Numerical solution of volterra functional integral equation by using cubic B‐spline scaling functions

In this article, we consider a class of nonlinear functional integral equations which has rather general form and contains a lot of particular cases such as functional equations and nonlinear integral equations of Volterra type. We use a combination of a fixed point method and cubic semiorthogonal B‐spline scaling functions to solve the integral equation numerically. We provide an error analysis for the method which shows that the approximate solution converges to the exact solution. Some numerical results for several test problems are given to confirm the accuracy and the ease of implementation of the method. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 699–722, 2014     

Genaration of a η6- arene/Cr(co)3-complexed diazonium ion; homolytic and heterolytic dediazoniation via metallic π-bonded aryl radicals and cations

The reaction of NO⁺ with o-toluidinechromium tricarbonyl has been studied. Diazotization (attack on N) competes with NO⁺ attack on the metal and decarbonylation. The Cr(CO)₃-complexed diazonium ion is unstable and dediazoniates even at low temperature. The dediazoniation mechanism is predominantly homolytic. Competing heterolytic dediazoniation is observed in highly ionizing, low nucleophilicity solvents such as CF₃SO₃H (TfOH), FSO₃H and CF₃CH₂OH (TFE).     

Rapid,green, and catalyst-free one-pot three-component syntheses of 5-substituted 1<Emphasis Type="Italic">H</Emphasis>-tetrazoles in magnetized water

The catalyst-free multi-component reactions of aldehydes, malononitrile, and sodium azide at a relatively low temperature in magnetized water provided 5-substituted 1H-tetrazoles in high-to-excellent yields. This method offers the advantages of short reaction times, low costs, quantitative reaction yields, simple work-up, green, and no need for any organic solvent.     

Influence of intensity and frequency of ultrasonic waves on capillary interaction and oil recovery from different rock types

Oil saturated cylindrical sandstone cores were placed into imbibition cells where they contacted with an aqueous phase and oil recovery performances were tested with and without ultrasonic radiation keeping all other conditions and parameters constant. Experiments were conducted for different initial water saturation, oil viscosity and wettability. The specifications of acoustic sources such as ultrasonic intensity (45–84 W/sq cm) and frequency (22 and 40 kHz) were also changed. An increase in recovery was observed with ultrasonic energy in all cases. This change was more remarkable for the oil-wet medium. The additional recovery with ultrasonic energy became lower as the oil viscosity increased. We also designed a setup to measure the ultrasonic energy penetration capacity in different media, namely air, water, and slurry (sand + water mixture). A one-meter long water or slurry filled medium was prepared and the ultrasonic intensity and frequency were monitored as a function of distance from the source. The imbibition cells were placed at certain distances from the sources and the oil recovery was recorded. Then, the imbibition recovery was related to the ultrasonic intensity, frequency, and distance from the ultrasonic source.     

A Simple Indirect Route for the Synthesis of N-Alkyl-4-imino-1,4-dihydro-2H-3,1-benzoxazin-2-ones

Summary. Novel N-alkyl-4-imino-1,4-dihydro-2H-3,1-benzoxazin-2-ones were synthesized in a single step by Baeyer–Villiger oxidation of N-alkyl-3-imino-2-indolinone derivatives in high yields. The structures of the products were determined by spectral data and by X-ray diffraction. Besides their novel structures, these compounds may have important biological activities and industrial applications.     

Operational Matrix of Fractional Integration Based on the Shifted Second Kind Chebyshev Polynomials for Solving Fractional Differential Equations

This paper is devoted to studying a computational method for solving multi-term differential equations based on new operational matrix of shifted second kind Chebyshev polynomials. The properties of the operational matrix of fractional integration are exploited to reduce the main problem to an algebraic equation. We present an upper bound for the error in our estimation that leads to achieve the convergence rate of O(M ^−κ). Numerical experiments are reported to demonstrate the applicability and efficiency of the proposed method.

