For each $n\geq 1$, let $FT_n$ be the free tree monoid of rank n and $E_n$ the full extensive transformation monoid over the finite chain $\{1, 2, \ldots , n\}$. It is shown that the monoids $FT_n$ and $E_{n+1}$ satisfy the same identities. Therefore, $FT_n$ is finitely based if and only if $n\leq 3$.

The Richtmyer–Meshkov instability at gas interfaces with controllable initial perturbation spectra under reshock conditions is investigated both experimentally and theoretically. A soap-film method is adopted to generate well-defined single-, dual- and triple-mode air/SF$_6$ interfaces. By inserting an acrylic block into the test section, a reflected shock with controllable reshock timing is created. The results reveal a complex relationship between the post-reshock perturbation growth rate and the pre-reshock interface morphology. For single-mode interfaces, the post-reshock growth rate exhibits a strong dependence on pre-reshock conditions. In contrast, for multi-mode interfaces, this dependence weakens significantly due to mode-coupling effects. It is found that, following reshock, each fundamental mode develops independently and later is significantly influenced by mode-coupling effects. Based on this finding, we propose an empirical model that matches the initial linear growth rate and the asymptotic growth rate, accurately predicting the evolution of fundamental modes from early to late stages across all three configurations. Furthermore, a theoretical formula is derived, linking the empirical coefficient in the model of Charakhch’An (2020 J. Appl. Mech. Tech. Phys. vol. 41, no. 1, pp. 23–31) to the initial perturbation. This provides a unified framework to explain the varying dependence of post-reshock growth rates on pre-reshock morphology observed in previous experiments.

Regenerative involution is crucial for renewing the mammary gland and maximizing milk production. However, the temporal profiles indicators of oxidative status during this phase are still unclear. In this study, Experiment 1 aimed to investigate the dynamic changes in indicators of oxidative status in plasma during regenerative involution. The dairy goats were dried off at 8 weeks (wk) before kidding (−8 wk, n = 14) or −12 wk (n = 6). The blood samples taken at −8, −7, −6, −5, −4, −3, −2, −1 wk, on the day for kidding (0 wk) and the first week after kidding (+1 wk, milk production 1.28 ± 0.31 kg per day). Experiment 2 aimed to investigate the dynamic changes in indicators of oxidative status in mammary cells. Seven selected goats were biopsied for tissue collection and cell isolation at −8, −4, −1, +1 wk (milk production 1.28 ± 0.31 kg per day), respectively. Plasma analysis in Experiment 1 showed an increase in reactive oxygen species (ROS) levels, peaking at −4 wk (P < 0.01). No significant differences were observed between the dry-off treatments (P = 0.36). The activity of superoxide dismutase (SOD) in plasma remained stable from −7 wk to the first week after kidding (+1 wk), while glutathione peroxidase (GSH-Px) activity peaked at −4 wk. An increased catalase activity was observed at +1 wk (P < 0.01), indicating its response to lactation. In Experiment 2, an increase in ROS levels in isolated mammary cells was observed at −4 wk, while SOD, GSH-Px, and malondialdehyde levels in tissue homogenates rose around kidding (P < 0.01). The dynamic change of the oxidative status suggests that targeted antioxidant strategies would be helpful for regenerative involution of mammary gland in ruminants.

This paper studies quasiconformal non-equivalence of Julia sets and limit sets. We proved that any Julia set is quasiconformally different from the Apollonian gasket. We also proved that any Julia set of a quadratic rational map is quasiconformally different from the gasket limit set of a geometrically finite Kleinian group.

We perform a comprehensive linear non-modal stability analysis of the Rayleigh–Bénard convection with and without a Poiseuille/Couette flow in Oldroyd-B fluids. In the absence of shear flow, unlike the Newtonian case in which the perturbation energy decays monotonically with time, the interaction between temperature gradient and polymeric stresses can surprisingly cause a transient growth up to 104. This transient growth is maximized at the Hopf bifurcation when the stationary instability dominant in the weakly elastic regime transitions to the oscillatory instability dominant in the strongly elastic regime. In the presence of a Poiseuille/Couette flow, the streamwise-uniform disturbances may achieve the greatest energy amplification, and similar to the pure bounded shear flows, Gmax ∝ Re2 and tmax ∝ Re, where Gmax is the maximum energy growth, tmax the time to attain Gmax, Re the Reynolds number. It is noteworthy that there exist two peaks during the transient energy growth at high-Re cases. Different from the first one which is less affected by the temperature gradient and elasticity, the second peak, at which the disturbance energy is the largest, is simultaneously determined by the temperature gradient, elasticity and shear intensity. Specifically, the polymeric stresses field absorbs energy from the temperature field and base flow, which is partially transferred into the perturbed hydrodynamic field eventually, driving the transient amplification of the perturbed wall-normal vorticity.

