Kink stability, propagation, and length-scale competition in the periodically modulated sine-gordon equation

We have examined the dynamical behavior of the kink solutions of the one-dimensional sine-Gordon equation in the presence of a spatially periodic parametric perturbation. Our study clarifies and extends the currently available knowledge on this and related nonlinear problems in four directions. First, we present the results of a numerical simulation program that are not compatible with the existence of a radiative threshold predicted by earlier calculations. Second, we carry out a perturbative calculation that helps interpret those previous predictions, enabling us to understand in depth our numerical results. Third, we apply the collective coordinate formalism to this system and demonstrate numerically that it reproduces accurately the observed kink dynamics. Fourth, we report on the occurrence of length-scale competition in this system and show how it can be understood by means of linear stability analysis. Finally, we conclude by summarizing the general physical framework that arises from our study.

Comment Letter on Rule 14a-8(I)(10), Securities & Exchange Commission, June 18, 2015

This letter focuses on SEC interpretations of Rule 14a-8(i)(10). The provision allows issuers to exclude shareholder proposals that have been “substantially implemented.” This has traditionally been used to allow for the exclusion of proposals rendered “moot” by the company’s actions. Companies, however, need not implement the shareholder proposal “exactly.” As a result, the staff is often asked to determine whether changes made by the company are substantial. The comment letter discusses positions taken by the staff where the company adopts a proposal asking that shareholders with a specified percentage of shares have the right to call a special meeting but limits eligible shares to those held for a specified period of time.

Comment on Rule 14a-8(i)(9), Securities and Exchange Commission, June 30, 2015

The Securities and Exchange Commission has been analyzing its interpretation under Subsection (i)(9) of Rule 14a-8. This provision allows for the exclusion of shareholder proposals that conflict with those submitted by management. The staff has been examining its interpretation since instructed to do so by the chair of the SEC following a no action appeal in a case involving Whole Foods. A number of letters and memos submitted in connection with the review have analyzed the issue. At least one asserted that any change in interpretation required the Commission to go through the process of notice and comment. This letter asserts that notice and comment is not required, relying extensively on Perez v. Mortgage Bankers Association.

The minimal overlap rule: restrictions on mergers for creditors’ consensus

As it is known, there is no rule satisfying additivity in the complete domain of bankruptcy problems. This paper proposes a notion of partial additivity in this context, to be called μ-additivity. We find out that this property, together with two quite compelling axioms, equal treatment of equals and continuity, identify the minimal overlap rule, introduced by O’Neill (Math. Soc. Sci. 2:345–371, 1982).

Rule, 1830 March 31

One-leaf containing handwritten instructions about drafting a paper.

Pennsylvanian invertebrates of the Mazon Creek Area, Illinois: the morphology and affinities of Tullimonstrum / Ralph Gordon Johnson -- and Eugene S. Richardson, Jr. --

v.12:no.8(1969)

Rule of selection of delinquents, 1801 April 8

Four-page handwritten draft of a public statement to the students from the Harvard Faculty related to the amendment of College Law XVIII, Chapter IV concerning the suppression of concealed disorders. The document appears to be in the hand of President Joseph Willard.

Rule of three : manuscript, 1774

An arithmetic copybook, with accounting problems concerning commercial transactions. There is a reference to the Boston Tea Party in problem no. 68.

John Gordon notebook, 1793-1795

A notebook containing handwriting exercises written by John Gordon at Atkinson Academy, New Hamsphire.

The European Union’s Rule of Law Promotion in its Neighbourhood: A Structural Foreign Policy Analysis. EU Diplomacy Paper 04/2013

The promotion of the rule of law has become an important dimension of the European Union’s relations towards its neighbourhood. The rule of law is, however, a complex and multifaceted notion and the EU’s rule of law promotion policy has often been criticised for being either inefficient or self-interested. This collection of short papers offers an analysis of various case studies using the analytical framework of structural foreign policy (SFP) developed by Stephan Keukeleire. It aims to promote an original analytical perspective on the EU’s foreign policy but also to critically test and further develop the SFP analytical framework. The contributions of this collection consist of the shortened version of students’ Master’s theses written at the College of Europe during the academic year 2011-2012 in the framework of the course “The EU as a Foreign Policy Actor” taught by Stephan Keukeleire, Chairholder of the TOTAL Chair of EU Foreign Policy in the Department of EU International Relations and Diplomacy Studies.

Rule of law or rule of thumb? A new Copenhagen mechanism for the EU. CEPS Policy Brief No. 303, 20 November 2013

This Policy Brief synthesises the main research findings and policy recommendations presented in the CEPS e-book entitled The Triangular Relationship between Fundamental Rights, Democracy and Rule of Law: Towards an EU Copenhagen Mechanism” (http://www.ceps.eu/book/triangular-relationship-between-fundamental-righ...). The authors examine the ways in which the European Union could strengthen and develop its competences in the assessment of member states’ fundamental rights, democracy and rule of law commitments. They argue that a strong political impetus is needed at Union level in order to set up a new supervisory “Copenhagen Mechanism” that would effectively and periodically evaluate member states’ compliance with democratic rule of law with fundamental rights on the basis of independent academic expertise, and by ensuring a high level of democratic accountability and judicial oversight at European levels. The Policy Brief also aims at summarising CEPS’ contribution to the upcoming Conference “Assises de la Justice: Shaping Justice Policies in Europe for the Years to Come” organised by the European Commission in Brussels on 21-22 November 2013.