6,444 research outputs found
Scaling functions in the square Ising model
We show and give the linear differential operators of
order q= n^2/4+n+7/8+(-1)^n/8, for the integrals which appear in the
two-point correlation scaling function of Ising model . The integrals are given in expansion around r= 0 in the basis of the formal
solutions of with transcendental combination
coefficients. We find that the expression is a solution
of the Painlev\'e VI equation in the scaling limit. Combinations of the
(analytic at ) solutions of sum to .
We show that the expression is the scaling limit of the
correlation function and . The differential Galois
groups of the factors occurring in the operators are
given.Comment: 26 page
General Existence Results for Reflected BSDE and BSDE
In this paper, we are concerned with the problem of existence of solutions
for generalized reflected backward stochastic differential equations (GRBSDEs
for short) and generalized backward stochastic differential equations (GBSDEs
for short) when the generator is continuous with general growth
with respect to the variable and stochastic quadratic growth with respect
to the variable . We deal with the case of a bounded terminal condition
and a bounded barrier as well as the case of unbounded ones. This is
done by using the notion of generalized BSDEs with two reflecting barriers
studied in \cite{EH}. The work is suggested by the interest the results might
have in finance, control and game theory.Comment: 23 page
Landau singularities and singularities of holonomic integrals of the Ising class
We consider families of multiple and simple integrals of the ``Ising class''
and the linear ordinary differential equations with polynomial coefficients
they are solutions of. We compare the full set of singularities given by the
roots of the head polynomial of these linear ODE's and the subset of
singularities occurring in the integrals, with the singularities obtained from
the Landau conditions. For these Ising class integrals, we show that the Landau
conditions can be worked out, either to give the singularities of the
corresponding linear differential equation or the singularities occurring in
the integral. The singular behavior of these integrals is obtained in the
self-dual variable , with , where is the
usual Ising model coupling constant. Switching to the variable , we show
that the singularities of the analytic continuation of series expansions of
these integrals actually break the Kramers-Wannier duality. We revisit the
singular behavior (J. Phys. A {\bf 38} (2005) 9439-9474) of the third
contribution to the magnetic susceptibility of Ising model at the
points and show that is not singular at the
corresponding points inside the unit circle , while its analytical
continuation in the variable is actually singular at the corresponding
points oustside the unit circle ().Comment: 34 pages, 1 figur
Acute Tubulo-interstitial Nephritis with Positive Anti-Neutrophil Cytoplasmic Antibodies
Introduction: Anti-neutrophil cytoplasmic antibody (ANCA) associated vasculitis involving the kidney usually comprises pauci-immune, necrotizing glomerulonephritis with crescents. Mononuclear tubulo-interstitial infiltrates are common in ANCA associated vasculitis, but these have usually been described in conjunction with glomerulitis. Acute tubulo-interstitial nephritis (ATIN) is a common cause of acute kidney injury that is most frequently induced by drugs or infections. Idiopathic ATIN has rarely been reported in association with the presence of a positive ANCA. These two entities seem to share a common immunological basis.Case report: We report a 75 years-old male patient who presented with acute kidney injury and his serum tested positive for p-ANCA by indirect immunofluoresence with a titer of 1/320. Testing by ELISA demonstrated anti-myeloperoxidase (MPO) specificity with a level of 28.8 IU/mL. His kidney biopsy showed features of ATIN with no glomerular involvement. Treatment with corticosteroids led to improvement of his kidney function and serology for ANCA became negative. In this case report ATIN seems to be associated with ANCA positivity, in the absence of other obvious causes for the acute tubulo-interstitial insult.Conclusion: ATIN can be associated with positive ANCA without features of renal-limited vasculitis or systemic vasculitis. This can occur in the absence of drug exposure. The outcome in our case was favorable with corticosteroid therapy.Key words: ANCA; Acute Tubulo-interstitial Nephritis; Pathogenesi
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