The mass of unimodular lattices

The purpose of this paper is to show how to obtain the mass of a unimodular lattice from the point of view of the Bruhat-Tits theory. This is achieved by relating the local stabilizer of the lattice to a maximal parahoric subgroup of the special orthogonal group, and appealing to an explicit mass formula for parahoric subgroups developed by Gan, Hanke and Yu. Of course, the exact mass formula for positive defined unimodular lattices is well-known. Moreover, the exact formula for lattices of signature (1,n) (which give rise to hyperbolic orbifolds) was obtained by Ratcliffe and Tschantz, starting from the fundamental work of Siegel. Our approach works uniformly for the lattices of arbitrary signature (r,s) and hopefully gives a more conceptual way of deriving the above known results.Comment: 15 pages, to appear in J. Number Theor

Parallel containers: a tool for applying parallel computing applications on clusters

Parallel and cluster computing remain somewhat difficult to apply quickly for many applications domains. Recent developments in computer libraries such as the Standard Template Library of the C++ language and the Message Passing Package associated with the Python Language provide a way to implement very high level parallel containers in support of application programming. A parallel container is an implementation of a data structure such as a list, or vector, or set, that has associated with it the necessary methods and state knowledge to distribute the contents of the structure across the memory of a parallel computer or a computer cluster. A key idea is that of the parallel iterator which allows a single high level statement written by the applications programmer to invoke a parallel operation across the entire data structure’s contents while avoiding the need for knowledge of how the distribution is actually carried out. This transparency approach means that optimised parallel algorithms can be separated from the applications domain code, maximising reuse of the parallel computing infrastructure and libraries. This paper describes our initial experiments with C++ parallel containers

Exponential decay of dispersion managed solitons for vanishing average dispersion

We show that any $L^2$ solution of the Gabitov-Turitsyn equation describing dispersion managed solitons decay exponentially in space and frequency domains. This confirms in the affirmative Lushnikov's conjecture of exponential decay of dispersion managed solitons.Comment: 15 pages, 1 figur

Electron acceleration by cascading reconnection in the solar corona I Magnetic gradient and curvature effects

Aims: We investigate the electron acceleration in convective electric fields of cascading magnetic reconnection in a flaring solar corona and show the resulting hard X-ray (HXR) radiation spectra caused by Bremsstrahlung for the coronal source. Methods: We perform test particle calculation of electron motions in the framework of a guiding center approximation. The electromagnetic fields and their derivatives along electron trajectories are obtained by linearly interpolating the results of high-resolution adaptive mesh refinement (AMR) MHD simulations of cascading magnetic reconnection. Hard X-ray (HXR) spectra are calculated using an optically thin Bremsstrahlung model. Results: Magnetic gradients and curvatures in cascading reconnection current sheet accelerate electrons: trapped in magnetic islands, precipitating to the chromosphere and ejected into the interplanetary space. The final location of an electron is determined by its initial position, pitch angle and velocity. These initial conditions also influence electron acceleration efficiency. Most of electrons have enhanced perpendicular energy. Trapped electrons are considered to cause the observed bright spots along coronal mass ejection CME-trailing current sheets as well as the flare loop-top HXR emissions.Comment: submitted to A&

Quo Vadis: An Integrated Direction for Catholic Media Technology Engagement

Over the years, the Catholic Church has explored issues of media technology and how it relates to education. At the same time, a number of profound, modern Catholic thinkers have wrestled with the nature of media technology and how it affects the human condition. These two threads have been independent of each other. An effective conceptual understanding of the role and meaning of media technology in Catholic education requires us to weave these two threads together to craft an integrated and coherent synthesis. The question I raise is: in a culture that promulgates the digital lifestyle as the standard and norm, is there a proper way for Catholics to engage media technology? And because education forms the foundation with which we transmit our values, heritage, and worldview, we ask the attendant question of how Catholics should integrate media technology in their education? Directed at Catholics, and particularly educators, administrators, policymakers, parents, communicators, as well as creators and recipients of media technologies, this dissertation proposes seven foundational policies or keys for effective media technology engagement. These keys are in turn grounded on fundamental precepts found in scripture, magisterial documents on social communications or education, as well as discerningly mined from a wide range of other sources that offer wisdom about education and/or media technology. A prototype for an instructional technology lesson that is naturally derived from these keys is the logical next step, and is proffered in anticipation that it may be adapted to various lesson plans, home schooling activities, as well as courses in other subject areas that have with them a goal to integrate media technologies. We are at a point in multimedia learning and educational technology where practical explorations can greatly help chart the direction, type, and methods of instruction. This exploration set at the intersection of Catholic education and media technology is a first step on the journey toward empowering Catholic institutions, parents, and educators to engage media technologies in a practical way while at the same time upholding and actively living the Catholic identity and philosophy of life (Ong, 1990, p. 347)