Growth and integrability of Fourier transforms on Euclidean space

A fundamental theme in classical Fourier analysis relates smoothness properties of functions to the growth and/or integrability of their Fourier transform. By using a suitable class of $L^{p}-$multipliers, a rather general inequality controlling the size of Fourier transforms for large and small argument is proved. As consequences, quantitative Riemann-Lebesgue estimates are obtained and an integrability result for the Fourier transform is developed extending ideas used by Titchmarsh in the one dimensional setting

Magnetic exponents of two-dimensional Ising spin glasses

The magnetic critical properties of two-dimensional Ising spin glasses are controversial. Using exact ground state determination, we extract the properties of clusters flipped when increasing continuously a uniform field. We show that these clusters have many holes but otherwise have statistical properties similar to those of zero-field droplets. A detailed analysis gives for the magnetization exponent delta = 1.30 +/- 0.02 using lattice sizes up to 80x80; this is compatible with the droplet model prediction delta = 1.282. The reason for previous disagreements stems from the need to analyze both singular and analytic contributions in the low-field regime.Comment: 4 pages, 4 figures, title now includes "Ising

Self Consistent Screening Approximation For Critical Dynamics

We generalise Bray's self-consistent screening approximation to describe the critical dynamics of the $\phi^4$ theory. In order to obtain the dynamical exponent $z$, we have to make an ansatz for the form of the scaling functions, which fortunately can be much constrained by general arguments. Numerical values of $z$ for $d=3$, and $n=1,...,10$ are obtained using two different ans\"atze, and differ by a very small amount. In particular, the value of $z \simeq 2.115$ obtained for the 3-d Ising model agrees well with recent Monte-Carlo simulations.Comment: 21 pages, LaTeX file + 4 (EPS) figure

Scalings of domain wall energies in two dimensional Ising spin glasses

We study domain wall energies of two dimensional spin glasses. The scaling of these energies depends on the model's distribution of quenched random couplings, falling into three different classes. The first class is associated with the exponent theta =-0.28, the other two classes have theta = 0, as can be justified theoretically. In contrast to previous claims, we find that theta=0 does not indicate d=d_l but rather d <= d_l, where d_l is the lower critical dimension.Comment: Clarifications and extra reference

Persistence in systems with conserved order parameter

We consider the low-temperature coarsening dynamics of a one-dimensional Ising ferromagnet with conserved Kawasaki-like dynamics in the domain representation. Domains diffuse with size-dependent diffusion constant, $D(l) \propto l^\gamma$ with $\gamma = -1$. We generalize this model to arbitrary $\gamma$, and derive an expression for the domain density, $N(t) \sim t^{-\phi}$ with $\phi=1/(2-\gamma)$, using a scaling argument. We also investigate numerically the persistence exponent $\theta$ characterizing the power-law decay of the number, $N_p(t)$, of persistent (unflipped) spins at time $t$, and find $N_{p}(t)\sim t^{-\theta}$ where $\theta$ depends on $\gamma$. We show how the results for $\phi$ and $\theta$ are related to similar calculations in diffusion-limited cluster-cluster aggregation (DLCA) where clusters with size-dependent diffusion constant diffuse through an immobile `empty' phase and aggregate irreversibly on impact. Simulations show that, while $\phi$ is the same in both models, $\theta$ is different except for $\gamma=0$. We also investigate models that interpolate between symmetric domain diffusion and DLCA.Comment: 9 pages, minor revision

Nonexistence of Generalized Apparent Horizons in Minkowski Space

We establish a Positive Mass Theorem for initial data sets of the Einstein equations having generalized trapped surface boundary. In particular we answer a question posed by R. Wald concerning the existence of generalized apparent horizons in Minkowski space

In vitro synergy and enhanced murine brain penetration of saquinavir coadministered with mefloquine.

Highly active antiretroviral therapy has substantially improved prognosis in human immunodeficiency virus (HIV). However, the integration of proviral DNA, development of viral resistance, and lack of permeability of drugs into sanctuary sites (e.g., brain and lymphocyte) are major limitations to current regimens. Previous studies have indicated that the antimalarial drug chloroquine (CQ) has antiviral efficacy and a synergism with HIV protease inhibitors. We have screened a panel of antimalarial compounds for activity against HIV-1 in vitro. A limited efficacy was observed for CQ, mefloquine (MQ), and mepacrine (MC). However, marked synergy was observed between MQ and saquinavir (SQV), but not CQ in U937 cells. Furthermore, enhancement of the antiviral activity of SQV and four other protease inhibitors (PIs) by MQ was observed in MT4 cells, indicating a class specific rather than a drug-specific phenomenon. We demonstrate that these observations are a result of inhibition of multiple drug efflux proteins by MQ and that MQ also displaces SQV from orosomucoid in vitro. Finally, coadministration of MQ and SQV in CD-1 mice dramatically altered the tissue distribution of SQV, resulting in a >3-fold and >2-fold increase in the tissue/blood ratio for brain and testis, respectively. This pharmacological enhancement of in vitro antiviral activity of PIs by MQ now warrants further examination in vivo

Book Reviews

Reviews of the following books: Maine Becomes A State: The Movement to Separate Maine from Massachusetts, 1785-1820 by Ronald F. Banks; The Eastern Frontier: The Settlement of Northern New England, 1620-1763 by Charles E. Clark; Enduring Friendships edited by Al Robert

Stress-free Spatial Anisotropy in Phase-Ordering

We find spatial anisotropy in the asymptotic correlations of two-dimensional Ising models under non-equilibrium phase-ordering. Anisotropy is seen for critical and off-critical quenches and both conserved and non-conserved dynamics. We argue that spatial anisotropy is generic for scalar systems (including Potts models) with an anisotropic surface tension. Correlation functions will not be universal in these systems since anisotropy will depend on, e.g., temperature, microscopic interactions and dynamics, disorder, and frustration.Comment: 4 pages, 4 figures include