A note on the Eisenbud-Mazur Conjecture

The Eisenbud-Mazur conjecture states that given an equicharacteristic zero, regular local ring (R,\mathfrak{m}) and a prime ideal P\subset R, we have that P^{(2)}\subseteq mP. In this paper, we computationally prove that the conjecture holds in the special case of certain prime ideals in formal power series rings.Comment: 21 page

Higher Order Corrections to Black Hole Entropy

A scheme for calculating corrections to all orders to the entropy of any thermodynamic system due to statistical fluctuations around equilibrium has been developed. It is then applied to the BTZ black hole, AdS-Schwarzschild black Hole and Schwarzschild black Hole in a cavity. The scheme that we present is a model-independent scheme and hence universally applicable to all classical black holes with positive specific heat. It has been seen earlier that the microcanonical entropy of a system can be more accurately reproduced by considering a logarithmic correction to the canonical entropy function. The higher order corrections will be a step further in calculating the microcanonical entropy of a black hole.Comment: 9 pages, Revised version to appear in Classical and Quantum Gravit

Interpreting the strongly lensed supernova iPTF16geu: time delay predictions, microlensing, and lensing rates

We present predictions for time delays between multiple images of the gravitationally lensed supernova, iPTF16geu, which was recently discovered from the intermediate Palomar Transient Factory (iPTF). As the supernova is of Type Ia where the intrinsic luminosity is usually well-known, accurately measured time delays of the multiple images could provide tight constraints on the Hubble constant. According to our lens mass models constrained by the {\it Hubble Space Telescope} F814W image, we expect the maximum relative time delay to be less than a day, which is consistent with the maximum of 100 hours reported by Goobar et al. but places a stringent upper limit. Furthermore, the fluxes of most of the supernova images depart from expected values suggesting that they are affected by microlensing. The microlensing timescales are small enough that they may pose significant problems to measure the time delays reliably. Our lensing rate calculation indicates that the occurrence of a lensed SN in iPTF is likely. However, the observed total magnification of iPTF16geu is larger than expected, given its redshift. This may be a further indication of ongoing microlensing in this system.Comment: 5 pages, 3 figures, 1 table, ApjL accepted, minor but important correction

Is there a connection between the tax administration and the political power?

This paper offers empirical evidence from Spain of a connection between the tax administration and the political power. Firstly, the regional tax administration is not immune to the budgetary situation of regional government, and tends to exert a greater (or lesser) effort in tax collection the greater (or lower) the (expected) public deficit. At the same time, the system of unconditional grants from the central layer of government provokes an income effect which disincentivises the efforts of the tax administration. Secondly, these efforts also decrease when the margin to lose a parliamentary seat in an electoral district is cut, although the importance of this disincentive decreases according to the parliamentary strength of the incumbent.political economy, tax administration

Tax Evasion in Interrelated Taxes

In 1969, Shoup postulated that the presence of interrelated taxes in a tax system would reinforce the system of tax penalty ("self-reinforcing penalty system of taxes"). In this paper, we have tried to formally develop this idea. We find that in order that tax re-enforcement holds, it is necessary that the interrelated taxes are administered by a single tax administration, or in the case that they are administered by different tax administrations, the level of collaboration between them has to be high enough. If that is the case, tax evasion in interrelated taxes might be considered as an alternative explanation of the existing gap between the levels of tax evasion that can be guessed in practice and those much lower predicted by the classical theory of tax evasion (Allingham and Sandmo, 1972; Yitzhaki, 1974). Otherwise, the result expected by Shoup might even reverse. Moreover, as long as collaboration is imperfect, the classical results of the comparative statics might change, since in some cases although global tax compliance increases in front of a variation in a tax parameter, it can decrease in a tax.Tax Evasion