Let $\mathbb{N}$ be the set of all non-negative integers. For any integer r and m, let $r+m\mathbb{N}=\{r+mk: k\in\mathbb{N}\}$. For $S\subseteq \mathbb{N}$ and $n\in \mathbb{N}$, let $R_{S}(n)$ denote the number of solutions of the equation $n=s+s'$ with $s, s'\in S$ and $s \lt s'$. Let $r_{1}, r_{2}, m$ be integers with $0 \lt r_{1} \lt r_{2} \lt m$ and $2\mid r_{1}$. In this paper, we prove that there exist two sets C and D with $C\cup D=\mathbb{N}$ and $C\cap D=(r_{1}+m\mathbb{N})\cup (r_{2}+m\mathbb{N})$ such that $R_{C}(n)=R_{D}(n)$ for all $n\in\mathbb{N}$ if and only if there exists a positive integer l such that $r_{1}=2^{2l+1}-2, r_{2}=2^{2l+1}-1, m=2^{2l+2}-2$.

The power scaling on short wavelength (SW) fiber lasers operating around 1 μm are in significant demand for applications in energy, environment and industry. The challenge for performance scalability of high-power SW lasers based on rare-earth-doped fiber primarily lies in the physical limitations, including reabsorption, amplified spontaneous emission and parasitic laser oscillation. Here, we demonstrate an all-fiberized, purely passive SW (1018 nm) random-distributed-feedback Raman fiber laser (RRFL) to validate the capability of achieving high-power output at SWs based on multimode laser diodes (LDs) direct pumping. Directly pumped by multimode LDs, the high-brightness RRFL delivers over 656 W, with an electro-optical efficiency of 20% relative to the power. The slope efficiency is 94%. The beam quality M2 factor is 2.9 (which is ~20 times that of the pump) at the maximum output signal power, achieving the highest brightness enhancement of 14.9 in RRFLs. To the best of our knowledge, this achievement also represents the highest power record of RRFLs utilizing multimode diodes for direct pumping. This work may not only provide a new insight into the realization of high-power, high-brightness RRFLs but also is a promising contender in the power scaling of SWs below 1 μm.

The production and industrial use of asbestos cement and other asbestos-containing materials have been restricted in most countries because of the potential detrimental effects on human health and the environment. Chrysotile is the most common form of asbestos and investigations into how to recycle this serpentine phyllosilicate mineral have attracted extensive attention. Chrysotile asbestos tailings can be transformed thermally, at high temperature, by in situ carbothermal reduction (CR). The CR method aims to maximize use of the chrysotile available and uses high temperatures and carbon to change the mineral form and structure of the chrysotile asbestos tailings. When chrysotile asbestos is employed as the raw material and coke (carbon) powder is used as the reducing agent for CR transformation, stable, high-temperature composites consisting of forsterite, stishovite, and silicon carbide are formed. Forsterite (Mg2SiO4) was the most abundant crystalline phase formed in samples heat treated below 1500ºC. At 1600ºC, forsterite was exhausted through decomposition and β-SiC formed by reduction of stishovite. A larger proportion of β-SiC was generated as the carbon content was increased. This research revealed that both temperature and carbon addition play key roles in the transformation of chrysotile asbestos tailings.

Microplastics (MPs) pollution has been a hot research topic in recent years. MPs are ubiquitous throughout the ecological environment and are eventually accumulated in organisms through inhalation or ingestion. However, given that MPs are inert pollutants, their effects on organisms are not clear. In previous study, we have investigated the effects of polyethylene terephthalate MPs on physiology of Drosophila. What is the effect of polypropylene microplastics (PP-MPs)? The results of our experiments show that being exposed to high concentration of PP-MPs have significant effect on Drosophila. PP-MPs exposure can significantly increase locomotor activity and shorten the time of group sleep in Drosophila. In the presence of high concentrations of PP-MPs, the triglyceride content was reduced in females and their ability of egg production was affected. However, there was no significant effect on the level of protein and carbohydrate, or on the food intake. Our experimental results can provide some preliminary data for assessing the potential hazard of PP-MPs to other organisms.

Let p be a prime with $p\equiv 1\pmod {4}$ . Gauss first proved that $2$ is a quartic residue modulo p if and only if $p=x^2+64y^2$ for some $x,y\in \Bbb Z$ and various expressions for the quartic residue symbol $(\frac {2}{p})_4$ are known. We give a new characterisation via a permutation, the sign of which is determined by $(\frac {2}{p})_4$ . The permutation is induced by the rule $x \mapsto y-x$ on the $(p-1)/4$ solutions $(x,y)$ to $x^2+y^2\equiv 0 \pmod {p}$ satisfying $1\leq x < y \leq (p-1)/2$ .

