Displaying similar documents to “On the domain of applicability of the Mori-Tanaka effective medium theory”

On tensor functions whose gradients have some skew-symmetries

Adriano Montanaro (1991)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Let V n be a real inner product space of any dimension; and let Q α 1 ⁢ … ⁢ α v = Q ⌃ α 1 ⁢ … ⁢ α v ⁢ X β ⁢ 1 ⁢ … ⁢ β τ be a C 2 -map relating any two tensor spaces on V n . We study the consequences imposed on the form of this function by the condition that its gradient should be skew-symmetric with respect to some pairs α μ , β η of indexes. Any such a condition is written as a system of linear partial differential equations, with constant coefficients, which is symmetric with respect to certain couples of independent variables. The solutions of these...

New criteria for H-tensors and an application

Feng Wang, Deshu Sun (2015)

Open Mathematics

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Some new criteria for identifying H-tensors are obtained. As an application, some sufficient conditions of the positive definiteness for an even-order real symmetric tensor are given. Advantages of results obtained are illustrated by numerical examples.