Let $\mathbb{N}$ be the set of all non-negative integers. For any integer r and m, let $r+m\mathbb{N}=\{r+mk: k\in\mathbb{N}\}$. For $S\subseteq \mathbb{N}$ and $n\in \mathbb{N}$, let $R_{S}(n)$ denote the number of solutions of the equation $n=s+s'$ with $s, s'\in S$ and $s \lt s'$. Let $r_{1}, r_{2}, m$ be integers with $0 \lt r_{1} \lt r_{2} \lt m$ and $2\mid r_{1}$. In this paper, we prove that there exist two sets C and D with $C\cup D=\mathbb{N}$ and $C\cap D=(r_{1}+m\mathbb{N})\cup (r_{2}+m\mathbb{N})$ such that $R_{C}(n)=R_{D}(n)$ for all $n\in\mathbb{N}$ if and only if there exists a positive integer l such that $r_{1}=2^{2l+1}-2, r_{2}=2^{2l+1}-1, m=2^{2l+2}-2$.

A high-energy pulsed vacuum ultraviolet (VUV) solid-state laser at 177 nm with high peak power by the sixth harmonic of a neodymium-doped yttrium aluminum garnet (Nd:YAG) amplifier in a KBe2BO3F2 prism-coupled device was demonstrated. The ultraviolet (UV) pump laser is a 352 ps pulsed, spatial top-hat super-Gaussian beam at 355 nm. A high energy of a 7.12 mJ VUV laser at 177 nm is obtained with a pulse width of 255 ps, indicating a peak power of 28 MW, and the conversion efficiency is 9.42% from 355 to 177 nm. The measured results fitted well with the theoretical prediction. It is the highest pulse energy and highest peak power ever reported in the VUV range for any solid-state lasers. The high-energy, high-peak-power, and high-spatial-uniformity VUV laser is of great interest for ultra-fine machining and particle-size measurements using UV in-line Fraunhofer holography diagnostics.

Fe2+-catalyzed transformation of poorly crystalline ferrihydrite into highly crystalline forms is critical in the biogeochemical cycles of Fe, nutrients, and trace elements. The co-existence of ferrihydrite and kaolinite is widespread in soils of tropical and subtropical regions. In this investigation, three associations of ferrihydrite–kaolinite with ratios of 10, 30, and 50% (10% Fhy–Kln, 30% Fhy–Kln, and 50% Fhy–Kln) were examined to study the impact of the initial Fe2+ concentration and pH on Fe2+-catalyzed transformation under anoxic conditions. The findings reveal that the ferrihydrite in the 10% Fhy–Kln associations has the smallest particle size and the largest number of surface hydroxyl groups. At 0.5 mM Fe2+ and pH 7.5, ferrihydrite underwent transformation into lepidocrocite, with the presence of kaolinite promoting the formation of goethite. Moreover, the presence of kaolinite influenced the morphology of the resulting transformation products. A decrease in pH hindered the transformation of ferrihydrite, while an increase in Fe2+ concentration resulted in the formation of magnetite. The impact of kaolinite in the association system on the transformations of ferrihydrite occurs primarily through alteration of the properties of ferrihydrite during its formation process.

The Righi–Leduc heat flux generated by the self-generated magnetic field in the ablative Rayleigh–Taylor instability driven by a laser irradiating thin targets is studied through two-dimensional extended-magnetohydrodynamic simulations. The perturbation structure gets into a low magnetization state though the peak strength of the self-generated magnetic field could reach hundreds of teslas. The Righi–Leduc effect plays an essential impact both in the linear and nonlinear stages, and it deflects the total heat flux towards the spike base. Compared to the case without the self-generated magnetic field included, less heat flux is concentrated at the spike tip, finally mitigating the ablative stabilization and leading to an increase in the velocity of the spike tip. It is shown that the linear growth rate is increased by about 10% and the amplitude during the nonlinear stage is increased by even more than 10% due to the feedback of the magnetic field, respectively. Our results reveal the importance of Righi–Leduc heat flux to the growth of the instability and promote deep understanding of the instability evolution together with the self-generated magnetic field, especially during the acceleration stage in inertial confinement fusion.

The laboratory generation and diagnosis of uniform near-critical-density (NCD) plasmas play critical roles in various studies and applications, such as fusion science, high energy density physics, astrophysics as well as relativistic electron beam generation. Here we successfully generated the quasistatic NCD plasma sample by heating a low-density tri-cellulose acetate (TCA) foam with the high-power-laser-driven hohlraum radiation. The temperature of the hohlraum is determined to be 20 eV by analyzing the spectra obtained with the transmission grating spectrometer. The single-order diffraction grating was employed to eliminate the high-order disturbance. The temperature of the heated foam is determined to be T = 16.8 ± 1.1 eV by analyzing the high-resolution spectra obtained with a flat-field grating spectrometer. The electron density of the heated foam is about $N_e=4.0\pm 0.3\times {10}^{20}{\text{cm}}^{-3}$ under the reasonable assumption of constant mass density.

