We prove a difference analogue of the celebrated Tumura–Hayman–Clunie theorem. Let f be a transcendental entire function, let c be a nonzero constant and let n be a positive integer. If f and $\Delta _c^n f$ omit zero in the whole complex plane, then either $f(z)=\exp (h_1(z)+C_1 z)$, where $h_1$ is an entire function of period c and $\exp (C_1 c)\neq 1$, or $f(z)=\exp (h_2(z)+C_2 z)$, where $h_2$ is an entire function of period $2c$ and $C_2$ satisfies

$$ \begin{align*} \bigg(\frac{1+\exp(C_2c)}{1-\exp(C_2 c)}\bigg)^{2n}=1. \end{align*} $$

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.

Giant panda Ailuropoda melanoleuca exhibits are popular attractions for zoos and wildlife parks. However, it remains to be investigated whether such exhibits enhance visitor knowledge about pandas and broader conservation issues. We conducted questionnaire surveys at giant panda exhibits at three city zoos and five wildlife parks in China. Although visitors were generally interested in the giant panda, this was not reflected in their post-exhibit knowledge of giant panda biology. Socio-demographically, men were more knowledgeable of giant panda biology than women. Knowledge correlated positively with respondent level of education. Younger respondents (< 45 years) knew most about giant pandas and expressed an interest in learning more about them using social media. The most informed respondents had visited other giant panda exhibits previously. Respondents were generally satisfied with the giant panda exhibits (mean score 4.44/5). Wildlife parks delivered a better educational outcome than city zoos. We recommend approaches to improve the visitor experience further and to leverage public interest in broader conservation engagement and action in China.

Aphids exhibit seasonally alternating asexual and sexual reproductive modes. Different morphs are produced throughout the life cycle. To evaluate morph-specific fitness during reproductive switching, holocyclic Sitobion avenae were induced continuously under short light conditions, and development and reproduction were compared in each morph. Seven morphs, including apterous and alate virginoparae, apterous and alate sexuparae, oviparae, males, and fundatrices, were produced during the life cycle. The greatest proportions of sexuparae, oviparae, males, and virginoparae were in the G1, G2, G3, and G4 generations, respectively. Regardless of asexual or sexual morphs, alate morphs exhibited a marked delay in age at maturity compared with that of apterous morphs. Among the alate morphs, males had the longest age at maturity, followed by sexuparae and virginoparae. Among the apterous morphs, sexuparae were older at maturity than the fundatrices, virginoparae, and oviparae. The nymphs of each morph had equal survival potentials. For the same wing morphs, apterous sexuparae and oviparae exhibited substantial delays in the pre-reproductive period and considerable reductions in fecundity, compared with those of apterous virginoparae and fundatrices, whereas alate sexuparae and alate virginoparae had similar fecundity. The seven morphs exhibited Deevey I survivorship throughout the life cycle. These results suggest that sexual production, particularly in males, has short-term development and reproduction costs. The coexistence of sexual and asexual morphs in sexuparae offspring may be regarded as an adaptive strategy for limiting the risk of low fitness in winter.

The purpose of this study is to further investigate the relationship between sweetener exposure and the risk of endometrial cancer (EC). Up until December 2022, a literature search in an electronic database was carried out utilizing PubMed, Web of Science, Ovid, and Scopus. The odds ratio (OR) and 95 % confidence interval (CI) were used to evaluate the results. Sweeteners were divided into nutritional sweeteners (generally refers to sugar, such as sucrose and glucose) and non-nutritional sweeteners (generally refers to artificial sweeteners, such saccharin and aspartame). Ten cohort studies and two case-control studies were eventually included. The study found that in 12 studies, compared with the non-exposed group, the incidence rate of EC in the sweetener exposed group was higher (OR = 1·15, 95 % CI = [1·07, 1·24]). Subgroup analysis showed that in 11 studies, the incidence rate of EC in the nutritional sweetener exposed group was higher than that in the non-exposed group (OR = 1·25, 95 % CI = [1·14, 1·38]). In 4 studies, there was no difference in the incidence rate of EC between individuals exposed to non-nutritional sweeteners and those who were not exposed to non-nutritional sweeteners (OR = 0·90, 95 % CI = [0·81, 1·01]). This study reported that the consumption of nutritional sweeteners may increase the risk of EC, whereas there was no significant relationship between the exposure of non-nutritional sweeteners and the incidence of EC. Based on the results of this study, it is recommended to reduce the intake of nutritional sweeteners, but it is uncertain whether use of on-nutritional sweeteners instead of nutritional sweetener.

The 4H-SiC crystal is found to have great potential in terahertz generation via nonlinear optical frequency conversion due to its extremely high optical damage threshold, wide transparent range, etc. In this paper, optical rectification (OR) with tilted-pulse-front (TPF) setting based on the 4H-SiC crystal is proposed. The theory accounts for the optimization of incident pulse pre-chirping in the TPF OR process under high-intensity femtosecond laser pumping. Compared with the currently recognized LiNbO3-based TPF OR, which generates a single-cycle terahertz pulse within 3 THz, 4H-SiC demonstrates a significant advantage in producing ultra-widely tunable (up to over 14 THz, TPF angle 31°–38°) terahertz waves with high efficiency (~10–2) and strong field (~MV/cm). Besides, the spectrum characteristics, as well as the evolution from single- to multi-cycle terahertz pulses can be modulated flexibly by pre-chirping. The simulation results show that 4H-SiC enables terahertz frequency extending to an unprecedent range by OR, which has extremely important potential in strong-field terahertz applications.

