Pointwise convergence of vector-valued Fourier series

We prove a vector-valued version of Carleson's theorem: Let Y=[X,H]_t be a complex interpolation space between a UMD space X and a Hilbert space H. For p\in(1,\infty) and f\in L^p(T;Y), the partial sums of the Fourier series of f converge to f pointwise almost everywhere. Apparently, all known examples of UMD spaces are of this intermediate form Y=[X,H]_t. In particular, we answer affirmatively a question of Rubio de Francia on the pointwise convergence of Fourier series of Schatten class valued functions.Comment: 26 page

On bilinear Littlewood-Paley square functions

On the real line, let the Fourier transform of $k_n$ be $\hat k_n(\xi)=\hat k(\xi-n)$ where $\hat k(\xi)$ is a smooth compactly supported function. Consider the bilinear operators $S_n(f,g)(x)=\int f(x+y)g(x-y)k_n(y)\,dy$. If $2\le p,q\le\infty$, with $1/p+1/q=1/2$, I prove that \sum_{n=-\zI}^\zI\|S_n(f,g)\|_2^2\le{}C^2\|f\|_p^2 \|g\|_q^2\,. The constant $C$ depends only upon $k$

Introduction to salinity - workshop manual for participants

This is the first in a series of workshops looking at dryland salinity and options to manage it. These ?Million hectares? workshops have the common themes of environmental improvement. They provide information to help participants identify the risks within the catchment and at a farm level, assess both the likelihood of the risk occurring and consequences if the risk is not managed and determine the best course of action for individual. Participants will determine their courses of action based on their specific circumstances and goals. There is no one recipe that is suited to all participants. The Participants Notes when completed should provide a documented record of the risks, their likely impact and planned activities to manage their risk

Introduction to salinity - workshop development guide for facilitator

Participants will be able to recognise landscape components on their farm, which are at risk of salinity (current, imminent or future) and will be aware of a range of available options available to them to managing this risk

Initial temperature and EoS of quark matter from direct photons

The time evolution of the quark gluon plasma created in gold-gold collisions of the Relativistic Heavy Ion Collider (RHIC) can be described by hydrodynamical models. Distribution of hadrons reflects the freeze-out state of the matter. To investigate the time evolution one needs to analyze penetrating probes, such as direct photon spectra. Distributions of low energy photons was published in 2010 by PHENIX. In this paper we analyze a 3+1 dimensional solution of relativistic hydrodynamics and calculate momentum distribution of direct photons. Using earlier fits of this model to hadronic spectra, we compare photon calculations to measurements and find that the initial temperature of the center of the fireball is at least 519+-12 MeV, while for the equation of state we get c_s= 0.36+-0.02.Comment: Talk at the VI Workshop on Particle Correlations and Femtoscopy, Kiev, September 14-18, 2010. 6 pages, 1 figure. This work was supported by the OTKA grant NK73143 and M. Csanad's Bolyai scholarshi

Cosmological Implications of the Fundamental Relations of X-ray Clusters

Based on the two-parameter family nature of X-ray clusters of galaxies obtained in a separate paper, we discuss the formation history of clusters and cosmological parameters of the universe. Utilizing the spherical collapse model of cluster formation, and assuming that the cluster X-ray core radius is proportional to the virial radius at the time of the cluster collapse, the observed relations among the density, radius, and temperature of clusters imply that cluster formation occurs in a wide range of redshift. The observed relations favor the low-density universe. Moreover, we find that the model of $n\sim -1$ is preferable.Comment: 7 pages, 4 figures. To be published in ApJ Letter

Characteristics of perrennial grasses [poster]

Growth Characteristics of perennial C3 grasses: this table presents information on a range of perennial grass species but it is not a recommendation for them. Consider species characteristics in relation to local conditions and then source specific variety information before making decisions. It is suggest you grow trial plots of grasses before planting large areas (see key below for rating system)

High-Redshift Galaxies: Their Predicted Size and Surface Brightness Distributions and Their Gravitational Lensing Probability

Direct observations of the first generation of luminous objects will likely become feasible over the next decade. The advent of the Next Generation Space Telescope (NGST) will allow imaging of numerous galaxies and mini-quasars at redshifts z>5. We apply semi-analytic models of structure formation to estimate the rate of multiple imaging of these sources by intervening gravitational lenses. Popular CDM models for galaxy formation yield a lensing optical depth of about 1% for sources at redshift 10. The expected slope of the luminosity function of the early sources implies an additional magnification bias of about 5, bringing the fraction of lensed sources at z=10 to about 5%. We estimate the angular size distribution of high-redshift disk galaxies and find that most of them are more extended than the resolution limit of NGST, roughly 0.06 arcseconds. We also show that there is only a modest redshift evolution in the mean surface brightness of galaxies at z>2. The expected increase by 1-2 orders of magnitude in the number of resolved sources on the sky, due to observations with NGST, will dramatically improve upon the statistical significance of existing weak lensing measurements. We show that, despite this increase in the density of sources, confusion noise from z>2 galaxies is expected to be small for NGST observations.Comment: 27 pages, 8 PostScript figures (of which two are new), revised version accepted for Ap