7,449 research outputs found
On the phonon-induced superconductivity of disordered alloys
A model of alloy is considered which includes both quenched disorder in the
electron subsystem (``alloy'' subsystem) and electron-phonon interaction. For
given approximate solution for the alloy part of the problem, which is assumed
to be conserving in Baym's sense, we construct the generating functional and
derive the Eliashberg-type equations which are valid to the lowest order in the
adiabatic parameter.The renormalization of bare electron-phonon interaction
vertices by disorder is taken into account consistently with the approximation
for the alloy self-energy. For the case of exact configurational averaging the
same set of equations is established within the usual T-matrix approach. We
demonstrate that for any conserving approximation for the alloy part of the
self-energy the Anderson's theorem holds in the case of isotropic singlet
pairing provided disorder renormalizations of the electron-phonon interaction
vertices are neglected. Taking account of the disorder renormalization of the
electron-phonon interaction we analyze general equations qualitatively and
present the expressions for for the case of weak and intermediate
electron-phonon coupling. Disorder renormalizations of the logarithmic
corrections to the effective coupling, which arise when the effective
interaction kernel for the Cooper channel has the second energy scale, as well
as the renormalization of the dilute paramagnetic impurity suppression are
discussed.Comment: 59 pages, 10 Eps figures, LaTe
Information completeness in Nelson algebras of rough sets induced by quasiorders
In this paper, we give an algebraic completeness theorem for constructive
logic with strong negation in terms of finite rough set-based Nelson algebras
determined by quasiorders. We show how for a quasiorder , its rough
set-based Nelson algebra can be obtained by applying the well-known
construction by Sendlewski. We prove that if the set of all -closed
elements, which may be viewed as the set of completely defined objects, is
cofinal, then the rough set-based Nelson algebra determined by a quasiorder
forms an effective lattice, that is, an algebraic model of the logic ,
which is characterised by a modal operator grasping the notion of "to be
classically valid". We present a necessary and sufficient condition under which
a Nelson algebra is isomorphic to a rough set-based effective lattice
determined by a quasiorder.Comment: 15 page
On partial order semantics for SAT/SMT-based symbolic encodings of weak memory concurrency
Concurrent systems are notoriously difficult to analyze, and technological
advances such as weak memory architectures greatly compound this problem. This
has renewed interest in partial order semantics as a theoretical foundation for
formal verification techniques. Among these, symbolic techniques have been
shown to be particularly effective at finding concurrency-related bugs because
they can leverage highly optimized decision procedures such as SAT/SMT solvers.
This paper gives new fundamental results on partial order semantics for
SAT/SMT-based symbolic encodings of weak memory concurrency. In particular, we
give the theoretical basis for a decision procedure that can handle a fragment
of concurrent programs endowed with least fixed point operators. In addition,
we show that a certain partial order semantics of relaxed sequential
consistency is equivalent to the conjunction of three extensively studied weak
memory axioms by Alglave et al. An important consequence of this equivalence is
an asymptotically smaller symbolic encoding for bounded model checking which
has only a quadratic number of partial order constraints compared to the
state-of-the-art cubic-size encoding.Comment: 15 pages, 3 figure
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