5,139 research outputs found
Discrete Morse theory for the collapsibility of supremum sections
The Dushnik-Miller dimension of a poset is the minimal number of
linear extensions of such that is the
intersection of . Supremum sections are simplicial
complexes introduced by Scarf and are linked to the Dushnik-Miller as follows:
the inclusion poset of a simplicial complex is of Dushnik-Miller dimension at
most if and only if it is included in a supremum section coming from a
representation of dimension . Collapsibility is a topoligical property of
simplicial complexes which has been introduced by Whitehead and which resembles
to shellability. While Ossona de Mendez proved in that a particular type of
supremum sections are shellable, we show in this article that supremum sections
are in general collapsible thanks to the discrete Morse theory developped by
Forman
Long String Scattering in c = 1 String Theory
We study the scattering of long strings in c = 1 string theory, both in the
worldsheet description and in the non-singlet sector of the dual matrix quantum
mechanics. From the worldsheet perspective, the scattering amplitudes of long
strings are obtained from a decoupling limit of open strings amplitudes on FZZT
branes, which we compute by integrating Virasoro conformal blocks along with
structure constants of boundary Liouville theory. In particular, we study the
tree level amplitudes of (1) a long string decaying by emitting a closed
string, and (2) the scattering of a pair of long strings. We show that they are
indeed well defined as limits of open string amplitudes, and that our results
are in striking numerical agreement with computations in the adjoint and
bi-adjoint sectors of the dual matrix model (based on proposals of Maldacena
and solutions due to Fidkowski), thereby providing strong evidence of the
duality.Comment: 42 pages, 18 figure
The c=1 String Theory S-Matrix Revisited
We revisit the perturbative S-matrix of c=1 string theory from the worldsheet
perspective. We clarify the origin of the leg pole factors, the non-analyticity
of the string amplitudes, and the validity as well as limitations of earlier
computations based on resonance momenta. We compute the tree level 4-point
amplitude and the genus one 2-point reflection amplitude by numerically
integrating Virasoro conformal blocks with DOZZ structure constants on the
sphere and on the torus, with sufficiently generic complex Liouville momenta,
and find agreement with known answers from the c=1 matrix model.Comment: 32 pages, 7 figures; footnote and references added, typos correcte
Gezondheidsrechtelijke reacties op psychische problemen: dwangopneming en bescherming van onbekwamen
Les relations canado-américaines : Nationalisme et continentalisme
This paper's objective is to bring forth some elements which confirm the following hypothesis : Canada is consigned to continentalism, namely to economic and cultural integration with the United States though this fact is shrouded in a Canadian nationalism of sorts. The continentalist mentality is rooted in the history of British North America, inhabited mostly by refugees from America who have remained inherently "Yankees" in spite of their anti-americanism. The Confederation itself is based on a sort of complicity with the United States. More recently there were talks of a "North American nationality", and continentalism both cultural and economic has come to be seen as a 'force of nature" which the governments, at the most, put into a chanelling process. Still, it is possible for Canadian nationalism to exist provided it does not go beyond the threshold whence it would run headlong into the continental mentality. Canada has defined itself through an international or non-national perspective far too long for today's nationalism not to remain weak and poorly established. But the Americans whose "manifest destiny" has succeeded in spreading over Canada without even their having tried to hoist their flag there find it to their advantage to maintain some form of Canadian sovereignty. Canada as a "friendly nation" can be of use to Washington. That is why there are almost as many advocates for Canada's independence in the United States as there are north of the border. Canadian nationalism can thus further the interests of some Canadian elites without seriously prejudicing continental integration which can very well afford not to be set up into formalized structures
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