A Comparison of Two Variational Methods

A discussion is given of the relation between the maximum functionaltheorem and Schwinger's variational principle, and it is shownthat the bound given by Schwinger's principle is better thanor the same as that given by the maximum functional theorem.     

On nearly pseudocompact spaces

A completely regular space X is called nearly pseudocompact if υX?X is dense in βX?X, where βX is the Stone-?ech compactification of X and υX is its Hewitt realcompactification. After characterizing nearly pseudocompact spaces in a variety of ways, we show that X is nearly pseudocompact if it has a dense locally compact pseudocompact subspace, or if no point of X has a closed realcompact neighborhood. Moreover, every nearly pseudocompact space X is the union of two regular closed subsets X₁, X₂ such that Int X₁ is locally compact, no points of X₂ has a closed realcompact neighborhood, and $\text{Int(X}{}_1\text{?X}{}_2\text{)=?}$. It follows that a product of two nearly pseudocompact spaces, one of which is locally compact, is also nearly pseudocompact.     

Development and validation of an HPLC method for quantitation of BA‐TPQ,a novel iminoquinone anticancer agent,and an initial pharmacokinetic study in mice

We herein describe the development and validation of an HPLC method for the quantitation of 7‐(benzylamino)‐1,3,4,8‐tetrahydropyrrolo [4,3,2‐de]quinolin‐8(1H)‐one (BA‐TPQ), a newly synthesized iminoquinone anticancer agent. BA‐TPQ was extracted from plasma and tissue samples by first precipitating proteins with acetonitrile followed by a liquid–liquid extraction with ethyl acetate. Chromatographic separation was carried out using a gradient flow rate on a Zorbax SB C₁₈ column, and the effluent was monitored by UV detection at 346 nm. The method was found to be precise, accurate, and specific, with a linear range of 3.91–1955.0 ng/mL in plasma, 19.55–1955.0 ng/mL in spleen, brain, and liver homogenates and 19.55–3910.0 ng/mL in heart, lung and kidney homogenates. The method was stable under all relevant conditions. Using this method, we also carried out an initial study determining plasma pharmacokinetics and tissue distribution of BA‐TPQ in mice following intravenous administration. In summary, this simple and sensitive HPLC method can be used in future preclinical and clinical studies of BA‐TPQ.     

Further Gurtin-type Variational Principles for Linear Initial Value Problems

Following the variational principles for linear initial valueproblems associated with the wave and heat conduction equationsdiscussed by Gurtin and Leitmann and using time convolutionsit is shown that general variational principles exist for theseproblems with sources on the boundaries and within the regionunder consideration.     

Modified Locally One Dimensional Methods for Parabolic Partial Differential Equations in Two Space Variables

In this note we consider the locally one dimensional methodas discussed in Gourlay & Mitchell (1969, 1972) and indicatehow this scheme can be used to solve accurately a parabolicpartial differential equation in two space variables.