A Simple Proof of the Sharp Weighted Estimate for Calderón–Zygmund Operators on Homogeneous Spaces

Here we show that Lerner’s method of local mean oscillation gives a simple proof of the A ₂ conjecture for spaces of homogeneous type, that is, the linear dependence on the A ₂ norm for weighted L ² Calderón–Zygmund operator estimates. In the Euclidean case, the result is due to Hytönen, and for geometrically doubling spaces, Nazarov, Reznikov, and Volberg obtained the linear bound.     

10‐Step Asymmetric Total Synthesis and Stereochemical Elucidation of (+)‐Dragmacidin D

The asymmetric synthesis of dragmacidin D ( 1 ) was completed in 10 steps. Its sole stereocenter was set by using direct asymmetric alkylation enabled by a C₂‐symmetric tetramine and lithium N‐(trimethylsilyl)‐tert‐butylamide as the enolization reagent. A central Larock indole synthesis was employed in a convergent assembly of the heterocyclic subunits. The stereochemical evidence from this work strongly supports the predicted S configuration at the 6′′′ position, which is consistent with other members of the dragmacidin family of natural products.     

Large Deviations from a Stationary Measure for a Class of Dissipative PDEs with Random Kicks

We study a class of dissipative PDEs perturbed by a bounded random kick force. It is assumed that the random force is nondegenerate, so that the Markov process obtained by the restriction of solutions to integer times has a unique stationary measure. The main result of the paper is a large deviations principle for occupation measures of the Markov process in question. The proof is based on Kifer's large‐deviation criterion, a coupling argument for Markov processes, and an abstract result on large‐time asymptotic for generalized Markov semigroups.© 2015 Wiley Periodicals, Inc.     

Concise Synthesis of (+)-[13C4]-Anatoxin-a by Dynamic Kinetic Resolution of a Cyclic Iminium Ion

An asymmetric total synthesis of [¹³C₄]-anatoxin-a ([¹³C₄]- 1 ) has been developed from commercially available ethyl [¹³C₄]-acetoacetate ([¹³C₄]- 15 ). The unique requirements associated with isotope incorporation inspired a new, robust, and highly scalable route, providing access to 0.110 g of this internal standard for use in the detection and precise quantification of anatoxin-a in freshwater. A highlight of the synthesis is a method that leverages a cyclic iminium ion racemization to achieve dynamic kinetic resolution in an enantioselective Morita–Baylis–Hillman (MBH) cyclization.     

Long-chain alkyl sulfonate micelle fission: a molecular dynamics study

In this study, we investigate micelle fission of long-chain alkyl sulfonate molecules using atomistic scale simulation. GROMACS software code with the united atom force field was applied. 0.5-μs parallel molecular dynamics simulation study was conducted for a surfactant/water system consisting of 192 sodium pentadecyl sulfonate and 40,553 water molecules. The large preassembled micelle was ruptured at Krafft above T?=?323-K temperature, and we track two ellipsoid-like micelles over the course of the production run. To estimate the micelle shape, we determined the principal moments of inertia and the eccentricity, which proved that the micelles have a pronounced prolate spheroid shape, which agrees well with our previous experimental data. The mechanism of micelle fission was explored in detail. The aggregation number, ionization degree, and other parameters obtained from simulation were consistent with existing experimental finding. The determined parameters in addition to simple visual inspection of trajectories revealed monomer-micelle exchange—with the estimated relaxation time τ ₁?=?10^??9s. We assume that the exchange process is conditioned by the unequal size of micelles leading to adjustment of aggregation number.     

Freudenthal duality and generalized special geometry

Freudenthal duality, introduced in Borsten et al. (2009) [1] and defined as an anti-involution on the dyonic charge vector in d=4 space-time dimensions for those dualities admitting a quartic invariant, is proved to be a symmetry not only of the classical Bekenstein-Hawking entropy but also of the critical points of the black hole potential.Furthermore, Freudenthal duality is extended to any generalized special geometry, thus encompassing all N>2 supergravities, as well as N=2 generic special geometry, not necessarily having a coset space structure.     

Novel C1-symmetric dibenzophosphole ligands: application in hydroformylation reactions

A new family of non-symmetrical disubstituted dibenzophospholes possessing different steric and electronic effects have been synthesized and characterized. Their preliminary evaluation in rhodium-catalyzed hydroformylation reactions is presented.