Todorokite is a common Mn oxide (with a tunnel structure) in the Earth surface environment, and can be obtained by hydrothermal treatment or refluxing process from precursor buserite with a layered structure. Several chemical reaction conditions for the phase transformation from Na-buserite to todorokite at atmospheric pressure were investigated, including temperature, pH, crystallinity of precursor Na-buserite, the amount of the interlayer Mg2+ of the Mg-buserite and clay minerals. The results showed that the conversion rate and crystallinity of todorokite decreased with falling temperature, and Mg-buserite could not be completely transformed to todorokite at lower temperatures (40°C). The poorly crystalline Na-buserite could be converted into todorokite more easily than highly crystalline Na-buserite. Todorokite can be prepared at pH 5–9, but the rate of conversion and crystallinity of todorokite did vary with pH in the order: neutral ≈ alkali > acidic. The conversion rate of todorokite decreased with decreasing interlayer Mg2+ content of the Mg-buserite. The presence of montmorillonite or goethite slowed the formation reaction of todorokite in the refluxing process, and the reaction time was prolonged when the amounts of those minerals were increased.

The G protein-coupled receptors (GPCR) sensing nutritional signals (amino acids, fatty acids, glucose, etc.) are not fully understood. In this research, we used transcriptome sequencing to analyse differentially expressed genes (DEG) in mouse mammary gland tissues at puberty, lactation and involution stages, in which eight GPCR were selected out and verified by qRT-PCR assay. It was further identified the role of GPR110-mediating nutrients including palmitic acid (PA) and methionine (Met) to improve milk synthesis using mouse mammary epithelial cell line HC11. PA but not Met affected GPR110 expression in a dose-dependent manner. GPR110 knockdown decreased milk protein and fat synthesis and cell proliferation and blocked the stimulation of PA on mechanistic target of rapamycin (mTOR) phosphorylation and sterol-regulatory element binding protein 1c (SREBP-1c) expression. In summary, these experimental results disclose DEG related to lactation and reveal that GPR110 mediates PA to activate the mTOR and SREBP-1c pathways to promote milk protein and fat synthesis.

We report here the first hundred-watt continuouswave fiber gas laser in H2-filled hollow-core photonic crystal fiber (PCF) by stimulated Raman scattering. The pump source is a homemade narrow-linewidth fiber oscillator with a 3 dB linewidth of 0.15 nm at the maximum output power of 380 W. To efficiently and stably couple several-hundred-watt pump power into the hollow core and seal the gas, a hollow-core fiber end-cap is fabricated and used at the input end. A maximum power of 110 W at 1153 nm is obtained in a 5 m long hollow-core PCF filled with 36 bar H2, and the conversion efficiency of the first Stokes power is around 48.9%. This work paves the way for high-power fiber gas Raman lasers.

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.

A method is presented for configuration selection to obtain the best tip-over stability of a modular reconfigurable mobile manipulator (MRMM) under various application situations. The said MRMM consists of a modular reconfigurable robot (MRR) mounted on a mobile platform. The MRR in different configurations creates different wrenches onto the mobile platform, leading to different tip-over moments of the MRMM, even though the joint speeds or tip speeds remain the same. The underlying problem pertains to selecting one configuration of MRR for reconfiguration that would obtain the best tip-over stability under a given application. First, all the permissible configurations are identified through an enumeration method. Then, the feasible configurations are determined based on application-oriented workspace classifications. At last, two workspace indices, vertical reach and horizontal reach, are used to select an optimal configuration. The tip-over stability analysis and evaluation of MRMM are carried out for verification for three cases including vertical, horizontal, and general 3D space applications. The results demonstrate the effectiveness of the proposed method.

The nutritional status experienced in the early development of life plays a vital role in the long-term metabolic state of the individual, which is known as nutritional programming. The present study investigated the long-term effects of vegetable oil (VO) nutritional programming during the early life of large yellow croaker. First, larvae were fed either a fish oil (FO) diet or a VO diet for 30 d. Subsequently, under the same conditions, all fish were fed a commercial diet for 90 d and thereafter challenged with an FO or VO diet for 30 d. The results showed that growth performance was significantly lower in larvae fed the VO diet than in those in fed the FO diet in the stimulus phase. Notably, VO nutritional history fish showed lower levels of liver lipids liver total triglycerides and serum nonesterified free fatty acids than the FO nutritional history fish when juveniles were challenged with the VO diet, which was consistent with the expression of lipogenesis-related genes and proteins. Moreover, the VO nutritional history fish showed lower liver damage and higher antioxidant capacity than FO nutritional history fish when challenged with the VO diet. In summary, this study showed that a short VO stimulus during the early life stage of large yellow croaker, had a long-term effect on lipid metabolism and the antioxidant system. Specifically, VO nutritional programming had a positive effect on alleviating abnormal lipid deposition on the liver, liver damage, and the reduction of hepatic antioxidant capacity caused by a VO diet.

