Vascular morphology by three-dimensional magnetic resonance imaging

A three-dimensional examination of blood vessels is provided using MR data from seven cases. The vascular surfaces are constructed with an algorithm that automatically follows the selected artery or vein and generates a projected three-dimensional gradient shaded image. Fast 3DFT pulse sequences were optimized to enhance the time-of-flight contrast of the intravascular region. By increasing the surface threshold value in a three-dimensional head study, the flesh of a patient's face was peeled away to demonstrate the superfacial temporal artery. Gated cardiac images show the great vessels and cardiac chambers. A three-dimensional view of the aorta shows an irregular surface in the vicinity of an adrenal tumor. 3D MR exams provide a non-invasive technique for assessing vascular morphology in a clinical setting.     

What are We Developing? A Case Study of a College Mathematics Program

Over one‐third of all college mathematics enrollments are in courses considered to be developmental. While such courses have been the subject of a large body of research, one question that seems not to have been studied empirically is the alignment of the content of developmental and college level mathematics courses. This paper gives the results of such a study, conducted at a medium sized public liberal arts university. While the content of the developmental mathematics courses was used subsequently in the Precalculus course, most of the content of the Intermediate Algebra course was not used in other college level mathematics courses. It is hoped that the results of this paper will serve as a catalyst for other institutions to examine carefully and define the mission of both their developmental and college level mathematics courses.     

Characterization of supercommuting matrices

For a given n-by-n matrix A, we consider the set of matrices which commute with A and all of whose principal submatrices commute with the corresponding principal submatrices of A. The properties of this set are examined, with particular attention to its dimension.     

Inertia-preserving secant updates

Corrections to the last two equations of Ref. 1 are given.     

The completely positive and doubly nonnegative completion problems

We prove the following. Let G be an undirected graph. Every partially specified symmetric matrix, the graph of whose specified entries is G and each of whose fully specified submatrices is completely positive (equal to BB^T for some entrywise nonnegative matrix B), may be completed to a completely positive matrix if and only if G is a block-clique graph (a chordal graph in which distinct maximal cliques overlap in at most one vertex). The same result holds for matrices that are doubly nonnegative (entrywise nonnegative and positive semidefinite).     

Coordinate transform invariance

A four-dimensional operator is shown to contain the operator-generators for rotation, scale, reflections, and boosts. The hypothesis is advanced that a physical system changes under this operator by at most a complex phase factor due to invariance against the choice of menial frame. A canonical transform gives a simple relation between space-time and energy-momentum. The basic conserved quantity is a four-dimensional angular momentum and/or coupling constant. The differential of this function contains a second-order differential product which is constrained as a power series in the independent variable. The analysis explores the consequences of the model and shows its degree of correspondence to the standard models.     

Comparison of fluorimetric methods of assay for 7 H-Benz(de)anthracen-7-one in airborne particulates and air pollution source effluents

Summary Various modifications of a thin-layer chromatography fluorimetric method for the determination of 7 H-benz(de)anthracen-7-one (BO) and phenalen-1-one (PO) in complex mixtures have been compared. The best modifications consisted of one-dimensional thin-layer chromatography followed by elution, evaporation, solution in trifluoroacetic acid, followed by either spectrophotofluorimetric or fluorimetric assay. In some cases a quenching agent was necessary to quench the fluorescence of the interferences. Urban atmospheres and air pollution source effluents can be analyzed by these micromethods. These methods with slight modification could be applied to the determination of the aza heterocyclic and the other ring-carbonyl compounds found in urban atmospheres and air pollution source effluents.

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Zusammenfassung Verschiedene Modifikationen einer dünnschichtchromatographischen, fluorimetrischen Methode zur Bestimmung von 7 H-Benz(de)-anthracen-7-on (BO) und Phenalen-1-on (PO) in komplexen Gemischen wurden verglichen. Am besten bewährte sich eindimensionale Dünnschichtchromatographie, nachfolgende Elution, Abdampfen, Aufnehmen in Trifluoressigsäure und schließlich Bestimmung durch Spektralfluoreszenz-oder Fluoreszenzmessung. In manchen Fällen war es nötig, die Fluoreszenz störender Substanzen mit einem geeigneten Reagens zu löschen. Stadtatmosphäre oder Quellen der Luftverunreinigung können mit diesen Mikromethoden analysiert werden. Sie eignen sich nach geringfügiger Modifikation auch zur Bestimmung von azaheterocyklischen und anderen Ring-Carbonylverbindungen in der Atmosphäre.

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Résumé On a comparé entre elles différentes modifications d'une méthode de fluorimétrie avec chromatographie en couche mince pour le dosage de la benzo-7 H anthracène-one-7 (BO) et de la phénalène-one-1 (PO) en mélanges complexes. Les modifications les meilleures ont consisté en une Chromatographie en couche mince unidimensionnelle suivie d'élution, évaporation, mise en solution dans l'acide trifluoroacétique, opérations suivies d'une recherche spectrophotofluorimétrique ou fluorimétrique. Dans certains cas, un agent d'extinction s'est montré nécessaire pour éteindre la fluorescence due aux interférences. On peut analyser par ces microméthodes les atmosphères urbaines et les écoulements sources de pollution de l'air. Ces méthodes ont pu être appliquées après légère modification au dosage des composés aza hétérocycliques et autres composés carbonyles cycliques trouvés dans les atmosphères urbaines et dans les écoulements sources de pollution de l'air.