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In this work, the eigenvalue problems of the symmetric tensor-block matrix of any even rank and sizes \(m\times {m}\), \(m\ge 1\) (sizes \(2\times 2\)) is formulated (studied). Some definitions and… (More)

Elementary information on polynomials with tensor coefficients and operations with them is given. A generalized Bezout theorem is stated and proved, and on this basis, the Hamilton–Cayley theorem is… (More)

In this work, we considered the new parametrization of a multilayer thin domain. In particular, in contrast to classic approaches, we used several base surfaces and an analytic method with the… (More)

We consider the questions on the decomposition of the initial boundary value problems of elasticity theory and thin bodies for some anisotropic media. In particular, the initial boundary problems of… (More)

We consider various methods for constructing linearly independent isotropic, gyrotropic, orthotropic, and transversally isotropic tensors. We state assertions and theorem that permit one to construct… (More)

In this paper, we consider the eigenvalue problem for a tensor of arbitrary even rank. In this connection, we state definitions and theorems related to the tensors of moduli ℂ2p(Ω) and ℝ2p(Ω), where… (More)

The parametrization of the domain occupied by a shell in the three-dimensional Euclidean space by using several base surfaces permits one to describe more accurately the variation of the… (More)