films were characterized by X-ray diffraction (XRD) and atomic force microscopy (AFM), with respect to the film thickness. The XRD analysis reveals that the films are polycrystalline with an anatase crystal structure and a preferred grain orientation in the (101) direction. The morphological properties were investigated by AFM, which shows a porous morphology structure for the films. The optical properties of the films were characterized by UV–Visible spectrophotometry, which shows that the films are highly transparent in the visible region and their transparency is slightly influenced by the film thickness, with an average value above 80 %. The dependence of the refractive index (n), extinction coefficient (k), and absorption coefficient (α) of the films on the wavelength was investigated. A shift in the optical band gap energy of the films from 3.75 to 3.54 eV, as a function of the film thickness, has been observed.