93,244 research outputs found
Stability and Convergence of Product Formulas for Operator Matrices
We present easy to verify conditions implying stability estimates for
operator matrix splittings which ensure convergence of the associated Trotter,
Strang and weighted product formulas. The results are applied to inhomogeneous
abstract Cauchy problems and to boundary feedback systems.Comment: to appear in Integral Equations and Operator Theory (ISSN: 1420-8989
Construction and separability of nonlinear soliton integrable couplings
A very natural construction of integrable extensions of soliton systems is
presented. The extension is made on the level of evolution equations by a
modification of the algebra of dynamical fields. The paper is motivated by
recent works of Wen-Xiu Ma et al. (Comp. Math. Appl. 60 (2010) 2601, Appl.
Math. Comp. 217 (2011) 7238), where new class of soliton systems, being
nonlinear integrable couplings, was introduced. The general form of solutions
of the considered class of coupled systems is described. Moreover, the
decoupling procedure is derived, which is also applicable to several other
coupling systems from the literature.Comment: letter, 10 page
Point evaluation and Hardy space on a homogeneous tree
We consider transfer functions of time--invariant systems as defined by
Basseville, Benveniste, Nikoukhah and Willsky when the discrete time is
replaced by the nodes of an homogeneous tree. The complex numbers are now
replaced by a C*-algebra built from the structure of the tree. We define a
point evaluation with values in this C*-algebra and a corresponding ``Hardy
space'' in which a Cauchy's formula holds. This point evaluation is used to
define in this context the counterpart of classical notions such as Blaschke
factors. There are deep analogies with the non stationary setting as developed
by the first author, Dewilde and Dym.Comment: Added references, changed notation
Approximate methods for the solution of quantum wires and dots : Connection rules between pyramidal, cuboidal, and cubic dots
Energy eigenvalues of the electronic ground state are calculated for rectangular and triangular GaAs/Ga(0.6)Al(0.4)As quantum wires as well as for cuboidal and pyramidal quantum dots of the same material. The wire (dot) geometries are approximated by a superposition of perpendicular independent finite one-dimensional potential wells. A perturbation is added to the system to improve the approximation. Excellent agreement with more complex treatments is obtained. The method is applied to investigate the ground state energy dependence on volume and aspect ratio for finite barrier cubic, cuboidal, and pyramidal quantum dots. It is shown that the energy eigenvalues of cubes are equal to those of cuboids of the same volume and aspect ratio similar to one. In addition, a relationship has been found between the volumes of pyramidal quantum dots (often the result of self-assembling in strain layered epitaxy) and cuboidal dots with the same ground state energy and aspect ratios close to one. © 1999 American Institute of Physics
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