LP relaxations for a class of linear semi-infinite programming problems

In this paper, we consider a subclass of linear semi-infinite programming problems whose constraint functions are polynomials in parameters and index sets are polyhedra. Based on Handelman’s representation of positive polynomials on a polyhedron, we propose two hierarchies of LP relaxations of the considered problem which respectively provide two sequences of upper and lower bounds of the optimum. These bounds converge to the optimum under some mild assumptions. Sparsity in the LP relaxations is explored for saving computational time and avoiding numerical ill behaviors.     

Cereusitin A,a cyclic tetrapeptide from a Bacillus cereus strain isolated from the soft coral Antillogorgia (syn. Pseudopterogorgia) elisabethae

Two new compounds, cereusitin A (1), the tetrapeptide cyclo-(L-phenylalanyl-trans-4-hydroxy-L-prolyl-L-leucyl-trans-4-hydroxy-L-proline and 4-(R)-hydroxysattabacin (2), along with the methyl, isopropyl, and propyl esters of p-hydroxybenzoic acid (3–5) were isolated from the organic extracts of the culture of the B. cereus RKHC-09 strain in two culture media (MOLP and B1), recovered from the sea fan Antillogorgia elisabethae (syn. Pseudopterogorgia elisabethae). Cereusitin A (1) showed mild antifungal activity against Colletotrichum gloeosporoides C26 (yam pathogen) but was inactive against Fusarium oxysporum f.sp. dianthi (carnation pathogen). The methyl and propyl esters of p-hydroxybenzoic acid (4 and 5) showed antimicrobial activity against S. aureus ATCC 33591 and S. cerevisiae, with an MIC of 2 μM.     

A short synthesis of 3-enoyltetramic acids employing a new acyl ylide conjugate of Meldrum’s acid

2,2-Dimethyl-5-(triphenylphosphoranylidene)acetyl-1,3-dioxan-4,6-dione (3) is a new activated β-ketoacyl equivalent, readily prepared in quantitative yield by reaction of Meldrum’s acid with the stable ylide Ph₃PCCO. Its reaction with α-amino esters affords the corresponding N-(β-ketoacyl)amino ester ylides which, when treated with aldehydes and KOtBu, undergo a simultaneous Wittig olefination cum Dieckmann cyclisation to yield the respective 3-enoyltetramic acids.     

N2O and NO emissions during wastewater denitrification step: Influence of temperature on the biological process

The denitrification process occurring in wastewater treatment plants (WWTPs) is responsible for nitrous oxide (N₂O) and nitric oxide (NO) emissions. These compounds indirectly lead to the global warming. In this study, we investigated the impact of the temperature on N₂O and NO emissions. Experiments were achieved at PH 7 in a batch reactor with acetate as the carbon source. The nitrogen source was nitrates (NO₃⁻) and the COD/N ratio was set to three. Results showed that NO and N₂O emissions increased when the temperature decreased. NO emissions appeared only at 10 °C and 5 °C, with respectively 8% and 18% of the total denitrified nitrogen. N₂O emissions increased from 13 to 40 then 82% of the total denitrified nitrogen, respectively at 20, 10 and 5 °C. Several hypotheses were suggested to explain these results: a general enzymatic slow down, enzymatic inhibitions, electron donor competition between the different enzymes and metabolic pathway alterations.     

快速显色法定性检测氨纶纺织品中4,4’-二氨基二苯甲烷

建立显色法测定氨纶纺织品中4,4’-二氨基二苯甲烷的方法。样品经二氯甲烷提取后,利用芳香胺重氮化产物与盐酸萘乙二胺发生偶合反应生成具有特征颜色的偶氮染料这一显色原理进行测定。方法检出限为5.0mg/kg。该方法显色灵敏,操作简便,快速,无需色谱仪器等大型设备。该方法可用于排除纺织品中含有4,4’-二氨基二苯甲烷。     

Defining the characteristics of spherical Janus particles by investigating the behavior of their corresponding particles at the oil/water interface in a Pickering emulsion

In this study, a new analytical/experimental method is proposed in order to investigate the adsorption of different-sized spherical silica particles at the oil/water interface in a Pickering emulsion system as a well-known method to produce Janus particles. Accordingly, the characteristic of the produced silica Janus particles was defined based on their penetration depth into dispersed oil droplets. To ensure the accuracy of the method, the penetration depth of silica particles was also measured using field emission scanning electron microscopy images of solidified oil droplets covered with particles. The results revealed that the penetration depth increases with the size of the particles.     

激发态光物理的拓扑控制:对(N,N'-二正癸基)氨基苯甲腈的簇集与光诱导分子内电荷转移

在水-二氧六环混合介质中,对二正癸基氨基苯甲腈(DDABN)分子,在水的体积分数超过0.5后,发生簇集并可观察到双重荧光发射且长波长发射带位置与在纯二氧六环中相近。该发射带被证实系分子内扭转电荷转移(TICT)带。吸收光谱表明DDABN簇集体为J-型。     

Some extensions of the initial value problem for second order evolution equations

The initial problem for second order linear evolution equation systems is discussed by using the contraction semigroup theory. A kind of initial value problem for second order is also discussed with variable coefficients for evolution equations by using the analytical semigroup theory, and is unified with the solutions of the initial value problem for this class of equations and those of first order temporally inhomogeneous evolution equations. This is an important class of equations in mathematical mechanics.