Diophantine properties of measures invariant with respect to the Gauss map

Motivated by the work of D. Y. Kleinbock, E. Lindenstrauss, G. A. Margulis, and B. Weiss [8, 9], we explore the Diophantine properties of probability measures invariant under the Gauss map. Specifically, we prove that every such measure which has finite Lyapunov exponent is extremal, i.e., gives zero measure to the set of very well approximable numbers. We show, on the other hand, that there exist examples where the Lyapunov exponent is infinite and the invariant measure is not extremal. Finally, we construct a family of Ahlfors regular measures and prove a Khinchine-type theorem for these measures. The series whose convergence or divergence is used to determine whether or not µ-almost every point is ψ-approximable is different from the series used for Lebesgue measure, so this theorem answers in the negative a question posed by Kleinbock, Lindenstrauss, and Weiss [8].     

Matrix-dependent adhesion of vascular and valvular endothelial cells in microfluidic channels

The interactions between endothelial cells and the underlying extracellular matrix regulate adhesion and cellular responses to microenvironmental stimuli, including flow-induced shear stress. In this study, we investigated the adhesion properties of primary porcine aortic endothelial cells (PAECs) and valve endothelial cells (PAVECs) in a microfluidic network. Taking advantage of the parallel arrangement of the microchannels, we compared adhesion of PAECs and PAVECs to fibronectin and type I collagen, two prominent extracellular matrix proteins, over a broad range of concentrations. Cell spreading was measured morphologically, based on cytoplasmic staining with a vital dye, while adhesion strength was characterized by the number of cells attached after application of shear stresses of 11, 110, and 220 dyn cm(-2). Results showed that PAVECs were more well spread on fibronectin than on type I collagen (P < 0.0001), particularly for coating concentrations of 100, 200, and 500 microg mL(-1). PAVECs also withstood shear significantly better on fibronectin than on collagen for 500 microg mL(-1). PAECs were more well spread on collagen compared to PAVECs (P < 0.0001), but did not have significantly better adhesion strength. These results demonstrate that cell adhesion is both cell-type and matrix dependent. Furthermore, they reveal important phenotypic differences between vascular and valvular endothelium, with implications for endothelial mechanobiology and the design of microdevices and engineered tissues.     

Effect of ozone oxidation on single-walled carbon nanotubes

Exposing single-walled carbon nanotubes to room-temperature UV-generated ozone leads to an irreversible increase in their electrical resistance. We demonstrate that the increased resistance is due to ozone oxidation on the sidewalls of the nanotubes rather than at the end caps. Raman and X-ray photoelectron spectroscopies show an increase in the defect density due to the oxidation of the nanotubes. Using ultraviolet photoelectron spectroscopy, we show that these defects represent the removal of pi-conjugated electron states near the Fermi level, leading to the observed increase in electrical resistance. Oxidation of carbon nanotubes is an important first step in many chemical functionalization processes. Because the oxidation rate can be controlled with short exposures, UV-generated ozone offers the potential for use as a low-thermal-budget processing tool.     

Unconventional transport in the "hole" regime of a si double quantum dot

Studies of electronic charge transport through semiconductor double quantum dots rely on a conventional "hole" model of transport in the three-electron regime. We show that experimental measurements of charge transport through a Si double quantum dot in this regime cannot be fully explained using the conventional picture. Using a Hartree-Fock (HF) formalism and relevant HF energy parameters extracted from transport data in the multiple-electron regime, we identify a novel spin-flip cotunneling process that lifts a singlet blockade.     

The mixed diol–dithiol 2,2‐bis(sulfanylmethyl)propane‐1,3‐diol: characterization of key intermediates on a new synthetic pathway

A new synthetic route to 2,2‐bis(sulfanylmethyl)propane‐1,3‐diol, (II), is described starting from the commercially available 2,2‐bis(hydroxymethyl)propane‐1,3‐diol. The structures of two intermediates on this route are described. 5,5‐Dimethenyl‐2,2‐dimethyl‐1,3‐dioxane bis(thiocyanate) (systematic name: {[5‐(cyanosulfanyl)‐2,2‐dimethyl‐1,3‐dioxan‐5‐yl]sulfanyl}formonitrile), C₁₀H₁₄N₂O₂S₂, (X), crystallizes in the space group P2₁/c with no symmetry relationship between the two thiocyanate groups. There is a short intramolecular N...S contact for one thiocyanate group, while the second group is positioned such that this type of interaction is not possible. 1,3‐(Hydroxymethyl)propane‐1,3‐diyl bis(thiocyanate), C₇H₁₀N₂O₂S₂, (XI), also features a single short N...S contact in the solid state. Hydrogen bonding between two molecules of compound (XI) results in the formation of dimers in the crystal, which are then linked together by a second hydrogen‐bond interaction between the dimers. In addition, the structures of two intermediates from an unsuccessful alternative synthesis of (II) are reported. 2,2‐Bis(chloromethyl)propane‐1,3‐diol, C₅H₁₀Cl₂O₂, (VI), crystallized as an inversion twin with a minor twin fraction of 0.43 (6). It forms a zigzag structure as a result of intermolecular hydrogen bonding. The structure of 9,9‐dimethyl‐2,4,8,10‐tetraoxa‐3λ⁴‐thiaspiro[5.5]undecan‐3‐one, C₈H₁₄O₅S, (VII), shows evidence for a weak S...O contact with a distance of 3.2529 (11) Å.