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*}

We investigate the coupling effect of buoyancy and shear based on an annular centrifugal Rayleigh–Bénard convection (ACRBC) system in which two cylinders rotate with an angular velocity difference. Direct numerical simulations are performed in a Rayleigh number range $10^6\leq Ra\leq 10^8$, at fixed Prandtl number $Pr=4.3$, inverse Rossby number $Ro^{-1}=20$, and radius ratio $\eta =0.5$. The shear, represented by the non-dimensional rotational speed difference $\varOmega$, varies from $0$ to $10$, corresponding to an ACRBC without shear and a radially heated Taylor–Couette flow with only the inner cylinder rotating, respectively. A stable regime is found in the middle part of the interval for $\varOmega$, and divides the whole parameter space into three regimes: buoyancy-dominated, stable and shear-dominated. Clear boundaries between the regimes are given by linear stability analysis, meaning the marginal state of the flow. In the buoyancy-dominated regime, the flow is a quasi-two-dimensional flow on the $r\varphi$ plane; as shear increases, both the growth rate of instability and the heat transfer are depressed. In the shear-dominated regime, the flow is mainly on the $rz$ plane. The shear is so strong that the temperature acts as a passive scalar, and the heat transfer is greatly enhanced. The study shows that shear can stabilize buoyancy-driven convection, makes a detailed analysis of the flow characteristics in different regimes, and reveals the complex coupling mechanism of shear and buoyancy, which may have implications for fundamental studies and industrial designs.

Aging plays a crucial role in the mechanisms of the impacts of genetic and environmental factors on blood pressure and serum lipids. However, to our knowledge, how the influence of genetic and environmental factors on the correlation between blood pressure and serum lipids changes with age remains to be determined. In this study, data from the Chinese National Twin Registry (CNTR) were used. Resting blood pressure, including systolic and diastolic blood pressure (SBP and DBP), and fasting serum lipids, including total cholesterol (TC), high-density lipoprotein cholesterol (HDL-C), low-density lipoprotein cholesterol (LDL-C) and triglycerides (TGs) were measured in 2378 participants (1189 twin pairs). Univariate and bivariate structural equation models examined the genetic and environmental influences on blood pressure and serum lipids among three age groups. All phenotypes showed moderate to high heritability (0.37–0.59) and moderate unique environmental variance (0.30–0.44). The heritability of all phenotypes showed a decreasing trend with age. Among all phenotypes, SBP and DBP showed a significant monotonic decreasing trend. For phenotype-phenotype pairs, the phenotypic correlation (Rph) of each pair ranged from −0.04 to 0.23, and the additive genetic correlation (Ra) ranged from 0.00 to 0.36. For TC&SBP, TC&DBP, TG&SBP and TGs&DBP, both the Rph and Ra declined with age, and the Ra difference between the young group and the older adult group is statistically significant (p < .05). The unique environmental correlation (Re) of each pair did not follow any pattern with age and remained relatively stable with age. In summary, we observed that the heritability of blood pressure was affected by age. Moreover, blood pressure and serum lipids shared common genetic backgrounds, and age had an impact on the phenotypic correlation and genetic correlations.

Although ethanol treatment is widely used to activate oocytes, the underlying mechanisms are largely unclear. Roles of intracellular calcium stores and extracellular calcium in ethanol-induced activation (EIA) of oocytes remain to be verified, and whether calcium-sensing receptor (CaSR) is involved in EIA is unknown. This study showed that calcium-free ageing (CFA) in vitro significantly decreased intracellular stored calcium (sCa) and CaSR expression, and impaired EIA, spindle/chromosome morphology and developmental potential of mouse oocytes. Although EIA in oocytes with full sCa after ageing with calcium does not require calcium influx, calcium influx is essential for EIA of oocytes with reduced sCa after CFA. Furthermore, the extremely low EIA rate in oocytes with CFA-downregulated CaSR expression and the fact that inhibiting CaSR significantly decreased the EIA of oocytes with a full complement of CaSR suggest that CaSR played a significant role in the EIA of ageing oocytes. In conclusion, CFA impaired EIA and the developmental potential of mouse oocytes by decreasing sCa and downregulating CaSR expression. Because mouse oocytes routinely treated for activation (18 h post hCG) are equipped with a full sCa complement and CaSR, the present results suggest that, while calcium influx is not essential, CaSR is required for the EIA of oocytes.

