Let $[a_1(x),a_2(x),\ldots ,a_n(x),\ldots ]$ be the continued fraction expansion of $x\in [0,1)$ and $q_n(x)$ be the denominator of its nth convergent. The irrationality exponent and Khintchine exponent of x are respectively defined by

$$ \begin{align*} \overline{v}(x)=2+\limsup_{n\to\infty}\frac{\log a_{n+1}(x)}{\log q_n(x)} \quad \text{and}\quad \gamma(x)=\lim_{n\to\infty}\frac{1}{n}\sum_{i=1}^{n}\log a_i(x). \end{align*} $$

We study the multifractal spectrum of the irrationality exponent and the Khintchine exponent for continued fractions with nondecreasing partial quotients. For any $v>2$, we completely determine the Hausdorff dimensions of the sets $\{x\in [0,1): a_1(x)\leq a_2(x)\leq \cdots , \overline {v}(x)=v\}$ and

$$ \begin{align*}\bigg\{x\in[0,1): a_1(x)\leq a_2(x)\leq\cdots, \lim\limits_{n\to\infty}\frac{\log a_1(x)+\log a_2(x)+\cdots+\log a_n(x)}{\psi(n)}=1\bigg\},\end{align*} $$

where $\psi :\mathbb {N}\rightarrow \mathbb {R}^+$ is a function satisfying $\psi (n)\to \infty $ as $n\to \infty $.

To meet the demands of laser-ion acceleration at a high repetition rate, we have developed a comprehensive diagnostic system for real-time and in situ monitoring of liquid sheet targets (LSTs). The spatially resolved rapid characterizations of an LST’s thickness, flatness, tilt angle and position are fulfilled by different subsystems with high accuracy. With the help of the diagnostic system, we reveal the dependence of thickness distribution on collision parameters and report the 238-nm liquid sheet generated by the collision of two liquid jets. Control methods for the flatness and tilt angle of LSTs have also been provided, which are essential for applications of laser-driven ion acceleration and others.

This experiment was conducted to investigate whether dietary chenodeoxycholic acid (CDCA) could attenuate high-fat (HF) diet-induced growth retardation, lipid accumulation and bile acid (BA) metabolism disorder in the liver of yellow catfish Pelteobagrus fulvidraco. Yellow catfish (initial weight: 4·40 (sem 0·08) g) were fed four diets: the control (105·8 g/kg lipid), HF diet (HF group, 159·6 g/kg lipid), the control supplemented with 0·9 g/kg CDCA (CDCA group) and HF diet supplemented with 0·9 g/kg CDCA (HF + CDCA group). CDCA supplemented in the HF diet significantly improved growth performance and feed utilisation of yellow catfish (P < 0·05). CDCA alleviated HF-induced increment of hepatic lipid and cholesterol contents by down-regulating the expressions of lipogenesis-related genes and proteins and up-regulating the expressions of lipololysis-related genes and proteins. Compared with the control group, CDCA group significantly reduced cholesterol level (P < 0·05). CDCA significantly inhibited BA biosynthesis and changed BA profile by activating farnesoid X receptor (P < 0·05). The contents of CDCA, taurochenodeoxycholic acid and glycochenodeoxycholic acid were significantly increased with the supplementation of CDCA (P < 0·05). HF-induced elevation of cholic acid content was significantly attenuated by the supplementation of CDCA (P < 0·05). Supplementation of CDCA in the control and HF groups could improve the liver antioxidant capacity. This study proved that CDCA could improve growth retardation, lipid accumulation and BA metabolism disorder induced by HF diet, which provided new insight into understanding the physiological functions of BA in fish.

Post-acceleration of protons in helical coil targets driven by intense, ultrashort laser pulses can enhance ion energy by utilizing the transient current from the targets’ self-discharge. The acceleration length of protons can exceed a few millimeters, and the acceleration gradient is of the order of GeV/m. How to ensure the synchronization between the accelerating electric field and the protons is a crucial problem for efficient post-acceleration. In this paper, we study how the electric field mismatch induced by current dispersion affects the synchronous acceleration of protons. We propose a scheme using a two-stage helical coil to control the current dispersion. With optimized parameters, the energy gain of protons is increased by four times. Proton energy is expected to reach 45 MeV using a hundreds-of-terawatts laser, or more than 100 MeV using a petawatt laser, by controlling the current dispersion.

The present study examined the association between adolescents’ extracurricular activities and bullying perpetration and victimisation. The sample was drawn from the 2016 National Survey of Children’s Health dataset. Analyses included descriptive statistics and logistic regression for the early adolescent and middle adolescent groups. Among early adolescents, sports were negatively associated with victimisation. Participation in clubs/organisations, organised activities or lessons, and community services were negatively associated, while employment was positively related to bullying perpetration. Among middle adolescents, all extracurricular activities were negatively related to victimisation. As for bullying perpetration, organised activities or lessons and community services were negatively associated with bullying. The study highlights the potential for sport and extracurricular involvement as ways to possibly deter bullying perpetration and victimisation. Future research should consider these associations longitudinally.