This paper focuses on the vanishing limit problem for the three-dimensional incompressible Phan-Thien–Tanner (PTT) system, which is commonly used to describe the dynamic properties of polymeric fluids. Our purpose is to show the relation of the PTT system to the well-known Oldroyd-B system (with or without damping mechanism). The suitable a priori estimates and global existence of strong solutions are established for the PTT system with small initial data. Taking advantage of uniform energy and decay estimates for the PTT system with respect to time $t$ and coefficients $a$ and $b$, then allows us to justify in particular the vanishing limit for all time. More precisely, we prove that the solution $(u,\,\tau )$ of PTT system with $0\leq b\leq Ca$ converges globally in time to some limit $(\widetilde {u},\,\widetilde {\tau })$ in a suitable Sobolev space when $a$ and $b$ go to zero simultaneously (or, only $b$ goes to zero). We may check that $(\widetilde {u},\,\widetilde {\tau })$ is indeed a global solution of the corresponding Oldroyd-B system. In addition, a rate of convergence involving explicit norm will be obtained. As a byproduct, similar results are also true for the local a priori estimates in large norm.

Marangoni spreading on thin films is widely observed in nature and applied in industry. It has serious implications for airway drug delivery, especially in surfactant displacement therapy. This paper reports the results of experimental investigations of a surfactant-laden droplet spreading on films made of more viscous Newtonian fluids as well as on films made of viscoelastic fluids. The experiments used particle seeding, the transmission-speckle method and particle tracking velocimetry (PTV) to determine the deformation of the film–droplet interface and to measure velocity fields. Radially aligned patterns were observed on Newtonian films. Similar patterns, but with much smaller wavenumber, were observed on viscoelastic films in combination with rapid azimuthal variations of the film thickness. The Saffman–Taylor instability at the film–droplet interface explains the formation of patterns on a more viscous Newtonian film, and their onset requires exceeding the critical capillary number. The pattern formation on viscoelastic films is correlated with an instability at the film–droplet–air contact line when the liquid is expelled radially by the spreading droplet. PTV revealed azimuthal variations of the velocity field in the vicinity of the contact line. The observed contact line instability is different from previously reported fingering instabilities of Newtonian thin films. A simple scaling law accounting for the Marangoni-stress-induced elastic shear deformation is proposed to describe the flow field in the patterns formed in the viscoelastic films.

Fin Ray soft grippers, as a notable passive compliant structures, can be easily actuated by external devices to adapt their shape to conform to a grasped object. Their unique ability is aided by their V-shaped structure and morphable material utilized by the Fin Ray finger. Thus, when the internal structure changes, the adaptability and grasping abilities also change. However, related works focus on the effects of changing key parameters on the grasping performance based on the Festo structure, and few works have explored the effects of changing the internal structure. To close the research gap, four different Fin Ray structures are presented in this article, and a parameter determination process was carried out by maximizing their adaptability by investigating the key parameters of each structure through finite element analysis. Then, the force responses of four selected Fin Ray structures are analyzed and experimentally validated. The results show that the No Internal Filling structure obtained by omitting the crossbeams is ideal for grasping delicate targets with the best adaptability and the minimum resultant force. The cross structure attained by adding vertical beams connected to crossbeams decreases the adaptability of the Fin Ray finger but significantly increases the contact force. The unsymmetric design of the branched structure significantly enhances the final contact force while improving the passive adaptation to objects. Thus, the application of the Fin Ray finger ranges from adaptive delicate grasping tasks to high-force manipulation tasks.

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.

This study focuses on the Hong Kong Lennon Walls and the communications posted there. We assert that the physical placement of COVID-19 related images on the Lennon Walls of Hong Kong and the replication of symbols and iconography from the Umbrella Movement and the Anti-ELAB Movement situated COVID-19 discourse not only physically within but also symbolically within the contentious politics of Hong Kong. We conclude that the messages and images posted on Lennon Walls between January and April 2020 have used COVID-19 to extend public expression of sentiment on the debates around the Hong Kong government and to further mobilize a sense of Hong Kong identity against China. The findings contribute to the understandings of how the cultural politics surrounding the pandemic became a collective action frame in the mobilization of a localized Hong Kong political identity against the Hong Kong and Chinese governments.

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.

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.

The subduction model of the Neo-Tethys during the Early Cretaceous has always been a controversial topic, and the scarcity of Early Cretaceous magmatic rocks in the southern part of the Gangdese batholith is the main cause of this debate. To address this issue, this article presents new zircon U–Pb chronology, zircon Hf isotope, whole-rock geochemistry and Sr–Nd isotope data for the Early Cretaceous quartz diorite dykes with adakite affinity in Liuqiong, Gongga. Zircon U–Pb dating of three samples yielded ages of c. 141–137 Ma, indicating that the Liuqiong quartz diorite was emplaced in the Early Cretaceous. The whole-rock geochemical analysis shows that the Liuqiong quartz diorite is enriched in large-ion lithophile elements (LILEs) and light rare-earth elements (LREEs) and is depleted in high-field-strength elements (HFSEs), which are related to slab subduction. Additionally, the Liuqiong quartz diorite has high SiO2, Al2O3 and Sr contents, high Sr/Y ratios and low heavy rare-earth element (HREE) and Y contents, which are compatible with typical adakite signatures. The initial 87Sr/86Sr values of the Liuqiong adakite range from 0.705617 to 0.705853, and the whole-rock ϵNd(t) values vary between +5.78 and +6.24. The zircon ϵHf(t) values vary from +11.5 to +16.4. Our results show that the Liuqiong adakite magma was derived from partial melting of the Neo-Tethyan oceanic plate (mid-ocean ridge basalt (MORB) + sediment + fluid), with some degree of subsequent peridotite interaction within the overlying mantle wedge. Combining regional data, we favour the interpretation that the Neo-Tethyan oceanic crust was subducted at a low angle beneath the Gangdese during the Early Cretaceous.