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Stability of microstructure for tetragonal to monoclinic martensitic transformations

Pavel Belik, Mitchell Luskin (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We give an analysis of the stability and uniqueness of the simply laminated microstructure for all three tetragonal to monoclinic martensitic transformations. The energy density for tetragonal to monoclinic transformations has four rotationally invariant wells since the transformation has four variants. One of these tetragonal to monoclinic martensitic transformations corresponds to the shearing of the rectangular side, one corresponds to the shearing of the square base, and one corresponds to...

Stability of quadratic interpolation polynomials in vertices of triangles without obtuse angles

Josef Dalík (1999)

Archivum Mathematicum

An explicit description of the basic Lagrange polynomials in two variables related to a six-tuple a 1 , ⋯ , a 6 of nodes is presented. Stability of the related Lagrange interpolation is proved under the following assumption: a 1 , ⋯ , a 6 are the vertices of triangles T 1 , ⋯ , T 4 without obtuse inner angles such that T 1 has one side common with T j for j = 2 , 3 , 4 .

Stability of the Endemic Coexistence Equilibrium for One Host and Two Parasites

T. Dhirasakdanon, H. R. Thieme (2010)

Mathematical Modelling of Natural Phenomena

For an SI type endemic model with one host and two parasite strains, we study the stability of the endemic coexistence equilibrium, where the host and both parasite strains are present. Our model, which is a system of three ordinary differential equations, assumes complete cross-protection between the parasite strains and reduced fertility and increased mortality of infected hosts. It also assumes that one parasite strain is exclusively vertically...

Stability of the Iteration Method for non Expansive Mappings

Lemaire, B. (1996)

Serdica Mathematical Journal

The general iteration method for nonexpansive mappings on a Banach space is considered. Under some assumption of fast enough convergence on the sequence of (“almost” nonexpansive) perturbed iteration mappings, if the basic method is τ−convergent for a suitable topology τ weaker than the norm topology, then the perturbed method is also τ−convergent. Application is presented to the gradient-prox method for monotone inclusions in Hilbert spaces.

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