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 $

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

$\Phi _1$

Understanding predator–prey interactions is essential for successful pest management by using predators, especially for the suppression of novel invasive pest. The green lacewing Chrysopa formosa is a promising polyphagous predator that is widely used in the biocontrol of various pests in China, but information on the control efficiency of this predator against the seriously invasive pest Spodoptera frugiperda and native Spodoptera litura is limited. Here we evaluated the predation efficiency of C. formosa adults on eggs and first- to third-instar larvae of S. frugiperda and S. litura through functional response experiments and determined the consumption capacity and prey preference of this chrysopid. Adults of C. formosa had a high consumption of eggs and earlier instar larvae of both prey species, and displayed a type II functional response on all prey stages. Attack rates of the chrysopid on different prey stages were statistically similar, but the handling time increased notably as the prey developed. The highest predation efficiency and shortest-handling time were observed for C. formosa feeding on Spodoptera eggs, followed by the first-instar larvae. C. formosa exhibited a significant preference for S. litura over S. frugiperda in a two-prey system. In addition, we summarized the functional response and predation efficiency of several chrysopids against noctuid pests and made a comparison with the results obtained from C. formosa. These results indicate that C. formosa has potential as an agent for biological control of noctuid pests, particularly for the newly invasive pest S. frugiperda in China.

This experiment was conducted to evaluate the impact of substituting rice straw with citrus pulp (CRP), sweet potato peels (SPP) and vines (SPV) on fermentation quality and in vitro digestibility when ensiled with or without wet brewers' grains (WBG). Seven treatments were set as follows: (i) rice straw only (control); (ii) 800 g rice straw/kg + 200 g CRP/kg (RC); (iii) 720 g rice straw/kg + 180 g CRP/kg + 100 g WBG/kg (RC+); (iv) 800 g rice straw/kg + 200 g SPP/kg (RP); (v) 720 g rice straw + 180 g SPP/kg + 100 g WBG/kg (RP+); (vi) 800 g rice straw/kg + 200 g SPV/kg (RV); (vii) 720 g rice straw/kg + 180 g SPV/kg + 100 g WBG/kg (RV+). After ensiling for 3, 7, 14, 30 and 60 days, silos were opened for fermentation profile, aerobic stability and in vitro parameter analyses. All substitution types improved fermentation quality, characterized by significantly lower pH and NH3-N content, higher lactic acid content and V-scores. WBG application promoted hetero-fermentation and significantly increased DM losses, acetic acid and ethanol contents. After 60 days of ensiling, the NDF, ADF and cellulose contents in mixed silages significantly decreased compared to control. During aerobic exposure, WBG application significantly prolonged aerobic stability. SPV substitution significantly improved in vitro digestibility of dry matter, NDF and ADF. In conclusion, the SPP substitution combined with WBG application was recommended as a result of the optimal balance of fermentation quality, aerobic stability and in vitro digestibility.

Athetis lepigone Möschler (Lepidoptera, Noctuidae) is a common maize pest in Europe and Asia. However, there is no long-term effective management strategy is available yet to suppress its population. Adults rely heavily on olfactory cues to locate their optimal host plants and oviposition sites. Pheromone-binding proteins (PBPs) are believed to be responsible for recognizing and transporting different odorant molecules to interact with receptor membrane proteins. In this study, the ligand-binding specificities of two AlepPBPs (AlepPBP2 and AlepPBP3) for sex pheromone components and host plant (maize) volatiles were measured by fluorescence ligand-binding assay. The results demonstrated that AlepPBP2 had a high affinity with two pheromones [(Z)-7-dodecenyl acetate, Ki = 1.11 ± 0.1 μM, (Z)-9-tetradecenyl acetate, Ki = 1.32 ± 0.15 μM] and ten plant volatiles, including (-)-limonene, α-pinene, myrcene, linalool, benzaldehyde, nonanal, 2-hexanone, 3-hexanone, 2-heptanone and 6-methyl-5-hepten-2-one. In contrast, we found that none of these chemicals could bind to AlepPBP3. Our results clearly show no significant differences in the functional characterization of the binding properties between AlepPBP2 and AlepPBP3 to sex pheromones and host plant volatiles. Furthermore, molecular docking was employed for further detail on some crucial amino acid residues involved in the ligand-binding of AlepPBP2. These findings will provide valuable information about the potential protein binding sites necessary for protein-ligand interactions which appear as attractive targets for the development of novel technologies and management strategies for insect pests.

