Let $[a_1(x),a_2(x),a_3(x),\ldots ]$ be the continued fraction expansion of an irrational number $x\in [0,1)$. We are concerned with the asymptotic behaviour of the product of consecutive partial quotients of x. We prove that, for Lebesgue almost all $x\in [0,1)$,

$$ \begin{align*} \liminf_{n \to \infty} \frac{\log (a_n(x)a_{n+1}(x))}{\log n} = 0\quad \text{and}\quad \limsup_{n \to \infty} \frac{\log (a_n(x)a_{n+1}(x))}{\log n}=1. \end{align*} $$

We also study the Baire category and the Hausdorff dimension of the set of points for which the above liminf and limsup have other different values and similarly analyse the weighted product of consecutive partial quotients.

This study evaluated the association between inflammatory diets as measured by the Dietary Inflammatory index (DII), inflammation biomarkers and the development of preeclampsia among the Chinese population. We followed the reporting guidelines of the Strengthening the Reporting of Observational Studies in Epidemiology statement for observational studies. A total of 466 preeclampsia cases aged over 18 years were recruited between March 2016 and June 2019, and 466 healthy controls were 1:1 ratio matched by age (±3 years), week of gestation (±1 week) and gestational diabetes mellitus. The energy-adjusted DII (E-DII) was computed based on dietary intake assessed using a seventy-nine item semiquantitative FFQ. Inflammatory biomarkers were analysed by ELISA kits. The mean E-DII scores were −0·65 ± 1·58 for cases and −1·19 ± 1·47 for controls (P value < 0·001). E-DII scores positively correlated with interferon-γ (r s = 0·194, P value = 0·001) and IL-4 (r s = 0·135, P value = 0·021). After multivariable adjustment, E-DII scores were positively related to preeclampsia risk (P trend < 0·001). The highest tertile of E-DII was 2·18 times the lowest tertiles (95 % CI = 1·52, 3·13). The odds of preeclampsia increased by 30 % (95 % CI = 18 %, 43 %, P value < 0·001) for each E-DII score increase. The preeclampsia risk was positively associated with IL-2 (OR = 1·07, 95 % CI = 1·03, 1·11), IL-4 (OR = 1·26, 95 % CI = 1·03, 1·54) and transforming growth factor beta (TGF-β) (OR = 1·17, 95 % CI = 1·06, 1·29). Therefore, proinflammatory diets, corresponding to higher IL-2, IL-4 and TGF-β levels, were associated with increased preeclampsia risk.

This study is performed to figure out how the presence of diabetes affects the infection, progression and prognosis of 2019 novel coronavirus disease (COVID-19), and the effective therapy that can treat the diabetes-complicated patients with COVID-19. A multicentre study was performed in four hospitals. COVID-19 patients with diabetes mellitus (DM) or hyperglycaemia were compared with those without these conditions and matched by propensity score matching for their clinical progress and outcome. Totally, 2444 confirmed COVID-19 patients were recruited, from whom 336 had DM. Compared to 1344 non-DM patients with age and sex matched, DM-COVID-19 patients had significantly higher rates of intensive care unit entrance (12.43% vs. 6.58%, P = 0.014), kidney failure (9.20% vs. 4.05%, P = 0.027) and mortality (25.00% vs. 18.15%, P < 0.001). Age and sex-stratified comparison revealed increased susceptibility to COVID-19 only from females with DM. For either non-DM or DM group, hyperglycaemia was associated with adverse outcomes, featured by higher rates of severe pneumonia and mortality, in comparison with non-hyperglycaemia. This was accompanied by significantly altered laboratory indicators including lymphocyte and neutrophil percentage, C-reactive protein and urea nitrogen level, all with correlation coefficients >0.35. Both diabetes and hyperglycaemia were independently associated with adverse prognosis of COVID-19, with hazard ratios of 10.41 and 3.58, respectively.