Germplasm innovation can provide materials for breeding sugarcane cultivars. Saccharum officinarum is the main source of high-sugar and high-yield genes in sugarcane breeding. ‘Nobilization’ is the theoretical basis for exploiting S. officinarum, and S. officinarum authenticity directly affects sugarcane nobility breeding efficiency. Herein, the authenticity of 22 SLC-series S. officinarum clones imported from Sri Lanka and preserved in the China National Germplasm Repository of Sugarcane (NGRS) was explored by four-primer amplification-arrested mutation PCR (ARMS PCR) and somatic chromosome number counting. The amplified bands from SLC 08 120 and SLC 08 131 were the same with those from S. officinarum clone Badila, i.e. a common band of 428 bp and a S. officinarum-specific band of 278 bp, hence they were tentatively assigned as S. officinarum clones. The other 20 SLC clones had both 278 bp (S. officinarum-specific) and 203 bp (S. spontaneum-specific) bands, which are hybrid characteristics. In addition, the chromosome numbers of SLC 08 120 and SLC 08 131 are both 80, belong to typical S. officinarum. While the chromosome numbers of the other 20 materials are ranging from 101 to 129, consistent with hybrids of S. officinarum and S. spontaneum. This molecular cytological characterization indicates that among the 22 introduced SLC-series clones, only two, SLC 08 120 and SLC 08 131, were S. officinarum. Future agronomic trait and resistance analyses could facilitate their use as crossing parents in sugarcane breeding.

A 10 kV distribution network is critical for ensuring power supply to residents and factories. The number of power maintenance operations is rapidly increasing, and aerial cable stripping is a significant branch of these routine maintenances. High-voltage cable stripping, on the other hand, is mostly done manually, which is inefficient and poses serious security risks. As a result, this paper proposes an automatic wire stripping robot for use in a 10 kV power grid. The mechanical structure of the stripping robot is designed for installation on the insulating rod based on the working environment of 10 kV overhead cables. The robot was subjected to electromagnetic field simulation, modal analysis, and rigid-flexible coupling analysis. Finally, the robot prototype is built, and the PID controller is designed. Stripping tests are performed on a cable with a cross-sectional area of 95, 120, 150, 240, and 300 mm2, and the results are satisfactory.

Trematodes of the genus Ogmocotyle are intestinal flukes that can infect a variety of definitive hosts, resulting in significant economic losses worldwide. However, there are few studies on molecular data of these trematodes. In this study, the mitochondrial (mt) genome of Ogmocotyle ailuri isolated from red panda (Ailurus fulgens) was determined and compared with those from Pronocephalata to investigate the mt genome content, genetic distance, gene rearrangements and phylogeny. The complete mt genome of O. ailuri is a typical closed circular molecule of 14 642 base pairs, comprising 12 protein-coding genes (PCGs), 22 transfer RNA genes, 2 ribosomal RNA genes and 2 non-coding regions. All genes are transcribed in the same direction. In addition, 23 intergenic spacers and 2 locations with gene overlaps were determined. Sequence identities and sliding window analysis indicated that cox1 is the most conserved gene among 12 PCGs in O. ailuri mt genome. The sequenced mt genomes of the 48 Plagiorchiida trematodes showed 5 types of gene arrangement based on all mt genome genes, with the gene arrangement of O. ailuri being type I. Phylogenetic analysis using concatenated amino acid sequences of 12 PCGs revealed that O. ailuri was closer to Ogmocotyle sikae than to Notocotylus intestinalis. These data enhance the Ogmocotyle mt genome database and provide molecular resources for further studies of Pronocephalata taxonomy, population genetics and systematics.

