Let $f(z)=\sum\limits_{j=0}^{\infty} a_j z^j$ be a transcendental entire function and let $f_\omega(z)=\sum\limits_{j=0}^{\infty}\chi_j(\omega) a_j z^j$ be a random entire function, where $\chi_j(\omega)$ are independent and identically distributed random variables defined on a probability space $(\Omega, \mathcal{F}, \mu)$. In this paper, we first define a family of random entire functions, which includes Gaussian, Rademacher and Steinhaus entire functions. We prove that, for almost all functions in the family and for any constant C > 1, there exist a constant $r_0=r_0(\omega)$ and a set $E\subset [e, \infty)$ of finite logarithmic measure such that, for $r \gt r_0$ and $r\notin E$,

\begin{equation*}|\log M(r, f)- N(r,0, f_\omega)|\le (C/A)^{\frac1{B}}\,\log^{\frac1{B}}\,\log M(r,f) +\log\,\log M(r, f), \qquad a.s.\end{equation*}

where $A, B$ are constants, $M(r, f)$ is the maximum modulus and $N(r, 0, f)$ is the integrated zero-counting function of f. As a by-product of our main results, we prove Nevanlinna’s second main theorem for random entire functions. Thus, the characteristic function of almost all functions in the family is bounded above by an integrated counting function, rather than by two integrated counting functions as in the classical Nevanlinna theory. For instance, we show that, for almost all Gaussian entire functions fω and for any ϵ > 0, there is r0 such that, for $r \gt r_0$,

\begin{equation*}T(r, f) \le N(r,0, f_\omega)+\left(\tfrac12+\epsilon\right) \log T(r, f).\end{equation*}

The lift generation mechanism of leading-edge vortex (LEV) in the case of a pitching and plunging plate is studied using an experimental approach and the improved discrete vortex method in this research. A formation condition of the secondary structure is introduced into the traditional discrete vortex method to compensate for the shortcomings in the simulation of the viscous effect between LEV and plate. The simulation of the secondary structure helps the improved method perform better in flow-field reconstruction and lift prediction. Accordingly, the lift generation mechanism of the LEV and influence of the secondary structure are studied. The lift contribution of the vortex structure is isolated and linearly decomposed into two parts according to sources of flow field: the quasi-potential flow part and the vortex-induced flow part. The vortex lift is defined as the lift contribution of the vortex structure in vortex-induced flow, which gives a new insight into the production of lift of the LEV. The lift generation mechanism through the discrete vortex method is verified and extended in viscous flow through experimental measurement. In addition, a vortex lift indicator based on the reverse flow of the LEV is proposed to examine the change of vortex lift in experimental measurement. The flow mechanism for the decline of vortex lift for different maximum effective angles of attack is revealed based on the vortex lift indicator. Furthermore, for the LEV-dominating flow, the indicator can also be applied in estimating the maximum value and corresponding critical time of overall lift in experiments.

The typical Mississippian shallow-water deposits of the Jiusi and Shangsi formations are well exposed in the Yashui section in southern Guizhou, South China. The strata are composed mainly of platform limestones intercalated with shales and sandstones. Conodonts obtained from the limestones are dominated by two assemblages of cavusgnathids: the Cavusgnathus aff. Cav. unicornis and Clydagnathus windsorensis assemblage from the upper Jiusi Formation and the Cavusgnathus unicornis assemblage from the lowest Shangsi Formation. Vogelgnathus campbelli (Rexroad, 1957) is reported for the first time in Eastern Paleotethys and is characterized by small lateral denticles. The evolutionary first occurrence of Cavusgnathus unicornis Youngquist and Miller, 1949 is recognized as a marker for the regional Shangsian stage. This biostratigraphic datum is interpreted to be correlative with other shallow-water conodont zones marked by Cavusgnathus unicornis s.l. and similar species from North America and Europe.