Mamyshev oscillators (MOs) demonstrate extraordinarily superior performance compared with fiber laser counterparts. However, the realization of a fully fiberized, monolithic laser system without pulse degradation remains a key challenge. Here we present a high-energy MO using large mode area Yb-doped fiber and fiber-integrable interferometric super-Gaussian spectral filters that directly generates a nearly diffraction-limited beam with approximately 9.84 W average power and 533 nJ pulse energy. By implementing pre-chirp management with anti-resonant hollow-core fiber (AR-HCF), the adverse effects of super-Gaussian filtering on pulse quality are effectively mitigated, enabling pulse compression to 1.23 times the transform limit. Furthermore, AR-HCF is employed to provide negative dispersion to compensate for the positive chirp of output pulses, resulting in approximately 37 fs de-chirped pulses with approximately 10 MW peak power. This approach represents a significant step toward the development of monolithic fiber lasers capable of generating and flexible delivery of sub-50-fs pulses with tens of megawatts peak power.

DNA barcoding approaches have been successfully applied for estimating diet composition. However, an accurate quantification in the diets of herbivores remains to be achieved. In the current study, we present a novel methodology that reveals the relationship between the actual proportions (by mass) of each herbage species in the diets and the relative proportions of the ITS2 gene sequences obtained from faecal samples to evaluate the diet composition of sheep in a meadow steppe. Nine common and 12 rare species of plants were employed for formulating 6 diets, along with the addition of feed supplements for improving the growth performance of sheep. Faecal samples were collected for DNA analysis over the period spanning days 7–12. A significant positive correlation (Spearman’s ρ = 0.389) was obtained between the actual proportions (by mass) of the herbage in the diet provided and the relative abundance of ITS2 sequences obtained from the faecal samples. A significant regression coefficient was found between the relative abundance of all common species and their respective herbage mass proportions. The accuracy of the relation equations, evaluated by utilizing the similarity coefficient, showed 84.69% similarity between the actual diet composition and the correct percentage. Taken together, the current study has provided empirical evidence for the accuracy and applicability of ITS2 as a DNA barcode for obtaining quantitative information about the diet composition of sheep grazing in species-rich grasslands.

In this paper, on–off switching digitization of a W-band variable gain power amplifier (VGPA) with above 60 dB dynamic range is introduced for large-scale phased array. Digitization techniques of on–off switching modified stacking transistors with partition are proposed to optimize configuration of control sub-cells. By the proposed techniques, gain control of a radio frequency variable gain amplifier (VGA) could be highly customized for both coarse and fine switching requirements instead of using additional digital-to-analog converters to tune the overall amplifier bias. The designed VGA in 130 nm SiGe has achieved switchable gain range from −46.4 to 20.6 dB and power range from −25.0 to 15.7 dBm at W band. The chip size of the fabricated VGPA is about 0.31 mm × 0.1 mm.

This study aims to investigate the effects of the vine of Lonicera japonica Thunb (VLT) and marine-derived Bacillus amyloliquefaciens-9 (BA-9) supplementation on the growth performance, antioxidant capacity, and gut microbiota of goat kids. A total of 32 4-week-old kids were randomly assigned into four groups: a control group (CON), a group supplemented with 0.3% BA-9 (BA-9), a group supplemented with 2% VLT (VLT), and a group supplemented with both 0.3% BA-9 and 2% VLT (MIX). The results indicated that VLT supplementation significantly increased both average daily (P < 0.001) and total weight gain (TWG) (P < 0.001), while BA-9 alone had no significant effect (P > 0.05) on the average daily and TWG. Biomarker analysis of oxidative stress revealed that supplementation of VLT or BA-9 alone enhanced antioxidant capacity. The MIX group showing a higher total antioxidant capacity (T-AOC) compared with the CON, VLT, and BA-9 groups (P < 0.05). Plasma albumin (ALB) levels were significantly increased in the both VLT and BA-9 groups. Microbiota analysis revealed significant differences in α-diversity and β-diversity between the MIX and CON groups, with specific genera such as Prevotellaceae_UCG.004 and Rikenellaceae_RC9_gut_group negatively correlated with average daily gain (ADG), while Alistipes was positively correlated with T-AOC. These findings suggest that the combined supplementation of VLT and BA-9 can significantly enhance growth performance and antioxidant capacity in goat kids by modulating the composition of gut microbiota and reducing oxidative stress.

Objectives: Indoor air pollution exposure is harmful to people’s physical and mental health, especially in the elderly population, and represents a major issue for human health. Natural ventilation can improve indoor air quality and remove indoor contamination, thus reducing the adverse effects of indoor air pollution exposure on physical and mental health. Depressive symptoms are the most common mental health issue among elderly individuals. However, evidence linking the frequency of indoor natural ventilation to depressive symptoms in the elderly population is limited.