The Emeishan large igneous province (ELIP) in SW China is considered to be a typical mantle-plume-derived LIP. The picrites formed at relatively high temperatures in the ELIP, providing one of the important lines of argument for the role of mantle plume. Here we report trace-element data on olivine phenocrysts in the Dali picrites from the ELIP. The olivines are Ni-rich, and characterized by high (>1.4) 100×Mn/Fe value and low (<13) 10 000×Zn/Fe value, indicating a peridotite-dominated source. Since the olivine–melt Ni partition coefficient (KDNiol/melt) will decrease at high temperatures and pressures, the picrites derived from peridotite melting at high pressure, and that crystallized olivines at lower pressure, can generate high concentrations of Ni in olivine phenocrysts, excluding the necessity of a metasomatic pyroxenite contribution. Based on the Al-in-olivine thermometer, olivine crystallization temperature and mantle potential temperature (TP) were calculated at c. 1491°C and c. 1559°C, respectively. Our results are c. 200°C higher than that of the normal asthenospheric mantle, and are consistent with the role of a mantle thermal plume for the ELIP.

The poultry red mite, Dermanyssus gallinae, is currently the most common ectoparasite affecting egg-laying hens. Since continuous culture of D. gallinae on birds is a biologically and economically costly endeavour, storage techniques for mites are urgently needed. Effects of temperature on adult and nymph survival were first studied to optimize storage conditions. Then, fecundity of D. gallinae was studied after mites were stored at optimal storage conditions. Results showed the survival rates of protonymphs (42.11%), deutonymphs (8.19%) and females (19.78%) at 5°C after 84 days were higher than those at 0, 25 and 30°C. Thereafter the fecundity and the capability of re-establishing colonies of D. gallinae were evaluated after they were stored for 40 and 80 days at 5°C. After storage, the mean number of eggs showed no statistical difference between treated (5°C for 40 or 80 days) and control groups (25°C for 7 days), while the hatching rates of eggs were in all cases above 97%. The dynamic changes of mite populations and egg numbers showed similar trends to the control group after the stored adult or nymph mites were fed on chicks. Dermanyssus gallinae can be successfully stored at 5°C for 80 days with no interference with the fecundity of mites, and the stored mites could re-establish colonies successfully. Adults and nymphs were two main stages with capability for low temperature storage. These results suggest that low temperature storage is a viable option for colony maintenance of D. gallinae under laboratory conditions.

Qi and Chapman [‘Two closed forms for the Bernoulli polynomials’, J. Number Theory159 (2016), 89–100] gave a closed form expression for the Bernoulli polynomials as polynomials with coefficients involving Stirling numbers of the second kind. We extend the formula to the degenerate Bernoulli polynomials, replacing the Stirling numbers by degenerate Stirling numbers of the second kind.

The dynamics of vortical structures in flow over a circular cylinder in the vicinity of a flat plate is investigated using particle image velocimetry (PIV). The cylinder is placed above the flat plate with its axis parallel to the wall and normal to the flow direction. The Reynolds number $Re_{D}$ based on the cylinder diameter $D$ is 1072 and the gap $G$ between the cylinder and the flat plate is varied from gap-to-diameter ratio $G/D=0$ to $G/D=3.0$. The flow statistics and vortex dynamics are strongly dependent on the gap ratio $G/D$. Statistics show that as the cylinder comes close to the wall ($G/D\leqslant 2.0$), the cylinder wake becomes more and more asymmetric and a boundary layer separation is induced on the flat plate downstream of the cylinder. The wake vortex shedding frequency increases with decreasing $G/D$ until a critical gap ratio (about $G/D=0.25$) below which the vortex shedding is irregular. The deflection of the gap flow away from the wall and its following interaction with the upper shear layer may be the cause of the higher shedding frequency. The vortex dynamics is investigated based on the phase-averaged flow field and virtual dye visualization in the instantaneous PIV velocity field. It is revealed that when the cylinder is close to the wall ($G/D=2.0$), the cylinder wake vortices can periodically induce secondary spanwise vortices near the wall. As the cylinder approaches the wall ($G/D=1.0$) the secondary vortex can directly interact with the lower wake vortex, and a further approaching of the cylinder ($G/D=0.5$) can result in more complex interactions among the secondary vortex, the lower wake vortex and the upper wake vortex. The breakdown of vortices into filamentary debris during vortex interactions is clearly revealed by the coloured virtual dye visualizations. For $G/D<0.25$, the lower shear layer is strongly inhibited and only the upper shear layer can shed vortices. Investigation of the vortex formation, evolution and interaction in the flow promotes the understanding of the flow physics for different gap ratios.

