Some general principles of dynamic instability of solid bodies

Résumé Ce travail représente une étude de l'équilibre des corps solides, avec un intérêt special accordé aux corps élastiques et à ceux de Voigt-Kelvin. Les efforts appliqués peuvent avoir des composants non conservatifs et gyroscopiques, quoique la dépendance explicite du temps soit exclue. Il est bien connu que, pour une catégorie de problèmes tellement large, l'établissement des conditions de la stabilité par les méthodes classiques de statique ou d'énergie n'est pas toujours applicable.Le traitement du problème essaie d'être assez compréhensif. En utilisant la méthode des vibrations modales on établie des critères généraux de stabilité sur la base d'une «énergie équivalente». Ces critères sont d'une telle généralité qu'ils contiennent, comme cas spéciaux, les critères publiés auparavant. En plus, de nouveaux principes ont été développés et démontrés à l'aide d'un exemple numérique.

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This work was supported by the National Science Foundation through Grant GK-368 to the University of Illinois at Chicago Circle.     

Polymer bound pyrrole compounds. Reversible anchoring of bilirubin and biliverdin to a polystyrene matrix

Both bilirubin and biliverdin, $\text{via}$ their cesium salts, have been covalently attached to an insoluble polystyrene matrix (the so-called Nbb-resin), some chemical transformations have been carried out upon the supported pigments, and the resulting products have been detached by alkaline methanol.     

A Synthesis of Prostaglandins: Strategy and Reality

The prostaglandin synthesis developed in the Woodward Research Institute at Basel serves to provide an unusual look behind the scenes. A candid account is presented of the sometimes tortuous chronological sequence of ideas and experiments during work on a challenging synthesis.     

One-pot, three-component, sequential Michael-Michael-ring-closure reactions. Annulation of meta-dicarboxylated aromatic rings. Total synthesis of juncunol

The preparative value of one-pot, multicomponent, sequential Michael-Michael-ring-closure reactions followed by aromatization is illustrated in two ways: (1) by a multi-gram example, and (2) by a total synthesis of juncunol, an unusual vinyldihydrophenanthrene.     

Aymmetric synthesis of (R) - and (S)-citramalate in high enantiomeric purity

An asymmetric synthesis of both isomers of dimethyl 2-acetoxycitramalate in over 96% enantiomeric excess is described.     

Neutrino masses in an extended gauge model with E6 particle content

Naturally light singlet neutrinos which mix with the usual doublet neutrinos are possible if the supersymmetric standard gauge model is extended to include a specific additional U(1) factor derivable from an E₆ decomposition. The low-energy particle content of the model is limited to the fundamental 27 representations of E₆.     

STABILITY PROPERTIES IN A MODEL OF FORAGE-UNGULATE-PREDATOR INTERACTIONS

This paper explores stability in a three differential equation model of ungulates, their forage and their predators. Stability most depends on the feeding efficiency of exploiters relative to the growth potential of those exploited. Stable, natural systems probably require relatively inefficient exploitation, refuges for the exploited population or prey switching by generalist exploiters. Increased exploitation of ungulates enhances ungulate-forage stability but, lacking prey refugia, eventually overexploits the ungulates. Multiple, stable equilibria representing sustained ungulate yield and ungulate extinction probably characterize big game. Under traditional management, game populations will approach the zone of attraction of the second of these equilibria.     

Determination of boron in geological materials by inductively-coupled plasma emission spectrometry

Determination of boron in international silicate reference materials with an argon plasma is demonstrated. Detection limits are about 5 ppm for rock samples.