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 $w= s/2/(1+s^2)$, with $s= \sinh(2K)$, where $K=J/kT$ is the usual Ising model coupling constant. Switching to the variable $s$, 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 $\chi^{(3)}$ at the points $1+3w+4w^2= 0$ and show that $\chi^{(3)}(s)$ is not singular at the corresponding points inside the unit circle $| s |=1$, while its analytical continuation in the variable $s$ is actually singular at the corresponding points $2+s+s^2=0$ oustside the unit circle ($| s | > 1$).Comment: 34 pages, 1 figur

In vitro inhibition of Helicobacter pylori urease with non and semi fermented Camellia sinensis

Purpose: Helicobacter pylori is the etiological agent in duodenal and peptic ulcers. The growing problem of antibiotic resistance by the organism demands the search for novel compounds, especially from natural sources. This study was conducted to evaluate the effect of Camellia sinensis extracts on the urease enzyme that is a major colonization factor for H. pylori. Methods: Minimum inhibitory concentrations of nonfermented and semifermented C. sinensis methanol: water extracts were assessed by broth dilution method. Examination of the urease function was performed by Mc Laren method, and urease production was detected on 12% SDS polyacrylamide gel electrophoresis from whole cell and membrane bound proteins. Results: Both extracts had inhibitory effects against H. pylori and urease production. At a concentration of 2.5 mg/ml of nonfermented extract and 3.5 mg/ml of semifermented extract the production of Ure A and Ure B subunits of the urease enzyme were inhibited completely. A concentration of 4 mg/ml of nonfermented and 5.5 mg/ml of semifermented extract were bactericidal for H. pylori. Conclusions: C. sinensis extracts, especially the nonfermented, could reduce H. pylori population and inhibit urease production at lower concentrations. The superior effect of nonfermented extract is due to its rich polyphenolic compounds and catechin contents

Renormalization, isogenies and rational symmetries of differential equations

We give an example of infinite order rational transformation that leaves a linear differential equation covariant. This example can be seen as a non-trivial but still simple illustration of an exact representation of the renormalization group.Comment: 36 page

Globally nilpotent differential operators and the square Ising model

We recall various multiple integrals related to the isotropic square Ising model, and corresponding, respectively, to the n-particle contributions of the magnetic susceptibility, to the (lattice) form factors, to the two-point correlation functions and to their lambda-extensions. These integrals are holonomic and even G-functions: they satisfy Fuchsian linear differential equations with polynomial coefficients and have some arithmetic properties. We recall the explicit forms, found in previous work, of these Fuchsian equations. These differential operators are very selected Fuchsian linear differential operators, and their remarkable properties have a deep geometrical origin: they are all globally nilpotent, or, sometimes, even have zero p-curvature. Focusing on the factorised parts of all these operators, we find out that the global nilpotence of the factors corresponds to a set of selected structures of algebraic geometry: elliptic curves, modular curves, and even a remarkable weight-1 modular form emerging in the three-particle contribution $\chi^{(3)}$ of the magnetic susceptibility of the square Ising model. In the case where we do not have G-functions, but Hamburger functions (one irregular singularity at 0 or $\infty$) that correspond to the confluence of singularities in the scaling limit, the p-curvature is also found to verify new structures associated with simple deformations of the nilpotent property.Comment: 55 page

Painleve versus Fuchs

The sigma form of the Painlev{\'e} VI equation contains four arbitrary parameters and generically the solutions can be said to be genuinely ``nonlinear'' because they do not satisfy linear differential equations of finite order. However, when there are certain restrictions on the four parameters there exist one parameter families of solutions which do satisfy (Fuchsian) differential equations of finite order. We here study this phenomena of Fuchsian solutions to the Painlev{\'e} equation with a focus on the particular PVI equation which is satisfied by the diagonal correlation function C(N,N) of the Ising model. We obtain Fuchsian equations of order $N+1$ for C(N,N) and show that the equation for C(N,N) is equivalent to the $N^{th}$ symmetric power of the equation for the elliptic integral $E$. We show that these Fuchsian equations correspond to rational algebraic curves with an additional Riccati structure and we show that the Malmquist Hamiltonian $p,q$ variables are rational functions in complete elliptic integrals. Fuchsian equations for off diagonal correlations $C(N,M)$ are given which extend our considerations to discrete generalizations of Painlev{\'e}.Comment: 18 pages, Dedicated to the centenary of the publication of the Painleve VI equation in the Comptes Rendus de l'Academie des Sciences de Paris by Richard Fuchs in 190

Virulence increasing of salmonella typhimurium in Balb/c Mice after heat-stress induction of phage shock protein A

View at Publisher| Export | Download | Add to List | More... Current Microbiology Volume 59, Issue 4, October 2009, Pages 446-450 Virulence increasing of salmonella typhimurium in Balb/c Mice after heat-stress induction of phage shock protein A (Article) Hassani, A.S.ab, Amirmozafari, N.c, Ghaemi, A.bd a Department of Microbiology, Fars Science and Research Branch of IAU, Shiraz, Fars, Iran b Young Researchers Club (YRC) of Science and Research Branch, Islamic Azad University, Tehran, Iran c Department of Microbiology, Iran University of Medical Sciences, Tehran, Iran View additional affiliations View references (39) Abstract Salmonella typhimurium is a potentially intracellular pathogen and is responsible for thousands of reported cases of acute gastroenteritis and diarrhea each year. Although many successful physiological and genetic approaches have been taken to conclude the key virulence determinants encoded by this organism, the total number of uncharacterized reading frames observed within the S. typhimurium genome suggests that many virulence factors remain to be discovered. This study was conducted to evaluate the role of heat induced phage shock protein A (PspA), in the pathogenicity of S. typhimurium. The stress proteins detected on sodium dodecyl sulfate-polyacrylamide gel electrophoresis were identified specifically by immunoblotting with polyclonal antibody against PspA. PspA was produced in response to heat stress at 45°C and it was over-expressed at 65°C. At this temperature, the stressed bacterial cells producing PspA were more virulent (16 folds greater) to female 6-8 week-old Balb/c mice. Correspondency between decrease in LD50 and increase in PspA production during heat stress and lower pathogenicity in non-producing cells that emerged during stress at 55°C represents PspA as an important virulence factor in heat stressed S. typhimurium. © 2009 Springer Science+Business Media, LLC