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 study presents an adaptive robust control method for the Pendubot subjects to matched and mismatched uncertainty. First, the control task is formatted as a reduced-dimension equality constraint of the system states. To handle the matched and mismatched uncertainties, an orthogonal decomposition method is employed to make the mismatched part disappear after decomposition. Based on the above, an adaptive robust control law based on constraint-following is devised. By the Lyapunov approach, it is rigorously proven that the proposed approach ensures the uniform boundedness and uniform ultimate boundedness of the closed-loop control system and thus renders approximate constraint-following, regardless of uncertainty. Simulation and experimental results are provided and discussed, demonstrating the good performance of the proposed approach.

Trailing-edge serrations inspired by owls are capable of reducing broadband noise. In this study, the wall-resolved large-eddy simulations (LES) are carried out on the flow over NACA-0012 airfoil with additional serrated trailing edges. The computations are conducted with the high-order flux reconstruction method on unstructured meshes. Three kinds of serrations with different lengths are studied and compared with the straight trailing-edge case, and all three types of serration achieved a certain degree of noise reduction. Presently, the medium-length serration achieves the best noise reduction effect. The maximum decrease of overall sound pressure level is approximately 2.4 dB, implying that the length of serration has a substantial impact on the noise reduction effect. The serration has no significant effect on the upstream turbulence statistics, but it changes the flow structure near the serration, such as inducing side vortex pairs attached to the serration edges. Moreover, dynamic mode decomposition shows that the pressure structures vary with the serration length. For the most unstable hydrodynamic wave, the spanwise coherence of the mode structure of pressure in the upstream boundary layer is weakened. In addition, serrations can redistribute the dipole sources on the surfaces of airfoil and serrations. The destructive interference is enhanced to some extent, which is favourable for noise reduction. In contrast with LES simulations, the pure dipole analysis shows that the longest serration case seems to be the best. Furthermore, a recently developed noise theory is used to evaluate the influence of serrations on the flow noise sources qualitatively and quantitatively. It is found that the serrations can mitigate noise source intensity near the serration edges but increase the source intensity in the near wake. The combined effect of serration on the dipole source and flow noise source determines the overall noise reduction effect. To conclude, destructive interference plays a primary role in suppressing noise radiation by serrated trailing edges, and the dual effect of flow noise sources should be considered in future serration designs. As the influence of turbulence structure will make it more difficult to find the optimal serration parameters, the position of high-fidelity simulation will become increasingly important.

The quantum defect (QD) is an important issue that demands prompt attention in high-power fiber lasers. A large QD may aggravate the thermal load in the laser, which would impact the frequency, amplitude noise and mode stability, and threaten the security of the high-power laser system. Here, we propose and demonstrate a cladding-pumped Raman fiber laser (RFL) with QD of less than 1%. Using the Raman gain of the boson peak in a phosphorus-doped fiber to enable the cladding pump, the QD is reduced to as low as 0.78% with a 23.7 W output power. To our knowledge, this is the lowest QD ever reported in a cladding-pumped RFL. Furthermore, the output power can be scaled to 47.7 W with a QD of 1.29%. This work not only offers a preliminary platform for the realization of high-power low-QD fiber lasers, but also proves the great potential of low-QD fiber lasers in power scaling.

The superfluorescent fiber source (SFS) with tunable optical spectrum has shown great application potential in the sensing, imaging, and spectral combination. Here, we demonstrate for the first time a 2-kW-level wavelength and linewidth tunable SFS. Based on a flexible filtered SFS seed and three stages of fiber amplifiers, the output power can be scaled from the milliwatt level to about 2 kW, with a wavelength tuning range of 1068–1092 nm and a linewidth tuning range of 2.5–9.7 nm. Moreover, a numerical simulation is conducted based on the generalized nonlinear Schrödinger equation, and the results reveal that the wavelength tuning range is limited by the decrease of seed power and the growth of amplified spontaneous emission, whereas the linewidth tuning range is determined by the gain competition and nonlinear Kerr effects. The developed wavelength and linewidth tunable SFS may be applied to scientific research and industrial processing.

The present study evaluated effects of dietary supplementation with tryptophan (Trp) on muscle growth, protein synthesis and antioxidant capacity in hybrid catfish Pelteobagrus vachelli♀ × Leiocassis longirostris♂. Fish were fed six different diets containing 2·6 (control), 3·1, 3·7, 4·2, 4·7 and 5·6 g Trp/kg diet for 56 d, respectively. Results showed that dietary Trp significantly (1) improved muscle protein content, fibre density and frequency of fibre diameter; (2) up-regulated the mRNA levels of PCNA, myf5, MyoD1, MyoG, MRF4, IGF-I, IGF-II, IGF-IR, PIK3Ca, TOR, 4EBP1 and S6K1; (3) increased phosphorylation levels of AKT, TOR and S6K1; (4) decreased contents of MDA and PC, and increased activities of CAT, GST, GR, ASA and AHR; (5) up-regulated mRNA levels of CuZnSOD, CAT, GST, GPx, GCLC and Nrf2, and decreased Keap1 mRNA level; (6) increased nuclear Nrf2 protein level and the intranuclear antioxidant response element-binding ability, and reduced Keap1 protein level. These results indicated that dietary Trp improved muscle growth, protein synthesis as well as antioxidant capacity, which might be partly related to myogenic regulatory factors, IGF/PIK3Ca/AKT/TOR and Keap1/Nrf2 signalling pathways. Finally, based on the quadratic regression analysis of muscle protein and MDA contents, the optimal Trp requirements of hybrid catfish (21·82–39·64 g) were estimated to be 3·94 and 3·93 g Trp/kg diet (9·57 and 9·54 g/kg of dietary protein), respectively.

