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.     

The Existence of Positive Solutions to Neutral Differential Equations

In this paper, we shall consider a class of neutral differential equations of the form

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where τ (0, ∞), σ [0, ∞), Q(t) C([t₀, ∞), R ⁺ ), r(t) C([t₀, ∞), (0, ∞)) with r(t) nondecreasing on [t₀ − τ, ∞). We shall show that all positive solutions of ( * ) can be classified into four types, A, B, C, and D, and we shall obtain sufficient and necessary conditions for the existence of A-type, B-type, and D-type positive solutions of ( * ), respectively. A sufficient condition for the existence of C-type positive solutions of ( * ) is also given. Finally, we shall offer a sharp oscillation result for all solutions of ( * ). Our results generalize and improve those established in B. Yang and B. G. Zhang (Funkcial. Ekvac.39 (1996), 347–362).     

Efficient and selective enzymatic acylation reaction: separation of furanosyl and pyranosyl nucleosides

Candida antarctica lipase-B (CAL-B) immobilized on lewatite selectively acylated the primary hydroxyl group of the furanosyl nucleoside in a mixture of 1-(alpha-D-arabinofuranosyl)thymine and 1-(alpha-D-arabinopyranosyl)thymine. This selective biocatalytic acylation of furanosyl nucleoside has enabled us an easy separation of arabinofuranosyl thymine from an inseparable mixture with arabinopyranosyl thymine. The primary hydroxyl selective acylation methodology of arabinonucleoside has also been successfully used for the separation of 1-(beta-D-xylofuranosyl)thymine and 1-(beta-D-xylopyranosyl)thymine from a mixture of the two, which demonstrate the generality of the enzymatic methodology for separation of furanosyl and pyranosyl nucleosides.     

Physico-mechanical properties and biodegradation of oxo-degradable HDPE/PLA blends

Blends of high density polyethylene/poly(lactic acid) with/without compatibilizer and pro-oxidant (cobalt stearate) were prepared by melt blending technique. In ratio 80/20, the blend revealed a good combination of tensile properties and optimum poly(lactic acid) content. The improvement in mechanical properties of this blend was achieved by addition of 4 phr compatibilizer. Cobalt stearate (CoSt) was added to 80/20 blends in 0.1% and 0.2% (w/w) ratios. The obtained blends were characterized by DSC, SEM, FTIR spectroscopy, rheological study, etc. All the prepared blends were able to biodegrade in composting environment and the blend containing pro-oxidant was maximum degraded.     

Low-velocity pneumatic conveying in horizontal pipe for coarse particles and fine powders

First,the characteristics of low-velocity conveying of particles having different hardness are experimentally investigated in a horizontal pipeline in terms of flow pattern and pressure drop to show that the slug flow can be classified into two types depending on the settling of particles along the pipeline,and the period is small for slug flow without the settled layer,which is called solitary slug flow.The pressure drop for soft particles is shown to be larger than that for hard particles.Then,experimental results are presented on horizontal fluidized-bed conveying of fine powders to show that air release from the top surface of the conveying channel is an important factor for high mass flow rate of particles.     

Optical properties of multilayered Period-Doubling and Rudin-Shapiro porous silicon dielectric heterostructures

To investigate the optical properties in quasi-regular porous-silicon-based dielectric Period-Doubling and Rudin-Shapiro multilayer systems, we study here the reflection of light from these structures. The Period-Doubling and Rudin-Shapiro structures are fabricated in such a way that the optical thickness of each layer is one quarter of 600 and 640 nm respectively. We find that porous silicon Period-Doubling dielectric multilayers could demonstrate the optical properties similar to the classical periodic Febry–Perot interference filters with one or multiple resonant peaks, but with an advantage of having total optical thickness much lesser than the periodic structures. Additionally, light propagation in porous silicon Rudin-Shapiro structures is investigated for the first time, both theoretically and experimentally. The reflectance spectra of the structures exhibit photonic band gaps centered at predetermined wavelengths. In both cases, numerical simulation of light transmission is performed using transfer matrix method.     

Gamma-irradiated onions as a biological indicator of radiation dose.

Post-irradiation identification and dose estimation are required to assess the radiation-induced effects on living things in any nuclear emergency. In this study, radiation-induced morphological/cytological changes i.e., number of root formation and its length, shooting length, reduction in mitotic index, micronuclei formation and chromosomal aberrations in the root tip cells of gamma-irradiated onions at lower doses (50-2000 cGy) are reported. The capabilities of this biological species to store the radiation-induced information are also studied.