Strongly residual coordinates over A[x]

For a domain A of characteristic zero, a polynomial f over A[x] is called a strongly residual coordinate if f becomes a coordinate (over A) upon going modulo x, and f becomes a coordinate upon inverting x. We study the question of when a strongly residual coordinate is a coordinate, a question closely related to the Dolgachev-Weisfeiler conjecture. It is known that all strongly residual coordinates are coordinates for n=2 . We show that a large class of strongly residual coordinates that are generated by elementaries upon inverting x are in fact coordinates for arbitrary n, with a stronger result in the n=3 case. As an application, we show that all Venereau-type polynomials are 1-stable coordinates.Comment: 15 pages. Some minor clarifications and notational improvements from the first versio

Roots of the affine Cremona group

Let k[x_1,...,x_n] be the polynomial algebra in n variables and let A^n=Spec k[x_1,...,x_n]. In this note we show that the root vectors of the affine Cremona group Aut(A^n) with respect to the diagonal torus are exactly the locally nilpotent derivations x^a\times d/dx_i, where x^a is any monomial not depending on x_i. This answers a question due to Popov.Comment: 4 page

On Proper Polynomial Maps of C2.\mathbb{C}^2.

Two proper polynomial maps $f_1, f_2 \colon \mathbb{C}^2 \longrightarrow \mathbb{C}^2$ are said to be \emph{equivalent} if there exist $\Phi_1, \Phi_2 \in \textrm{Aut}(\mathbb{C}^2)$ such that $f_2=\Phi_2 \circ f_1 \circ \Phi_1$. We investigate proper polynomial maps of arbitrary topological degree $d \geq 2$ up to equivalence. Under the further assumption that the maps are Galois coverings we also provide the complete description of equivalence classes. This widely extends previous results obtained by Lamy in the case $d=2$.Comment: 15 pages. Final version, to appear in Journal of Geometric Analysi

Affine T-varieties of complexity one and locally nilpotent derivations

Let X=spec A be a normal affine variety over an algebraically closed field k of characteristic 0 endowed with an effective action of a torus T of dimension n. Let also D be a homogeneous locally nilpotent derivation on the normal affine Z^n-graded domain A, so that D generates a k_+-action on X that is normalized by the T-action. We provide a complete classification of pairs (X,D) in two cases: for toric varieties (n=\dim X) and in the case where n=\dim X-1. This generalizes previously known results for surfaces due to Flenner and Zaidenberg. As an application we compute the homogeneous Makar-Limanov invariant of such varieties. In particular we exhibit a family of non-rational varieties with trivial Makar-Limanov invariant.Comment: 31 pages. Minor changes in the structure. Fixed some typo

Langevin equation for the extended Rayleigh model with an asymmetric bath

In this paper a one-dimensional model of two infinite gases separated by a movable heavy piston is considered. The non-linear Langevin equation for the motion of the piston is derived from first principles for the case when the thermodynamic parameters and/or the molecular masses of gas particles on left and right sides of the piston are different. Microscopic expressions involving time correlation functions of the force between bath particles and the piston are obtained for all parameters appearing in the non-linear Langevin equation. It is demonstrated that the equation has stationary solutions corresponding to directional fluctuation-induced drift in the absence of systematic forces. In the case of ideal gases interacting with the piston via a quadratic repulsive potential, the model is exactly solvable and explicit expressions for the kinetic coefficients in the non-linear Langevin equation are derived. The transient solution of the non-linear Langevin equation is analyzed perturbatively and it is demonstrated that previously obtained results for systems with the hard-wall interaction are recovered.Comment: 10 pages. To appear in Phys. Rev.

Evidence of short time dynamical correlations in simple liquids

We report a molecular dynamics (MD) study of the collective dynamics of a simple monatomic liquid -interacting through a two body potential that mimics that of lithium- across the liquid-glass transition. In the glassy phase we find evidences of a fast relaxation process similar to that recently found in Lennard-Jones glasses. The origin of this process is ascribed to the topological disorder, i.e. to the dephasing of the different momentum $Q$ Fourier components of the actual normal modes of vibration of the disordered structure. More important, we find that the fast relaxation persists in the liquid phase with almost no temperature dependence of its characteristic parameters (strength and relaxation time). We conclude, therefore, that in the liquid phase well above the melting point, at variance with the usual assumption of {\it un-correlated} binary collisions, the short time particles motion is strongly {\it correlated} and can be described via a normal mode expansion of the atomic dynamics.Comment: 7 pages, 7 .eps figs. To appear in Phys. Rev.

Charge multiplication effect in thin diamond films

Herein, we report on the enhanced sensitivity for the detection of charged particles in single crystal chemical vapour deposition (scCVD) diamond radiation detectors. The experimental results demonstrate charge multiplication in thin planar diamond membrane detectors, upon impact of 18MeV O ions, under high electric field conditions. Avalanche multiplication is widely exploited in devices such as avalanche photo diodes, but has never before been reproducibly observed in intrinsic CVD diamond. Because enhanced sensitivity for charged particle detection is obtained for short charge drift lengths without dark counts, this effect could be further exploited in the development of sensors based on avalanche multiplication and radiation detectors with extreme radiation hardnes

Beta-glucan reflects liver injury after preservation and transplantation in dogs.

Graft failure and extrahepatic organ complications, which frequently develop after transplantation, may be related to inflammatory mediators stimulated by endotoxin (ET). The role of endotoxemia after liver transplantation is controversial and may depend upon differences in the ET assay method used in the various contradicting studies. While the standard Limulus amebocyte lysate (LAL) is reactive for ET and beta-glucan, a novel turbidimetric assay method enables separate determinations of ET and beta-glucan. Beagle dogs undergoing orthotopic liver transplantation were divided into two groups. In Group I (n = 6) the grafts were transplanted immediately and in Group II (n = 6) grafts were preserved for 48 h in University of Wisconsin (UW) solution. Animals received cyclosporine immunosuppression and were followed for 14 days. Daily measurements of aspartate aminotransferase (AST), alanine aminotransferase (ALT), and lactate dehydrogenase (LDH) were performed. Samples for ET and beta-glucan measurement were collected serially and processed using the turbidimetric assay method. While no graft failure was seen in Group I, three of six Group II animals died from graft failure within 1 day after transplantation. Preservation and reperfusion injury was much more severe in the Group II grafts than in Group I grafts. While endotoxemia could not be detected, postoperative beta-glucan levels (undetectable pretransplant) were seen in both groups. Beta-glucan levels were much higher in Group II grafts than in Group I grafts, and correlated with the severity of liver damage. In conclusion, this study shows that beta-glucan, instead of ET, appears during the early posttransplant period. We believe that posttransplant elevation of beta-glucan is related to liver damage, especially endothelial damage by preservation and reperfusion