The target backsheath field acceleration mechanism is one of the main mechanisms of laser-driven proton acceleration (LDPA) and strongly depends on the comprehensive performance of the ultrashort ultra-intense lasers used as the driving sources. The successful use of the SG-II Peta-watt (SG-II PW) laser facility for LDPA and its applications in radiographic diagnoses have been manifested by the good performance of the SG-II PW facility. Recently, the SG-II PW laser facility has undergone extensive maintenance and a comprehensive technical upgrade in terms of the seed source, laser contrast and terminal focus. LDPA experiments were performed using the maintained SG-II PW laser beam, and the highest cutoff energy of the proton beam was obviously increased. Accordingly, a double-film target structure was used, and the maximum cutoff energy of the proton beam was up to 70 MeV. These results demonstrate that the comprehensive performance of the SG-II PW laser facility was improved significantly.

Light has a substantial effect on the behaviour and physiology of nocturnal moths. Ectropis grisescens is a major nocturnal tea pest in China, and light traps are commonly used to control geometrid moths because of their positive phototaxis. However, some moths gather around light traps and enter the light adaptation state, which decreases the efficacy of light traps in controlling this pest. We identified opsin genes and the spectral sensitivities of the photoreceptors of E. grisescens moths. We also determined the effects of several monochromatic lights on opsin gene expression and light adaptation. We detected three types of opsin genes and six spectral sensitive peaks (at 370, 390, 480, 530, 550, and 580 nm). We also observed significant changes in the diurnal rhythm of opsin gene expression under different light conditions. When active males were suddenly exposed to different monochromatic lights, they quickly entered the light adaptation state, and the adaptation time was negatively correlated with the light intensity. Males were most sensitive to 390 nm wavelengths, followed by 544 nm, 457 nm, and 593 nm. Red light (627 nm) did not affect the activity of E. grisescens males but had detectable physiological effects.

To explore the effect of yield stress on the secondary breakup of gel drops, experimental and theoretical investigations are carried out by employing a high-speed camera. A unique hemline-type breakup, as a modified behaviour of sheet-thinning breakup, occurs when the air velocity increases to a high region. The edges of the drops constantly deform into thin membranes when the high-velocity air skims over the gel drops. These membranes vibrate vertically, and breaking points occur at high amplitudes, causing the formation of reticular fragments. The results of linear stability analysis indicated that the yield stress of the gel drops has an influence on the formation and breakup of the gel membranes. The breakup regime map and breakup times are also studied.

This study aimed to explore the mediation effects of one-carbon metabolism (OCM) related nutrients on the association between MTHFR rs1801133 polymorphism and gestational diabetes mellitus (GDM). Folate, vitamin B12 and homocysteine (Hcy) were measured in the serum of 1254 pregnant women. Linear and logistic regressions were used to estimate the associations of OCM nutrients and MTHFR rs1801133 polymorphism with blood glucose levels and GDM risk. Mediation analysis was applied to test the mediation effects of folate, vitamin B12 and Hcy on the association of MTHFR rs1801133 polymorphism with blood glucose concentrations and GDM. Pregnant women with MTHFR rs1801133 CC genotype had higher serum folate (10·75 v. 8·90 and 9·40 ng/ml) and lower serum Hcy (4·84 v. 4·93 and 5·20 μmol/l) than those with CT and TT genotypes. Folate concentrations were positively associated with fasting plasma glucose (FPG), 1-h plasma glucose (1-h PG), 2-h plasma glucose (2-h PG) and GDM risk. Vitamin B12 levels were negatively correlated with FPG and GDM. Although no direct association was found between MTHFR rs1801133 genotypes and GDM, there were significant indirect effects of MTHFR rs1801133 CC genotype on FPG (β: 0·005; 95 % CI: 0·001, 0·013), 1-h PG (β: 0·006; 95 % CI: 0·001, 0·014), 2-h PG (β: 0·007; 95 % CI: 0·001, 0·015) and GDM (β: 0·006; 95 % CI: 0·001, 0·014) via folate. In conclusion, serum folate mediates the effect of MTHFR rs1801133 on blood glucose levels and GDM. Our findings potentially provide a feasible GDM prevention strategy via individualised folate supplementation according to the MTHFR genotypes.

