Some properties of q-biorthogonal polynomials

Almost four decades ago, Konhauser introduced and studied a pair of biorthogonal polynomials

     

The normal subgroup structure of the extended Hecke groups

We consider the extended Hecke groups generated by T(z) = −1/z, S(z) = −1/(z + λ) and R(z) = 1/z with λ ≥ 2. In this paper, firstly, we study the fundamental region of the extended Hecke groups . Then, we determine the abstract group structure of the commutator subgroups , the even subgroup , and the power subgroups of the extended Hecke groups . Also, finally, we give some relations between them.     

The sensitive capillary electrophoretic‐LIF method for simultaneous determination of curcuminoids in turmeric by enhancing fluorescence intensities of molecules upon inclusion into (2‐hydroxypropyl)‐β‐cyclodextrin

Curcuminoids have received great attention in the past decades due to their health benefit properties. The aim of this study is to develop a very simple, rapid, and sensitive capillary zone electrophoresis technique coupled with a laser induced fluorescence detector (LIF) for the simultaneous determination of three major curcuminoids of turmeric, namely, curcumin, demethoxy curcumin (DMC), and bisdemethoxy curcumin (BDMC). Background electrolyte was selected as borate at pH 9.6 and (2‐hydroxypropyl)‐β‐cyclodextrin (2‐HP‐β‐CD) was added to prevent rapid alkali degradation of curcuminoids in buffer and to increase fluorescence intensities of molecules. With the addition of 2‐HP‐β‐CD to the separation electrolyte, the fluorescence signal intensities of curcuminoids were enhanced considerably by 30, 40, and 54 fold for curcumin, DMC, and BDMC, respectively. The three curcuminoids of turmeric were fully separated and quantified in less than 4.5 min. The repeatability of the peak areas of curcuminoids for intra‐day and inter‐day experiments was in the satisfactory range of 2.26 and 2.55%, respectively. The LOD and LOQ values for the developed method were equal to or less than 0.081 and 0.270 μg/mL, respectively, for all curcuminoids. The developed method was successfully applied to find curcuminoids amount in turmeric samples and herbal supplements.     

Enantiospecific Synthesis of (R)‐3‐Amino‐4‐(2,4,5‐trifluorophenyl)butanoic Acid Using (S)‐Serine as a Chiral Pool

Starting from (S)‐serine, a new method was developed for the synthesis of the β‐amino acid part of sitagliptin in ten steps and with an overall yield of 30%. The crucial step of the synthesis was the ring opening of N‐ and O‐protected (R)‐aziridin‐2‐methanol with (2,4,5‐trifluorophenyl)magnesium bromide to give N‐ and O‐protected (R)‐2‐amino‐3‐(2,4,5‐trifluorophenyl)propan‐1‐ol.     

Spectroscopic characterization,X-ray structure and DFT studies on 4-[3-(2,5-dimethylphenyl)-3-methylcyclobutyl]-N-methylthiazol-2-amine

The titled molecule 4-[3-(2,5-dimethylphenyl)-3-methylcyclobutyl]-N-methylthiazol-2-amine (C₁₇H₂₂N₂S) is synthesized and characterized by ¹H NMR, ¹³C NMR, IR, and X-ray single crystal determination. The compound crystallizes in the monoclinic space group P2_1/c with a = 6.3972(4) Å, b = 9.4988(6) Å, c = 26.016(2) Å and β = 93.496(7)°. In addition to the molecular geometry from the X-ray determination, vibrational frequencies and gauge, including the atomic orbital (GIAO), ¹H and ¹³C NMR chemical shift values of the titled compound in the ground state are calculated using the density functional (B3LYP) method with 6-31G(d), 6-31++G(d,p) and 6-311+G(2d,p) basis sets. The calculated results show that the optimized geometries can well reproduce the crystal structure. Moreover, the theoretical vibrational frequencies and chemical shift values show good agreement with the experimental values. The predicted nonlinear optical properties of the titled compound are greater than those of urea. DFT calculations of the molecular electrostatic potentials and frontier molecular orbitals of the titled compound are carried out at the B3LYP/6-31G(d) level of theory.     

Fabrication of photo‐cross‐linked polyethyleneimine‐based barriers for CO2 capture

In this study, first, polyethyleneimine was acrylated and mixed with polyvinyl alcohol solution to prepare photo‐crosslinked polyethyleneimine (PEI)‐based nanofibers by utilizing ultraviolet and electrospinning technique at the same time. For CO₂ permeability testing, same formulations were prepared by using solvent casting technique and exposed to ultraviolet light to have polyethyleneimine‐based membrane films. The chemical structures of the nanofibers were characterized by Fourier transform infrared spectroscopy. The thermal properties of nanofibers were examined by thermal gravimetric analysis and differential scanning calorimeter. The morphology of nanofibers was investigated by scanning electron microscopy. CO₂ permeabilities of samples were also measured. Copyright © 2015 John Wiley & Sons, Ltd.     

