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: 7

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

Wyniki wyszukiwania

help Sortuj według:

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

Generalized telegraph equation and the Sova-Kurtz version of the Trotter-Kato theorem

100%
Bobrowski A.
Annales Polonici Mathematici
|
1996
|
tom 64
|
nr 1
37-45
EN
The Sova-Kurtz approximation theorem for semigroups is applied to prove convergence of solutions of the telegraph equation with small parameter. Convergence of the solutions of the diffusion equation with varying boundary conditions is also considered.
2
Content available remote

A note on convergence of semigroups

100%
Bobrowski A.
Annales Polonici Mathematici
|
1998
|
tom 69
|
nr 2
107-127
EN
Convergence of semigroups which do not converge in the Trotter-Kato-Neveu sense is considered.
3
Content available remote

From convergence of operator semigroups to gene expression, and back again

100%
Bobrowski A.
Banach Center Publications
|
2008
|
tom 80
|
nr 1
83-99
EN
The subject of the paper is reciprocal influence of pure mathematics and applied sciences. We illustrate the idea by giving a review of mathematical results obtained recently, related to the model of stochastic gene expression due to Lipniacki et al. [38]. In this model, featuring mRNA and protein levels, and gene activity, the stochastic part of processes involved in gene expression is distinguished from the part that seems to be mostly deterministic, and the dynamics is expressed by means of a piece-wise deterministic Markov process. Mathematical results pertain to asymptotic behavior of the process in time as well as limit behavior when certain parameters may be assumed to be large. These results are but an inspiration to considering the ways applied sciences influence pure mathematics by supplying fresh ideas and providing new challenges. On the other hand, they may also be seen as an exemplification of the fact that statements that seem to be almost obvious and are often taken for granted in applied sciences may require mathematical scrutiny and non-standard proofs.
4
Content available remote

On the Yosida approximation and the Widder-Arendt representation theorem

100%
Bobrowski A.
Studia Mathematica
|
1997
|
tom 124
|
nr 3
281-290
EN
The Yosida approximation is treated as an inversion formula for the Laplace transform.
5
Content available remote

Semigroups generated by convex combinations of several Feller generators in models of mathematical biology

64%
Bobrowski A., Bogucki R.
Studia Mathematica
|
2008
|
tom 189
|
nr 3
287-300
EN
Let 𝓢 be a locally compact Hausdorff space. Let $A_{i}$, i = 0,1,...,N, be generators of Feller semigroups in C₀(𝓢) with related Feller processes $X_{i} = {X_{i}(t), t ≥ 0}$ and let $α_{i}$, i = 0,...,N, be non-negative continuous functions on 𝓢 with $∑_{i=0}^{N} α_{i} = 1$. Assume that the closure A of $∑_{k=0}^{N} α_{k}A_{k}$ defined on $⋂_{i=0}^{N} 𝓓(A_{i})$ generates a Feller semigroup {T(t), t ≥ 0} in C₀(𝓢). A natural interpretation of a related Feller process X = {X(t), t ≥ 0} is that it evolves according to the following heuristic rules: conditional on being at a point p ∈ 𝓢, with probability $α_{i}(p)$, the process behaves like $X_{i}$, i = 0,1,...,N. We provide an approximation of {T(t), t ≥ 0} via a sequence of semigroups acting in the Cartesian product of N + 1 copies of C₀(𝓢) that supports this interpretation, thus generalizing the main theorem of Bobrowski [J. Evolution Equations 7 (2007)] where the case N = 1 is treated. The result is motivated by examples from mathematical biology involving models of gene expression, gene regulation and fish dynamics.
6
Content available remote

Isolated points of some sets of bounded cosine families, bounded semigroups, and bounded groups on a Banach space

64%
Bobrowski A., Chojnacki W.
Studia Mathematica
|
2013
|
tom 217
|
nr 3
219-241
EN
We show that if the set of all bounded strongly continuous cosine families on a Banach space X is treated as a metric space under the metric of the uniform convergence associated with the operator norm on the space 𝓛(X) of all bounded linear operators on X, then the isolated points of this set are precisely the scalar cosine families. By definition, a scalar cosine family is a cosine family whose members are all scalar multiples of the identity operator. We also show that if the sets of all bounded cosine families and of all bounded strongly continuous cosine families on an infinite-dimensional separable Banach space X are viewed as topological spaces under the topology of the uniform convergence associated with the strong operator topology on 𝓛(X), then these sets have no isolated points. We present counterparts of all the above results for semigroups and groups of operators, relating to both the norm and strong operator topologies.
7
Content available remote

On a functional equation with derivative and symmetrization

64%
Bobrowski A., Kubalińska M.
Annales Polonici Mathematici
|
2006
|
tom 89
|
nr 1
13-24
EN
We study existence, uniqueness and form of solutions to the equation $αg - βg' + γg_{e} = f$ where α, β, γ and f are given, and $g_{e}$ stands for the even part of a searched-for differentiable function g. This equation emerged naturally as a result of the analysis of the distribution of a certain random process modelling a population genetics phenomenon.
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.