Traveling waves in rational expressions of exponential functions to the conformable time fractional Jimbo–Miwa and Zakharov–Kuznetsov equations

The conformable time fractional Jimbo–Miwa and Zakharov–Kuznetsov equations are solved by the generalized form of the Kudryashov method. A simple compatible wave transformation is employed to reduce the dimension of the equations to one. The predicted solution is of the form of a rational expression of two finite series at both the numerator and the denominator. The terms of both series are of the powers of some functions having exponential expressions satisfying a particular ODE. The exact solutions are expressed explicitly in terms of powers of some exponential functions in form of rational expressions.     

Halogenated secondary metabolites from Laurencia obtusa

A new sesquiterpene (1), and a halogenated C15 acetogenin (2), a stereoisomer of neoisoprelaurefucin were isolated from Laurencia obtusa. Four known compounds laurencienyne (3), rogiolenyne B (4), obtusenol (5), and (3E)-dactomelyne (6) were also isolated from this alga. Rogiolenyne B (4) and (3E)-dactomelyne (6) were found for the first from this species. The structures of these compounds were elucidated by spectroscopic methods. The unambiguous assignments of the 1H and 13C NMR spectral data of (5) and 13C NMR data of (6) were also reported for the first time.     

Parallel synthesis of an indole-based library via an iterative Mannich reaction sequence

A library of 1,3-disubstituted indoles has been prepared via an iterative Mannich reaction sequence. The first Mannich reaction with secondary amines and formaldehyde preferentially yields 3-aminomethyl indoles, while the second Mannich reaction introduces an additional aminomethyl group at the N1-position of the indole ring. A library of 25 substituted indoles has thus been prepared in moderate to good yields with purity.     

Vibronic Dynamics of Photodissociating ICN from Simulations of Ultrafast X-Ray Absorption Spectroscopy

Ultrafast UV-pump/soft-X-ray-probe spectroscopy is a subject of great interest since it can provide detailed information about dynamical photochemical processes with ultrafast resolution and atomic specificity. Here, we focus on the photodissociation of ICN in the ¹Π₁ excited state, with emphasis on the transient response in the soft-X-ray spectral region as described by the ab initio spectral lineshape averaged over the nuclear wavepacket probability density. We find that the carbon K-edge spectral region reveals a rich transient response that provides direct insights into the dynamics of frontier orbitals during the I−CN bond cleavage process. The simulated UV-pump/soft-X-ray-probe spectra exhibit detailed dynamical information, including a time-domain signature for coherent vibration associated with the photogenerated CN fragment.     

Investigation of equilibrium, kinetic, thermodynamic and mechanism of Basic Blue 16 adsorption by montmorillonitic clay

The adsorption of a cationic dye, Basic Blue 16 (BB16), by montmorillonitic clay was studied in detail. Changes in the molecular structure during adsorption were analyzed by FTIR spectroscopy. BB16 adsorption onto the clay mainly results from hydrogen bonding between OH and NH₂ groups of dye molecules and OH groups of clay and electrostatic interaction between the negatively charged clay surface and cationic dye. The montmorillonitic clay dose had an inverse effect on the adsorption performance, while the highest dye removal was 305 mg/g at pH 3.6. An increase in temperature and dye concentration positively enhanced the adsorption capacity of the montmorillonitic clay. Temperature had no effect on the adsorption at a dye concentration less than 500 mg/L, while dye adsorption was positively enhanced at elevated dye concentrations. Three-parameter equations provided higher better fitting than two-parameter equations while the Freundlich model had the highest correlation coefficient and the lowest error values with experimental data. The BB16 adsorption was well followed by pseudo-second order model and the rate of adsorption process was controlled by surface and intraparticle diffusion. Thermodynamic evaluations revealed that the adsorption process was spontaneous and endothermic, while the randomness increased during adsorption. Experimental results indicate that montmorillonitic clay from Eskisehir is a promising adsorbent for the removal of cationic dye molecules from aqueous solutions.     

Elliptical Harmonic Motion and Euler–Savary Formula

In this paper, we have introduced elliptical harmonic motion in terms of elliptical numbers. In addition, we have found the relationships between the absolute, the relative and the sliding velocities and accelerations of the aforesaid motion. Furthermore, the canonical relative system of the motion has been defined. At last, we have obtained the Euler–Savary formula for the motion with the help of this relative system.     

2 dimensional electron gas uniformity of GaN HFET layers on SiC

As GaN power transistor technology matures it is increasingly important to understand any links between substrate “quality”, epi-layer growth and electrical characteristics of the 2-dimensional electron gas (2DEG), which forms the active part of devices. We present a study, which makes use of full wafer mapping techniques to examine these relationships. Substrate off-cut is shown to be an important parameter in controlling the uniformity of GaN HFET device layers on SiC substrates.     

Effect of diffusion on absorption and saturation of infrared radiation in molecular gases

Effect of diffusion on absorption of infrared radiation and saturation of absorption in molecular gases is considered. Incorporating the diffusion term, a theory is developed from multi-level rate equations, both for homogeneous and inhomogeneous broadening cases. It is shown that the effect of diffusion is characterized by a diffusion functionK'(k ₂ a), which varies inversely with the radius of the laser beam at low pressures and small beam sizes. Experimental results with seven molecular gases pumped by the CO₂ laser beam around 10.6 μm are reported.     

One-Parameter Homothetic Motion in the Hyperbolic Plane and Euler-Savary Formula

In [10] one-parameter planar motion was first introduced and the relations between absolute, relative, sliding velocities (and accelerations) in the Euclidean plane \mathbb E²{{\mathbb E}^2} were obtained. Moreover, the relations between the complex velocities of one-parameter motion in the complex plane were provided by [10]. One-parameter planar homothetic motion was defined in the complex plane, [9]. In this paper, analogous to homothetic motion in the complex plane given by [9], one-parameter planar homothetic motion is defined in the hyperbolic plane. Some characteristic properties about the velocity vectors, the acceleration vectors and the pole curves are given. Moreover, in the case of homothetic scale h identically equal to 1, the results given in [15] are obtained as a special case. In addition, three hyperbolic planes, of which two are moving and the other one is fixed, are taken into consideration and a canonical relative system for one-parameter planar hyperbolic homothetic motion is defined. Euler-Savary formula, which gives the relationship between the curvatures of trajectory curves, is obtained with the help of this relative system.