Certain Integral Transforms of Generalized k-Bessel Function

The objective of this note is to provide some(potentially useful) integral transforms(for example, Euler, Laplace, Whittaker etc.) associated with the generalized k-Bessel function defined by Saiful and Nisar [3]. We have also discussed some other transforms as special cases of our main results.     

Development of New Atom Transfer Radical Polymerization System by Iron (III)‐Metal Salts Without Using any External Initiator and Reducing Agent

Atom transfer radical polymerization (ATRP) catalyzed by high oxidation state metal salts of FeX₃ is developed for the first time in the absence of both external initiator and reducing agent. Methyl methacrylate (MMA) and styrene are polymerized successfully using FeX₃/Phosphorous ligands with well‐controlled molecular weight distributions (=1.5). The molecular weight of the polymers increases with monomer consumption with the progress of time and the polymerization behaviors show a decent ATRP trend. Activators and initiators are suggested to generate in situ by the addition reaction of MMA and one equivalent of FeX₃. The PMMA synthesized from without‐initiator system is characterized by ¹H, ¹³C and DEPT (distortionless enhancement by polarization transfer nuclear magnetic resonance) nuclear magnetic resonance spectroscopy. Chain extension and copolymerization experiments prove the livingness of the obtained polymer.

     

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.     

When Some Complement of a Submodule Is a Summand

A module M is said to satisfy the C ₁₁ condition if every submodule of M has a (i.e., at least one) complement which is a direct summand. It is known that the C ₁ condition implies the C ₁₁ condition and that the class of C ₁₁-modules is closed under direct sums but not under direct summands. We show that if M = M ₁ ⊕ M ₂, where M has C ₁₁ and M ₁ is a fully invariant submodule of M, then both M ₁ and M ₂ are C ₁₁-modules. Moreover, the C ₁₁ condition is shown to be closed under formation of the ring of column finite matrices of size Γ, the ring of m-by-m upper triangular matrices and right essential overrings. For a module M, we also show that all essential extensions of M satisfying C ₁₁ are essential extensions of C ₁₁-modules constructed from M and certain subsets of idempotent elements of the ring of endomorphisms of the injective hull of M. Finally, we prove that if M is a C ₁₁-module, then so is its rational hull. Examples are provided to illustrate and delimit the theory.     

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.     

Deciphering key proteins of oil palm (Elaeis guineensis Jacq.) fruit mesocarp development by proteomics and chemometrics

Palm oil is an edible vegetable oil derived from lipid‐rich fleshy mesocarp tissue of oil palm (Elaeis guineensis Jacq.) fruit and is of global economic and nutritional relevance. While the understanding of oil biosynthesis in plants is improving, the fundamentals of oil biosynthesis in oil palm still require further investigations. To gain insight into the systemic mechanisms that govern oil synthesis during oil palm fruit ripening, the proteomics approach combining gel‐based electrophoresis and mass spectrometry was used to profile protein changes and classify the patterns of protein accumulation during these complex physiological processes. Protein profiles from different stages of fruit ripening at 10, 12, 14, 15, 16, 18 and 20 weeks after anthesis (WAA) were analysed by two‐dimensional gel electrophoresis (2DE). The proteome data were then visualised using a multivariate statistical analysis of principal component analysis (PCA) to get an overview of the proteome changes during the development of oil palm mesocarp. A total of 68 differentially expressed protein spots were successfully identified by matrix‐assisted laser desorption/ionisation‐time of flight (MALDI‐TOF/TOF) and functionally classified using ontology analysis. Proteins related to lipid production, energy, secondary metabolites and amino acid metabolism are the most significantly changed proteins during fruit development representing potential candidates for oil yield improvement endeavors. Data are available via ProteomeXchange with identifier PXD009579. This study provides important proteome information for protein regulation during oil palm fruit ripening and oil synthesis.     

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...     

In reply to “A query on the Mg2p of MgO”

Research on Chemical Intermediates -     

Determining the feasibility of H2O2 production at a graphite cathode using bond dissociation energy: comparing simple and nitrogen doped cathodes

Research on Chemical Intermediates - Hydrogen peroxide (H2O2) is commercially produced by catalytic oxidation of anthrahydroquinone, which is energy-intensive. Electrochemical production of...