An acute gastroenteritis (AGE) outbreak caused by a norovirus occurred at a hospital in Shanghai, China, was studied for molecular epidemiology, host susceptibility and serological roles. Rectal and environmental swabs, paired serum samples and saliva specimens were collected. Pathogens were detected by real-time polymerase chain reaction and DNA sequencing. Histo-blood group antigens (HBGA) phenotypes of saliva samples and their binding to norovirus protruding proteins were determined by enzyme-linked immunosorbent assay. The HBGA-binding interfaces and the surrounding region were analysed by the MegAlign program of DNAstar 7.1. Twenty-seven individuals in two care units were attacked with AGE at attack rates of 9.02 and 11.68%. Eighteen (78.2%) symptomatic and five (38.4%) asymptomatic individuals were GII.6/b norovirus positive. Saliva-based HBGA phenotyping showed that all symptomatic and asymptomatic cases belonged to A, B, AB or O secretors. Only four (16.7%) out of the 24 tested serum samples showed low blockade activity against HBGA-norovirus binding at the acute phase, whereas 11 (45.8%) samples at the convalescence stage showed seroconversion of such blockade. Specific blockade antibody in the population played an essential role in this norovirus epidemic. A wide HBGA-binding spectrum of GII.6 supports a need for continuous health attention and surveillance in different settings.

In this study, we analysed the prevalence of diabetes in Inner Mongolia and explored the relationship between dietary patterns and diabetes using the Chinese Dietary Balance Index-16 (DBI-16). This study was a surveillance survey of Chronic Disease and Nutrition Monitoring among Chinese Adults in Inner Mongolia in 2015. Dietary data were collected using the 24-h dietary recall and weighing method over three consecutive days. Dietary quality was evaluated via the DBI-16. A generalised linear model was used to examine the associations between the DBI-16 and dietary patterns. The relationship between dietary patterns and diabetes was analysed using logistic regression. In Inner Mongolia, the diabetes prevalence was 8·5 % and the estimated standardised prevalence was 6·0 %. Four major dietary patterns were identified: ‘meat/dairy products’, ‘traditional northern’, ‘high cereal/tuber’ and ‘high-salt/alcohol’. Generalised linear models showed that the ‘meat/dairy product’ pattern was relatively balanced (βLBS = –1·993, βHBS = –0·206, βDQD = –2·199; all P < 0·05) and was associated with a lower diabetes risk (OR 0·565; 95 % CI 0·338, 0·945; P < 0·05) after adjusting for potential confounders. The other three dietary patterns (i.e. ‘traditional northern’, ‘high cereal/tuber’ and ‘high-salt/alcohol’) exhibited relatively unbalanced dietary quality and were unassociated with diabetes risk. Diabetes prevalence in Inner Mongolia was moderate. The dietary quality of the ‘meat/dairy product’ pattern was relatively balanced and was correlated with a decreased risk of diabetes prevalence, suggesting that dietary quality may help decrease diabetes prevalence and provide a suggestion for local dietary guidelines.

In this paper, we propose an integral equation approach for pricing an American-style Parisian up-and-out call option under the Black–Scholes framework. The main difficulty of pricing this option lies in the determination of its optimal exercise price, which is a three-dimensional surface, instead of a two-dimensional (2-D) curve as is the case for a “one-touch” barrier option. In our approach, we first reduce the 3-D pricing problem to a 2-D one by using the “moving window” technique developed by Zhu and Chen (2013, Pricing Parisian and Parasian options analytically. Journal of Economic Dynamics and Control, 37(4): 875-896), then apply the Fourier sine transform to the 2-D problem to obtain two coupled integral equations in terms of two unknown quantities: the option price at the asset barrier and the optimal exercise price. Once the integral equations are solved numerically by using an iterative procedure, the calculation of the option price and the hedging parameters is straightforward from their integral representations. Our approach is validated by a comparison between our results and those of the trusted finite difference method. Numerical results are also provided to show some interesting features of the prices of American-style Parisian up-and-out call options and the behaviour of the associated optimal exercise boundaries.

Laser-driven relativistic electrons can be focused onto a high-Z convertor for generating high-brightness γ-rays, which in turn can be used to induce photonuclear reactions. In this work, photo-transmutation of long-lived radionuclide 135Cs induced by laser–plasma–interaction-driven electron source is demonstrated using Geant4 simulation (Agostinelli et al., 2003 Nucl. Instrum. Meth. A506, 250). High-energy electron generation, bremsstrahlung, as well as photonuclear reaction are observed at four different laser intensities: 1020, 5 × 1020, 1021, and 5 × 1021 W/cm2. The transmutation efficiency depends on the laser intensity and target size. An optimum laser intensity, namely 1021 W/cm2, was found, with the corresponding photonuclear reaction yield reaching 108 J−1 of the laser energy. Laser-generated electrons can therefore be a promising tool for transmutation reactions. Potential application in nuclear waste management is suggested.

We derive an analytical solution for the value of Parisian up-and-in calls by using the “moving window” technique for pricing European-style Parisian up-and-out calls. Our pricing formula can be applied to both European-style and American-style Parisian up-and-in calls, due to the fact that with an “in” barrier, the option holder cannot do or decide on anything before the option is activated, and once the option is activated it is just a plain vanilla call, which could be of American style or European style.

