Determination of a Type of Permutation Trinomials over Finite Fields

Let $f=a{\tt x} +b{\tt x}^q+{\tt x}^{2q-1}\in\Bbb F_q[{\tt x}]$. We find explicit conditions on $a$ and $b$ that are necessary and sufficient for $f$ to be a permutation polynomial of $\Bbb F_{q^2}$. This result allows us to solve a related problem. Let $g_{n,q}\in\Bbb F_p[{\tt x}]$ ($n\ge 0$, $p=\text{char}\,\Bbb F_q$) be the polynomial defined by the functional equation $\sum_{c\in\Bbb F_q}({\tt x}+c)^n=g_{n,q}({\tt x}^q-{\tt x})$. We determine all $n$ of the form $n=q^\alpha-q^\beta-1$, $\alpha>\beta\ge 0$, for which $g_{n,q}$ is a permutation polynomial of $\Bbb F_{q^2}$.Comment: 28 page

Scale Transformations on the Noncommutative Plane and the Seiberg-Witten Map

We write down three kinds of scale transformations {\tt i-iii)} on the noncommutative plane. {\tt i)} is the analogue of standard dilations on the plane, {\tt ii)} is a re-scaling of the noncommutative parameter $\theta$, and {\tt iii)} is a combination of the previous two, whereby the defining relations for the noncommutative plane are preserved. The action of the three transformations is defined on gauge fields evaluated at fixed coordinates and $\theta$. The transformations are obtained only up to terms which transform covariantly under gauge transformations. We give possible constraints on these terms. We show how the transformations {\tt i)} and {\tt ii)} depend on the choice of star product, and show the relation of {\tt ii)} to Seiberg-Witten transformations. Because {\tt iii)} preserves the fundamental commutation relations it is a symmetry of the algebra. One has the possibility of implementing it as a symmetry of the dynamics, as well, in noncommutative field theories where $\theta$ is not fixed.Comment: 20 page

Donor IFNL4 Genotype Is Associated with Early Post-Transplant Fibrosis in Recipients with Hepatitis C

Background and Aims Early post-transplant hepatic fibrosis is associated with poor outcomes and may be influenced by donor/recipient genetic factors. The rs368234815 IFNL4 polymorphism is related to the previously described IL28B polymorphism, which predicts etiology-independent hepatic fibrosis. The aim of this study was to identify the impact of donor and/or recipient IFNL4 genotype on early fibrosis among patients transplanted for hepatitis C (HCV). Methods Clinical data were collected for 302 consecutive patients transplanted for HCV. 116 patients who had available liver biopsies and donor/recipient DNA were included. 28% of these patients with stage 2 fibrosis or greater were compared to patients without significant post-transplant fibrosis with respect to clinical features as well as donor/recipient IFNL4 genotype. Results The IFNL4 TT/TT genotype was found in 26.0% of recipients and 38.6% of donors. Patients who developed early post-transplant fibrosis had a 3.45 adjusted odds of having donor IFNL4 TT/TT genotype (p = 0.012). Donor IFNL4 TT/TT genotype also predicted decreased overall survival compared to non-TT/TT genotypes (p = 0.016). Conclusions Donor IFNL4 TT/TT genotype, a favorable predictor of spontaneous HCV clearance pre-transplant, is associated with increased early post-transplant fibrosis and decreased survival

The real photon structure functions in massive parton model in NLO

We investigate the one-gluon-exchange ($\alpha \alpha_s$) corrections to the real photon structure functions $W_{TT}$, $W_{LT}$, $W_{TT}^{a}$ and $W_{TT}^\tau$ in the massive parton model. We employ a technique based on the Cutkosky rules and the reduction of Feynman integrals to master integrals. We show that a positivity constraint, which is derived from the Cauchy-Schwarz inequality, is satisfied among the unpolarized and polarized structure functions $W_{TT}$, $W_{TT}^a$ and $W_{TT}^\tau$ calculated up to the next-to-leading order in QCD.Comment: arXiv admin note: text overlap with arXiv:1110.262

Tippe Top Equations and Equations for the Related Mechanical Systems

The equations of motion for the rolling and gliding Tippe Top (TT) are nonintegrable and difficult to analyze. The only existing arguments about TT inversion are based on analysis of stability of asymptotic solutions and the LaSalle type theorem. They do not explain the dynamics of inversion. To approach this problem we review and analyze here the equations of motion for the rolling and gliding TT in three equivalent forms, each one providing different bits of information about motion of TT. They lead to the main equation for the TT, which describes well the oscillatory character of motion of the symmetry axis $\mathbf{\hat{3}}$ during the inversion. We show also that the equations of motion of TT give rise to equations of motion for two other simpler mechanical systems: the gliding heavy symmetric top and the gliding eccentric cylinder. These systems can be of aid in understanding the dynamics of the inverting TT

Impact of IFN lambda 3/4 single nucleotide polymorphisms on the cytomegalovirus reactivation in autologous stem cell transplant patients

Cytomegalovirus (CMV) infection represents one of the main cause mortality after Stem Cell Transplantation. Recently, a protective effect of the T allele of rs12979860 IL28B Single Nucleotide Polymorphisms (SNPs) against CMV infection in the allogenic stem cell transplantation was suggested. We investigate whether the rs12979860 IL28B SNP and the relative rs368234815 (IFNλ4) genotype may affect the incidence of active CMV infection in Autologous stem cell transplantation (Auto-SCT) setting. The study included 99 patients who underwent to Auto-SCT. IL28 and IFNΔ4 SNPs were correlated with CMV reactivation along with other clinical and treatment parameters. CMV reactivation by CMV DNAemia was evaluated once a week until day 100 from Auto-SCT. CMV reactivation was documented in 50% (TT-ΔG/ΔG), 35% (CC-TT/TT) and 29.2% (CT-TT/ΔG) of the patients respectively. No differences in CMV copies number were recorded at reactivation between different IL28/IFNλ4 genotypes. The analysis of patients older than 60 years showed a significantly higher incidence of active CMV infection in the TT-ΔG/ΔG (83%) population with respect to CC-TT/TT (21%) and CT-TT/ΔG (40%) patients. Our data suggest a negative role of TT-ΔG/ΔG genotype in the CMV reactivation in Auto-SCT. The exposure to rituximab and the pre-infusion presence of anti CMV IgG also significantly influenced CMV reactivation