On Producing Multiple Solutions Using Repeated Trials

The number of trials that is required by an algorithm to produce a given fraction of the problem solutions with a specified level of confidence is analyzed. The analysis indicates that the number of trials required to find a large fraction of the solutions rapidly decreases as the number of solutions obtained on each trial by an algorithm increases. In applications where multiple solutions are sought, this decrease in the number of trials could potentially offset the additional computational cost of algorithms that produce multiple solutions on a single trial. The analysis framework presented is used to compare the efficiency of a homotopy algorithm to that of a Newton method by measuring both the number of trials and the number of calculations required to obtain a specified fraction of the solutions.     

Synthesis and thermal crosslinking of oxazolidine‐functionalized polyurethanes

A new oxazolidine derivative was obtained from phenol, 2‐amino‐2‐methylpropane‐1,3‐diol and paraformaldehyde. The reaction of this novel oxazolidine diol with phenylisocyanate lead to a urethane model compound which can be polymerized thermally by oxazolidine ring opening to give a Mannich bridge structure. Linear segmented polyurethanes were prepared by reaction of different ratios of oxazolidine diol and commercial polyethylenglycol (M_w ～ 400) with 4,4′‐methylenbis (cyclohexylisocyanate) (HMDI, 90% isomers mixture). The polyurethanes were thermally characterized and crosslinked by oxazolidine ring opening to obtain materials which showed improved thermal stability. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 4965–4973, 2007     

Active set algorithms for isotonic regression; A unifying framework

In this and subsequent papers we will show that several algorithms for the isotonic regression problem may be viewed as active set methods. The active set approach provides a unifying framework for studying algorithms for isotonic regression, simplifies the exposition of existing algorithms and leads to several new efficient algorithms. We also investigate the computational complexity of several algorithms.In this paper we consider the isotonic regression problem with respect to a complete order where eachw _i is strictly positive and eachy _i is an arbitrary real number. We show that the Pool Adjacent Violators algorithm (due to Ayer et al., 1955; Miles, 1959; Kruskal, 1964), is a dual feasible active set method and that the Minimum Lower Set algorithm (due to Brunk et al., 1957) is a primal feasible active set method of computational complexity O(n ²). We present a new O(n) primal feasible active set algorithm. Finally we discuss Van Eeden's method and show that it is of worst-case exponential time complexity.This work was supported by the National Science and Engineering Research Council of Canada under Research Grant A8189 and an Ontario Graduate Scholarship.     

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Flow-injection spectrofluorimetric determination of ethylenethiourea

A flow-injection configuration is proposed for the fluorimetric determination of ethylenethiourea. The procedure is based on the inhibitory effect of ethylenethiourea on the oxidation of thiamine to thiochrome by mercury(II). A linear calibration graph was obtained between 0.1 and 2.0 μg mL^–1, with a sampling rate of 40 samples per hour and a relative standard deviation of about 1.11%. The usefulness of the method was tested for the determination of ethylenethiourea residues in water, milk, potatoes, pear, grape and apple. Received: 26 January 1998 / Revised: 6 April 1998 / Accepted: 9 April 1998     

Effect of reaction media on the growth and photoluminescence of colloidal CdSe nanocrystals

Using cadium oxide (CdO) as the Cd precursor and tri-n-octylphosphine selenide (TOPSe) as the Se source, TOP-capped and TOP/tri-n-octylphosphine oxide (TOPO)-capped CdSe nanocrystals were synthesized without the use of an acid. The synthetic approach involved the addition of a TOPSe/TOP solution into a CdO/TOP solution with or without TOPO at one temperature and subsequent growth at a lower temperature. The temporal evolution of the optical properties, namely, absorption and luminescence, of the growing nanocrystals was monitored in detail. A comprehensive examination on the control of the photoluminescence (PL) properties was performed by systematically varying the TOP/TOPO weight ratio of the reaction media. Surprisingly, a rational choice of 100% TOP or 80% TOP was found to produce "quality" nanocrystals when monitored under the present experimental conditions and growth-time scale. The term "quality" is mainly based on the sharp features and rich substructure exhibited in the absorption spectra of the growing nanocrystals, as well as the sharp features in the emission spectra with narrow full width at half-maximum (fwhm). There are two distinguishable stages of growth: an early stage (<5 min) and a later stage. TOP plays a major role in the control of a slow growth rate in the early stage, while TOPO controls slow growth in the later stage. The optical sensitivity of the growing nanocrystals when dispersed in nonpolar or polar solvents was studied, including two size-dependent parameters, namely, the solvent sensitivity (PL intensity) and nonresonant Stokes shift (NRSS). The insights gained from the present study enable a synthetic approach in which high-quality CdSe nanocrystals are achieved with high synthetic reproducibility.     

Synthesis of tridimensional polymers by the copolymerization of phenylglycidylether with aromatic diglycidylethers

Copolymers from phenylglycidylether and several aromatic diglycidylethers are prepared using different ratios of difunctional comonomers and the AIP/ZnCl₂ initiator system. It is found that the percentage of incorporated comonomer depends on the nature of the aromatic moiety introduced. The copolymers are characterized by ¹³C-NMR spectroscopy and turn out to be completely regular and with a high degree of isotacticity (about 80%) that confirms the high degree of regio- and stereoselectivity of the initiator system used. The thermal characteristics of copolymer networks are investigated using differential scanning calorimetry and thermogravimetry. Two fusion endotherms are observed which vary with the degree of crosslinking. By thermogravimetric analyses the thermal stability is found to increase when the crosslinking degree does. © 1994 John Wiley & Sons, Inc.