On Schrödinger-Virasoro type Lie conformal algebras

In this paper, two classes of Schrödinger-Virasoro type Lie conformal algebras TSV(a,b) and TSV(c) which are non-simple are introduced for some a, b, c∈?. Moreover, central extensions, conformal derivations and free conformal modules of rank 1 of TSV(a,b) and TSV(c) are determined.     

Rational curves in CICYs in products of two projective spaces

Let X be the product of two projective spaces and consider the general CICY threefold Y in X with configuration matrix A. We prove the finiteness part of the analogue of the Clemens’ conjecture for such a CICY in low bidegrees. More precisely, we prove that the number of smooth rational curves on Y with low bidegree and with nondegenerate birational projection is at most finite (even in cases in which positive dimensional families of degenerate rational curves are known).     

On the composition subalgebras of Bridgeland’s Hall algebras

Let A be a finite dimensional hereditary algebra over a finite field k and 𝒫 the category consisting of finite dimensional projective (left) A-modules. In this paper, we consider the composition subalgebra of Bridgeland’s Hall algebra of the category 𝒞_m(𝒫) of m-cyclic complexes for any positive integer m≥2 and determine its generating relations.     

Sur les identités polynomiales vérifiées par les algèbres de rétrocroisement

We study the ideal of polynomial identities of a single indeterminate satisfied by all backcrossing algebras. For this we distinguish two categories according to whether or not these algebras satisfy an identity for the plenary powers. For each category, we give the generators for the vector space of identities, a condition for any object belonging to one of these two categories verify a given identity, a necessary and su?cient condition that a polynomial is an identity and we study the existence of an idempotent element. We give a method which brings the search of identities satified by the backcrossing algebras to the solution of linear systems and we illustrate this method by constructing generators of homogeneous and non homogeneous identities of degrees less than 8.     

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。