Characterizing student mathematics teachers’ levels of understanding in spherical geometry

This article presents an exploratory study aimed at the identification of students’ levels of understanding in spherical geometry as van Hiele did for Euclidean geometry. To do this, we developed and implemented a spherical geometry course for student mathematics teachers. Six structured, task-based interviews were held with eight student mathematics teachers at particular times through the course to determine the spherical geometry learning levels. After identifying the properties of spherical geometry levels, we developed Understandings in Spherical Geometry Test to test whether or not the levels form hierarchy, and 58 student mathematics teachers took the test. The outcomes seemed to support our theoretical perspective that there are some understanding levels in spherical geometry that progress through a hierarchical order as van Hiele levels in Euclidean geometry.     

Mathematical analysis of an influenza epidemic model,formulation of different controlling strategies using optimal control and estimation of basic reproduction number

In this article, a deterministic model is formulated to perform a thorough investigation of the transmission dynamics of influenza. In particular, our model takes into account the effects of medication as well as hospitalization. An in-depth stability analysis of the model is performed, and it is subsequently shown that the model is locally, as well as globally asymptotically stable, when R₀ > 1. It is also shown that there exists a unique endemic equilibrium whenever R₀ > 1. After estimating the effective contact rate, we estimate the basic reproduction number, using both an ordinary least squares and generalized least squares methodology. We also estimated confidence intervals for the effective contact rate using parametric bootstrapping. Furthermore, we perform uncertainty and sensitivity analysis to recognize the impact of crucial model parameters on R₀. In addition, using ideas from the optimal control theory, optimal medication and hospitalization strategies are proposed to eliminate the disease.     

vic‐Tricarbonyl Compounds of Quinolines: Analogues of Ninhydrin: A Short Review

Derivatives of ninhydrin are extensively used in the field of forensic sciences as important latent fingerprint reagents. Many works have been performed upon their synthesis and reactivity, but there are many spaces to work on the compounds of quinoline‐2,3,4(1H)‐triones—analogues of ninhydrin, in both dimensions: synthesis and reactivity, and according to the best of our knowledge, not a single detailed or short compiled article has been published for these compounds. This review briefly summarizes the chemistry of quinoline‐2,3,4(1H)‐triones.     

Effect of ring substitution on synthesis of benzimidazolium salts and their silver(I) complexes: characterization,electrochemical studies and evaluation of anticancer potential

Transition Metal Chemistry - A series of bidendate 5,6-dimethyl benzimidazolium-based N-heterocyclic carbene (NHC) proligands and their silver complexes were synthesized. The synthetic approaches...     

Thiourea Derivatives,Simple in Structure but Efficient Enzyme Inhibitors and Mercury Sensors

In this study six unsymmetrical thiourea derivatives, 1-isobutyl-3-cyclohexylthiourea (1), 1-tert-butyl-3-cyclohexylthiourea (2), 1-(3-chlorophenyl)-3-cyclohexylthiourea (3), 1-(1,1-dibutyl)-3-phenylthiourea (4), 1-(2-chlorophenyl)-3-phenylthiourea (5) and 1-(4-chlorophenyl)-3-phenylthiourea (6) were obtained in the laboratory under aerobic conditions. Compounds 3 and 4 are crystalline and their structure was determined for their single crystal. Compounds 3 is monoclinic system with space group P2₁/n while compound 4 is trigonal, space group R³:H. Compounds (1–6) were tested for their anti-cholinesterase activity against acetylcholinesterase and butyrylcholinesterase (hereafter abbreviated as, AChE and BChE, respectively). Potentials (all compounds) as sensing probes for determination of deadly toxic metal (mercury) using spectrofluorimetric technique were also investigated. Compound 3 exhibited better enzyme inhibition IC₅₀ values of 50, and 60 µg/mL against AChE and BChE with docking score of −10.01, and −8.04 kJ/mol, respectively. The compound also showed moderate sensitivity during fluorescence studies.     

Photosensitive peptide hydrogels as smart materials for applications

Photosensitive supramolecular peptide hydrogels with the gelators forming by the integration of photosensitive moieties and peptides have been briefly summarized the hydrogelation capabilities, the expressing manner serving as smart materials, and practical applications.     

