Correct order on some certain weighted representation functions

Let $\mathbb{N}$ be the set of all nonnegative integers. For any positive integer $k$ and any subset $A$ of nonnegative integers, let $r_{1,k}(A,n)$ be the number of solutions $(a_1,a_2)$ to the equation $n=a_1+ka_2$. In 2016, Qu proved that $$\liminf_{n\rightarrow\infty}r_{1,k}(A,n)=\infty$$ providing that $r_{1,k}(A,n)=r_{1,k}(\mathbb{N}\setminus A,n)$ for all sufficiently large integers, which answered affirmatively a 2012 problem of Yang and Chen. In a very recent article, another Chen (the first named author) slightly improved Qu's result and obtained that $$\liminf_{n\rightarrow\infty}\frac{r_{1,k}(A,n)}{\log n}>0.$$ In this note, we further improve the lower bound on $r_{1,k}(A,n)$ by showing that $$\liminf_{n\rightarrow\infty}\frac{r_{1,k}(A,n)}{n}>0.$$ Our bound reflects the correct order of magnitude of the representation function $r_{1,k}(A,n)$ under the above restrictions due to the trivial fact that $r_{1,k}(A,n)\le n/k.

A Contamination Sensor Based on an Array of Microfibers with Nanoscale-Structured Film

A contamination sensor based on an array of microfibers with nanoscale-structured film using evanescent field is proposed and demonstrated theoretically and experimentally. When the molecular contaminants deposit on the nanoscale-structured film, the refractive index of the film will change and the additional loss will be produced due to the disturbance of evanescent field. The possibility of the sensor is demonstrated theoretically by using three-dimensional finite-difference time domain (3D-FDTD). The corresponding experiments have also been carried out in order to demonstrate the theoretical results. Microfibers are fabricated by using hydrogen-oxygen flame-heated scanning fiber drawing method and the nanoscale-structured film coated on the surface of microfibers is deposited by using dip coating process. Then an array of microfibers is assembled to demonstrate the feasibility of the device. The experimental results show that contaminants detection with the device can agree well with the results measured by the laser-scattering particle counter, which demonstrates the feasibility of the new type of contaminant sensor. The device can be used to monitor contaminants on-line in the high-power laser system

Laser-Induced Damage Initiation and Growth of Optical Materials

The lifetime of optical components is determined by the combination of laser-induced damage initiation probability and damage propagation rate during subsequent laser shots. This paper reviews both theoretical and experimental investigations on laser-induced damage initiation and growth at the surface of optics. The damage mechanism is generally considered as thermal absorption and electron avalanche, which play dominant roles for the different laser pulse durations. The typical damage morphology in the surface of components observed in experiments is also closely related to the damage mechanism. The damage crater in thermal absorption process, which can be estimated by thermal diffusion model, is typical distortion, melting, and ablation debris often with an elevated rim caused by melted material flow and resolidification. However, damage initiated by electron avalanche is often accompanied by generation of plasma, crush, and fracture, which can be explained by thermal explosion model. Damage growth at rear surface of components is extremely severe which can be explained by several models, such as fireball growth, impact crater, brittle fracture, and electric field enhancement. All the physical effects are not independent but mutually coupling. Developing theoretical models of multiphysics coupling are an important trend for future theoretical research. Meanwhile, more attention should be paid to integrated analysis both in theory and experiment

The Three Rivers Source Region Alpine Grassland Ecosystem Was a Weak Carbon Sink Based on BEPS Model Analysis

