477,417 research outputs found
Computability of simple games: A characterization and application to the core
The class of algorithmically computable simple games (i) includes the class
of games that have finite carriers and (ii) is included in the class of games
that have finite winning coalitions. This paper characterizes computable games,
strengthens the earlier result that computable games violate anonymity, and
gives examples showing that the above inclusions are strict. It also extends
Nakamura's theorem about the nonemptyness of the core and shows that computable
games have a finite Nakamura number, implying that the number of alternatives
that the players can deal with rationally is restricted.Comment: 35 pages; To appear in Journal of Mathematical Economics; Appendix
added, Propositions, Remarks, etc. are renumbere
A Bloch wave numerical scheme for scattering problems in periodic wave-guides
We present a new numerical scheme to solve the Helmholtz equation in a
wave-guide. We consider a medium that is bounded in the -direction,
unbounded in the -direction and -periodic for large ,
allowing different media on the left and on the right. We suggest a new
numerical method that is based on a truncation of the domain and the use of
Bloch wave ansatz functions in radiation boxes. We prove the existence and a
stability estimate for the infinite dimensional version of the proposed
problem. The scheme is tested on several interfaces of homogeneous and periodic
media and it is used to investigate the effect of negative refraction at the
interface of a photonic crystal with a positive effective refractive index.Comment: 25 pages, 10 figure
On the completeness of quantum computation models
The notion of computability is stable (i.e. independent of the choice of an
indexing) over infinite-dimensional vector spaces provided they have a finite
"tensorial dimension". Such vector spaces with a finite tensorial dimension
permit to define an absolute notion of completeness for quantum computation
models and give a precise meaning to the Church-Turing thesis in the framework
of quantum theory. (Extra keywords: quantum programming languages, denotational
semantics, universality.)Comment: 15 pages, LaTe
Computation with Advice
Computation with advice is suggested as generalization of both computation
with discrete advice and Type-2 Nondeterminism. Several embodiments of the
generic concept are discussed, and the close connection to Weihrauch
reducibility is pointed out. As a novel concept, computability with random
advice is studied; which corresponds to correct solutions being guessable with
positive probability. In the framework of computation with advice, it is
possible to define computational complexity for certain concepts of
hypercomputation. Finally, some examples are given which illuminate the
interplay of uniform and non-uniform techniques in order to investigate both
computability with advice and the Weihrauch lattice
Elimination of the linearization error and improved basis-set convergence within the FLAPW method
We analyze in detail the error that arises from the linearization in
linearized augmented-plane-wave (LAPW) basis functions around predetermined
energies and show that it can lead to undesirable dependences of the
calculated results on method-inherent parameters such as energy parameters
and muffin-tin sphere radii. To overcome these dependences, we evaluate
approaches that eliminate the linearization error systematically by adding
local orbitals (LOs) to the basis set. We consider two kinds of LOs: (i)
constructed from solutions to the scalar-relativistic approximation
of the radial Dirac equation with and (ii) constructed from second
energy derivatives at . We find
that the latter eliminates the error most efficiently and yields the density
functional answer to many electronic and materials properties with very high
precision. Finally, we demonstrate that the so constructed LAPW+LO basis shows
a more favorable convergence behavior than the conventional LAPW basis due to a
better decoupling of muffin-tin and interstitial regions, similarly to the
related APW+lo approach, which requires an extra set of LOs to reach the same
total energy, though.Comment: 12 pages, 15 figure
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