We study how channel width variations influence the dynamics of free-surface granular flows. For this purpose, we extend a continuum model framework to granular flows passing through channels that narrow or widen. Our theory uses a linearized approximation to an established dense granular flow rheology and a Coulomb friction law to model interaction between flow and sidewalls. We test the theoretical predictions using two novel 40 cm-diameter drums (convex and concave) filled halfway with 2 mm diameter particles rotated at rates in which the shear layer remains shallow and dense. We apply particle tracking velocimetry to enable quantitative comparisons between experimental data and theoretical predictions. We find that our experimental kinematics and energy profiles largely agree with the theoretical predictions. In general, flows through narrowing channels are faster and deeper than flows through widening channels. The influence of width variations grows with increasing flow speed, and the form of the rate dependence changes fundamentally as the regime changes from one in which kinetic energy is dissipated locally to one in which it is advected downstream. For both regimes, theoretical scaling analysis leads us to experimentally validated power laws, in which the exponent depends on the flow regime, and the multiplicative coefficient depends on channel geometry alone. Finally, we discuss how the differences between theoretical predictions and experimental data may be useful for improving our understanding of flows through non-uniform channels.

We conducted three studies to examine the relationship between spicy tastes and risk seeking. In Study 1, results from a personality judgment task indicated that people were more inclined to attribute a higher level of risk seeking to individuals who enjoy spicy foods. The second study examined whether people who like spicy foods are actually more risk seeking. In fact, people who reported a preference for spicy tastes scored higher on risk taking, as assessed via the Domain-Specific Risk-Taking Scale (Chinese version). Finally, Study 3 employed an experimental design to manipulate risk-seeking tendencies by having participants experience spicy food tastes in the lab. Momentarily savoring spicy foods increased participants’ risk taking in the Iowa Gambling Task. The present findings suggest that preferences for spicy tastes could relate to risk-seeking tendencies and subsequent risk-seeking behaviors.

Shame leads to devaluation of the social self, and thus to a desire to improve self-esteem. Money, which is related to the notion of one’s ability, may help people demonstrate competence and gain self-esteem and respect from others. Based on the perspectives of feelings-as-information and threatened ego, we tested the hypothesis that a sense of shame heightens the desire for money, prompting self-interested behaviors as reflected by monetary donations and social value orientation. The results showed that subjects in the shame condition donated less money (Experiment 1) and exhibited more self-interested choices in the modified decomposed game (Experiment 2). The desire for money as reflected in overestimated coin sizes mediated the effect of shame on self-interested behavior. Our findings suggest that shame elicits the desire to acquire money to amend the threatened social self and improve self-esteem; however, it may induce a self-interested inclination that could harm social relationships.

In this study, a toroidal quartz ( $20\overline{2}3$ ) crystal is designed for monochromatic X-ray imaging at 72.3°. The designed crystal produces excellent images of a laser-produced plasma emitting He-like Ti X-rays at 4.75 keV. Based on the simulations, the imaging resolutions of the spherical and toroidal crystals in the sagittal direction are found to be 15 and 5 μm, respectively. Moreover, the simulation results show that a higher resolution image of the source can be obtained by using a toroidal crystal. An X-ray backlight imaging experiment is conducted using 4.75 keV He-like Ti X-rays, a 3 × 3 metal grid, an imaging plate and a toroidal quartz crystal with a lattice constant of 2d = 0.2749 nm. The meridional and sagittal radii of the toroidal α-quartz crystal are 295.6 and 268.5 mm, respectively. A highly resolved image of the microgrid, with a spatial resolution of 10 μm, is obtained in the experiment. By using similar toroidal crystal designs, the application of a spatially resolved spectrometer with high-resolution X-ray imaging ability is capable of providing imaging data with the same magnification ratio in the sagittal and meridional planes.

