On exact solutions for time-fractional Korteweg-de Vries and Korteweg-de Vries-Burger’s equations using homotopy analysis transform method

In this paper we consider the homotopy analysis transform method (HATM) to solve the time fractional order Korteweg-de Vries (KdV) and Korteweg-de Vries-Burger’s (KdVB) equations. The HATM is a combination of the Laplace decomposition method (LDM) and the homotopy analysis method (HAM). The fractional derivatives are defined in the Caputo sense. This method gives the solution in the form of a rapidly convergent series with h-curves are used to determine the intervals of convergent. Averaged residual errors are used to find the optimal values of h. It is found that the optimal h accelerates the convergence of the HATM, with the rate of convergence depending on the parameters in the KdV and KdVB equations. The HATM solutions are compared with exact solutions and excellent agreement is found.     

Facile synthesis and antimicrobial evaluations of some novel pyrazolo[3,4-b]selenolo[3,2-e]pyrazines and their related heterocycles

A new series of pyrazolopyrazinoselenolotriazolopyrimidines was synthesized by a facile method based on condensation of 5-amino-3-methyl-1-phenyl-1H-pyrazolo[3,4-b]selenolo[3,2-e]pyrazine-6-carbonitrile ( 3 ) with triethyl orthoformate followed by intramolecular cyclization with hydrazine to afford 7-amino-8-imino-3-methyl-1-phenyl-1,8-dihydro-7H-pyrazolo[3″,4″:5′,6′]pyrazino[2′,3′:4,5] selenolo[3,2-d]pyrimidine ( 5 ). The latter compound was utilized as a multipurpose precursor for the construction of other new triazoles fused to the pyrazolopyrazino- selenolopyrimidine moiety. Alternatively, acetylation and chloro-acetylation of compound 3 using acetic anhydride and chloroacetyl chloride yielded the acetyl amino 11 and chloroacetamido 12 derivatives, respectively. Compound 12 underwent nucleophilic substitution upon reaction with morpholine to provide the morpholinyl acetamide 13 . Furthermore, the pyrazolopyridoselenolopyrazine ring system 14 was synthesized by the reaction of the o-amino-carbonitrile 3 with malononitrile. Assignment of the chemical structures for the new compounds was confirmed depending on elemental and spectral techniques. On the other hand, most of the synthesized compounds revealed promising results against various bacterial and fungal strains.     

Clusters decay half-live of various heavy deformed nuclei with mass numbers in the range 221 ≤ A ≤ 242

Decay half-live of several clusters between ¹⁴C and ³⁴Si emitted from various heavy deformed nuclei with mass numbers in the range 221 ≤ A ≤ 242 are calculated using nuclear Woods-Saxon (V_N(r, θ)), Coulomb (V_C(r, θ)) and rotational (V_l(r)) potentials considering deformation for both daughter and cluster and spherical configuration for them. Half-live of these decays are also obtained using a semi-empirical formula. Obtained results considering deformation are compared with the half-live of spherical configuration, results of a semi-empirical formula as well as the available experimental data. The comparison indicates that the calculated half-lives considering deformation are better agreed with the experimental data than the results of spherical configuration and the out put of semi-empirical formula. Also, The obtained results using deformation is better confirmed the Geiger-Nuttall low of alpha decay, especially for emission of light clusters as expected.     

A new hyperbolic auxiliary function method and exact solutions of the mBBM equation

We propose a new hyperbolic auxiliary function method in this communication. Applying this, exact traveling wave solutions for the modified Benjamin–Bona–Mahoney are constructed.     

Enhancement of free space optical link in heavy rain attenuation using multiple beam concept

Free space optics (FSO) has attracted a lot of attention for a variety of applications in telecommunications area, and it is dream of every researcher and telecommunication society to make it a real alternative solution for the last mile problem, to replace fiber optics. FSO is much preferred because of its low maintenance cost and deployment time. FSO with single-beam system is vulnerable to atmospheric attenuation, so to overcome this, a multiple-beam FSO transceiver system has become prominent and is usually used. In this paper, average rain attenuation is evaluated from the collected rain intensity data which are collected for a period of seven months, and implemented in the study concerning results relating link distance, and received optical power of using multiple-beam FSO system in tropical rainy weather. Comparison is made in terms of received optical power, geometrical losses, atmospheric losses, and bit error rate (BER) on using different number of optical beams, based on simulation at data rate of 1 Gb/s. From the results it is clear that the quality of received power is improved by using up to four beams, along with link distance up to 1141.2 m as compared to one-beam, two-beam, and three-beam, with link distances 833.3 m, 991.0 m, 1075.4 m, respectively.     

