GG-prime and GG-primary GG-ideals on GG-schemes

Let $G$ be a flat finite-type group scheme over a scheme $S$, and $X$ a noetherian $S$-scheme on which $G$-acts. We define and study $G$-prime and $G$-primary $G$-ideals on $X$ and study their basic properties. In particular, we prove the existence of minimal $G$-primary decomposition and the well-definedness of $G$-associated $G$-primes. We also prove a generalization of Matijevic-Roberts type theorem. In particular, we prove Matijevic-Roberts type theorem on graded rings for $F$-regular and $F$-rational properties.Comment: 54pages, added Example 6.16 and the reference [8]. The final versio

Boundary WZW, G/H, G/G and CS theories

We extend the analysis of the canonical structure of the Wess-Zumino-Witten theory to the bulk and boundary coset G/H models. The phase spaces of the coset theories in the closed and in the open geometry appear to coincide with those of a double Chern-Simons theory on two different 3-manifolds. In particular, we obtain an explicit description of the canonical structure of the boundary G/G coset theory. The latter may be easily quantized leading to an example of a two-dimensional topological boundary field theory.Comment: latex, 33 pages, 21 figure

qQCD2_2 and G/G model

The 2D lattice gauge theory with a quantum gauge group $SL_q(2)$ is considered. When $q=e^{i\frac{2\pi}{k+2}}$, its weak coupling partition function coincides with the one of the G/G coset model ({\em i.e.} equals the Verlinde numbers). However, despite such a remarkable coincidence, these models are not equivalent but, in some certain sense, dual to each other.Comment: 7pp, NBI-HE-93-27, revised. Small changes: several fixed inaccuracies + updated reference

Sorption Mechanism of Lead Ions From Aqueous Solution By Imperata Cylindrica Dried Leaf Particle: Effect of Temperatures

This study was conducted to investigate the sorption mechanism of Pb2+ ions from aqueous solution onto Imperata cylindrica (IC) dried leaf particles. The effect of temperatures (30, 35 and 40oC) was scrutinised from a batch adsorption system using a synthetic liquid waste containing Pb2+ ions. Adsorption of lead ions mechanism was investigated by intraparticle diffusion model. The results showed that higher adsorption rate occurred at higher temperature, and obeyed the pseudo second order adsorption model. The overall rate of lead uptake was found to be controlled by external mass transfer at the beginning of adsorption, then gradually changes to intraparticle diffusion controlled at a later stage. The intraparticle diffusion constant increased with increasing temperature. The values of effective diffusion coefficient (Di) increased at higher temperatures, which were 5.5466 × 10−9, 6.8215 × 10−9, and 7.3726 × 10−9 m2/s at 30, 35, and 40 ◦C, respectivel

GG-martingale representation in the GG-L'evy setting

In this paper we give the decomposition of a martingale under the sublinear expectation associated with a $G$-L'evy process X with finite activity and without drift. We prove that such a martingale consists of an Ito integral w.r.t. continuous part of a $G$-L'evy process, compensated Ito-L'evy integral w.r.t. jump measure associated with $X$ and a non-increasing continuous $G$-martingale starting at 0

The gluon polarization ΔG/G\Delta G/G at COMPASS

The COMPASS experiment will determine the gluon polarization in the nucleon $\Delta G/G$ from the double helicity asymmetry measured in the scattering of a 160 GeV muon beam on a longitudinally polarized deuteron target, by selecting the photon-gluon fusion reaction. This reaction can be tagged either by the production of open charm, or by the production of high $p_T$ hadron pairs. The first asymmetry obtained with the latter method is presented.Comment: 4 pages, 7 figure

Random G-expectations

We construct a time-consistent sublinear expectation in the setting of volatility uncertainty. This mapping extends Peng's G-expectation by allowing the range of the volatility uncertainty to be stochastic. Our construction is purely probabilistic and based on an optimal control formulation with path-dependent control sets.Comment: Published in at http://dx.doi.org/10.1214/12-AAP885 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

G/GG/G--Topological Field Theories by Cosetting GkG_k

$G/G$ topological field theories based on $G_k$ WZW models are constructed and studied. These coset models are formulated as Complex BRST cohomology in $G^c_k$, the complexified level $k$ current algebra. The finite physical spectrum corresponds to the conformal blocks of $G_k$ .The amplitudes for $G/G$ theories are argued to be given in terms of the $G_k$ fusion rules. The $G_k/G_k$ character is the Kac-Weyl numerator of $G_k$ and is interpreted as an index. The Complex BRST cohomology is found to contain states of arbitrary ghost number. Intriguing similarities of $G/G$ to $c\leq 1$ matter systems coupled to two dimensional gravity are pointed out.Comment: 40 pages (52/2 if use the little option of harvmac.tex