Land expropriation, where peasants’ property rights are encroached by the state, has been recognized as a primary source of social dissension in rural China. Since the end of the last century, the Administrative Litigation Law (ALL) has provided people with a legal weapon to defend themselves against violations by state power. Drawing on the theory of relative deprivation, this paper proposes that peasants are more likely to sue the state when they feel deprived. To examine this hypothesis, we first present a case study to depict the causal process and then use quantitative research to improve the external validity of our findings. We created a novel and unique database of prefecture-level administrative litigations and relative deprivation for Poisson regression analysis. The quantitative results prove that the more peasants feel relatively deprived, the more likely they are to sue the state. Furthermore, the positive effect of relative deprivation on administrative litigations has become more significant over time, implying peasants’ growing awareness of legal resistance. This paper concludes that a critical step towards eliminating social inequity and maintaining social stability in rural China is to reduce the relative deprivation of peasants by, for example, allowing them to share in land value appreciation in the process of urbanization.

Spectral observations with high temporal and frequency resolution are of great significance for studying the fine structures of solar radio bursts. In addition, it is helpful to understand the physical processes of solar eruptions. In this paper, we present the design of a system to observe solar radio bursts with high temporal and frequency resolutions at frequencies of 25–110 MHz. To reduce the impact of analog devices and improve the system flexibility, we employ various digital signal processing methods to achieve the function of analog devices, such as polarisation synthesis and beamforming. The resourceful field programmable gate array is used to process radio signals. The system has a frequency resolution of $\sim$ 30 kHz and a temporal resolution of up to 0.2 ms. The left/right circular polarisation signals can be simultaneously observed. At present, the system has been installed at Chashan Solar Observatory operated by the Institute of Space Science, Shandong University. The system is running well, multiple bursts have been observed, and relevant data have been obtained.

We report the experimental results of the commissioning phase in the 10 PW laser beamline of the Shanghai Superintense Ultrafast Laser Facility (SULF). The peak power reaches 2.4 PW on target without the last amplifying during the experiment. The laser energy of 72 ± 9 J is directed to a focal spot of approximately 6 μm diameter (full width at half maximum) in 30 fs pulse duration, yielding a focused peak intensity around 2.0 × 1021 W/cm2. The first laser-proton acceleration experiment is performed using plain copper and plastic targets. High-energy proton beams with maximum cut-off energy up to 62.5 MeV are achieved using copper foils at the optimum target thickness of 4 μm via target normal sheath acceleration. For plastic targets of tens of nanometers thick, the proton cut-off energy is approximately 20 MeV, showing ring-like or filamented density distributions. These experimental results reflect the capabilities of the SULF-10 PW beamline, for example, both ultrahigh intensity and relatively good beam contrast. Further optimization for these key parameters is underway, where peak laser intensities of 1022–1023 W/cm2 are anticipated to support various experiments on extreme field physics.

Immunoprophylaxis has not completely eliminated hepatitis B virus (HBV) infection due to hyporesponsiveness to hepatitis B vaccine (HepB). We explored the impact of folic acid supplementation (FAS) in pregnant women with positive hepatitis B surface antigen (HBsAg) on their infant hepatitis B surface antibody (anti-HBs) and the mediation effect of infant interleukin-4 (IL-4). We recruited HBsAg-positive mothers and their neonates at baseline. Maternal FAS was obtained via a questionnaire, and neonatal anti-HBs and IL-4 were detected. Follow-up was performed at 11–13 months of age of infants, when anti-HBs and IL-4 were measured. We applied univariate and multivariate analyses. A mediation effect model was performed to explore the mediating role of IL-4. A total of 399 mother–neonate pairs were enrolled and 195 mother–infant pairs were eligible for this analysis. The infant anti-HBs geometric mean concentrations in the maternal FAS group were significnatly higher than those in the no-FAS group (383·8 mIU/ml, 95 % CI: 294·2 mIU/ml to 500·7 mIU/ml v. 217·0 mIU/ml, 95 % CI: 147·0 mIU/ml to 320·4 mIU/ml, z = –3·2, P = 0·001). Infants born to women who took folic acid (FA) within the first trimester were more likely to have high anti-HBs titres (adjusted β-value = 194·1, P = 0·003). The fold change in IL-4 from neonates to infants partially mediated the beneficial influence of maternal FAS on infant anti-HBs (24·7 % mediation effect) after adjusting for confounding factors. FAS during the first trimester to HBsAg-positive mothers could facilitate higher anti-HBs levels in infants aged 11–13 months partly by upregulating IL-4 in infants.