PIV applied to eckart streaming produced by a medical ultrasound transducer.

Particle image velocimetry (PIV) is applied for the first time to study Eckart streaming induced by a medical ultrasonic transducer operating at a frequency of 3.3 MHz and effective acoustic intensities of 0.25 and 3 Wcm(-2). A temporal series of velocities in a two-dimensional plane were recorded resulting in an experimental set comprising over half a million velocity data points. These enabled average and fluctuating properties to be determined and clearly indicated the quasi-steady nature of the flow. The average large scale velocity fluctuations along the axis caused by this quasi-steady property were calculated to be 2 and 20 m ms(-1) at effective intensities of 0.25 and 3 Wcm(-2) respectively corresponding to approximately 25% of the peak flow velocity in both cases. Furthermore averaged shear rates were calculated with peak values of 1 and 8 s(-1) for the low and high intensities respectively. The present investigation indicates the usefulness of PIV for such studies and serves as a prelude to investigations of streaming in biological type fluids.     

A note on nonnegative rank factorizations

A nonnegative weakly monotone matrix of rank r has a nonnegative rank factorization if and only if it possesses an rxr monomial submatrix.     

Infrared Spectral/Structural Investigation of the Heat Treatment of Tetramethoxysilane/Diethoxydimethylsilane-Derived Gels

Structural changes occurring during the heat treatment of gels that were prepared from binary tetramethoxysilane (TMOS)/diethoxydimethylsilane (DEDMS) mixtures were investigated using infrared spectra. Analysis of the spectral data indicated that the Si-O networks of the heat-treated gels increased their connectivity with increased dehydration due to increased treatment temperature or time. Four- and three-membered (Si-O)_n rings were noted for appropriate heat-treated gel compositions. At higher heat-treatment temperatures, methyl groups were removed from the gel network.     

AlmostP 0-matrices and the classQ

This paper demonstrates that within the class of thosen × n real matrices, each of which has a negative determinant, nonnegative proper principal minors and inverse with at least one positive entry, the class ofQ-matrices coincides with the class of regular matrices. Each of these classes of matrices plays an important role in the theory of the linear complementarity problem. Lastly, analogous results are obtained for nonsingular matrices which possess only nonpositive principal minors.     

Nonnegative (s, t)-potent matrices

This paper contains a study of matrices satisfying A^s = A^t for different positive integers s and t. Representations, similar to Flor's well-known characterization of a nonnegative idempotent matrix, are obtained for nonnegative matrices of this type.     

Carbocyclic synthesis via boranes: stereochemical implications of boron annulation

Boron annulation, hydroboration-carbonylation, of substituted 1,5,9-decatrienes was utilized to prepare the cadinane sesquiterpene system. Stereochemical aspects of the triene hydroboration process and the carbonylation reaction have been analyzed through glc separation of boronate esters. Structural assignments for these esters and their oxidation (H₂O₂/NaOH) products were made through high field ¹H-NMR and other physical and spectral considerations.     

A numerical investigation of the resonance of gas-filled microbubbles: resonance dependence on acoustic pressure amplitude

The general Keller-Herring equation for free gas bubbles is augmented by specific terms to describe the elasticity, viscosity and thickness of the encapsulating shell in ultrasound contrast agent microbubbles. A numerical investigation that analyses the acoustic backscatter from bubbles is employed to identify resonance frequencies that can be compared, for increasing driving pressure amplitude, with linear approximations obtained via analytical considerations. Calculations for bubbles of the size employed in diagnostic ultrasound, between 2 and 6 mum diameter, that are immersed in water and blood and exposed to monochromatic insonation, causing the bubbles to undergo stable cavitation, reveal that the resonance frequency diverges from the linear approximation as the pressure amplitude is increased. The shift in resonance, to lower frequency values, is found to be more pronounced for larger bubbles with the calculated value differing by up to 40% from the linear approximation. The results of this simulation might be potentially useful in preparation of formulations of ultrasound contrast agents with the specifically desired features, such as for instance resonance frequency.     

A Formal,Decision-Theoretic Approach to Flexibility and Robustness

Traditional decision-making techniques only deal with a limited type of uncertainty: that which can be foreseen sufficiently to be expressed as a number of alternate moves between which nature will choose. A plan is formulated which specifies how the decision-maker should respond to nature's moves. Such a plan makes no allowance for uncertainty which could not be foreseen. Unforeseeable uncertainty can only be dealt with if the decision-maker's response to nature's moves is not fixed in advance but is itself uncertain. Flexibility is then defined as the entropy of that uncertainty. It is a measure of both the number of alternative sequences of moves which are open to the decision-maker and his attitude to them. Robustness is a way of trading off flexibility against expected value as estimated under foreseeable uncertainty. The cost of flexibility may be estimated and controlled.     

Annulation of ketones with vinamidinium hexafluorophosphate salts: an efficient preparation of trisubstituted pyridines

alpha-Aryl ketones react with vinamidinium hexafluorophosphate salts to give access to the corresponding 3-arylpyridines. The annulation reactions proceed in good to excellent yields with vinamidinium salts containing electron-withdrawing groups at the beta-position (R(2)). The reaction was applied to the preparation of the COX-2 specific inhibitor 5-chloro-3-(4-methylsulfonyl)phenyl-2-(2-methyl-5-pyridinyl)pyridine (1), as well as a series of analogues.