Failure of the discrete maximum principle for an elliptic finite element problem

There has been a long-standing question of whether certain mesh restrictions are required for a maximum condition to hold for the discrete equations arising from a finite element approximation of an elliptic problem. This is related to knowing whether the discrete Green's function is positive for triangular meshes allowing sufficiently good approximation of functions. We study this question for the Poisson problem in two dimensions discretized via the Galerkin method with continuous piecewise linears. We give examples which show that in general the answer is negative, and furthermore we extend the number of cases where it is known to be positive. Our techniques utilize some new results about discrete Green's functions that are of independent interest.

     

Pure tone audiograms and possible aminoglycoside-induced hearing loss in belugas (Delphinapterus leucas)

A behavioral response paradigm was used to measure pure-tone hearing sensitivities in two belugas (Delphinapterus leucas). Tests were conducted over a 20-month period at the Point Defiance Zoo and Aquarium, in Tacoma, WA. Subjects were two males, aged 8-10 and 9-11 during the course of the study. Subjects were born in an oceanarium and had been housed together for all of their lives. Hearing thresholds were measured using a modified up/down staircase procedure and acoustic response paradigm where subjects were trained to produce audible responses to test tones and to remain quiet otherwise. Test frequencies ranged from approximately 2 to 130 kHz. Best sensitivities ranged from approximately 40 to 50 dB re 1 microPa at 50-80 kHz and 30-35 kHz for the two subjects. Although both subjects possessed traditional "U-shaped" mammalian audiograms, one subject exhibited significant high-frequency hearing loss above 37 kHz compared to previously published data for belugas. Hearing loss in this subject was estimated to approach 90 dB for frequencies above 50 kHz. Similar ages, ancestry, and environmental conditions between subjects, but a history of ototoxic drug administration in only one subject, suggest that the observed hearing loss was a result of the aminoglycoside antibiotic amikacin.     

Auditory and behavioral responses of bottlenose dolphins (Tursiops truncatus) and a beluga whale (Delphinapterus leucas) to impulsive sounds resembling distant signatures of underwater explosions

A behavioral response paradigm was used to measure masked underwater hearing thresholds in two bottlenose dolphins and one beluga whale before and after exposure to impulsive underwater sounds with waveforms resembling distant signatures of underwater explosions. An array of piezoelectric transducers was used to generate impulsive sounds with waveforms approximating those predicted from 5 or 500 kg HBX-1 charges at ranges from 1.5 to 55.6 km. At the conclusion of the study, no temporary shifts in masked-hearing thresholds (MTTSs), defined as a 6-dB or larger increase in threshold over pre-exposure levels, had been observed at the highest impulse level generated (500 kg at 1.7 km, peak pressure 70 kPa); however, disruptions of the animals' trained behaviors began to occur at exposures corresponding to 5 kg at 9.3 km and 5 kg at 1.5 km for the dolphins and 500 kg at 1.9 km for the beluga whale. These data are the first direct information regarding the effects of distant underwater explosion signatures on the hearing abilities of odontocetes.     

Lipid-lowering effects of ethyl 2-phenacyl-3-aryl-1H-pyrrole- 4-carboxylates in rodents

A series of substituted 2-phenacyl-3-phenyl-1H-pyrrole-4-carboxylates were prepared from substituted acetophenones in 6 steps. The final condensations between a chloroenal and an aminoketone were carried out under neutral conditions in parallel to yield the series listed below. Selected pyrrole derivatives proved to be potent hypolipidemic agents lowering serum triglyceride concentrations in CF-1 male mice after 14 days of I.P. administration. One agent orally lowered serum cholesterol in Sprague-Dawley male rats at 2mg/kg/day after 14 days. The agents demonstrated a lowering of mouse serum LDL- cholesterol levels and selected compounds showed an elevation of serum HDL-cholesterol levels. The cholesterol concentrations in the liver were raised while the cholesterol and triglyceride contents of the aorta were significantly lowered by the selected trisubstituted pyrrole.     

Catalytic asymmetric synthesis of glutamate analogues

Utilizing our lateral metalation coupled with Jacobsen's catalytic asymmetric amino nitrile synthesis, we have demonstrated the ability to synthesize isoxazole-containing amino acid glutamate analogues in high yield and high enantiomeric excesses. Chiral centers alpha or beta at the C-5 position do not detract from diastereoselectivity of the Jacobsen-Strecker reaction. [reaction: see text]     

Noncompliant oligopolistic firms and marketable pollution permits: Statics and dynamics

In this paper, we consider the modeling, analysis, and computation of solutions to both static and dynamic models of multiproduct, multipollutant noncompliant oligopolistic firms who engage in a market for pollution permits. In the case of the static model, we utilize variational inequality theory for the formulation of the governing equilibrium conditions as well as the qualitative analysis of the equilibrium pattern, including sensitivity analysis. We then propose a dynamic model, using the theory of projected dynamical systems, whose set of stationary points coincides with the set of solutions to the variational inequality problem. We propose an algorithm, which is a discretization in time of the dynamic adjustment process, and provide convergence results using the stability analysis results that are also provided herein. Finally, we apply the algorithm to several numerical examples to compute the profit-maximized quantities of the oligopolistic firms' products and the quantities of emissions, along with the equilibrium allocation of licenses and their prices, as well as the possible noncompliant overflows and underflows. This is the first time that these methodologies have been utilized in conjunction to study a problem drawn from environmental policy modeling and analysis.     

Constructing NFC-pigment composite surface treatment for enhanced paper stiffness and surface properties

The use of nano- or microfibrillar cellulose (NFC or MFC) in papermaking is generally hampered by high cost and potentially wasteful use in typical wet end applications. The solubility and fines nature of the material makes it inefficient to retain, and when retained it is generally inefficiently applied within the spatial distribution of the paper fibre matrix. To illustrate the benefits of capturing the important NFC in a layer structure to enhance surface and stiffness properties of paper and board, we present a study whereby NFC is entrapped at the surface of a fibrous web by forming an in situ composite using a porous coating layer, consisting in the exemplified case of modified calcium carbonate. It is shown that NFC can integrate itself within the porous structure providing excellent holdout and thin layer continuity essential in developing an efficient concentration of the NFC at the surface of the substrate. The effect is likened to the well-known I-beam construction. An additional feature is the potential for recycling the remaining fibrous content in the NFC or, more particularly, MFC product after the nanocrystalline cellulose (NCC) gel fraction has been absorbed, allowing for further efficient processing if needed and hence providing a potential cost reduction in the overall NFC/MFC production. The increased smoothness and uniformity obtained is illustrated by confocal laser profilometry and electron microscopy. The effect on permeability is also illustrated.