沿一类平坦曲线的Hilbert变换的有界性

讨论了沿平面平坦曲线的Ｈｉｌｂｅｒｔ变换的有界性。证明了对“凸”组合型曲线这类算子是Ｌｐ（Ｒ２）上的有界算子，其中１＜ｐ＜∞。     

AQUAZUR V型滤池应用刍议

本文主要介绍了ＡｑｕａｚｕｒＶ型滤池的构造、工艺流程及几个技术问题。该滤池在国内应用的情况，可供科研、设计及管理人员参考。     

集值映射的一致有界定理

建立了一类集值映射的一致有界定理，进而讨论了这类集值映射的连续性与有界性之间的联系，使得单值映射的相应结果作为本文的一种特例。     

制备致密UO_2微球的全胶凝方法

为了制备高温气冷反应堆用燃料芯核,致密UO_2微球,研究了一种新的溶胶-凝胶工艺.该流程具有经典的溶胶-凝胶工艺的优点,但克服了它们的缺点.已经知道,合理的配方设计和良好的干燥条件是克服破裂困难的关键因素.影响胶滴尺寸及其分布的控制因素是:极限流量、几何因子、物理因子和振动因子.微球干燥和焙烧参数的优化是依据热分析曲线来确定的.用SEM方法观察了热处理过程中的微观结构的变化.观察了真空烧结的重结晶现象.观察了UO_2·nH_2O的化学气相沉积.结果表明:晶粒大小随烧结温度增加而增加.本工艺适合于制备500μm直径的微球.其产率为90%.球度优于1.08.球径范围为470-530μm.1400-1450℃真空条件下的烧结密度范围为10.71-10.76 g/cm~3.     

关于一致性区域

对R~n中区域D引入了一种特征参数α_D.当且仅当α_D<∞时D是一致性区域。当D是球或半空间时α_D=1。本文证明在R~n中区域的可分解性与一致性是等价的,还讨论了有关一致性区域和分解域的一些问题。     

平面生态系统的研究现状与Brauer定理的否定

本文概要介绍了生物数学领域中平面生态系统定性分析的研究现状,并通过反例对美国学者Brauer教授在1978年提出的一般平面生态系统的有界性定理予以否定,提出重建有界性定理的新课题。     

The Interaction in Electrolyte Additives Accelerates Ion Transport to Achieve High-Energy Non-Aqueous Lithium Metal Batteries

Electrolyte engineering is a feasible strategy to realize high energy density lithium metal batteries. However, stabilizing both lithium metal anodes and nickel-rich layered cathodes is extremely challenging. To break through this bottleneck, a dual-additives electrolyte containing fluoroethylene carbonate (10 vol.%) and 1-methoxy-2-propylamine (1 vol.%) in conventional LiPF₆-containing carbonate-based electrolyte is reported. The two additives can polymerize and thus generate dense and uniform LiF and Li₃N-containing interphases on both electrodes’ surfaces. Such robust ionic conductive interphases not only prevent lithium dendrite formation in lithium metal anode but also suppress stress-corrosion cracking and phase transformation in nickel-rich layered cathode. The advanced electrolyte enables Li||LiNi_0.8Co_0.1Mn_0.1O₂ stably cycle for 80 cycles at 60 mA g⁻¹ with a specific discharge capacity retention of 91.2% under harsh conditions.     

Response surface method based on uniform design and weighted least squares for non-probabilistic reliability analysis

The non-probabilistic reliability theory is a promising methodology for implementing structural reliability analysis in case of scarce statistical data. One of the main obstacles to implement non-probabilistic reliability analysis is the implication of the limit state function (LSF) for complex structures. This paper aims to establish a surrogate model of the LSF with higher simulation precision, and whereby proposes a response surface method based on the combination of uniform design (UD) and weighted least squares (WLS). At first, the UD method is selected as the sampling method of interval variables to realize the uniform space-filling of the initial samples, and the sample set is updated by gradually adding the approximate optimal points to increase the sampling density of critical domain. Then, the WLS method is applied to improve the precision of the response surface by adjusting the importance of samples to the function fitting. Finally, a method of constructing sample weights is developed. Two examples are applied to validate the feasibility and efficiency of the proposed method. Results show that the proposed method is effective for non-probabilistic reliability analysis of complex structures owning to high computational precision and low computational cost in both numerical and case study.     

中低频集中质量悬臂式簧片仪基频分析方法研究

簧片仪是一种中低频冲击响应谱测量装置,设计时可将其简化为端部附带集中质量的悬臂梁。簧片仪的振型方程中存在超越函数,对于等截面簧片仪来说,可使用二分法等数值方法求解,计算量较大,该方法不适用于复杂截面簧片仪基频设计。首先利用悬臂梁自由端受集中力的挠度公式,推导出其等效刚度等效单自由度的弹簧振子系统,利用弹簧振子相关频率公式解决求解集中质量等截面悬臂梁的基频问题,该方法与振型方程求解的基频对比,发现在10 Hz以下的中低频区域,可以很好的保证等截面悬臂梁的基频精度,大于10 Hz的中频段,误差随频率的升高而迅速增大。接下来,通过Mohr积分的方法,推导出等强度集中质量悬臂梁自由端的最大挠度,并给出其基频的设计公式,该方法与试验进行对比,发现误差与等截面悬臂梁有相同趋势,因此利用瑞利能量法修正设计公式中的质量参数,修正后与实验误差在5%左右。经理论与试验验证,所提出的簧片仪设计方法简单可行、计算结果可信。     

Scheduling on uniform parallel machines with periodic unavailability constraints

Scheduling problems under unavailability constraints has become a popular research topic in the last few years. Despite it’s important application in the real world, the uniform parallel machine scheduling problem was the least studied due to its complexity. In this paper, we investigated the uniform parallel machine scheduling problem under deterministic availability constraints. Each machine is subject to one unavailability period. Different versions of the problem regarding the type of jobs (identical and non-identical) and the performance measures (the total completion times and the makespan) were studied. For the case of identical jobs and for both performance measures, we developed linear programming models and optimal algorithms to provide a solution to the problem. For the case of non-identical jobs, we proved that the problem is NP-hard and propose a quadratic program. Because, this later cannot solve problems with very large number of jobs and machines, a heuristic was developed to find near optimal solutions to the problem especially with very large number of jobs and machines. The computational results showed that the heuristic’s performance is very high regardless the dimensions of problem instances.