An Infinite Number of Closed FLRW Universes for Any Value of the Spatial Curvature

The Friedman-Lemaitre-Robertson-Walker (FLRW) cosmological models are based on the assumptions of large-scale homogeneity and isotropy of the distribution of matter and energy. They are usually taken to have spatial sections that are simply connected; they have finite volume in the positive curvature case, and infinite volume in the null and negative curvature ones. I want to call the attention to the existence of an infinite number of models, which are based on these same metrics, but have compact, finite volume, multiply connected spatial sections. Some observational implications are briefly mentioned.Comment: 4 pages. Contribution to the 5th International Workshop on Astronomy and Relativistic Astrophysics (Joao Pessoa, PB, Brazil, October 10-12, 2011) and to the 1o. Simposio Jayme Tiomno (Brasilia, DF, Brazil, October 27-28, 2011). In version 2: a few minor corrections; two new references added. In this version: title correction in Ref. 3; dedication paragraph at the en

Lessons From the Latest Data on U.S. Productivity

La croissance de la productivité est examinée par les macro-économistes car elle joue des rôles clés dans la compréhension de l’épargne dans le secteur privé, les sources des chocs macroéconomiques, l’évolution de la compétitivité internationale et la solvabilité des régimes de retraite publics. Toutefois, les estimations des taux de croissance de la productivité anticipées et conjoncturelles souffrent de deux problèmes potentiels : (i) les estimations des tendances récentes sont imprécises, et (ii) les données récemment publiées subissent souvent d’importantes révisions. Cette étude met en évidence la (non-) fiabilité de plusieurs mesures de croissance de la productivité agrégée aux États-Unis en examinant la mesure dans laquelle elles sont révisées au fil du temps. Nous examinons également dans quelle mesure ces révisions contribuent aux erreurs dans les prévisions de croissance de la productivité des États-Unis. Nous constatons que les révisions de données provoquent généralement des changements appréciables des estimations des taux de croissance de la productivité publiés à travers une gamme de différentes mesures de la productivité. D'importantes révisions surviennent souvent des années après la première publication des données, ce qui contribue significativement à l'incertitude générale à laquelle nos décideurs politiques doivent faire face. Cela souligne le besoin de moyens pour réduire l'incertitude à laquelle sont confrontés les décideurs politiques et les politiques robustes à l'incertitude sur les conditions économiques actuelles. La croissance de la productivité est examinée par les macro-économistes car elle joue des rôles clés dans la compréhension de l’épargne dans le secteur privé, les sources des chocs macroéconomiques, l’évolution de la compétitivité internationale et la solvabilité des régimes de retraite publics. Toutefois, les estimations des taux de croissance de la productivité anticipées et conjoncturelles souffrent de deux problèmes potentiels : (i) les estimations des tendances récentes sont imprécises, et (ii) les données récemment publiées subissent souvent d’importantes révisions. Cette étude met en évidence la (non-) fiabilité de plusieurs mesures de croissance de la productivité agrégée aux États-Unis en examinant la mesure dans laquelle elles sont révisées au fil du temps. Nous examinons également dans quelle mesure ces révisions contribuent aux erreurs dans les prévisions de croissance de la productivité des États-Unis. Nous constatons que les révisions de données provoquent généralement des changements appréciables des estimations des taux de croissance de la productivité publiés à travers une gamme de différentes mesures de la productivité. D'importantes révisions surviennent souvent des années après la première publication des données, ce qui contribue significativement à l'incertitude générale à laquelle nos décideurs politiques doivent faire face. Cela souligne le besoin de moyens pour réduire l'incertitude à laquelle sont confrontés les décideurs politiques et les politiques robustes à l'incertitude sur les conditions économiques actuelles.Productivité, analyses en temps réel, révisions de données, projections Greenbook projections , Productivité, analyses en temps réel, révisions de données, projections Greenbook projections

Extending invariant complex structures

We study the problem of extending a complex structure to a given Lie algebra g, which is firstly defined on an ideal h of g. We consider the next situations: h is either complex or it is totally real. The next question is to equip g with an additional structure, such as a (non)-definite metric or a symplectic structure and to ask either h is non-degenerate, isotropic, etc. with respect to this structure, by imposing a compatibility assumption. We show that this implies certain constraints on the algebraic structure of g. Constructive examples illustrating this situation are shown, in particular computations in dimension six are given.Comment: 22 pages, plus an Addendu

