Numerical computation of real or complex elliptic integrals

Algorithms for numerical computation of symmetric elliptic integrals of all three kinds are improved in several ways and extended to complex values of the variables (with some restrictions in the case of the integral of the third kind). Numerical check values, consistency checks, and relations to Legendre's integrals and Bulirsch's integrals are included

Spatiotemporal correlations of earthquakes in the continuum limit of the one-dimensional Burridge-Knopoff model

Spatiotemporal correlations of the one-dimensional spring-block (Burridge-Knopoff) model of earthquakes, either with or without the viscosity term, are studied by means of numerical computer simulations. The continuum limit of the model is examined by systematically investigating the model properties with varying the block-size parameter a toward a\to 0. The Kelvin viscosity term is introduced so that the model dynamics possesses a sensible continuum limit. In the presence of the viscosity term, many of the properties of the original discrete BK model are kept qualitatively unchanged even in the continuum limit, although the size of minimum earthquake gets smaller as a gets smaller. One notable exception is the existence/non-existence of the doughnut-like quiescence prior to the mainshock. Although large events of the original discrete BK model accompany seismic acceleration together with a doughnut-like quiescence just before the mainshock, the spatial range of the doughnut-like quiescence becomes narrower as a gets smaller, and in the continuum limit, the doughnut-like quiescence might vanish altogether. The doughnut-like quiescence observed in the discrete BK model is then a phenomenon closely related to the short-length cut-off scale of the model

Infinitesimal Variations of Hodge Structure at Infinity

By analyzing the local and infinitesimal behavior of degenerating polarized variations of Hodge structure the notion of infinitesimal variation of Hodge structure at infinity is introduced. It is shown that all such structures can be integrated to polarized variations of Hodge structure and that, conversely, all are limits of infinitesimal variations of Hodge structure (IVHS) at finite points. As an illustration of the rich information encoded in this new structure, some instances of the maximal dimension problem for this type of infinitesimal variation are presented and contrasted with the "classical" case of IVHS at finite points

Series expansions for the third incomplete elliptic integral via partial fraction decompositions

We find convergent double series expansions for Legendre's third incomplete elliptic integral valid in overlapping subdomains of the unit square. Truncated expansions provide asymptotic approximations in the neighbourhood of the logarithmic singularity $(1,1)$ if one of the variables approaches this point faster than the other. Each approximation is accompanied by an error bound. For a curve with an arbitrary slope at $(1,1)$ our expansions can be rearranged into asymptotic expansions depending on a point on the curve. For reader's convenience we give some numeric examples and explicit expressions for low-order approximations.Comment: The paper has been substantially updated (hopefully improved) and divided in two parts. This part is about third incomplete elliptic integral. 10 page

Critical race theory in a swedish context

Race has been a term avoided in the Swedish debates, while at the same time, protections with respect to unlawful discrimination on the basis of race or ethnic origins have not been vigilantly upheld by the courts. This paper looks at the treatment of race by the Swedish legislature, as well as the treatment by the courts, specifically the Labour Court, with respect to claims of unlawful discrimination in employment on the basis of ethnic origins, against the background of Critical Race Theory. The disparities between the intent of the legislature and the outcome of the cases brought to the Swedish courts can be in least in part explained through the lens of Critical Race Theory, particularly with respect to the liberal approach taken by the courts when applying the law

Community Use of the Sacred Heart School

In October 2005, the Edmonton Social Planning Council (ESPC) released a report entitled The Sacred Heart Collective: An Effective Use of a Closed School? which evaluated the unique initiative implemented by the Sacred Heart Collective (the Collective), a group of seven non-profits located in the former Sacred Heart School. In agreement with Edmonton Catholic Schools, the Collective sought to provide free access to meeting and recreational space located in the school to other non-profits and local community groups.The following is a follow-up to the October 2005 report, and details usage of the Sacred Heart facilities for a six month period, from August 2005 to end of January 2006

Myopic Models of Population Dynamics on Infinite Networks

Reaction-diffusion equations are treated on infinite networks using semigroup methods. To blend high fidelity local analysis with coarse remote modeling, initial data and solutions come from a uniformly closed algebra generated by functions which are flat at infinity. The algebra is associated with a compactification of the network which facilitates the description of spatial asymptotics. Diffusive effects disappear at infinity, greatly simplifying the remote dynamics. Accelerated diffusion models with conventional eigenfunctions expansions are constructed to provide opportunities for finite dimensional approximation.Comment: 36 pages. arXiv admin note: text overlap with arXiv:1109.313