A general method for constructing essential uniform algebras

A general method for constructing essential uniform algebras with prescribed properties is presented. Using the method, the following examples are constructed: an essential, natural, regular uniform algebra on the closed unit disc; an essential, natural counterexample to the peak point conjecture on each manifold-with-boundary of dimension at least three; and an essential, natural uniform algebra on the unit sphere in C3 containing the ball algebra and invariant under the action of the 3-torus. These examples show that a smoothness hypothesis in some results of Anderson and Izzo cannot be omitted

Patents and Industrialisation. An Historical Overview of the British Case, 1624-1907

A Report to the Strategic Advisory Board on Intellectual Property Policy (SABIP), U

TOI-1338 : TESS' first transiting circumbinary planet

Funding: Funding for the DPAC has been provided by national institutions, in particular, the institutions participating in the Gaia Multilateral Agreement. W.F.W. and J.A.O.thank John Hood Jr. for his generous support of exoplanet research at SDSU. Support was also provided and acknowledged through NASA Habitable Worlds grant 80NSSC17K0741 and NASA XRP grant 80NSSC18K0519. This work is partly supported by NASA Habitable Worlds grant 80NSSC17K0741. This material is based upon work supported by the National Science Foundation Graduate Research Fellowship Program under grant No.(DGE-1746045). A.H.M.J.T. has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 803193/BEBOP) and from a Leverhulme Trust Research Project grant No. RPG-2018-418. A.C. acknowledges support by CFisUC strategic project (UID/FIS/04564/2019).We report the detection of the first circumbinary planet (CBP) found by Transiting Exoplanet Survey Satellite (TESS). The target, a known eclipsing binary, was observed in sectors 1 through 12 at 30 minute cadence and in sectors 4 through 12 at 2 minute cadence. It consists of two stars with masses of 1.1 M⊙ and 0.3 M⊙ on a slightly eccentric (0.16), 14.6 day orbit, producing prominent primary eclipses and shallow secondary eclipses. The planet has a radius of ∼6.9 R⊕ and was observed to make three transits across the primary star of roughly equal depths (∼0.2%) but different durations—a common signature of transiting CBPs. Its orbit is nearly circular (e ≍ 0.09) with an orbital period of 95.2 days. The orbital planes of the binary and the planet are aligned to within ∼1°. To obtain a complete solution for the system, we combined the TESS photometry with existing ground-based radial-velocity observations in a numerical photometric-dynamical model. The system demonstrates the discovery potential of TESS for CBPs and provides further understanding of the formation and evolution of planets orbiting close binary stars.Publisher PDFPeer reviewe

The seeds of divergence: the economy of French North America, 1688 to 1760

Generally, Canada has been ignored in the literature on the colonial origins of divergence with most of the attention going to the United States. Late nineteenth century estimates of income per capita show that Canada was relatively poorer than the United States and that within Canada, the French and Catholic population of Quebec was considerably poorer. Was this gap long standing? Some evidence has been advanced for earlier periods, but it is quite limited and not well-suited for comparison with other societies. This thesis aims to contribute both to Canadian economic history and to comparative work on inequality across nations during the early modern period. With the use of novel prices and wages from Quebec—which was then the largest settlement in Canada and under French rule—a price index, a series of real wages and a measurement of Gross Domestic Product (GDP) are constructed. They are used to shed light both on the course of economic development until the French were defeated by the British in 1760 and on standards of living in that colony relative to the mother country, France, as well as the American colonies. The work is divided into three components. The first component relates to the construction of a price index. The absence of such an index has been a thorn in the side of Canadian historians as it has limited the ability of historians to obtain real values of wages, output and living standards. This index shows that prices did not follow any trend and remained at a stable level. However, there were episodes of wide swings—mostly due to wars and the monetary experiment of playing card money. The creation of this index lays the foundation of the next component. The second component constructs a standardized real wage series in the form of welfare ratios (a consumption basket divided by nominal wage rate multiplied by length of work year) to compare Canada with France, England and Colonial America. Two measures are derived. The first relies on a “bare bones” definition of consumption with a large share of land-intensive goods. This measure indicates that Canada was poorer than England and Colonial America and not appreciably richer than France. However, this measure overestimates the relative position of Canada to the Old World because of the strong presence of land-intensive goods. A second measure is created using a “respectable” definition of consumption in which the basket includes a larger share of manufactured goods and capital-intensive goods. This second basket better reflects differences in living standards since the abundance of land in Canada (and Colonial America) made it easy to achieve bare subsistence, but the scarcity of capital and skilled labor made the consumption of luxuries and manufactured goods (clothing, lighting, imported goods) highly expensive. With this measure, the advantage of New France over France evaporates and turns slightly negative. In comparison with Britain and Colonial America, the gap widens appreciably. This element is the most important for future research. By showing a reversal because of a shift to a different type of basket, it shows that Old World and New World comparisons are very sensitive to how we measure the cost of living. Furthermore, there are no sustained improvements in living standards over the period regardless of the measure used. Gaps in living standards observed later in the nineteenth century existed as far back as the seventeenth century. In a wider American perspective that includes the Spanish colonies, Canada fares better. The third component computes a new series for Gross Domestic Product (GDP). This is to avoid problems associated with using real wages in the form of welfare ratios which assume a constant labor supply. This assumption is hard to defend in the case of Colonial Canada as there were many signs of increasing industriousness during the eighteenth and nineteenth centuries. The GDP series suggest no long-run trend in living standards (from 1688 to circa 1765). The long peace era of 1713 to 1740 was marked by modest economic growth which offset a steady decline that had started in 1688, but by 1760 (as a result of constant warfare) living standards had sunk below their 1688 levels. These developments are accompanied by observations that suggest that other indicators of living standard declined. The flat-lining of incomes is accompanied by substantial increases in the amount of time worked, rising mortality and rising infant mortality. In addition, comparisons of incomes with the American colonies confirm the results obtained with wages— Canada was considerably poorer. At the end, a long conclusion is provides an exploratory discussion of why Canada would have diverged early on. In structural terms, it is argued that the French colony was plagued by the problem of a small population which prohibited the existence of scale effects. In combination with the fact that it was dispersed throughout the territory, the small population of New France limited the scope for specialization and economies of scale. However, this problem was in part created, and in part aggravated, by institutional factors like seigneurial tenure. The colonial origins of French America’s divergence from the rest of North America are thus partly institutional

Why do we do proofs?

The aim of this session is to motivate students to understand why we might want to do proofs, why proofs are important, and how they can help us. In particular, the student will learn the following: proofs can help you to really see WHY a result is true; problems that are easy to state can be hard to solve (Fermat's Last Theorem); sometimes statements which appear to be intuitively obvious may turn out to be false (the Hospitals paradox); the answer to a question will often depend crucially on the definitions you are working with. Target audience: suitable for anyone with a knowledge of elementary algebra and prime numbers, as may be obtained by studying A level mathematics.