Context-free grammars for triangular arrays

We consider context-free grammars of the form G = {f → fb1+b2+1ga1+a2, g → fb1 ga1+1},where ai and bi are integers sub ject to certain positivity conditions. Such a grammar G gives rise to triangular arrays {T(n, k)}0≤k≤n satisfying a three-term recurrence relation. Many combinatorial sequences can be generated in this way. Let Tn (x) =∑nk=0T(n, k)xk. Based on the differential operator with respect to G, we define a sequence of linear operators Pn such that Tn+1(x) = Pn(Tn(x)). Applying the characterization of real stability preserving linear operators on the multivariate polynomials due to Borcea and Br?ndén, we obtain a necessary and sufficient condition for the operator Pn to be real stability preserving for any n. As a consequence, we are led to a sufficient condition for the real-rootedness of the polynomials defined by certain triangular arrays, obtained by Wang and Yeh.Moreover, as special cases we obtain grammars that lead to identities involving the Whitney numbers and the Bessel numbers.     

Development of an Enantioselective Allylic Alkylation of Acyclic α-Fluoro-β-ketoesters for Asymmetric Synthesis of 3-Fluoropiperidines

The first useful enantioselective Pd-catalyzed asymmetric allylic alkylation of α-fluoro-β-ketoesters has been achieved using the Trost family of chiral ligands yielding products in up to 92 % ee. This work provides new insights regarding the typically modest selectivities associated with acyclic α-fluoroenolates and shows experimental evidence that the typically poor levels of enantiocontrol associated with these systems are not necessarily due to the presence of E/Z enolate mixtures. Finally, this methodology allows the easy preparation of useful 3-fluoropiperidine intermediates, and it is demonstrated that these systems are applicable to a range of functionalization reactions leading to new building blocks for the discovery of bioactive products.     

Improved rejection of multiply scattered photons in confocal microscopy using dual-axes architecture

We perform Monte Carlo simulations to show that the dual-axes (DA) confocal architecture has superior rejection of multiply scattered photons in tissue to that of single axis. As a result, the DA configuration provides improved signal-to-noise ratio and dynamic range, and thus is sensitive to ballistic photons from deeper within tissue, features that are particularly useful for performing vertical cross-sectional reflectance images in tissue.     

Stability of AgIII towards Halides in Organosilver(III) Complexes

The involvement of silver in two-electron Ag^I/Ag^III processes is currently emerging. However, the range of stability of the required and uncommon Ag^III species is virtually unknown. Here, the stability of Ag^III towards the whole set of halide ligands in the organosilver(III) complex frame [(CF₃)₃AgX]⁻ (X=F, Cl, Br, I, At) is theoretically analyzed. The results obtained depend on a single factor: the nature of X. Even the softest and least electronegative halides (I and At) are found to form reasonably stable Ag^III−X bonds. Our estimates were confirmed by experiment. The whole series of nonradiative halide complexes [PPh₄][(CF₃)₃AgX] (X=F, Cl, Br, I) has been experimentally prepared and all its constituents have been isolated in pure form. The pseudohalides [PPh₄][(CF₃)₃AgCN] and [PPh₄][(CF₃)₃Ag(N₃)] have also been isolated, the latter being the first silver(III) azido complex. Except for the iodo compound, all the crystal and molecular structures have been established by single-crystal X-ray diffraction methods. The decomposition paths of the [(CF₃)₃AgX]⁻ entities at the unimolecular level have been examined in the gas phase by multistage mass spectrometry (MSⁿ). The experimental detection of the two series of mixed complexes [CF₃AgX]⁻ and [FAgX]⁻ arising from the corresponding parent species [(CF₃)₃AgX]⁻ demonstrate that the Ag−X bond is particularly robust. Our experimental observations are rationalized with the aid of theoretical methods. Smooth variation with the electronegativity of X is also observed in the thermolyses of bulk samples. The thermal stability in the solid state gradually decreases from X=F (145 °C, dec.) to X=I (78 °C, dec.) The experimentally established compatibility of Ag^III with the heaviest halides is of particular relevance to silver-mediated or silver-catalyzed processes.     

PET Imaging of Bacterial Infections with Fluorine‐18‐Labeled Maltohexaose

A positron emission tomography (PET) tracer composed of ¹⁸F‐labeled maltohexaose (MH¹⁸F) can image bacteria in vivo with a sensitivity and specificity that are orders of magnitude higher than those of fluorodeoxyglucose (¹⁸FDG). MH¹⁸F can detect early‐stage infections composed of as few as 10⁵ E. coli colony‐forming units (CFUs), and can identify drug resistance in bacteria in vivo. MH¹⁸F has the potential to improve the diagnosis of bacterial infections given its unique combination of high specificity and sensitivity for bacteria.     

Hierarchical Hybrid Peroxidase Catalysts for Remediation of Phenol Wastewater

We report a new family of hierarchical hybrid catalysts comprised of horseradish peroxidase (HRP)–magnetic nanoparticles for advanced oxidation processes and demonstrate their utility in the removal of phenol from water. The immobilized HRP catalyzes the oxidation of phenols in the presence of H₂O₂, producing free radicals. The phenoxy radicals react with each other in a non‐enzymatic process to form polymers, which can be removed by precipitation with salts or condensation. The hybrid peroxidase catalysts exhibit three times higher activity than free HRP and are able to remove three times more phenol from water compared to free HRP under similar conditions. In addition, the hybrid catalysts reduce substrate inhibition and limit inactivation from reaction products, which are common problems with free or conventionally immobilized enzymes. Reusability is improved when the HRP–magnetic nanoparticle hybrids are supported on micron‐scale magnetic particles, and can be retained with a specially designed magnetically driven reactor. The performance of the hybrid catalysts makes them attractive for several industrial and environmental applications and their development might pave the way for practical applications by eliminating most of the limitations that have prevented the use of free or conventionally immobilized enzymes.