Environmental hypoxia exposure causes fertility problems in human and animals. Compelling evidence suggests that chronic hypoxia impairs spermatogenesis and reduces sperm motility. However, it is unclear whether paternal hypoxic exposure affects fertilization and early embryo development. In the present study, we exposed male mice to high altitude (3200 m above sea level) for 7 or 60 days to evaluate the effects of hypoxia on sperm quality, zygotic DNA methylation and blastocyst formation. Compared with age-matched controls, hypoxia-treated males exhibited reduced fertility after mating with normoxic females as a result of defects in sperm motility and function. Results of in vitro fertilization (IVF) experiments revealed that 60 days’ exposure significantly reduced cleavage and blastocyst rates by 30% and 70%, respectively. Immunohistochemical staining of pronuclear formation indicated that the pronuclear formation process was disturbed and expression of imprinted genes was reduced in early embryos after paternal hypoxia. Overall, the findings of this study suggested that exposing male mice to hypoxia impaired sperm function and affected key events during early embryo development in mammals.

Spatial profiles of impurity emission measurements in the extreme ultraviolet (EUV) spectroscopic range in radiofrequency (RF)-heated discharges are combined with one-dimensional and three-dimensional transport simulations to study the effects of resonant magnetic perturbations (RMPs) on core impurity accumulation at EAST. The amount of impurity line emission mitigation by RMPs appears to be correlated with the ion Z for lithium, carbon, iron and tungsten monitored, i.e. stronger suppression of accumulation for heavier ions. The targeted effect on the most detrimental high-Z impurities suggests a possible advantage using RMPs for impurity control. Profiles of transport coefficients are calculated with the STRAHL one-dimensional impurity transport code, keeping $\nu /D$ fixed and using the measured spatial profiles of $\textrm{F}{\textrm{e}^{20 + }}$, $\textrm{F}{\textrm{e}^{21 + }}$ and $\textrm{F}{\textrm{e}^{22 + }}$ to disentangle the transport coefficients. The iron diffusion coefficient ${D_{\textrm{Fe}}}$ increases from $1.0- 2.0\;{\textrm{m}^2}\;{\textrm{s}^{ - 1}}$ to $1.5- 3.0\;{\textrm{m}^2}\;{\textrm{s}^{ - 1}}$ from the core region to the edge region $(\rho \gt 0.5)$ after the onset of RMPs. Meanwhile, an inward pinch of iron convective velocity ${\nu _{\textrm{Fe}}}$ decreases in magnitude in the inner core region and increases significantly in the outer confined region, simultaneously contributing to preserving centrally peaked $\textrm{Fe}$ profiles and exhausting the impurities. The ${D_{\textrm{Fe}}}$ and ${\nu _{\textrm{Fe}}}$ variations lead to reduced impurity contents in the plasma. The three-dimensional edge impurity transport code EMC3-EIRENE was also applied for a case of RMP-mitigated high-Z accumulation at EAST and compared to that of low-Z carbon. The exhaust of ${\textrm{C}^{6 + }}$ toward the scrape-off layer accompanying an overall suppression of heavier ${\textrm{W}^{30 + }}$ is observed when using RMPs.

Protoporphyrinogen oxidase (PPO) is an important target for discovering new herbicides that interfere with the synthesis of porphyrin. To discover new PPO inhibitors with improved biological activity, a series of new diphenyl ethers containing tetrahydrophthalimide were designed and synthesized. Among them, J6.1 (IC50 = 4.7 nM) and J6.3 (IC50 = 30.0 nM) show higher maize (Zea mays L.) PPO inhibitory activity than the commercial herbicides oxyfluorfen (IC50 = 117.9 nM) and flumioxazin (IC50 = 157.1 nM). The greenhouse herbicidal activity of J6.3 is comparable to that of oxyfluorfen, and it is greater than that of flumioxazin. Even at a dose of 300 g ai ha−1, cotton (Gossypium hirsutum L.) and peanut (Arachis hypogaea L.) show greater tolerance to J6.3, suggesting that J6.3 could be used for further development of new herbicide candidates in those fields. In addition, molecular docking has been used to further study the mechanism of action of J6.3. The results show that the introduction of a nitro group and tetrahydrophthalimide into the diphenyl ether structure is beneficial to biological activity.

