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

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

The Ysz--Yx Scaling Relation as Determined from Planck and Chandra

SZ clusters surveys like Planck, the South Pole Telescope, and the Atacama Cosmology Telescope, will soon be publishing several hundred SZ-selected systems. The key ingredient required to transport the mass calibration from current X-ray selected cluster samples to these SZ systems is the Ysz--Yx scaling relation. We constrain the amplitude, slope, and scatter of the Ysz--Yx scaling relation using SZ data from Planck, and X-ray data from Chandra. We find a best fit amplitude of \ln (D_A^2\Ysz/CY_X) = -0.202 \pm 0.024 at the pivot point CY_X=8\times 10^{-5} Mpc^2. This corresponds to a Ysz/Yx-ratio of 0.82\pm 0.024, in good agreement with X-ray expectations after including the effects of gas clumping. The slope of the relation is \alpha=0.916\pm 0.032, consistent with unity at \approx 2.3\sigma. We are unable to detect intrinsic scatter, and find no evidence that the scaling relation depends on cluster dynamical state