The inverse scattering problem on half-axis, in other words, in the
spherically symmetric case, consists of finding the unknown potential
from a suitable class from the scattering data S. The other problem of
practical ...
We introduce a reproducing kernel structure for Hilbert spaces of functions where differences of point evaluations are bounded. The associated reproducing kernels are characterized in terms of conditionally negative functions.
From the scattering data one finds the support function or the principal curvatures of the surface of a reflecting obstacle. From either of these data the surface is effectively reconstructed.
It is proved that any potential of a single layer v is identically equal to a potential of a double layer w in the bounded domain, D, and a necessary and sufficient condition for v≡w in Ω=R³/D, the exterior domain, is given.
Ramm, Alexander G.(Science Publishing Corporation, 2015)
A simple proof is given for the explicit formula which allows one to recover a C2 – smooth vector field A=A(x) in R3, decaying at infinity, from the knowledge of its ∇×A and ∇⋅A. The representation of A as a sum of the ...
Many-body quantum-mechanical scattering problem is solved asymptotically when
the size of the scatterers (inhomogeneities) tends to zero and their number tends to
infinity.
A method is given for calculation of the number ...
Combining an asymptotic method and computational modelling the authors propose a method for creating materials with the desired electrodynamical characteristics, in particular, with a desired refraction
coefficient. The ...
Formulas are derived for solutions of many-body wave scattering problems by small
particles in the case of acoustically soft, hard, and impedance particles embedded
in an inhomogeneous medium. The limiting case is ...
Formulas are derived for solutions of many-body wave scattering problems by small
particles in the case of acoustically soft, hard, and impedance particles embedded in
an inhomogeneous medium. The limiting case is ...
A class of infinite-dimensional dissipative dynamical systems is defined for
which the slow invariant manifolds can be calculated. Large-time behavior of
the evolution of such systems is studied.
A review of the author’s results is given. Inversion formulas and stability results
for the solutions to 3D inverse scattering problems with fixed energy data are obtained. Inversion of exact and noisy data is considered. ...
A novel approach to an old symmetry problem is developed. A new proof is given for the following symmetry problem, studied earlier: if Δu = 1 in D ⊂ R[superscript 3], u = 0 on S, the boundary of D, and u[subscript N] = ...
Many three-dimensional manifolds are two-fold branched covers of the three-dimensional sphere. However, there are some that are not. This paper includes exposition about two-fold branched covers and includes many examples. ...