Partitioning arrangements of lines II: Applications

In this paper we present efficient deterministic algorithms for various problems involving lines or segments in the plane, using the partitioning algorithm described in a companion paper [A3]. These applications include: (i) anO(m ^2/3 n ^2/3 · log^2/3 n · log^/3 (m/n)+(m+n) logn) algorithm to compute all incidences betweenm points andn lines, where is a constant <3.33; (ii) anO(m ^2/3 n ^2/3 · log^5/3 n · log^/3 (m/n)+(m+n) logn) algorithm to computem faces in an arrangement ofn lines; (iii) anO(n ^4/3 log^(+2)/3 n) algorithm to count the number of intersections in a set ofn segments; (iv) anO(n ^4/3 log^{( + 2)/3} n) algorithm to count red-blue intersections between two sets of segments, and (v) anO(n ^3/2 log^/3 n) algorithm to compute spanning trees with low stabbing number for a set ofn points. We also present an algorithm that, given set ofn points in the plane, preprocesses it, in timeO(nm log^+1/2 n), into a data structure of sizeO(m) forn lognmn ², so that the number of points ofS lying inside a query triangle can be computed inO((n/m) log^3/2 n) time.Work on this paper has been supported by Office of Naval Research Grant N00014-87-K-0129, by National Science Foundation Grant DCR-83-20085, and by grants from the Digital Equipment Corporation and the IBM Corporation. A preliminary version of this paper appears in theProceedings of the 5th ACM Symposium on Computational Geometry, 1989, pp. 11–22.     

Adsorption Equilibrium and Kinetics of Egg-White Proteins on Immobilized Metal Ion Affinity Gels for Designing Fractionation

Designing an Immobilized Metal ion Affinity (IMA) chromatographic process on large scale demands a thorough understanding to be developed regarding the adsorption behaviour of proteins on metal loaded IMA (IMA-M(II)) gels and the characteristic adsorption parameters to be evaluated. This research investigation illustrates the significance of these aspects for the proposed fractionation of chicken egg-white proteins on these gels. Consequently, a systematic investigation of the adsorption characteristics of three chicken egg-white proteins viz., ovalbumin, conalbumin and lysozyme on Cu(II) and Ni(II) loaded IMA gels, iminodiacetate (IDA) and tris(2-aminoethyl)amine (TREN), has been undertaken. These gels differ in their selectivity towards the proteins of interest under the identical sets of experimental conditions. While TREN-Ni(II) was selective only for lysozyme, IDA-Cu(II), IDA-Ni(II) and TREN-Cu(II) showed varying affinities for all the three proteins. The equilibrium and kinetic data were analysed using various theoretical models and adsorption parameters were quantified. On the basis of these investigations, various strategies have been proposed for the efficient large-scale fractionation of chicken egg-white proteins on these gels.     

LC-MS–MS Determination of Pregabalin in Human Plasma

A rapid, sensitive and specific method to quantify pregabalin in human plasma using metaxalone as the internal standard is described. Sample preparation involved simple protein precipitation by using acetronitrile as solvent. The extract was analyzed by high-performance liquid chromatography coupled to electrospray tandem mass spectrometry (LC-MS–MS). Chromatography was performed isocratically on Thermo Hypurity C₁₈ 5 μm analytical column, (50 mm × 4.6 mm i.d.). The assay of pegabalin was linear calibration curve over the range 10.000–10000.000 ng mL^?1. The lower limit of quantification was 10.000 ng mL^?1 in plasma. The method was successfully applied to the bioequivalence study of pregabalin capsules (150.0 mg) administered as a single oral dose.     

Angular heterocycles. Utilization of arylaminonaphthoquinones in the synthesis of benzophenothiazines

Substituted 6-ethoxyanilino-5H-benzo[a]phenothiazin-5-ones (3a-f) were synthesized by the cyclocondensation of 2-chloro-3-ethoxyanilino-1,4-naphthoquinones with zinc mercaptides of 2-aminothiophenol in pyridine. The nmr, ir and mass spectral data are presented and discussed.     

Phase transitions in chlorobenzene-cis-decalin mixtures

The dielectric constant ?' and loss tangent tan δ of chlorobenzene-cis-decalin mixtures have been measured in the temperature range 77 K to 330 K and frequency range 0.1 to 100 kHz. On cooling, ?' increases with decreasing temperature upto about 135 K, after which it drops rapidly with decreasing T followed by a slow decrease. This indicates that the liquid mixture goes to an amorphous phase which transforms to a glass phase of restricted dipole rotation below T_g; however, the peak in ?' is due to relaxation in the amorphous phase (α relaxation) and does not give an exact T_g. On heating, the behaviour of the cooling curve is retraced upto 160 K, after which ?' drops suddenly to a value lower than that at 77 K in the glass phase. This indicates the transition to a crystalline phase in which dipole rotational freedom is completely lost. The crystalline phase changes to a eutectic liquid phase of high ?' at a temperature (200 K) lower than the melting point of chlorobenzene and cis-decalin. Dielectric dispersion is observed only in the glass and amorphous phases. The dielectric relaxation time is independent of the concentration of chlorobenzene.     

Dip-pen nanolithography in tapping mode

Dip-pen nanolithography (DPN) is becoming a popular nano-patterning technique for depositing materials onto a substrate using the probe of an atomic force microscope (AFM). Here, we demonstrate the deposition of a short synthetic peptide by DPN using the Tapping Mode of AFM rather than the commonly used contact mode. DPN in Tapping Mode requires drive amplitude modifications for deposition, yet allows for gentle imaging of the deposited material and enables deposition on soft surfaces.     

Protic acid (HClO4 supported on silica gel)-mediated synthesis of 2,3-unsaturated-O-glucosides and a chiral furan diol from 2,3-glycals

Perchloric acid supported on silica gel acts as an excellent reagent system in converting glucals into 2,3-unsaturated-O-glucosides in good to excellent yields in short reaction time with good alpha selectivity. Primary, secondary, and allylic alcohols, phenols, and thiols react with 3,4,6-tri-O-acetyl glucal with equal ease. In addition to this, a chiral furan diol is obtained from unprotected D-glucal or D-galactal in good yields.     

A proposal for Ramsey interferences when spontaneous emission can occur between two interaction zones

The possibility of observing Ramsey fringes in situations where the time separation between two interaction zones is larger than the lifetime is discussed. The spectral characteristics of emission exhibit interferences which are shown to be due to the fact that the spontaneous emission event can occur in two different zones and thus erasing any Welcher-Weg information.It is indeed a great honor for me to contribute an article on the occasion of H. Walther's 60th birthday