EM-Wave Diffraction by a Finite Plate with Dirichlet Conditions in the Ionosphere of Cold Plasma

In the current communication, the problem of plane wave diffraction by a conductible plate of finite length in the presence of cold plasma is investigated. The boundary-value problem corresponding to this model is formulated by Fourier transform which then leads to the Wiener?Hopf equation. The resulting equation has been solved by the Wiener?Hopf procedure in a standard way. The separated field (diffracted field) is analyzed in an anisotropic medium using asymptotic expansion and modified stationary phase method. The problem can be made simple by assuming ε₂→0, where ε₂ is the element of permittivity tensor. This happens, if the operating frequency is assumed to be very large as compared to ω_c (cyclotron frequency) while it is of same order of ω_p (the plasma frequency). The case ε₁ =1, ε₂→0 leads to the results for soft plate of finite length in an isotropic medium. Graphical study is performed to investigate the behavior of separated field for various physical parameters for isotropic and anisotropic media.     

Lithium‐Salt‐Containing High‐Molecular‐Weight Polystyrene‐block‐Polyethylene Oxide Block Copolymer Films

Ionic conductivity in relation to the morphology of lithium‐doped high‐molecular‐weight polystyrene‐block‐polyethylene oxide (PS‐b‐PEO) diblock copolymer films was investigated as solid‐state membranes for lithium‐ion batteries. The tendency of the polyethylene (PEO) block to crystallize was highly suppressed by increasing both the salt‐doping level and the temperature. The PEO crystallites completely vanished at a salt‐doping ratio of Li/EO>0.08, at which the PEO segments were hindered from entering the crystalline unit of the PEO chain. A kinetically trapped lamella morphology of PS‐b‐PEO was observed, due to PEO crystallization. The increase in the lamella spacing with increasing salt concentration was attributed to the conformation of the PEO chain rather than the volume contribution of the salt or the previously reported increase in the effective interaction parameter. Upon loading the salt, the PEO chains changed from a compact/highly folded conformation to an amorphous/expanded‐like conformation. The ionic conductivity was enhanced by amorphization of PEO and thereby the mobility of the PEO blocks increased upon increasing the salt‐doping level.     

Preparation, spectral and biological investigation of formaldehyde-based ligand containing piperazine moiety and its various polymer metal complexes

A novel tetradentate salicylic acid-formaldehyde ligand containing piperazine moiety (SFP) was synthesized by condensation of salicylic acid, formaldehyde and piperazine in presence of base catalyst, which was subjected for the preparation of coordination polymers with metal ions like manganese(II), cobalt(II), copper(II), nickel(II) and zinc(II). All the synthesized polymeric compounds were characterized by elemental analysis, IR, (1)H NMR and electronic spectral studies. The thermal stability was determined by thermogravimetric analysis and thermal data revealed that all the polymer metal complexes show good thermal stability than their parent ligand. Electronic spectral data and magnetic moment values revealed that polymer metal complexes of Mn(II), Co(II) and Ni(II) show an octahedral geometry while Cu(II) and Zn(II) show distorted octahedral and tetrahedral geometry respectively. The antimicrobial screening of the ligand and coordination polymers was done by using Agar well diffusion method against various bacteria and fungi. It was evident from the data that antibacterial and antifungal activity increased on chelation and all the polymer metal complexes show excellent antimicrobial activity than their parent ligand.     

Fourth power diophantine equations in Gaussian integers

In this paper, we examine a class of fourth power diophantine equations of the form \(x^4+kx^2y^2+y^4=z^2\) and \(ax^4+by^4=cz^2\), in the Gaussian integers, where a and b are prime integers.     

Dual Gold‐Catalyzed Cycloaromatization of Unconjugated (E)‐Enediynes

A synthesis of unconjugated (E)‐enediynes from allenyl amino alcohols is reported and their gold‐catalyzed cascade cycloaromatization to a broad range of enantioenriched substituted isoindolinones has been developed. Experimental and computational studies support the reaction proceeding via a dual‐gold σ,π‐activation mode, involving a key gold‐vinylidene‐ and allenyl‐gold‐containing intermediate.     

New terpenoids from Stachys parviflora Benth

Two new triterpenoidal saponins were isolated from the n-butanolic extract of Stachys parviflora (Lamiaceae). Their structures were elucidated on the basis of spectral data as stachyssaponin A; 3beta, 15alpha, 19alpha, 21beta, 22alpha-pentahydroxyolean-12-ene-28-oic acid 3-O-{alpha-L-rhamnopyranosyl-(1 --> 3)-beta-D-glucopyranoside}-22-O-{alpha-L-arabinofuranosyl-(1 --> 3)-beta-D-glucopyranoside} (1) and stachyssaponin B; 2beta, 3beta, 15alpha, 21beta-tetrahydroxyolean-12-ene-28-oic acid 2-O-[alpha-L-arabinofuranoside]-3, 21-bis-O-[beta-D-glucopyranoside] (2).     

An Analytical Technique,Based on Natural Transform to Solve Fractional-Order Parabolic Equations

This research article is dedicated to solving fractional-order parabolic equations using an innovative analytical technique. The Adomian decomposition method is well supported by natural transform to establish closed form solutions for targeted problems. The procedure is simple, attractive and is preferred over other methods because it provides a closed form solution for the given problems. The solution graphs are plotted for both integer and fractional-order, which shows that the obtained results are in good contact with the exact solution of the problems. It is also observed that the solution of fractional-order problems are convergent to the solution of integer-order problem. In conclusion, the current technique is an accurate and straightforward approximate method that can be applied to solve other fractional-order partial differential equations.