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.     

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.     

A review of the relationship between quality control and donor sample results obtained from serological assays used for screening blood donations for anti-HIV and hepatitis B surface antigen

Quality control principles, initially designed for manufacturing, have been applied to clinical chemistry and later to serological testing for infectious diseases. Methods for setting control limits have been included using the effects of assay performance on clinical outcomes. However, this approach assumes that the reactivity of patient samples change proportionally with the results of quality control samples tested in the same assay. Although this may be the case for clinical chemistry, this assumption has never been tested for serological assays. During a 9-month period, 177910 and 185684 donor test results for HBsAg and anti-HIV, respectively, were analysed and compared with 712 HBsAg and 710 anti-HIV results obtained from a single batch of a multimarker quality control sample obtained from the same assays. Results of the analysis showed that the negative donor results did not change in proportion with the changes experienced by the quality control sample results as determined by regression coefficients, particularly when results obtained from different reagent batches were compared. There were insufficient results obtained from positive samples for a similar analysis. However, investigations show that, even if the reactivity of positive donor samples changed in proportion with the change in reactivity of the quality control sample, few false-negative donor test results would have occurred.     

Localized surface plasmon resonances of anisotropic semiconductor nanocrystals

We demonstrate that anisotropic semiconductor nanocrystals display localized surface plasmon resonances that are dependent on the nanocrystal shape and cover a broad spectral region in the near-IR wavelengths. In-plane and out-of-plane dipolar resonances were observed for colloidal dispersions of Cu(2-x)S nanodisks, and the wavelengths of these resonances are in good agreement with calculations carried out in the electrostatic limit. The wavelength, line shape, and relative intensities of these plasmon bands can be tuned during the synthetic process by controlling the geometric aspect ratio of the disk or using a postsynthetic thermal-processing step to increase the free carrier densities.     

A Novel Xanthone from Garcinia oligantha

One novel xanthone, oliganthone A ( 1 ), was isolated from the stems of the plant Garcinia oligantha. It features the O‐bearing C(3)‐atom and absence of C(4) compared with the structures of related known xanthones, which have never been reported before. The structure of this compound was elucidated by spectroscopic analysis. Compound 1 showed strong HeLa cell growth‐inhibiting effects with IC₅₀ values below 10 μM .