A trend toward greater body size in dizygotic (DZ) than in monozygotic (MZ) twins has been suggested by some but not all studies, and this difference may also vary by age. We analyzed zygosity differences in mean values and variances of height and body mass index (BMI) among male and female twins from infancy to old age. Data were derived from an international database of 54 twin cohorts participating in the COllaborative project of Development of Anthropometrical measures in Twins (CODATwins), and included 842,951 height and BMI measurements from twins aged 1 to 102 years. The results showed that DZ twins were consistently taller than MZ twins, with differences of up to 2.0 cm in childhood and adolescence and up to 0.9 cm in adulthood. Similarly, a greater mean BMI of up to 0.3 kg/m2 in childhood and adolescence and up to 0.2 kg/m2 in adulthood was observed in DZ twins, although the pattern was less consistent. DZ twins presented up to 1.7% greater height and 1.9% greater BMI than MZ twins; these percentage differences were largest in middle and late childhood and decreased with age in both sexes. The variance of height was similar in MZ and DZ twins at most ages. In contrast, the variance of BMI was significantly higher in DZ than in MZ twins, particularly in childhood. In conclusion, DZ twins were generally taller and had greater BMI than MZ twins, but the differences decreased with age in both sexes.

Ancylostoma ceylanicum is a common zoonotic nematode. Cats act as natural reservoirs of the hookworm and are involved in transmitting infection to humans, thus posing a potential risk to public health. The prevalence of feline A. ceylanicum in Guangzhou (South China) was surveyed by polymerase chain reaction–restriction fragment length polymorphism (PCR-RFLP). In total, 112 faecal samples were examined; 34.8% (39/112) and 43.8% (49/112) samples were positive with hookworms by microscopy and PCR method, respectively. Among them, 40.8% of samples harboured A. ceylanicum. Twelve positive A. ceylanicum samples were selected randomly and used for cox 1 sequence analysis. Sequencing results revealed that they had 97–99% similarity with A. ceylanicumcox 1 gene sequences deposited in GenBank. A phylogenetic tree showed that A. ceylanicum isolates were divided into two groups: one comprising four isolates from Guangzhou (South China), and the other comprising those from Malaysia, Cambodia and Guangzhou. In the latter group, all A. ceylanicum isolates from Guangzhou were clustered into a minor group again. The results indicate that the high prevalence of A. ceylanicum in stray cats in South China poses a potential risk of hookworm transmission from pet cats to humans, and that A. ceylanicum may be a species complex worldwide.

For over 100 years, the genetics of human anthropometric traits has attracted scientific interest. In particular, height and body mass index (BMI, calculated as kg/m2) have been under intensive genetic research. However, it is still largely unknown whether and how heritability estimates vary between human populations. Opportunities to address this question have increased recently because of the establishment of many new twin cohorts and the increasing accumulation of data in established twin cohorts. We started a new research project to analyze systematically (1) the variation of heritability estimates of height, BMI and their trajectories over the life course between birth cohorts, ethnicities and countries, and (2) to study the effects of birth-related factors, education and smoking on these anthropometric traits and whether these effects vary between twin cohorts. We identified 67 twin projects, including both monozygotic (MZ) and dizygotic (DZ) twins, using various sources. We asked for individual level data on height and weight including repeated measurements, birth related traits, background variables, education and smoking. By the end of 2014, 48 projects participated. Together, we have 893,458 height and weight measures (52% females) from 434,723 twin individuals, including 201,192 complete twin pairs (40% monozygotic, 40% same-sex dizygotic and 20% opposite-sex dizygotic) representing 22 countries. This project demonstrates that large-scale international twin studies are feasible and can promote the use of existing data for novel research purposes.

Introduction: The mortality of Parkinson’s disease (PD) and its associated risk factors among clinically definite PD patients in China has been rarely investigated. Our study aimed to identify the mortality rates and predictors of death in PD patients in China. Methods: 157 consecutive, clinically definite PD patients from the urban area of Shanghai were recruited from a central hospital based movement disorder clinic in 2006. All patients were regularly followed up at the clinic until December 31, 2011, or death. Mortality and associations with baseline demographics, health and medical factors were then determined within the cohort. Results: After 5 years, 11(7%) patients had died. The standardised mortality ratio was 0.62 (95% CI 0.32 to 1.07, P=0.104). The main causes of death were pneumonia (54.5%, 6/11) and digestive disorders (18.2%, 2/11), respectively. Age at onset, independent living, the mini mental state examination score, the Parkinson’s disease sleep scale score and the Epworth sleepiness scale score at baseline were statistically significantly different between the survival group and the deceased group (P<0.05). Across all participants, risk factors for death included low mini mental state examination score, and high Epworth sleepiness scale score according to a binary variable logistic regression analysis. Conclusions: This study confirms the similar survival of patients with PD to the control population up to a follow-up of 5 years. Interventions tailored to potential risk factors associated with death may offer further benefits.