Pełnotekstowe zasoby PLDML oraz innych baz dziedzinowych są już dostępne w nowej Bibliotece Nauki.
Zapraszamy na https://bibliotekanauki.pl
Preferencje help
Polish version English version Język
Widoczny [Schowaj] Abstrakt
Liczba wyników

Znaleziono wyników: 5

Liczba wyników na stronie
first rewind previous Strona / 1 next fast forward last

Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych:  algebraic analysis
help Sortuj według:

help Ogranicz wyniki do:
first rewind previous Strona / 1 next fast forward last
1
Content available remote

Some highlights in the development of algebraic analysis

100%
Synowiec J. A.
Banach Center Publications
|
2000
|
tom 53
|
nr 1
11-46
2
Content available remote

Two centuries of the term "algebraic analysis"

80%
Przeworska-Rolewicz D.
Banach Center Publications
|
2000
|
tom 53
|
nr 1
47-70
EN
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.
3
Content available remote

Non-Leibniz algebras with logarithms do not have the trigonometric identity

61%
Przeworska-Rolewicz D.
Banach Center Publications
|
2000
|
tom 53
|
nr 1
177-189
EN
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.
4
Content available remote

A functorial approach to the behaviour of multidimensional control systems

61%
Pommaret J.-F., Quadrat A.
International Journal of Applied Mathematics and Computer Science
|
2003
|
tom 13
|
nr 1
7-13
EN
We show how to use the extension and torsion functors in order to compute the torsion submodule of a differential module associated with a multidimensional control system. In particular, we show that the concept of the weak primeness of matrices corresponds to the torsion-freeness of a certain module.
5
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
Content available

Fourier-like methods for equations with separable variables

41%
Przeworska-Rolewicz D.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2009
|
tom 29
|
nr 1
19-42
EN
It is well known that a power of a right invertible operator is again right invertible, as well as a polynomial in a right invertible operator under appropriate assumptions. However, a linear combination of right invertible operators (in particular, their sum and/or difference) in general is not right invertible. It will be shown how to solve equations with linear combinations of right invertible operators in commutative algebras using properties of logarithmic and antilogarithmic mappings. The used method is, in a sense, a kind of the variables separation method. We shall obtain also an analogue of the classical Fourier method for partial differential equations. Note that the results concerning the Fourier method are proved under weaker assumptions than these obtained in [6] (cf. also [7, 8, 11]).
first rewind previous Strona / 1 next fast forward last
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.