Convergence in Variation for Bernstein-Type Operators

In this paper, we deal with Bernstein-type operators defined by Cárdenas-Morales et al. as \({B_{n}(f \circ \tau^{-1}) \circ \tau}\), where \({B_{n}}\) is the nth Bernstein polynomial (Comput Math Appl 62(1):158–163, 2011). Assuming that \({\tau}\) and f are absolutely continuous functions on \({[0, 1]}\) and inf \({\tau ^{\prime} (x) \geq m > 0}\) as well as \({\tau (0) = 0}\) and \({\tau (1) = 1,}\) we study the convergence of Bernstein-type operators to f in variation seminorm. Moreover, we give a Voronovskaja-type formula and a Jackson-type estimate in the sense of Bardaro et al. (Analysis 23:299–340, 2003).     

On discrete Picard operators

The present paper is concerned with the approximation properties of discrete version of Picard operators. We first give exact equalities for the moments of the operators. In calculations of these moments, Eulerian numbers play a crucial role. We discuss convergence of these operators in weighted spaces and give Voronovskaya‐type asymptotic formula. The weighted approximation of the operators in quantitative mean in terms of different modulus of continuities is also considered. We emphasize that the rate of convergence of the operators is better than the one obtained in 1 . Copyright © 2016 John Wiley & Sons, Ltd.     

LC-HRMS Profiling and Antidiabetic,Anticholinergic, and Antioxidant Activities of Aerial Parts of Kınkor (Ferulago stellata)

Kınkor (Ferulago stellata) is Turkish medicinal plant species and used in folk medicine against some diseases. As far as we know, the data are not available on the biological activities and chemical composition of this medicinal plant. In this study, the phytochemical composition; some metabolic enzyme inhibition; and antidiabetic, anticholinergic, and antioxidant activities of this plant were assessed. In order to evaluate the antioxidant activity of evaporated ethanolic extract (EEFS) and lyophilized water extract (WEFS) of kınkor (Ferulago stellata), some putative antioxidant methods such as DPPH· scavenging activity, ABTS^•+ scavenging activity, ferric ions (Fe³⁺) reduction method, cupric ions (Cu²⁺) reducing capacity, and ferrous ions (Fe²⁺)-binding activities were separately performed. Furthermore, ascorbic acid, BHT, and α-tocopherol were used as the standard compounds. Additionally, the main phenolic compounds that are responsible for antioxidant abilities of ethanol and water extracts of kınkor (Ferulago stellata) were determined by liquid chromatography-high-resolution mass spectrometry (LC-HRMS). Ethanol and water extracts of kınkor (Ferulago stellata) demonstrated effective antioxidant abilities when compared to standards. Moreover, ethanol extract of kınkor (Ferulago stellata) demonstrated IC₅₀ values of 1.772 μg/mL against acetylcholinesterase (AChE), 33.56 ± 2.96 μg/mL against α-glycosidase, and 0.639 μg/mL against α-amylase enzyme respectively.     

Effect of extraction conditions on measured total polyphenol contents and antioxidant and antibacterial activities of black tea

Black tea was extracted for 2, 8 and 18 h with absolute acetone, N,N-dimethyl-formamide (DMF), ethanol and methanol and their 50% aqueous solutions. The extracts were screened for total polyphenol contents, antioxidant and antibacterial activities. The polyphenol content of the extracts was found to be in the range of 0.44-114.01 mg gallic acid equivalents (GAE)/g dry weight tea, depending on the solvent used and the length of the extraction process. In general, aqueous acetone or DMF extracts displayed the highest polyphenol contents and antioxidant activity, while absolute acetone was the least efficient solvent. Antioxidant activities of tea extracts tested using the reducing power and 2,2-diphenyl-1-picryhydrazyl (DPPH) radical methods ranged from 0.09 to 1.18 and from 2.60 to 95.42 %, respectively, depending on the extraction conditions and the antioxidant activities correlated well with the polyphenol concentrations. Aqueous solvent black tea extracts also possessed antibacterial activity, depending on the solvent used and bacterial species tested. Staphylococcus aureus was found to be the most sensitive to all tea extracts, except for the methanol extract. Tea extracts were not effective against Y. enterocolitica, L. monocytogenes and E. coli O157:H7.     

Reactions of (1E)‐Buta‐1,3‐dien‐1‐yl Acetate with Diazocarbonyl Compounds

Carbene transfer to appropriate substrates is a highly versatile tool for the construction of carbon frameworks with increased functional and structural complexity. In this study, some novel cyclopropane derivatives were synthesized via carbenoid reactions and their further reactivities were investigated. (1E)‐Buta‐1,3‐dien‐1‐yl acetate was reacted with four different diazocarbonyl compounds, ethyl diazoacetate, dimethyl diazomalonate, 1‐diazo‐1‐phenylpropan‐2‐one, and methyl (3E)‐2‐diazo‐4‐phenylbut‐3‐enoate, in the presence of two catalysts. All synthesized substituted cyclopropanes were obtained chemoselectively with respect to less‐hindered C?C bonds. Under the applied conditions, while cyclopropanes 7a and 7d underwent further reactions, cyclopropanes 7b and 7c were stable enough. Cyclopropanes 7a and an additional equivalent of ethyl diazoacetate yielded polyfunctionalized cyclohexenes. Cyclopropanes from methyl (3E)‐2‐diazo‐4‐phenylbut‐3‐enoate yielded polyfunctionalyzed cycloheptadiene isomers by Cope rearrangement.     

