Given a group $G$ and an integer $n\geq 0$, we consider the family ${\mathcal F}_n$ of all virtually abelian subgroups of $G$ of $\textrm{rank}$ at most $n$. In this article, we prove that for each $n\ge 2$ the Bredon cohomology, with respect to the family ${\mathcal F}_n$, of a free abelian group with $\textrm{rank}$ $k \gt n$ is nontrivial in dimension $k+n$; this answers a question of Corob Cook et al. (Homology Homotopy Appl. 19(2) (2017), 83–87, Question 2.7). As an application, we compute the minimal dimension of a classifying space for the family ${\mathcal F}_n$ for braid groups, right-angled Artin groups, and graphs of groups whose vertex groups are infinite finitely generated virtually abelian groups, for all $n\ge 2$. The main tools that we use are the Mayer–Vietoris sequence for Bredon cohomology, Bass–Serre theory, and the Lück–Weiermann construction.

Little and Meng (L&M) (2023) question the prevailing narrative of widespread democratic backsliding by showing that various objective indicators of democracy are flat over time. However, because recent democratic decline is concentrated in democracies, the objective indicators can accurately test for backsliding only if they can track democratic quality within democracies. This response article shows that they cannot, for conceptual and empirical reasons. The indicators generally can distinguish democracies from autocracies but are blind to variation in quality within democracies. L&M, therefore, are showing that one form of variation in democracy is stagnant but are systematically missing the very type of variation that has most informed current warnings about backsliding.

Diagnostic stewardship seeks to improve ordering, collection, performance, and reporting of tests. Test results play an important role in reportable HAIs. The inclusion of HAIs in public reporting and pay for performance programs has highlighted the value of diagnostic stewardship as part of infection prevention initiatives. Inappropriate testing should be discouraged, and approaches that seek to alter testing solely to impact a reportable metric should be avoided. HAI definitions should be further adapted to new testing technologies, with focus on actionable and clinically relevant test results that will improve patient care.

Congress recently enacted significant reforms to the laws governing the reporting and publication of international agreements in the United States. These reforms were adopted in December 2022 and took effect in September 2023, and the State Department issued regulations implementing them in early October 2023.

The study aims to understand the interplay between sustainability strategy and the approach to sustainability reporting in small- and medium-sized enterprises (SMEs). To achieve this purpose, a case study is developed, examining four companies that exemplify different sustainability strategy types delineated by Baumgartner: introverted, extroverted, conservative, and visionary. According to the findings of the research, while it is possible to identify sustainability strategies based on the key defining elements of the adopted conceptual map, and to interpret the company’s perception and approach to sustainability reporting considering the sustainability strategy, integrating owner-manager values, stakeholder proximity, and supply chain dynamics the conceptual map becomes a more adaptable and practical tool for SMEs seeking to thrive in an increasingly sustainability-focused business landscape. The incorporation of these insights extends Baumgartner’s work, enhancing the comprehension of sustainability strategies within SMEs and providing implications for regulatory bodies, consultants, and managers.

Let T be the theory of dense cyclically ordered sets with at least two elements. We determine the classifying space of $\mathsf {Mod}(T)$ to be homotopically equivalent to $\mathbb {CP}^\infty $. In particular, $\pi _2(\lvert \mathsf {Mod}(T)\rvert )=\mathbb {Z}$, which answers a question in our previous work. The computation is based on Connes’ cycle category $\Lambda $.

Let Σ be a σ-algebra of subsets of a set Ω and $B(\Sigma)$ be the Banach space of all bounded Σ-measurable scalar functions on Ω. Let $\tau(B(\Sigma),ca(\Sigma))$ denote the natural Mackey topology on $B(\Sigma)$. It is shown that a linear operator T from $B(\Sigma)$ to a Banach space E is Bochner representable if and only if T is a nuclear operator between the locally convex space $(B(\Sigma),\tau(B(\Sigma),ca(\Sigma)))$ and the Banach space E. We derive a formula for the trace of a Bochner representable operator $T:B({\cal B} o)\rightarrow B({\cal B} o)$ generated by a function $f\in L^1({\cal B} o, C(\Omega))$, where Ω is a compact Hausdorff space.

