This article studies the question of which classes of numberings can be generated by the direct sums of computable uniformly minimal sequences of numberings (in particular, Friedberg and positive numberings). For the class of Friedberg numberings, this question was initiated by Britta Schinzel in her 1982 paper. In this article, we show that the class of Gödel numberings is generated by the direct sums of computable uniformly positive sequences of universal numberings and that there exists a conull class of oracles computing sequences of Friedberg numberings with programmable direct sums. We further show that all computable numberings of a fairly wide class of families of total recursive functions (containing, for example, the family of all primitive recursion functions) are generated by the direct sums of computable sequences of their incomparable Friedberg numberings. On the other hand we prove that no family of partial recursive functions has a computable sequence of Friedberg numberings whose direct sum is acceptable.

This review aims to highlight some of the key bioactive functionalities that a range of components in milk can potentially make to reduce risks to health at key life stages. Such functionalities cannot be adequately explained by traditional estimates of nutrient supply. The benefits of gangliosides from the milk fat globule membrane (MFGM) for neonatal neurodevelopment are examined along with milk proteins for growth stimulation of children via the proteins’ ability to stimulate insulin-like growth factor-1 (IGF-1). Exosomes in bovine milk and their miRNA are bioavailable, with an animal study indicating that placenta development and embryo survival were both enhanced. Concerning bone health, the unique characteristics of the casein micelle for supplying Ca, P and Mg to the GI tract were considered. The so-called dairy food matrix and the hypotensive effect of some peptides from milk proteins may be compensatory factors for SFA regarding CVD risk. The recent rise in use of glucagon-like peptide-1 (GLP-1) receptor agonists for adiposity reduction and improving glycaemic control is noted alongside evidence that milk proteins can stimulate GLP-1 synthesis potentially reducing GLP-1 receptor agonist need in high milk protein consumers. Other functionality included the ability of whey proteins to stimulate synthesis of skeletal muscle protein, crucial for bone protection and glycaemic control and the role of milk/Ca for reducing colorectal cancer risk. Perhaps the most exciting functionality is that of polar phospholipids in the MFGM potentially improving cognition and reducing the risk of dementia in the elderly. Clearly more human studies are needed.

This paper investigates the welfare implications of the rise of shadow banking in China, driven by regulatory arbitrage and implicit guarantees. Although shadow banking can improve social welfare by relaxing constraints on banks’ capacity to expand credit, it may also hurt social welfare due to the risk-taking behavior induced by implicit guarantees. We study the optimal level of guarantees and shadow banking in a model that balances these benefits and costs. Our findings suggest that reducing the existing degree of guarantees and shrinking the shadow banking sector could enhance social welfare in China.

Teleological explanations are those that explain a phenomenon in virtue of a consequence it brings about. This has long been challenged on the grounds that it invokes backward causation. The classic resolution to this is to show that these consequences explain as causes which occurred in the past. An alternative characterizes teleology as a form of non-causal explanation. Against the widespread assumption that teleological explanations are univocal, I argue that causal and non-causal variants are compatible insofar as they explain different aspects of the same purposive phenomena. I conclude that we ought to be pluralists about teleological explanation.

The long-chain omega-3 polyunsaturated fatty acids (LC n-3PUFA) eicosapentaenoic acid (EPA; 20:5n-3), docosapentaenoic acid (DPA, 22:5n-3) and docosahexaenoic acid (DHA; 22:6n-3) are beneficial for health. The aim of this review is to provide an overview of worldwide dietary recommendations for LC n-3PUFA across life-stages for general healthy populations from technical and scientific documents (TSD) that underpin food based dietary guidelines (FBDG) or TSD from expert groups. Using the Food and Agriculture Organization global online repository of FBDG and structured Google searches, forty-two TSD were identified for inclusion. Seventy-one percent of TSD included quantitative dietary intake recommendations which varied widely across life-stages with gaps for some groups, 62% included health messages related to LC n-3PUFA consumption, 33% discussed supplementation and 29% gave guidance on high intakes. The most frequently recommended intakes for adults were 250 mg/day EPA + DHA and 250 mg/day EPA + DHA plus an additional 100–200 mg/day DHA in pregnancy. This overview is useful for nutrition science, medical, industry and consumer communities since it identifies the recommendations available and the gaps of interest to national or international groups wishing to set dietary intake recommendations for LC n-3PUFA. Low dietary intake of LC n-3PUFA from seafood is a risk factor for suboptimal health. Intake recommendations can be challenging to achieve. Most countries for which data are available show that LC n-3PUFA intakes fail to meet recommended targets, highlighting the need for accessible, innovative, sustainable alternative EPA + DHA sources e.g. bio-enriched foods and supplements to support higher population intakes, LC n-3PUFA status and health benefits.

Multiple mobile manipulators (MMs) show superiority in the tasks requiring mobility and dexterity compared with a single robot, especially when manipulating/transporting bulky objects. However, closed-chain of the system, redundancy of each MM, and obstacles in the environment bring challenges to the motion planning problem. In this paper, we propose a novel semi-coupled hierarchical framework (SCHF), which decomposes the problem into two semi-coupled sub-problems. To be specific, the centralized layer plans the object’s motion first, and then the decentralized layer independently explores the redundancy of each robot in real-time. A notable feature is that the lower bound of the redundancy constraint metric is ensured, besides the closed-chain and obstacle-avoidance constraints in the centralized layer, which ensures the object’s motion can be executed by each robot in the decentralized layer. Simulated results show that the success rate and time cost of SCHF outperform the fully centralized planner and fully decoupled hierarchical planner significantly. In addition, cluttered real-world experiments also show the feasibility of the SCHF in the transportation tasks. A video clip in various scenarios can be found at https://youtu.be/Y8ZrnspIuBg.

