In this paper,the linear space $\mathcal F$ of a special type of fractal interpolation functions (FIFs) on an interval I is considered. Each FIF in $\mathcal F$ is established from a continuous function on I. We show that, for a finite set of linearly independent continuous functions on I, we get linearly independent FIFs. Then we study a finite-dimensional reproducing kernel Hilbert space (RKHS) $\mathcal F_{\mathcal B}\subset\mathcal F$, and the reproducing kernel $\mathbf k$ for $\mathcal F_{\mathcal B}$ is defined by a basis of $\mathcal F_{\mathcal B}$. For a given data set $\mathcal D=\{(t_k, y_k) : k=0,1,\ldots,N\}$, we apply our results to curve fitting problems of minimizing the regularized empirical error based on functions of the form $f_{\mathcal V}+f_{\mathcal B}$, where $f_{\mathcal V}\in C_{\mathcal V}$ and $f_{\mathcal B}\in \mathcal F_{\mathcal B}$. Here $C_{\mathcal V}$ is another finite-dimensional RKHS of some classes of regular continuous functions with the reproducing kernel $\mathbf k^*$. We show that the solution function can be written in the form $f_{\mathcal V}+f_{\mathcal B}=\sum_{m=0}^N\gamma_m\mathbf k^*_{t_m} +\sum_{j=0}^N \alpha_j\mathbf k_{t_j}$, where ${\mathbf k}_{t_m}^\ast(\cdot)={\mathbf k}^\ast(\cdot,t_m)$ and $\mathbf k_{t_j}(\cdot)=\mathbf k(\cdot,t_j)$, and the coefficients γm and αj can be solved by a system of linear equations.

In this paper, we investigate Kolmogorov-type theorems for small perturbations of degenerate Hamiltonian systems. These systems are index by a parameter ξ as $ H(y,x,\xi) = \langle\omega(\xi),y\rangle {+ \bar h(y,\xi)}+\varepsilon P(y,x,\xi,\varepsilon) $, where ɛ > 0. We assume that the frequency mapping $\omega(\cdot)$, $\bar h(y,\cdot)=O(|y|^2)$ and the perturbation $\varepsilon P(y,x,\cdot, \varepsilon)$ maintain Hölder continuity about ξ. We prove that the persistent invariant tori retain the same frequency as those of the unperturbed tori, under a certain topological degree condition and a weak convexity condition for the frequency mapping. Notably, this paper presents, to our understanding, pioneering results on the KAM theorem under such conditions with only assumption of Hölder continuous dependence of frequency mapping ω on the parameter.

Well-posedness in time-weighted spaces of certain quasilinear (and semilinear) parabolic evolution equations $u'=A(u)u+f(u)$ is established. The focus lies on the case of strict inclusions $\mathrm{dom}(f)\subsetneq \mathrm{dom}(A)$ of the domains of the nonlinearities $u\mapsto f(u)$ and $u\mapsto A(u)$. Based on regularizing effects of parabolic equations it is shown that a semiflow is generated in intermediate spaces. In applications this allows one to derive global existence from weaker a priori estimates. The result is illustrated by examples of chemotaxis systems.

The aim of this randomised controlled trial was to investigate the effects of breakfast high or low in protein on body composition and cardiometabolic markers in young women with overweight. In total, fifty-six women aged 18–30 years consumed a breakfast containing either high protein (34 g protein, n 26) or low protein (6 g protein, n 30) for 12 weeks. Measurements of body composition by dual-energy X-ray absorptiometry, waist circumference, glucose tolerance, fasting glucose, insulin and lipid profile were performed before and after this period. The primary outcome was fat mass. Satiety and hunger were evaluated by self-reported Visual Analogue Scale (VAS) scores. Dietary intake was estimated by 4-d dietary records, and calcium intake was estimated by FFQ. At baseline, relative daily protein intake was 15·2 ± 2·8 E%, which increased to 19·3 ± 3·4 E% in high protein but was unchanged in low protein (P < 0·001 between groups). High protein reported higher satiety compared with low protein (P = 0·02). Yet, no group differences were observed in changes in energy intake, body composition, blood lipid profile or measures of glucose tolerance (all P > 0·10). However, bone mineral content tended to increase in high protein (P = 0·05) and decrease in low protein (P = 0·07, interaction effect: P = 0·01). Conclusively, a high v. low content of protein in breakfast increased satiety but did not affect body composition or cardiometabolic markers in young women with overweight. This study adds to the sparse evidence on the effects of breakfast with different macronutrient compositions on health parameters in women with overweight. Registered at clinicaltrials.gov: NCT04518605.

Based on fieldwork with two related Afro-Brazilian religions, Umbanda and Quimbanda, this article explores the value of Donald Davidson’s semantic theory for making sense of ethnographic fieldwork. Specifically, we look at the role of scriptedness in communication, including religious ritual. We first clarify the role of social externalities in Davidson’s view of communicative interpretation, which is broader than his initial framework of radical interpretation. We then offer an account of what constitutes communicative and interpretational success, by drawing on Davidson’s account of prior and passing theory. Prior theories are interpreters’ initial hypothetical frameworks, ranging from general (e.g., the rational, intentional nature of self and other, and a shared perceivable world) to local (e.g., assumptions about cultural, social, and institutional contexts). Passing theories are tactical, on-the-fly modifications that we hypothesize in order to get mutual understanding back on track. We introduce the concept of ‘semantic reduction’ to operationalize the view that specific, local social externalities provide clues that help keep interpretation on track. In the case of religious ethnography, these include ritual, doctrinal, narrative, symbolic, material, temporal, and spatial frames that constrain the generation of passing theories. Examples from fieldwork illustrate the potential value of our appeal to Davidson’s ideas.

