The pos/neg-weighted 2-medians in balanced trees with subtree-shaped customers

This paper deals with the pos/neg-weighted p-median problem on tree graphs where all customers are modeled as subtrees. We present a polynomial algorithm for the 2-median problem on an arbitrary tree. Then we improve the time complexity to O(n log n) for the problem on a balanced tree, where n is the number of the vertices in the tree.     

On the Semicircular Law of Large-Dimensional Random Quaternion Matrices

It is well known that the Gaussian symplectic ensemble is defined on the space of \(n\times n\) quaternion self-dual Hermitian matrices with Gaussian random elements. There is a huge body of literature regarding this kind of matrices based on the exact known form of the density function of the eigenvalues (see Erd?s in Russ Math Surv 66(3):507–626, 2011; Erd?s in Probab Theory Relat Fields 154(1–2):341–407, 2012; Erd?s et al. in Adv Math 229(3):1435–1515, 2012; Knowles and Yin in Probab Theory Relat Fields, 155(3–4):543–582, 2013; Tao and Vu in Acta Math 206(1):127–204, 2011; Tao and Vu in Electron J Probab 16(77):2104–2121, 2011). Due to the fact that multiplication of quaternions is not commutative, few works about large-dimensional quaternion self-dual Hermitian matrices are seen without normality assumptions. As in natural, we shall get more universal results by removing the Gaussian condition. For the first step, in this paper, we prove that the empirical spectral distribution of the common quaternion self-dual Hermitian matrices tends to the semicircular law. The main tool to establish the universal result is given as a lemma in this paper as well.     

Escape rate of Brownian particles from a metastable potential well under time derivative Ornstein-Uhlenbeck noise

We investigate the escape rate of Brownian particles that move in a cubic metastablepotential subjected to an internal time derivative Ornstein-Uhlenbeck noise (DOUN). Thisnoise can induce the ballistic diffusion of force-free Brownian particles. Some newfeatures are found. The escape rate for DOUN shows qualitative different dependence onpotential well width compared with OUN which induces normal diffusion. As the potentialbarrier height decreases, the escape rate of DOUN deviates from Arrhenius law considerablyearlier than that of Ornstein-Uhlenbeck noise (OUN). The Brownian particles escape fasterunder DOUN than that under OUN. A quasi-periodic oscillation occurs in transient state. Asolvable case is presented to demonstrate the significant cancellation behavior in thebarrier region that governs most of these phenomena. The physical mechanism of thefindings can be clarified by the noise features. These characteristics should be commonfor internal noises that induce superdiffusion, especially the ballistic diffusion.     

一种多频局域共振型声子晶体板的低频带隙与减振特性

设计了一种多频局域共振型声子晶体板结构, 该结构由一薄板上附加周期性排列的多个双悬臂梁式子结构而构成. 由于多个双悬臂梁式子结构的低频振动与薄板振动的相互耦合作用, 这种局域共振型板结构可产生多个低频弯曲波带隙(禁带); 带隙频率范围内的板弯曲波会被禁止传播, 利用带隙可以实现对薄板的多个目标频率处低频减振. 本文针对这种局域共振型板结构进行了简化, 并基于平面波展开法建立了其弯曲波带隙计算理论模型; 基于该模型, 结合具体算例进行了带隙特性理论分析. 设计、制备了一种存在两个低频弯曲波带隙的局域共振型板结构样件, 通过激光扫描测振仪测试证实该结构存在两个低频带隙, 在带隙频率范围的板弯曲振动被显著衰减.     

超短超强激光脉冲辐照超薄碳膜电离状态研究

为了进一步理解极端条件下物质的电离特性, 特别是超短超强激光脉冲辐照超薄靶时等离子体的形成与分布, 本文以超薄碳膜为例, 细致研究了超短超强激光脉冲辐照下原子的离化过程. 分析和比较了强激光场直接作用电离和靶内静电场电离等两种场致电离形式, 在碰撞电离可以忽略的情况下, 发现更多的电离份额是来自靶内静电场的电离方式. 研究了激光脉冲强度对电离的影响, 发现激光脉冲强度越强, 电离速度越快, 产生的高价态离子所占比例也越高.当激光强度为1×10²⁰ W/cm²时, 尽管该强度高于电离生成C⁺⁶所需要的激光强度阈值, 但该激光脉冲并不能将整个靶电离成C⁺⁶离子, 对此本文进行了详细的分析. 在研究激光脉冲宽度的影响时, 发现激光脉宽越小, 电离速度越快, 但越小的激光脉冲电离获得的高价态离子越少.     

Polymeric micelles formed by splitting of micellar cluster

Polystyrene-b-poly(acrylic acid) (PS-b-PAA) diblock copolymer chains form aggregates with bimodal distribution in toluene. The introduction of polystyrene-b-poly(ethylene oxide) (PS-b-PEO) chains leads to the formation of mixed micellar cluster due to the hydrogen-bonding complexation between PAA and PEO. By using laser light scattering and transmission electron microscopy, we have investigated the structural evolution of the mixed micellar cluster. As the standing time increases, the cluster split into regular complex micelles composed of PS-b-PAA and PS-b-PEO chains. Our results reveal that the hydrogen-bonding complexation between PAA and PEO in the core and the repulsion between PS chains in the corona as a function of the molar ratio (r) of PEO to PAA manipulate the evolution.     

Effect of pressure on the selectivity for the esterification of ethylene glycol with propionic acid in supercritical CO2

The esterification of ethylene glycol with propionic acid was investigated in supercritical CO2 at 50.0 degrees C. The effect of pressure on equilibrium conversion and selectivity of ethylene glycol monopropionate (monoester) and ethylene glycol dipropinonate (diester) was studied systematically. It was shown that the equilibrium conversion and selectivity was nearly independent of pressure as pressure was lower than 9 MPa. At higher pressure, however, the yield and selectivity of the diester increased considerably, while those of the monoester decreased with increasing pressure. The main reason was that reactants and products distributed between the vapor phase and liquid phase at higher pressures. The solvent power of CO2 for the diester is stronger than that for the monoester. More diester molecules in the liquid phase were extracted into the vapor at higher pressures, which shifted equilibrium of the consecutive reversible reactions.     

Identification and analysis of alpha1,6-fucosylated proteins in human normal liver tissues by a target glycoproteomic approach

alpha1,6-Fucose residues within the N-glycan core structures were commonly observed in many glycoproteins. Our previous studies showed that aberrantly alpha1,6-fucosylated glycoproteins might be associated with metastasis of hepatocellular carcinoma (HCC). Little is known about human normal liver tissues (HNLTs) in the literatures. In this study, a target glycoproteomic approach which consists of lectin-affinity chromatography, 2-DE, protein immunoprecipitation and lectin blot, and MALDI-MS/MS, was utilized to screen physiologically alpha1,6-fucosylated glycoproteins. Lens culinaris agglutinin (LCA)-affinity glycoprotein profiles of HNLT were established and analyzed, which allowed identification of 53 proteins by MS analysis, including haptoglobin precursor, alpha-enolase, etc. Gene ontology (GO) annotation proved that these proteins distribute predominately in organelle and play crucial roles in binding and catalytic reactions. The present methodology enabled the identification of all the specific subsets of glycoprotein, and the corresponding data could contribute to the finding of more aberrantly alpha1,6-fucosylated glycoproteins related to liver diseases.