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

Three examples concerning the interaction of dry friction and oscillations

We discuss recent work concerning the interaction of dry friction, which is a rate independent effect, and temporal oscillations. First, we consider the temporal averaging of highly oscillatory friction coefficients. Here the effective dry friction is obtained as an infimal convolution. Second, we show that simple models with state-dependent friction may induce a Hopf bifurcation, where constant shear rates give rise to periodic behavior where sticking phases alternate with sliding motion. The essential feature here is the dependence of the friction coefficient on the internal state, which has an internal relaxation time. Finally, we present a simple model for rocking toy animal where walking is made possible by a periodic motion of the body that unloads the legs to be moved

On the generalized Davenport constant and the Noether number

Known results on the generalized Davenport constant related to zero-sum sequences over a finite abelian group are extended to the generalized Noether number related to the rings of polynomial invariants of an arbitrary finite group. An improved general upper bound is given on the degrees of polynomial invariants of a non-cyclic finite group which cut out the zero vector.Comment: 14 page

Standard monomial theory for wonderful varieties

A general setting for a standard monomial theory on a multiset is introduced and applied to the Cox ring of a wonderful variety. This gives a degeneration result of the Cox ring to a multicone over a partial flag variety. Further, we deduce that the Cox ring has rational singularities.Comment: v3: 20 pages, final version to appear on Algebras and Representation Theory. The final publication is available at Springer via http://dx.doi.org/10.1007/s10468-015-9586-z. v2: 20 pages, examples added in Section 3 and in Section

Transmission Electron Microscopy Reveals Distinct Macrophage- and Tick Cell-Specific Morphological Stages of Ehrlichia chaffeensis

Background: Ehrlichia chaffeensis is an emerging tick-borne rickettsial pathogen responsible for human monocytic ehrlichiosis. Despite the induction of an active host immune response, the pathogen has evolved to persist in its vertebrate and tick hosts. Understanding how the organism progresses in tick and vertebrate host cells is critical in identifying effective strategies to block the pathogen transmission. Our recent molecular and proteomic studies revealed differences in numerous expressed proteins of the organism during its growth in different host environments. Methodology/Principal Findings: Transmission electron microscopy analysis was performed to assess morphological changes in the bacterium within macrophages and tick cells. The stages of pathogen progression observed included the attachment of the organism to the host cells, its engulfment and replication within a morulae by binary fission and release of the organisms from infected host cells by complete host cell lysis or by exocytosis. E. chaffeensis grown in tick cells was highly pleomorphic and appears to replicate by both binary fission and filamentous type cell divisions. The presence of Ehrlichia-like inclusions was also observed within the nucleus of both macrophages and tick cells. This observation was confirmed by confocal microscopy and immunoblot analysis. Conclusions/Significance: Morphological differences in the pathogen’s progression, replication, and processing within macrophages and tick cells provide further evidence that E. chaffeensis employs unique host-cell specific strategies in support of adaptation to vertebrate and tick cell environments

Pure spinor superfields -- an overview

Maximally supersymmetric theories do not allow off-shell superspace formulations with traditional superfields containing a finite set of auxiliary fields. It has become clear that off-shell supersymmetric action formulations of such models can be achieved by the introduction of pure spinors. In this talk, an overview of this formalism is given, with emphasis on D=10 super-Yang-Mills theory and D=11 supergravity. This a somewhat expanded version of a talk presented at the workshop "Breaking of supersymmetry and ultraviolet divergences in extended supergravity" (BUDS), Laboratori Nazionali di Frascati, March 25-28, 2013.Comment: 34 pp., 2 figs., contributions to the proceedings of the workshop "Breaking of supersymmetry and ultraviolet divergences in extended supergravity" (BUDS), Laboratori Nazionali di Frascati, March 25-28, 201

Geometry of GL_n(C) on infinity: complete collineations, projective compactifications, and universal boundary

Consider a finite dimensional (generally reducible) polynomial representation \rho of GL_n. A projective compactification of GL_n is the closure of \rho(GL_n) in the space of all operators defined up to a factor (this class of spaces can be characterized as equivariant projective normal compactifications of GL_n). We give an expicit description for all projective compactifications. We also construct explicitly (in elementary geometrical terms) a universal object for all projective compactifications of GL_n.Comment: 24 pages, corrected varian

Acute aortic dissection type A discloses Corpus alienum

We report an unusual case of an aortic type A dissection with a corpus alienum which compresses the right ventricle. The patient successfully underwent an aortic root replacement in deep hypothermia with re-implantation of the coronary arteries using a modified Bentall procedure and the resection of the corpus alienum. Intraoperative finding reveals 3 greatly adhered gauze compresses, which were most likely forgotten in the operation 34 years ago

Multilayer Modelling of Lubricated Contacts: A New Approach Based on a Potential Field Description

A first integral approach, derived in an analogous fashion to Maxwell’s use of potential fields, is employed to investigate the flow characteristics, with a view to minimising friction, of shear-driven fluid motion between rigid surfaces in parallel alignment as a model for a lubricated joint, whether naturally occurring or engineered replacement. For a viscous bilayer arrangement comprised of immiscible liquids, it is shown how the flow and the shear stress along the separating interface is influenced by the mean thickness of the layers and the ratio of their respective viscosities. Considered in addition, is how the method can be extended for application to the more challenging problem of when one, or both, of the layers is a viscoelastic material

Measurement of the top quark mass using the matrix element technique in dilepton final states

We present a measurement of the top quark mass in pp¯ collisions at a center-of-mass energy of 1.96 TeV at the Fermilab Tevatron collider. The data were collected by the D0 experiment corresponding to an integrated luminosity of 9.7  fb−1. The matrix element technique is applied to tt¯ events in the final state containing leptons (electrons or muons) with high transverse momenta and at least two jets. The calibration of the jet energy scale determined in the lepton+jets final state of tt¯ decays is applied to jet energies. This correction provides a substantial reduction in systematic uncertainties. We obtain a top quark mass of mt=173.93±1.84  GeV