In this paper, we will investigate the following inequality

\begin{equation*}(a_{n+1}a_{n+2} - a_{n}a_{n+3})^2 -(a_{n+1}^2 -a_{n}a_{n+2})(a_{n+2}^2 - a_{n}a_{n+4}) \gt 0,\end{equation*}

which arises from the iterated Laguerre operator on functions. We will prove the sequence $\{a_n\}$ of a unified form given by Griffin, Ono, Rolen and Zagier asymptotically satisfies this inequality while the Maclaurin coefficients of the functions in Laguerre-Pólya class have not to possess this inequality. We also prove the companion version of this inequality. As a consequence, we show the Maclaurin coefficients of the Riemann Ξ-function asymptotically satisfy this property. Moreover, we make this approach effective and give the exact thresholds for the positivity of this inequalityfor the partition function, the overpartition function and the smallest part function.

Diagnostic classification models assume the existence of latent attribute profiles, the possession of which increases the probability of responding correctly to questions requiring the corresponding attributes. Through the use of longitudinally administered exams, the degree to which students are acquiring core attributes over time can be assessed. While past approaches to longitudinal diagnostic classification modeling perform inference on the overall probability of acquiring particular attributes, there is particular interest in the relationship between student progression and student covariates such as intervention effects. To address this need, we propose an integrated Bayesian model for student progression in a longitudinal diagnostic classification modeling framework. Using Pòlya-gamma augmentation with two logistic link functions, we achieve computationally efficient posterior estimation with a conditionally Gibbs sampling procedure. We show that this approach achieves accurate parameter recovery when evaluated using simulated data. We also demonstrate the method on a real-world educational testing data set.

Cavitation bubble pulsation and liquid jet loads are the main causes of hydraulic machinery erosion. Methods to weaken the load influences have always been hot topics of related research. In this work, a method of attaching a viscous layer to a rigid wall is investigated in order to reduce cavitation pulsations and liquid jet loads, using both numerical simulations and experiments. A multiphase flow model incorporating viscous effects has been developed using the Eulerian finite element method (EFEM), and experimental methods of a laser-induced bubble near the viscous layer attached on a rigid wall have been carefully designed. The effects of the initial bubble–wall distance, the thickness of the viscous layer, and the viscosity on bubble pulsation, migration and wall pressure load are investigated. The results show that the bubble migration distance, the normalised thickness of the oil layer and the wall load generally decrease with the initial bubble–wall distance or the oil-layer parameters. Quantitative analysis reveals that when the initial bubble–wall distance remains unchanged, there exists a demarcation line for the comparison of the bubble period and the reference period (the bubble period without viscous layer under the same initial bubble–wall distance), and a logarithmic relationship is observed that $\delta \propto \log_{10} \mu ^*$, where $\delta =h/R_{max}$ is the thickness of the viscous layer h normalised by the maximum bubble radius $R_{max}$, $\mu ^* = \mu /({R_{max }}\sqrt {{\rho }{{\mathop {P}\nolimits } _{{atm}}}})$ is the dynamic viscosity $\mu$ normalised by water density $ \rho $ and atmospheric pressure $P_{atm}$. The results of this paper can provide technical support for related studies of hydraulic cavitation erosion.

With the escalating laser peak power, modulating and detecting the intensity, duration, phase and polarization of ultra-intense laser pulses progressively becomes increasingly arduous due to the limited damage thresholds of conventional optical components. In particular, the generation and detection of ultra-intense vortex lasers pose great challenges for current laser technologies, which has limited the widely potential applications of relativistic vortex lasers in various domains. In this study, we propose to reconstruct the vortex phase and generate and amplify the relativistic vortex lasers via surface plasma holograms (SPHs). By interfering with the object laser and reference laser, SPHs are formed on the target and the phase of the interfering laser is imprinted through the modulation of surface plasma density. In particular, using the quadrature phase-shift interference, the vortex phase of the object laser can be well reconstructed. The generated vortex lasers can be focused and enhanced further by one order of magnitude, up to $1.7\times {10}^{21}$ W/cm${}^2$, which has been demonstrated by full three-dimensional particle-in-cell simulations. For the first time, we provide a practical way to detect the phase of relativistic vortex lasers, which can be applied in large 1–10 PW laser facilities. This will promote future experimental research of vortex-laser–plasma interaction and open a new avenue of plasma optics in the ultra-relativistic regime.

