It\u27s a \u27Criming Shame\u27: Moving from Land Use Ethics to Criminalization of Behavior Leading to Permits and Other Zoning Related Acts

In the past, land use ethics inquiries predominately involved conflicts of interest or an official holding public office while engaging in a previously held business or law practice. Now, prosecutors are looking at the underlying criminality of the unethical acts carried out in the context of land use decisions. With a wide array of criminal statutes in the hands of federal prosecutors, almost all forms of unethical conduct could in some way also violate a federal criminal statute.Part II of this article reviews the federal statutes most often used by federal prosecutors and provides some examples of recent reported cases in which the underlying illegal or unethical conduct involved alleged criminal activity. Part III offers some examples of recent reported state court cases in which criminal acts involving land use permitting or decision-making were the underlying cause of the subsequent or reported court action. Part IV concludes with the caveat that municipal attorneys and public officials can no longer simply view ethical issues in land use as a local or state civil matter, and those who work in and advise those in the public sector should be mindful of the tools at the disposal of federal investigators and prosecutors

It\u27s a \u27Criming Shame\u27: Moving from Land Use Ethics to Criminalization of Behavior Leading to Permits and Other Zoning Related Acts

In the past, land use ethics inquiries predominately involved conflicts of interest or an official holding public office while engaging in a previously held business or law practice. Now, prosecutors are looking at the underlying criminality of the unethical acts carried out in the context of land use decisions. With a wide array of criminal statutes in the hands of federal prosecutors, almost all forms of unethical conduct could in some way also violate a federal criminal statute.Part II of this article reviews the federal statutes most often used by federal prosecutors and provides some examples of recent reported cases in which the underlying illegal or unethical conduct involved alleged criminal activity. Part III offers some examples of recent reported state court cases in which criminal acts involving land use permitting or decision-making were the underlying cause of the subsequent or reported court action. Part IV concludes with the caveat that municipal attorneys and public officials can no longer simply view ethical issues in land use as a local or state civil matter, and those who work in and advise those in the public sector should be mindful of the tools at the disposal of federal investigators and prosecutors

Identities between Appell's and hypergeometric functions

Univariate specializations of Appell's hypergeometric functions F1, F2, F3, F4 satisfy ordinary Fuchsian equations of order at most 4. In special cases, these differential equations are of order 2, and could be simple (pullback) transformations of Euler's differential equation for the Gauss hypergeometric function. The paper classifies these cases, and presents corresponding relations between univariate specializations of Appell's functions and univariate hypergeometric functions. The computational aspect and interesting identities are discussed.Comment: 30 pages; A few wrong evaluations of the published version are rectified (see arXiv:0906.1861

Densities of short uniform random walks

We study the densities of uniform random walks in the plane. A special focus is on the case of short walks with three or four steps and less completely those with five steps. As one of the main results, we obtain a hypergeometric representation of the density for four steps, which complements the classical elliptic representation in the case of three steps. It appears unrealistic to expect similar results for more than five steps. New results are also presented concerning the moments of uniform random walks and, in particular, their derivatives. Relations with Mahler measures are discussed.Comment: 32 pages, 9 figure

Period- and mirror-maps for the quartic K3

We study in detail mirror symmetry for the quartic K3 surface in P3 and the mirror family obtained by the orbifold construction. As explained by Aspinwall and Morrison, mirror symmetry for K3 surfaces can be entirely described in terms of Hodge structures. (1) We give an explicit computation of the Hodge structures and period maps for these families of K3 surfaces. (2) We identify a mirror map, i.e. an isomorphism between the complex and symplectic deformation parameters, and explicit isomorphisms between the Hodge structures at these points. (3) We show compatibility of our mirror map with the one defined by Morrison near the point of maximal unipotent monodromy. Our results rely on earlier work by Narumiyah-Shiga, Dolgachev and Nagura-Sugiyama.Comment: 29 pages, 3 figure

Experimental mathematics on the magnetic susceptibility of the square lattice Ising model

We calculate very long low- and high-temperature series for the susceptibility $\chi$ of the square lattice Ising model as well as very long series for the five-particle contribution $\chi^{(5)}$ and six-particle contribution $\chi^{(6)}$. These calculations have been made possible by the use of highly optimized polynomial time modular algorithms and a total of more than 150000 CPU hours on computer clusters. For $\chi^{(5)}$ 10000 terms of the series are calculated {\it modulo} a single prime, and have been used to find the linear ODE satisfied by $\chi^{(5)}$ {\it modulo} a prime. A diff-Pad\'e analysis of 2000 terms series for $\chi^{(5)}$ and $\chi^{(6)}$ confirms to a very high degree of confidence previous conjectures about the location and strength of the singularities of the $n$-particle components of the susceptibility, up to a small set of ``additional'' singularities. We find the presence of singularities at $w=1/2$ for the linear ODE of $\chi^{(5)}$, and $w^2= 1/8$ for the ODE of $\chi^{(6)}$, which are {\it not} singularities of the ``physical'' $\chi^{(5)}$ and $\chi^{(6)},$ that is to say the series-solutions of the ODE's which are analytic at $w =0$. Furthermore, analysis of the long series for $\chi^{(5)}$ (and $\chi^{(6)}$) combined with the corresponding long series for the full susceptibility $\chi$ yields previously conjectured singularities in some $\chi^{(n)}$, $n \ge 7$. We also present a mechanism of resummation of the logarithmic singularities of the $\chi^{(n)}$ leading to the known power-law critical behaviour occurring in the full $\chi$, and perform a power spectrum analysis giving strong arguments in favor of the existence of a natural boundary for the full susceptibility $\chi$.Comment: 54 pages, 2 figure