Temat: algebraic analysis - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Artykuł

Skocz do pozycji: 2.

Tytuł:: Two centuries of the term "algebraic analysis"
Autorzy:: Przeworska-Rolewicz, Danuta
Powiązania:: https://bibliotekanauki.pl/articles/1207439.pdf
Data publikacji:: 2000
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: algebraic analysis
right invertible operator
operational calculus
Opis:: The term "Algebraic Analysis" in the last two decades is used in two completely different senses. It seems that at least one is far away from its historical roots. Thus, in order to explain this misunderstanding, the history of this term from its origins is recalled.
Źródło:: Banach Center Publications; 2000, 53, 1; 47-70
0137-6934
Pojawia się w:: Banach Center Publications
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 3.

Tytuł:: Non-Leibniz algebras with logarithms do not have the trigonometric identity
Autorzy:: Przeworska-Rolewicz, D.
Powiązania:: https://bibliotekanauki.pl/articles/1207627.pdf
Data publikacji:: 2000
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: sine mapping
algebra with unit
algebraic analysis
logarithmic mapping
Leibniz condition
cosine mapping
Opis:: Let X be a Leibniz algebra with unit e, i.e. an algebra with a right invertible linear operator D satisfying the Leibniz condition: D(xy) = xDy + (Dx)y for x,y belonging to the domain of D. If logarithmic mappings exist in X, then cosine and sine elements C(x) and S(x) defined by means of antilogarithmic mappings satisfy the Trigonometric Identity, i.e. $[C(x)]^2 + [S(x)]^2 = e$ whenever x belongs to the domain of these mappings. The following question arises: Do there exist non-Leibniz algebras with logarithms such that the Trigonometric Identity is satisfied? We shall show that in non-Leibniz algebras with logarithms the Trigonometric Identity does not exist. This means that the above question has a negative answer, i.e. the Leibniz condition in algebras with logarithms is a necessary and sufficient condition for the Trigonometric Identity to hold.
Źródło:: Banach Center Publications; 2000, 53, 1; 177-189
0137-6934
Pojawia się w:: Banach Center Publications
Dostawca treści:: Biblioteka Nauki

Artykuł

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