Strike-slip earthquakes near major subduction zones have received less attention than thrust or reverse earthquakes in subduction zone areas. The occurrence of the 2018 Palu Mw 7.5 earthquake in eastern Indonesia provides an unprecedented opportunity to investigate the characteristics of one of these events. The Palu earthquake occurred on the left-lateral, north–south-striking Palu–Koro fault, which is the main plate boundary structure accommodating the convergence between blocks in a triple junction area. It excited a significant tsunami, which unusually is associated with strike-slip earthquakes, and also ruptured at a supershear speed, which is mostly observed on strike-slip faults in continents. Based on our fieldwork, we speculate that the normal slip component of the offshore rupture section in Palu bay on the middle segment probably favours tsunami genesis. Our field investigation has revealed evidence of a simple geometry as well as slip partitioning of dip-slip and strike-slip motion on two subparallel strands on the main segment, both of which may have contributed to the supershear of the rupture propagation. Instead of only a transtensive behaviour of the middle segment, our results also illustrate the transpressional property of the northern and southern rupture segments, which shows more complex behaviour than that of a common continental strike-slip fault.

Extensive magmatism in NE China, eastern Central Asian Orogenic Belt, has produced multi-stage granitic plutons and accompanying W mineralization. The Narenwula complex in the southwestern Great Xing’an Range provides important insights into the petrogenesis, geodynamic processes and relationship with W mineralization. The complex comprises granodiorites, monzogranites and granite porphyry. Mafic microgranular enclaves are common in the granodiorites, and have similar zircon U–Pb ages as their host rocks (258.5–253.9 Ma), whereas the W-bearing granitoids yield emplacement ages of 149.8–148.1 Ma. Permian granodiorites are I-type granites that are enriched in large-ion lithophile elements and light rare earth elements, and depleted in high field strength elements and heavy rare earth elements. Both the mafic microgranular enclaves and granodiorites have nearly identical zircon Hf isotopic compositions. The results suggest that the mafic microgranular enclaves and granodiorites formed by the mixing of mafic and felsic magmas. W-bearing granitoids are highly fractionated A-type granites, enriched in Rb, Th, U and Pb, and depleted in Ba, Sr, P, Ti and Eu. They have higher W concentrations and Rb/Sr ratios, and lower Nb/Ta, Zr/Hf and K/Rb ratios than the W-barren granodiorites. These data and negative ϵHf(t) values (–6.0 to –2.1) suggest that they were derived from the partial melting of ancient lower crust and subsequently underwent extreme fractional crystallization. Based on the regional geology, we propose that the granodiorites were generated in a volcanic arc setting related to the subduction of the Palaeo-Asian Ocean, whereas the W-bearing granitoids and associated deposits formed in a post-orogenic extensional setting controlled by the Mongol–Okhotsk Ocean and Palaeo-Pacific Ocean tectonic regimes.

The optimization of laser pulse shapes is of great importance and a major challenge for laser direct-drive implosions. In this paper, we propose an efficient intelligent method to perform laser pulse optimization via hydrodynamic simulations guided by the genetic algorithm and random forest algorithm. Compared to manual optimizations, the machine-learning guided method is able to efficiently improve the areal density by a factor of 63% and reduce the in-flight-aspect ratio by a factor of 30% at the same time. A relationship between the maximum areal density and ion temperature is also achieved by the analysis of the big simulation dataset. This design method has been successfully demonstrated by the 2021 summer double-cone ignition experiments conducted at the SG-II upgrade laser facility and has great prospects for the design of other inertial fusion experiments.

