Interrelations among x-ray scattering,electron densities,and ionization potentials

From the general formalism of elastic x-ray scattering and a few meaningful assumptions we have shown that for an atom, ∫ρ²dτ is an experimentally measurable quantity related to the intensity scattered by an element. We have labeled this quantity (p), the “average electron density.” If ψ obeys the virial theorem, within the Thomas–Fermi approximation we show (within a multiplicative constant) that 〈ρ〉 is a lower bound to (∑ ionization potentials )^3/2. Thus, the scattered intensity of x rays is related quantitatively to the energy of the scattering atoms. Inequalities have been developed to express these relationships and have been confirmed for the more exact Hartree–Fock wave functions.     

Pions as spin waves: Chiral symmetry breaking in lattice gauge theory

In hamiltonian lattice gauge theory, the fermion vacuum at lowest order in 1/g² can be determined from degenerate perturbation theory plus mean field-spin wave techniques. Using compact QED as an example, we show that: (i) chiral symmetry is spontaneously broken; and (ii) $\text{m}{}_{\mathrm{<mtext>pseudoGoldstone</mtext>}}{}^2\text{∝ m}{}_{\mathrm{<mtext>fermion</mtext>}}\text{〈}\text{ψ}\text{ψ〉}$. The pseudoscalar pseudoGoldstone particles—the “pions” of this abelian theory—correspond to antiferromagnetic spin wave excitations of the fermion vacuum.     

Protection of cortical cells by equine estrogens against glutamate-induced excitotoxicity is mediated through a calcium independent mechanism

Background  

High concentrations of glutamate can accumulate in the brain and may be involved in the pathogenesis of neurodegenerative disorders such as Alzheimer's disease. This form of neurotoxicity involves changes in the regulation of cellular calcium (Ca²⁺) and generation of free radicals such as peroxynitrite (ONOO^-). Estrogen may protect against glutamate-induced cell death by reducing the excitotoxic Ca²⁺ influx associated with glutamate excitotoxicity. In this study, the inhibition of N-methyl-D-aspartate (NMDA) receptor and nitric oxide synthase (NOS) along with the effect of 17β-estradiol (17β-E₂) and a more potent antioxidant Δ⁸, 17β-estradiol (Δ⁸, 17β-E₂) on cell viability and intracellular Ca²⁺ ([Ca²⁺]_i), following treatment of rat cortical cells with glutamate, was investigated.     

Large molecular motions are tolerated in crystals of diamine double salt of trans-chlorocinnamic acids with trans-1,2-diaminocyclohexane

Contrary to the general assumption that photoreactions in crystals may not proceed with large molecular motions, a pedal-like motion prompted by electronic excitation is believed to be involved during the beta-dimer formation from the crystals of the diamine double salt of trans-2,4-dichlorocinnamic acid and trans-1,2-diaminocyclohexane.     

Incompressible quantum liquids and new conservation laws

In this Letter, we investigate a class of Hamiltonians which, in addition to the usual center-of-mass momentum conservation, also have center-of-mass position conservation. We find that, regardless of the particle statistics, the energy spectrum is at least q-fold degenerate when the filling factor is p/q, where and are coprime integers. Interestingly, the simplest Hamiltonian respecting this type of symmetry encapsulates two prominent examples of novel states of matter, namely, the fractional quantum Hall liquid and the quantum dimer liquid. We discuss the relevance of this class of Hamiltonian to the search for featureless Mott insulators.     

A Bernstein type theorem on a Randers space

We consider Finsler spaces with a Randers metric F=+, on the three-dimensional real vector space, where is the Euclidean metric and is a 1-form with norm b,0 b1. By using the notion of mean curvature for immersions in Finsler spaces, introduced by Z. Shen, we obtain the partial differential equation that characterizes the minimal surfaces which are graphs of functions. For each b, 0 b1/, we prove that it is an elliptic equation of mean curvature type. Then the Bernstein type theorem and other properties, such as the nonexistence of isolated singularities, of the solutions of this equation follow from the theory developped by L. Simon. For b 1/, the differential equation is not elliptic. Moreover, for every b, 1/b1 we provide solutions, which describe minimal cones, with an isolated singularity at the origin.Partially supported by CAPES/PROCAD.Partially supported by NSF grant DMS-0072242.Partially supported by CNPq and CAPES/PROCAD.     

Dark matter profile in the galactic center

We describe a quasiequilibrium profile of dark matter particles in the inner parsec of the Galaxy, rhodm proportional to r(-3/2). This "minicusp" profile is caused by scattering with the dense stellar cluster around the supermassive black hole in Sgr A* and is independent of the initial conditions. The implications for detection of gamma rays from annihilation of weakly interacting massive dark matter particle in the Galactic center are a mild enhancement of the flux and a characteristic central feature in the angular distribution which could be detectable by high-resolution atmospheric Cherenkov telescopes.     

A Two Dimensional Fermi Liquid. Part 2: Convergence

Using results established in other papers in our series, we prove the existence of the infinite volume, temperature zero, thermodynamic Greens functions of a two dimensional, weakly coupled fermion gas with an asymmetric Fermi curve and short range interactions. This is done by showing that our sequence of renormalization group maps converges.Research supported in part by the Natural Sciences and Engineering Research Council of Canada and the Forschunginstitut für Mathematik, ETH Zürich.     

The Piracicaba River basin: isotope hydrology of a tropical river basin under anthropogenic stress

The stable isotope content of samples of precipitation and of the river water throughout the Piracicaba basin in Brazil was measured over a two-year period. The isotope values of precipitation follow a consistent pattern of relatively depleted values of both deuterium and oxygen 18 during the rainy summers and enriched ones during the dry winters, with all values aligned slightly above the Global Meteoric Water Line. The isotopic composition of the river water throughout the basin shows a remarkable spatial coherence and much smaller scatter of data than those of the precipitation. The isotope composition of river water is close to that of the precipitation in the rainy season, however, with a consistent lower d-excess value by 1/1000-2/1000. This is attributed to evaporative water loss in the basin, in part an expression of the recycling of water due to the anthropogenic activity in the region. The more divergent values are recorded during high-water stages in the rivers. In many cases, the floods during the beginning of the rainy season are characterized by an enrichment of the heavy isotopes and lower d-excess values when compared to the precipitation, with the opposite situation later in the rainy season. This is interpreted as resulting from the watershed/riverflow interaction pattern, and it thus suggests that the isotope composition can monitor the hydrologic situation in the basin and its changes.