Romyar Sharifi has constructed a map $\varpi _M$ from the first homology of the modular curve $X_1(M)$ to the K-group $K_2(\operatorname {\mathrm {\mathbf {Z}}}[\zeta _M+\zeta _M^{-1}, \frac {1}{M}]) \otimes \operatorname {\mathrm {\mathbf {Z}}}[1/2]$, where $\zeta _M$ is a primitive Mth root of unity. Sharifi conjectured that $\varpi _M$ is annihilated by a certain Eisenstein ideal. Fukaya and Kato proved this conjecture after tensoring with $\operatorname {\mathrm {\mathbf {Z}}}_p$ for a prime $p\geq 5$ dividing M. More recently, Sharifi and Venkatesh proved the conjecture for Hecke operators away from M. In this note, we prove two main results. First, we give a relation between $\varpi _M$ and $\varpi _{M'}$ when $M' \mid M$. Our method relies on the techniques developed by Sharifi and Venkatesh. We then use this result in combination with results of Fukaya and Kato in order to get the Eisenstein property of $\varpi _M$ for Hecke operators of index dividing M.

According to the public data collected from the Health Commission of Gansu Province, China, regarding the COVID-19 pandemic during the summer epidemic cycle in 2022, the epidemiological analysis showed that the pandemic spread stability and the symptom rate (the number of confirmed cases divided by the sum of the number of asymptomatic cases and the number of confirmed cases) of COVID-19 were different among 3 main epidemic regions, Lanzhou, Linxia, and Gannan; both the symptom rate and the daily instantaneous symptom rate (daily number of confirmed cases divided by the sum of daily number of asymptomatic cases and daily number of confirmed cases) in Lanzhou were substantially higher than those in Linxia and Gannan. The difference in the food sources due to the high difference of the population ethnic composition in the 3 regions was probably the main driver for the difference of the symptom rates among the 3 regions. This work provides potential values for prevention and control of COVID-19 in different regions.

As intense, ultrashort, kHz-repetition-rate laser systems become commercially available, pulse cumulative effects are critical for laser filament-based applications. In this work, the pulse repetition-rate effect on femtosecond laser filamentation in air was investigated both numerically and experimentally. The pulse repetition-rate effect has negligible influence at the leading edge of the filament. Clear intensity enhancement from a high-repetition pulse is observed at the peak and tailing edge of the laser filament. As the repetition rate of the laser pulses increases from 100 to 1000 Hz, the length of the filament extends and the intensity inside the filament increases. A physical picture based on the pulse repetition-rate dependent ‘low-density hole’ effect on filamentation is proposed to explain the obtained results well.

There is still controversy about optimal dietary iodine intake as the Universal Salt Iodization policy enforcement in China. A modified iodine balance study was thus conducted to explore the suitable iodine intake in Chinese adult males using the iodine overflow hypothesis. In this study, thirty-eight apparently healthy males (19·1 (sd 0·6) years) were recruited and provided with designed diets. After the 14-d iodine depletion, daily iodine intake gradually increased in the 30-d iodine supplementation, consisting of six stages and each of 5 d. All foods and excreta (urine, faeces) were collected to examine daily iodine intake, iodine excretion and the changes of iodine increment in relation to those values at stage 1. The dose–response associations of iodine intake increment with excretion increment were fitted by the mixed effects models, as well as with retention increment. Daily iodine intake and excretion were 16·3 and 54·3 μg/d at stage 1, and iodine intake increment increased from 11·2 μg/d at stage 2 to 118·0 μg/d at stage 6, while excretion increment elevated from 21·5 to 95·0 μg/d. A zero iodine balance was dynamically achieved as 48·0 μg/d of iodine intake. The estimated average requirement and recommended nutrient intake were severally 48·0 and 67·2 μg/d, which could be corresponded to a daily iodine intake of 0·74 and 1·04 μg/kg per d. The results of our study indicate that roughly half of current iodine intakes recommendation could be enough in Chinese adult males, which would be beneficial for the revision of dietary reference intakes.