We are humbled by the quantity and quality of the commentaries on our article in this special issue. Our goal was not to answer definitively how global democracy has changed in recent years but rather to provoke a debate about how we collectively can improve the scholarship on this question. The range of viewpoints raised in this special issue have made important advances on this goal.

Li, Ma and Wang have provided in [13] a partial classification of the so-called Moebius deformable hypersurfaces, that is, the umbilic-free Euclidean hypersurfaces $f\colon M^n\to \mathbb{R}^{n+1}$ that admit non-trivial deformations preserving the Moebius metric. For $n\geq 5$, the classification was completed by the authors in [12]. In this article we obtain an infinitesimal version of that classification. Namely, we introduce the notion of an infinitesimal Moebius variation of an umbilic-free immersion $f\colon M^n\to \mathbb{R}^m$ into Euclidean space as a one-parameter family of immersions $f_t\colon M^n\to \mathbb{R}^m$, with $t\in (-\epsilon, \epsilon)$ and $f_0=f$, such that the Moebius metrics determined by ft coincide up to the first order. Then we characterize isometric immersions $f\colon M^n\to \mathbb{R}^m$ of arbitrary codimension that admit a non-trivial infinitesimal Moebius variation among those that admit a non-trivial conformal infinitesimal variation, and use such characterization to classify the umbilic-free Euclidean hypersurfaces of dimension $n\geq 5$ that admit non-trivial infinitesimal Moebius variations.

In 1936 Gianni Caproni, one of the biggest aircraft producers in Italy, bought one of the biggest engineering companies in Emilia Romagna, the Officine Meccaniche Reggiane, and started manufacturing and exporting some of the topmost fighters ever produced in Italy. Based on different archival sources this paper would like to shed light on why, despite a national technological obsolescence in the field a company, which focused on the production of railway material, was able to come up with the most technologically innovative fighters (the Re. 2000 and successive models) which soon conquered the Italian and foreign markets. The author would like to indicate the original characteristics which help explain its primacy: the unique features of the Reggiane, the role of the new owner, risk-taker and forward-looking entrepreneur Gianni Caproni and in particular the importance of the transmission of knowledge, which in those autarchic years and in this particular case was reached by attracting human capital from abroad. The general argumentation of the paper would like to show the importance of deeply excavating in the company’s history, managerial choices, risk-taking attitudes, and knowledge transfer in explaining an otherwise almost inexplicable international business success in a such a competitive sector. The approach is not purely descriptive: the paper analyses the facts and figures of the Officine Meccaniche Reggiane before and after the Caproni takeover, it evaluates the company’s innovative production strategy in the new field of aircraft production and offers new interpretations on its success story in this field.

In this article, we introduce and study the notion of Goldie dimension for C*-algebras. We prove that a C*-algebra A has Goldie dimension n if and only if the dimension of the center of its local multiplier algebra is n. In this case, A has finite-dimensional center and its primitive spectrum is extremally disconnected. If moreover, A is extending, we show that it decomposes into a direct sum of n prime C*-algebras. In particular, every stably finite, exact C*-algebra with Goldie dimension, that has the projection property and a strictly full element, admits a full projection and a non-zero densely defined lower semi-continuous trace. Finally we show that certain C*-algebras with Goldie dimension (not necessarily simple, separable or nuclear) are classifiable by the Elliott invariant.

This study examined the effect of perceived ethnic marginalization, perception towards Nigerian democracy, and socioeconomic condition on support for secession among members of the Igbo ethnic group. Perceived ethnic marginalization and negative perceptions toward Nigerian democracy were found to positively correlate with support for secession. Socioeconomic condition was measured at the household and communal levels. The household measure had no effect on support for secession, but the communal measure did: socioeconomic condition at the communal level positively correlated with support for secession. Igbo ethnicity increased the likelihood of supporting secession, while belonging to the Hausa/Fulani and Yoruba ethnic groups reduced the likelihood of supporting secession.