For $ \beta>1 $, let $ T_\beta $ be the $\beta $-transformation on $ [0,1) $. Let $ \beta _1,\ldots ,\beta _d>1 $ and let $ \mathcal P=\{P_n\}_{n\ge 1} $ be a sequence of parallelepipeds in $ [0,1)^d $. Define

$$ \begin{align*}W(\mathcal P)=\{\mathbf{x}\in[0,1)^d:(T_{\beta_1}\times\cdots \times T_{\beta_d})^n(\mathbf{x})\in P_n\text{ infinitely often}\}.\end{align*} $$

$ P_n $

$\dim _{\mathrm {H}} W(\mathcal P)$

$\dim _{\mathrm {H}}$

$ P_n $

$\dim _{\mathrm {H}} W(\mathcal P)$

$\dim _{\mathrm {H}} W(\mathcal P)$

The neurodiversity movement takes a societal view of individual differences by suggesting that people should be respected and not necessarily medically treated based on personal attributes. This commentary article discusses how human differences in intellectual capacities should be considered as another form of diversity with the requirement for medical intervention needing to be considered in terms of overall social change. As a significant portion of the overall workforce could be considered as people with some form of neurological disability this article analyses how co-creation processes occur meaning neurodiverse individuals should be accepted in society regardless of their differences. This article contributes to societal discussions around managing diversity as in society the socio-demographic categories such as age and gender are well established, but newer categories such as neurodiversity are required.

The COVID-19 pandemic in 2020 significantly impacted Australia’s resources sector, particularly mining, oil, and gas industries, posing challenges for operational leaders. This study applied Adaptive Crisis Management Theory (ACMT) to understand how these leaders adapted during the crisis. Through interviews with 32 operational leaders, it was found that their roles evolved as crisis demands changed. Initially, they addressed immediate needs, then shifted focus to remote work facilitation and digital transformation, and finally emphasised recovery, trust, and resilience. These adaptations influenced leaders’ behaviours, highlighting the importance of flexibility in supporting employee wellbeing and organisational continuity during crises.

This article scrutinizes the role of transparency in the United Nations Framework Convention on Climate Change (UNFCCC). Specifically, it examines a widely heard claim that ‘transparency is the backbone of the Paris Agreement’, and the assumption that mandatory transparency (reporting and review) is essential to fill potential gaps in climate action left by voluntary, nationally determined climate targets. We subject this claim to critical scrutiny by tracing the political contestations around the desired role of transparency in the UNFCCC, with a focus on mitigation-related transparency. Our analysis shows that, despite developing countries expressing concerns during the pre-Paris negotiations, the Paris Agreement's enhanced transparency framework (ETF) is almost exclusively ‘enhanced’ (compared with earlier provisions) for developing countries, with some instances of regression for developed countries. Furthermore, the effects of such enhanced reporting are not straightforward and might de facto have an impact on countries’ autonomy to nationally determine their mitigation targets in diverse ways, even as all the detailed reporting does not facilitate comparability of effort. With implementation of the ETF due to start in 2024, our analysis provides a timely exploration of the extent to which transparency is really a backbone of the Paris Agreement, and for whom and with what implications for ambitious action from all under the international climate regime. It calls into question whether the transformative potential of transparency, much extolled within the UNFCCC process, will materialize for all countries in a similar manner or rather will have an impact on countries differentially.

