Almost periodic solutions for an impulsive delay Nicholson’s blowflies model

By means of the contraction mapping principle and Gronwall-Bellman’s inequality, we prove the existence and exponential stability of positive almost periodic solution for an impulsive delay Nicholson’s blowflies model. The main results are illustrated by an example.     

Communicating Experience of 3D Space: Mathematical and Everyday Discourse

In this article we consider data arising from student-teacher-researcher interactions taking place in the context of an experimental teaching program making use of multiple modes of communication and representation to explore three-dimensional (3D) shape. As teachers/researchers attempted to support student use of a logo-like formal language for constructing 3D trajectories and figures in a computer microworld, a system of gestures emerged. Observations of multimodal classroom communication suggest that teachers/researchers and students used similar words and gestures to represent different types of movement. We discuss possible sources of these differences, contrasting formal mathematical and everyday systems of representation of 3D space. More generally, we argue that understanding the structures of everyday discourse and their relationships to the structures of specialized mathematical discourse can provide insight into student interactions.     

Quantitative determination of potential genotoxic impurity 3-aminopyridine in linagliptin active pharmaceutical ingredient using HILIC–UV

This study aimed to develop an analytical method to determine the quantity of the impurity 3-aminopyridine (3AP). 3-Aminopyridine is a reactive reagent in the synthesis of linagliptin. The method was sensitive at level of 30.0 ppm of 3AP relative to linagliptin. The analysis was carried out using hydrophilic interaction liquid chromatography. The analytical column was Tracer Extrasil Silica (150 × 4.0 mm, 3 μm). A mobile phase of water–acetonitrile (10:90, v/v) containing 10.0 mM ammonium acetate was prepared and adjusted to pH 6.0. A UV detector was used to detect the amount of 3AP at a wavelength of 298 nm. Validation of the method was performed as per the International Council for Harmonization of Technical Requirements for Pharmaceuticals for Human Use in terms of detection limit, quantitation limit, linearity, accuracy, precision, specificity and robustness. The calibration curve was linear (r² = 0.999) for 3AP concentration in the range of 30.0–450.0 ppm. This method showed a good sensitivity with a detection limit and a quantitation limit of 7.5 and 25.0 ppm, respectively.     

Investigating the geometry curriculum in Palestinian textbooks: towards multimodal analysis of Arabic mathematics discourse

ABSTRACT

The analytical scheme used in the project The Evolution of the Discourse of School Mathematics (EDSM) was developed to analyse the change over time in examination texts. An adapted version of the EDSM scheme has been deployed to analyse the nature of mathematics construed in Palestinian schools’ textbooks and the mathematical activity expected of students in the geometry textbooks for students aged 10 to 16 years. The adaptation includes adding further tools for analysing visual components of texts, as well as accounting for some differences between English and Arabic. This article outlines these adaptations and illustrates the use of the adapted scheme with a different genre of texts from those studied in the EDSM project. Some of the challenges in the adaptation process in relation to Arabic mathematics discourse are discussed.     

On fractional Langevin differential equations with anti-periodic boundary conditions

In this paper, we provide existence criteria for the solutions of p-Laplacian fractional Langevin differential equations with anti-periodic boundary conditions. The Caputo fractional as well as Caputo q-fractional operators are used to address the derivatives. The main results are verified by the help of Leray–Schaefer’s fixed point theorem. We construct an example to illustrate the feasibility of the main theorems. Our results are new and provide extensions to some known theorems in the literature.     

New Criteria on Oscillatory and Asymptotic Behavior of Third-Order Nonlinear Dynamic Equations with Nonlinear Neutral Terms

In the paper, we provide sufficient conditions for the oscillatory and asymptotic behavior of a new type of third-order nonlinear dynamic equations with mixed nonlinear neutral terms. Our theorems not only improve and extend existing theorems in the literature but also provide a new approach as far as the nonlinear neutral terms are concerned. The main results are illustrated by some particular examples.     

Mittag-Leffler stability and adaptive impulsive synchronization of fractional order neural networks in quaternion field

Fractional order quaternion-valued neural networks are a type of fractional order neural networks for which neuron state, synaptic connection strengths, and neuron activation functions are quaternion. This paper is dealing with the Mittag-Leffler stability and adaptive impulsive synchronization of fractional order neural networks in quaternion field. The fractional order quaternion-valued neural networks are separated into four real-valued systems forming an equivalent four real-valued fractional order neural networks, which decreases the computational complexity by avoiding the noncommutativity of quaternion multiplication. Via some fractional inequality techniques and suitable Lyapunov functional, a brand new criterion is proposed first to ensure the Mittag-Leffler stability for the addressed neural networks. Besides, the combination of quaternion-valued adaptive and impulsive control is intended to realize the asymptotically synchronization between two fractional order quaternion-valued neural networks. Ultimately, two numerical simulations are provided to check the accuracy and validity of our obtained theoretical results.     

Self-cleaning perovskite type catalysts for the dry reforming of methane

Gas-to-liquid processes are generally used to convert natural gas or other gaseous hydrocarbons into liquid fuels via an intermediate syngas stream. This includes the production of liquid fuels from biomass-derived sources such as biogas. For example, the dry reforming of methane is done by reacting CH₄ and CO₂, the two main components of natural biogas, into more valuable products, i.e., CO and H₂. Nickel containing perovskite type catalysts can promote this reaction, yielding good conversions and selectivities; however, they are prone to coke laydown under certain operating conditions. We investigated the addition of high oxygen mobility dopants such as CeO₂, ZrO₂, or YSZ to reduce carbon laydown, particularly using reaction conditions that normally result in rapid coking. While doping with YSZ, YDC, GDC, and SDC did not result in any improvement, we show that a Ni perovskite catalyst (Na_0.5La_0.5Ni_0.3Al_0.7O_2.5) doped with 80.9 ZrO₂ 15.2 CeO₂ gave the lowest amount of carbon formation at 800 ℃ and activity was maintained over the operating time.     

Discovery of Novel Epoxyketone Peptides as Lipase Inhibitors

Obesity is the most common nutritional disorder in the developed world and is associated with important comorbidities. Pancreatic lipase (PL) inhibitors play a key role in the metabolism of human fat. A series of novel epoxyketones peptide derivatives were investigated for their pancreatic lipase inhibitory activity. The epoxyketone moiety is a well-known reactive electrophile group that has been used as part of proteasome inhibitors in cancer therapy, and it is widely believed that these are very selective for targeting the proteasome active site. Here we investigated various peptide derivatives with an epoxide warhead for their anti-lipase activity. The assessment of these novel epoxyketones was performed by an in-house method that we developed for rapid screening and identification of lipase inhibitors using GC-FID. Herein, we present a novel anti-lipase pharmacophore based on epoxyketone peptide derivatives that showed potent anti-lipase activity. Many of these derivatives had comparable or more potent activity than the clinically used lipase inhibitors such as orlistat. In addition, the lipase appears to be inhibited by a wide range of epoxyketone analogues regardless of the configuration of the epoxide in the epoxyketone moiety. The presented data in this study shows the first example of the use of epoxyketone peptides as novel lipase inhibitors.     

On c-Normal Subgroups of Finite Groups

Let G be a finite group. We fix in every noncyclic Sylow subgroup P of G some subgroup D satisfying 1 < |D| < |P| and study the structure of G under the assumption that all subgroups H of P with |H| = |D| are c-normal in G.