We prove that a polynomial map from Rn to itself with non-zero constant Jacobian determinant is a stably tame automorphism if its linear part is the identity and all the coefficients of its higher order terms are non-positive. We also prove that the Jacobian conjecture holds for any number of variables and any field of characteristic zero, if one can show that every polynomial map of Rn to itself is injective when it has a non-zero constant Jacobian determinant and has linear part the identity, and all the coefficients of higher order terms Basket Nike Blazer Mid are non-negative. The proofs use special properties of matrices with non-positive off-diagonal elements and non-negative principal minors, and of matrices with vanishing principal minors. Furthermore we reduce the Jacobian conjecture to a polynomial matrix problem. Moreover, if the matrix has a positive answer, then every real polynomial automorphism is stably tame.
Shiga toxins (Stx) are believed to play a key role in the pathogenesis of diseases caused by Stx-producing Escherichia coli (STEC), including the potentially life-threatening hemolytic uremic syndrome (HUS). In this study, 201 STEC strains collected from patients and Basket Blazer Nike Pas Cher environmental sources were investigated with regard to the stx genotypes and pathogenicity. The stx2 and stx2c alleles were associated with high virulence and the ability to cause HUS, whereas stx2d, stx2e,stx1, and stx1c occurred in milder or asymptomatic infections. Quantification of Stx using an enzyme immunoassay and the Vero cell cytotoxicity assay showed no significant differences between the strains associated with HUS and those causing milder diseases. We hypothesize that the stx genotype and perhaps other yet unknown virulence factors rather than Basket Blazer Nike Pas Cher the amount of Stx or the in vitro cytotoxicity correlate with the development of HUS.
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