Small Ubiquitin-Like Modifier Protein 3 Enhances the Solubilization of Human Bone Morphogenetic Protein 2 in <Emphasis Type="Italic">E. coli</Emphasis>

Small ubiquitin-like modifier (SUMO) fusion technology is widely used in the production of heterologous proteins from prokaryotic system to aid in protein solubilization and refolding. Due to an extensive clinical application of human bone morphogenetic protein 2 (hBMP2) in bone augmentation, total RNA was isolated from human gingival tissue and mature gene was amplified through RT-PCR, cloned (pET21a), sequence analyzed, and submitted to GenBank (Accession no. KF250425). To obtain soluble expression, SUMO3 was tagged at the N-terminus of hBMP2 gene (pET21a/SUMO3-hBMP2), transferred in BL21 codon+, and ~?40% soluble expression was obtained on induction with IPTG. The dimerized hBMP2 was confirmed with Western blot, native PAGE analysis, and purified by fast protein liquid chromatography with 0.5 M NaCl elution. The cleavage of SUMO3 tag from hBMP2 converted it to an insoluble form. Computational 3D structural analysis of the SUMO3-hBMP2 was performed and optimized by molecular dynamic simulation. Protein-protein interaction of SUMO3-hBMP2 with BMP2 receptor was carried out using HADDOCK and inferred stable interaction. The alkaline phosphatase assay of SUMO3-hBMP2 on C2C12 cells showed maximum 200-ng/ml dose-dependent activity. We conclude that SUMO3-tagged hBMP2 is more suited for generation of soluble form of the protein and addition of SUMO3 tag does not affect the functional activity of hBMP2.     

Lipase-catalyzed green synthesis of starch–maleate monoesters and its characterization

The present study reports the green synthesis of starch–maleate (SM) at ambient temperature in solvent-free system using Rhizopus arrhizus lipase as a biocatalyst and maleic acid (MA) as an esterification agent. The synthetic scheme was found to be efficient, economical, and ecofriendly. The newly synthesized SM samples were characterized using Fourier transform infrared (FTIR) and proton nuclear magnetic resonance (¹H NMR) spectroscopic techniques. The degree of substitution (DS) was found in the range of 0.53–0.62. Moreover, DS was found to be temperature and time-dependent. X-ray diffraction (XRD) exhibited that maleation did not change the crystalline nature of native starch. Scanning electron microscopy (SEM) revealed that size of SM granules was in the range of 4–18 µm. The activation energy (E_a) of SM formation was calculated to be 42.94 kcal mol^?1 which clearly indicated the effective and rapid interaction of functional groups. Hence, the solvent-free solid-state synthetic methodology proved to be excellent for the synthesis of novel biomaterials with appreciable high DS for drug delivery and sorption of heavy metal ions from water.     

Addition of alkyl radicals to transition-metal-coordinated CO: calculation of the reaction of [Ru(CO)5] and related complexes and relevance to alkane carbonylation

Electronic structure methods have been used to study the transition state and products of the reaction between alkyl radicals and CO coordinated in transition-metal complexes. At the B3LYP DFT level, methyl addition to a carbonyl of [Ru(CO)5] or [Ru(CO)3(dmpe)] is calculated to be about 6 kcal/mol more exothermic than addition to free CO. In contrast, methyl addition to [Mo(CO)6] is 12 kcal/mol less exothermic than addition to CO, while the reaction enthalpy of methyl addition to [Pd(CO)4] is comparable to that of free CO. Related results are obtained at the CCSD-T level and for the reactions of the cyclohexyl radical. The transition state for these reactions is characterized by significant distortion of the geometry of the reactant complex, which include lengthening and bending of the M-CO bond, but with negligible C-C bond formation. Accordingly, the activation energy for addition to coordinated carbonyls is 2-10 kcal/mol greater than that of addition to free CO. Additional calculations were also carried out on representative unsaturated metal carbonyls. The calculated results afford an understanding of the mechanism of previously reported photochemical alkane carbonylation systems utilizing d(8)-ML5 metal carbonyls as cocatalysts. In particular, it is strongly indicated that such systems operate via direct attack by an alkyl radical at a CO ligand, a reaction that has not previously been proposed.     

A Photoferroelectric Perovskite‐Type Organometallic Halide with Exceptional Anisotropy of Bulk Photovoltaic Effects

Perovskite‐type ferroelectrics composed of organometallic halides are emerging as a promising alternative to conventional photovoltaic devices because of their unique photovoltaic effects (PVEs). A new layered perovskite‐type photoferroelectric, bis(cyclohexylaminium) tetrabromo lead ( 1 ), is presented. The material exhibits an exceptional anisotropy of bulk PVEs. Upon photoexcitation, superior photovoltaic behaviors are created along its inorganic layers, which are composed of corner‐sharing PbBr₆ octahedra. Semiconducting activity with remarkable photoconductivity is achieved in the vertical direction, showing sizeable on/off current ratios (>10⁴), which compete with the most active photovoltaic material CH₃NH₃PbI₃. In 1 the temperature‐dependence of photovoltage coincides fairly well with that of polarization, confirming the dominant role of ferroelectricity in such highly anisotropic PVEs. This finding sheds light on bulk PVEs in ferroelectric materials, and promotes their application in optoelectronic devices.