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     

Acoustic wavefront imaging

We introduce a new class of experiments which provide graphic insights into the propagation of acoustic waves in anisotropic media. Simply stated, we have devised a means of observing the expanding acoustic wavefront from a point disturbance in a solid. The data may be viewed as a movie or a series of snapshots. The observed wavefronts represent the group-velocity surfaces of acoustic waves, which reflect the basic elastic anisotropy of the solid. The technique has been applied to coherent acoustic waves with frequencies in the megahertz range (at ambient temperatures) and to incoherent heat pulses in the hundred-gigahertz range (at liquid-helium temperatures). In this article, we first provide a pedagogical introduction to wave propagation in elastically anisotropic media, reviewing some early methods for visualizing acoustic waves. Next, we describe the “acoustic wavefront imaging” method and give representative results in crystals and composite materials. Finally, we show how this method relates to recent advances in phonon imaging and internal diffraction of ultrasound.     

Toward a microchip-based solid-phase extraction method for isolation of nucleic acids

A silica-based solid-phase extraction system suitable for incorporation into a microchip platform (nu-total analytical system; nu-TAS) would find utility in a variety of genetic analysis protocols, including DNA sequencing. The extraction procedure utilized is based on adsorption of the DNA onto bare silica. The procedure involves three steps: (i) DNA adsorption in the presence of a chaotropic salt, (ii) removal of contaminants with an alcohol/water solution, and (iii) elution of the adsorbed DNA in a small volume of buffer suitable for polymerase chain reaction (PCR) amplification. Multiple approaches for incorporation of this protocol into a microchip were examined with regard to extraction efficiency, reproducibility, stability, and the potential to provide PCR-amplifiable DNA. These included packing microchannels with silica beads only, generating a continuous silica network via sol-gel chemistry, and combinations of these. The optimal approach was found to involve immobilizing silica beads packed into the channel using a sol-gel network. This method allowed for successful extraction and elution of nanogram quantities of DNA in less than 25 min, with the DNA obtained in the elution buffer fraction. Evaluation of the eluted DNA indicated that it was of suitable quality for subsequent amplification by PCR.     

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.