This paper exploited an alternative approach to prepare high-quality speckle patterns by uniformly dispersing nano-silica particles onto sample surfaces, helping digital image correlation (DIC) acquire the maximum spatial resolution of local strain up to 92 nm. A case study was carried out by combining this speckle pattern fabrication method with SEM-DIC and electron backscattering diffraction (EBSD). Thus, in situ mapping of local strain with ultra-high spatial resolution and microstructure in commercially pure titanium during plastic deformation could be achieved, which favored revealing the effect of slip transfer on shear strain near grain boundaries. Moreover, the slip systems could be easily identified via the combination of the SEM-DIC and EBSD techniques even though no obvious deformation trace was captured in secondary electron images. Additionally, the complex geometric compatibility factor $( {m}^{\prime}_c)$ relating to geometric compatibility factors (mʹ) and Schmid factors was proposed to predict the shear strain (εxy) at grain boundaries.

Streptococcus agalactiae (S. agalactiae) infection is a significant cause of mastitis, resulting in loss of cellular homeostasis and tissue damage. Autophagy plays an essential function in cell survival, defense, and the preservation of cellular homeostasis, and is often part of the response to pathogenic challenge. However, the effect of autophagy induced by S. agalactiae in bovine mammary epithelial cells (bMECs) is mainly unknown. So in this study, an intracellular S. agalactiae infection model was established. Through evaluating the autophagy-related indicators, we observed that after S. agalactiae infection, a significant quantity of LC3-I was converted to LC3-II, p62 was degraded, and levels of Beclin1 and Bcl2 increased significantly in bMECs, indicating that S. agalactiae induced autophagy. The increase in levels of LAMP2 and LysoTracker Deep Red fluorescent spots indicated that lysosomes had participated in the degradation of autophagic contents. After autophagy was activated by rapamycin (Rapa), the amount of p-Akt and p-mTOR decreased significantly, whilst the amount of intracellular S. agalactiae increased significantly. Whereas the autophagy was inhibited by 3-methyladenine (3MA), the number of intracellular pathogens decreased. In conclusion, the results demonstrated that S. agalactiae could induce autophagy through PI3K/Akt/mTOR pathway and utilize autophagy to survive in bMECs.

Biomacromolecules have gained much attention as biomedicine carriers in recent years due to their remarkable biophysical and biochemical properties including sustainability, non-toxicity, biocompatibility, biodegradability, long systemic circulation time and ability to target. Recent developments in a variety of biological functions of biomacromolecules and progress in the study of biological drug carriers suggest that these carriers may have advantages over carriers of synthetic materials in terms of half-life, durability, protection and manufacturing facility. Despite the full pledge advancements in the applications of biomacromolecules, its clinical use is hindered by certain factors that allow the pre-mature release of loaded cargos before reaching the target site. The delivery therapeutics are degraded by systemic nucleases, cleared by reticulo-endothelial system, cleared by pulmonary mucus cilia or engulfed by lysosome during cellular uptake that has led to the failure of clinical therapy. It clearly indicates that there is a wide range of gaps in the results of experimental work and clinical applications of biomacromolecules. This review focuses mainly on the barriers (intracellular/extracellular) and hurdles to the delivery of biomacromolecules with special emphasis on siRNA as well as the delivery of antisense oligos in multiple pulmonary diseases, particularly focusing on lung cancer. Also, the challenges posed to such delivery and possible solutions have been highlighted.

Electrochemical energy-storage systems such as supercapacitors and lithium-ion batteries require complex intertwined networks that provide fast transport pathways for ions and electrons without interfering with their energy density. Self-assembly of nanomaterials into hierarchical structures offers exciting possibilities to create such pathways. This article summarizes recent research achievements in self-assembled zero-dimensional, one-dimensional, and two-dimensional nanomaterials, ordered pore structure materials, and the interfaces between these. We analyze how self-assembly strategies can create storage architectures that improve device performance toward higher energy densities, longevity, rate capability, and device safety. At the end, the remaining challenges of scalable low-cost manufacturing and future opportunities such as self-healing are discussed.