Dirichlet’s theorem, including the uniform setting and asymptotic setting, is one of the most fundamental results in Diophantine approximation. The improvement of the asymptotic setting leads to the well-approximable set (in words of continued fractions)

$$ \begin{align*} \mathcal{K}(\Phi):=\{x:a_{n+1}(x)\ge\Phi(q_{n}(x))\ \textrm{for infinitely many }n\in \mathbb{N}\}; \end{align*} $$

$$ \begin{align*} \mathcal{G}(\Phi):=\{x:a_{n}(x)a_{n+1}(x)\ge\Phi(q_{n}(x))\ \textrm{for infinitely many }n\in \mathbb{N}\}. \end{align*} $$

$\Phi _{1},\Phi _{2}:[1,+\infty )\rightarrow \mathbb {R}^{+}$

$\mathcal {G}(\Phi _{1})\!\setminus\! \mathcal {K}(\Phi _{2})$

$\mathcal {G}(\Phi )$

$\mathcal {K}(\Phi )$

$\Phi $

$\mathcal {G}(\Phi _{1})\!\setminus\! \mathcal {K}(\Phi _{2})$

$\Phi _1$

The high-altitude landscape of western Tibet is one of the most extreme environments in which humans have managed to introduce crop cultivation. To date, only sparse palaeoeconomic data have been reported from this region. The authors present archaeobotanical evidence from five sites (dating from the late first millennium BC and the early first millennium AD) located in the cold-arid landscape of western Tibet. The data indicate that barley was widely grown in this region by c. 400 BC but probably fulfilled differing roles within local ecological constraints on cultivation. Additionally, larger sites are characterised by more diverse crop assemblages than smaller sites, suggesting a role for social diversity in the development of high-altitude agriculture.

Maternal gestational weight gain (GWG) is an important determinant of infant birth weight, and having adequate total GWG has been widely recommended. However, the association of timing of GWG with birth weight remains controversial. We aimed to evaluate this association, especially among women with adequate total GWG. In a prospective cohort study, pregnant women’s weight was routinely measured during pregnancy, and their GWG was calculated for the ten intervals: the first 13, 14–18, 19–23, 24–28, 29–30, 31–32, 33–34, 35–36, 37–38 and 39–40 weeks. Birth weight was measured, and small-for-gestational-age (SGA) and large-for-gestational-age were assessed. Generalized linear and Poisson models were used to evaluate the associations of GWG with birth weight and its outcomes after multivariate adjustment, respectively. Of the 5049 women, increased GWG in the first 30 weeks was associated with increased birth weight for male infants, and increased GWG in the first 28 weeks was associated with increased birth weight for females. Among 1713 women with adequate total GWG, increased GWG percent between 14 and 23 weeks was associated with increased birth weight. Moreover, inadequate GWG between 14 and 23 weeks, compared with the adequate GWG, was associated with an increased risk of SGA (43 (13·7 %) v. 42 (7·2 %); relative risk 1·83, 95 % CI 1·21, 2·76). Timing of GWG may influence infant birth weight differentially, and women with inadequate GWG between 14 and 23 weeks may be at higher risk of delivering SGA infants, despite having adequate total GWG.

The purpose of the current study was to research the factors influencing thyroid volume (TVOL) in 6–12-year-old children and update the reference values. A cross-sectional study was carried out in iodine-sufficient areas of four provinces in China. Urine, edible salt and drinking water samples were collected from children. Children’s height, weight and TVOL were measured. Ridge regression was used to screen variables for solving the multicollinearity problem. Quantile regression was used to analyse the relationship between the quantiles of TVOL and other variables. In total, 5653 children aged 6–12 years were enrolled in this study, including 2838 boys and 2815 girls. There was no significant difference in TVOL between boys and girls (P > 0·05). Spearman correlation analysis showed that total TVOL was positively correlated with age, height, weight, body surface area (BSA) and BMI, and the correlation coefficients were 0·616, 0·663, 0·669, 0·685 and 0·479, respectively. Among them, the correlation between TVOL and BSA was the strongest. According to the ridge regression results, age and BSA influenced TVOL, and the ridge regression coefficients were 0·13 and 0·94, respectively. Quantile regression further showed that age and BSA had significant influences on the whole TVOL distribution (P < 0·001). Therefore, the TVOL of children aged 6–12 years in China was mainly influenced by age and BSA, and reference values for TVOL of different genders based on age and BSA were established.

