Bounded Arithmetic in Free Logic

One of the central open questions in bounded arithmetic is whether Buss' hierarchy of theories of bounded arithmetic collapses or not. In this paper, we reformulate Buss' theories using free logic and conjecture that such theories are easier to handle. To show this, we first prove that Buss' theories prove consistencies of induction-free fragments of our theories whose formulae have bounded complexity. Next, we prove that although our theories are based on an apparently weaker logic, we can interpret theories in Buss' hierarchy by our theories using a simple translation. Finally, we investigate finitistic G\"odel sentences in our systems in the hope of proving that a theory in a lower level of Buss' hierarchy cannot prove consistency of induction-free fragments of our theories whose formulae have higher complexity

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

Asteroseismological Observations of the Central Star of the Planetary Nebula NGC 1501

We report on a global CCD time-series photometric campaign to decode the pulsations of the nucleus of the planetary nebula NGC1501. The star is hot and hydrogen-deficient, similar to the pre-white-dwarf PG 1159 stars. NGC1501 shows pulsational brightness variations of a few percent with periods ranging from 19 to 87 minutes. The variations are very complex, suggesting a pulsation spectrum that requires a long unbroken time series to resolve. Our CCD photometry of the star covers a two-week period in 1991 November, and used a global network of observatories. We obtained nearly continuous coverage over an interval of one week in the middle of the run. We have identified 10 pulsation periods, ranging from 5235 s down to 1154 s. We find strong evidence that the modes are indeed nonradial g-modes. The ratios of the frequencies of the largest-amplitude modes agree with those expected for modes that are trapped by a density discontinuity in the outer layers. We offer a model for the pulsation spectrum that includes a common period spacing of 22.3 s and a rotation period of 1.17 days; the period spacing allows us to assign a seismological mass of 0.55+/-0.03 Msun.Comment: 12 pages, AASTEX, 7 tables, 6 EPS figures, to appear in AJ, 12/96 Corrected version repairs table formatting and adds missing Table

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

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 $t_{\rm Eout}$ 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

Comparação entre tipificação fenotípica e genotípica de isolados de Pasteurella multocida de suínos.

Os sorotipos A e D da Pasteurella multocida (Pm) estão comumente associados a casos de pneumonias e pleurites em suínos. Para a identificação desses sorotipos podem ser empregadas técnicas fenotípicas, como os testes de hialuronidase e acriflavina, e genotípica, como o PCR. Assim, o objetivo desse trabalho foi comparar a tipificação capsular de isolados de Pm (tipo A e tipo D) de suínos utilizando técnicas fenotípicas (testes de hialuronidade e de acriflavina) e genotípica (PCR multiplex). Foram analisados na Embrapa Suínos e Aves, em Concórdia/SC, 86 isolados liofilizados de Pm obtidos no período de 1981 a 1997, provenientes do Instituto de Pesquisas Veterinárias Desidério Finamor (IPVDF). Após realizado o cultivo desses isolados de Pm, 44 dos 86 foram recuperados (51,1%). Os testes fenotípicos foram então realizados, sendo 2 amostras do tipo D (4,5%), 40 amostras do tipo A (91%) e 2 amostras sem tipificação (4,5%), uma vez que tiveram resultados positivos para os testes de hialuronidase e acriflavina. No entanto, após esses isolados recuperados serem submetidos ao teste genotípico (PCR), 38 foram classificados como tipo A (86,4%) e 6 como tipo D (13,6%). Os resultados desse trabalho mostram que, em alguns casos, não existe equivalência entre a tipificação fenotípica e genotípica de Pm, neste estudo diferindo em 4/44 isolados (9%). Ainda, uma vez que o resultado do PCR é direto, sem a necessidade de interpretação por parte do executor, essa técnica se torna mais confiável

A Note on the Ordinal Analysis of RCA0+WO(σ)

We fill an apparent gap in the literature by giving a short and self-contained proof that the ordinal of the theory RCA0+WO(σ) is σω , for any ordinal σ satisfying ω⋅σ=σ (e.g., ωω , ωωω , ε0 ). Theories of the form RCA0+WO(σ) are of interest in Proof Theory and Reverse Mathematics because of their connections to a number of well-investigated combinatorial principles related to various subsystems of arithmetic

A Note on Universal Measures for Weak Implicit Computational Complexity

Abstract. This note is a case study for finding universal measures for weak implicit computational complexity. We will instantiate “univer-sal measures ” by “dynamic ordinals”, and “weak implicit computational complexity ” by “bounded arithmetic”. Concretely, we will describe the connection between dynamic ordinals and witness oracle Turing ma-chines for bounded arithmetic theories