Imagine that you go for a walk with your friend. You walk along a closed loop around a university campus, finishing at the point where you started. You and your friend keep the same distance throughout your walk. You walk on the ‘outside’.

In an era of hypercompetition, research and development (R&D) investments are vital for organizations to stay competitive. This microlevel study draws on dynamic managerial capability (DMC) theory to explore the mechanisms contributing to competitive advantages. It posits that DMCs enhance firm performance by increasing R&D spending, and explores the moderating role of slack resources due to their effect on resource availability. Employing hierarchical regression analysis and bootstrapping methods on a longitudinal sample comprising 31 German DAX firms, the findings robustly demonstrate that DMCs facilitate firm performance by fostering R&D expenditures and confirm the moderating effect of specific slack resources. However, only internal but not external slack resources amplify the relationship between DMCs and R&D intensity. Overall, this study emphasizes the critical role of managers’ microlevel capabilities in determining firm performance and sheds light on how different slack resources influence the relationships between DMCs, R&D intensity, and firm performance.

This article describes the ways in which the spectra of electroacoustic music compositions can be structured coherently. It begins by describing the straightjacket that composers and listeners are constrained by when using the concept of ‘source bonding’ and how this needs to be discarded for effective listening. It then describes the concept of spectral merging and how ideas of musical timbre are formed, and finally discusses the many ways that spectra can be structured with both harmonic and inharmonic components. Examples are given from the author’s own music and other well-known works in the literature of electroacoustic music.

Let $l\in \mathbb {N}_{\ge 1}$ and $\alpha : \mathbb {Z}^l\rightarrow \text {Aut}(\mathscr {N})$ be an action of $\mathbb {Z}^l$ by automorphisms on a compact nilmanifold $\mathscr{N}$. We assume the action of every $\alpha (z)$ is ergodic for $z\in \mathbb {Z}^l\smallsetminus \{0\}$ and show that $\alpha $ satisfies exponential n-mixing for any integer $n\geq 2$. This extends the results of Gorodnik and Spatzier [Mixing properties of commuting nilmanifold automorphisms. Acta Math. 215 (2015), 127–159].

In this article I explore changing state–citizen relationships in Mauritius. To do so, I outline and provide analysis of the system through which this Indian Ocean island has historically managed its diversity – a process that I call conscripting communalism. Conscripting communalism was formulated at independence in a context of behavioural predictions for the future that the internet era has challenged in powerful ways. To illustrate my argument, I explore three specific moments when ethnic and religious discourses were surpassed by collective concern within a rapidly authoritarianizing state: first, the sinking of the Wakashio oil tanker off the coast of Mauritius in 2020, which resulted in national solidarity towards the environment rather than communal violence; second, proposed legislation put forward by the Mauritian Information and Communication Technology Authority (ICTA) in 2021, which attempted to enable state surveillance of social media and which was soundly resisted by both domestic and external parties. And finally, I explore 2022 accusations that the Mauritian government authorized the installation of digital interception technology by representatives of the Indian state on one of the country’s fibre optic cables. The article argues that Mauritius represents an important site of analysis of the tensions between competing global visions of human rights, political autonomy, surveillance, solidarity and expectations for the future and the role of the internet in shaping these competing visions. I explore how new technologies have become the tools of both repression and resistance. The implications ripple far beyond the island.

Recall that for a 2π-periodic function f , the Fourier coefficients on the interval (–Π, Π) are

and the Fourier series for f is

We study a class of ordinary differential equations with a non-Lipschitz point singularity that admits non-unique solutions through this point. As a selection criterion, we introduce stochastic regularizations depending on a parameter $\nu $: the regularized dynamics is globally defined for each $\nu> 0$, and the original singular system is recovered in the limit of vanishing $\nu $. We prove that this limit yields a unique statistical solution independent of regularization when the deterministic system possesses a chaotic attractor having a physical measure with the convergence to equilibrium property. In this case, solutions become spontaneously stochastic after passing through the singularity: they are selected randomly with an intrinsic probability distribution.

Women remain underrepresented in cabinets, especially in high-prestige, “masculine” portfolios. Still, a growing number of states have appointed women to the finance ministry—a powerful position typically reserved for men. Drawing on the “glass cliff” phenomenon, we examine the relationship between financial crises and women’s ascension to, and survival in, this post. With an original dataset on appointments to finance ministries worldwide (1972–2017), we show that women are more likely to first come to power during a banking crisis. These results also hold for currency and inflation crises and even when accounting for the political and economic conditions that might otherwise explain this relationship. Subsequent examination of almost 3,000 finance ministers’ tenures shows that, once in office, crises shorten men’s (but not women’s) time in the post. Together, these results suggest that women can sometimes seize on crises as opportunities to access traditionally male-dominated positions.

In teaching mathematics to first-year undergraduates, and thus in the appropriate calculus textbooks, the task of calculating an integral that satisfies a specific first-order or second-order recurrence relation often appears. These relations are obtained mainly by applying the method of integration by parts. Calculating such integrals is usually tedious, especially for an integer n > 2, time-consuming, and presents the possibility of making a large number of errors when computing involves multiple iterative steps. In [1], it is shown that in two cases (Theorems 2.1. and 2.3), the process of calculating integrals satisfying first-order recurrence relations can be performed quickly using easily memorised closed-form formulas for corresponding primitive functions. The question can rightly be asked whether there is a faster way to calculate other integrals of this type. In this paper, our goal is to give an affirmative answer to such a question, though without convering all situations. Since each recurrence relation is equivalent to a difference equation of the same order, the calculation of integrals mentioned above can be reduced to solving the corresponding difference equations. Since every first-order or second-order linear difference equation is solvable, it follows that for every integral which can be reduced to a first- order or second-order recurrence formula, it is possible to find corresponding primitive functions directly. Sometimes such a procedure is much faster than iterative solving of the integral. Closed-form formulas for the integrals discussed in the following sections are not unknown (see [2]). However, here our goal is to present the idea of computing indefinite integrals using difference equations. We will discuss it in more detail in Section 2. In Section 3, we discuss the application of the results obtained to calculate several improper integrals and the application of some of them in different sciences. An exciting example of such an application is the integral , which in the case n = 1 is used in the kinetic theory of gases, particularly in the Maxwell-Boltzmann distribution of gas molecules by energies (see Remark 4). Also, we compare the formulas obtained by the method of difference equations with the formulas obtained using Wolfram Alpha software (see Remark 5).