<abstract xmlns="http://www.w3.org/1999/xhtml">

By rewriting the differential entropy in a form of a differ-integral function’s limit, and deforming the ordinary derivative to a fractional-order one, we derive in this paper a novel generalized fractional-order differential entropy along with its related information measures. When the order of fractional differentiation <italic>α</italic> → 1, the ordinary Shannon’s differential entropy is recovered, which corresponds to the results from first-order ordinary differentiation.
</abstract>

Some theoretical results on fractional-order continuous information measures

<abstract xmlns="http://www.w3.org/1999/xhtml">

In this note we provide a complete classification of weak combinatorics of the so-called maximizing line arrangements in the complex projective plane.
</abstract>

On maximizing line arrangements in the complex plane

<abstract xmlns="http://www.w3.org/1999/xhtml">

The aim of this article is to introduce the concept of centrally-extended Jordan epimorphisms and proving that if <italic>R</italic> is a non-commutative prime ring (∗-ring) of characteristic not two, and <italic>G</italic> is a CE-Jordan epimorphism such that [<italic>G</italic>(<italic>x</italic>), <italic>x</italic>] ∈ <italic>Z</italic>(<italic>R</italic>) ([<italic>G</italic>(<italic>x</italic>), <italic>x</italic>∗] ∈ <italic>Z</italic>(<italic>R</italic>)) for all <italic>x</italic> ∈ <italic>R</italic>, then <italic>R</italic> is an order in a central simple algebra of dimension at most 4 over its center or there is an element <italic>λ</italic> in the extended centroid of <italic>R</italic> such that <italic>G</italic>(<italic>x</italic>) = <italic>λx</italic> (<italic>G</italic>(<italic>x</italic>) = <italic>λx</italic>∗) for all <italic>x</italic> ∈ <italic>R</italic>.
</abstract>

Rings with centrally-extended Jordan epimorphisms

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Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

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Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

Volume 23 (2024): Issue 1 (January 2024)

Some theoretical results on fractional-order continuous information measures

On maximizing line arrangements in the complex plane

Rings with centrally-extended Jordan epimorphisms

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