The Three Rivers Source Region (TRSR) is a natural habitat for rare animals and a genetic treasure trove of plateau organisms. It is an important eco-safety barrier in China and even Asia, and a priority of China’s to promote ecological advancement. Precisely assessing the dynamics and mechanisms of alpine grassland ecosystem carbon budgets is beneficial for quantifying the response to climate change on a regional scale. The spatial distribution and dynamic changes in carbon fluxes in the TRSR from 1985 to 2018 were analyzed by the Theil–Sen + Mann–Kendall and ensemble empirical mode decomposition (EEMD) methods, and multiple linear regression was used to quantify the contribution of meteorological elements to the carbon flux trends. The results indicated that (1) the alpine grassland ecosystem was a weak carbon sink. The multiyear mean gross primary production (GPP) and net ecosystem production (NEP) in the TRSR were 147.86 and 11.27 g C/m2/yr, respectively. The distribution of carbon fluxes progressively decreased from east to west. (2) The carbon fluxes of the alpine grassland ecosystem were dominated by a monotonically increasing trend, with increasing rates of GPP and NEP of 1.31 and 0.40 g C/m2/yr, respectively. A total of 48.60% of the alpine grassland showed a significant increase in NEP, whereas only 0.21% showed a significant decrease during the research term. (3) The alpine meadow sequestered carbon better than the alpine steppe did and accounted for more than 60% of the regional carbon sink. (4) In a correlation analysis between NEP and temperature, precipitation and solar radiation, the positive correlation accounted for 89.67%, 90.51%, and 21.16% of the TRSR, respectively. Rising temperatures and increased precipitation were the main drivers contributing to the increase in NEP. Research on carbon budget variability and mechanisms can help guide preservation zoning initiatives in national parks

Sur les plus grands facteurs premiers d'entiers consécutifs

Denote by P + (n) the largest prime factor of an integer n. One of Erdős-Turán's conjectures asserts that the asymptotic density of integers n satisfying P + (n) < P + (n + 1) is 1/2. In this paper, we prove that this density is larger than 0.2017, which improves the previous result " 0.1356 " of the second author

The Three Rivers Source Region Alpine Grassland Ecosystem Was a Weak Carbon Sink Based on BEPS Model Analysis

The Three Rivers Source Region (TRSR) is a natural habitat for rare animals and a genetic treasure trove of plateau organisms. It is an important eco-safety barrier in China and even Asia, and a priority of China’s to promote ecological advancement. Precisely assessing the dynamics and mechanisms of alpine grassland ecosystem carbon budgets is beneficial for quantifying the response to climate change on a regional scale. The spatial distribution and dynamic changes in carbon fluxes in the TRSR from 1985 to 2018 were analyzed by the Theil–Sen + Mann–Kendall and ensemble empirical mode decomposition (EEMD) methods, and multiple linear regression was used to quantify the contribution of meteorological elements to the carbon flux trends. The results indicated that (1) the alpine grassland ecosystem was a weak carbon sink. The multiyear mean gross primary production (GPP) and net ecosystem production (NEP) in the TRSR were 147.86 and 11.27 g C/m2/yr, respectively. The distribution of carbon fluxes progressively decreased from east to west. (2) The carbon fluxes of the alpine grassland ecosystem were dominated by a monotonically increasing trend, with increasing rates of GPP and NEP of 1.31 and 0.40 g C/m2/yr, respectively. A total of 48.60% of the alpine grassland showed a significant increase in NEP, whereas only 0.21% showed a significant decrease during the research term. (3) The alpine meadow sequestered carbon better than the alpine steppe did and accounted for more than 60% of the regional carbon sink. (4) In a correlation analysis between NEP and temperature, precipitation and solar radiation, the positive correlation accounted for 89.67%, 90.51%, and 21.16% of the TRSR, respectively. Rising temperatures and increased precipitation were the main drivers contributing to the increase in NEP. Research on carbon budget variability and mechanisms can help guide preservation zoning initiatives in national parks

Design and Test of Peanut Root-Disk Full-Feeding Longitudinal Axial Flow Pod-Picking Device

