Whitney's type theorems for infinite dimensional spaces

It is proved that for any $f$ is an element of $C^k(L,R)$, where k is a natural number and L is a closed linear subspace of a nuclear Frechet space $X$, the function $f$ can be extended to a function of class $C^{k-1}$ defined on the entire space $X$. It is also proved that for any $f$ is an element of $C^k(L, R)$, where $k$ is a natural number of infinity and L is a closed linear subspace of a dual $X$ of a nuclear Frechet space, the function $f$ can be extended to a function of class $C^k$ defined on the entire space $X$. In addition, it is proved that under these conditions, the existence of a linear extension operator is equivalent to the complementability of the subspace.

Rule Britannia!: British Stock Market Returns, 1825-1870

This article presents a new series of monthly equity returns for the British stock market for the period 1825-1870. In addition to calculating capital appreciation and dividend yields, the article also estimates the effect of survivorship bias on returns. Three notable findings emerge from this study. First, stock market returns in the 1825-1870 period are broadly similar for Britain and the United States, although the British market is less risky. Second, real returns in the 1825-1870 period are higher than in subsequent epochs of British history. Third, unlike the modern era, dividends are the most important component of returns.

The rate of return on equity across industrial sectors on the British stock market, 1825-70

This article assesses the contribution of the various industrial sectors to the growth of the British equity market in the 1825–70 period. It also provides estimates of the rates of return on these industrial sectors in this period. The article then proceeds to examine whether differences in rates of return across the various sectors can be explained by risk or other financial factors. One of the main findings is that the relatively high rates of return in the banking, insurance, and miscellaneous sectors appear to be in some measure explained by the presence of extended liability and uncalled capital.

Materials in extreme environments for energy, accelerators and space applications at ELI-NP.

As a leading facility in laser-driven nuclear physics, ELI-NP will develop innovative research in the fields of materials behavior in extreme environments and radiobiology, with applications in the development of accelerator components, new materials for next generation fusion and fission reactors, shielding solutions for equipment and human crew in long term space missions and new biomedical technologies. The specific properties of the laser-driven radiation produced with two lasers of 1 PW at a pulse repetition rate of 1 Hz each are an ultra-short time scale, a relatively broadband spectrum and the possibility to provide simultaneously several types of radiation. Complex, cosmic-like radiation will be produced in a ground-based laboratory allowing comprehensive investigations of their effects on materials and biological systems. The expected maximum energy and intensity of the radiation beams are 19 MeV with 10^9 photon/pulse for photon radiation, 2 GeV with 108 electron/pulse for electron beams, 60 MeV with 10^12 proton/pulse for proton and ion beams and 60 MeV with 107 neutron/pulse for a neutron source. Research efforts will be directed also towards measurements for radioprotection of the prompt and activated dose, as a function of laser and target characteristics and to the development and testing of various dosimetric methods and equipment.

Integration between the London and New York Stock Exchanges, 1825-1925

The integration between the London and New York Stock Exchanges is analyzed during the era when they were still developing as asset markets. The domestic securities on both exchanges showed little sustained integration, even when controlling for the different characteristics of stocks, implying that the pricing of securities in the US and UK were still being driven by local factors. However, there was considerable integration between New York and those listings on London which operated internationally. These results place a limit on the view that pre-World War I was the first era of globalization in terms of capital markets, and suggest that the listing of foreign securities may be one of the primary mechanisms driving asset market integration.