Study of electrical conductivity and phase transition in Bi2O3–V2O5 system

The solid solutions of bismuth–vanadate were prepared by the conventional solid-state reaction. The sample characterization and the study of phase transition were done by using FT-IR, X-ray diffraction (XRD) and DSC measurements. AC impedance measurements proved that the oxide ion conductivity predominantly arises from the grain and grain boundary contributions as two well-defined semicircles are clearly seen along with an inclined spike. The electrical conductivity of Bi₂O₃–V₂O₅ has been studied at different temperatures for various molar ratios. The isothermal conductivity increases with an increase in the concentration of V₂O₅ due to the vacancy migration phenomenon. It has been found that the conductivity of different compositions of Bi₂O₃–V₂O₅ increases and shows a jump in the temperature range 230–260°C due to the phase transition of BiVO₄ from monoclinic scheelite type to that of tetragonal scheelite type. The endothermic peak in DSC at around 260°C reveals the phase transition, which is also confirmed by the XRD and FT-IR analysis. The XRD patterns confirmed the monoclinic structure of BiVO₄.     

Spectroscopic properties and amplified spontaneous emission of a new derivative of fluorescein

The new laser dye, 2-(6-acryloyloxy-3-oxo-3H-xanthen-9-yl)-benzoic acid ethyl ester [AOXBE] has been synthesized. Its chemical structure was confirmed by ¹HNMR, IR, MS and elemental analysis. This new dye was covalently bonded with methyl methacrylate (MMA) and 2-hydroxy ethyl-methacrylate (HEMA) copolymer backbone. Its optical properties were experimentally investigated. Amplified spontaneous emission (ASE) and photostability were studied by pumping the dye polymeric sample with a 355 nm (8 ns) pulsed Nd:YAG laser. PACS 42.55.Mv; 42.70.Hj; 42.70.Jk; 42.55.Px     

Ligand influence on the electrochemical behavior of some copper(II) thiosemicarbazone complexes

The redox properties of the title mono- and binuclear copper(II) chelates have been investigated by cyclic voltammetry in DMF at a working platinum electrode. The cathodic reduction and anodic oxidation of the investigated chelates produced the corresponding electrochemical Cu^I and Cu^IIIspecies stable only in the voltammetric time scale, The effects of substituents on E_1/2, redox properties and stability towards oxidation of the complexes were related to the electron-withdrawing or releasing ability of the substituents on the C=N¹[H, CH₃ or C₆H₅] and/or N⁴H [H, C₂H₅, C₆H₅ or pClC₆H₄] groups, The electron attracting substituents stabilize the Cu(II) complexes while electron-donating groups favor oxidation to Cu(III). Changes in the E_1/2 for the complexes due to remote substituent effects could be related to changes in basicity of N⁴H.Thus, variation in N⁴1-J has more influence on E_1/2 than changes in C=N¹. The correlation between E_1/2 of the complexes and pK_a of the ligands has been attributed to the spherical potential generated by the electron density of the donor atoms at the antibonding d orbitals.     

Correlation between phase structure and electrical conduction in BISNVOX system for intermediate temperature solid oxide fuel cells (IT-SOFC)

Samples of Sn⁴⁺-substituted bismuth vanadate, formulated as Bi₄Sn _x V_{2? x} O_{11?( x /2)? δ} in the composition range 0.07 ≤ x ≤ 0.30, were prepared by standard solid-state reactions. Sample characterization and the principal phase transitions (α ? β, β ? γ and γ′ ? γ) were investigated by FT-IR spectroscopy, X-ray powder diffraction, differential thermal analysis (DTA) and AC impedance spectroscopy. For composition x = 0.07, the α ? β and β ? γ phase transitions were observed at temperatures of 451 and 536°C, respectively. DTA thermograms and Arrhenius plots of conductivities revealed the γ′ ? γ phase transition at 411 and 423°C for x = 0.20 and 0.30, respectively. AC impedance plots showed that conductivity is mainly due to the grain contribution, which is evident in the enhanced short-range diffusion of oxide ion vacancy in the grains with increasing temperature. The highest ionic conductivity (5.03 × 10^?5 S cm^?1 at 300°C) was observed for the x = 0.17 solid solution with less pronounced thermal hysteresis.     

Photo-physical properties and amplified spontaneous emission of a new derivative of fluorescein

The synthesis of new high-performance dyes and the implementation of new ways of incorporating the organic molecules into the solid host matrices have produced a great deal of activity in the field of solid-state dye lasers. In this article, the new laser dye, 2-(6-allyl-3-oxo-3H-xanthen-9-yl)-benzoic acid ethyl ester [AXBE] has been synthesized, and its chemical structure was confirmed by ¹H NMR, ¹³C NMR, IR and elemental analysis. This new dye was covalently bonded with methyl methacrylate (MMA) and 2-hydroxy ethyl methacrylate (HEMA) copolymer backbone and evaluated as the active medium of the solid-state laser dye. Its optical properties were experimentally investigated. Amplified spontaneous emission (ASE) and photostability were studied by pumping the dye sample with 355 nm (8 ns) pulsed Nd-YAG laser.