Hydrogen atom in space with a compactified extra dimension and potential defined by Gauss' law

We investigate the consequences of one extra spatial dimension for the stability and energy spectrum of the non-relativistic hydrogen atom with a potential defined by Gauss' law, i.e. proportional to 1 /| x | 2 . The additional spatial dimension is considered to be either infinite or curled-up in a circle of radius R. In both cases, the energy spectrum is bounded from below for charges smaller than the same critical value and unbounded from below otherwise. As a consequence of compactification, negative energy eigenstates appear: if R is smaller than a quarter of the Bohr radius, the corresponding Hamiltonian possesses an infinite number of bound states with minimal energy extending at least to the ground state of the hydrogen atom.

Non-tariff barriers, integration and the transatlantic economy

We examine the potential impact of TTIP through trade-cost reductions, applying a mix of econometric and computational methods to develop estimates of the benefits (and costs) for the EU, United States, and third countries. Econometric results point to an approximate 80% growth in bilateral trade with an ambitious trade agreement. However, at the same time, computable general equilibrium (CGE) estimates highlight distributional impacts across countries and factors not evident from econometrics alone. Translated through our CGE framework, while bilateral trade increases roughly 80%, there is a fall of about 2.5% in trade with the rest of the world in our central case. The estimated gains in annual consumption range between 1% and 2.25% for the United States and EU, respectively. A purely discriminatory agreement would harm most countries outside the agreement, while the direction of third-country effects hinges critically on whether NTB reductions end up being discriminatory or not. Within the United States and EU, while labour gains across skill categories, the impact on farmers is mixed.

Benford's Law and Fraud Detection. Facts and Legends

Is Benford's law a good instrument to detect fraud in reports of statistical and scientific data? For a valid test the probability of "false positives" and "false negatives" has to be low. However, it is very doubtful whether the Benford distribution is an appropriate tool to discriminate between manipulated and non-manipulated estimates. Further research should focus more on the validity of the test and test results should be interpreted more carefully.