Knowledge of Ascophyllum nodosum extracts (ANEs) is still limited to avocado ‘Hass’ in the tropics. The objective of this study was to evaluate the effects of two ANEs application methods (foliar v. drench) at four different doses (0, 2.5, 5 and 7.5 ml/l) on the physiological response of three different avocado stages (seedlings and young and adult trees). Foliar or drench ANEs applications were performed monthly for all plants for 16 weeks. The evaluated variables were recorded at 4 and 20 weeks after the start of treatment (WAT). The results showed that ANEs can be applied to the drench or foliar method at doses ≥5 ml/l in the different growth stages evaluated. In seedlings, foliar or drench ANEs applications increased total dry weight (34.5 and 57.9 g for 0 and ≥5 ml/l, respectively) and stomatal conductance (gs) (380 and 205 mmol/m2s for 0 and ≥5 ml/l, respectively) at 20 WAT. In young trees, both application methods also improved growing index (88.6 and 102 cm for 0 and ≥5 ml/l, respectively) and gs (516 and 636 mmol/m2s for 0 and ≥5 ml/l, respectively) at the last sampling point. Adult trees showed that foliar or drench applications at higher doses also caused an increase in fruit yield (3.4 and 8.7 kg/tree for 0 and ≥5 ml/l, respectively) at 20 WAT. In conclusion, the use of foliar and soil ANEs applications at higher doses (≥5 ml/l) can be considered for integrated crop management of ‘Hass’ avocado.

I respond to challenges posed by Andrew Dole, Joanna Leidenhag, Kevin Schilbrack, and Sameer Yadav. Key topics include: whether the engagement between analytic theology and the academic study of religion really is mutually beneficial, distinguishing analytic theology from science-engaged theology, restrictive methodological naturalism, and whether I misconstrue analytic theology’s ‘characteristic damage’.

This article was written before Andrea Robin Skinner, daughter of Alice Munro, wrote an essay in the Toronto Star on July 7, 2024, describing her mother's silence in the face of her abuse at the hands of Munro's husband/Skinner's stepfather, Gerald Fremlin. I wish to honour Skinner's story and her courage in coming forward, as well as her wish that “… this story, my story, to become part of the stories people tell about my mother.” I, like so many others, will continue to grapple with Munro's writing and her reflections on intimate human relationships — as well as her literary legacy — following these revelations.

A fourth-order bandpass filter with dual-wide passbands is proposed in this article. The novelty of the proposed work is the realization of a dual-band bandpass filter with closely spaced passbands, wide passband bandwidth, high rejection between the passbands, using a novel combination of open stub tapped series coupled lines (CLs) and shunt transmission line loaded with end connected CLs. The characteristics of the proposed dual-wideband bandpass filter are investigated by adopting even–odd mode analysis. The transmission zeros generated by the transmission line loaded with an end-connected CL and open stub are utilized to achieve a high skirt rate. A rejection better than 55 dB is achieved with a single transmission zero between the two passbands indicating high isolation and close passbands. The dual-wideband filter is designed and manufactured to operate at 1.33 and 2.32 GHz. The experimented 3-dB fractional bandwidths of the two pass frequency bands are 40.6% and 24.13%. The proposed filter’s tested frequency responses agree well with simulated results. The proposed device can be used in various applications such as telecommunications, satellite communications, radar systems, imaging, and spectroscopy.

The Pension Benefit Guaranty Corporation (PBGC) becomes the trustee for private defined benefit plans that have defaulted. The PBGC pays retirement benefits as provided by the plan and that are consistent with federal guidelines concerning the type and amounts of distributions. In response to a Freedom of Information Request, the PBGC provided us with relevant information on all individuals who received retirement benefits from the PBGC in the last 10 years, over 250,000 retirees. Individuals requesting payouts from PBGC managed plans have the option of selecting either a single-life annuity or a joint-and-survivor (J&S) annuity. We examine the PBGC distributions chosen over the last decade and how they vary by age at retirement, sex, months of service, and other relevant variables. Key findings indicate that men are much more likely to choose a joint and survivor annuity compared to female claimants, and the difference increases with age. Conditional on selecting a J&S annuity, men are more likely to select a 100 percent survivor's annuity, while women tend to choose a 50 percent survivor's benefit.