Evolution of Lagrangian coherent structures (LCS) in a flat plate boundary layer transition induced by the wake of a circular cylinder is investigated. Both hydrogen bubble visualization and particle image velocimetry (PIV) techniques are used. It is found that downstream of the cylinder, the disturbance in the boundary layer experiences a fast growth followed by a slow decay in the transition. Lagrangian coherent structures are revealed by qualitative hydrogen bubble visualizations and quantitative finite-time Lyapunov exponents (FTLE) fields derived from the PIV data. The evolution of the LCS is considered from the very beginning of the transition up to when the boundary layer becomes fully developed turbulent flow. The mean convection velocity and average inclination angle of the LCS are first extracted from the FTLE fields. The streamwise length of the low-speed streaks seems to increase, while their spanwise distance decreases in the boundary layer transition. Proper orthogonal decomposition (POD) of the PIV data shows that low-speed streaks associated with the hairpin vortices and hairpin packets are the dominant coherent structures close to the wall in the transitional and turbulent boundary layer. The POD modes also reveal a variety of scales in the turbulent boundary layer. Moreover, it is found that large-scale coherent structures can modulate the amplitude of the small-scale ones.

The solid-state phase equilibria of the copper (Cu)–dysprosium (Dy)–titanium (Ti) ternary system at 973 K has been experimentally investigated. The existence of nine binary compounds, Cu4Ti, Cu3Ti2, Cu4Ti3, CuTi, CuTi2, CuTi3, CuDy, Cu2Dy, and Cu5Dy was confirmed. The controversial phase of CuTi3 was found in this work. The temperature range of Cu7Dy was determined to be from 1112 to 1183 K. The phase relations at 973 K are governed by ten ternary phase regions, 21 binary phase regions, and 12 single-phase regions. The solid solubility of Cu in Dy is undetectable. None of the other phase in this system reveals a remarkable homogeneity range at 973 K.

Suppose that $k_0\geq 3.5\times 10^6$ and $\mathcal{H}=\{h_1,\ldots,h_{k_0}\}$ is admissible. Then, for any $m\geq 1$, the set $\{m(h_j-h_i):\, h_i<h_j\}$ contains at least one Polignac number.

The 2010 World Exposition in Shanghai China (Expo) was the largest mass gathering in world history, attracting a record 72 million visitors. More than 190 countries participated in the Expo, along with more than 50 international organizations. The 2010 Expo was six months in duration (May 1 through October 30, 2010), and the size of the venue site comprised 5.28 square kilometers. Great challenges were imposed on the public health system in Shanghai due to the high number and density of visitors, long duration of the event, and other risk factors such as high temperatures, typhoon, etc.

As the major metropolitan public health agency in Shanghai, the Shanghai Municipal Center for Disease Control and Prevention (SCDC) implemented a series of actions in preparing for, and responding to, the potential health impact of the world's largest mass gathering to date, which included partnerships for capacity building, enhancement of internal organizational structure, risk assessment, strengthened surveillance, disaster planning and exercises, laboratory management, vaccination campaign, health education, health intervention, risk communication and mass media surveillance, and technical support for health inspection. The clear-cut organizational structures and job responsibilities, as well as comprehensive operational and scientific preparations, were key elements to ensure the success of the 2010 World Exposition.

YiH, Zheng'anY, FanW, XiangG, ChenD, YongchaoH, XiaodongS, HaoP, MahanyM, KeimM. Public Health Preparedness for the World's Largest Mass Gathering: 2010 World Exposition in Shanghai, China. Prehosp Disaster Med. 2012;27(6):1-6.

For $k\geq 2$ and $r\geq 1$, we prove that the number of odd $k$-perfect numbers with $r$ distinct prime factors is at most $4^{r^2}(k-1)^{2r^2+3}$.

We report that the high crystalline and high efficiency green emission semipolar {101̅1} InGaN/GaN multiple quantum wells (MQWs) grown on the {101̅1} facets of GaN nanopyramid arrays by selective area epitaxy. Clear and sharp interfaces of the semipolar {101̅1} InGaN/GaN MQWs was observed by transmission electron microscopy images. As comparing with (0001) MQWs, the internal electric field of {101̅1} MQWs was remarkably reduced from 1.7 MV/cm to 0.5 MV/cm, and the room temperature (RT) internal quantum efficiency (IQE) at green emission was enhanced by about 80%. This greatly enhancement of IQE is due to suppress the polarization effect in the {101̅1} MQWs which shorten the radiative recombination to compete with nonradiative recombination at RT. These results evince that the {101̅1} planes are promising for solving the efficiency green gap of III-nitride light emitters.

Flat-plate boundary layer transition induced by the wake vortex of a two-dimensional circular cylinder is experimentally investigated. Combined visualization and velocity measurements show a different transition route from the Klebanoff mode in free-stream turbulence-induced transition. This transition scenario is mainly characterized as: (i) generation of secondary transverse vortical structures near the flat plate surface in response to the von Kármán vortex street of the cylinder; (ii) formation of hairpin vortices due to the secondary instability of secondary vortical structures; (iii) growth of hairpins which is accelerated by wake-vortex induction; (iv) formation of hairpin packets and the associated streaky structures. Detailed investigation shows that during transition the evolution dynamics and self-sustaining mechanisms of hairpins, hairpin packets and streaks are consistent with those in a turbulent boundary layer. The wake vortex mainly plays the role of generating and destabilizing secondary transverse vortices. After that, the internal mechanisms become dominant and lead to the setting up of a self-sustained turbulent boundary layer.