Following Faber–Pandharipande, we use the virtual localization formula for the moduli space of stable maps to $\mathbb {P}^{1}$ to compute relations between Hodge integrals. We prove that certain generating series of these integrals are polynomials.

Goodstein’s principle is arguably the first purely number-theoretic statement known to be independent of Peano arithmetic. It involves sequences of natural numbers which at first appear to diverge, but eventually decrease to zero. These sequences are defined relative to a notation system based on exponentiation for the natural numbers. In this article, we provide a self-contained and modern analysis of Goodstein’s principle, obtaining some variations and improvements. We explore notions of optimality for notation systems and apply them to the classical Goodstein process and to a weaker variant based on multiplication rather than exponentiation. In particular, we introduce the notion of base-change maximality, and show how it leads to far-reaching extensions of Goodstein’s result. We moreover show that by varying the initial base of the Goodstein process, one readily obtains independence results for each of the fragments $\mathsf {I}\Sigma _n$ of Peano arithmetic.

This article discusses houses on the periphery of Barcelona and in particular in the El Carmel neighbourhood, which were built by poor country-to-city migrants from southern Spain in the post-World War II period. They were constructed following two typologies: barracas (sheds), one-storey huts on an irregular street plan, and coreas (‘Korea houses’), more formally looking one- to three-storey structures lined up on orderly laid-out streets. Based on archival documents, contemporaneous publications and interviews with former autoconstructores (self-builders), the article analyses both social conditions and physical structures. While these buildings were often unauthorized and constructed by informal means, they were just as often built with the landowner’s consent, involving architects and building professionals, and retroactively legalized. The article concludes that in this respect Barcelona’s ‘informal neighbourhoods’ in fact straddled the realms of the formal and the informal, to the extent that the habitual distinction between formal and informal architecture has to be considered inadequate.

U.S. military veterans are an average 20 years older than non-veterans and have elevated rates of certain health conditions. While negative aging stereotypes have been linked to increased risk for various health conditions, little is known about the prevalence and correlates of these stereotypes in this population. Using data from a nationally representative sample of 4,069 U.S. veterans surveyed between 11/19 and 3/20, we examined (1) the current prevalence of negative aging stereotypes related to physical, mental, and cognitive health and (2) sociodemographic, health, and psychosocial factors associated with these stereotypes. Multivariable regression and relative weight analyses were conducted to identify independent correlates of negative aging stereotypes. Results revealed that 82.3%, 71.1%, and 30.0% of veterans endorsed negative aging stereotypes related to physical, cognitive, and emotional health, respectively. Older age (36.6% relative variance explained), grit (23.6%), and optimism (17.5%) explained the majority of the variance in negative age stereotypes related to physical aging; grit (46.6%), openness to experiences (31.5%), and older age (15.1%) in negative age stereotypes related to cognitive aging; and emotional stability (28.8%), purpose in life (28.8%), and grit (25.3%) in negative age stereotypes related to emotional aging. This study provides an up-to-date characterization of the prevalence and correlates of negative aging stereotypes in U.S. veterans. Results underscore the importance of targeting key correlates of negative aging stereotypes, such as lower grit, as part of efforts to promote health and functioning in this population.

Transient numerical simulations were conducted to investigate the influence of large amplitude and fast impact backpressure on a shock train. The fundamental problem consists of a shock train within a constant-area channel with a Ma=1.61 inflow and a pulse backpressure applied to the outlet. The pressure disturbance in the isolator has an intense forcing-response lag. From the moment of the backpressure peak appearance, it takes 36 times the backpressure duration for the pressure disturbance to reach the upstream end. It moves upstream with time in the form of a normal shock wave. As time progresses, the normal shock degenerates into a $\lambda $ shock and a compression wave behind due to the action of viscous dissipation in the boundary layer. Eventually, a multi-stage shock train is formed. The maximum backpropagation distance is a quadratic function of both the pulse backpressure peak and duration, and the relationship between these variables was determined by fitting. When the integral value of backpressure to time is fixed, reducing the backpressure peak while increasing the duration will reduce the backpressure pulsation at the isolator outlet, which will be more conducive to shortening the maximum backpropagation distance than reducing the duration and increasing the backpressure peak. The values of backpressure peak and duration are obtained from the detonation combustion case, which ensures the authenticity of backpressure characteristics. The relevant research conclusions can provide a reference for the design of the isolator of pulse detonation ramjet.

We offer an account of the metaphysics of persons rooted in Latter-day Saint scripture that vindicates the essentiality of origins. We then give theological support for the claim that prospects for the success of God's soul making project are bound up in God creating particular persons. We observe that these persons would not have existed were it not for the occurrence of a variety of evils (of even the worst kinds), and we conclude that Latter-day saint theology has the resources to endorse a strong soul-making non-identity theodicy. We then introduce two complications for this account rooted in the problem of horrendous evils. First, horrendous evils threaten to undermine our confidence that God is good to each created person within the context of their life. And second, horrendous evils raise concerns about the value of persons whose existence depends on the occurrence of those evils. We may wonder whether those whose existence depends on the occurrence of horrendous evils are valuable enough to motivate God's allowance of those evils. We show that by attending to important structural features of a post-mortem, pre-eschatological state called the spirit world, Latter-day Saints can ameliorate these concerns about horrendous evils.

Although older people who live alone might be in a vulnerable situation, they have often managed their everyday life for a long time, frequently with health challenges. In this article, we explore how nine older persons who live alone, who receive home care and are identified by home care professionals as being frail, manage their everyday lives by inquiring into their stories about living alone and receiving home care. We conducted three qualitative interviews with each of the nine participants over a period of eight months and analysed the data using thematic analysis and a narrative positioning analysis. Using the concept of resilience as our analytic lens, we identified three thematic threads: continuity, adaptation and resistance. In the narrative positioning analysis of three participants' stories, we identified that the participants used the processes of continuity, adaptation and resistance strategically and interchangeably. The study thus provides insight into how older people who live alone and use home care services narrate their balancing of strengths and vulnerabilities, and engage in the construction and maintenance of a sense of self through positioning in relation to master narratives. Older people's narrations are nuanced and complex, and this study indicates that encouraging storytelling and engaging with older people's narrations might support how older people enact resilience and thus their management of everyday life when living alone and ageing in place.