On strong pseudomonotonicity and (semi)strict quasimonotonicity

New concepts of strong pseudomonotonicity, strict quasimonotonicity, and semistrict quasimonotonicity of a map are introduced and their properties are studied. In the case of a differentiable gradient map, we show that strong pseudomonotonicity of the gradient is equivalent to strong pseudoconvexity of the underlying function. This does not hold for a different concept of strong pseudomonotonicity in Ref. 1. Analogous results are shown for strict quasimonotonicity and semistrict quasimonotonicity.     

Second-order characterizations of pseudoconvex quadratic functions

The paper deals with strictly pseudoconvex quadratic functions on open convex sets. It presents second-order conditions in terms of an extended Hessian and in terms of bordered determinants. All of the conditions are both necessary and sufficient.The author wishes to thank Professor M. Avriel, visiting Stanford University, for helpful discussions. He is also grateful to Professor R. W. Cottle, Stanford University, for his suggestions.     

Schallgeschwindigkeitsmessungen in Schmelzen aus den Systemen Al−Mg,Al−Sn,Mg−Sn und Fe−C

The concentration dependency of sound velocity was measured in molten alloys of the three systems Al–Mg, Al–Sn, and Mg–Sn in the temperature region between liquidus and 1000°C. Furthermore it was measured in molten alloys of the system Fe–C in the temperature range between liquidus temperatureT _L andT _L+150°C. From the velocities the compressibilities were calculated, whose concentration dependency revealed changes in the structure of the melts.The structure of the three systems Al–Mg, Al–Sn, and Mg–Sn in the molten state was already investigated by X-Ray diffraction. These results were compared with the results of velocity measurements. Inhomogeneities in the melts yield increased values of compressibility compared with the values to be expected for statistical distribution of the atoms. This result was used for the discussion of the structure of molten Fe-C-alloys:The conclusion can be drawn, that within the melts of the system Fe–C above 3^w/0 C inhomogeneities are existent.From the values of sound velocity in the molten elements the temperature dependency of the structure factorsI(0) was calculated and compared with experimental values.

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Teil der Dissertation von U. Maier, Universität Stuttgart, 1972.