EPA and DHA are essential for maternal and fetal health, but epidemiological data are sparse in China. We examined the trends of EPA alone and a combination of EPA plus DHA in pregnant and lactating women in three distinct geographic regions in China and explored their potential influencing factors. A total of 1015 healthy women during mid-pregnancy, late pregnancy or lactation were recruited from Weihai (coastland), Yueyang (lakeland) and Baotou (inland) cities of China between May and July of 2014. Maternal EPA and DHA concentrations (percentage of total fatty acids) in plasma and erythrocytes were measured by capillary GC. Adjusted EPA plus DHA concentrations in both plasma and erythrocytes significantly declined from mid-pregnancy (2·92 %, 6·95 %) to late pregnancy (2·20 %, 6·42 %) and lactation (2·40 %, 6·29 %) (Ptrend < 0·001); and both concentrations were highest in coastland, followed by lakeland, and lowest in inland (P < 0·001). Regarding EPA alone, the concentrations were higher in women during lactation or late pregnancy and in women in coastland and inland areas. Moreover, concentrations of EPA or EPA plus DHA were higher in women with older age, higher education, higher annual family income per capita and higher dietary intake of marine aquatic product and mutton. In lactating women, erythrocyte EPA concentration was higher in those having breast-feeding partially v. exclusively. In conclusion, maternal plasma and erythrocyte concentrations of EPA plus DHA or EPA alone differed with geographic regions, physiological periods and maternal characteristics, indicating a need of population-specific health strategies to improve fatty acids status in pregnant and lactating women.

The present study aimed to explore the association between dietary patterns in abdominal obesity obtained by reduced-rank regression (RRR) with visceral fat index (VFI) as a dependent variable and dyslipidemia in rural adults in Henan, China. A total of 29538 people aged 18–79 were selected from the Henan Rural Cohort Study. RRR analysis was used to identify dietary patterns; logistic regression analysis and restricted cubic spline regression models were applied to analyze the association between dietary patterns in abdominal obesity and dyslipidemia. VFI was used as a mediator to estimate the mediation effect. The dietary pattern in abdominal obesity was characterized by high carbohydrate and red meat intake and low consumption of fresh fruits, vegetables, milk, etc. After full adjustment, the highest quartile of dietary pattern scores was significantly associated with an increased risk of dyslipidemia (OR: 1·33, 95 % CI 1·23–1·44, Ptrend < 0·001), there was a non-linear dose–response relationship between them (Poverall-association < 0·001, Pnon-lin-association = 0·022). The result was similar in dose-response between the dietary pattern scores and VFI. The indirect effect partially mediated by VFI was significant (OR: 1·07, 95 % CI 1·06–1·08). VIF explained approximately 53·3 % of odds of dyslipidemia related to the dietary pattern. Abdominal obesity dietary pattern scores positively affected VFI and dyslipidemia; there was a dose-response in both relationships. Dyslipidemia progression increased with higher abdominal obesity dietary pattern scores. In addition, VFI played a partial mediating role in relationship between abdominal obesity dietary pattern and dyslipidemia.

To explore the characteristics of the mitochondrial genome (mitogenome) of the squeaking silkmoths Rhodinia, a genus of wild silkmoths in the family Saturniidae of Lepidoptera, and reveal phylogenetic relationships, the mitogenome of Rhodinia fugax Butler was determined. This wild silkmoth spins a green cocoon that has potential significance in sericulture, and exhibits a unique feature that its larvae can squeak loudly when touched. The mitogenome of R. fugax is a circular molecule of 15,334 bp long and comprises 13 protein-coding genes, two ribosomal RNA genes, 22 transfer RNA genes, and an A + T-rich region, consistent with previous observations of Saturniidae species. The 370-bp A + T-rich region of R. fugax contains no tandem repeat elements and harbors several features common to the Bombycidea insects, but microsatellite AT repeat sequence preceded by the ATTTA motif is not present. Mitogenome-based phylogenetic analysis shows that R. fugax belongs to Attacini, instead of Saturniini. This study presents the first mitogenome for Rhodinia genus.

