Splitting Behavior of SnS_n-Polynomials

We analyze the probability that, for a fixed finite set of primes S, a random, monic, degree n polynomial f(x) with integer coefficients in a box of side B around 0 satisfies: (i) f(x) is irreducible over the rationals, with splitting field over the rationals having Galois group $S_n$; (ii) the polynomial discriminant Disc(f) is relatively prime to all primes in S; (iii) f(x) has a prescribed splitting type at each prime p in S. The limit probabilities as $B \to \infty$ are described in terms of values of a one-parameter family of measures on $S_n$, called splitting measures, with parameter $z$ evaluated at the primes p in S. We study properties of these measures. We deduce that there exist degree n extensions of the rationals with Galois closure having Galois group $S_n$ with a given finite set of primes S having given Artin symbols, with some restrictions on allowed Artin symbols for p<n. We compare the distributions of these measures with distributions formulated by Bhargava for splitting probabilities for a fixed prime $p$ in such degree $n$ extensions ordered by size of discriminant, conditioned to be relatively prime to $p$.Comment: 33 pages, v2 34 pages, introduction revise

Regions of the T cell receptor alpha and beta chains that are responsible for interactions with CD3.

The T cell antigen receptor consists of the Ti alpha/beta heterodimer which recognizes antigen, and the associated CD3 chains, thought to be involved in signal transduction. To understand the nature of the interaction between Ti and CD3, chimeric molecules which included the COOH-terminal segments of Ti alpha or beta linked to the extracellular segment of CD8, were transfected into a mutant T cell deficient in Ti beta chain expression and cell surface CD3. Both chimeric chains were required to express the chimeric Ti and to restore CD3 surface expression. CD8/Ti and CD3 cointernalized and coimmunoprecipitated. Stimulation of the chimeric receptor induced transmembrane signaling events and cell activation. These results demonstrate that the Ti alpha and beta COOH termini containing the transmembrane domains are sufficient for structural and functional coupling of Ti to CD3

A parabolic free boundary problem with Bernoulli type condition on the free boundary

Consider the parabolic free boundary problem $$\Delta u - \partial_t u = 0 \textrm{in} \{u>0\}, |\nabla u|=1 \textrm{on} \partial\{u>0\} .$$ For a realistic class of solutions, containing for example {\em all} limits of the singular perturbation problem $$\Delta u_\epsilon - \partial_t u_\epsilon = \beta_\epsilon(u_\epsilon) \textrm{as} \epsilon\to 0,$$ we prove that one-sided flatness of the free boundary implies regularity. In particular, we show that the topological free boundary $\partial\{u>0\}$ can be decomposed into an {\em open} regular set (relative to $\partial\{u>0\}$) which is locally a surface with H\"older-continuous space normal, and a closed singular set. Our result extends the main theorem in the paper by H.W. Alt-L.A. Caffarelli (1981) to more general solutions as well as the time-dependent case. Our proof uses methods developed in H.W. Alt-L.A. Caffarelli (1981), however we replace the core of that paper, which relies on non-positive mean curvature at singular points, by an argument based on scaling discrepancies, which promises to be applicable to more general free boundary or free discontinuity problems

Identification of Coulomb blockade and macroscopic quantum tunneling by noise

The effects of Macroscopic Quantum Tunneling (MQT) and Coulomb Blockade (CB) in Josephson junctions are of considerable significance both for the manifestations of quantum mechanics on the macroscopic scale and potential technological applications. These two complementary effects are shown to be clearly distinguishable from the associated noise spectra. The current noise is determined exactly and a rather sharp crossover between flux noise in the MQT and charge noise in the CB regions is found as the applied voltage is changed. Related results hold for the voltage noise in current-biased junctions.Comment: 6 pages, 3 figures, epl.cls include

On the controllability of delay-differential systems

Optimal control problems for systems described by delay differential equation