THE ENERGY ASPECT OF THE RECIPROCAL INTERACTIONS OF PAIRS OF TWO DIFFERENT VIBRATION MODES OF A CLAMPED ANNULAR PLATE

The standardized mutual active and reactive sound power of a clamped plate, representing the energy aspect of the reciprocal interactions of two different in vacuo modes, has been computed. It was assumed that the vibrations are axisymmetric, elastic and time harmonic, the plate's transverse deflection is small as compared with the plate's size, and that the vibration velocity is small as compared with the acoustic wavenumber generated. The Kirchhoff-Love theory of a perfectly elastic plate was used. The integral formulae for the mutual sound power were transformed into their Hankel representations which made possible their subsequent computation. A closed path integral was used to express the integral in its Hankel representation to compute the mutual active sound power. The asymptotic stationary phase method was used to compute the two magnitudes, i.e., the mutual active and reactive sound power. The results obtained are the asymptotic formulae valid for the acoustically fast waves. The oscillating as well as the non-oscillating terms have been identified in the formulae to make possible their further separate analysis. The availability of the asymptotic formulae makes possible some fast numerical computations of the mutual sound power. Moreover, the formulae presented herein, together with those for the individual modes known from the literature, make a complete basis for further computations of the total sound power of the plate's damped and forced vibrations in fluid.     

Preservice Elementary Teachers' Use of Mathematics in a Project‐Based Science Approach

The use of a project‐based science (PBS) approach to teaching encourages students to integrate mathematics and science in meaningful ways as they create projects. As a beginning study of how students use mathematics in such an approach, an analysis of 23 projects developed by preservice elementary teachers enrolled in an elementary science course was conducted. Findings showed that students made a number of different types of mathematical errors and underutilized data representation and summary forms. Implications included the importance of developing methods for supporting the use of mathematical tools in utilizing a project‐based approach and considering ways that such tools mediate scientific thinking.     

Studies of the kinetics of the reduction of chromate by glutathione and related thiols

The reduction of chromate by glutathione, its mono- and diethyl esters, -cysteine, 2-mercapto-propionic acid and mercapto-succinic acid has been studied. The empirical rate law k_obs = ab[Thiol]²/(1 + b[Thiol]) is obeyed by all of these thiols, at neutral pH. No evidence could be obtained for a first-order pathway in glutathione under these conditions. These observations are used to comment on the stability of intermediates potentially important in explaining chromate toxicity.     

Thiol–norbornene materials: Approaches to develop high Tg thiol–ene polymers

The ability to prepare high T_g low shrinkage thiol–ene materials is attractive for applications such as coatings and dental restoratives. However, thiol and nonacrylated vinyl materials typically consist of a flexible backbone, limiting the utility of these polymers. Hence, it is of importance to synthesize and investigate thiol and vinyl materials of varying backbone chemistry and stiffness. Here, we investigate the effect of backbone chemistry and functionality of norbornene resins on polymerization kinetics and glass transition temperature (T_g) for several thiol–norbornene materials. Results indicate that T_gs as high as 94 °C are achievable in thiol–norbornene resins of appropriately controlled chemistry. Furthermore, both the backbone chemistry and the norbornene moiety are important factors in the development of high T_g materials. In particular, as much as a 70 °C increase in T_g was observed in a norbornene–thiol specimen when compared with a sample prepared using allyl ether monomer of analogous backbone chemistry. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 5686–5696, 2007     

Oxygen inhibition in thiol–acrylate photopolymerizations

The overall effects of oxygen on thiol–acrylate photopolymerizations were characterized. Specially, the choice of thiol monomer chemistry, functionality, and concentration on the extent of oxygen inhibition were considered. As thiol concentration was increased, the degree of oxygen inhibition was greatly reduced because of chain transfer from the peroxy radical to the thiol. When comparing the copolymerization of 1,6‐hexanediol diacrylate with the alkane‐based thiol (1,6‐hexane dithiol) to the copolymerization with the propionate thiol (glycol dimercaptopropionate), it was found that the propionate system was much more reactive and polymerized to a greater extent in the presence of oxygen. In addition, the functionality was considered where the glycol dimercaptopropionate was compared to a tetrafunctional propionate of similar chemistry (pentaerythritol tetrakis(mercaptopropionate)). Given the same thiol concentration, the higher functionality thiol imparted a faster polymerization rate, due to the increased polymer system viscosity, which limited oxygen diffusion and decreased the extent of overall oxygen inhibition. Thus, preliminary insight is provided into how thiol monomer choice affects the extent of oxygen inhibition in thiol–acrylate photopolymerization. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 2007–2014, 2006     

Monotonicity of the number of self-avoiding walks

It is shown that the numberc _n of self-avoiding walks of lengthn in ^d is an increasing function ofn.     

The synthesis and chemical reactions of certain pyrazolo[1,5-a]-1,3,5-triazines

3-Aminopyrazole was utilized as a starting material for the preparation of certain pyrazolo-[1,5-a]-1,3,5-triazines. 4-Chloro-2-methylthiopyrazolo[1,5-a]-1,3,5-triazine was prepared and used for studies of nucleophilic displacement reactions, and it has been found that both the chloro and methylthio groups may be displaced by nucleophiles. By modifications of these procedures we have prepared the adenine, hypoxanthine, and xanthine analogs of the pyrazolo-[1,5-a]-1,3,5-triazine ring system. Electrophilic substitution occurs in the 8-position of this ring system. The methyl group was introduced into the 4-position by a novel ring opening and ring closing of the 1,3,5-triazine ring.     

Synthesis,stereochemistry and pharmacological activity of rac.-cis-tetrahydro-6-hydroxy-7-(4-methoxyphenyl)-1,4-thiazepin-5(2H)-ones

Reaction of 2-aminoethanethiol ( 3 ) with trans-3-(p-methoxyplienyl)glycidate ( 4 ) gave the rac.-cis-1,4-thiazepinone 5 and a by-product 6 . The structure of 5 was proven by X-ray crystallography. The X-ray data revealed that this compound adopts the chair conformation in the solid state and the heterocyclic ring is sevenmembered. The structure of the by-product 6 was elucidated on the basis of spectral data. Compounds 9 and 10 were inactive as calcium channel blocking agents.     

Electrokinetic molecular separation in nanoscale fluidic channels

This report presents a study of electrokinetic transport in a series of integrated macro- to nano-fluidic chips that allow for controlled injection of molecular mixtures into high-density arrays of nanochannels. The high-aspect-ratio nanochannels were fabricated on a Si wafer using interferometric lithography and standard semiconductor industry processes, and are capped with a transparent Pyrex cover slip to allow for experimental observations. Confocal laser scanning microscopy was used to examine the electrokinetic transport of a negatively charged dye (Alexa 488) and a neutral dye (rhodamine B) within nanochannels that varied in width from 35 to 200 nm with electric field strengths equal to or below 2000 V m-1. In the negatively charged channels, nanoconfinement and interactions between the respective solutes and channel walls give rise to higher electroosmotic velocities for the negatively charged dye than for the neutral dye, towards the negative electrode, resulting in an anomalous separation that occurs over a relatively short distance (<1 mm). Increasing the channel widths leads to a switch in the electroosmotic transport behavior observed in microscale channels, where neutral molecules move faster because the negatively charged molecules are slowed by the electrophoretic drag. Thus a clear distinction between "nano-" and "microfluidic" regimes is established. We present an analytical model that accounts for the electrokinetic transport and adsorption (of the neutral dye) at the channel walls, and is in good agreement with the experimental data. The observed effects have potential for use in new nano-separation technologies.