The effect of vitamin D (VD) on the risk of preeclampsia (PE) is uncertain. Few of previous studies focused on the relationship between dietary VD intake and PE risk. Therefore, we conducted this 1:1 matched case–control study to explore the association of dietary VD intake and serum VD concentrations with PE risk in Chinese pregnant women. A total of 440 pairs of participants were recruited during March 2016 to June 2019. Dietary information was obtained using a seventy-eight-item semi-quantitative FFQ. Serum concentrations of 25(OH)D2 and 25(OH)D3 were measured by liquid chromatography–tandem MS. Multivariate conditional logistic regression was used to estimate OR and 95 % CI. Restricted cubic splines (RCS) were plotted to evaluate the dose–response relationship of dietary VD intake and serum VD concentrations with PE risk. Compared with the lowest quartile, the OR of the highest quartile were 0·45 (95 % CI 0·29, 0·71, Ptrend = 0·001) for VD dietary intake and 0·26 (95 % CI 0·11, 0·60, Ptrend = 0·003) for serum levels after adjusting for confounders. In addition, the RCS analysis suggested a reverse J-shaped relationship between dietary VD intake and PE risk (P-nonlinearity = 0·02). A similar association was also found between serum concentrations of total 25(OH)D and PE risk (P-nonlinearity = 0·02). In conclusion, this study provides evidence that higher dietary intake and serum levels of VD are associated with the lower risk of PE in Chinese pregnant women.

Inflammation is a central mechanism in metabolic disorders associated with morbidity and mortality and dietary factors can modulate inflammation. We aimed to prospectively investigate the association between an empirically developed, food-based dietary inflammatory pattern (EDIP) score and the risk of overall and cause-specific mortality, using data from the US National Health and Nutrition Examination Survey from 1999 to 2014. EDIP score was derived by entering thirty-nine predefined commonly consumed food groups into the reduced rank regression models followed by stepwise linear regression, which was most predictive of two plasma inflammation biomarkers including C-reactive protein and leucocyte count among 25 500 US adults. This score was further validated in a testing set of 9466 adults. Deaths from baseline until 31 December 2015 were identified through record linkage to the National Death Index. During a median follow-up of 7·8 years among 40 074 participants, we documented 4904 deaths. Compared with participants in the lowest quintile of EDIP score, those in the highest quintile had a higher risk of overall death (hazard ratio (HR) = 1·19, 95 % CI 1·08, 1·32, Ptrend = 0·002), and deaths from cancer (HR = 1·41, 95 % CI 1·14, 1·74, Ptrend = 0·017) and CVD (HR = 1·22, 95 % CI 0·98, 1·53, Ptrend = 0·211). When stratified by age, the association of EDIP with overall mortality was stronger among individuals under 65 years of age (Pinteraction = 0·001). Diets with a higher inflammatory potential were associated with increased risk of overall and cancer-specific mortality. Interventions to reduce the adverse effect of pro-inflammatory diets may potentially promote health and longevity.

We have proposed and experimentally demonstrated a novel scheme for efficient mid-infrared difference-frequency generation based on passively synchronized fiber lasers. The adoption of coincident seeding pulses in the nonlinear conversion process could substantially lower the pumping threshold for mid-infrared parametric emission. Consequently, a picosecond mid-infrared source at 3.1 μm was prepared with watt-level average power, and a maximum power conversion efficiency of 77% was realized from pump to down-converted light. Additionally, the long-term stability of generated power was manifested with a relative fluctuation as low as 0.17% over one hour. Thanks to the all-optical passive synchronization and all-polarization-maintaining fiber architecture, the implemented laser system was also featured with simplicity, compactness and robustness, which would favor subsequent applications beyond laboratory operation.

Findings for the roles of dairy products, Ca and vitamin D on ovarian cancer risk remain controversial. We aimed to assess these associations by using an updated meta-analysis. Five electronic databases (e.g. PubMed and Embase) were searched from inception to 24 December 2019. Pooled relative risks (RR) with 95 % CI were calculated. A total of twenty-nine case–control or cohort studies were included. For comparisons of the highest v. lowest intakes, higher whole milk intake was associated with increased ovarian cancer risk (RR 1·35; 95 % CI 1·15, 1·59), whereas decreased risks were observed for higher intakes of low-fat milk (RR 0·84; 95 % CI 0·73, 0·96), dietary Ca (RR 0·71; 95 % CI 0·60, 0·84) and dietary vitamin D (RR 0·80; 95 % CI 0·67, 0·95). Additionally, for every 100 g/d increment, increased ovarian cancer risks were found for total dairy products (RR 1·03; 95 % CI 1·01, 1·04) and for whole milk (RR 1·07; 95 % CI 1·03, 1·11); however, decreased risks were found for 100 g/d increased intakes of low-fat milk (RR 0·95; 95 % CI 0·91, 0·99), cheese (RR 0·87; 95 % CI 0·76, 0·98), dietary Ca (RR 0·96; 95 % CI 0·95, 0·98), total Ca (RR 0·98; 95 % CI 0·97, 0·99), dietary vitamin D (RR 0·92; 95 % CI 0·87, 0·97) and increased levels of circulating vitamin D (RR 0·84; 95 % CI 0·72, 0·97). These results show that whole milk intake might contribute to a higher ovarian cancer risk, whereas low-fat milk, dietary Ca and dietary vitamin D might reduce the risk.