Methods: This study included 7887 individuals 65 years and older from 2017 to 2018 in the China Longitudinal Healthy Longevity Survey (CLHLS). The frequency of indoor natural ventilation was measured as the self-reported frequency of window opening per week in each season. Depressive symptoms were measured by the 10-item Center for Epidemiologic Studies Short Depression Scale (CES-D). Using a model adjusted for demographic, socio- economic, health status, and environmental factors, the correlation between indoor ventilation frequency and depressive symptoms was verified through logistic regression.

Results: Among the 7887 elderly people included in this study, 1952 (24.7%) had symptoms of depression. In the fully adjusted model, compared with the lower indoor overall ventilation frequency group (indoor ventilation frequency: 0–3 times/week), the higher indoor overall ventilation frequency group (indoor ventilation frequency: 6–8 times/week) showed a decrease in depressive symptoms by 33 % [OR: 0.67, 95 % (CI): 0.51–0.88]. Subgroup analysis and sensitivity analysis yielded similar results.

Conclusions: High frequency of indoor ventilation is significantly associated with the reduction of depressive symptoms in Chinese individuals 65 years old or older. This result provides strong evidence for health intervention and policy formulation. Encouraging an increase in indoor ventilation frequency will be an economically beneficial measure to promote healthy aging of the Chinese population.

We study the existence and strong instability of standing wave solutions for the fractional nonlinear Schrödinger equation

\begin{equation*}\begin{cases}\mathrm{i} \psi_{t}=\left(-\Delta\right)^s \psi-\left(|\psi|^{p-2}\psi+\mu|\psi|^{q-2}\psi\right), & \quad(t,x)\in(0,\infty)\times\mathbb{R}^N,\\\psi(0,x)=\psi_0(x),&\quad x\in\mathbb{R}^N,\end{cases}\end{equation*}

where $N\geq2$, $0 \lt s \lt 1$, $2 \lt q \lt p \lt 2_s^*=2N/(N-2s)$, and $\mu\in\mathbb{R}$. The primary challenge lies in the inhomogeneity of the nonlinearity.We deal with the following three cases: (i) for $2 \lt q \lt p \lt 2+4s/N$ and µ < 0, there exists a threshold mass a0 for the existence of the least energy normalized solution; (ii) for $2+4s/N \lt q \lt p \lt 2_s^*$ and µ > 0, we reveal the existence of the ground state solution, explore the strong instability of standing waves, and provide a blow-up criterion; (iii) for $2 \lt q\leq2+4s/N \lt p \lt 2_s^*$ and µ < 0, the strong instability of standing wave solutions is demonstrated. These findings are illuminated through variational characterizations, the profile decomposition, and the virial estimate.

The incidence of obesity-related glomerulopathy (ORG) is rising worldwide with very limited treatment methods. Paralleled with the gut–kidney axis theory, the beneficial effects of butyrate, one of the short-chain fatty acids (SCFA) produced by gut microbiota, on metabolism and certain kidney diseases have gained growing attention. However, the effects of butyrate on ORG and its underlying mechanism are largely unexplored. In this study, a mice model of ORG was established with a high-fat diet feeding for 16 weeks, and sodium butyrate treatment was initiated at the 8th week. Podocyte injury, oxidative stress and mitochondria function were evaluated in mice kidney and validated in vitro in palmitic acid-treated-mouse podocyte cell lines. Further, the molecular mechanisms of butyrate on podocytes were explored. Compared with controls, sodium butyrate treatment alleviated kidney injuries and renal oxidative stress in high-fat diet-fed mice. In mouse podocyte cell lines, butyrate ameliorated palmitic acid-induced podocyte damage and helped maintain the structure and function of the mitochondria. Moreover, the effects of butyrate on podocytes were mediated via the GPR43-Sirt3 signal pathway, as evidenced by the diminished effects of butyrate with the intervention of GPR43 or Sirt3 inhibitors. In summary, we conclude that butyrate has therapeutic potential for the treatment of ORG. It attenuates high-fat diet-induced ORG and podocyte injuries through the activation of the GPR43-Sirt3 signalling pathway.

