54 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
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
Microlensing optical depth towards the Galactic bulge from MOA observations during 2000 with Difference Image Analysis
We analyze the data of the gravitational microlensing survey carried out by
by the MOA group during 2000 towards the Galactic Bulge (GB). Our observations
are designed to detect efficiently high magnification events with faint source
stars and short timescale events, by increasing the the sampling rate up to 6
times per night and using Difference Image Analysis (DIA). We detect 28
microlensing candidates in 12 GB fields corresponding to 16 deg^2. We use Monte
Carlo simulations to estimate our microlensing event detection efficiency,
where we construct the I-band extinction map of our GB fields in order to find
dereddened magnitudes. We find a systematic bias and large uncertainty in the
measured value of the timescale in our simulations. They are
associated with blending and unresolved sources, and are allowed for in our
measurements. We compute an optical depth tau = 2.59_{-0.64}^{+0.84} \times
10^{-6} towards the GB for events with timescales 0.3<t_E<200 days. We consider
disk-disk lensing, and obtain an optical depth tau_{bulge} =
3.36_{-0.81}^{+1.11} \times 10^{-6}[0.77/(1-f_{disk})] for the bulge component
assuming a 23% stellar contribution from disk stars. These observed optical
depths are consistent with previous measurements by the MACHO and OGLE groups,
and still higher than those predicted by existing Galactic models. We present
the timescale distribution of the observed events, and find there are no
significant short events of a few days, in spite of our high detection
efficiency for short timescale events down to t_E = 0.3 days. We find that half
of all our detected events have high magnification (>10). These events are
useful for studies of extra-solar planets.Comment: 65 pages and 30 figures, accepted for publication in ApJ. A
systematic bias and uncertainty in the optical depth measurement has been
quantified by simulation
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
`What is a Thing?': Topos Theory in the Foundations of Physics
The goal of this paper is to summarise the first steps in developing a
fundamentally new way of constructing theories of physics. The motivation comes
from a desire to address certain deep issues that arise when contemplating
quantum theories of space and time. In doing so we provide a new answer to
Heidegger's timeless question ``What is a thing?''.
Our basic contention is that constructing a theory of physics is equivalent
to finding a representation in a topos of a certain formal language that is
attached to the system. Classical physics uses the topos of sets. Other
theories involve a different topos. For the types of theory discussed in this
paper, a key goal is to represent any physical quantity with an arrow
\breve{A}_\phi:\Si_\phi\map\R_\phi where \Si_\phi and are two
special objects (the `state-object' and `quantity-value object') in the
appropriate topos, .
We discuss two different types of language that can be attached to a system,
. The first, \PL{S}, is a propositional language; the second, \L{S}, is
a higher-order, typed language. Both languages provide deductive systems with
an intuitionistic logic. With the aid of \PL{S} we expand and develop some of
the earlier work (By CJI and collaborators.) on topos theory and quantum
physics. A key step is a process we term `daseinisation' by which a projection
operator is mapped to a sub-object of the spectral presheaf \Sig--the topos
quantum analogue of a classical state space. The topos concerned is \SetH{}:
the category of contravariant set-valued functors on the category (partially
ordered set) \V{} of commutative sub-algebras of the algebra of bounded
operators on the quantum Hilbert space \Hi.Comment: To appear in ``New Structures in Physics'' ed R. Coeck
On Relating Theories: Proof-Theoretical Reduction
The notion of proof-theoretical or finitistic reduction of one theory to another has a long tradition. Feferman and Sieg (Buchholz et al., Iterated inductive definitions and subsystems of analysis. Springer, Berlin, 1981, Chap. 1) and Feferman in (J Symbol Logic 53:364â384, 1988) made first steps to delineate it in more formal terms. The first goal of this paper is to corroborate their view that this notion has the greatest explanatory reach and is superior to others, especially in the context of foundational theories, i.e., theories devised for the purpose of formalizing and presenting various chunks of mathematics.
A second goal is to address a certain puzzlement that was expressed in Fefermanâs title of his Clermont-Ferrand lectures at the Logic Colloquium 1994: âHow is it that finitary proof theory became infinitary?â Hilbertâs aim was to use proof theory as a tool in his finitary consistency program to eliminate the actual infinite in mathematics from proofs of real statements. Beginning in the 1950s, however, proof theory began to employ infinitary methods. Infinitary rules and concepts, such as ordinals, entered the stage.
In general, the more that such infinitary methods were employed, the farther did proof theory depart from its initial aims and methods, and the closer did it come instead to ongoing developments in recursion theory, particularly as generalized to admissible sets; in both one makes use of analogues of regular cardinals, as well as âlargeâ cardinals (inaccessible, Mahlo, etc.). (Feferman 1994).
The current paper aims to explain how these infinitary tools, despite appearances to the contrary, can be formalized in an intuitionistic theory that is finitistically reducible to (actually Î 02
-conservative over) intuitionistic first order arithmetic, also known as Heyting arithmetic. Thus we have a beautiful example of Hilbertâs program at work, exemplifying the Hilbertian goal of moving from the ideal to the real by eliminating ideal elements
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