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Search results for: WEAK CONVERGENCE
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Weak Stability of Centred Quadratic Stochastic Operators
PublicationWe consider the weak convergence of iterates of so-called centred quadratic stochastic operators. These iterations allow us to study the discrete time evolution of probability distributions of vector-valued traits in populations of inbreeding or hermaphroditic species, whenever the offspring’s trait is equal to an additively perturbed arithmetic mean of the parents’ traits. It is shown that for the existence of a weak limit, it...
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Upward convergence patterns in chosen environmental-related SDGs
PublicationSustainable development is a challenge facing humanity. EU countries not only strive to reach their specific objectives, but they also work collaboratively towards shared goals. There is a need to balance synergies and compromises to address these objectives effectively. When discussing countries' development and people's well-being, one often focuses on socio-economic development. However, it is crucial not to overlook the environmental...
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On weak solutions of the boundary value problem within linear dilatational strain gradient elasticity for polyhedral Lipschitz domains
PublicationWe provide the proof of an existence and uniqueness theorem for weak solutions of the equilibrium problem in linear dilatational strain gradient elasticity for bodies occupying, in the reference configuration, Lipschitz domains with edges. The considered elastic model belongs to the class of so-called incomplete strain gradient continua whose potential energy density depends quadratically on linear strains and on the gradient of...
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Quadratic stochastic operators on Banach lattices
PublicationWe study the convergence of iterates of quadratic stochastic operators that are mean monotonic. They are defined on the convex set of probability measures concentrated on a weakly compact order interval S = [0, f] of a fixed Banach lattice F. We study their regularity and identify the limits of trajectories either as the “infimum” or “supremum” of the support of initial distributions.