Computing residue currents of monomial ideals using comparison formulas

Given a free resolution of an ideal a$\mathfrak{a}$ of holomorphic functions, one can construct a vector-valued residue current R  , which coincides with the classical Coleff–Herrera product if a$\mathfrak{a}$ is a complete intersection ideal and whose annihilator ideal is precisely a$\mathfrak{a}$.     

New homochiral binaphthol-modified organolanthanide reagents for the enantioselective addition to aldehydes

Optically active secondary alcohols were obtained in high chemical yield and optical purity (up to 85% ee) from the lanthanide-mediated enantioselective addition of alkyl nucleophiles to aromatic aldehydes.     

Partitioning linear spaces into complete quadrilaterals andN-gons

In this paper we find the set of integers for which there exists a linear space having all lines of degree four with the property that the set of lines can be partitioned into the classical configurations: complete quadrilaterals, triangles and 4-gons.     

Size exclusion chromatography with dual-beam refractive index gradient detection of polystyrene samples

Non-aqueous size exclusion chromatography (SEC) of polystyrenes (as model analytes) is examined using the microscale molar mass sensor (μ-MMS) for detection. The μ-MMS is combined with SEC to demonstrate this simultaneously universal and molar mass selective detection method for polymer characterization. The μ-MMS is based on measuring the refractive index gradient (RIG) at two positions (upstream and downstream) within a T-shaped microfluidic channel. The RIG is produced from a sample stream (eluting analytes in the mobile phase) merging with a mobile phase stream (mobile phase only). The magnitude of the RIG is measured as a probe beam deflection angle and is related to analyte diffusion coefficient, the time allowed for analyte diffusion from the sample stream toward the mobile phase stream, and the bulk phase analyte refractive index difference relative to the mobile phase. Thus, two deflection angles are measured simultaneously, the upstream angle and the downstream angle. An angle ratio is calculated by dividing the downstream angle by the upstream angle. The μ-MMS was found to extend the useful molar mass calibration range of the SEC system (nominally limited by the total exclusion and total permeation regions from ∼100,000 g/mol to ∼800 g/mol), to a range of 3,114,000-162 g/mol. The injected concentration LOD (based on 3 s statistics) was 2 ppm for the upstream detection position. The point-by-point time-dependent ratio, termed a ‘ratiogram’, is demonstrated for resolved and overlapped peaks. Within detector band broadening produces some anomalies in the ratiogram shapes, but with highly overlapped distributions of peaks this problem is diminished. Ratiogram plots are converted to molar mass as a function of time, demonstrating the utility of SEC/μ-MMS to examine a complex polymer mixture.     

Sodium silver tricobalt bis(diphosphate) and sodium silver copper(II) diphosphate

The crystal structures of two new diphosphates, sodium silver tricobalt bis(diphosphate), (Na_1.42Ag_0.58)Co₃(P₂O₇)₂, and sodium silver copper(II) diphosphate, (Na_1.12Ag_0.88)CuP₂O₇, provide examples of the effect of mixing Na and Ag in the same site of known host phosphate compounds. The small differences in ionic radii of the two monocations do not lead to significant differences in the structural details. In the latter compound, the Cu atom lies on an inversion center.     

Synthesis of 3,5-disubstituted 1,2,4-triazoles containing trimethoxyphenyl groups: Potential antagonists of platelet activating factor

In an effort to develop a new class of Platelet Activating Factor antagonists, 3,5-disubstituted 1,2,4-triazoles containing trimethoxyphenyl groups have been synthesized. The synthesis of symmetrical triazoles 5 and 6 , as well as two methods of synthesizing unsymmetrical triazole 7 , are reported.     

Ab initio study on the thermolysis of β-hydroxyolefins in gas phase

Thermolysis studies of β-hydroxyolefins in gas phase were realized using ab initio MP2 and DFT methods at the 6-31G^* levels to explore the possibility of determining a possible concerted process with a six-membered cyclic transition state (TS). Vibrational frequency calculations were carried out in order to confirm the stationary states, including TS structures. IRC calculations have been performed in all cases in order to verify that localized TS structures connect with the corresponding minimum stationary points associated with the reactant and products. With the aim of corroborating the postulated mechanism in the experimental study, we present a theoretical study in order to calculate the rate constants and the activation parameters. The results obtained are in accordance with the experimental conclusions.