We use a special tiling for the hyperbolic d-space $\mathbb {H}^d$ for $d=2,3,4$ to construct an (almost) explicit isomorphism between the Lipschitz-free space $\mathcal {F}(\mathbb {H}^d)$ and $\mathcal {F}(P)\oplus \mathcal {F}(\mathcal {N})$, where P is a polytope in $\mathbb {R}^d$ and $\mathcal {N}$ a net in $\mathbb {H}^d$ coming from the tiling. This implies that the spaces $\mathcal {F}(\mathbb {H}^d)$ and $\mathcal {F}(\mathbb {R}^d)\oplus \mathcal {F}(\mathcal {M})$ are isomorphic for every net $\mathcal {M}$ in $\mathbb {H}^d$. In particular, we obtain that, for $d=2,3,4$, $\mathcal {F}(\mathbb {H}^d)$ has a Schauder basis. Moreover, using a similar method, we also give an explicit isomorphism between $\mathrm {Lip}(\mathbb {H}^d)$ and $\mathrm {Lip}(\mathbb {R}^d)$.

We develop a new method suitable for establishing lower bounds on the ball measure of noncompactness of operators acting between considerably general quasinormed function spaces. This new method removes some of the restrictions oft-presented in the previous work. Most notably, the target function space need not be disjointly superadditive nor equipped with a norm. Instead, a property that is far more often at our disposal is exploited—namely the absolute continuity of the target quasinorm.

We use this new method to prove that limiting Sobolev embeddings into spaces of Brezis–Wainger type are so-called maximally noncompact, i.e. their ball measure of noncompactness is the worst possible.

Sleep is vital for the maintenance of physical and mental health, recovery and performance in athletes. Sleep also has a restorative effect on the immune system and the endocrine system. Sleep must be of adequate duration, timing and quality to promote recovery following training and competition. Inadequate sleep adversely impacts carbohydrate metabolism, appetite, energy intake and protein synthesis affecting recovery from the energy demands of daily living and training/competition related fatigue. Sleep’s role in overall health and well-being has been established. Athletes have high sleep needs and are particularly vulnerable to sleep difficulties due to high training and competition demands, as such the implementation of the potential nutritional interventions to improve sleep duration and quality is commonplace. The use of certain nutrition strategies and supplements has an evidence base i.e. carbohydrate, caffeine, creatine, kiwifruit, magnesium, meal make-up and timing, protein and tart cherry. However, further research involving both foods and supplements is necessary to clarify the interactions between nutrition and the circadian system as there is potential to improve sleep and recovery. Additional research is necessary to clarify guidelines and develop products and protocols for foods and supplements to benefit athlete health, performance and/or recovery. The purpose of this review is to highlight the potential interaction between sleep and nutrition for athletes and how these interactions might benefit sleep and/or recovery.

It is estimated that more than one-tenth of adults aged ≥60 years are now classified as having sarcopenic obesity (SO), a clinical condition characterised by the concurrent presence of sarcopenia (low muscle mass and weakness) and obesity (excessive fat mass). Independently, sarcopenia and obesity are associated with a high risk of numerous adverse health outcomes including CVD and neurological conditions (e.g. dementia), but SO may confer a greater risk, exceeding either condition alone. This imposes a substantial burden on individuals, healthcare systems and society. In recent years, an increasing number of observational studies have explored the association between SO and the risk of CVD; however, results are mixed. Moreover, the pathophysiology of SO is governed by a complex interplay of multiple mechanisms including insulin resistance, inflammation, oxidative stress, hormonal shifts and alteration of energy balance, which may also play a role in the occurrence of various CVD. Yet, the exact mechanisms underlying the pathological connection between these two complex conditions remain largely unexplored. The aim of this review is to examine the association between SO and CVD. Specifically, we seek to: (1) discuss the definition, epidemiology and diagnosis of SO; (2) reconcile previously inconsistent findings by synthesising evidence from longitudinal studies on the epidemiological link between SO and CVD and (3) discuss critical mechanisms that may elucidate the complex and potentially bidirectional relationships between SO and CVD.

In the present article, we study compact complex manifolds admitting a Hermitian metric which is strong Kähler with torsion (SKT) and Calabi–Yau with torsion (CYT) and whose Bismut torsion is parallel. We first obtain a characterization of the universal cover of such manifolds as a product of a Kähler Ricci-flat manifold with a Bismut flat one. Then, using a mapping torus construction, we provide non-Bismut flat examples. The existence of generalized Kähler structures is also investigated.