In this paper, the recent studies of laboratory astrophysics with strong magnetic fields in China have been reviewed. On the Shenguang-II laser facility of the National Laboratory on High-Power Lasers and Physics, a laser-driven strong magnetic field up to 200 T has been achieved. The experiment was performed to model the interaction of solar wind with dayside magnetosphere. Also the low beta plasma magnetic reconnection (MR) has been studied. Theoretically, the model has been developed to deal with the atomic structures and processes in strong magnetic field. Also the study of shock wave generation in the magnetized counter-streaming plasmas is introduced.

The relationship between climate, crop growth and crop yield is complicated. This study aimed to determine the ratio of CO2–C emission to grain yield, the field treatments were initiated in 2003, but the measurements for this analysis were collected during the summer maize-growing seasons of 2011 and 2012 in the North China Plain. The experiment showed that conventional tillage with straw application significantly increased grain yield and the ratio of CO2–C emission to grain yield of summer maize. The mean soil CO2–C emission rate with no tillage was significantly lower than that when conventional tillage was used; however, straw application significantly increased the soil CO2–C emission rate, irrespective of whether tillage was performed or not. This was mainly because straw application changed the soil total porosity and organic carbon content. In conclusion, the results of this study support the hypothesis that the ratio of CO2–C emission to grain yield in the North China Plain can be increased by straw application, whereas no tillage decreases this ratio.

Many studies have suggested that folate-related one-carbon metabolism-related nutrients may play a role in certain cancer risks, but few studies have assessed their associations with the risk for nasopharyngeal carcinoma (NPC). In this study, we investigated the association between four folate-related one-carbon metabolism-related nutrients (folate, vitamin B6, vitamin B12 and methionine) and NPC risk in Chinese adults. A total of 600 patients newly diagnosed (within 3 months) with NPC were individually matched with 600 hospital-based controls by age, sex and household type (urban v. rural). Folate, vitamin B6, vitamin B12 and methionine intakes were measured using a validated seventy-eight-item FFQ. A higher dietary folate or vitamin B6 intake was associated with a lower NPC risk after adjusting for potential confounders. The adjusted OR of NPC for quartiles 2–4 (v. 1) were 0·66 (95 % CI 0·48, 0·91), 0·52 (95 % CI 0·37, 0·74) and 0·34 (95 % CI 0·23, 0·50) (Ptrend<0·001) for folate and 0·72 (95 % CI 0·52, 1·00), 0·55 (95 % CI 0·39, 0·78) and 0·44 (95 % CI 0·30, 0·63) (Ptrend<0·001) for vitamin B6. No significant association with NPC risk was observed for dietary vitamin B12 or methionine intake. The risk for NPC with dietary folate intake was more evident in the participants who were not exposed to toxic substances than in those who were exposed (Pinteraction=0·014). This study suggests that dietary folate and vitamin B6 may be protective for NPC in a high-risk population.

The selection of young stellar objects (YSOs) based on excess emission in the infrared is easily contaminated by post-main-sequence stars and various types of emission line stars with similar properties. We define in this paper stringent criteria for an efficient selection and classification of stellar sources with infrared excess emission based on combined Two Micron All Sky Survey (2MASS) and AKARI colors.

