Interlacing of the zeros of Jacobi polynomials with different parameters

We prove results for the interlacing of zeros of Jacobi polynomials of the same or adjacent degree as one or both of the parameters are shifted continuously within a certain range. Numerical examples are given to illustrate situations where interlacing fails to occur.     

Age-related declines in a two-day reference memory task are associated with changes in NMDA receptor subunits in mice

Background  

C57BL/6 mice show a relationship during aging between NMDA receptor expression and spatial reference memory performance in a 12-day task. The present study was designed to determine if age-related deficits could be detected with a shorter testing protocol and whether these deficits showed a relationship with NMDA receptors. Mice were trained in a reference memory task for two days in a Morris water maze. Cued testing was performed either after or prior to reference memory testing. Crude synaptosomes were prepared from prefrontal/frontal cortex and hippocampus of the mice that underwent reference memory testing first. NMDA receptor subunit and syntaxin proteins were analyzed with Western blotting.     

Transitivität und Homogenität projektiver Ebenen

Ohne Zusammenfassung     

Extraction and gas chromatographic determination of methyl-, ethyl-, and methoxyethylmercury(II) halides

The separation, identification, and determination of methyl-, ethyl-, and methoxyethylmercury(II) halides in biological materials were studied. The procedure developed involved a 24-h leach with 1 M sodium iodide, equilibration of the aqueous phase for 2 min with an equal volume of benzene, and then injection of an aliquot of the benzene phase onto a gas Chromatographic column consisting of 5% cyclohexanedimethanol succinate held on Anakrom ABS. Excellent baseline separation of the Chromatographic peaks was obtained. The extraction steps were monitored with RHgX compounds tagged with ²⁰³Hg. Partition coefficients are reported for methyl- and ethylmercury(II) chlorides, bromides, and iodides; several overall formation constants of the anionic complexes RHgCl_n^1-n (n=2, 3) were determined. Results are reported for the recovery of methyl- and ethylmercury(II) halides from inoculated rye seed, humic and inorganic sediment, and fish grown in an aquarium.     

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.