Flat forms, bi-Lipschitz parametrizations, and smoothability of manifolds

We give a sufficient condition for a metric (homology) manifold to be locally bi-Lipschitz equivalent to an open subset in R ⁿ . The condition is a Sobolev condition for a measurable coframe of flat 1-forms. In combination with an earlier work of D. Sullivan, our methods also yield an analytic characterization for smoothability of a Lipschitz manifold in terms of a Sobolev regularity for frames in a cotangent structure. In the proofs, we exploit the duality between flat chains and flat forms, and recently established differential analysis on metric measure spaces. When specialized to R ⁿ , our result gives a kind of asymptotic and Lipschitz version of the measurable Riemann mapping theorem as suggested by Sullivan.     

Iterative process for G-multi degree reduction of Bézier curves

In this paper, the issue of multi-degree reduction of Bézier curves with C¹ and G²-continuity at the end points of the curve is considered. An iterative method, which is the first of this type, is derived. It is shown that this algorithm converges and can be applied iteratively to get the required accuracy. Some examples and figures are given to demonstrate the efficiency of this method.     

On the Stanley depth of squarefree Veronese ideals

Let K be a field and S=K[x ₁,…,x _n ]. In 1982, Stanley defined what is now called the Stanley depth of an S-module M, denoted sdepth (M), and conjectured that depth (M)≤sdepth (M) for all finitely generated S-modules M. This conjecture remains open for most cases. However, Herzog, Vladoiu and Zheng recently proposed a method of attack in the case when M=I/J with J⊂I being monomial S-ideals. Specifically, their method associates M with a partially ordered set. In this paper we take advantage of this association by using combinatorial tools to analyze squarefree Veronese ideals in S. In particular, if I _n,d is the squarefree Veronese ideal generated by all squarefree monomials of degree d, we show that if 1≤d≤n<5d+4, then sdepth (I _n,d )=⌊(n−d)/(d+1)⌋+d, and if d≥1 and n≥5d+4, then d+3≤sdepth (I _n,d )≤⌊(n−d)/(d+1)⌋+d.     

Mechanically induced scission and subsequent thermal remending of perfluorocyclobutane polymers

Perfluorocyclobutane (PFCB) polymer solutions were subjected to pulsed ultrasound, leading to mechanically induced chain scission and molecular weight degradation. (19)F NMR revealed that the new, mechanically generated end groups are trifluorovinyl ethers formed by cycloreversion of the PFCB groups, a process that differs from thermal degradation pathways. One consequence of the mechanochemical process is that the trifluorovinyl ether end groups can be remended simply by subjecting the polymer solution to the original polymerization conditions, that is, heating to >150 °C. Stereochemical changes in the PFCBs, in combination with radical trapping experiments, indicate that PFCB scission proceeds via a stepwise mechanism with a 1,4-diradical intermediate, offering a potential mechanism for localized functionalization and cross-linking in regions of high stress.     

Phosphorescent sensor for biological mobile zinc

A new phosphorescent zinc sensor (ZIrF) was constructed, based on an Ir(III) complex bearing two 2-(2,4-difluorophenyl)pyridine (dfppy) cyclometalating ligands and a neutral 1,10-phenanthroline (phen) ligand. A zinc-specific di(2-picolyl)amine (DPA) receptor was introduced at the 4-position of the phen ligand via a methylene linker. The cationic Ir(III) complex exhibited dual phosphorescence bands in CH(3)CN solutions originating from blue and yellow emission of the dfppy and phen ligands, respectively. Zinc coordination selectively enhanced the latter, affording a phosphorescence ratiometric response. Electrochemical techniques, quantum chemical calculations, and steady-state and femtosecond spectroscopy were employed to establish a photophysical mechanism for this phosphorescence response. The studies revealed that zinc coordination perturbs nonemissive processes of photoinduced electron transfer and intraligand charge-transfer transition occurring between DPA and phen. ZIrF can detect zinc ions in a reversible and selective manner in buffered solution (pH 7.0, 25 mM PIPES) with K(d) = 11 nM and pK(a) = 4.16. Enhanced signal-to-noise ratios were achieved by time-gated acquisition of long-lived phosphorescence signals. The sensor was applied to image biological free zinc ions in live A549 cells by confocal laser scanning microscopy. A fluorescence lifetime imaging microscope detected an increase in photoluminescence lifetime for zinc-treated A549 cells as compared to controls. ZIrF is the first successful phosphorescent sensor that detects zinc ions in biological samples.     