Considérons un espace de Berkovich sur un bon anneau de Banach et la droite projective relative sur celui-ci. (C’est un espace dont les fibres sont des droites projectives sur différents corps valués complets.) Pour tout endomorphisme polarisé de cette droite, nous montrons que la famille des mesures d’équilibre associées aux restrictions de l’endomorphisme aux fibres est continue. Le résultat vaut, par exemple, lorsque l’anneau de Banach est un corps valué complet, un corps hybride, un anneau de valuation discrète complet ou un anneau d’entiers de corps de nombres.

A phenomenon distinctive to attention-deficit hyperactivity disorder (ADHD) is that the effects of stimulants are evident in domains of attention, mood, energy and focus, independent of the presence of an ADHD diagnosis. This reflects recreational use of stimulants for these and other effects. Perceived treatment response probably reinforces diagnosis, and hence diagnostic and prescribing habits.

Three motor sledges were taken on Captain Robert Falcon Scott’s expedition to Antarctica in 1910. They performed poorly, making only small contributions to the polar journey and making no contribution to the expedition’s scientific programme.

The motor sledges have received little attention from historians and researchers. No definitive work has been published. The purpose of this article is to provide an authoritative, reliable and complete history of Scott’s Antarctic motor sledges.

This article studies Belton Hamilton’s concept for a “chain track” vehicle, then traces its development path through two prototype vehicles and two snow trials in Norway. The outcomes of the snow trials and associated recommendations are reviewed. The article then considers Scott’s detailed plans to reach the South Pole and his instructions to the Motor Party in pursuit of that goal. Four major problems that prevented the motor sledges from satisfying Scott’s instructions are identified.

Several conclusions are drawn. It is apparent that the vehicles were flawed from the outset by poor engineering decisions about track design, engine power and carburetion/airflow. It is unlikely that experimentation or minor refinement in the Antarctic would have produced vehicles reliable enough to make a major contribution to the polar journey.

This article develops a new test to detect changes in generalized autoregressive conditionally heteroscedastic (GARCH(1,1)) processes without imposing a stationary assumption. Specifically, the procedure tests the null hypothesis of a GARCH process with constant parameters, either in (strictly) stationary or explosive regimes, against the alternative hypothesis of parameter changes. We derive the limiting distribution of the test statistics and establish their asymptotic consistency. Monte Carlo simulations show that the proposed test has good size control and high power. We demonstrate a prototype application on a small group of stocks and report a further extensive application to more than ten thousand U.S. stocks.

This paper investigates sharp stability estimates for the fractional Hardy–Sobolev inequality:

\begin{align*}\ \ \ \ \ \ \ \ \ \mu_{s,t}\left(\mathbb{R}^N\right) \left(\int_{\mathbb{R}^N} \frac{|u|^{2^*_s(t)}}{|x|^t} \,\mathrm{d}x \right)^{\frac{2}{2^*_s(t)}} \leq \int_{\mathbb{R}^N} \left|(-\Delta)^{\frac{s}{2}} u \right|^2 \,\mathrm{d}x, \quad \text{for all } u \in \dot{H}^s\left(\mathbb{R}^N\right)\end{align*}

where $s \in (0,1)$, $0 \lt t \lt 2s$, $N \gt 2s$ is an integer, and $2^*_s(t) = \frac{2(N-t)}{N-2s}$. Here, $\mu_{s,t}\left(\mathbb{R}^N\right)$ represents the best constant in the inequality. The primary focus is on the quantitative stability results of the above inequality and the corresponding Euler–Lagrange equation near a positive ground-state solution. Additionally, a qualitative stability result is established for the Euler–Lagrange equation, offering a thorough characterization of the Palais–Smale sequences for the associated energy functional. These results generalize the sharp quantitative stability results for the classical Sobolev inequality in $\mathbb{R}^N$, originally obtained by Bianchi and Egnell [J. Funct. Anal. 1991] as well as the corresponding critical exponent problem in $\mathbb{R}^N$, explored by Ciraolo, Figalli, and Maggi [Int. Math. Res. Not. 2017] in the framework of fractional calculus.

I argue that attempts to integrate marginalized epistemic standpoints into dominant frameworks risk treating them as resources for mainstream appropriation. Using a queer activist slogan from the AIDS crisis as a representative example, I warn that because knowledge forged in resistance is often oppositional and always situated, incorporating it into dominant frameworks can dilute its meaning or harm its creators. This points to a deeper tension within standpoint theory: emancipatory projects that seek to engage marginalized imaginaries can reproduce the very hierarchies they aim to dismantle when they fail to recognize these standpoints’ own priorities, limits, and forms of gatekeeping.

This study explores the marriage matching of only-child individuals and the related outcomes. Specifically, we analyze two aspects: First, we investigate the marriage patterns of only children, examining whether people choose mates in a positive or negative assortative manner regarding only-child status. We find that, along with being more likely to remain single, only children are more likely to marry another only child. Second, we measure the matching premium or penalty as the difference in partners’ socioeconomic status between only-child and non-only-child individuals, where socioeconomic status is approximated by years of schooling. Our estimates indicate that among women who marry an only-child husband, only children are penalized, as their partners’ educational attainment is 0.63 years lower. Finally, we discuss the potential sources of this penalty in light of our empirical findings.