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Evolutes and involutes of frontals in the euclidean plane

Fukunaga T., Takahashi M.

Demonstratio Mathematica

2015

Vol. 48, nr 2

147--166

We have already defined the evolutes and the involutes of fronts without inflection points. For regular curves or fronts, we can not define the evolutes at inflection points. On the other hand, the involutes can be defined at inflection points. In this case, the involute is not a front but a frontal at inflection points. We define evolutes of frontals under conditions. The definition is a generalisation of both evolutes of regular curves and of fronts. By using relationship between evolutes and involutes of frontals, we give an existence condition of the evolute with inflection points. We also give properties of evolutes and involutes of frontals.

On a shape-preserving thermodynamic optimization

Malakhov D. V.

Archives of Metallurgy and Materials

2008

Vol. 53, iss. 4

1097-1106

It is demonstrated that topological constraints can be used to control the sign of the curvature of phase boundaries and thus to preserve their shapes in the course of the thermodynamic optimization. In such a way, the unwanted or suspicious inflection points on the phase boundaries may be avoided.

Wykazano, że zastosowanie pewnych ograniczeń matematycznych można zastosować do kontroli krzywizny granic mię-dzyfazowych w procesie optymalizacji. W ten sposób można uniknąć pojawiania się niepożądanych punktów przegięcia na granicach międzyfazowych.