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: 9

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

Attractors of Strongly Dissipative Systems

100%
Ramm A.
Bulletin of the Polish Academy of Sciences. Mathematics
|
2009
|
tom 57
|
nr 1
25-31
EN
A class of infinite-dimensional dissipative dynamical systems is defined for which there exists a unique equilibrium point, and the rate of convergence to this point of the trajectories of a dynamical system from the above class is exponential. All the trajectories of the system converge to this point as t → +∞, no matter what the initial conditions are. This class consists of strongly dissipative systems. An example of such systems is provided by passive systems in network theory (see, e.g., MR0601947 (83m:45002)).
2
Content available remote

Property C for ODE and Applications to an Inverse Problem for a Heat Equation

100%
Ramm A.
Bulletin of the Polish Academy of Sciences. Mathematics
|
2009
|
tom 57
|
nr 3
243-249
EN
Let $ℓ_j:= -d²/dx² + k²q_j(x)$, k = const > 0, j = 1,2, $0 < ess inf q_j(x) ≤ ess sup q_j(x) < ∞$. Suppose that (*) $∫_{0}^{1} p(x)u₁(x,k)u₂(x,k)dx = 0$ for all k > 0, where p is an arbitrary fixed bounded piecewise-analytic function on [0,1], which changes sign finitely many times, and $u_j$ solves the problem $ℓ_ju_j = 0$, 0 ≤ x ≤ 1, $u'_j(0,k) = 0$, $u_j(0,k) = 1$. It is proved that (*) implies p = 0. This result is applied to an inverse problem for a heat equation.
3
Content available remote

A symmetry problem

100%
Ramm A.
Annales Polonici Mathematici
|
2007
|
tom 92
|
nr 1
49-54
EN
Consider the Newtonian potential of a homogeneous bounded body D ⊂ ℝ³ with known constant density and connected complement. If this potential equals c/|x| in a neighborhood of infinity, where c>0 is a constant, then the body is a ball. This known result is now proved by a different simple method. The method can be applied to other problems.
4
Content available remote

Dynamical systems method for solving linear ill-posed problems

100%
Ramm A.
Annales Polonici Mathematici
|
2009
|
tom 95
|
nr 3
253-272
EN
Various versions of the Dynamical Systems Method (DSM) are proposed for solving linear ill-posed problems with bounded and unbounded operators. Convergence of the proposed methods is proved. Some new results concerning the discrepancy principle for choosing the regularization parameter are obtained.
5
Content available remote

A DSM proof of surjectivity of monotone nonlinear mappings

100%
Ramm A.
Annales Polonici Mathematici
|
2009
|
tom 95
|
nr 2
135-139
EN
A simple proof is given of a basic surjectivity result for monotone operators. The proof is based on the dynamical systems method (DSM).
6
Content available remote

On the Relation between the S-matrix and the Spectrum of the Interior Laplacian

100%
Ramm A.
Bulletin of the Polish Academy of Sciences. Mathematics
|
2009
|
tom 57
|
nr 2
181-188
EN
The main results of this paper are: 1) a proof that a necessary condition for 1 to be an eigenvalue of the S-matrix is real analyticity of the boundary of the obstacle, 2) a short proof that if 1 is an eigenvalue of the S-matrix, then k² is an eigenvalue of the Laplacian of the interior problem, and that in this case there exists a solution to the interior Dirichlet problem for the Laplacian, which admits an analytic continuation to the whole space ℝ³ as an entire function.
7
Content available remote

Invisible obstacles

100%
Ramm A.
Annales Polonici Mathematici
|
2007
|
tom 90
|
nr 2
145-148
EN
It is proved that one can choose a control function on an arbitrarilly small open subset of the boundary of an obstacle so that the total radiation from this obstacle for a fixed direction of the incident plane wave and for a fixed wave number will be as small as one wishes. The obstacle is called "invisible" in this case.
8
Content available remote

Dynamical systems method for solving linear finite-rank operator equations

64%
Hoang N., Ramm A.
Annales Polonici Mathematici
|
2009
|
tom 95
|
nr 1
77-93
EN
A version of the dynamical systems method (DSM) for solving ill-conditioned linear algebraic systems is studied. An a priori and an a posteriori stopping rules are justified. An iterative scheme is constructed for solving ill-conditioned linear algebraic systems.
9
Content available remote

Symmetry problems 2

64%
Hoang N., Ramm A.
Annales Polonici Mathematici
|
2009
|
tom 96
|
nr 1
61-64
EN
Some symmetry problems are formulated and solved. New simple proofs are given for some symmetry problems studied earlier. One of the results is as follows: if a single-layer potential of a surface, homeomorphic to a sphere, with a constant charge density, is equal to c/|x| for all sufficiently large |x|, where c > 0 is a constant, then the surface is a sphere.
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.