Nonexistence results for the Korteweg-deVries and Kadomtsev-Petviashvili equations

We study characteristic Cauchy problems for the Korteweg-deVries (KdV) equation $u_t=uu_x+u_{xxx}$, and the Kadomtsev-Petviashvili (KP) equation $u_{yy}=\bigl(u_{xxx}+uu_x+u_t\bigr)_x$ with holomorphic initial data possessing nonnegative Taylor coefficients around the origin. For the KdV equation with initial value $u(0,x)=u_0(x)$, we show that there is no solution holomorphic in any neighbourhood of $(t,x)=(0,0)$ in ${\mathbb C}^2$ unless $u_0(x)=a_0+a_1x$. This also furnishes a nonexistence result for a class of $y$-independent solutions of the KP equation. We extend this to $y$-dependent cases by considering initial values given at $y=0$, $u(t,x,0)=u_0(x,t)$, $u_y(t,x,0)=u_1(x,t)$, where the Taylor coefficients of $u_0$ and $u_1$ around $t=0$, $x=0$ are assumed nonnegative. We prove that there is no holomorphic solution around the origin in ${\mathbb C}^3$ unless $u_0$ and $u_1$ are polynomials of degree 2 or lower.Comment: 17 pages in LaTeX2e, to appear in Stud. Appl. Mat

Radio Observations of GRB Host Galaxies

We present 5.5 and 9.0 GHz observations of a sample of seventeen GRB host galaxies at 0.5<z<1.4, using the radio continuum to explore their star formation properties in the context of the small but growing sample of galaxies with similar observations. Four sources are detected, one of those (GRB 100418A) likely due to lingering afterglow emission. We suggest that the previously-reported radio afterglow of GRB 100621A may instead be due to host galaxy flux. We see no strong evidence for redshift evolution in the typical star formation rate of GRB hosts, but note that the fraction of `dark' bursts with detections is higher than would be expected given constraints on the more typical long GRB population. We also determine the average radio-derived star formation rates of core collapse supernovae at comparable redshift, and show that these are still well below the limits obtained for GRB hosts, and show evidence for a rise in typical star formation rate with redshift in supernova hosts.Comment: 15 pages, MNRAS accepte

Renormalization group scaling in nonrelativistic QCD

We discuss the matching conditions and renormalization group evolution of non-relativistic QCD. A variant of the conventional MS-bar scheme is proposed in which a subtraction velocity nu is used rather than a subtraction scale mu. We derive a novel renormalization group equation in velocity space which can be used to sum logarithms of v in the effective theory. We apply our method to several examples. In particular we show that our formulation correctly reproduces the two-loop anomalous dimension of the heavy quark production current near threshold.Comment: (27 pages, revtex

An evolutionary model with Turing machines

The development of a large non-coding fraction in eukaryotic DNA and the phenomenon of the code-bloat in the field of evolutionary computations show a striking similarity. This seems to suggest that (in the presence of mechanisms of code growth) the evolution of a complex code can't be attained without maintaining a large inactive fraction. To test this hypothesis we performed computer simulations of an evolutionary toy model for Turing machines, studying the relations among fitness and coding/non-coding ratio while varying mutation and code growth rates. The results suggest that, in our model, having a large reservoir of non-coding states constitutes a great (long term) evolutionary advantage.Comment: 16 pages, 7 figure

Recent Progress in Heavy Quark Physics

Some of the recent progress in heavy quark physics is reviewed. Special attention is paid to inclusive methods for determining Vub and factorization in nonleptonic B decays. Theoretical predictions for top-antitop production near threshold are also discussed.Comment: talk given at 2001 Lepton Photon Meeting, 10 pages, 5 figure

Comprehension as social and intellectual practice: Rebuilding curriculum in low socioeconomic and cultural minority schools

This article reframes the concept of comprehension as a social and intellectual practice. It reviews current approaches to reading instruction for linguistically and culturally diverse and low socioeconomic students, noting an emphasis on comprehension as autonomous skills. The Four Resources model (Freebody &amp; Luke, 1990) is used to make the case for the integration of comprehension instruction with an emphasis on student cultural and community knowledge, and substantive intellectual and sociocultural content in elementary school curricula. Illustrations are drawn from research underway on the teaching of literacy in primary schools in low SES communities