The longitudinal fields of a tightly focused Laguerre–Gaussian (LG) laser can be used to accelerate electron pulse trains when it is reflected from a solid plasma. However, the normal transverse mode of laser beams in high-power laser systems is approximately Gaussian. A routine and reliable way to obtain high-intensity LG lasers in experiments remains a major challenge. One approach involves utilizing a solid plasma with a ‘light fan’ structure to reflect the Gaussian laser and obtain a relativistic intense LG laser. In this work, we propose a way to combine the mode transformation of a relativistic laser and the process of electron injection and acceleration. It demonstrates that by integrating a nanowire structure at the center of the ‘light fan’, electrons can be efficiently injected and accelerated during the twisted laser generation process. Using three-dimensional particle-in-cell simulations, it is shown that a circularly polarized Gaussian beam with ${a}_0=20$ can efficiently inject electrons into the laser beam in interaction with the solid plasma. The electrons injected close to the laser axis are driven by a longitudinal electric field to gain longitudinal momentum, forming bunches with a low energy spread and a small divergence angle. The most energetic bunch exhibits an energy of 310 MeV, with a spread of 6%. The bunch charge is 57 pC, the duration is 400 as and the divergence angle is less than 50 mrad. By employing Gaussian beams, our proposed approach has the potential to reduce experimental complexity in the demonstrations of twisted laser-driven electron acceleration.

Previous research has suggested a potential link between folic acid (FA) supplementary therapy and gastric ulcers (GU). To investigate this relationship further, we conducted a Mendelian randomisation (MR) analysis using data from the UK Biobank. Our analysis primarily employed inverse-variance weighted (IVW) methods, including both fixed-effect and random-effect models. To ensure the robustness of our findings, additional methods such as the simple median, the weighted median and the penalised weighted median were also applied. The MR analysis aimed to explore the causal effect of FA supplementary therapy on GU. Seven SNP at genetic loci associated with FA supplementary therapy were identified. Both the random-effect and fixed-effect IVW models indicated that genetically predicted FA supplementary therapy significantly reduced the risk of GU (OR, 0·870; 95 % CI 0·826, 0·917, P < 0·001). This result was consistent across other methods, with similar outcomes observed using the simple median (OR, 0·835; 95 % CI 0·773, 0·901, P < 0·001), the weighted median (OR, 0·854; 95 % CI 0·794, 0·919, P < 0·001) and the penalised weighted median (OR, 0·849; 95 % CI 0·789, 0·914, P < 0·001). Leave-one-out sensitivity analysis confirmed that no individual SNP significantly drove the association between FA supplementary therapy and GU. This MR study provides genetic evidence that FA supplementary therapy may decrease the risk of GU.

Species of epiphytic microbiota are closely associated with the fermentation performance of natural forage silage. This study aimed to evaluate the dynamic microbial communities, fermentation parameters, and aerobic stability of Napier grass silage from the same variety and growth period but harvested from three different regions (NGP1, NGP2, and NGP3). After 60 days of ensiling, triplicate silos were opened for sampling and testing aerobic stability. The epiphytic microbiota with higher relative abundances in fresh Napier grass (NGP1, NGP2, and NGP3) were Weissella, Enterobacter, and Lactococcus, respectively. After 60 days of ensiling, NGP3 exhibited higher fermentation quality, indicated by higher lactic acid (LA) concentration and lower pH than that of NGP1 and NGP2. The NH3–N content of all treatments was lower than 100 g/kg total nitrogen. Compared with NGP1 and NGP2 silage, NGP3 silage exhibited a sharp rise in pH and LA consumption during air exposure. After 7 days of air exposure, NGP3 had higher ethanol concentrations and pH. Ruminiclostridium_5, Pediococcus, and Lactobacillus predominated in NGP1, NGP2, and NGP3 silages, respectively, whereas Candida and Monascus predominated in air-exposed NGP3 silage. The bacterial co-occurrence networks from fresh samples to ensiling and air exposure became more complex; however, NGP3 had a higher negative correlation with co-occurrence after air exposure. Different regions had significant effects on the fermentation patterns, bacterial communities, and aerobic stability of Napier grass silage. This was mainly due to variable epiphytic microbiota. Higher fermentation quality of Napier grass silage may also result in accelerated spoilage due to air exposure. Candida and Monascus were primarily responsible for the lower dry matter recovery and higher ethanol contents and air exposure spoilage of Napier grass silage.