In this paper, an automatic obstacle avoidance trajectory planning strategy is proposed for the simultaneous motion of multi-robots, which perform anthropomorphic skill operations in a large curved preformed three-dimensional (3D) weaving environment with multiple obstacles and limited space, to eliminate tedious manual calibration work of robot path in engineering. Firstly, an Adaptive Goal-guided Rapidly-exploring Random Trees (AGG-RRT) algorithm is proposed, combined with the robot obstacle avoidance strategy, to search the discrete position of the collision-free path of the end-effector gradually from the starting point to the ending point. Then the optimization of the path is completed by bidirectional pruning of redundant nodes and cubic non-uniform rational B-spline (NURBS) curve fitting. And finally, the robot trajectory is interpolated based on S-shaped acceleration/deceleration planning to ensure smooth robot joint motion. The simulation results demonstrate the superiority of the AGG-RRT algorithm over the basic RRT algorithm and related improved algorithms in terms of search time and success rate. The simulated experiments also achieve the smooth trajectory planning of multiple robotic arms with the synchronous obstacle avoidance motion, which shows that the AGG-RRT algorithm is successfully applied and the collision-free trajectory planning strategy is effective.

Due to the lack of research between the inner layers in the structure of colonic mucous and the metabolism of fatty acid in the constipation model, we aim to determine the changes in the mucous phenotype of the colonic glycocalyx and the microbial community structure following treatment with Rhubarb extract in our research. The constipation and treatment models are generated using adult male C57BL/6N mice. We perform light microscopy and transmission electron microscopy (TEM) to detect a Muc2-rich inner mucus layer attached to mice colon under different conditions. In addition, 16S rDNA sequencing is performed to examine the intestinal flora. According to TEM images, we demonstrate that Rhubarb can promote mucin secretion and find direct evidence of dendritic structure-linked mucus structures with its assembly into a lamellar network in a pore size distribution in the isolated colon section. Moreover, the diversity of intestinal flora has noticeable changes in constipated mice. The present study characterizes a dendritic structure and persistent cross-links have significant changes accompanied by the alteration of intestinal flora in feces in models of constipation and pretreatment with Rhubarb extract.

In the past 10–15 years, the government of China has made various efforts in tackling excessive antibiotics use. Yet, little is known about their effects at rural primary care settings. This study aimed to determine the impact of government policies and the COVID-19 pandemic on antibiotic prescribing practices at such settings utilizing data from separate studies carried out pre- and during the pandemic, in 2016 and 2021 in Anhui province, China, using identical sampling and survey approaches. Data on antibiotics prescribed, diagnosis, socio-demographic, etc., were obtained through non-participative observation and a structured exit survey. Data analysis comprised mainly descriptive comparisons of 1153 and 762 patients with respiratory infections recruited in 2016 and 2021, respectively. The overall antibiotics prescription rate decreased from 89.6% in 2016 to 69.1% in 2021, and the proportion of prescriptions for two or more classes of antibiotics was estimated as 35.9% in 2016 and 11.0% in 2021. There was a statistically significant decrease in the number of days from symptom onset to clinic visits between the year groups. In conclusion, measures to constrain excessive prescription of antibiotics have led to some improvements at the rural primary care level, and the COVID-19 pandemic has had varying effects on antibiotic use.

The 4.2 ka event is widely presumed to be a globally widespread aridity event and has been linked to several episodes of societal changes across the globe. Whether this climate event impacted the cultural development in south-central China remains uncertain due to a lack of regional paleorainfall records. We present here stalagmite stable carbon isotope and trace element–based reconstruction of hydroclimatic conditions from south-central China. Our data reveal a sub–millennial scale (~5.6 to 4.3 ka) drying trend in the region followed by a gradual transition to wetter conditions during the 4.2 ka event (4.3–3.9 ka). Together with the existing archaeological evidence, our data suggest that the drier climate before 4.3 ka may have promoted the Shijiahe culture, while the pluvial conditions during the 4.2 ka event may have adversely affected its settlements in low-lying areas. While military conflicts with the Wangwan III culture may have accelerated the collapse of Shijiahe culture, we suggest that the joint effects of climate and the region's topography also played important causal roles in its demise.

