3,428 research outputs found
Moduli of mathematical instanton vector bundles with odd c_2 on projective space
The problem of irreducibility of the moduli space I_n of rank-2 mathematical
instanton vector bundles with arbitrary positive second Chern class n on the
projective 3-space is considered. The irreducibility of I_n was known for small
values of n: Barth 1977 (n=1), Hartshorne 1978 (n=2), Ellingsrud and Stromme
1981 (n=3), Barth 1981 (n=4), Coanda, Tikhomirov and Trautmann 2003 (n=5). In
this paper we prove the irreducibility of I_n for an arbitrary odd n.Comment: 62 page
The pre-WDVV ring of physics and its topology
We show how a simplicial complex arising from the WDVV
(Witten-Dijkgraaf-Verlinde-Verlinde) equations of string theory is the
Whitehouse complex. Using discrete Morse theory, we give an elementary proof
that the Whitehouse complex is homotopy equivalent to a wedge of
spheres of dimension . We also verify the Cohen-Macaulay
property. Additionally, recurrences are given for the face enumeration of the
complex and the Hilbert series of the associated pre-WDVV ring.Comment: 13 pages, 4 figures, 2 table
Higher Loop Spin Field Correlators in D=4 Superstring Theory
We develop calculational tools to determine higher loop superstring
correlators involving massless fermionic and spin fields in four space time
dimensions. These correlation functions are basic ingredients for the
calculation of loop amplitudes involving both bosons and fermions in D=4
heterotic and superstring theories. To obtain the full amplitudes in Lorentz
covariant form the loop correlators of fermionic and spin fields have to be
expressed in terms of SO(1,3) tensors. This is one of the main achievements in
this work.Comment: 59 pages, 1 figure; v2: final version published in JHE
On the numerical evaluation of algebro-geometric solutions to integrable equations
Physically meaningful periodic solutions to certain integrable partial
differential equations are given in terms of multi-dimensional theta functions
associated to real Riemann surfaces. Typical analytical problems in the
numerical evaluation of these solutions are studied. In the case of
hyperelliptic surfaces efficient algorithms exist even for almost degenerate
surfaces. This allows the numerical study of solitonic limits. For general real
Riemann surfaces, the choice of a homology basis adapted to the
anti-holomorphic involution is important for a convenient formulation of the
solutions and smoothness conditions. Since existing algorithms for algebraic
curves produce a homology basis not related to automorphisms of the curve, we
study symplectic transformations to an adapted basis and give explicit formulae
for M-curves. As examples we discuss solutions of the Davey-Stewartson and the
multi-component nonlinear Schr\"odinger equations.Comment: 29 pages, 20 figure
On Bohr-Sommerfeld bases
This paper combines algebraic and Lagrangian geometry to construct a special
basis in every space of conformal blocks, the Bohr-Sommerfeld (BS) basis. We
use the method of [D. Borthwick, T. Paul and A. Uribe, Legendrian distributions
with applications to the non-vanishing of Poincar\'e series of large weight,
Invent. math, 122 (1995), 359-402, preprint hep-th/9406036], whereby every
vector of a BS basis is defined by some half-weighted Legendrian distribution
coming from a Bohr-Sommerfeld fibre of a real polarization of the underlying
symplectic manifold. The advantage of BS bases (compared to bases of theta
functions in [A. Tyurin, Quantization and ``theta functions'', Jussieu preprint
216 (Apr 1999), e-print math.AG/9904046, 32pp.]) is that we can use information
from the skillful analysis of the asymptotics of quantum states. This gives
that Bohr-Sommerfeld bases are unitary quasi-classically. Thus we can apply
these bases to compare the Hitchin connection with the KZ connection defined by
the monodromy of the Knizhnik-Zamolodchikov equation in combinatorial theory
(see, for example, [T. Kohno, Topological invariants for 3-manifolds using
representations of mapping class group I, Topology 31 (1992), 203-230; II,
Contemp. math 175} (1994), 193-217]).Comment: 43 pages, uses: latex2e with amsmath,amsfonts,theore
Invariants of pseudogroup actions: Homological methods and Finiteness theorem
We study the equivalence problem of submanifolds with respect to a transitive
pseudogroup action. The corresponding differential invariants are determined
via formal theory and lead to the notions of k-variants and k-covariants, even
in the case of non-integrable pseudogroup. Their calculation is based on the
cohomological machinery: We introduce a complex for covariants, define their
cohomology and prove the finiteness theorem. This implies the well-known
Lie-Tresse theorem about differential invariants. We also generalize this
theorem to the case of pseudogroup action on differential equations.Comment: v2: some remarks and references addee
The modified tetrahedron equation and its solutions
A large class of 3-dimensional integrable lattice spin models is constructed.
The starting point is an invertible canonical mapping operator in the space of
a triple Weyl algebra. This operator is derived postulating a current branching
principle together with a Baxter Z-invariance. The tetrahedron equation for
this operator follows without further calculations. If the Weyl parameter is
taken to be a root of unity, the mapping operator decomposes into a matrix
conjugation and a C-number functional mapping. The operator of the matrix
conjugation satisfies a modified tetrahedron equation (MTE) in which the
"rapidities" are solutions of a classical integrable Hirota-type equation. The
matrix elements of this operator can be represented in terms of the
Bazhanov-Baxter Fermat curve cyclic functions, or alternatively in terms of
Gauss functions. The paper summarizes several recent publications on the
subject.Comment: 24 pages, 6 figures using epic/eepic package, Contribution to the
proceedings of the 6th International Conference on CFTs and Integrable
Models, Chernogolovka, Spetember 2002, reference adde
Psychiatric rating scales in Urdu: a systematic review
<p>Abstract</p> <p>Background</p> <p>Researchers setting out to conduct research employing questionnaires in non-English speaking populations need instruments that have been validated in the indigenous languages. In this study we have tried to review the literature on the status of cross-cultural and/or criterion validity of all the questionnaires measuring psychiatric symptoms available in Urdu language.</p> <p>Methods</p> <p>A search of Medline, Embase, PsycINFO and <url>http://www.pakmedinet.com</url> was conducted using the search terms; Urdu psychiatric rating scale, and Urdu and Psychiatry. References of retrieved articles were searched. Only studies describing either cross-cultural or criterion validation of a questionnaire in Urdu measuring psychiatric symptoms were included.</p> <p>Results</p> <p>Thirty two studies describing validation of 19 questionnaires were identified. Six of these questionnaires were developed indigenously in Urdu while thirteen had been translated from English. Of the six indigenous questionnaires five had had their criterion validity examined. Of the thirteen translated questionnaires only four had had both their cross-cultural and criterion validity assessed.</p> <p>Conclusion</p> <p>There is a paucity of validated questionnaires assessing psychiatric symptoms in Urdu. The BSI, SRQ and AKUADS are the questionnaires that have been most thoroughly evaluated in Urdu.</p
Analytic representations with theta functions for systems on ℤ(d) and on .
yesAn analytic representation with Theta functions on a torus, for systems with variables in ℤ(d),
is considered. Another analytic representation with Theta functions on a strip, for systems with
positions in a circle S and momenta in Z, is also considered. The reproducing kernel formalism for these two systems is studied. Wigner and Weyl functions in this language, are also studied
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