Stationary and convergent strategies in Choquet games

If NONEMPTY has a winning strategy against EMPTY in the Choquet game on a space, the space is said to be a Choquet space. Such a winning strategy allows NONEMPTY to consider the entire finite history of previous moves before making each new move; a stationary strategy only permits NONEMPTY to consider the previous move by EMPTY. We show that NONEMPTY has a stationary winning strategy for every second countable T1 Choquet space. More generally, NONEMPTY has a stationary winning strategy for any T1 Choquet space with an open-finite basis. We also study convergent strategies for the Choquet game, proving the following results. (1) A T1 space X is the open image of a complete metric space if and only if NONEMPTY has a convergent winning strategy in the Choquet game on X. (2) A T1 space X is the compact open image of a metric space if and only if X is metacompact and NONEMPTY has a stationary convergent strategy in the Choquet game on X. (3) A T1 space X is the compact open image of a complete metric space if and only if X is metacompact and NONEMPTY has a stationary convergent winning strategy in the Choquet game on X.Comment: 24 page

RD-flatness and RD-injectivity

It is proved that every commutative ring whose RD-injective modules are $\Sigma$-RD-injective is the product of a pure semi-simple ring and a finite ring. A complete characterization of commutative rings for which each artinian (respectively simple) module is RD-injective, is given. These results can be obtained by using the properties of RD-flat modules and RD-coflat modules which are respectively the RD-relativization of flat modules and fp-injective modules. It is also shown that a commutative ring is perfect if and only if each RD-flat module is RD-projective.Comment: A new section is added to the version published in Communications in Algebra where a complete proof of Theorem 3.1 is give

Beyond Oaxaca-Blinder: Accounting for Differences in Household Income Distributions Across Countries

This paper develops a micro-econometric method to account for differences across distributions of household income. Going beyond the determination of earnings in labor markets, we also estimate statistical models for occupational choice and for the conditional distributions of education, fertility and non-labor incomes. We import combinations of estimated parameters from these models to simulate counterfactual income distributions. This allows us to decompose differences between functionals of two income distributions (such as inequality or poverty measures) into shares due to differences in the structure of labor market returns (price effects); differences in the occupational structure; and differences in the underlying distribution of assets (endowment effects). We apply the method to the differences between the Brazilian income distribution and those of the United States and Mexico, and find that most of Brazil's excess income inequality is due to underlying inequalities in the distribution of two key endowments: access to education and to sources of non-labor income, mainly pensions.http://deepblue.lib.umich.edu/bitstream/2027.42/39863/3/wp478.pd

Ex-ante Evaluation of Conditional Cash Transfer Programs: The Case of Bolsa Escola

Cash transfers targeted to poor people, but conditional on some behavior on their part, such as school attendance or regular visits to health care facilities, are being adopted in a growing number of developing countries. Even where ex-post impact evaluations have been conducted, a number of policy-relevant counterfactual questions have remained unanswered. These are questions about the potential impact of changes in program design, such as benefit levels or the choice of the means-test, on both the current welfare and the behavioral response of household members. This paper proposes a method to simulate the effects of those alternative program designs on welfare and behavior, based on micro-econometrically estimated models of household behavior. In an application to Brazil’s recently introduced federal Bolsa Escola program, we find a surprisingly strong effect of the conditionality on school attendance, but a muted impact of the transfers on the reduction of current poverty and inequality levels.http://deepblue.lib.umich.edu/bitstream/2027.42/39901/3/wp516.pd

Phase separation and self-assembly in vitrimers: hierarchical morphology of molten and semi-crystalline polyethylene/dioxaborolane maleimide systems

Vitrimers - a class of polymer networks which are covalently crosslinked and insoluble like thermosets, but flow when heated like thermoplastics - contain dynamic links and/or crosslinks that undergo an associative exchange reaction. These dynamic crosslinks enable vitrimers to have interesting mechanical/rheological behavior, self-healing, adhesive, and shape memory properties. We demonstrate that vitrimers can self-assemble into complex meso- and nanostructures when crosslinks and backbone monomers strongly interact. Vitrimers featuring polyethylene (PE) as the backbone and dioxaborolane maleimide as the crosslinkable moiety were studied in both the molten and semi-crystalline states. We observed that PE vitrimers macroscopically phase separated into dioxaborolane maleimide rich and poor regions, and characterized the extent of phase separation by optical transmission measurements. This phase separation can explain the relatively low insoluble fractions and overall crystallinities of PE vitrimers. Using synchrotron-sourced small-angle X-ray scattering (SAXS), we discovered that PE vitrimers and their linear precursors micro-phase separated into hierarchical nanostructures. Fitting of the SAXS patterns to a scattering model strongly suggests that the nanostructures - which persist in both the melt and amorphous fraction of the semi-crystalline state - may be described as dioxaborolane maleimide rich aggregates packed in a mass fractal arrangement. These findings of hierarchical meso- and nanostructures point out that incompatibility effects between network components and resulting self-assembly must be considered for understanding behavior and the rational design of vitrimer materials

Reverse Mathematics and Algebraic Field Extensions

This paper analyzes theorems about algebraic field extensions using the techniques of reverse mathematics. In section 2, we show that $\mathsf{WKL}_0$ is equivalent to the ability to extend $F$-automorphisms of field extensions to automorphisms of $\bar{F}$, the algebraic closure of $F$. Section 3 explores finitary conditions for embeddability. Normal and Galois extensions are discussed in section 4, and the Galois correspondence theorems for infinite field extensions are treated in section 5.Comment: 25 page

Kepler-10 c: a 2.2 Earth Radius Transiting Planet in a Multiple System

The Kepler mission has recently announced the discovery of Kepler-10 b, the smallest exoplanet discovered to date and the first rocky planet found by the spacecraft. A second, 45 day period transit-like signal present in the photometry from the first eight months of data could not be confirmed as being caused by a planet at the time of that announcement. Here we apply the light curve modeling technique known as BLENDER to explore the possibility that the signal might be due to an astrophysical false positive (blend). To aid in this analysis we report the observation of two transits with the Spitzer Space Telescope at 4.5 μm. When combined, they yield a transit depth of 344 ± 85 ppm that is consistent with the depth in the Kepler passband (376 ± 9 ppm, ignoring limb darkening), which rules out blends with an eclipsing binary of a significantly different color than the target. Using these observations along with other constraints from high-resolution imaging and spectroscopy, we are able to exclude the vast majority of possible false positives. We assess the likelihood of the remaining blends, and arrive conservatively at a false alarm rate of 1.6 × 10^(–5) that is small enough to validate the candidate as a planet (designated Kepler-10 c) with a very high level of confidence. The radius of this object is measured to be R_p = 2.227^(+0.052)_(–0.057) R_⊕ (in which the error includes the uncertainty in the stellar properties), but currently available radial-velocity measurements only place an upper limit on its mass of about 20 M_⊕. Kepler-10 c represents another example (with Kepler-9 d and Kepler-11 g) of statistical "validation" of a transiting exoplanet, as opposed to the usual "confirmation" that can take place when the Doppler signal is detected or transit timing variations are measured. It is anticipated that many of Kepler's smaller candidates will receive a similar treatment since dynamical confirmation may be difficult or impractical with the sensitivity of current instrumentation