Global complexification of real analytic globally subanalytic functions

We show that a globally subanalytic function that is real analytic can be extended in a globally subanalytic way to a holomorphic function. We also establish a parametric version of this result. For other important ominimal structures, we show that unary definable real analytic functions can be extended definably to a holomorphic function.     

Differential Response of Pentanal and Hexanal Exhalation to Supplemental Oxygen and Mechanical Ventilation in Rats

High inspired oxygen during mechanical ventilation may influence the exhalation of the previously proposed breath biomarkers pentanal and hexanal, and additionally induce systemic inflammation. We therefore investigated the effect of various concentrations of inspired oxygen on pentanal and hexanal exhalation and serum interleukin concentrations in 30 Sprague Dawley rats mechanically ventilated with 30, 60, or 93% inspired oxygen for 12 h. Pentanal exhalation did not differ as a function of inspired oxygen but increased by an average of 0.4 (95%CI: 0.3; 0.5) ppb per hour, with concentrations doubling from 3.8 (IQR: 2.8; 5.1) ppb at baseline to 7.3 (IQR: 5.0; 10.8) ppb after 12 h. Hexanal exhalation was slightly higher at 93% of inspired oxygen with an average difference of 0.09 (95%CI: 0.002; 0.172) ppb compared to 30%. Serum IL-6 did not differ by inspired oxygen, whereas IL-10 at 60% and 93% of inspired oxygen was greater than with 30%. Both interleukins increased over 12 h of mechanical ventilation at all oxygen concentrations. Mechanical ventilation at high inspired oxygen promotes pulmonary lipid peroxidation and systemic inflammation. However, the response of pentanal and hexanal exhalation varies, with pentanal increasing by mechanical ventilation, whereas hexanal increases by high inspired oxygen concentrations.     

Synthesis,Structure, and DFT Analysis of the THF Solvate of 2-Picolyllithium: A 2-Picolyllithium Solvate with Significant Carbanionic Character

Previous studies of different solvates of 2-methylpyridyllithium (2-picolyllithium) have uncovered electronic structures corresponding to aza-allyl and enamido resonance forms of the metallated pyridine-based compounds. Here, we report the synthesis and characterization of [2-CH₂Li(THF)₂C₅H₄N], a new THF solvate. X-ray crystallographic studies reveal a dimeric arrangement featuring a non-planar eight-membered [NCCLi]₂ ring, in which the primary cation-anion interaction is between the central Li atom and the C atom of the deprotonated methyl group [length, 2.285(2) Å], suggesting a new carbanionic resonance structure for this 2-picolyllithium series. The significant carbanionic character of [2-CH₂Li(THF)₂C₅H₄N] was confirmed by gas-phase DFT calculations [B3LYP/6-311+G(d)] with the calculated electron density interrogated by means of quantum theory of atoms in molecules (QTAIM) and natural bond orbital (NBO) analyses. For comparison these computational analyses were also performed on the literature structures of [2-CH₂Li(2-Picoline)C₅H₄N] and [2-CH₂Li(PMDETA)C₅H₄N]. In a reactivity study, [2-CH₂Li(THF)₂C₅H₄N] was found to undergo nucleophilic addition to pyridine to generate dipyridylmethane in a good yield.     

A Bernstein Type Theorem for Entire Willmore Graphs

We show that every two-dimensional entire graphical solution of the Willmore equation with square integrable second fundamental form is a plane.     

Crystal structures of functional building blocks derived from bis(benzo[b]thiophen‐2‐yl)methane

The syntheses of three bis(benzo[b]thiophen‐2‐yl)methane derivatives, namely bis(benzo[b]thiophen‐2‐yl)methanone, C₁₇H₁₀OS₂, (I), 1,1‐bis(benzo[b]thiophen‐2‐yl)‐3‐(trimethylsilyl)prop‐2‐yn‐1‐ol, C₂₂H₂₀OS₂Si, (II), and 1,1‐bis(benzo[b]thiophen‐2‐yl)prop‐2‐yn‐1‐ol, C₁₉H₁₂OS₂, (III), are described and their crystal structures discussed comparatively. The conformation of ketone (I) and the respective analogues are rather similar for most of the compounds compared. This is true for the interplanar angles, the C_aryl—C_bridge—C_aryl angles and the dihedral angles. The best resemblance is found for a bioisotere of (I), viz. 2,2′‐dinaphthyl ketone, (VII). By way of interest, the crystal packings also reveal similarities between (I) and (VII). In (I), the edge‐to‐face interactions seen between two napthyl residues in (VII) are substituted by S…π contacts between the benzo[b]thiophen‐2‐yl units in (I). In the structures of the bis(benzo[b]thiophen‐2‐yl)methanols, i.e. (II) and (III), the interplanar angles are also quite similar compared with analogues and related active pharmaceutical ingredients (APIs) containing the dithiophen‐2‐ylmethane scaffold, though the dihedral angles show a larger variability and produce unsymmetrical molecules.