Proof of a generalized Geroch conjecture for the hyperbolic Ernst equation

We enunciate and prove here a generalization of Geroch's famous conjecture concerning analytic solutions of the elliptic Ernst equation. Our generalization is stated for solutions of the hyperbolic Ernst equation that are not necessarily analytic, although it can be formulated also for solutions of the elliptic Ernst equation that are nowhere axis-accessible.Comment: 75 pages (plus optional table of contents). Sign errors in elliptic case equations (1A.13), (1A.15) and (1A.25) are corrected. Not relevant to proof contained in pape

Avoiding initiation of repair in L2 conversations-for-learning

Using audio-recorded data from second language (L2) English conversations-for-learning between an L2 user of English and a first language (L1) user of English (the researcher), this study analyzes cases in which the L1 user avoids initiation of repair. In each case, the L2 user appears to have misunderstood something said by the L1 user. Instead of initiating repair in next turn on the L2 user’s talk, or in third position on his own talk, the L1 user goes along, at least briefly, with the direction set by the L2 user. Often, the L1 user, sooner or later, returns to the misunderstood talk. Avoidance of repair initiation is one way in which the L1 user contributes to the construction of the L2 user as interactionally competent to participate in conversations-for-learning

A New Approach to Yakubovich's s-Lemma

Subject to regularity assumptions, Yakubovich's s-Lemma characterizes the quadratic functions f(x) defined on a finite-dimensional space which are copositive with a given quadratic function q(x). This result has far-reaching consequences in optimization and control theory. Several approaches to its proof are known, some of which generalize to Hilbert spaces. In this paper we explore a new geometric approach to the proof of this classical result

The S-Procedure via dual cone calculus

Given a quadratic function h that satisfies a Slater condition, Yakubovich’s S-Procedure (or S-Lemma) gives a characterization of all other quadratic functions that are copositive with $h$ in a form that is amenable to numerical computations. In this paper we present a deep-rooted connection between the S-Procedure and the dual cone calculus formula $(K_{1} \cap K_{2})^{*} = K^{*}_{1} + K^{*}_{2}$, which holds for closed convex cones in $R^{2}$. To establish the link with the S-Procedure, we generalize the dual cone calculus formula to a situation where $K_{1}$ is nonclosed, nonconvex and nonconic but exhibits sufficient mathematical resemblance to a closed convex one. As a result, we obtain a new proof of the S-Lemma and an extension to Hilbert space kernels

The Nesterov-Todd Direction and its Relation to Weighted Analytic Centers

The subject of this report concerns differential-geometric properties of the Nesterov-Todd search direction for linear optimization over symmetric cones. In particular, we investigate the rescaled asymptotics of the associated flow near the central path. Our results imply that the Nesterov-Todd direction arises as the solution of a Newton system defined in terms of a certain transformation of the primal-dual feasible domain. This transformation has especially appealing properties which generalize the notion of weighted analytic centers for linear programming

Sharing is caring vs. stealing is wrong: a moral argument for limiting copyright protection

Copyright is at the centre of both popular and academic debate. That emotions are running high is hardly surprising – copyright influences who contributes what to culture, how culture is used, and even the kind of persons we are and come to be. Consequentialist, Lockean, and personality interest accounts are generally advanced in the literature to morally justify copyright law. I argue that these approaches fail to ground extensive authorial rights in intellectual creations and that only a small subset of the rights accorded by copyright law is justified. The pared-down version of copyright that I defend consists of the right to attribution, the right to have one’s non-endorsement of modifications or uses of one’s work explicitly noted, and the right to a share of the profit resulting from the commercial uses of one’s work. I also cursorily explore whether contribution to another person’s work gives rise to moral interests