Motions about a fixed point by hypergeometric functions: new non-complex analytical solutions and integration of the herpolhode

We study four problems in the dynamics of a body moving about a fixed point, providing a non-complex, analytical solution for all of them. For the first two, we will work on the motion first integrals. For the symmetrical heavy body, that is the Lagrange-Poisson case, we compute the second and third Euler angles in explicit and real forms by means of multiple hypergeometric functions (Lauricella, functions). Releasing the weight load but adding the complication of the asymmetry, by means of elliptic integrals of third kind, we provide the precession angle completing some previous treatments of the Euler-Poinsot case. Integrating then the relevant differential equation, we reach the finite polar equation of a special trajectory named the {\it herpolhode}. In the last problem we keep the symmetry of the first problem, but without the weight, and take into account a viscous dissipation. The approach of first integrals is no longer practicable in this situation and the Euler equations are faced directly leading to dumped goniometric functions obtained as particular occurrences of Bessel functions of order $-1/2$.Comment: This is a pre-print of an article published in Celestial Mechanics and Dynamical Astronomy. The final authenticated version is available online at: DOI: 10.1007/s10569-018-9837-

On computing some special values of hypergeometric functions

The theoretical computing of special values assumed by the hypergeometric functions has a high interest not only on its own, but also in sight of the remarkable implications to both pure Mathematics and Mathematical Physics. Accordingly, in this paper we continue the path of research started in two our previous papers appeared on [30] and [31] providing some contribution to such functions computability inside and outside their disk of convergence. This is accomplished through two different approaches. The first is to provide some new results in the spirit of theorem 3.1 of 31] obtaining formulae for multivariable hypergeometric functions by generalizing a well known Kummer's identity to the hypergeometric functions of two or more variable like those of Appell and Lauricella.Comment: 21 pages. Sixth version. To appear in Journal of Mathematical Analysis and Application

International development aid and the politics of scale

Much international development assistance has been delivered in the form of statebuilding interventions over the past 20 years, especially in post-conflict or fragile states. The apparent failure of many international statebuilding interventions has prompted a ‘political economy’ turn in development studies. This article critically assesses the key approaches that have emerged to address the interrelations between interveners and recipients, and advances an approach that places the politics of scale at the core of the conflicts shaping the outcomes of international intervention. Different scales privilege different interests, unevenly allocating power, resources and political opportunity structures. Interveners and recipients thus pursue scalar strategies and establish socio-political alliances that reinforce their power and marginalise rivals. This approach is harnessed towards examining the uneven results of the Aceh Government Transformation Programme, financed by the World Bank-managed Multi Donor Trust Fund following the 2005 peace agreement and implemented by the UNDP and the Aceh provincial government

Legendre hyperelliptic integrals, π new formulae and Lauricella functions through the elliptic singular moduli

This paper, pursuing the work started by tha authots, holds six new formulae for π through ratios of first kind complete elliptic integrals and some values of hypergeometric functions of three or four variables of Lauricella type. This will be accomplished by reducing some hyperelliptic integrals to elliptic through the methods Legendre taught in his treatise. The complete elliptic integrals of first kind have complementary moduli: as a consequence we can find their ratio through the Lauricella functions. In such a way we succeed in obtaining, through the theory of elliptic singular moduli, some particular values of Lauricella's themselves

Statutory Redundancy: Why Congress Should Overhaul the Endangered Species Act to Exclude Critical Habitat Designation

There is much debate concerning the enforcement of the critical habitat designation provisions of the Endangered Species Act. Most scholars argue that the Secretary of the Interior abuses the “not prudent” and “not determinable” exceptions to avoid making such designations when endangered or threatened species are listed. The Endangered Species Act of 1973 was enacted to achieve the dual goals of species conservation and species recovery, achieved primarily through ecosystem conservation. Section 7 of the Endangered Species Act requires all federal agencies to consult with the Secretary of the Interior to evaluate the consequences of proposed federal actions to ensure they neither jeopardize the existence of the endangered species nor destroy or modify a designated critical habitat. Because these standards overlap, the critical habitat designation provision should be excluded from the Endangered Species Act, since it serves as nothing more than a weapon for environmentalists to block land development. It forces the Department of the Interior to spend its time defending lawsuits, rather than listing more species and thoroughly analyzing federal actions that may jeopardize vital ecosystems