The aim of the present study was to compare the rate of preterm birth (PTB) and growth from birth to 18 years between twins conceived by in vitro fertilization (IVF) and twins conceived by spontaneous conception (SC) in mainland China. The retrospective cohort study included 1164 twins resulting from IVF and 25,654 twins conceived spontaneously, of which 494 from IVF and 6338 from SC were opposite-sex twins. PTB and low birth weight (LBW), and growth, including length/height and weight, were compared between the two groups at five stages: infancy (0 year), toddler period (1–2 years), preschool (3–5 years), primary or elementary school (6–11 years), and adolescence (10–18 years). Few statistically significant differences were found for LBW and growth between the two groups after adjusting for PTB and other confounders. Twins born by IVF faced an increased risk of PTB compared with those born by SC (adjusted odds ratio [aOR] 8.21, 95% confidence interval [CI] [3.19, 21.13], p < .001 in all twins and aOR 10.12, 95% CI [2.32, 44.04], p = .002 in opposite-sex twins). Twins born by IVF experienced a similar growth at five stages (0–18 years old) when compared with those born by SC. PTB risk, however, is significantly higher for twins conceived by IVF than those conceived by SC.

Maternal folic acid (FA) plays an important role in the fetus development, but it is unknown the response of hepatic metabolism in the offspring from different litter sizes to maternal FA supplementation. In the present study, this was done by feeding the ewes with 0, 16 and 32 mg/(kg·DM) FA supplemented diet during pregnancy and analysing the hepatic one-carbon metabolism-related indices and gene expression in the neonatal lambs of different litter sizes (twins, TW; triplets, TR). Regardless of litter sizes, the concentrations of folate, methionine, S-adenosylmethionine and DNA methyltransferase increased significantly, but homocysteine and S-adenosylhomocysteine decreased in the liver of newborn lambs from ewes whose diet was supplemented with FA. In TW, maternal FA status has little effect on hepatic genes expression profile of newborn lambs, and no significant enriched pathway was found. However, DEG involved in cell proliferation such as CCNA2, CCNB2, CCNE2, CDK1 and BUB1 were significantly enriched when the ewes were supplemented with FA in TR groups. In addition, nucleotide synthesis-related genes such as POLD1, POLD2, MCM4 and MCM5 were enriched markedly in DNA replication and pyrimidine metabolism pathways in triplets when a higher FA ingestion [32 mg/(kg·DM)] was implemented in ewes. This finding demonstrated that the hepatic methyl metabolism in TW and TR newborn lambs was regulated by maternal FA status. The hepatic cell proliferation and nucleotide metabolism related genes in TR were more susceptible to maternal dietary FA supplementation during pregnancy.

The generation of germ cells from embryonic stem cells in vitro has current historical significance. Western blot, qPCR, immunofluorescence and flow cytometry assays were used to investigate the differences in expression levels of totipotency and specific markers for Wnt regulation and the related signalling pathways during primordial germ cell-like cell (PGCLC) induction and differentiation. During PGCLC induction, activation of WNT3a increased the expression of NANOG, SOX2 and OCT4, but Mvh, DAZL, Blimp1, TFAP2C, Gata4, SOX17, EOMES, Brachyury and PRDM1 expression levels were significantly reduced. Inhibition of the WNT signal demonstrated the opposite effect. Similarly, inhibitors of BMP and the Nodal/Activin signal were used to determine the effect of signal pathways on differentiation. CER1 affected the Wnt signal and differentiation, but the inhibitor SB only regulated differentiation. BMP–WNT–NODAL were mainly responsible for regulating differentiation. Our results provide a reliable theoretical basis and feasibility for further clinical medical research.