Normal frames and the validity of the equivalence principle. I. Cases in a neighborhood and at a point

A treatment in a neighborhood and at a point of the equivalence principle on the basis of derivations of the tensor algebra over a manifold is given. Necessary and sufficient conditions are given for the existence of local bases, called normal frames, in which the components of derivations vanish in a neighborhood or at a point. These frames (bases), if any, are explicitly described and the problem of their holonomicity is considered. In particular, the obtained results concern symmetric as well as nonsymmetric linear connections.Comment: LaTeX2e, 9 pages, to be published in Journal of Physics A: Mathematical and Genera

Can GDP measurement be further improved? Data revision and reconciliation

Recent years have seen many attempts to combine expenditure-side estimates of U.S. real output (GDE) growth with income-side estimates (GDI) to improve estimates of real GDP growth. We show how to incorporate information from multiple releases of noisy data to provide more precise estimates while avoiding some of the identifying assumptions required in earlier work. This relies on a new insight: using multiple data releases allows us to distinguish news and noise measurement errors in situations where a single vintage does not. Our new measure, GDP++, fits the data better than GDP+, the GDP growth measure of Aruoba et al. (2016) published by the Federal Reserve Bank of Philadephia. Historical decompositions show that GDE releases are more informative than GDI, while the use of multiple data releases is particularly important in the quarters leading up to the Great Recession

Can GDP Measurement Be Further Improved? Data Revision and Reconciliation

Recent years have seen many attempts to combine expenditure-side estimates of U.S. real output (GDE) growth with income-side estimates (GDI) to improve estimates of real GDP growth. We show how to incorporate information from multiple releases of noisy data to provide more precise estimates while avoiding some of the identifying assumptions required in earlier work. This relies on a new insight: using multiple data releases allows us to distinguish news and noise measurement errors in situations where a single vintage does not. We find that (a) the data prefer averaging across multiple releases instead of discarding early releases in favor of later ones, and (b) that initial estimates of GDI are quite informative. Our new measure, GDP(++), undergoes smaller revisions and tracks expenditure measures of GDP growth more closely than either the simple average of the expenditure and income measures published by the BEA or the GDP growth measure of Aruoba et al. published by the Federal Reserve Bank of Philadelphia

Broadband Meter-Wavelength Observations of Ionospheric Scintillation

Intensity scintillations of cosmic radio sources are used to study astrophysical plasmas like the ionosphere, the solar wind, and the interstellar medium. Normally these observations are relatively narrow band. With Low Frequency Array (LOFAR) technology at the Kilpisj\"arvi Atmospheric Imaging Receiver Array (KAIRA) station in northern Finland we have observed scintillations over a 3 octave bandwidth. ``Parabolic arcs'', which were discovered in interstellar scintillations of pulsars, can provide precise estimates of the distance and velocity of the scattering plasma. Here we report the first observations of such arcs in the ionosphere and the first broad-band observations of arcs anywhere, raising hopes that study of the phenomenon may similarly improve the analysis of ionospheric scintillations. These observations were made of the strong natural radio source Cygnus-A and covered the entire 30-250\,MHz band of KAIRA. Well-defined parabolic arcs were seen early in the observations, before transit, and disappeared after transit although scintillations continued to be obvious during the entire observation. We show that this can be attributed to the structure of Cygnus-A. Initial results from modeling these scintillation arcs are consistent with simultaneous ionospheric soundings taken with other instruments, and indicate that scattering is most likely to be associated more with the topside ionosphere than the F-region peak altitude. Further modeling and possible extension to interferometric observations, using international LOFAR stations, are discussed.Comment: 11 pages, 17 figure

Frames of reference in spaces with affine connections and metrics

A generalized definition of a frame of reference in spaces with affine connections and metrics is proposed based on the set of the following differential-geometric objects: (a) a non-null (non-isotropic) vector field, (b) the orthogonal to the vector field sub space, (c) an affine connection and the related to it covariant differential operator determining a transport along the given non-null vector filed. On the grounds of this definition other definitions related to the notions of accelerated, inertial, proper accelerated and proper inertial frames of reference are introduced and applied to some mathematical models for the space-time. The auto-parallel equation is obtained as an Euler-Lagrange's equation. Einstein's theory of gravitation appears as a theory for determination of a special frame of reference (with the gravitational force as inertial force) by means of the metrics and the characteristics of a material distribution. PACS numbers: 0490, 0450, 1210G, 0240VComment: 17 pages, LaTeX 2