Cohomology of Real Diagonal Subspace Arrangements via Resolutions

We express the cohomology of the complement of a real subspace arrangement of diagonal linear subspaces in terms of the Betti numbers of a minimal free resolution. This leads to formulas for the cohomology in some cases, and also to a cohomology vanishing theorem valid for all arrangements.     

The dependence of nuclear magnetic resonance (NMR) image contrast on intrinsic and pulse sequence timing parameters

In Nuclear Magnetic Resonance (NMR) the image pixel value is governed by at least three major intrinsic parameters: the spin density N (H), the spin-lattice relaxation time T1, and the spin-spin relaxation time T2. The extent to which the signal is weighted toward one or several parameters is related to the history of the spin system preceding detection. On the simplifying, though not generally warranted assumption that the spin density does not vary significantly in soft tissues, relative tissue contrast can be predicted quantitatively provided the relaxation times are known. Signal intensities and contrast were computed on the basis of the Bloch equations and experimentally determined relaxation times as a function of pulse timing parameters and the data compared with those in images recorded at 0.5T field strength. Significant deviations from the equal density hypothesis were found for gray and white substance. Notably partial saturation but also spin echo and inversion-recovery images are not in full accordance with predictions made on the basis of relaxation times alone.     

The efficacy of exclusive territory assignments to delivery vehicle drivers

A supporting logic for having a vehicle driver exclusively assigned to serve the same territory on every delivery trip is the deepening of the driver’s knowledge of the territory and the customers therein. This contributes to the driver’s proficiency in serving that territory. However, in situations of randomness in day-to-day customer demands, the choice of exclusive territory assignments entails the sacrifice of sub-optimal route configuration. This study quantifies the extent of that sacrifice in order to depict the cost implications of exclusive territory assignments vis-à-vis tactics that keep pace with day-to-day demand fluctuations by allowing for flexibility in the assignments. The study’s analysis of exclusive territory assignments covers those that involve territory sharing among a team of drivers.     

Thin-layer chromatography-matrix-assisted laser desorption ionisation-time-of-flight mass spectrometry using particle suspension matrices

Particle suspension matrices have been successfully utilized for the analysis of tetracycline antibiotics by thin-layer chromatography-matrix-assisted laser desorption ionisation-time-of-flight mass spectrometry (TLC-MALDI-TOF-MS). Particles of different materials and sizes have been investigated (Co-UFP, TiN, TiO2, Graphite and Silicon) by applying particle suspensions to eluted TLC plates. Mass spectra and mass chromatograms have been recorded directly from the TLC plates. Strong cationization by sodium and potassium was obtained in the positive ion mode, with [M+Na-NH3]+ ions being the predominant signals. The TLC-MALDI mass spectra recorded from graphite suspensions showed the lowest background noise and the highest peak intensities from the range of suspension matrices studied. The mass accuracy from graphite films was improved by adding the peptide Phe-Phe to the graphite suspensions. This allowed internal recalibration of the TLC-MALDI mass spectra acquired during a run. One major potential advantage of TLC-MALDI-TOF-MS has been demonstrated in the analysis of chlortetracycline and tetracycline in a mixture of oxytetracycline, chlortetracycline, tetracycline and minocycline. Examination of the TLC plate prior to MALDI analysis showed only an unresolved spot for chlortetracycline and tetracycline. However by investigation of the MALDI mass spectra and plotting of single ion chromatograms separate peaks for chlortetracycline and tetracycline could be obtained.     

Inflation and bifurcation of compressible spherical membranes

The inflation and bifurcation of spherical membranes is considered. The membrane material is assumed to be isotropic and hyperelastic but may be arbitrarily compressible. Qualitatively the behaviour of compressible membranes is shown to be the same as that of incompressible membranes but specific forms of strain-energy functions are chosen to illustrate possible quantitative differences.     

Two Sample Tests for Mean 3D Projective Shapes from Digital Camera Images

In this article, we extend mean 3D projective shape change in matched pairs to independent samples. We provide a brief introduction of projective shapes of spatial configurations obtained from their digital camera images, building on previous results of Crane and Patrangenaru (J Multivar Anal 102:225–237, 2011). The manifold of projective shapes of k-ads in 3D containing a projective frame at five given landmark indices has a natural Lie group structure, which is inherited from the quaternion multiplication. Here, given the small sample size, one estimates the mean 3D projective shape change in two populations, based on independent random samples of possibly different sizes using Efron’s nonparametric bootstrap. This methodology is applied in three relevant applications of analysis of 3D scenes from digital images: visual quality control, face recognition, and scene recognition.     

Solid-phase extraction-fluorimetric high performance liquid chromatographic determination of domoic acid in natural seawater mediated by an amorphous titania sorbent

The feasibility of using sol-gel amorphous titania (TiO₂) as a solid-phase sorbent for the pre-concentration of domoic acid (DA), a potent amnesic shellfish poisoning (ASP) toxin, directly from seawater was explored. The sol-gel titania material is able to adsorb DA from seawater, via the formation of ester-linkage between the carboxylic moieties of DA and the Ti-OH groups on the sorbent surface, at low pH and desorb it at high pH. The chemisorption process is not significantly interfered by the seawater matrix. The optimum pH values for the adsorption and desorption of DA were found to be pH 4 and 11, respectively. The optimal sorbent loading for the batch-type solid-phase extraction of DA was 0.67 mg-TiO₂ ng-DA⁻¹ and adsorption equilibrium was achieved in 2 h at room temperature. The desorbed DA in 500 μL of 0.1 M alkaline borate buffer can be directly derviatized by 4-fluoro-7-nitro-2,1,3-benzoxadiazole (NBD-F) in aqueous media for fluorimetric HPLC quantification. Analyte recovery, repeatability and detection limit of this titania SPE-fluorimetric HPLC determination are 89%, 6.2% and 120 pg-DA mL⁻¹ (n = 7, P < 0.05), respectively, for a sample volume of 30 mL. This titania SPE technique should also be applicable to the pre-concentration of other polar carboxylate- and phosphonate-containing biomolecules and pharmaceuticals in complex and interfering environmental sample matrices.