     

A cellular uptake and cytotoxicity properties study of gallic acid-loaded mesoporous silica nanoparticles on Caco-2 cells

In this study, the effects of intracellular delivery of various concentrations of gallic acid (GA) as a semistable antioxidant, gallic acid-loaded mesoporous silica nanoparticles (MSNs-GA), and cellular uptake of nanoparticles into Caco-2 cells were investigated. MSNs were synthesized and loaded with GA, then characterized using transmission electron microscopy (TEM), scanning electron microscopy (SEM), Fourier transform infrared spectroscopy, N₂ adsorption isotherms, X-ray diffraction, and thermal gravimetric analysis. The cytotoxicity of MSNs and MSNs-GA at low and high concentrations were studied by means of 3-[4,5-dimethylthiazol-2-yl]-2,5-diphenyltetrazolium bromide (MTT) test and flow cytometry. MSNs did not show significant toxicity in various concentrations (0–500 μg/ml) on Caco-2 cells. For MSNs-GA, cell viability was reduced as a function of incubation time and different concentrations of nanoparticles. The in vitro GA release from MSNs-GA exhibited the same antitumor properties as free GA on Caco-2 cells. Flow cytometry results confirmed those obtained using MTT assay. TEM and fluorescent microscopy confirmed the internalization of MSNs by Caco-2 cells through nonspecific cellular uptake. MSNs can easily internalize into Caco-2 cells without deleterious effects on cell viability. The cell viability of Caco-2 cells was affected during MSNs-GA uptake. MSNs could be designed as suitable nanocarriers for antioxidants delivery.     

High precision refractometry based on Fresnel diffraction from phase plates

When a transparent plane-parallel plate is illuminated at a boundary region by a monochromatic parallel beam of light, Fresnel diffraction occurs because of the abrupt change in phase imposed by the finite change in refractive index at the plate boundary. The visibility of the diffraction fringes varies periodically with changes in incident angle. The visibility period depends on the plate thickness and the refractive indices of the plate and the surrounding medium. Plotting the phase change versus incident angle or counting the visibility repetition in an incident-angle interval provides, for a given plate thickness, the refractive index of the plate very accurately. It is shown here that the refractive index of a plate can be determined without knowing the plate thickness. Therefore, the technique can be utilized for measuring plate thickness with high precision. In addition, by installing a plate with known refractive index in a rectangular cell filled with a liquid and following the described procedures, the refractive index of the liquid is obtained. The technique is applied to measure the refractive indices of a glass slide, distilled water, and ethanol. The potential and merits of the technique are also discussed.     

A Cutting Plane Algorithm for Linear Reverse Convex Programs

In this paper, global optimization of linear programs with an additional reverse convex constraint is considered. This type of problem arises in many applications such as engineering design, communications networks, and many management decision support systems with budget constraints and economies-of-scale. The main difficulty with this type of problem is the presence of the complicated reverse convex constraint, which destroys the convexity and possibly the connectivity of the feasible region, putting the problem in a class of difficult and mathematically intractable problems. We present a cutting plane method within the scope of a branch-and-bound scheme that efficiently partitions the polytope associated with the linear constraints and systematically fathoms these portions through the use of the bounds. An upper bound and a lower bound for the optimal value is found and improved at each iteration. The algorithm terminates when all the generated subdivisions have been fathomed.     

Monitoring of small‐scale anionic polymerization of caprolactam; a method to be used in an additive manufacturing process

The anionic polymerization of caprolactam using small quantities of reactants was investigated as part of a project aimed at producing polyamide parts by additive manufacturing. Various methods were used to monitor the polymerization and crystallization processes. Drop on drop small‐scale polymerization was carried out on a hot surface and monitored by Fourier transform infrared, which showed that PA6 had been polymerized successfully. PA6 synthesis was carried out in a differential scanning calorimetry cell to monitor the exothermic and endothermic processes during polymerization, and the processes were also observed by hot stage microscopy. It was found that polymerization and crystallization occurred simultaneously at slow heating rates. The amount of crystallinity produced during polymerization decreased as the heating rate increased. Copyright © 2013 John Wiley & Sons, Ltd.