Facile synthesis of α-hydroxy carboxylic acids from the corresponding α-amino acids

An effective and improved procedure is developed for the synthesis of α-hydroxy carboxylic acids by treatment of the corresponding protonated α-amino acid with tert-butyl nitrite in 1,4-dioxane–water. The amino moiety must be protonated and located α to a carboxylic acid function in order to undergo initial diazotization and successive hydroxylation, since neither β-amino acids nor acid derivatives such as esters and amides undergo hydroxylations. The method is successfully applied for the synthesis of 18 proteinogenic amino acids.     

Surface effects on nonlinear free vibration of functionally graded nanobeams using nonlocal elasticity

In this paper, to consider all surface effects including surface elasticity, surface stress, and surface density, on the nonlinear free vibration analysis of simply-supported functionally graded Euler–Bernoulli nanobeams using nonlocal elasticity theory, the balance conditions between FG nanobeam bulk and its surfaces are considered to be satisfied assuming a cubic variation for the component of the normal stress through the FG nanobeam thickness. The nonlinear governing equation includes the von Kármán geometric nonlinearity and the material properties change continuously through the thickness of the FG nanobeam according to a power-law distribution of the volume fraction of the constituents. The multiple scale method is employed as an analytical solution for the nonlinear governing equation to obtain the nonlinear natural frequencies of FG nanobeams. The effect of the gradient index, the nanobeam length, thickness to length ratio, mode number, amplitude of deflection to radius of gyration ratio and nonlocal parameter on the frequency ratios of FG nanobeams is investigated.     

Exact solutions for free flexural vibration of Lévy-type rectangular thick plates via third-order shear deformation plate theory

In this paper, exact closed-form solutions in explicit forms are presented for transverse vibration analysis of rectangular thick plates having two opposite edges hard simply supported (i.e., Lévy-type rectangular plates) based on the Reddy’s third-order shear deformation plate theory. Two other edges may be restrained by different combinations of free, soft simply supported, hard simply supported or clamped boundary conditions. Hamilton’s principle is used to derive the equations of motion and natural boundary conditions of the plate. Several comparison studies with analytical and numerical techniques reported in literature are carried out to demonstrate accuracy of the present new formulation. Comprehensive benchmark results for natural frequencies of rectangular plates with different combinations of boundary conditions are tabulated in dimensionless form for various values of aspect ratios and thickness to length ratios. A set of three-dimensional (3-D) vibration mode shapes along with their corresponding contour plots are plotted by using exact transverse displacements of Lévy-type rectangular Reddy plates. Due to the inherent features of the present exact closed-form solution, the present findings will be a useful benchmark for evaluating the accuracy of other analytical and numerical methods, which will be developed by researchers in the future.     

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.     

Free vibration of functionally graded rectangular plates using first-order shear deformation plate theory

The main objective of this research work is to present analytical solutions for free vibration analysis of moderately thick rectangular plates, which are composed of functionally graded materials (FGMs) and supported by either Winkler or Pasternak elastic foundations. The proposed rectangular plates have two opposite edges simply-supported, while all possible combinations of free, simply-supported and clamped boundary conditions are applied to the other two edges. In order to capture fundamental frequencies of the functionally graded (FG) rectangular plates resting on elastic foundation, the analysis procedure is based on the first-order shear deformation plate theory (FSDT) to derive and solve exactly the equations of motion. The mechanical properties of the FG plates are assumed to vary continuously through the thickness of the plate and obey a power law distribution of the volume fraction of the constituents, whereas Poisson’s ratio is set to be constant. First, a new formula for the shear correction factors, used in the Mindlin plate theory, is obtained for FG plates. Then the excellent accuracy of the present analytical solutions is confirmed by making some comparisons of the results with those available in literature. The effect of foundation stiffness parameters on the free vibration of the FG plates, constrained by different combinations of classical boundary conditions, is also presented for various values of aspect ratios, gradient indices, and thickness to length ratios.     

