Markov processes conditioned on their location at large exponential times

Suppose that ${\left(X_t\right)}_{t\ge 0}$ is a one-dimensional Brownian motion with negative drift $?\mu$. It is possible to make sense of conditioning this process to be in the state 0 at an independent exponential random time and if we kill the conditioned process at the exponential time the resulting process is Markov. If we let the rate parameter of the random time go to 0, then the limit of the killed Markov process evolves like $X$ conditioned to hit 0, after which time it behaves as $X$ killed at the last time $X$ visits 0. Equivalently, the limit process has the dynamics of the killed “bang–bang” Brownian motion that evolves like Brownian motion with positive drift $+\mu$ when it is negative, like Brownian motion with negative drift $?\mu$ when it is positive, and is killed according to the local time spent at 0.An extension of this result holds in great generality for a Borel right process conditioned to be in some state $a$ at an exponential random time, at which time it is killed. Our proofs involve understanding the Campbell measures associated with local times, the use of excursion theory, and the development of a suitable analogue of the “bang–bang” construction for a general Markov process.As examples, we consider the special case when the transient Borel right process is a one-dimensional diffusion. Characterizing the limiting conditioned and killed process via its infinitesimal generator leads to an investigation of the $h$-transforms of transient one-dimensional diffusion processes that goes beyond what is known and is of independent interest.     

Avoiding problems with hydrogen misplacement in reporting crystal structures

Intermolecular hydrogen bonding is an integral part of many crystal structures. Hydrogen bonding sometimes results in one‐, two‐ or three‐dimensional supramolecular assemblies, a common feature of which is positional disorder of H atoms related to space‐group symmetry. Yet some reported structures fail to include all possible donor–acceptor close contacts, or to seek H‐atom electron densities associated with apparent D—H...A trios, while some H‐atom positions violate principles of chemistry or crystal physics. Modern diffraction equipment and sophisticated computing systems provide high‐quality data; thus, failure to characterize and report fully an accurate, complete and physically correct hydrogen‐bonding model should not be acceptable. We illustrate the relevant issues with three published examples in the hope of slowing the proliferation of these problems, with the scientifically desirable goal of improving the accuracy of crystallographic models while also providing improved search keys for information retrieval.     

An Improved Procedure for the Synthesis of Prostaglandin Analogues

Hydrozirconation-iodination of a terminal acetylene followed by lithium-iodide exchange and finally dilithio cyanocuprate mediated conjugate addition to an appropriate cyclopentenone is reported as an efficient method for the synthesis of prostaglandin analogues.     

Syntheses of 2‐Keto‐3‐deoxy‐D‐xylonate and 2‐Keto‐3‐deoxy‐L‐arabinonate as Stereochemical Probes for Demonstrating the Metabolic Promiscuity of Sulfolobus solfataricus Towards D‐Xylose and L‐Arabinose

Practical syntheses of 2‐keto‐3‐deoxy‐D ‐xylonate (D ‐KDX) and 2‐keto‐3‐deoxy‐L ‐arabinonate (L ‐KDA) that rely on reaction of the anion of ethyl 2‐[(tert‐butyldimethylsilyl)oxy]‐2‐(dimethoxy phosphoryl) acetate with enantiopure glyceraldehyde acetonide, followed by global deprotection of the resultant O‐silyl‐enol esters, have been developed. This has enabled us to confirm that a 2‐keto‐3‐deoxy‐D ‐gluconate aldolase from the archaeon Sulfolobus solfataricus demonstrates good activity for catalysis of the retro‐aldol cleavage of both these enantiomers to afford pyruvate and glycolaldehyde. The stereochemical promiscuity of this aldolase towards these enantiomeric aldol substrates confirms that this organism employs a metabolically promiscuous pathway to catabolise the C5‐sugars D ‐xylose and L ‐arabinose.     

The refocused INADEQUATE MAS NMR experiment in multiple spin-systems: interpreting observed correlation peaks and optimising lineshapes

The robustness of the refocused INADEQUATE MAS NMR pulse sequence for probing through-bond connectivities has been demonstrated in a large range of solid-state applications. This pulse sequence nevertheless suffers from artifacts when applied to multispin systems, e.g. uniformly labeled (13)C solids, which distort the lineshapes and can potentially result in misleading correlation peaks. In this paper, we present a detailed account that combines product-operator analysis, numerical simulations and experiments of the behavior of a three-spin system during the refocused INADEQUATE pulse sequence. The origin of undesired anti-phase contributions to the spectral lineshapes are described, and we show that they do not interfere with the observation of long-range correlations (e.g. two-bond (13)C-(13)C correlations). The suppression of undesired contributions to the refocused INADEQUATE spectra is shown to require the removal of zero-quantum coherences within a z-filter. A method is proposed to eliminate zero-quantum coherences through dephasing by heteronuclear dipolar couplings, which leads to pure in-phase spectra.     

Iodonium Metathesis Reactions

A metathesis reaction occurs when a diaryliodonium triflate is heated with an aryl iodide, resulting in the formation of a new diaryliodonium triflate.     

Nickel-Catalyzed 1,2-Diarylation of Alkenyl Carboxylates: A Gateway to 1,2,3-Trifunctionalized Building Blocks

A nickel-catalyzed conjunctive cross-coupling of alkenyl carboxylic acids, aryl iodides, and aryl/alkenyl boronic esters is reported. The reaction delivers the desired 1,2-diarylated and 1,2-arylalkenylated products with excellent regiocontrol. To demonstrate the synthetic utility of the method, a representative product is prepared on gram scale and then diversified to eight 1,2,3-trifunctionalized building blocks using two-electron and one-electron logic. Using this method, three routes toward bioactive molecules are improved in terms of yield and/or step count. This method represents the first example of catalytic 1,2-diarylation of an alkene directed by a native carboxylate group.