Multiscale expansion and integrability properties of the lattice potential KdV equation

We apply the discrete multiscale expansion to the Lax pair and to the first few symmetries of the lattice potential Korteweg-de Vries equation. From these calculations we show that, like the lowest order secularity conditions give a nonlinear Schroedinger equation, the Lax pair gives at the same order the Zakharov and Shabat spectral problem and the symmetries the hierarchy of point and generalized symmetries of the nonlinear Schroedinger equation.Comment: 10 pages, contribution to the proceedings of the NEEDS 2007 Conferenc

Expanding perfect fluid generalizations of the C-metric

We reexamine Petrov type D gravitational fields generated by a perfect fluid with spatially homogeneous energy density and in which the flow lines form a timelike non-shearing and non-rotating congruence. It is shown that the anisotropic such spacetimes, which comprise the vacuum C-metric as a limit case, can have \emph{non-zero} expansion, contrary to the conclusion in the original investigation by Barnes (Gen. Rel. Grav. 4, 105 (1973)). This class consists of cosmological models with generically one and at most two Killing vectors. We construct their line element and discuss some important properties. The methods used in this investigation incite to deduce testable criteria regarding shearfree normality and staticity op Petrov type $D$ spacetimes in general, which we add in an appendix.Comment: 16 pages, extended and amended versio

A very low temperature STM for the local spectroscopy of mesoscopic structures

We present the design and operation of a very-low temperature Scanning Tunneling Microscope (STM) working at $60 mK$ in a dilution refrigerator. The STM features both atomic resolution and micron-sized scanning range at low temperature. This work is the first experimental realization of a local spectroscopy of mesoscopic structures at very low temperature. We present high-resolution current-voltage characteristics of tunnel contacts and the deduced local density of states of hybrid Superconductor-Normal metal systems.Comment: 5 pages, 5 figures, slightly corrected versio

They Were Meant for Each Other: Professor Edward Cooper and the Rules Enabling Act

This introduction to the essays in this Symposium illuminates Professor Ed Cooper\u27s years as Reporter to the Civil Rules Committee by first briefly describing those who preceded him in the position and his own background. We then describe some of Ed Cooper\u27s many contributions to the Civil Rules Committee, the Federal Rules, rulemaking, and civil procedure by examining the present state of the Rules Committees\u27 work under the Rules Enabling Act. We conclude that after almost eighty years of experience under that Act, it is working well in large part because of the sound leadership provided by Ed Cooper over his twenty years as Reporter. It was during these years that the Committee developed an approach to rulemaking that was at once transparent and empirical, with multiple opportunities for participation by members of the public, the bench, the academy, and the bar; with many informal opportunities for consultation with members of Congress and the Executive Branch; and with an understanding by the Committee of its role in relation to the courts, Congress, and the Executive. Two episodes of recent rulemaking and related activity are described as examples of how well the Rules Enabling Act is working, in large part because of the very flexibility and discretion the Act has provided since 1934. One of those episodes occurred when Judge Anthony Scirica chaired the Standing Committee and then- Judge David Levi chaired the Civil Rules Committee. The other occurred when Judge Lee Rosenthal and Judge Mark Kravitz were the chairs of the Standing and Civil Rules Committees, respectively. Both episodes provide a basis for optimism about the future. And they make clear Ed Cooper\u27s continued steady role in supporting and cultivating the robust good health of the rulemaking process and the institutional values it protects

Programming languages in economics: a comparison among Fortran77, C++, and Java

The main objective of this paper was to compare the computer programming languages Fortran77, C++, and Java under four aspects: runtime efficiency, readability, ease of learning, and reliability. For this comparison, we revised the specialized literature on programming languages and used pieces of codes of these three programming languages. The purpose of this comparison was to provide some objective information for economists interested in learning one or more of these languages.Programming language, Runtime efficiency, Readability, Reliability, Teaching/Communication/Extension/Profession,