The free solution mobility of DNA in Tris-acetate-EDTA buffers of different concentrations,with and without added NaCl

The free solution mobility of a high-molecular-weight DNA, linear pUC19, and a 20-bp oligomer called dsA5 have been studied as a function of Tris-acetate-EDTA (TAE) buffer concentration, with and without added NaCl. The two DNAs migrate as separate peaks during capillary electrophoresis, because the mobility of linear pUC19 is higher than that of the 20-bp oligomer. In TAE buffers ranging from 10-400 mM in concentration, the migration times and peak areas of the two DNAs are independent of whether they are electrophoresed separately or in mixtures, indicating that DNA-DNA and DNA-buffer interactions are absent in these solutions. The migration times of the two DNAs vary and the peak areas are not additive when the TAE buffer concentration is reduced to 5 mM or below, indicating that DNA-DNA and DNA-buffer interactions are occurring at very low TAE buffer concentrations. The mobilities of linear pUC19 and dsA5 decrease slowly with increasing conductivity or ionic strength when the conductivity is increased by increasing the TAE buffer concentration. When the Tris buffer concentration is held constant and the conductivity is increased by adding various concentrations of NaCl to the solution, the mobilities of linear pUC19 and dsA5 first increase slightly, then become independent of solution conductivity (or ionic strength), and finally decrease when the NaCl concentration is increased above approximately 50 mM. The mobility variations observed in the various TAE and TAE-NaCl solutions are described qualitatively by Manning's theory, although quantitative agreement is not achieved. The free solution mobilities of single-stranded pUC19 and two 20-base oligonucleotides have also been measured. The free solution mobility of single-stranded pUC19 is approximately 15% lower than that of native pUC19, in agreement with other results in the literature. Somewhat surprisingly, the mobilities of the single- and double-stranded 20-mers are equal to each other in TAE buffers with and without added NaCl.     

Making use of social prototypes: From fuzzy concepts to firm decisions

Evidence suggestive of the ‘fuzzy’ structure of many natural language (as opposed to scientific) categories is reviewed. Examples are drawn from categorization schemes for objects, such as cars, fruit or tables, as well as for people, such as extroverts, hippies and ‘fraternity types’. It is argued that despite the fuzziness of natural categories, there is orderliness and utility to these concepts, as well. Specifically, natural categories are organized around prototypes, representative category members, which serve as reference points for the category. The identification of category members involves a prototype-matching process. Prototypes about ‘kinds of people’ can be very useful in decisions about people with whom to affiliate and places in which to live. This process was illustrated by reference to a case analysis of students' preferences for university housing. It was concluded that natural categories may well be fuzzy, but they are far from being dispensible.     

An equivalent subproblem relaxation for improving the solution of a class of transportation scheduling problems

In this paper an algorithm is presented for determining the K best paths that may contain cycles in a directed network.The basic idea behind the algorithm is quite simple. Once the best path has been determined it is excluded from the network in such a way that no new path is formed and no more paths are excluded. This step leads to an enlarged network where all the paths, but the best one, can be determined. The method is repeated until the desired paths have been computed.The proposed algorithm can be used not only for the classical K shortest paths problem but also for ranking paths under a nonlinear objective function, provided that an algorithm to determine the best path exists.Computational results are presented and comparisons with other approaches for the classical problem are made.     

New amino-functionalized 1,3-alternate calix[4]arene bis- and mono-(benzo-crown-6 ethers) for pH-switched cesium nitrate extraction

Four calix[4]arene benzo-crown-6 ethers functionalized with primary amine groups in various positions have been synthesized. The cesium extraction behavior under alkaline and acidic conditions has been measured for these compounds and compared with that of non-amine containing analogs. Extraction strength when the amine group is neutral is not affected by the amino substituent, but protonation causes a marked decrease in extraction strength, permitting pH-switched back-extraction.     

Surface modification of iron oxide nanoparticles by a phosphate‐based macromonomer and further encapsulation into submicrometer polystyrene particles by miniemulsion polymerization

A new strategy relying on the use of a phosphate‐based macromonomer (PAM200) to modify the surface of iron oxide nanoparticles was developed for the synthesis of submicrometer polystyrene (PS) magnetic particles. First, iron oxide nanoparticles were synthesized using the coprecipitation of ferrous and ferric salts in alkaline medium. Besides the classical oleic acid (OA)/octane‐based ferrofluid, styrene‐based ferrofluids were elaborated with either OA or PAM200 as the stabilizer. In all cases, maghemite (γ‐Fe₂O₃) was clearly identified, with nanoparticles rather spherical in shape but exhibiting broad particle size distribution (PSD). Both OA and PAM200 led to stable maghemite‐based ferrofluids showing superparamagnetic properties. Further use of these ferrofluids in styrene miniemulsion polymerization resulted in inhomogeneous distribution of maghemite among and inside the polymer particles with OA‐based ferrofluids, whereas PAM200/styrene‐based ferrofluids led to magnetic particles with homogeneous distribution of maghemite inside PS particles. Broad PSD and small nonmagnetic particles were however observed. The true mechanisms operating in these systems are still to elucidate, but this study validates PAM200 as an efficient compatibilizing agent between hydrophilic maghemite and hydrophobic PS. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 327–340, 2008     

Liouville-type theorems for some complex hypoelliptic operators

It is shown that the natural analogue of Liouville's theorem holds for the well-known hypoelliptic operators _α (for ¦α¦ < n) introduced and studied by Folland and Stein on the Heisenberg group H_n. Since these operators are non-real for α ≠ 0, the usual methods of potential theory fail and are replaced by an explicit use of the fundamental solution.     

CAPACITY AND PRICE OF NONRENEWABLE RESOURCE DEPOSITS

This paper develops a model to determine the planned rate of production from a nonrenewable resource deposit and applies the model to the U.S. copper industry to estimate changes in aggregate planned copper production as a function of copper price expectations. Standard investment theory is applied in the model to examine the choice of the planned rate of extraction from limited volume resource deposits. A setting is analyzed in which the total production volume from any site is fixed by the size of the resource deposit at that site. Within this setting, the planned rate of resource extraction is a fully endogenous solution of the model. Properties of the model are investigated to determine changes in the planned rate of production caused by variation in operating cost, investment cost and output price parameters. The planned rate of production from any deposit is found to increase at a decreasing rate, given incremental increases in the output price, ceteris paribus. The finding is illustrated with data describing mined and yet-to-be mined copper deposits in the United States. A close match is observed between the calculated production rate for mined copper deposits and the mine capacity (rate of production) chosen by the owners of those deposits, given plausible assumptions about mine owner price expectations. The planned rate of production is aggregated across all deposits and plotted as a function of output price. An aggregate medium run copper supply curve is obtained, indicating the elasticity of planned production to changes in the expected long run output price of copper. This empirical example suggests that doubling the output price from $1 to $2 per pound copper, would triple aggregate planned copper production in the United States.     

Parent Beliefs about Technology and Innovative Mathematics Instruction

Parent beliefs about roles of education, teachers, computers, and innovative mathematics instruction were examined through factor analysis. Strong relationships between parent beliefs regarding teacher and computer roles were found. The beliefs of parents about the similar roles of teachers and computers in education may impact the implementation of innovations in mathematics education and the uses of computers in education. Reciprocally, the ways computers are implemented in education may impact the beliefs parents have about the purposes of education.