1,579 research outputs found
Late-time expansion in the semiclassical theory of the Hawking radiation
We give a detailed treatment of the back-reaction effects on the Hawking
spectrum in the late-time expansion within the semiclassical approach to the
Hawking radiation. We find that the boundary value problem defining the action
of the modes which are regular at the horizon admits in general the presence of
caustics. We show that for radii less that a certain critical value no
caustic occurs for all values of the wave number and time and we give a
rigorous lower bound on such a critical value. We solve the exact system of non
linear equations defining the motion, by an iterative procedure rigorously
convergent at late times. The first two terms of such an expansion give the
correction to the Hawking spectrum.Comment: 17 pages, 1 figure, LaTex, typos corrected, one intermediate formula
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Toda Fields on Riemann Surfaces: remarks on the Miura transformation
We point out that the Miura transformation is related to a holomorphic
foliation in a relative flag manifold over a Riemann Surface. Certain
differential operators corresponding to a free field description of
--algebras are thus interpreted as partial connections associated to the
foliation.Comment: AmsLatex 1.1, 10 page
Large Chiral Diffeomorphisms on Riemann Surfaces and W-algebras
The diffeomorphism action lifted on truncated (chiral) Taylor expansion of a
complex scalar field over a Riemann surface is presented in the paper under the
name of large diffeomorphisms. After an heuristic approach, we show how a
linear truncation in the Taylor expansion can generate an algebra of symmetry
characterized by some structure functions. Such a linear truncation is
explicitly realized by introducing the notion of Forsyth frame over the Riemann
surface with the help of a conformally covariant algebraic differential
equation. The large chiral diffeomorphism action is then implemented through a
B.R.S. formulation (for a given order of truncation) leading to a more
algebraic set up. In this context the ghost fields behave as holomorphically
covariant jets. Subsequently, the link with the so called W-algebras is made
explicit once the ghost parameters are turned from jets into tensorial ghost
ones. We give a general solution with the help of the structure functions
pertaining to all the possible truncations lower or equal to the given order.
This provides another contribution to the relationship between KdV flows and
W-diffeomorphimsComment: LaTeX file, 31 pages, no figure. Version to appear in J. Math. Phys.
Work partly supported by Region PACA and INF
On a problem of A. Weil
A topological invariant of the geodesic laminations on a modular surface is
constructed. The invariant has a continuous part (the tail of a continued
fraction) and a combinatorial part (the singularity data). It is shown, that
the invariant is complete, i.e. the geodesic lamination can be recovered from
the invariant. The continuous part of the invariant has geometric meaning of a
slope of lamination on the surface.Comment: to appear Beitr\"age zur Algebra und Geometri
A Manifesto for Attuned Teaching
Our focus in this chapter is how we can adopt an attuned teaching approach and why this would be supportive of all children and young people. We explore its significance for children who may have experienced trauma through loss of, or separation from, birth family or other significant life experience causing vulnerability. We have chosen to write as if we are in a shared space with you, perhaps you can imagine a conversation in the staffroom. We are hoping our experiences and knowledge help you to reflect and provide you with ideas of how to develop your professional practice and to gain confidence
The Complex Langevin method: When can it be trusted?
We analyze to what extent the complex Langevin method, which is in principle
capable of solving the so-called sign problems, can be considered as reliable.
We give a formal derivation of the correctness and then point out various
mathematical loopholes. The detailed study of some simple examples leads to
practical suggestions about the application of the method.Comment: 14 pages, including several eps figures and tables; clarification and
minor corrections added, to appear in PR
From the 'cinematic' to the 'anime-ic': Issues of movement in anime
This is the author's accepted manuscript. The final published article is available from the link below.This article explores the way that movement is formally depicted in anime. Drawing on Thomas Lamarre's concepts of the `cinematic' and the `anime-ic', the article interrogates further the differences in movement and action in anime from traditional filmic form. While often considered in terms of `flatness', anime offers spectacle, character development and, ironically, depth through the very form of movement put to use in such texts.The article questions whether the modes of address at work in anime are unique to this form of animation.Taking into account how the terms `cinematic' and `anime-ic' can be understood (and by extension the cinematic and animatic apparatus), the article also begins to explore how viewers might identify with such images
The Digital Flynn Effect: Complexity of Posts on Social Media Increases over Time
Parents and teachers often express concern about the extensive use of social
media by youngsters. Some of them see emoticons, undecipherable initialisms and
loose grammar typical for social media as evidence of language degradation. In
this paper, we use a simple measure of text complexity to investigate how the
complexity of public posts on a popular social networking site changes over
time. We analyze a unique dataset that contains texts posted by 942, 336 users
from a large European city across nine years. We show that the chosen
complexity measure is correlated with the academic performance of users: users
from high-performing schools produce more complex texts than users from
low-performing schools. We also find that complexity of posts increases with
age. Finally, we demonstrate that overall language complexity of posts on the
social networking site is constantly increasing. We call this phenomenon the
digital Flynn effect. Our results may suggest that the worries about language
degradation are not warranted
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