The maximum multiplicity of the largest k-th eigenvalue in a matrix whose graph is acyclic or unicyclic

Given a graph $G$ we are interested in studying the symmetric matrices associated to $G$ with a fixed number of negative eigenvalues. For this class of matrices we focus on the maximum possible nullity. For trees this parameter has already been studied and plenty of applications are known. In this work we derive a formula for the maximum nullity and completely describe its behavior as a function of the number of negative eigenvalues. In addition, we also carefully describe the matrices associated with trees that attain this maximum nullity. The analysis is then extended to the more general class of unicyclic graphs. Further our work is applied to re-describing all possible partial inertias associated with trees, and is employed to study an instance of the inverse eigenvalue problem for certain trees.     

Effect of matrices and additives on phosphorylated and ketodeoxyoctonic acid lipids A analysis by matrix‐assisted laser desorption ionization‐mass spectrometry

Lipid A is a major compound of the outer membrane of gram‐negative bacteria and is a key factor of bacterial virulence. As lipid A's structure differs among bacterial species and varies between strains of the same species, knowing its modifications is essential to understand its implications in the infectious process. To analyze these lipids, matrix‐assisted laser desorption ionization‐mass spectrometry (MALDI‐MS) is a well‐suited method that is fast and efficient. However, there are limitations with the matrix and additives used, such as the suppression of signal or prompt fragmentations that could give a false overview of lipid A composition in biological samples. For a comprehensive analysis of the entire lipid A species present in a sample, we tested 16 matrices and 11 additives on two commercial lipids A. The first commercial one contains single phosphorylation group, and the second contains two phosphorylation and two ketodeoxyoctonic acid (KDO) groups. The lipid A containing KDO groups was essentially detected by the 3‐hydroxypicolinic acid (3‐HPA) matrix, whereas the monophosphorylated lipid A could be detected by 13 matrices out of the 16. We also demonstrated that the signal of diphosphorylated lipid A can be enhanced with the use of additives in the matrix. Our study indicated that the best conditions to obtain a clear signal of both lipids A without prompt fragmentation was the use of 3‐HPA with 10mM trifluoroacetic acid (TFA).     

New strategy for reversal tolerant anode for automotive polymer electrolyte fuel cell

New approach for the reversal tolerant anode for polymer electrolyte membrane fuel cell is suggested by using the multifunctional IrRu alloy catalyst having concurrent superior activities towards hydrogen oxidation reaction and oxygen evolution reaction to mitigate the degradation of anode under the fuel starvation condition.     

小实验大道理 ——从热缩片小制品DIY看高分子材料的熵致形变

A little experiment concerning the pyrocondensation materials was introduced in this paper. The aim was to help the public understand the principles of entropy induced deformation of polymer materials.     

Solvable Model of a Generic Driven Mixture of Trapped Bose–Einstein Condensates and Properties of a Many-Boson Floquet State at the Limit of an Infinite Number of Particles

A solvable model of a periodically driven trapped mixture of Bose–Einstein condensates, consisting of N1 interacting bosons of mass m1 driven by a force of amplitude fL,1 and N2 interacting bosons of mass m2 driven by a force of amplitude fL,2, is presented. The model generalizes the harmonic-interaction model for mixtures to the time-dependent domain. The resulting many-particle ground Floquet wavefunction and quasienergy, as well as the time-dependent densities and reduced density matrices, are prescribed explicitly and analyzed at the many-body and mean-field levels of theory for finite systems and at the limit of an infinite number of particles. We prove that the time-dependent densities per particle are given at the limit of an infinite number of particles by their respective mean-field quantities, and that the time-dependent reduced one-particle and two-particle density matrices per particle of the driven mixture are 100% condensed. Interestingly, the quasienergy per particle does not coincide with the mean-field value at this limit, unless the relative center-of-mass coordinate of the two Bose–Einstein condensates is not activated by the driving forces fL,1 and fL,2. As an application, we investigate the imprinting of angular momentum and its fluctuations when steering a Bose–Einstein condensate by an interacting bosonic impurity and the resulting modes of rotations. Whereas the expectation values per particle of the angular-momentum operator for the many-body and mean-field solutions coincide at the limit of an infinite number of particles, the respective fluctuations can differ substantially. The results are analyzed in terms of the transformation properties of the angular-momentum operator under translations and boosts, and as a function of the interactions between the particles. Implications are briefly discussed.     

不断向自然与金属冶金学习的高分子加工

总结了高分子材料加工的发展趋势及发展历程,并指出过去很多加工新技术的出现都得益于从自然现象及其他材料行业中获得很好的借鉴,如从蜘蛛吐丝发展出溶液纺丝成型、从玻璃吹制发展出吹塑成型、从金属锻造发展出压延成型及固相拉拔成型等;随后针对生物基可生物降解的立构复合型聚乳酸难以采用传统熔融加工方法成型的问题,借鉴金属粉末冶金加工的思路,提出了一种通过低温烧结制备高性能立构复合型聚乳酸制品的新方法.通过这种加工方法不仅可以有效解决立构复合型聚乳酸在熔融加工过程中熔体稳定性差、易降解的问题,而且可以制得耐热性好、光学透明度高、耐水解降解性佳、综合力学性能优异的高性能聚乳酸制品.