Link distance and shortest path problems in the plane

This paper describes algorithms to compute Voronoi diagrams, shortest path maps, the Hausdorff distance, and the Fréchet distance in the plane with polygonal obstacles. The underlying distance measures for these algorithms are either shortest path distances or link distances. The link distance between a pair of points is the minimum number of edges needed to connect the two points with a polygonal path that avoids a set of obstacles. The motivation for minimizing the number of edges on a path comes from robotic motions and wireless communications because turns are more difficult in these settings than straight movements.Link-based Voronoi diagrams are different from traditional Voronoi diagrams because a query point in the interior of a Voronoi face can have multiple nearest sites. Our site-based Voronoi diagram ensures that all points in a face have the same set of nearest sites. Our distance-based Voronoi diagram ensures that all points in a face have the same distance to a nearest site.The shortest path maps in this paper support queries from any source point on a fixed line segment. This is a middle-ground approach because traditional shortest path maps typically support queries from either a fixed point or from all possible points in the plane.The Hausdorff distance and Fréchet distance are fundamental similarity metrics for shape matching. This paper shows how to compute new variations of these metrics using shortest paths or link-based paths that avoid polygonal obstacles in the plane.     

On the Number of Cylinders Touching a Ball

In this note we prove an upper bound of seven for the maximum number of unit cylinders touching a unit ball in a packing. This improves a previous bound of eight by Heppers and Szab. The value conjectured by Kuperberg in 1990 is six.     

Validated assay for the simultaneous quantification of total vincristine and actinomycin‐D concentrations in human EDTA plasma and of vincristine concentrations in human plasma ultrafiltrate by high‐performance liquid chromatography coupled with tandem mass spectrometry

A sensitive, specific and efficient high‐performance liquid chromatography/tandem mass spectrometry (HPLC/MS/MS) assay for the simultaneous determination of total vincristine and actinomycin‐D concentrations in human plasma and an assay for the determination of unbound vincristine are presented. Electrospray ionization (ESI), atmospheric pressure chemical ionization (APCI) and heated electrospray ionization (H‐ESI) were tested as ionization interfaces. For reasons of robustness ESI was chosen followed by tandem mass spectrometry (ESI‐MS/MS). For the plasma assay a 30 µL aliquot was protein precipitated with acetonitrile/methanol (50:50, v/v) containing the internal standard vinorelbine and 10 µL volumes were injected onto the HPLC system. To determine unbound vincristine, ultrafiltrate was produced from plasma using 30 kDa centrifugal filter units. The plasma ultrafiltrate was mixed with methanol (50:50, v/v), internal standard vinorelbine was added and 20 µL aliquots were injected onto the HPLC system. Separation was achieved on a 50 × 2.1 mm i.d. Xbridge C₁₈ column using 1 mM ammonium acetate/acetonitrile (30:70, v/v) adjusted to pH 10.5 with ammonia, run in a gradient with methanol at a flow rate of 0.4 mL/min. HPLC run time was 6 min. The assay quantifies in plasma vincristine from 0.25 to 100 ng/mL and actinomycin‐D from 0.5 to 250 ng/mL using plasma sample volumes of only 30 µL. Vincristine in plasma ultrafiltrate can be quantified from 1 to 100 ng/mL. Validation results demonstrate that vincristine and actinomycin‐D can be accurately and precisely quantified in human plasma and plasma ultrafiltrate with the presented methods. The assays are now in use to support clinical pharmacological studies in children treated with vincristine and actinomycin‐D. Copyright © 2009 John Wiley & Sons, Ltd.     

Photochromic behaviour of ozonated and photoirradiated cellulose studied by fluorescence spectroscopy

Samples of ozonated pure cotton cellulose have been subjected to three extended periods of irradiation with monochromatic light at 350 nm, with intervening dark periods. The changes during the treatments were monitored using fluorescence spectroscopy. Photochromic behaviour, comprising a fairly rapid emission intensity decrease during irradiation and a slower recovery of the emission intensity in the dark at ambient temperature, was observed. Starting from the completion of the first irradiation/dark treatment the intervening dark reaction almost completely restored the situation prevailing before irradiation. The photochromism observed for a reference sample of cellulose not pretreated with ozone and for microcrystalline cellulose was similar but differed both in amplitude and in fluorescence recovery during the dark periods. The ozonated sample was also irradiated with the entire spectrum of a medium pressure Hg lamp. This treatment caused a strong increase in the emission intensity and a red-shift of the emission maximum. The changes caused by ozonation and irradiation were also studied by diffuse reflectance FT-IR and UV-visible reflectance spectroscopy.     

Use of tryptophan peptides for an HPLC racemization test with fluorescence detection

A new HPLC test has been developed for monitoring the racemiza-tion which occurs during the coupling of Z-Ala-Trp-OH with Val-OMe by various methods. It is based on reversed phase HPLC separation of tripeptide diastereomers (LLL – LDL ) and fluorescence rather than UV detection. The extent of racemization has been estimated for different carbodiimides, mixed anhydrides, and additive-releasing reagents.     

Antiviral effect and mode of action of methanolic extract of Verbascum thapsus L. on pseudorabies virus (strain RC/79)

The methanolic extract of Verbascum thapsus was evaluated for its antiviral activity against the pseudorabies virus strain RC/79 (PrV), and also for its cytotoxic activity on Vero cells. The extract showed CC?? values of 1100?μg?mL?1 and 1426?μg?mL?1 by NRU and MTT assays, respectively. The 50% inhibitory concentration of the extract for PrV plaque formation was determined at 35?μg?mL?1, and selectivity indices were 31.4 (NRU) and 40.7 (MTT). When cells were pre-treated with the extract prior to virus infection, the inhibition in plaque formation was 70%. PrV was highly inhibited when it was incubated with plant extract or when the extract was added during the adsorption phase (99%). However, no inhibitory effect was observed when the extract was added to the cells after the adsorption period. Thus, these results suggest that the methanolic extract of Verbascum thapsus may contain bioactive compound(s) that affect PrV mostly in the adsorption phase.     

Dumbbells of Five-Connected Silicon Atoms and Superconductivity in the Binary Silicides MSi(3) (M = Ca, Y, Lu)

The new metastable binary silicides MSi(3) (M = Ca, Y, Lu) have been synthesized by high-pressure, high-temperature reactions at pressures between 12(2) and 15(2) GPa and temperatures from 900(100) to 1400(150) K. The atomic patterns comprise intricate silicon layers of condensed molecule-like Si(2) dimers. The alkaline-earth element adopts the oxidation state +2, while the rare-earth and transition metals realize +3. All of the compounds exhibit BCS-type superconductivity with weak electron-phonon coupling below critical temperatures of up to 7 K.     

The Infrared and 1H-NMR Spectra of 8-Hydroxyquinoline Adducts of 8-Hydroxyquinoline Complexes of Dioxouranium(VI), Thorium(IV) and Scandium(III)

The ¹H-nmr and infrared spectra of the complexes [M(ox)_n(Hox)] where M = UO₂ (n = 2), Th (n = 4) or Sc (n = 3) and Hox = 8-hydroxyquinoline are discussed. The nmr spectra of the adducts are uninformative with respect to the bonding and structure of these molecules since they dissociate in solution. The solid state ir spectra show that the adducted molecule of 8-hydroxyquinoline is bound to the metal through the phenolic oxygen, the proton forming an intramolecular hydrogen bond between the nitrogen atom of the adducted molecule and the oxygen atom of a neighbouring chelate ring. The mid-and far-ir spectra are reported for the first time and assignments for the δN-H, νM-O and νM-N modes have been made.