Numerical solution of fractional differential equations via a Volterra integral equation approach

The main focus of this paper is to present a numerical method for the solution of fractional differential equations. In this method, the properties of the Caputo derivative are used to reduce the given fractional differential equation into a Volterra integral equation. The entire domain is divided into several small domains, and by collocating the integral equation at two adjacent points a system of two algebraic equations in two unknowns is obtained. The method is applied to solve linear and nonlinear fractional differential equations. Also the error analysis is presented. Some examples are given and the numerical simulations are also provided to illustrate the effectiveness of the new method.     

An accurate mathematical study on the free vibration of stepped thickness circular/annular Mindlin functionally graded plates

An analytical solution based on a new exact closed form procedure is presented for free vibration analysis of stepped circular and annular FG plates via first order shear deformation plate theory of Mindlin. The material properties change continuously through the thickness of the plate, which can vary according to a power-law distribution of the volume fraction of the constituents, whereas Poisson’s ratio is set to be constant. Based on the domain decomposition technique, five highly coupled governing partial differential equations of motion for freely vibrating FG plates were exactly solved by introducing the new potential functions as well as using the method of separation of variables. Several comparison studies were presented by those reported in the literature and the FEM analysis, for various thickness values and combinations of stepped thickness variations of circular/annular FG plates to demonstrate highly stability and accuracy of present exact procedure. The effect of the geometrical and material plate parameters such as step thickness ratios, step locations and the power law index on the natural frequencies of FG plates is investigated.     

A Novel LSB Based Quantum Watermarking

Quantum watermarking is a technique which embeds the invisible quantum signal such as the owners identification into quantum multimedia data (such as audio, video and image) for copyright protection. In this paper, using a quantum representation of digital images a new quantum watermarking protocol including quantum image scrambling based on Least Significant Bit (LSB) is proposed. In this protocol, by using m-bit embedding key K₁ and m-bit extracting key K₂ a m-pixel gray scale image is watermarked in a m-pixel carrier image by the original owner of the carrier image. For validation of the presented scheme the peak-signal-to-noise ratio (PSNR) and histogram graphs of the images are analyzed.     

Nonlocal modeling for dynamic stability of spinning nanotube under axial load

Spinning nanotubes are the main part of different high precision nano-machines such as nano sensors, nano motors, and nano pumps. Nanotubes experience various types of loads in such devices. In this paper, different type of instability for a spinning nanotube under tangential load is investigated. For this purpose, Euler and Timoshenko nonlocal beam theory is used. Equations of motion are obtained by applying Hamilton’s principle on the energy terms of nanotube by considering rotational velocity and compressive tangential load. Numerical results are exactly calculated for different parameters and are checked by comparing them with literature. Results show that there are two type of instability for simply supported spinning nanotubes as divergent and flutter, generally. Also, effects of different nonlocal parameter, geometry and rotational speed on these instabilities are investigated, comprehensively. It is approved that nonlocal parameter has significant effect on both of the instabilities.

     

Quantum mechanically derived AMBER-compatible heme parameters for various states of the cytochrome P450 catalytic cycle

Molecular mechanics (MM) methods are computationally affordable tools for screening chemical libraries of novel compounds for sites of P450 metabolism. One challenge for MM methods has been the absence of a consistent and transferable set of parameters for the heme within the P450 active site. Experimental data indicate that mammalian P450 enzymes vary greatly in the size, architecture, and plasticity of their active sites. Thus, obtaining X-ray-based geometries for the development of accurate MM parameters for the major classes of hepatic P450 remains a daunting task. Our previous work with preliminary gas-phase quantum mechanics (QM)-derived atomic partial charges greatly improved the accuracy of docking studies of raloxifene to CYP3A4. We have therefore developed and tested a consistent set of transferable MM parameters based on gas-phase QM calculations of two model systems of the heme-a truncated (T-HM) and a full (F-HM) for four states of the P450 catalytic cycle. Our results indicate that the use of the atomic partial charges from the F-HM further improves the accuracy of docked predictions for raloxifene to CYP3A4. Different patterns for substrate docking are also observed depending on the choice of heme model and state. Newly parameterized heme models are tested in implicit and explicitly solvated MD simulations in the absence and presence of enzyme structures, for CYP3A4, and appear to be stable on the nanosecond simulation timescale. The new force field for the various heme states may aid the community for simulations of P450 enzymes and other heme-containing enzymes.