Singular solutions for the constant Q-curvature problem

This paper is devoted to the construction of weak solutions to the singular constant Q-curvature problem. We build on several tools developed in the last years. This is the first construction of singular metrics on closed manifolds of sufficiently large dimension with constant (positive) Q-curvature.     

Formal proofs of operator identities by a single formal computation

A formal computation proving a new operator identity from known ones is, in principle, restricted by domains and codomains of linear operators involved, since not any two operators can be added or composed. Algebraically, identities can be modelled by noncommutative polynomials and such a formal computation proves that the polynomial corresponding to the new identity lies in the ideal generated by the polynomials corresponding to the known identities. In order to prove an operator identity, however, just proving membership of the polynomial in the ideal is not enough, since the ring of noncommutative polynomials ignores domains and codomains. We show that it suffices to additionally verify compatibility of this polynomial and of the generators of the ideal with the labelled quiver that encodes which polynomials can be realized as linear operators. Then, for every consistent representation of such a quiver in a linear category, there exists a computation in the category that proves the corresponding instance of the identity. Moreover, by assigning the same label to several edges of the quiver, the algebraic framework developed allows to model different versions of an operator by the same indeterminate in the noncommutative polynomials.     

Well-posedness of two pseudo-parabolic problems for electrical conduction in heterogeneous media

We prove a well-posedness result for two pseudo-parabolic problems, which can be seen as two models for the same electrical conduction phenomenon in heterogeneous media, neglecting the magnetic field. One of the problems is the concentration limit of the other one, when the thickness of the dielectric inclusions goes to zero. The concentrated problem involves a transmission condition through interfaces, which is mediated by a suitable Laplace-Beltrami type equation.     

基于TOPSIS模型的机场网络节点重要度评估

在机场网络中单个机场节点的失效往往会对其他的节点产生影响,特别是关键节点的失效会波及整个网络.准确客观的识别重要节点机场关乎整个机场网络的安全运营.本文分析了机场网络拓扑特性中的度、集聚系数和接近度指标,考虑了机场旅客吞吐量和所在城市人口等交通经济特性指标,使用熵权法确定权重的基础上,应用TOPSIS法构建综合评价体系模型,最后以华东地区机场网络为例进行节点重要度排序.结果表明与单一指标的评估结果相比,该方法更加全面客观的确定不同属性指标的权重,避免了不同指标取值的差异性,使评价更加全面,更符合机场网络实际运营情况.     

p-Adic函数空间上Hardy型算子的多线性交换子估计

在p-adic域上研究分数次Hardy型算子与CMO(Q_p~n)函数生成的多线性交换子,建立了交换子在Lebesgue空间和Herz空间上的有界性.对Hardy算子的多线性交换子也得到了相应的结果.     

Modifying the physicochemical properties,solubility and foaming capacity of milk proteins by ultrasound-assisted alkaline pH-shifting treatment

This study investigated the effects of different treatment of alkaline pH-shifting on milk protein concentrate (MPC), micellar casein concentrate (MCC) and whey protein isolate (WPI) assisted by the same ultrasound conditions, including changes in the physicochemical properties, solubility and foaming capacity. The solubility of milk proteins had a significant increase with gradual enhancement of ultrasound-assisted alkaline pH-shifting (p < 0.05), especially for MCC up to 99.50 %. Also, treatment made a significant decline in the particle size of MPC and MCC, as well as the turbidity of the proteins (p < 0.05). The foaming capacity of MPC, MCC, and WPI was all improved, especially at pH 11, and at this pH, the milk protein also showed the highest surface hydrophobicity. The best foaming capacity at pH 11 was the result of the combined effect of particle size, potential, protein conformation, solubility, and surface hydrophobicity. In conclusion, ultrasound-assisted pH-shifting treatment was found to be effective in improving the physicochemical properties and solubility and foaming capacity of milk proteins, especially MCC, with promising application prospect in food industry.     

Cyclohexane‐1,3‐dione as a derivatizing agent for the analysis of aldehydes by micelar electrokinetic chromatography with diode array detection

Aldehydes are important compounds in a large number of samples, especially food and beverages. In this work, for the first time, cyclohexane‐1,3‐dione (CHD) was used as a derivatizing reagent aiming aldehyde (formaldehyde, acetaldehyde, propionaldehyde, and valeraldehyde) analysis by MEKC‐DAD. The optimized separation of the derivates was performed using a voltage program (+20 kV, 0–15 min.; +23 kV, 15–17 min.) at a temperature of 26°C, and using as the running buffer a mixture containing 100 mmol/L of sodium dodecyl sulfate and 29 mmol/L of sodium tetraborate at pH 9.2, with maximum absorbance at 260 nm. CHD was compared with two other derivatizing agents: 3‐methyl‐2‐benzothiazolinone hydrazone and phenylhydrazine‐4‐sulfonic acid. The CHD‐aldehyde derivatives were also characterized by LC‐MS. The calibration curves for all aldehydes had r² above 0.999 and LODs ranged from 0.01 to 0.7 mg/L. The optimized methodology was applied in sugar cane brandy (cachaça) samples successfully. CHD showed to be an alternative derivatization reagent due to its stability, aqueous solubility, high selectivity and sensitivity, reduced impurities, and simple preparation steps.