One of the most common harmful mites in edible fungi is Histiostoma feroniarum Dufour (Acaridida: Histiostomatidae), a fungivorous astigmatid mite that feeds on hyphae and fruiting bodies, thereby transmitting pathogens. This study examined the effects of seven constant temperatures and 10 types of mushrooms on the growth and development of H. feroniarum, as well as its host preference. Developmental time for the total immature stages was significantly affected by the type of mushroom species, ranging from 4.3 ± 0.4 days (reared on Pleurotus eryngii var. tuoliensis Mou at 28°C) to 17.1 ± 2.3 days (reared on Auricularia polytricha Sacc. at 19°C). The temperature was a major factor in the formation of facultative heteromorphic deutonymphs (hypopi). The mite entered the hypopus stage when the temperature dropped to 16°C or rose above 31°C. The growth and development of this mite were significantly influenced by the type of species and variety of mushrooms. Moreover, the fungivorous astigmatid mite preferred to feed on the ‘Wuxiang No. 1’ strain of Lentinula edodes (Berk.) Pegler and the ‘Gaowenxiu’ strain of P. pulmonarius (Fr.) Quél., with a shorter development period compared with that of feeding on other strains. These results therefore quantify the effect of host type and temperature on fungivorous astigmatid mite growth and development rates, and provide a reference for applying mushroom cultivar resistance to biological pest control.

We present a high-energy, hundred-picosecond (ps) pulsed mid-ultraviolet solid-state laser at 266 nm by a direct second harmonic generation (SHG) in a barium borate (BaB2O4, BBO) nonlinear crystal. The green pump source is a 710 mJ, 330 ps pulsed laser at a wavelength of 532 nm with a repetition rate of 1 Hz. Under a green pump energy of 710 mJ, a maximum output energy of 253.3 mJ at 266 nm is achieved with 250 ps pulse duration resulting in a peak power of more than 1 GW, corresponding to an SHG conversion efficiency of 35.7% from 532 to 266 nm. The experimental data were well consistent with the theoretical prediction. To the best of our knowledge, this laser exhibits both the highest output energy and highest peak power ever achieved in a hundred-ps/ps regime at 266 nm for BBO-SHG.

A dual-band dual-linearly polarized waveguide slot array antenna is proposed in this paper. Two orthogonal slots share a short-circuit wall on broad side. The horizontal and vertical slots, which actualize dual-frequency bands and dual-linear polarization, generate vertically polarized electric fields in 9.39–9.78 GHz and horizontally polarized electric fields in 11.62–12.3 GHz, respectively. The equivalent permittivity of the waveguide is changed by two grooves at the bottom of the waveguide, which improves phase velocity. Two grooves can also reduce the distance between the elements while suppressing the side lobes. Compared to filling the medium in the waveguide, two grooves have less losses. Moreover, the antenna is simple with one input port. The array antenna also overcomes the problems of beam scanning compared with the traditional waveguide slot array antenna. A 1 × 8 antenna array is fabricated and measured to verify the design. The horizontal polarization is formed in 9.39–9.78 GHz, the vertical polarization is generated in 11.62–12.3 GHz, and the antenna gain can reach 15 dBi.

In order to decrease the influence of system parameters and load on the dynamic performance of permanent magnet synchronous motor (PMSM) in cooperative robot joint modules, a practical model-based robust control method was proposed. It inherits the traditional proportional-integral-derivative (PID) control and robust control based on error and model-based control. We first set up the nominal controller using the dynamics model. In order to limit the influence of uncertainty on dynamic performance, a robust controller is established based on Lyapunov method. The control can be regarded as an improved PID control or a redesigned robust control. Compared with the traditional control method, it is simple to implement and has practical effects. It is proved by theoretical analysis that the controller can guarantee the uniform boundedness and uniform final boundedness of the system. In addition, the prototype of fast controller cSPACE is built on the experiment platform, which averts long-time programming and debugging. It offers immense convenience for practical operation. Finally, numerical simulation and real-time experiment results are presented. Based on cSPACE and a PMSM in the joint module of a practical cooperative robot, the availability of the control design and the achievable control performance are verified.