Transmission of varicella occurs frequently in schools and households. We investigated the characteristics of varicella cases derived from within-household transmission and the modes of varicella transmission between school and household settings in Shanghai, China, from 2009 to 2018. Within-household transmission occurred in 278 households, of which 134 transmission events were between children. Sixty-one household varicella transmission events may be attributed to isolation procedures for infected students during school outbreaks, and 7.6% of school outbreaks were caused by schoolchildren cases derived from within-household transmission. The frequency of ‘school-household-school’ transmission adds an additional layer of complexity to the control of school varicella outbreaks. Administration of varicella vaccine as post-exposure prophylaxis after exposure is considered to be an effective measure to control varicella spread within households and schools.

The experiment was conducted to investigate the effects of dietary threonine (Thr) on growth performance and muscle growth, protein synthesis and antioxidant-related signalling pathways of hybrid catfish Pelteobagrus vachelli♀ × Leiocassis longirostris♂. A total of 1200 fish (14·19 (se 0·13) g) were randomly distributed into six groups with four replicates each, fed six diets with graded level of Thr (9·5, 11·5, 13·5, 15·4, 17·4 and 19·3 g/kg diets) for 56 d. Results showed (P < 0·05) that dietary Thr (1) increased percentage weight gain, specific growth rate, feed efficiency and protein efficiency ratio; (2) up-regulated growth hormone (GH), insulin-like growth factor 1 (IGF-1), proliferating cell nuclear antigen, myogenic regulation factors (MyoD, Myf5, MyoG and Mrf4) and myosin heavy chain (MyHC) mRNA levels; (3) increased muscle protein content via regulating the protein kinase B/target of rapamycin signalling pathway and (4) decreased malondialdehyde and protein carbonyl contents, increased catalase, glutathione-S-transferase, glutathione reductase and GSH activities, up-regulated mRNA levels of antioxidant enzymes related to NFE2-related factor 2 and γ-glutamylcysteine ligase catalytic subunit. These results suggest that Thr has a potential role to improve muscle growth and protein synthesis, which might be due to the regulation of GH-IGF system, muscle growth-related gene, antioxidative capacity and protein synthesis-related signalling pathways. Based on the quadratic regression analysis of specific growth rate, the Thr requirement of hybrid catfish (14·19–25·77 g) was estimated to be 13·77 g/kg of the diet (33·40 g/kg of dietary protein).

In this perspective, the authors challenge the status quo of polymer innovation. The authors first explore how research in polymer design is conducted today, which is both time consuming and unable to capture the multi-scale complexities of polymers. The authors discuss strategies that could be employed in bringing together machine learning, data curation, high-throughput experimentation, and simulations, to build a system that can accurately predict polymer properties from their descriptors and enable inverse design that is capable of designing polymers based on desired properties.

High power superfluorescent fiber sources (SFSs), which could find wide applications in many fields such as middle infrared laser generation, Raman fiber laser pumping and spectral beam combination, have experienced a flourishing time in recent years for its unique properties, such as short coherence length and high temporal stability. The challenge for performance scalability of powerful SFS mainly lies on the physical issues including parasitic laser oscillation and modal instability (MI). In this contribution, by employing in-band pumping avenue and high-order transverse-mode management, we explore a high power SFS with record power, near-diffraction-limited beam quality and spectral manipulation flexibility. An ultimate output power of 3.14 kW can be obtained with high temporal stability and a beam quality of $M^{2}=1.59$ for the amplified light. Furthermore, the dynamics of spectral evolutions, including red-shifting of central wavelength and unsymmetrical broadening in spectral wings, of the main amplifier with different seed linewidths are investigated contrastively. Benefiting from the unique high pump brightness and high MI threshold of in-band pumping scheme, the demonstrated system also manifests promising performance scaling potential.

In this paper, we experimentally investigated the extreme frequency shift in high-power Raman fiber laser (RFL). The RFL was developed by using a pair of fiber Bragg gratings with fixed and matched central wavelength (1120 nm) combined with a piece of 31-m-long polarization maintaining (PM) passive fiber adopted as Raman gain medium. The pump source was a homemade high-power, linearly polarized (LP) wavelength-tunable master oscillator power amplifier (MOPA) source with ${\sim}25~\text{nm}$ tunable working range (1055–1080 nm). High-power and high-efficiency RFL with extreme frequency shift between the pump and Stokes light was explored. It is found that frequency shift located within 10.6 THz and 15.2 THz can ensure efficient Raman lasing, where the conversion efficiency is more than 95% of the maximal value, 71.3%. In addition, a maximum output power of 147.1 W was obtained with an optical efficiency of 71.3%, which is the highest power ever reported in LP RFLs to the best of our knowledge.

In the past few years, we have performed a 22 GHz H2O maser survey towards hundreds of BGPS sources using the 25-meter Nanshan Radio Telescope (NSRT) of the Xinjiang Astronomical Observatory, and detected more than one hundred masers. Our aim is to study star formation activities associated with these sources, as well as search for any correlations that may exist between 22 GHz H2O masers and the evolutionary stage of high-mass star formation regions. The NSRT has been upgraded and have now an effective diameter of 26 meter. Besides, cryogenically cooled dual-beam receiver systems covering seven millimeter-wave observing bands have been installed on the NSRT. For the next step of maser observation, we will continue to do H2O and SiO masers survey of massive dust clumps and monitor some maser sources.