Capable Lie algebras with the derived subalgebra of dimension 2 over an arbitrary field

In this paper, we classify all capable nilpotent Lie algebras with the derived subalgebra of dimension 2 over an arbitrary field. Moreover, the explicit structure of such Lie algebras of class 3 is given.     

Linear and nonlinear intersubband optical absorption and refractive index changes of asymmetric double semi-parabolic quantum wells

The optical properties of the asymmetric double semi-parabolic quantum wells (DSPQWs) are investigated numerically for typical GaAs/Al_xGa_1−xAs. Optical properties are obtained using the compact density matrix approach. In this work, effects of the structure parameters such as the barrier width and the well widths on the optical properties of the asymmetric DSPQWs are investigated. The results show that the linear and nonlinear optical properties of asymmetric DSPQW are non-monotonic functions of these structure parameters. The behavior of the refractive index changes of asymmetric DSPQW with the variation of the barrier width is different substantially with that of symmetric DSPQW. Results reveal that the resonant peak values of the total absorption coefficient of asymmetric DSPQW is usually greater than that of symmetric DSPQW. Our calculations also show that the total absorption coefficient of asymmetric DSPQW is larger than that of asymmetric double square quantum well.     

Coupled-mode analysis for linear fiber Bragg grating made of metamaterial

We derive the coupled-mode equations for a metamaterial fiber Bragg gratings (FBGs). The coupled-mode theory describing wave propagation in periodic structures such as FBG is generalized for studying the transmission and reflection of electromagnetic waves through a FBG containing metamaterial layers. This approach shows that the band gap becomes broader in comparison with a conventional FBG. It is observed that the central frequency of the band gap has a shift in regard of changing metamaterial thickness. We verify this investigation through attaining the transmission and reflection spectra of a conventional FBG while we are setting related parameters. Furthermore, this proposed structure can be applied as a tunable filter.     

An Efficient One‐Pot,Four‐Component Synthesis of {[(1H‐1,2,3‐Triazol‐4‐yl)methoxy]phenyl}‐1H‐pyrazolo[1,2‐b]phthalazine‐5,10‐dione Derivatives

The 1‐{[(1H‐1,2,3‐Triazol‐4‐yl)methoxy]phenyl}‐1H‐pyrazolo[1,2‐b]phthalazine‐5,10‐dione derivatives 5 were synthesized by a simple and efficient method, i.e., by the four‐component, one‐pot condensation reaction of phthalohydrazide 4 , a (propargyloxy)benzaldehyde 1 , an active methylene compound 3 (malononitrile or ethyl cyanoacetate), and an azide 2 in the presence of Cu(OAc)₂/sodium L ‐ascorbate as catalyst and 1‐methyl‐1H‐imidazolium trifluoroacetate ([Hmim](CF₃COO)) as an ionic‐liquid medium in good to excellent yields (Scheme 1).     

SOME NEW EXTENSIONS OF EDELSTEIN-SUZUKI-TYPE FIXED POINT THEOREM TO G-METRIC AND G-CONE METRIC SPACES

In this paper, we prove some fixed point theorems for generalized contractions in the setting of G-metric spaces. Our results extend a result of Edelstein [M. Edelstein, On fixed and periodic points under contractive mappings, J. London Math. Soc., 37 （1962）, 74-79] and a result of Suzuki [T. Suzuki, A new type of fixed point theorem in metric spaces, Nonlinear Anal., 71 （2009）, 5313-5317]. We prove, also, a fixed point theorem in the setting of G-cone metric spaces.     

A facile procedure for the one-pot synthesis of unsymmetrical 2,5-disubstituted 1,3,4-oxadiazoles

Unsymmetrically 2,5-disubstituted 1,3,4-oxadiazoles were efficiently synthesized from the cyclization-oxidation reaction of acyl hydrazones. Also, the synthesis of the title compounds was achieved by the condensation of acyl hydrazides and aromatic aldehydes in the presence of ceric ammonium nitrate in dichloromethane.     

Calix[4]arene-based crab-like molecular sensors for highly selective detection of mercury and copper ions

In this work, two novel chemosensors based on calix[4]arene bearing (thio)barbituric acid groups (BC1 and BC2) were synthesised, and their structures were characterised by HRMS, NMR and FTIR. Furthermore, their binding properties towards various biologically relevant metal ions were studied by fluorescence titrations, ¹H NMR spectroscopies and Job’s plot evaluations. The chemosensor BC1 displayed excellent binding affinity and selectivity towards Cu²⁺, which was characterised using fluorescence spectroscopy. On the other hand, BC2 exhibited a very remarkable fluorescence enhancement as well as visible colour change from pale green to sunset yellow, in presence of Hg²⁺ ions. Finally, Job’s plot method revealed 1:1 binding stoichiometry for both BC1:Cu²⁺ complex and BC2:Hg²⁺ complex.     

Exact and approximation product solutions form of heat equation with nonlocal boundary conditions using Ritz–Galerkin method with Bernoulli polynomials basis

In this article, a new method is introduced for finding the exact solution of the product form of parabolic equation with nonlocal boundary conditions. Approximation solution of the present problem is implemented by the Ritz–Galerkin method in Bernoulli polynomials basis. The properties of Bernoulli polynomials are first presented, then Ritz–Galerkin method in Bernoulli polynomials is used to reduce the given differential equation to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the techniques presented in this article for finding the exact and approximation solutions. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1143–1158, 2017     

An efficient one-pot method for the synthesis of novel ferrocene-triamide conjugates via pseudo five-component reaction

A simple and efficient one-pot synthesis of novel ferrocene-triamide conjugates from the reaction of ferrocenecarboxaldehyde with Meldrum’s acid and isocyanides in the presence of NH-containing compounds is described. This transformation proceeds through the creation of two CC bonds, two CN bonds, and one CO bond, leading to three peptide bonds, and presumably occurs via a domino sequence involving Knoevenagel condensation, [1+4] cycloaddition, deacetonation, and aminolysis reactions.