In order to understand the star formation process under the influence of H ii regions, we have carried out extensive investigations to well selected star-forming regions which all have been profoundly affected by existing massive O type stars. On the basis of multi-wavelength data from mid-infrared to millimeter collected using Spitzer, Herschel, and ground based radio telescopes, the physical status of interstellar medium and star formation in these regions have been revealed. In a relatively large infrared dust bubble, active star formation is undergoing and the shell is still expanding. Signs of compressed gas and triggered star formation have been tentatively detected in a relatively small bubble. The dense cores in the Rosette Molecular Complex detected at 1.1 mm using SMA have been speculated to have a likely triggered origin according to their spatial distribution. Although some observational results have been obtained, more efforts are necessary to reach trustworthy conclusions.

The robust spines and sclerites of the early to middle Cambrian ‘mollusc’ Wiwaxia are ubiquitous in suitably preserved deposits, but are strikingly absent from the Chengjiang Lagerstätte (Cambrian Stage 3, Yunnan Province, SW China). Here we provide the first record of Wiwaxia sclerites from this rich deposit, extending the record of the genus to the earliest Cambrian Series 2. This reinforces the cosmopolitan distribution of this iconic Cambrian lophotrochozoan and demonstrates the strong faunal continuity that unites distant Cambrian Lagerstätten.

It has not been established which specific measures of obesity might be most appropriate for predicting CVD risk in Asians. The objectives of the present study were to determine the associations of BMI, waist circumference (WC) and waist:height ratio (WHtR) with CVD risk factors and to evaluate the optimal cut-off values to define overweight or obesity in Chinese adults. Data collected from seven nationwide health examination centres during 2008 and 2009 were analysed. The BMI, WC and WHtR of 244 266 Chinese adults aged ≥ 20 years included in the study were measured. Logistic regression models were fit to evaluate the OR of each CVD risk factor according to various anthropometric indices. Receiver operating characteristic (ROC) analyses were conducted to assess the optimal cut-off values to predict the risk of diabetes, hypertension, dyslipidaemia and the metabolic syndrome. WHtR had the largest areas under the ROC curve for all CVD risk factors in both sexes, followed by WC and BMI. The optimal cut-off values were approximately 24·0 and 23·0 kg/m2 for BMI, 85·0 and 75·0 cm for WC, and 0·50 and 0·48 for WHtR for men and women, respectively. According to well-established cut-off values, BMI was found to be a more sensitive indicator of hypertension in both men and women, while WC and WHtR were found to be better indicators of diabetes and dyslipidaemia. A combination of BMI and central obesity measures was found to be associated with greater OR of CVD risk factors than either of them alone in both sexes. The present study demonstrated that WHtR and WC may be better indicators of CVD risk factors for Chinese people than BMI.

The experiment was conducted to evaluate the effects of dietary threonine (Thr) supplement on reproductive performance and immune function of the male mice challenged with pseudorabies virus (PRV). Kun-Ming male mice were assigned randomly to four groups with different Thr levels (0.70%, 0.88%, 1.10% and 1.30%). Half of the mice in each group were injected with PRV or phosphate-buffered saline (PBS) after 5 weeks’ adaptation to diets. The second experiment examined the effects of dietary Thr level on copulation rate, pregnancy rate and average number per litter of PRV- or PBS-challenged male mice that copulated with adult female mice on the 9th day post PRV challenge. Sperm quality and testosterone of mice were decreased after PRV infection, but this effect was attenuated by increasing Thr levels. Copulation and conception rates were increased with increasing Thr levels (P = 0.14), but litter size was not affected (P > 0.05). In the PBS and PRV groups, mice fed higher levels of Thr had increased immunoglobulin (Ig)G, IgA and IgM concentrations. The PRV-specific antibody level, interleukin (IL)-1β and tumor necrosis factor (TNF)-α concentration in PRV groups enhanced with increasing Thr levels; however, there was no difference in PBS groups. Furthermore, higher toll-like receptor (TLR)2 and TLR9 expressions in testis were observed by PRV challenge compared with PBS groups, and higher Thr supplement attenuated PRV-challenged induced the upregulation effect of TLR2 and TLR9 mRNA expression in testis (P < 0.05). These data suggest that higher Thr consumption was recommended in order to counteract the deleterious effects of virus invasion, possibly through the downregulated expression of TLRs, and thus to improve immunity and reproduction performance of male mice challenged with PRV.