A Hardy–Trudinger–Moser Inequality Involving LpNorm in the Hyperbolic Space

Let B be the unit disc in R~2, H be the completion of C_0∞(B) under the norm■ .By the method of blow-up analysis and an argument of rearrangement with respect to the standard hyperbolic metric ■, we prove that, for any fixed■ ,the supremum■ .This is an analog of early results of Lu–Yang(Discrete Contin. Dyn. Syst., 2009) and Yang(Trans.Amer. Math. Soc., 2007), and extends those of Wang–Ye(Adv. Math., 2012) and Yang–Zhu(Ann.Global Anal. Geom., 2016).     

On Current Developments in Partial Differential Equations

The first part of this article is an overview on some recent major developments in the field of analysis and partial different equations.It is a brief presentation given by the author at a round table discussion.The second part is a supplement of various details provided by several outstanding researchers on subjects.     

Asymptotic analysis for multi-objective sequential stochastic assignment problems

ABSTRACT

We provide an asymptotic analysis of multi-objective sequential stochastic assignment problems (MOSSAP). In MOSSAP, a fixed number of tasks arrive sequentially, with an n-dimensional value vector revealed upon arrival. Each task is assigned to one of a group of known workers immediately upon arrival, with the reward given by an n-dimensional product-form vector. The objective is to maximize each component of the expected reward vector. We provide expressions for the asymptotic expected reward per task for each component of the reward vector and compare the convergence rates for three classes of Pareto optimal policies.     

宽体液腔Janus-Helmholtz换能器

本文使用有限元方法对宽体液腔Janus-Helmholtz(JH)换能器进行了仿真分析,得出了壳体宽度拓展增量对JH换能器工作性能的影响规律。使用三维建模的方式,分析了连接部分对换能器性能的影响及宽体壳体的的模态,证明了三维建模的必要性。依据仿真优化结构设计了一款宽体液腔JH换能器并进行了湖上测试。最终测试结果与仿真结果有很好的一致性,相较直筒JH换能器其谐振频率降低300Hz,发射电压响应最高可达144dB。     

碳纳米管的可控长度拾取及导电性分析

拾取指定长度的半导体性碳纳米管对大规模制造碳纳米管场效应管具有重要意义.本文提出了一种利用原子力显微镜探针和钨针对碳纳米管进行可控长度拾取的方法并进行了碳纳米管导电性分析.在扫描电子显微镜下搭建微纳操作系统,针对切割操作过程中原子力显微镜探针、钨针和碳纳米管的接触情况进行了力学建模和拾取长度误差分析.建立了单根金属性碳纳米管、单根半导体性碳纳米管及碳纳米管束与钨针接触的电路模型,推导了接入不同性质碳纳米管后电路的电流电压特性方程.使用原子力显微镜探针对碳纳米管的空间位姿进行调整,控制钨针对碳纳米管上目标位置进行通电切割,同时获取切割电路中的电流电压数据.实验结果表明,本文提出的方法能够有效控制所拾取碳纳米管的长度,增加碳纳米管与原子力显微镜探针的水平接触长度能够减小碳纳米管形变导致的拾取长度误差,建立的电流电压特性方程能够用于分析碳纳米管的导电性.     

利用反射太赫兹时域强度分布定量检测沙粒中的微量原油

原油污染是海洋生物和环境安全的主要威胁之一,检测近海沙粒中的微量原油对于环境保护和原油勘探有着重要意义.本文采用反射式太赫兹时域波形对近海沙粒中的原油进行定量检测,详细地分析了延迟时间与沙粒中的原油浓度的关系.结果表明,原油浓度与延迟时间呈线性递减关系,反射式太赫兹时域波形是一种具有潜力的污染定量检测方法.     

双向粘弹性节理岩体时域等效分析

以双向粘弹性节理岩体为研究对象,基于一种简单等效假定和自适应算法,并结合有限元方法,得到递推格式的等效本构模型和等效粘弹性场计算模型.通过算例,将等效解与基于ANSYS的非均质解进行比较.从计算精度和效率平衡的角度而言,等效模型的结果是令人满意的.     

Meshing Requirements for Tidal Modeling in the Western North Atlantic

This paper presents an a posteriori approach to unstructured mesh generation via a localized truncation error analysis and applies it to the Western North Atlantic Tidal (WNAT) model domain. The WNAT model domain encompasses the Gulf of Mexico, the Caribbean Sea, and the North Atlantic Ocean east to the 60°W Meridian. Herein, we pay particular attention to the area surrounding the Bahamas.

A bathymetric data set with fine resolution is employed in seven separate linear, harmonic simulations of shallow water tidal flow for seven different tidal-forcing constituents. Each set of simulation results is used to perform a truncation error analysis of a linear, harmonic form of the depth-averaged momentum equations for each of the seven different tidal-forcing frequencies. Truncation error is then driven to a more uniform, domain-wide value by solving for local node spacing requirements. The process is built upon successful research aiming to produce unstructured grids for large-scale domains that can be used in the accurate and efficient modeling of shallow water flow. The methodology described herein can also be transferred to other modeling applications.     

Effect of atmospheric parameters on fine particulate concentration in suburban Shanghai

A study was conducted on the effect of atmospheric parameters,including temperature,wind speed,and relative humidity,on fine particulate mass concentrations measured in Jiading District of Shanghai,China, during the period from January 2009 to January 2010.A sensitivity analysis was applied to investigate the interaction between atmospheric parameters and particulate mass concentration.The experiment revealed that the concentration of particulates increased with particle size from 0.1 to 1.0μm,and decreased with the increase of particle size from 1.0 to 2.5μm.The effects of atmospheric parameters on fine mass concentrations were significantly particle size-dependent.The PM_1.0-2.5 may come from the size increase of smaller particulates after moisture absorption.And the variation of concentrations of PM_0.1-1.0 was mainly attributed to the accumulation of PM_0.1.The ventilation index and dilution index were calculated on the basis of data collected in December 2009.A correlation analysis indicated that there was a significant relation between these two indexes and the particulate concentration by examining the three particle size ranges,0.0-0.1,0.1-1.0,and 1.0-2.5μm.The Spearman correlation coefficients that related the ventilation index to the concentration for the three particle size ranges were -0.45,-0.56 and -0.47, respectively,while the coefficients that related the dilution index to the concentration were -0.36,-0.42 and -0.45,respectively.