Search for Scalar Leptoquarks with polarized protons (and neutrons) at HERA and future ep(n)ep(n) Machines

The effects of Scalar Leptoquarks in various channels have been analysed for the HERA collider and also for an eventual new $ep$ machine running at higher energies. We emphasize the relevance of polarized beams.Comment: Latex file, 3 pages and 3 ps fig. Need style files : twoside,fleqn,espcrc2,epsfig. To appear in the proceedings of the DIS99 Workshop, DESY-Zeuthen, Germany, April 199

Density results for Sobolev, Besov and Triebel--Lizorkin spaces on rough sets

We investigate two density questions for Sobolev, Besov and Triebel--Lizorkin spaces on rough sets. Our main results, stated in the simplest Sobolev space setting, are that: (i) for an open set $\Omega\subset\mathbb R^n$, $\mathcal{D}(\Omega)$ is dense in $\{u\in H^s(\mathbb R^n):{\rm supp}\, u\subset \overline{\Omega}\}$ whenever $\partial\Omega$ has zero Lebesgue measure and $\Omega$ is "thick" (in the sense of Triebel); and (ii) for a $d$-set $\Gamma\subset\mathbb R^n$ ($0<d<n$), $\{u\in H^{s_1}(\mathbb R^n):{\rm supp}\, u\subset \Gamma\}$ is dense in $\{u\in H^{s_2}(\mathbb R^n):{\rm supp}\, u\subset \Gamma\}$ whenever $-\frac{n-d}{2}-m-1<s_{2}\leq s_{1}<-\frac{n-d}{2}-m$ for some $m\in\mathbb N_0$. For (ii), we provide concrete examples, for any $m\in\mathbb N_0$, where density fails when $s_1$ and $s_2$ are on opposite sides of $-\frac{n-d}{2}-m$. The results (i) and (ii) are related in a number of ways, including via their connection to the question of whether $\{u\in H^s(\mathbb R^n):{\rm supp}\, u\subset \Gamma\}=\{0\}$ for a given closed set $\Gamma\subset\mathbb R^n$ and $s\in \mathbb R$. They also both arise naturally in the study of boundary integral equation formulations of acoustic wave scattering by fractal screens. We additionally provide analogous results in the more general setting of Besov and Triebel--Lizorkin spaces.Comment: 38 pages, 6 figure

Spectroscopy of the optical Einstein ring 0047-2808

We present optical and near-infrared spectroscopic observations of the optical Einstein ring 0047-2808. We detect both [OIII] lines 4959, 5007 near 2.3 micron, confirming the redshift of the lensed source as z=3.595. The Ly-a line is redshifted relative to the [OIII] line by 140+-20 km/s. Similar velocity shifts have been seen in nearby starburst galaxies. The [OIII] line is very narrow, 130 km/s FWHM. If the ring is the image of the centre of a galaxy the one-dimensional stellar velocity dispersion sigma=55 km/s is considerably smaller than the value predicted by Baugh et al. (1998) for the somewhat brighter Lyman-break galaxies. The Ly-a line is significantly broader than the [OIII] line, probably due to resonant scattering. The stellar central velocity dispersion of the early-type deflector galaxy at z=0.485 is 250+-30 km/s. This value is in good agreement both with the value predicted from the radius of the Einstein ring (and a singular isothermal sphere model for the deflector), and the value estimated from the D_n-sigma relation.Comment: 7 pages, 3 figures, accepted for publication in MNRA

Physical degrees of freedom in stabilized brane world models

We consider brane world models with interbrane separation stabilized by the Goldberger-Wise scalar field. For arbitrary background, or vacuum configurations of the gravitational and scalar fields in such models, we construct the second variation Lagrangian, study its gauge invariance, find the corresponding equations of motion and decouple them in a suitable gauge. We also derive an effective four-dimensional Lagrangian for such models, which describes the massless graviton, a tower of massive gravitons and a tower of massive scalars. It is shown that for a special choice of the background solution the masses of the graviton excitations may be of the order of a few TeV, the radion mass of the order of 100 GeV, the inverse size of the extra dimension being tens of GeV. In this case the coupling of the radion to matter on the negative tension brane is approximately the same as in the unstabilized model with the same values of the fundamental five-dimensional energy scale and the interbrane distance.Comment: 17 pages, LaTeX, corrected typos, amended the normalization constants of the scalar modes and their coupling constants to matte