Electric-analog studies of impact dampers

An experimental study is made of the general behavior of single-particle impact dampers, using an electronic-analog computer and a mechanical model. It is found that, under practically realizable conditions, impact damping is effective in reducing the vibration-amplitude levels resulting from sinusoidal or random excitation. Paper was presented at 1966 SESA Spring Meeting held in Detroit, Mich., on May 4–6.     

Quantum Effect on the Energy Levels of Eu2+ Doped K2Ca2(SO4)3 Nanoparticles

Quantum confinement effect on the energy levels of Eu²⁺ doped K₂Ca₂(SO₄)₃ nanoparticles has been observed. The broad photoluminescence (PL) emission band of Eu²⁺ doped K₂Ca₂(SO₄)₃ microcrystalline sample observed at ～436 nm is found to split into two narrow well resolved bands, located at 422 and 445 nm in the nanostructure form of this material. This has been attributed to the reduction in the crystal field strength of the nanomaterials, which results in widening the energy band gap and splitting the broad 4f⁶5d energy level of Eu²⁺. Energy band gap values of the micro and nanocrystalline K₂Ca₂(SO₄)₃ samples were also determined by measuring the UV–visible absorption spectra. These values are 3.34 and 3.44 eV for the micro and nanocrystalline samples, respectively. These remarkable results suggest that activators having wide emission bands might be subjected to weak crystal strength via nanostructure materials to modify their electronic transitions. This might prove a powerful technique for producing new-advanced materials for use in the fields of solid state lasers and optoelectronic devises.     

Fast HPLC method for the determination of glimepiride, glibenclamide, and related substances using monolithic column and flow program

This work presents a fast method for the simultaneous separation and determination of glimepiride, glibenclamide, and two related substances by RP LC. The separation was performed on a Chromolith Performance (RP-18e, 100 mm x 4.6 mm) column. As mobile phase, a mixture of phosphate buffer pH 3, 7.4 mM, and ACN (55:45 v/v) was used. Column oven temperature was set to 30 degrees C. The total chromatographic run time was 80 s. This was achieved using a flow program from 5 to 9.9 mL/min. Precisions of the interday and the intraday assay for both retention times and peak areas for the four analyzed compounds were less than 1.2%. The method showed good linearity and recovery. The short analysis time makes the method very valuable for quality control and stability testing of drugs and their pharmaceutical preparations.     

A Fractional Schrödinger Equation and Its Solution

This paper presents a fractional Schrödinger equation and its solution. The fractional Schrödinger equation may be obtained using a fractional variational principle and a fractional Klein-Gordon equation; both methods are considered here. We extend the variational formulations for fractional discrete systems to fractional field systems defined in terms of Caputo derivatives to obtain the fractional Euler-Lagrange equations of motion. We present the Lagrangian for the fractional Schrödinger equation of order α. We also use a fractional Klein-Gordon equation to obtain the fractional Schrödinger equation which is the same as that obtained using the fractional variational principle. As an example, we consider the eigensolutions of a particle in an infinite potential well. The solutions are obtained in terms of the sines of the Mittag-Leffler function.     

Riesz Fractional Derivatives and Fractional Dimensional Space

The Fourier transform method is used to solve fractional Poisson’s equation with Riesz fractional derivative of order α. It is shown that the solution is given in terms of the fractional dimensional space D. Gauss law for the electrostatic problem is given and the total electric flux is obtained in terms of α and D.     

On hypoellipticity of generators of Lévy processes

We give a sufficient condition on a Lévy measure μ which ensures that the generator L of the corresponding pure jump Lévy process is (locally) hypoelliptic, i.e., \(\mathop {\mathrm {sing\,supp}}u\subseteq \mathop {\mathrm {sing\,supp}}Lu\) for all admissible u. In particular, we assume that \(\mu|_{\mathbb {R}^{d}\setminus \{0\}}\in C^{\infty}(\mathbb {R}^{d}\setminus \{0\})\). We also show that this condition is necessary provided that \(\mathop {\mathrm {supp}}\mu\) is compact.     

On convergence of homotopy analysis method and its modification for fractional modified KdV equations

In this paper, the homotopy analysis method (HAM) and its modification (MHAM) are applied to solve the nonlinear time- and space-fractional modified Korteweg-de Vries (fmKdV). The fractional derivatives are described by Caputo’s sense. Approximate and exact analytical solutions of the fmKdV are obtained. The MHAM in particular overcomes the computing difficulty encountered in HAM. Convergence theorems for both the homogeneous and non-homogeneous cases are given. The results of applying this procedure to the studied cases show the high accuracy and efficiency of the approach.     

The extended tanh method for solving systems of nonlinear wave equations

The extended tanh method with a computerized symbolic computation is used for constructing the traveling wave solutions of coupled nonlinear equations arising in physics. The obtained solutions include solitons, kinks and plane periodic solutions. The applied method will be used to solve the generalized coupled Hirota Satsuma KdV equation.