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.     

Price coordination in distribution channels: A dynamic perspective

In this study, we investigate two important questions related to dynamic pricing in distribution channels: (i) Are coordinated pricing decisions efficient in a context where prices have carry-over effects on demand? (ii) Should firms practice a skimming or a penetration strategy if they choose to coordinate or to decentralize their activities? To answer these questions, we consider a differential game that takes place in a bilateral monopoly where the past retail prices paid by consumers contribute to the building of a reference price. The latter is used by consumers as a benchmark to evaluate the value of the product, and by firms to decide whether to adopt a skimming or a penetration strategy.     

基于模式跳变的井下便携式高精度CH_4浓度监测系统设计

为了在矿井中实现快速、便携式的甲烷浓度检测,同时系统还具备高灵敏度及长的工作周期,设计了基于半导体激光器模式跳变的差分光学光谱吸收法,建立了井下甲烷浓度无线检测系统。系统利用调制电流使半导体激光器的输出波长发生模式跳变,从而获得了两个相近波长的激光,其中一个在甲烷的特征吸收峰上,而另一个基本不被吸收。实验中将两束光分别照射被测气室时,两束光的光强之差代入比尔朗伯定律即可求解气室内的甲烷浓度。实验结果显示,调制电流从20.0 mA增大到60.0 mA过程中,输出波长在电流达到48.3 mA时发生跳变,由1 650.888 nm改变为1 651.020 m。通过HITRAN光谱数据库可知,波长1 650.888 nm位置可作特征吸收峰,而波长1 651.020 nm适合作参考波长。在此基础上,对密闭容器内标准浓度的甲烷气体进行测试,采用H-BD5GD410-HC型便携式甲烷检测仪的测试数据作对比。两种检测结果相近,但随着浓度不断地增高,该系统的检测误差相对平稳,略优于甲烷检测仪。系统的检测误差均低于0.050%,在不采用昂贵的锁相器、检相电路的条件下,实现了精度优于0.10%的井下甲烷浓度检测。     

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.     

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.     

On the feedback solutions of differential oligopoly games with hyperbolic demand curve and capacity accumulation

To safeguard analytical tractability and the concavity of objective functions, the vast majority of models belonging to oligopoly theory relies on the restrictive assumption of linear demand functions. Here we lay out the analytical solution of a differential Cournot game with hyperbolic inverse demand, where firms accumulate capacity over time à la Ramsey. The subgame perfect equilibrium is characterized via the Hamilton–Jacobi–Bellman equations solved in closed form both on infinite and on finite horizon setups. To illustrate the applicability of our model and its implications, we analyze the feasibility of horizontal mergers in both static and dynamic settings, and find appropriate conditions for their profitability under both circumstances. Static profitability of a merger implies dynamic profitability of the same merger. It appears that such a demand structure makes mergers more likely to occur than they would on the basis of the standard linear inverse demand.