Wages earned by men are often used as an indicator of the material standard of living (MSoL). However, this indicator relies on several assumptions when used for comparisons across time and space. Considering these assumptions will improve estimates of the MSoL from wages. One necessary assumption is that households in the compared populations relied on the primary income of the male head of household to a comparable degree. I demonstrate that the degree of reliance on the male income was closely associated with the complexity of households within the population. Nuclear households – typical of English-speaking countries – were more reliant on the male income than more complex households found elsewhere. Consequently, estimates based on male wages are less accurate for populations with complex households, likely underestimating their MSoL. While the complexity of households in historical populations is seldom known, it can be predicted using demographic and economic indicators. I conclude that populations at similar stages of industrialization and the demographic transition are the most comparable when using male wages to estimate their MSoL. Further, I use a reductive model to show that a household’s MSoL is determined by the following three factors: time spent on productive work, the market wage for men, and the female/male (F/M) wage ratio. My analysis shows that including the F/M wage ratio does not change the ranking of the MSoL based on male wages. Nonetheless, I argue that there are compelling reasons to expect the wage ratio to be a useful addition when comparing the MSoL of historical populations.

An avoshift is a subshift where for each set C from a suitable family of subsets of the shift group, the set of all possible valid extensions of a globally valid pattern on C to the identity element is determined by a bounded subpattern. This property is shared (for various families of sets C) by, for example, cellwise quasigroup shifts, totally extremally permutive (TEP) subshifts, and subshifts of finite type (SFTs) with a safe symbol. In this paper, we concentrate on avoshifts on polycyclic groups, when the sets C are what we call ‘inductive intervals’. We show that then, avoshifts are a recursively enumerable subset of subshifts of finite type. Furthermore, we can effectively compute lower-dimensional projective subdynamics and certain factors (avofactors), and we can decide equality and inclusion for subshifts in this class. These results were previously known for group shifts, but our class also covers many non-algebraic examples as well as many SFTs without dense periodic points. The theory also yields new proofs of decidability of inclusion for SFTs on free groups, and SFTness of subshifts with the topological strong spatial mixing property.

We consider $L^q$-spectra of planar graph-directed self-affine measures generated by diagonal or anti-diagonal matrices. Assuming the directed graph is strongly connected and the system satisfies the rectangular open set condition, we obtain a general closed form expression for the $L^q$-spectra. Consequently, we obtain a closed form expression for box dimensions of associated planar graph-directed box-like self-affine sets. We also provide a precise answer to a question posed by Fraser [On the $L^q$-spectrum of planar self-affine measures. Trans. Amer. Math. Soc. 368(8) (2016), 5579–5620] concerning the $L^q$-spectra of planar self-affine measures generated by diagonal matrices. An interesting observation of the closed form expression is that it is possible to calculate the $L^q$-spectrum of a measure without involving the exact $L^q$-spectra of its projections to the axes.

States are measured and ranked on an ever-expanding array of country performance indicators (CPIs). Such indicators are seductive because they provide actionable, accessible, and ostensibly objective information on complex phenomena to time-pressed officials and enable citizens to hold governments to account. At the same time, a sizeable body of research has explored how CPIs entail ‘black boxing’ and depoliticisation of political phenomena. This article advances our understanding of the consequences of governance by indicators by examining how CPIs generate specific forms of politicization that can undermine a given CPI’s authority over time. We contend that CPIs rely upon two different claims to authority that operate in tension with one another: i) the claim to provide expert, objective knowledge and ii) the claim to render the world more transparent and to secure democratic accountability. Analysing CPIs in the field of education, economic governance, and health and development, we theorize and empirically document how this tension leads to three distinct forms of politicisation: scrutiny from experts that politicises the value judgements embodied in a CPI; competition whereby rival CPIs contest the objectivity of knowledge of leading CPIs; and corruption, where gaming of CPIs challenges its claim to securing transparent access to social reality. While the analysis identifies multiple paths to the politicization and undermining of specific CPIs’ authority, the article elaborates why these processes tend to leave intact and even reproduce the legitimacy of CPIs as a governance technology.

This paper presents a highly isolated diplexer-antenna and a dual-band filtenna with high-frequency selectivity. The precise design procedure for the diplexer based on substrate-integrated waveguide technology is presented and effectively integrated with magnetoelectric dipole antenna/microstrip patch antennas to achieve a diplexer-antenna and dual-band filtenna. The proposed configuration enables the design and control of the filtering response of the channels individually. To verify the proposed method, a diplexer-antenna and a dual-band filtenna with operating frequencies of 26.5–27.5 and 28.5–29.5 GHz, a fourth-degree Chebyshev response, and two symmetric radiation nulls for each band are designed and simulated. Finally, the proposed dual-band filtenna is fabricated and measured. The measured peak realized gains for the lower and higher bands are 4 and 4.5 dBi, respectively. Besides, a high out-of-band suppression with a deep roll-off of better than 20 dBi is obtained.

We consider quasilinear Schrödinger equations in $\mathbb {R}^N$ of the form $-\Delta u+V(x)u-u\Delta (u^2)=g(u)$, where the potential V is allowed to be sign-changing and the nonlinearity g is sublinear at zero. Except for being subcritical, no additional condition is imposed on $g(u)$ for $|u|$ large. We obtain a sequence of solutions with negative energy and converging to zero via Clark’s theorem. We also obtain a similar result for fourth-order quasilinear Schrödinger equations in $\mathbb {R}^N$ of the form $\Delta ^2u-\Delta u+ V(x)u-u\Delta (u^2)=g(u)$.

Money and Edinburgh go back a long way. The Bank of Scotland was founded in 1695, just a year after the Bank of England. Three centuries later, the first edition of the Global Financial Centres Index (in 2007) confirmed what everyone had always assumed: second only to London in the UK, sixth in Europe. But how? This small city, its population only topping 500,000 in the twenty-first century, was far from the centers of power and finance, with only a modest trading and manufacturing base of its own. This paper marries fresh oral history from the city’s mid-twentieth century financial elite—that is, an Edinburgh before the Global Financial Crash—with Pierre Bourdieu’s theory of habitus in the relatively new paradigm of Historical Organisation Studies, treating the industry as a single unit across banking, life assurance, and investment management. This reveals their personal characteristics and demonstrates the “symbolic violence” which socialized them into absorbing and embracing both the values and practices of the organizations where they worked and the external structures, including professional bodies and, not least, the Church of Scotland, which helped maintain some of those values.