Fabrication of collagen immobilized electrospun poly (vinyl alcohol) scaffolds

In the development of tissue engineering scaffolds, the interactions between material surface and cells play crucial roles. The biomimetic 3‐D scaffolds absolutely provide better results for fulfilling requirements such as porosity, interconnectivity, cell attachment and proliferation. In this study, 3‐D electrospun scaffolds were prepared by using an electrospinning technique. Photo cross‐linkable polyvinyl alcohol was used as a polymeric matrix. During the electrospinning, the nanofibers were cross‐linked with in situ ultraviolet radiation. The crosslinked polymer fibers were achieved in a simple process at a single step. Nanofiber surface was modified with collagen by a chemical approach. The chemical structures were proven by attentuated total reflectance Fourier transform infrared spectroscopy and proton nuclear magnetic resonance. The surface morphology of the nanofibers was characterized by scanning electron microscope (SEM). Morphological investigations show that the resulting nanofibrous matrix has uniform morphology with a diameter of 220–250 nm. In vitro attachment and growth of 3T3 mouse fibroblasts and human umbilical vein endothelial cells (ECV304) cells on polyvinyl alcohol‐based nanofiber mats were also investigated. Cell attachment, proliferation, and methylthiazole tetrazolium cytotoxicity assays indicated good cell viability throughout the culture time, which was also confirmed by SEM analysis. Copyright © 2015 John Wiley & Sons, Ltd.     

In vitro biological activities and fatty acid profiles of Pistacia terebinthus fruits and Pistacia khinjuk seeds

This study reports in vitro anticholinesterase, antioxidant and antimicrobial effects of the n-hexane, dichloromethane, ethanol and ethanol–water extracts prepared from Pistacia terebinthus L. fruits and Pistacia khinjuk Stocks seeds as well as their total phenolic and flavonoid contents, and fatty acid compositions. Ethanol and ethanol–water extracts of both species exhibited higher anticholinesterase activity than galanthamine. Among ABTS, DPPH and CUPRAC assays, the highest antioxidant capacity of the extracts was found in the last one. P. terebinthus ethanol extract being rich in flavonoid content showed the best cupric reducing effect. All extracts possessed no antimicrobial activity. The main fatty acid in P. terebinthus fruits (52.52%) and P. khinjuk seeds (59.44%) was found to be oleic acid. Our results indicate that P. terebinthus fruits and P. khinjuk seeds could be a good source of anticholinesterase compounds, and could be phytochemically investigated.     

State-of-the-art computations of dipole moments using analytic gradients of high-level density-fitted coupled-cluster methods with focal-point approximations

Using the analytic derivatives approach, dipole moments of high-level density-fitted coupled-cluster (CC) methods, such as coupled-cluster singles and doubles (CCSD), and coupled-cluster singles and doubles with perturbative triples [CCSD(T)], are presented. To obtain the high accuracy results, the computed dipole moments are extrapolated to the complete basis set (CBS) limits applying focal-point approximations. Dipole moments of the CC methods considered are compared with the experimental gas-phase values, as well as with the common DFT functionals, such as B3LYP, BP86, M06-2X, and BLYP. For all test sets considered, the CCSD(T) method provides substantial improvements over Hartree–Fock (HF), by 0.076–0.213 D, and its mean absolute errors are lower than 0.06 D. Furthermore, our results indicate that even though the performances of the common DFT functionals considered are significantly better than that of HF, their results are not comparable with the CC methods. Our results demonstrate that the CCSD(T)/CBS level of theory provides highly-accurate dipole moments, and its quality approaching the experimental results. © 2019 Wiley Periodicals, Inc.     

Large-scale simulations and parameter study for a simple recrystallization model

Distance function-based diffusion-generated motion, a highly efficient numerical algorithm, is used to simulate a classical model of recrystallization in unprecedented detail and in physically relevant parameter regimes not attainable with many previous techniques. The algorithm represents interfaces implicitly and is closely related to the level set method. In particular, it allows for automatic topological changes and arbitrarily large time-steps. Large-scale simulations of recrystallization for physically relevant parameter values are presented in detail. In addition, new analytical estimates for the distribution of surviving nuclei are obtained and compared with the numerical results.