We present model predictions for the spectrum of CP N −1 in a periodic box and use them to interpret the strong finite size effects observed in lattice simulations at medium values of N. The asymptotic scaling behaviour of alternative lattice actions is discussed along with some aspects of multigrid algorithm efficiency. Introduction There has been considerable recent interest in simulations of...

 An $(n, r)$-arc is a set of $n$ points of a projective plane such that some $r$, but no $r+1$ of them, are collinear. The maximum size of an $(n, r)$-arc in  PG(2, q) is denoted by $m_r(2,q)$. In this paper thirteen new $(n, r)$-arc in  PG(2,,29) and a table with the best known lower and upper bounds on $m_r(2,29)$ are presented. The results are obtained by non-exhaustive local computer search.

in order to improve uv and visible lights photocatalytic activities of the pure anatase tio2, a novel and efficient n-doped tio2 photocatalyst was prepared by sol-gel method. n-doped titania is prepared using triethylamine (with difference molar ratios) as the nitrogen source. the crystalline structure, morphology, particle size, absorbance and band-gap and chemical structure of n-doped tio2 wa...