Lower-crust-derived adakitic rocks in the Gangdese belt provide important constraints on the timing of Tibetan crustal thickening and on the relative contributions of magmatic and tectonic processes. Here we present geochronological and geochemical data for the Wangdui porphyritic monzogranites in the western Gangdese belt. Zircon U–Pb dating yields emplacement ages of 46–44 Ma. All samples have high Sr (321–599 ppm), low Yb (0.76–1.33 ppm) and Y (10.6–18.3 ppm) contents, with high La/Yb (51.1–72.3) and Sr/Y (21.0–51.4) ratios, indicating adakitic affinities. The low MgO (0.97–1.76 wt %), Cr (7.49–53.6 ppm) and Ni (4.75–29.1 ppm) contents, as well as high 87Sr/86Sr(i) (0.7143–0.7145), low ϵNd(t) (−10.4 to −9.8) and zircon ϵHf(t) (−17.7 to 0.4) values, suggest that the Wangdui pluton most likely originated from partial melting of the thickened ancient lower crust. In combination with previously published data, despite the east–west-trending heterogeneity of crustal composition in the Gangdese belt, the La/Yb ratios of magmatic rocks reveal that both western and eastern segments experienced remarkable crustal thickening in the Eocene. However, in contrast to the thickened juvenile lower crust in the eastern segment formed by the underplating of mantle-derived magmas, tectonic shortening plays a more crucial role in thickening of the ancient basement in western Gangdese. In fact, such Eocene-thickened ancient lower-crust-derived adakitic rocks are widely distributed in the central Himalayan–Tibetan orogen. This, together with the extensive development of fold–thrust belts, suggests that tectonic shortening might be the main mechanism accounting for the crustal thickening associated with the India–Asia collision.

Dietary l-carnitine (LC) is a nutritional factor that reduces liver lipid content. However, whether dietary LC can improve lipid metabolism via simultaneous activation of mitochondrial fatty acid (FA) β-oxidation and suppression of endoplasmic reticulum (ER) stress is still unknown. Large yellow croaker were fed with a high-fat diet (HFD) supplemented with dietary LC at 0, 1·2 or 2·4 ‰ for 10 weeks. The results indicated that a HFD supplemented with LC reduced the liver total lipid and TAG content and improved serum lipid profiles. LC supplementation administered to this fish increased the liver antioxidant capacity by decreasing serum and liver malondialdehyde levels and enhancing the liver antioxidant capacity, which then relieved the liver damage. Dietary LC increased the ATP dynamic process and mitochondrial number, decreased mitochondrial DNA damage and enhanced the protein expression of mitochondrial β-oxidation, biogenesis and mitophagy. Furthermore, dietary LC supplementation increased the expression of genes and proteins related to peroxisomal β-oxidation and biogenesis. Interestingly, feeding fish with LC-enriched diets decreased the protein levels indicative of ER stress, such as glucose-regulated protein 78, p-eukaryotic translational initiation factor 2a and activating transcription factor 6. Dietary LC supplementation downregulated mRNA expression relative to FA synthesis, reduced liver lipid and relieved liver damage through regulating β-oxidation and biogenesis of mitochondria and peroxisomes, as well as the ER stress pathway in fish fed with HFD. The present study provides the first evidence that dietary LC can improve lipid metabolism via simultaneously promoting FA β-oxidation capability and suppressing the ER stress pathway in fish.

Cardiac amyloidosis presented with normal interventricular septum is an extremely rare entity, and diagnosis may be difficult. This report discusses a 44-year-old female who presented with worsening dyspnoea on exertion, orthopnoea, and lower-extremity oedema. Electrocardiogram depicted low voltage in limb leads and a pseudoinfarct pattern. Echocardiogram revealed biatrial dilatation without changes of ventricular chambers and restrictive filling physiology. A diagnosis of cardiac amyloidosis was considered. Cardiac MRI was pursued, showing delayed gadolinium enhancement, and this ultimately led to the myocardial biopsy confirming the diagnosis of cardiac amyloidosis. The case suggests that patients who present with heart failure of uncertain aetiology, amyloidosis could be a cause of cardiomyopathy despite the absence of “classical” echocardiographic features of amyloid deposition such as an increased interventricular septum thickness or“brilliant sparkled”appearance of the myocardium.

Energy homeostasis is essential for organisms to maintain fluctuation in energy accumulation, mobilization. Lipids as the main energy reserve in insects, their metabolism is under the control of many physiological program. This study aimed to determine whether the adipokinetic hormone receptor (AKHR) was involved in the lipid mobilization in the Spodoptera litura. A full-length cDNA encoding AKHR was isolated from S. litura. The SlAKHR protein has a conserved seven-transmembrane domain which is the character of a putative G protein receptor. Expression profile investigation revealed that SlAKHR mRNA was highly expressed in immatural stage and abundant in fat body in newly emerged female adults. Knockdown of SlAKHR expression was achieved through RNAi by injecting double-stranded RNA (dsRNA) into the 6th instar larvae. The content of triacylgycerol (TAG) in the fat body increased significantly after the SlAKHR gene was knockdown. And decrease of TAG releasing to hemolymph with increase of free fatty acid (FFA) in hemolymph were observed when the SlAKHR gene was knowned-down. In addition, lipid droplets increased in fat body was also found. These results suggested that SlAKHR is critical for insects to regulate lipids metabolism.