Margaret Cavendish's materialist critique of van Helmontian chymistry

A striking omission in the scholarship on the reception of the chymical philosophy of Jan Baptista van Helmont in England in the seventeenth century is the work of the mid-seventeenth-century natural philosopher Margaret Cavendish, Duchess of Newcastle. In her Philosophical Letters (1664), Cavendish offers an extended critique of Van Helmont's work (whose Ortus Medicince had recently been translated into English by John Sadler). In this paper, I compare Cavendish's criticisms with those of Robert Boyle in his Sceptical Chymist (1661). Both Boyle and Cavendish attacked Van Helmont for the obscurity of his chymical vocabulary and concepts, and attacked his seminalism. Although their critiques had much in common, they diverged in their attitudes to Van Helmont's experiments. As an opponent of the experimental philosophy, Cavendish had little interest in the quality of Van Helmont's experimental claims, whereas Boyle was critical of their unreplicability. I also try to show that the two writers had very different polemical agendas, with Boyle defending his vision of chymistry based on a corpuscularian natural philosophy, and Cavendish being as much concerned with establishing her religious orthodoxy as with defending the truth claims of her own materialist vitalism. For Cavendish, Van Helmont was an example of the dangers of mingling theology and natural philosophy.     

Palladium-catalyzed carbohalogenation: bromide to iodide exchange and domino processes

Aryl bromides have been used to prepare a variety of nitrogen- and oxygen-containing heterocycles featuring new carbon-carbon and carbon-iodine bonds. This palladium-catalyzed carbohalogenation requires potassium iodide for the reaction to proceed in high yields. Additionally, the first examples of domino carbohalogenation reactions have been demonstrated using both aryl iodide and aryl bromide starting materials. Complex products with multiple rings and stereogenic centers are generated in excellent yields with moderate to excellent diastereoselectivities.     

Controlled formation of peptide bonds in the gas phase

Photoexcitation (using 157 nm vacuum ultraviolet radiation) of proton-bound peptide complexes leads to water elimination and the formation of longer amino acid chains. Thus, it appears that proton-bound dimers are long-lived intermediates along the pathway to peptide formation. Product specificity can be controlled by selection of specific complexes and the incorporation of blocking groups at the N- or C-termini. The product peptide sequences are confirmed using collision-induced dissociation.     

Insights into the different dioxygen activation pathways of methane and toluene monooxygenase hydroxylases

The methane and toluene monooxygenase hydroxylases (MMOH and TMOH, respectively) have almost identical active sites, yet the physical and chemical properties of their oxygenated intermediates, designated P*, H(peroxo), Q, and Q* in MMOH and ToMOH(peroxo) in a subclass of TMOH, ToMOH, are substantially different. We review and compare the structural differences in the vicinity of the active sites of these enzymes and discuss which changes could give rise to the different behavior of H(peroxo) and Q. In particular, analysis of multiple crystal structures reveals that T213 in MMOH and the analogous T201 in TMOH, located in the immediate vicinity of the active site, have different rotatory configurations. We study the rotational energy profiles of these threonine residues with the use of molecular mechanics (MM) and quantum mechanics/molecular mechanics (QM/MM) computational methods and put forward a hypothesis according to which T213 and T201 play an important role in the formation of different types of peroxodiiron(III) species in MMOH and ToMOH. The hypothesis is indirectly supported by the QM/MM calculations of the peroxodiiron(III) models of ToMOH and the theoretically computed Mo?ssbauer spectra. It also helps explain the formation of two distinct peroxodiiron(III) species in the T201S mutant of ToMOH. Additionally, a role for the ToMOD regulatory protein, which is essential for intermediate formation and protein functioning in the ToMO system, is advanced. We find that the low quadrupole splitting parameter in the Mo?ssbauer spectrum observed for a ToMOH(peroxo) intermediate can be explained by protonation of the peroxo moiety, possibly stabilized by the T201 residue. Finally, similarities between the oxygen activation mechanisms of the monooxygenases and cytochrome P450 are discussed.     

Reversible luminescence switching of a redox-active ferrocene-europium dyad

The copper-catalyzed cycloaddition reaction between a propargyl-appended europium complex and azidomethylferrocene yields a d-f dyad whose photophysical properties can be reversibly switched by varying the oxidation state of the ferrocene chromophore.