Quantization on Curves

Deformation quantization on varieties with singularities offers perspectives that are not found on manifolds. Essential deformations are classified by the Harrison component of Hochschild cohomology, that vanishes on smooth manifolds and reflects information about singularities. The Harrison 2-cochains are symmetric and are interpreted in terms of abelian $*$-products. This paper begins a study of abelian quantization on plane curves over \Crm, being algebraic varieties of the form R2/I where I is a polynomial in two variables; that is, abelian deformations of the coordinate algebra C[x,y]/(I). To understand the connection between the singularities of a variety and cohomology we determine the algebraic Hochschild (co-)homology and its Barr-Gerstenhaber-Schack decomposition. Homology is the same for all plane curves C[x,y]/(I), but the cohomology depends on the local algebra of the singularity of I at the origin.Comment: 21 pages, LaTex format. To appear in Letters Mathematical Physic

Consistent Anisotropic Repulsions for Simple Molecules

We extract atom-atom potentials from the effective spherical potentials that suc cessfully model Hugoniot experiments on molecular fluids, e.g., $O_2$ and $N_2$. In the case of $O_2$ the resulting potentials compare very well with the atom-atom potentials used in studies of solid-state propertie s, while for $N_2$ they are considerably softer at short distances. Ground state (T=0K) and room temperatu re calculations performed with the new $N-N$ potential resolve the previous discrepancy between experimental and theoretical results.Comment: RevTeX, 5 figure

Direct Detection of Electroweak-Interacting Dark Matter

Assuming that the lightest neutral component in an SU(2)L gauge multiplet is the main ingredient of dark matter in the universe, we calculate the elastic scattering cross section of the dark matter with nucleon, which is an important quantity for the direct detection experiments. When the dark matter is a real scalar or a Majorana fermion which has only electroweak gauge interactions, the scattering with quarks and gluon are induced through one- and two-loop quantum processes, respectively, and both of them give rise to comparable contributions to the elastic scattering cross section. We evaluate all of the contributions at the leading order and find that there is an accidental cancellation among them. As a result, the spin-independent cross section is found to be O(10^-(46-48)) cm^2, which is far below the current experimental bounds.Comment: 19 pages, 7 figures, published versio

Wigner Trajectory Characteristics in Phase Space and Field Theory

Exact characteristic trajectories are specified for the time-propagating Wigner phase-space distribution function. They are especially simple---indeed, classical---for the quantized simple harmonic oscillator, which serves as the underpinning of the field theoretic Wigner functional formulation introduced. Scalar field theory is thus reformulated in terms of distributions in field phase space. Applications to duality transformations in field theory are discussed.Comment: 9 pages, LaTex2

Influência da assepsia na germinação de sementes de Paspalum regnellii Mez.

CONGREGA

Singularities, Lax degeneracies and Maslov indices of the periodic Toda chain

The n-particle periodic Toda chain is a well known example of an integrable but nonseparable Hamiltonian system in R^{2n}. We show that Sigma_k, the k-fold singularities of the Toda chain, ie points where there exist k independent linear relations amongst the gradients of the integrals of motion, coincide with points where there are k (doubly) degenerate eigenvalues of representatives L and Lbar of the two inequivalent classes of Lax matrices (corresponding to degenerate periodic or antiperiodic solutions of the associated second-order difference equation). The singularities are shown to be nondegenerate, so that Sigma_k is a codimension-2k symplectic submanifold. Sigma_k is shown to be of elliptic type, and the frequencies of transverse oscillations under Hamiltonians which fix Sigma_k are computed in terms of spectral data of the Lax matrices. If mu(C) is the (even) Maslov index of a closed curve C in the regular component of R^{2n}, then (-1)^{\mu(C)/2} is given by the product of the holonomies (equal to +/- 1) of the even- (or odd-) indexed eigenvector bundles of L and Lmat.Comment: 25 pages; published versio

The definability criterions for convex projective polyhedral reflection groups

Following Vinberg, we find the criterions for a subgroup generated by reflections \Gamma \subset \SL^{\pm}(n+1,\mathbb{R}) and its finite-index subgroups to be definable over $\mathbb{A}$ where $\mathbb{A}$ is an integrally closed Noetherian ring in the field $\mathbb{R}$. We apply the criterions for groups generated by reflections that act cocompactly on irreducible properly convex open subdomains of the $n$-dimensional projective sphere. This gives a method for constructing injective group homomorphisms from such Coxeter groups to \SL^{\pm}(n+1,\mathbb{Z}). Finally we provide some examples of \SL^{\pm}(n+1,\mathbb{Z})-representations of such Coxeter groups. In particular, we consider simplicial reflection groups that are isomorphic to hyperbolic simplicial groups and classify all the conjugacy classes of the reflection subgroups in \SL^{\pm}(n+1,\mathbb{R}) that are definable over $\mathbb{Z}$. These were known by Goldman, Benoist, and so on previously.Comment: 31 pages, 8 figure

Proteolytic processing of human cytomegalovirus glycoprotein B (gpUL55) is mediatedby the human endoprotease furin

AbstractInhibition of endoproteolytic cleavage of glycoprotein B (gB; gpUL55) of human cytomegalovirus was achieved by treatmentof infected fibroblasts with decanoyl peptidyl chloromethyl ketone (decRVKR-CMK), which inhibits the action of cellular subtilisin-like endoproteases with the amino acid recognition motif R × K/R R. Uncleaved gB precusor molecules of 160 kDa that were accumulated were endoglycosidase H resistant, suggesting that correct cellular transport occurred in the presence of the drug. The inhibitor also prevented endoproteolytic gB processing in CV-1 cells infected with a recombinant vaccinia virus-gB construct (VVgB). Evidence for direct involvement of the ubiquitous subtilisin-like endoprotease furin in gB cleavage was obtained from the observation that coinfection of CV-1 cells with WgB and a recombinant vaccinia-human furin construct reestablished endoproteolytic activity which was normally absent late after infection with WgB alone

Delayed subsidence of the Dead Sea shore due to hydro-meteorological changes

Many studies show the sensitivity of our environment to manmade changes, especially the anthropogenic impact on atmospheric and hydrological processes. The effect on Solid Earth processes such as subsidence is less straightforward. Subsidence is usually slow and relates to the interplay of complex hydro-mechanical processes, thus making relations to atmospheric changes difficult to observe. In the Dead Sea (DS) region, however, climatic forcing is strong and over-use of fresh water is massive. An observation period of 3 years was thus sufficient to link the high evaporation (97 cm/year) and the subsequent drop of the Dead Sea lake level (− 110 cm/year), with high subsidence rates of the Earth’s surface (− 15 cm/year). Applying innovative Global Navigation Satellite System (GNSS) techniques, we are able to resolve this subsidence of the “Solid Earth” even on a monthly basis and show that it behaves synchronous to atmospheric and hydrological changes with a time lag of two months. We show that the amplitude and fluctuation period of ground deformation is related to poro-elastic hydro-mechanical soil response to lake level changes. This provides, to our knowledge, a first direct link between shore subsidence, lake-level drop and evaporation