A version of Hörmander’s theorem for the fractional Brownian motion

It is shown that the law of an SDE driven by fractional Brownian motion with Hurst parameter greater than 1/2 has a smooth density with respect to Lebesgue measure, provided that the driving vector fields satisfy Hörmander’s condition. The main new ingredient of the proof is an extension of Norris’ lemma to this situation.     

Total synthesis of everninomicin 13,384-1--Part 1: retrosynthetic analysis and synthesis of the A1B(A)C fragment

In this first of a series of four articles we introduce everninomicin 13,384-1 (1), a powerful antibiotic effective against drug resistant bacteria, as a target for total synthesis and discuss its retrosynthetic analysis. From the three defined fragments required for the synthesis (2: A1B(A)C fragment; 4: DE fragment; 5: FGHA2 fragment), we describe herein two approaches to the A1B(A)C block. The first strategy relied on an olefin metathesis reaction to construct a common intermediate for rings B and C, but was faced with final protecting group problems. The second, and successful approach, involved a 1,2-phenylsulfeno migration and a sulfur directed glycosidation procedure to link rings B and C, as well as an acyl fluoride intermediate to install the sterically hindered aryl ester moiety (ring A1). The final stages of the synthesis of the required 2-phenylseleno glycosyl fluoride 2 required introduction of a phenylseleno group at C-1 of ring C followed by a novel, DAST-promoted 1,2-migration to produce the desired 2-beta-phenylseleno glycosyl fluoride moiety.     

Divergent Synthesis of Bioactive Dithiodiketopiperazine Natural Products Based on a Double C(sp3)−H Activation Strategy

This article provides a detailed report of our efforts to synthesize the dithiodiketopiperazine (DTP) natural products (−)-epicoccin G and (−)-rostratin A using a double C(sp³)−H activation strategy. The strategy's viability was first established on a model system lacking the C8/C8’ alcohols. Then, an efficient stereoselective route including an organocatalytic epoxidation was secured to access a key bis-triflate substrate. This bis-triflate served as the functional handles for the key transformation of the synthesis: a double C(sp³)−H activation. The successful double activation opened access to a common intermediate for both natural products in high overall yield and on a multigram scale. After several unsuccessful attempts, this intermediate was efficiently converted to (−)-epicoccin G and to the more challenging (−)-rostratin A via suitable oxidation/reduction and protecting group sequences, and via a final sulfuration that occurred in good yield and high diastereoselectivity. These efforts culminated in the synthesis of (−)-epicoccin G and (−)-rostratin A in high overall yields (19.6 % over 14 steps and 12.7 % over 17 steps, respectively), with the latter being obtained on a 500 mg scale. Toxicity assessments of these natural products and several analogues (including the newly synthesized epicoccin K) in the leukemia cell line K562 confirmed the importance of the disulfide bridge for activity and identified dianhydrorostratin A as a 20x more potent analogue.     

Structures and stabilization of low calorific value gas turbulent partially premixed flames in a conical burner

Experiments are carried out on partially premixed turbulent flames stabilized in a conical burner. The investigated gaseous fuels are methane, methane diluted with nitrogen, and mixtures of CH₄, CO, CO₂, H₂ and N₂, simulating typical products from gasification of biomass, and co-firing of gasification gas with methane. The fuel and air are partially premixed in concentric tubes. Flame stabilization behavior is investigated and significantly different stabilization characteristics are observed in flames with and without the cone. Planar laser induced fluorescence (LIF) imaging of a fuel-tracer species, acetone, and OH radicals is carried out to characterize the flame structures. Large eddy simulations of the conical flames are carried out to gain further understanding of the flame/flow interaction in the cone. The data show that the flames with the cone are more stable than those without the cone. Without the cone (i.e. jet burner) the critical jet velocities for blowoff and liftoff of biomass derived gases are higher than that for methane/nitrogen mixture with the same heating values, indicating the enhanced flame stabilization by hydrogen in the mixture. With the cone the stability of flames is not sensitive to the compositions of the fuels, owing to the different flame stabilization mechanism in the conical flames than that in the jet flames. From the PLIF images it is shown that in the conical burner, the flame is stabilized by the cone at nearly the same position for different fuels. From large eddy simulations, the flames are shown to be controlled by the recirculation flows inside cone, which depends on the cone angle, but less sensitive to the fuel compositions and flow speed. The flames tend to be hold in the recirculation zones even at very high flow speed. Flame blowoff occurs when significant local extinction in the main body of the flame appears at high turbulence intensities.     

Brownian Chen series and Atiyah-Singer theorem

The purpose of this work is to give a new and short proof of the Atiyah-Singer local index theorem for the Dirac operator on the spin bundle. This proof is obtained by using heat semigroups approximations based on the truncation of Brownian Chen series.     

Functionalization of Organic Molecules by Transition‐Metal‐Catalyzed C(sp3)?H Activation

Transition‐metal‐catalyzed C? H activation has recently emerged as a powerful tool for the functionalization of organic molecules. While many efforts have focused on the functionalization of arenes and heteroarenes by this strategy in the past two decades, much less research has been devoted to the activation of non‐acidic C? H bonds of alkyl groups. This Minireview highlights recent work in this area, with a particular emphasis on synthetically useful methods.     

DFT study of the mechanism of benzocyclobutene formation by palladium-catalysed C(sp3)-H activation: role of the nature of the base and the phosphine

DFT(B3PW91) calculations of the mechanism of the intramolecular C(sp(3))-H arylation of 2-bromo-tert-butylbenzene to form benzocyclobutene catalysed by Pd(PR(3)) (R = Me, (t)Bu) and a base (acetate, bicarbonate, carbonate) show that the preferred mechanism is highly dependent on the nature of the phosphine and the base used in the calculations. With the experimental reagents (P(t)Bu(3) and carbonate) the rate-determining step is C-H activation with the base coordinated trans to the C-H bond. An agostic interaction of a geminal C-H bond with respect to the bond to be cleaved induces a lowering of the activation barrier.