Locally Farkas-Minkowski linear inequality systems

This paper introduces thelocally Farkas-Minkowski (LFM) linear inequality systems in a finite dimensional Euclidean space. These systems are those ones that satisfy that any consequence of the system that is active at some solution point is also a consequence of some finite subsystem. This class includes the Farkas-Minkowski systems and verifies most of the properties that these systems possess. Moreover, it contains the locally polyhedral systems, which are the natural external representation of quasi-polyhedral sets. TheLFM systems appear to be the natural external representation of closed convex sets. A characterization based on their properties under the union of systems is provided. In linear semi-infinite programming, theLFM property is the more general constraint qualification such that the Karush-Kuhn-Tucker condition characterizes the optimal points. Furthermore, the pair of Haar dual problems has no duality gap.     

Instrumental barriers in biological Fourier transform infrared spectroscopy

Biological applications of infrared spectroscopy have pressed for ever greater instrumental capabilities in terms of spectral sensitivity and quantitative exactness. Improved instrumentation has provided measurement of many vibrational modes in biological samples that previously were lost in noise. With highly optimized sampling conditions, useful measurements have been made with a peak-to-peak noise level less than 5 microabsorbance (5×10^–6 absorbance), at 0.5 cm^–1 resolution. However, optical and instrumental instabilities often result in sine waves that are not totally removed by the ratio of sample to reference. These often limit effective spectral sensitivity to 50 or 100 microabsorbance, peak-to-peak, and constitute a non-random noise. Non-atmospheric absorptions, especially one at 1959 cm^–1 with 0.8 cm^–1 band width (FWHM) are reported. The latter is due to a trace impurity in the KBr beam splitter substrate and compensator plate. Improvements in instrumentation and sampling conditions are expected to yield measurements of absorption bands as small as 50 microabsorbance with excellent signal/noise.     

2,5‐Dichloro‐2,5‐dihydro­thio­phene 1‐oxide: determinaton of the complete stereochemistry

The title five‐membered heterocycle, C₄H₄Cl₂OS, adopts an envelope conformation with the S atom at the tip of the flap. All three ring substituents, viz. the sulfoxide O atom and the two Cl atoms, are cis to each other. The two C atoms α to the sulfoxide group are also bonded to chlorine. The electron‐withdrawing chlorine substituents give rise to weak C—H·O hydrogen bonds with the sulfoxide O atom of a symmetry‐related mol­ecule [H·O = 2.44 (2) and 2.61 (2) Å, C·O = 3.143 (3) and 3.302 (2) Å and C—H·O = 129.9 (19) and 135.1 (19)°]. There is also a possible weak C—H·Cl inter­action. Chains of mol­ecules held together by these weak inter­actions run parallel to the a axis.     

On the boundedness of bilinear operators on products of Besov and Lebesgue spaces

We prove mapping properties of the form and , for certain related indices p₁,p₂,p₃,q₁,q₂,α₁,α₂∈R, where T is a bilinear Hörmander-Mihlin multiplier or a molecular paraproduct. Applications to bilinear Littlewood-Paley theory are discussed.     

Isotropic-nematic phase transition of single-walled carbon nanotubes in strong acids

We present the first quantitative assessment of the maximum amount of nanotubes that can exist in the isotropic phase () of single-walled carbon nanotubes (SWNTs) in Br?nsted-Lowry acids. We employ a centrifugation technique in conjunction with UV-vis-nIR spectroscopy to quantify , which is also the critical concentration of the isotropic-nematic transition of SWNTs in strong acids. Centrifugation of biphasic dispersions of SWNTs, that is, acid dispersions consisting of an isotropic phase in equilibrium with an ordered nematic liquid crystalline phase, results in a clear phase separation, where the isotropic phase is supernatant. Dilution of the isotropic phase with a known amount of acid followed by UV-vis-nIR absorbance measurements yields , that is, the maximum concentration of SWNTs that can exist in the isotropic phase in a given acid for a given SWNTs' length distribution. At low SWNT concentration (below 200 ppm) in superacids, light absorbance in the range from 400 to 1400 nm scales linearly with concentration. This Beer's law behavior yields calibration curves for measuring SWNTs' concentration in acids. We find that the critical concentration of the isotropic-nematic transition increases with acid strength in accordance with the previously proposed sidewall protonation mechanism for dispersing SWNTs in acids.     

Polyatomic anion assistance in the assembly of [2]pseudorotaxanes

We describe the use of polyatomic anions for the quantitative assembly of ion-paired complexes displaying pseudorotaxane topology. Our approach exploits the unique ion-pair recognition properties exhibited by noncovalent neutral receptors assembled through hydrogen-bonding interactions between a bis-calix[4]pyrrole macrocycle and linear bis-amidepyridyl-N-oxides. The complexation of bidentate polyatomic anions that are complementary in size and shape to the receptor's cavity, in which six NH hydrogen-bond donors converge, induces the exclusive formation of four particle-threaded assemblies.     

Conformational basis for asymmetric seeding barrier in filaments of three- and four-repeat tau

Tau pathology in Alzheimer's disease is intimately linked to the deposition of proteinacious filaments, which akin to infectious prions, have been proposed to spread via seeded conversion. Here we use double electron-electron resonance (DEER) spectroscopy in combination with extensive computational analysis to show that filaments of three- (3R) and four-repeat (4R) tau are conformationally distinct. Distance measurements between spin labels in the third repeat, reveal tau amyloid filaments as ensembles of known β-strand-turn-β-strand U-turn motifs. Whereas filaments seeded with 3R tau are structurally homogeneous, filaments seeded with 4R tau are heterogeneous, composed of at least three distinct conformers. These findings establish a molecular basis for the seeding barrier between different tau isoforms and offer a new powerful approach for investigating the composition and dynamics of amyloid fibril ensembles.     

Derivation of the near-surface dielectric function of amorphous silicon from photoelectron loss spectra

The near-surface dielectric function ε(?ω) of hydrogenated amorphous silicon (a-Si:H) films has been derived from X-ray photoelectron energy-loss spectra, over the energy range 0–40 eV. Removal of low lying single-electron excitations is a prerequisite step to proceed to the derivation of the single plasmon energy loss function Im[? 1/ε(?ω)] due to collective electron oscillations. Several methods are compared to separate interband transitions from bulk or surface plasmons excitation. The shape of interband excitation loss in the range 1–10 eV can be described by a Henke function; alternatively, its removal using a sigmoid weighting function is a low-noise and reliable method. After deconvolution of multiple plasmon losses and self-consistent elimination of surface plasmon excitation, the single plasmon loss distribution allows recovery of optical (ellipsometry) data measured in the near-UV to visible range.