Many studies have investigated the positivity rate of hepatitis B surface antibody (HBsAb) after hepatitis B vaccine (HepB) immunization. However, the antibody level, assessed monthly or at more frequent intervals after each of the three doses, particularly within the first year after birth, has not been previously reported. To elucidate the level of antibody formation at various times after vaccination, the current study used the available detection data of HBsAb in hospitalized children to analyze the HBsAb level after immunization combined with their vaccination history. Both the positivity rate and geometric mean concentration (GMC) increased sequentially with immunization doses, reaching their peaks earlier after the third dose than after the first two doses, and the rate of HBsAb positivity was able to reach 100% between 11 and 90 days after completing the three doses of HepB. Within one year after receiving the three doses, the antibody positivity rate and GMC were maintained above 90% and 100 mIU/mL, respectively, and subsequently steadily declined, reaching the lowest value in the 9th and 10th years. The current findings reveal, in more detail, the level of antibody formation at different times following each dose of HepB in hospitalized children, particularly in the age group up to one year after vaccination. For the subjects of this study, we prefer to believe that the proportion of HBsAb non-response should be less than 5% after full immunization with HepB, provided that the appropriate time for blood collection is chosen.

The purpose of this study was to analyse the clinical characteristics of patients with severe acute respiratory syndrome coronavirus 2 (SARS-COV-2) PCR re-positivity after recovering from coronavirus disease 2019 (COVID-19). Patients (n = 1391) from Guangzhou, China, who had recovered from COVID-19 were recruited between 7 September 2021 and 11 March 2022. Data on epidemiology, symptoms, laboratory test results and treatment were analysed. In this study, 42.7% of recovered patients had re-positive result. Most re-positive patients were asymptomatic, did not have severe comorbidities, and were not contagious. The re-positivity rate was 39%, 46%, 11% and 25% in patients who had received inactivated, mRNA, adenovirus vector and recombinant subunit vaccines, respectively. Seven independent risk factors for testing re-positive were identified, and a predictive model was constructed using these variables. The predictors of re-positivity were COVID-19 vaccination status, previous SARs-CoV-12 infection prior to the most recent episode, renal function, SARS-CoV-2 IgG and IgM antibody levels and white blood cell count. The predictive model could benefit the control of the spread of COVID-19.

Microplastics (MPs) pollution has been a hot research topic in recent years. MPs are ubiquitous throughout the ecological environment and are eventually accumulated in organisms through inhalation or ingestion. However, given that MPs are inert pollutants, their effects on organisms are not clear. In previous study, we have investigated the effects of polyethylene terephthalate MPs on physiology of Drosophila. What is the effect of polypropylene microplastics (PP-MPs)? The results of our experiments show that being exposed to high concentration of PP-MPs have significant effect on Drosophila. PP-MPs exposure can significantly increase locomotor activity and shorten the time of group sleep in Drosophila. In the presence of high concentrations of PP-MPs, the triglyceride content was reduced in females and their ability of egg production was affected. However, there was no significant effect on the level of protein and carbohydrate, or on the food intake. Our experimental results can provide some preliminary data for assessing the potential hazard of PP-MPs to other organisms.

The random fiber laser (RFL) has been an excellent platform for exploring novel optical dynamics and developing new functional optoelectronic devices. However, it is challenging for RFLs to regulate their emission into regular narrow pulses due to their intrinsic randomness. Here, through engineering the laser configuration (cavity Q value, gain distribution and nonlinearity), we demonstrate that narrow (~2.5 ns) pulses with record peak power as high as 64.3  kW are achieved from a self-Q-switched random ytterbium fiber laser. Based on high intracavity intensity and efficient interplay of multiple nonlinear processes (stimulated Brillouin scattering, stimulated Raman scattering and four-wave mixing), an over-one-octave visible-near-infrared (NIR) Raman-frequency comb is generated from single-mode silica fibers for the first time. After spectrally filtering the Raman peaks, wavelength-tunable pulses with durations of several hundreds of picoseconds are obtained. Such a high-peak-power random Q-switched fiber laser and wide frequency comb in the visible-NIR region can find applications in diverse areas, such as spectroscopy, biomedical imaging and quantum information.