To improve the pod-picking efficiency of the combine harvester for both peanut seedlings and peanuts, a longitudinal axial flow pod-picking device is designed in this study. The fixation and adjustment modes of the pod-picking rod were determined. The pod-picking roller’s rotational speed, the pod-picking roller’s diameter, the pod-picking roller, the pod-picking roller’s effective rod-picking length, and the screw-feeding stirrer’s critical parameters were determined by theoretical calculation. A combined design of quadratic regression orthogonal rotation was achieved by using Box-Behnken design (BBD) response surface optimization analysis in Design-Expert, with the linear speed of the pod-picking roller, the clearance between the concave screen and the pod-picking roller, and the spacing between the pod-picking rods as the testing factors, and the picking rate and the crushing rate as the indicators. The optimized parameters are as follows: a linear speed of the pod-picking roller of 6.8 m/s, a clearance between the concave screen and the pod-picking roller of 28.5 mm, and a spacing between the pod-picking rods of 18.60 mm. The performances of conventional peanut full-feeding pod-picking devices and the proposed peanut root-disk full-feeding longitudinal axial flow pod-picking device were investigated and compared to clarify the pod-picking performance of the proposed peanut root-disk full-feeding longitudinal axial flow pod-picking device under optimized parameters. The results showed that the picking and crushing rates of the proposed peanut root-disk full-feeding longitudinal axial flow pod-picking device under optimized parameters were 98.93 and 1.62%, respectively, both of which were superior to those of conventional peanut full-feeding pod-picking devices. A pod-picking device matching the combine harvester for peanut seedlings and peanuts was processed under optimized parameters. Field tests revealed that the picking and crushing rates of the proposed harvester were 99.07 and 1.58%, respectively, meeting the industry standards. These findings are instrumental in the further improvement of peanut pod-picking devices

Study on aerosol characteristics of electrostatic minimum quantity lubrication and its turning performance 静电微量润滑气雾特性及其切削加工性能研究

The technology of electrostatic minimum quantity lubrication (EMQL) can not only enhance the depositing rate of lubricant droplets on the cutting area, but also increase their wetting and penetration to the contact interface, which thus improve droplet lubrication and cooling, as well as reduce concentration of the oil mist floating in the cutting environment. As a EMQL cutting system is developed, the effect of charging voltages on the diameter and distribution of lubricant droplets are investigated, and droplet wettability and deposition on the cutting interface are analyzed. The heat transfer capacity of EMQL in steady stage and its machining performance and oil-mist concentration after turning are comparatively studied. By use of tool wear analysis, the lubrication mechanism of EMQL in the cutting process is revealed. Results indicate that as lubricant charged, droplet diameter decrease and its distribution improve with an enhancement in the wettability and deposition. The cutting temperature, oil mist concentration, tool wear and workpiece surface roughness of EMQL are 14%, 8%, 37% and 28% lower than those of the traditional MQL, respectively. When EMQL is used, the improved wettability and reduced droplet diameter allow lubricant droplets to enter and cover the tool-workpiece interface more easily, which would help lubricate and cool the cutting interface, and thus achieve a better cutting performance

Micro/Nanofiber with Hollow Silica Nanoparticles Thin-Film for Airborne Molecular Contaminants Real-Time Sensing

A novel chemical sensing approach detecting airborne molecular contaminants (AMCs) or compounds is demonstrated by using single-mode optical microfibre (OMF) coated with hollow silica nanoparticles (HSNs). The concentration of AMCs, which were volatilized on the surface of the tapered microfibre coated with HSNs, influences the transmission loss of the microfibre. Tapered OMF was fabricated using a high-precision electrically controlled setup, and coatings of HSNs were prepared by meniscus coating method. The transmission loss of three OMFs with different diameters and the same thick coating were tested to determine the relationship between AMC concentrations and transmission loss of coated OMFs. Experimental results showed that the transmission loss increases with increasing concentration of AMCs. The sensitivity for volatile simethicone was 0.0263 dB/mg/m3 obtained by the coated OMF with diameter of 2.5 μm, and the sensitivity values of coated OMF with diameters of 5 μm and 6 μm were 0.0024 and 0.0018 dB/mg/m3, respectively. Thus the proposed coated OMF can be used in enclosed space for AMCs sensing