159 research outputs found
Double-Mode Stellar Pulsations
The status of the hydrodynamical modelling of nonlinear multi-mode stellar
pulsations is discussed. The hydrodynamical modelling of steady double-mode
(DM) pulsations has been a long-standing quest that is finally being concluded.
Recent progress has been made thanks to the introduction of turbulent
convection in the numerical hydrodynamical codes which provide detailed results
for individual models. An overview of the modal selection problem in the HR
diagram can be obtained in the form of bifurcation diagrams with the help of
simple nonresonant amplitude equations that capture the DM phenomenon.Comment: 34 pages, to appear as a chapter in Nonlinear Stellar Pulsation in
the Astrophysics and Space Science Library (ASSL), Editors: M. Takeuti & D.
Sasselov (prints double column with pstops
'2:[email protected](22.0cm,-2cm)[email protected](22.0cm,11.0cm)' in.ps out.ps
Integrating a Global Induction Mechanism into a Sequent Calculus
Most interesting proofs in mathematics contain an inductive argument which
requires an extension of the LK-calculus to formalize. The most commonly used
calculi for induction contain a separate rule or axiom which reduces the valid
proof theoretic properties of the calculus. To the best of our knowledge, there
are no such calculi which allow cut-elimination to a normal form with the
subformula property, i.e. every formula occurring in the proof is a subformula
of the end sequent. Proof schemata are a variant of LK-proofs able to simulate
induction by linking proofs together. There exists a schematic normal form
which has comparable proof theoretic behaviour to normal forms with the
subformula property. However, a calculus for the construction of proof schemata
does not exist. In this paper, we introduce a calculus for proof schemata and
prove soundness and completeness with respect to a fragment of the inductive
arguments formalizable in Peano arithmetic.Comment: 16 page
Constructive pointfree topology eliminates non-constructive representation theorems from Riesz space theory
In Riesz space theory it is good practice to avoid representation theorems
which depend on the axiom of choice. Here we present a general methodology to
do this using pointfree topology. To illustrate the technique we show that
almost f-algebras are commutative. The proof is obtained relatively
straightforward from the proof by Buskes and van Rooij by using the pointfree
Stone-Yosida representation theorem by Coquand and Spitters
Full regularity for a C*-algebra of the Canonical Commutation Relations. (Erratum added)
The Weyl algebra,- the usual C*-algebra employed to model the canonical
commutation relations (CCRs), has a well-known defect in that it has a large
number of representations which are not regular and these cannot model physical
fields. Here, we construct explicitly a C*-algebra which can reproduce the CCRs
of a countably dimensional symplectic space (S,B) and such that its
representation set is exactly the full set of regular representations of the
CCRs. This construction uses Blackadar's version of infinite tensor products of
nonunital C*-algebras, and it produces a "host algebra" (i.e. a generalised
group algebra, explained below) for the \sigma-representation theory of the
abelian group S where \sigma(.,.):=e^{iB(.,.)/2}.
As an easy application, it then follows that for every regular representation
of the Weyl algebra of (S,B) on a separable Hilbert space, there is a direct
integral decomposition of it into irreducible regular representations (a known
result).
An Erratum for this paper is added at the end.Comment: An erratum was added to the original pape
Quantum Reality and Measurement: A Quantum Logical Approach
The recently established universal uncertainty principle revealed that two
nowhere commuting observables can be measured simultaneously in some state,
whereas they have no joint probability distribution in any state. Thus, one
measuring apparatus can simultaneously measure two observables that have no
simultaneous reality. In order to reconcile this discrepancy, an approach based
on quantum logic is proposed to establish the relation between quantum reality
and measurement. We provide a language speaking of values of observables
independent of measurement based on quantum logic and we construct in this
language the state-dependent notions of joint determinateness, value identity,
and simultaneous measurability. This naturally provides a contextual
interpretation, in which we can safely claim such a statement that one
measuring apparatus measures one observable in one context and simultaneously
it measures another nowhere commuting observable in another incompatible
context.Comment: 16 pages, Latex. Presented at the Conference "Quantum Theory:
Reconsideration of Foundations, 5 (QTRF5)," Vaxjo, Sweden, 15 June 2009. To
appear in Foundations of Physics
A Cauchy-Dirac delta function
The Dirac delta function has solid roots in 19th century work in Fourier
analysis and singular integrals by Cauchy and others, anticipating Dirac's
discovery by over a century, and illuminating the nature of Cauchy's
infinitesimals and his infinitesimal definition of delta.Comment: 24 pages, 2 figures; Foundations of Science, 201
Syntactic Cut-Elimination for Intuitionistic Fuzzy Logic via Linear Nested Sequents
This paper employs the linear nested sequent framework to design a new
cut-free calculus LNIF for intuitionistic fuzzy logic--the first-order G\"odel
logic characterized by linear relational frames with constant domains. Linear
nested sequents--which are nested sequents restricted to linear
structures--prove to be a well-suited proof-theoretic formalism for
intuitionistic fuzzy logic. We show that the calculus LNIF possesses highly
desirable proof-theoretic properties such as invertibility of all rules,
admissibility of structural rules, and syntactic cut-elimination.Comment: Appended version of the paper "Syntactic Cut-Elimination for
Intuitionistic Fuzzy Logic via Linear Nested Sequents", accepted to the
International Symposium on Logical Foundations of Computer Science (LFCS
2020
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