Aircraft ground taxiing contributes significantly to carbon emissions and engine wear. The electric towing tractor (ETT) addresses these issues by towing the aircraft to the runway end, thereby minimising ground taxiing. As the complexity of ETT towing operations increases, both the towing distance and time increase significantly, and the original method for estimating the number of ETTs is no longer applicable. Due to the substantial acquisition cost of ETT and the need to reduce waste while ensuring operational efficiency, this paper introduces for the first time an ETT quantity estimation model that combines simulation and vehicle scheduling models. The simulation model simulates the impact of ETT on apron operations, taxiing on taxiways and takeoffs and landings on runways. Key timing points for ETT usage by each aircraft are identified through simulation, forming the basis for determining the minimum number of vehicles required for airport operations using a hard-time window vehicle scheduling model. To ensure the validity of the model, simulation model verification is conducted. Furthermore, the study explores the influence of vehicle speed and airport scale on the required number of ETTs. The results demonstrate the effective representation of real-airport operations by the simulation model. ETT speed, airport runway and taxiway configurations, takeoff and landing frequencies and imbalances during peak periods all impact the required quantity of ETTs. A comprehensive approach considering these factors is necessary to determine the optimal number of ETTs.

This study aimed to understand the potassium voltage-gated channel KQT-like subfamily, member 1 gene polymorphism in a rural elderly population in a county in Guangxi and to explore the possible relationship between its gene polymorphism and blood sugar. The 6 SNP loci of blood DNA samples from 4355 individuals were typed using the imLDRTM Multiple SNP Typing Kit from Shanghai Tianhao Biotechnology Co. The data combining epidemiological information (baseline questionnaire and physical examination results) and genotyping results were statistically analyzed using GMDR0.9 software and SPSS22.0 software. A total of 4355 elderly people aged 60 years and above were surveyed in this survey, and the total abnormal rate of glucose metabolism was 16·11 % (699/4355). Among them, male:female ratio was 1:1·48; the age group of 60–69 years old accounted for the highest proportion, with 2337 people, accounting for 53·66 % (2337/4355). The results of multivariate analysis showed that usually not doing farm work (OR 1·26; 95 % CI 1·06, 1·50), TAG ≥ 1·70 mmol/l (OR 1·19; 95 % CI 1·11, 1·27), hyperuricaemia (OR 1·034; 95 % CI 1·01, 1·66) and BMI ≥ 24 kg/m2 (OR 1·06; 95 % CI 1·03, 1·09) may be risk factors for abnormal glucose metabolism. Among all participants, rs151290 locus AA genotype, A allele carriers (AA+AC) were 0.70 times more likely (0.54 to 0.91) and 0.82 times more likely (0.70 to 0.97) to develop abnormal glucose metabolism than CC genotype carriers, respectively. Carriers of the T allele at the rs2237892 locus (CT+TT) were 0.85 times more likely to have abnormal glucose metabolism than carriers of the CC genotype (0.72 to 0.99); rs2237897 locus CT gene. The possibility of abnormal glucose metabolism in the carriers of CC genotype, TT genotype and T allele (CT + TT) is 0·79 times (0·67–0·94), 0·74 times (0·55–0·99) and 0·78 times (0·66, 0·92). The results of multifactor dimensionality reduction showed that the optimal interaction model was a three-factor model consisting of farm work, TAG and rs2237897. The best model dendrogram found that the interaction between TAG and rs2237897 had the strongest effect on fasting blood glucose in the elderly in rural areas, and they were mutually antagonistic. Environment–gene interaction is an important factor affecting abnormal glucose metabolism in the elderly of a county in Hechi City, Guangxi.

We present direct numerical simulation (DNS) and modelling of incompressible, turbulent, generalized Couette–Poiseuille flow. A particular example is specified by spherical coordinates $(Re,\theta,\phi )$, where $Re = 6000$ is a global Reynolds number, $\phi$ denotes the angle between the moving plate, velocity-difference vector and the volume-flow vector and $\tan \theta$ specifies the ratio of the mean volume-flow speed to the plate speed. The limits $\phi \to 0^\circ$ and $\phi \to 90^\circ$ give alignment and orthogonality, respectively, while $\theta \to 0^\circ,\ \theta \to 90^\circ$ correspond respectively to pure Couette flow in the $x$ direction and pure Poiseuille flow at angle $\phi$ to the $x$ axis. Competition between the Couette-flow shear and the forced volume flow produces a mean-velocity profile with directional twist between the confining walls. Resultant mean-speed profiles relative to each wall generally show a log-like region. An empirical flow model is constructed based on component log and log-wake velocity profiles relative to the two walls. This gives predictions of four independent components of shear stress and also mean-velocity profiles as functions of $(Re,\theta,\phi )$. The model captures DNS results including the mean-flow twist. Premultiplied energy spectra are obtained for symmetric flows with $\phi =90^\circ$. With increasing $\theta$, the energy peak gradually moves in the direction of increasing $k_x$ and decreasing $k_z$. Rotation of the energy spectrum produced by the faster moving velocity near the wall is also observed. Rapid weakening of a spike maxima in the Couette-type flow regime indicates attenuation of large-scale roll structures, which is also shown in the $Q$-criterion visualization of a three-dimensional time-averaged flow.