Nonclassical pseudospectral method for the solution of brachistochrone problem

In this paper, nonclassical pseudospectral method is proposed for solving the classic brachistochrone problem. The brachistochrone problem is first formulated as a nonlinear optimal control problem. Properties of nonclassical pseudospectral method are presented, these properties are then utilized to reduce the computation of brachistochrone problem to the solution of algebraic equations. Using this method, the solution to the brachistochrone problem is compared with those in the literature.     

Efficient regio- and stereoselective ring opening of epoxides with alcohols, acetic acid and water catalyzed by ammonium decatungstocerate(IV)

Epoxides can be cleaved in a regio- and stereoselective manner under neutral conditions with alcohols and acetic acid in the presence of catalytic amounts of decatungstocerate(IV) ion, ([CeW₁₀O₃₆]⁸⁻), affording the corresponding β-alkoxy and β-acetoxy alcohols in high yields. In water, ring opening of epoxides occurs with this catalyst to produce the corresponding diols in good yields.     

Microwave Thermolysis: A Rapid and Selective Method for the Cleavage of THP Ethers Using CrO 3 Supported onto Zeolite in Solventless System

Oxidative deprotection of tetrahydropyranyl ethers (THP ethers) using chromium trioxide supported onto zeolite under microwave irradiation in solvent free condition is described.     

Intramolecular cyclization of <Emphasis Type="Italic">N</Emphasis>-propargyl anilines: a new synthetic entry into highly substituted indoles

Indole derivatives are an important class of heterocycle found in a large number of natural products and synthetic pharmaceuticals. Given the low cost and easy availability of N-propargyl anilines, synthesis of indole cores from these versatile structural motifs has attracted a lot of attention in the past decade. In this review, we summarize the most representative and interesting reports on this rapidly advancing area, with special emphasis on mechanistic aspects of the reactions.     

Numerical solution of the two-dimensional Fredholm integral equations using Gaussian radial basis function

In this paper, we introduce a numerical method for the solution of two-dimensional Fredholm integral equations. The method is based on interpolation by Gaussian radial basis function based on Legendre-Gauss-Lobatto nodes and weights. Numerical examples are presented and results are compared with the analytical solution to demonstrate the validity and applicability of the method.     

Analytical solutions to nonlinear equations arising in heat transfer by variational iteration,homotopy perturbation,and Adomian decomposition methods

As thermal conductivity plays an important role on fin efficiency, we tried to solve heat transfer equation with thermal conductivity as a function of temperature. In this research, some new analytical methods called homotopy perturbation method, variational iteration method, and Adomian decomposition method are introduced to be applied to solve the nonlinear heat transfer equations, and also the comparison of the applied methods (together) is shown graphically. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010     

Analytical solution for laminar flow through leaky tube

The laminar flow through a leaky tube is investigated, and the momentum and conservation of energy equations are solved analytically. By using the Hagen-Poiseuille velocity profile and defining unknown functions for the axial and radial velocity components, the pressure and mass transfer equations are obtained, and their profiles are plotted according to different parameters. The results indicate that the axial velocity, the radial velocity, the mass transfer parameter, and the pressure in the tube decrease as the fluid moves along the tube.     

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.     

Intracavity phase interferometry: frequency combs sensor inside a laser cavity

In traditional interferometric measurements, a physical quantity that changes the phase of a resonator is monitored through a change of its transmission. Interferometry inside a laser exploits the ultimate Q‐factor of that resonator, and converts the phase to be measured into a frequency. A mode‐locked laser with two intracavity pulses emits two frequency combs of the same repetition rate. The quantity to be measured (a sub‐nano displacement, a nonlinear index, an acceleration or rotation, a magnetic or electric field) produces a minute phase change ( rad) in one of the two intracavity pulses, which is converted into a frequency, measured by beating the two pulse trains emitted by the laser. This paper presents methods of operating mode‐locked lasers in which two independent pulses circulate, producing two frequency combs of the same repetition rate. Various examples of physical quantities that can be measured through this technique are presented.     

Rapid micromachining of high aspect ratio holes in fused silica glass by high repetition rate picosecond laser

We present multiple methods of high aspect ratio hole drilling in fused silica glass, taking advantage of high power and high repetition rate picosecond lasers and flexible beam delivery methods to excise deep holes with minimal collateral damage. Combinations of static and synchronous scanning of laser focus were explored over a range of laser repetition rates and burst-train profiles that dramatically vary laser plume interaction dynamics, heat-affected zone, and heat accumulation physics. Chemically assisted etching of picosecond laser modification tracks are also presented as an extension from femtosecond laser writing of volume nanograting to form high aspect ratio (77) channels. Processing windows are identified for the various beam delivery methods that optimize the laser exposure over energy, wavelength, and repetition rate to reduce microcracking and deleterious heating effects. The results show the benefits of femtosecond laser interactions in glass extend into the picosecond domain, where the attributes of higher power further yield wide processing windows and significantly faster fabrication speed. High aspect ratio holes of 400 μm depth were formed over widely varying rates of 333 holes per second for mildly cracked holes in static-focal positioning through to one hole per second for low-damage and taper free holes in synchronous scanning.