A dynamic free-entry oligopoly with sluggish entry and exit adjustments

We study a dynamic free-entry oligopoly with sluggish entry and exit of firms under general demand and cost functions. We show that the number of firms in a steady-state open-loop solution for a dynamic free-entry oligopoly is smaller than that at static equilibrium and that the number of firms in a steady-state memoryless closed-loop solution is larger than that in an open-loop solution.     

A differential-equation-based model of the glass ceiling in career progression

ABSTRACT

We introduce a model based on Ordinary Differential Equations to describe how two mutually exclusive groups progress through a career hierarchy, whether in a single organization, or in an entire economic sector. The intended application is to gender imbalance at the top of the academic hierarchy in European Universities; however, the model is entirely generic and may be applied in other contexts also. Previous research on gender imbalance in European universities has focused on large-scale statistical studies. Our model represents a point of departure, as it is deterministic (i.e., based on Ordinary Differential Equations). The model requires a precise definition of the progression rates for the different groups through the hierarchy; these are key parameters governing the dynamics of career progression. The progression rate for each group can be decomposed into a product: the proportion of group members at a low level in the hierarchy who compete for promotion to the next level a given year, multiplied by the in-competition success rate for the group in question. Either of these two parameters can differ across the groups under consideration; this introduces a group asymmetry into the organization’s composition. We introduce a glass-ceiling index to summarize this asymmetry succinctly. Using case studies from the literature, we demonstrate how the mathematical framework can pinpoint the proximate cause of the glass ceiling in European academia.     

Generalization of the Kelvin equation for arbitrarily curved surfaces

Capillary condensation, which takes place in confined geometries, is the first-order vapor-to-liquid phase transition and is explained by the Kelvin equation, but the equation's applicability for arbitrarily curved surface has been long debated and is severe problem. Recently, we have proposed generic dynamic equations for moving surfaces. Application of the equations to the vapor/fluid interfaces in chemical equilibrium conditions nearly trivially solves the generalization problem for the Kelvin equation. The equations are universally true for any surfaces: atomic, molecular, micro or macro scale, real or virtual, Riemannian or pseudo-Riemannian, active or passive.     

On the boomerang uniformity of a class of permutation quadrinomials over finite fields

Let ${\mathbb{F}}_{2^n}$ be a finite field with $2^n$ elements and $f_{\underset{\_}{c}}(x)=c_0{x}^{2^m(2^k+1)}+c_1{x}^{2^{m+k}+1}+c_2{x}^{2^m+2^k}+c_3{x}^{2^k+1}\in {\mathbb{F}}_{2^n}[x]$, where n, m and k are positive integers with $n=2m$ and $\gcd ?(m,k)=e$. In this paper, motivated by a recent work of Li, Xiong and Zeng (Li et al. (2021) [12]), we further study the boomerang uniformity of $f_{\underset{\_}{c}}(x)$ by using similar ideas and carrying out particular techniques in solving equations over finite fields. As a consequence, we generalize Li, Xiong and Zeng's result from the case of m being odd and $e=1$ to that of both $m/e$ and $k/e$ being odd.     

Electrochemical Detection of Artemisinin Using Cobalt Sulphide/Reduced Graphene Oxide Nanocomposite

Solvothermally synthesized cobalt sulphide/reduced graphene oxide (CoS/rGO) was used to fabricate an electrochemical sensor for detection of artemisinin. Microscopic techniques were used to characterize CoS/rGO nanocomposite. The electrochemical sensor was fabricated by modifying the surface of glassy carbon electrode with CoS/rGO nanocomposite. [Fe(CN)6]^3−/4− was used as a mediator to aid oxidation of artemisinin. Differential pulse voltammetric technique was used for the detection of artemisinin. A linear range of 30–100 μM was used. Experimentally, a detection limit of 0.5 μM was obtained. Therefore, the developed sensor can be used for quality control of artemisinin.     

Voltammetric Determination of Favipiravir Used as an Antiviral Drug for the Treatment of Covid-19 at Pencil Graphite Electrode

This work describes the sensitive voltammetric determination of favipiravir (FAV) based on its reduction for the first time with a low-cost and disposable pencil graphite electrode (PGE). In addition, the determination of FAV was also performed based on its oxidation. Differential pulse (DP) voltammograms recorded in 0.5 M H₂SO₄ for the reduction of FAV show that peak currents increase linearly in the range of 1.0 to 600.0 μM with a limit of detection of 0.35 μM. The acceptable recovery values (98.9–106.0 %) obtained from a pharmaceutical tablet, real human urine, and artificial blood serum samples spiked with FAV confirm the high accuracy of the proposed method.