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A note on the entropy of a doubly stochastic operator

Brunon Kamiński, José de Sam Lazaro (2000)

Colloquium Mathematicae

We investigate the properties of the entropy and conditional entropy of measurable partitions of unity in the space of essentially bounded functions defined on a Lebesgue probability space.

A note on the fundamental matrix of variational equations in 3

Ladislav Adamec (2003)

Mathematica Bohemica

The paper is devoted to the question whether some kind of additional information makes it possible to determine the fundamental matrix of variational equations in 3 . An application concerning computation of a derivative of a scalar Poincaré mapping is given.

A note on the structure of quadratic Julia sets

Karsten Keller (1997)

Commentationes Mathematicae Universitatis Carolinae

In a series of papers, Bandt and the author have given a symbolic and topological description of locally connected quadratic Julia sets by use of special closed equivalence relations on the circle called Julia equivalences. These equivalence relations reflect the landing behaviour of external rays in the case of local connectivity, and do not apply completely if a Julia set is connected but fails to be locally connected. However, rational external rays land also in the general case. The present...

A note on γ-radonifying and summing operators

Zdzisław Brzeźniak, Hongwei Long (2015)

Banach Center Publications

In this note, we discuss certain generalizations of γ-radonifying operators and their applications to the regularity for linear stochastic evolution equations on some special Banach spaces. Furthermore, we also consider a more general class of operators, namely the so-called summing operators and discuss the application to the compactness of the heat semi-group between weighted L p -spaces.

A novel LMI-based robust model predictive control for DFIG-based wind energy conversion systems

Amir Gholami, Alireza Sahab, Abdolreza Tavakoli, Behnam Alizadeh (2019)

Kybernetika

The optimal and reliable performance of doubly fed induction generator is essential for the efficient and optimal operation of wind energy conversion systems. This paper considers the nonlinear dynamic of a DFIG linked to a power grid and presents a new robust model predictive control technique of active and reactive power by the use of the linear matrix inequality in DFIG-based WECS. The control law is obtained through the LMI-based model predictive control that allows considering both economic...

A p -adic approach to local analytic dynamics: analytic conjugacy of analytic maps tangent to the identity

Adrian Jenkins, Steven Spallone (2009)

Annales de la faculté des sciences de Toulouse Mathématiques

In this note, we consider the question of local analytic equivalence of analytic functions which fix the origin and are tangent to the identity. All mappings and equivalences are considered in the non-archimedean context e.g. all norms can be considered p -adic norms. We show that any two mappings f and g which are formally equivalent are also analytically equivalent. We consider the related questions of roots and centralizers for analytic mappings. In this setting, anything which can be done formally...

A p-adic behaviour of dynamical systems.

Stany De Smedt, Andrew Khrennikov (1999)

Revista Matemática Complutense

We study dynamical systems in the non-Archimedean number fields (i.e. fields with non-Archimedean valuation). The main results are obtained for the fields of p-adic numbers and complex p-adic numbers. Already the simplest p-adic dynamical systems have a very rich structure. There exist attractors, Siegel disks and cycles. There also appear new structures such as fuzzy cycles. A prime number p plays the role of parameter of a dynamical system. The behavior of the iterations depends on this parameter...

A p-adic Perron-Frobenius theorem

Robert Costa, Patrick Dynes, Clayton Petsche (2016)

Acta Arithmetica

We prove that if an n×n matrix defined over ℚ ₚ (or more generally an arbitrary complete, discretely-valued, non-Archimedean field) satisfies a certain congruence property, then it has a strictly maximal eigenvalue in ℚ ₚ, and that iteration of the (normalized) matrix converges to a projection operator onto the corresponding eigenspace. This result may be viewed as a p-adic analogue of the Perron-Frobenius theorem for positive real matrices.

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