Synthesis and biological activity of new 1,3-dioxolanes as potential antibacterial and antifungal compounds

A series of new enantiomerically pure and racemic 1,3-dioxolanes 1-8 was synthesized in good yields and short reaction times by the reaction of salicylaldehyde with commercially available diols using a catalytic amount of Mont K10. Elemental analysis and spectroscopic characterization established the structure of all the newly synthesized compounds. These compounds were tested for their possible antibacterial and antifungal activity. Biological screening showed that all the tested compounds, except 1, show excellent antifungal activity against C. albicans, while most of the compounds have also shown significant antibacterial activity against S. aureus, S. epidermidis, E. faecalis and P. aeruginosa.     

Theoretical study on HF elimination and aromatization mechanisms: a case of pyridoxal 5' phosphate-dependent enzyme

Pyridoxal 5-phosphate (PLP), the phosphorylated and the oxidized form of vitamin B6 is an organic cofactor. PLP forms a Schiff base with the ?-amino group of a lysine residue of PLP-dependent enzymes. γ-Aminobutyric acid (GABA) aminotransferase is a PLP-dependent enzyme that degrades GABA to succinic semialdehyde, while reduction of GABA concentration in the brain causes convolution besides several neurological diseases. The fluorine-containing substrate analogues for the inactivation of the GABA-AT are synthesized extensively in cases where the inactivation mechanisms involve HF elimination. Although two proposed mechanisms are present for the HF elimination, the details of the base-induced HF elimination are not well identified. In this density functional theory (DFT) study, fluorine-containing substrate analogue, 5-amino-2-fluorocyclohex-3-enecarboxylic acid, is particularly chosen in order to explain the details of the HF elimination reactions. On the other hand, the experimental studies revealed that aromatization competes with Michael addition mechanism in the presence of 5-amino-2-fluorocyclohex-3-enecarboxylic acid. The results allowed us to draw a conclusion for the nature of HF elimination, besides the elucidation of the mechanism preference for the inactivation mechanism. Furthermore, the solvent phase calculations carried out in this study ensure that the proton transfer steps should be assisted either by a water molecule or a base for lower activation energy barriers.     

Synthesis, photophysical and thermal studies of symmetrical and unsymmetrical zinc phthalocyanines

The novel zinc phthalocyanine (3) with malonylester and chloro groups on each benzo unit was synthesized from 4-diethoxymalonyl-5-chloro-phthalonitrile (1). The unsymmetrically substituted zinc phthalocyanine (5), carrying hexylthio, malonylester and chloro groups at the periphery, was obtained from 4-diethoxymalonyl-5-chloro-phthalonitrile (1) and 4,5-bis-hexylsulfanyl-phthalonitrile (2) by a statistical condensation method as an A₃B type unsymmetrical phthalocyanine compound. Transesterification of the malonyl esters of the new symmetrical and unsymmetrical phthalocyanines occurred during the cyclotetramerization of dinitriles with Zn(CH₃COO)₂ in 1-pentanol in the presence of DBU. Octa-hexylthio-substituted zinc phthalocyanine (4) was prepared according to the literature. The photophysical and thermal properties of all the phthalocyanine complexes are described for the first time. These novel symmetrical and unsymmetrical phthalocyanine macrocycles have been characterized by a series of spectroscopic methods including ¹H NMR, electronic absorption, IR and mass spectroscopy, in addition to elemental analysis. Their narrow long wavelength absorption band shows that the bulky substituents on the periphery prevent aggregation. The unsymmetrically substituted phthalocyanine (5) gave a greater fluorescence quantum yield in chloroform than the symmetrical analogues (3 and 4).     

Preparation, characterization and antimicrobial property of micro-nano sized Na-borosilicate glass powder with spherical shape

Spherical glass powders are potential materials for the production of a high performance coating where uniform porosities are obtainable with a high hydrophilic nature. Coating with antimicrobial properties increases the engineering properties of the materials. In this study, Ag₂O doped (0.5-5 wt.% Ag₂O) Na-borosilicate micro (1.227 μm) and nano (134 nm) sized glass powders were prepared by ultrasonic spray pyrolysis. The antimicrobial properties against gram positive bacteria (Bacillus cereus and Staphylococcus aureus), gram negative bacteria (Escherichia coli) and yeast (Candida albicans) were determined using the agar-disc diffusion and modified agar well methods. The results show that the prepared powders are spherical, of amorphous structure and have a very smooth surface. The increase in silver oxide content increased the powders' antimicrobial activity. Powders with 2.5 wt.% Ag₂O content are highly active (?) against the three types of microorganisms. The nano sized powder also increased antimicrobial activity.     

Prediction of protein pKa with representation learning

The behavior of proteins is closely related to the protonation states of the residues. Therefore, prediction and measurement of pK_a are essential to understand the basic functions of proteins. In this work, we develop a new empirical scheme for protein pK_a prediction that is based on deep representation learning. It combines machine learning with atomic environment vector (AEV) and learned quantum mechanical representation from ANI-2x neural network potential (J. Chem. Theory Comput. 2020, 16, 4192). The scheme requires only the coordinate information of a protein as the input and separately estimates the pK_a for all five titratable amino acid types. The accuracy of the approach was analyzed with both cross-validation and an external test set of proteins. Obtained results were compared with the widely used empirical approach PROPKA. The new empirical model provides accuracy with MAEs below 0.5 for all amino acid types. It surpasses the accuracy of PROPKA and performs significantly better than the null model. Our model is also sensitive to the local conformational changes and molecular interactions.

We developed new empirical ML model for protein pK_a prediction with MAEs below 0.5 for all amino acid types.