For commuting contractions $T_1,\dots,T_n$ acting on a Hilbert space $\mathscr{H}$ with $T=\prod_{i=1}^n T_i$, we find a necessary and sufficient condition such that $(T_1,\dots,T_n)$ dilates to a commuting tuple of isometries $(V_1,\dots,V_n)$ on the minimal isometric dilation space of T with $V=\prod_{i=1}^nV_i$ being the minimal isometric dilation of T. This isometric dilation provides a commutant lifting of $(T_1, \dots, T_n)$ on the minimal isometric dilation space of T. We construct both Schäffer and Sz. Nagy–Foias-type isometric dilations for $(T_1,\dots,T_n)$ on the minimal dilation spaces of T. Also, a different dilation is constructed when the product T is a $C._0$ contraction, that is, ${T^*}^n \rightarrow 0$ as $n \rightarrow \infty$. As a consequence of these dilation theorems, we obtain different functional models for $(T_1,\dots,T_n)$ in terms of multiplication operators on vectorial Hardy spaces. One notable fact about our models is that the multipliers are all analytic functions in one variable. The dilation when T is a $C._0$ contraction leads to a conditional factorization of T. Several examples have been constructed.

The increased risk for psychopathology associated with interpersonal violence exposure (IPV, e.g., physical abuse, sexual assault) is partially mediated by neurobiological alterations in threat-related processes. Evidence supports parsing neural circuitry related to transient and sustained threat, as they appear to be separable processes with distinct neurobiological underpinnings. Although childhood is a sensitive period for neurodevelopment, most prior work has been conducted in adult samples. Further, it is unknown how IPV exposure may impact transient-sustained threat neural interactions. The current study tested the moderating role of IPV exposure on sustained vmPFC-transient amygdala co-activation during an fMRI task during which threat and neutral cues were predictably or unpredictably presented. Analyses were conducted in a sample of 212 community-recruited youth (M/SDage = 11.77/2.44 years old; 51.9% male; 56.1% White/Caucasian). IPV-exposed youth evidenced a positive sustained vmPFC-transient amygdala co-activation, while youth with no IPV exposure did not show this association. Consistent with theoretical models, effects were specific to unpredictable, negative trials and to exposure to IPV (i.e., unrelated to non-IPV traumatic experiences). Although preliminary, these findings provide novel insight into how childhood IPV exposure may alter neural circuity involved in specific facets of threat processing.

This work delves into advancements in wireless power transfer (WPT) and radiofrequency (RF) energy harvesting (EH), focusing on on-demand beamforming and wide-dynamic power range technologies. These innovations promise significant improvements in efficiency and adaptability for wireless energy systems. For transmitting RF power, on-demand beamforming enhances power delivery precision by accurately targeting specific devices, minimizing energy waste, and maximizing received power. This technology is particularly useful in dynamic environments with constantly changing device positions, ensuring stable power levels and effective real-time power transfer, such as for mobile device charging. For receiving RF power, wide-dynamic power range implementation allows EH and WPT systems to adjust power output across a broad spectrum, optimizing energy use and extending device lifespan. This capability supports scalability, accommodating devices with varied power needs, also enabling new applications in consumer electronics, healthcare, smart homes, and cities, and enhancing energy management in smart infrastructures. Additionally, this study explores three-dimensional (3D)-printable antennas and RF circuitries for battery-free applications. The versatility of 3D printing allows the creation of complex, efficient, and customizable RF components, fostering innovative battery-free solutions. Integrating on-demand beamforming and wide-dynamic power range technologies in EH systems promise improved energy transfer efficiencies, reduced losses, and sustainable, cost-effective wireless power systems.

We study the geometry of tropical extensions of hyperfields, including the ordinary, signed, and complex tropical hyperfields. We introduce the framework of ‘enriched valuations’ as hyperfield homomorphisms to tropical extensions and show that a notable family of them are relatively algebraically closed. Our main results are hyperfield analogues of Kapranov’s theorem and the Fundamental theorem of tropical geometry. Utilizing these theorems, we introduce fine tropical varieties and prove a structure theorem for them in terms of their initial ideals.

This paper delves into the influence of network media on the efficacy of emergency response during natural disasters. Given the frequent occurrence of disasters that pose significant risks to urban areas, effective emergency response mechanisms are paramount. Leveraging the Data Envelopment Analysis (DEA) model, this study assesses disaster response efficiency by analyzing network information. It explores the distinct characteristics of disaster response across different types of natural disasters and their various occurrence stages. To this end, three emblematic disasters are chosen for empirical analysis: the 2021 Zhengzhou heavy rainstorm, the 2022 Super Typhoon Chaba, and the 2022 Luding earthquake. Our findings reveal disparities in response efficiency among these disaster types, with Zhengzhou’s rainstorm response demonstrating the highest efficiency, followed by the Super Typhoon Chaba, and the Luding earthquake yielding the lowest efficiency. Furthermore, this study meticulously discusses the pivotal factors that shape response efficiency, encompassing government decision-making, emergency rescue operations, and social assistance. By pinpointing optimal response strategies tailored to distinct disaster stages, this paper underscores its contribution toward augmenting disaster response efficiency and fostering urban safety and disaster preparedness.