Paper surfaces and dynamical limits

It is very common in mathematics to construct surfaces by identifying the sides of a polygon together in pairs: For example, identifying opposite sides of a square yields a torus. In this article the construction is considered in the case where infinitely many pairs of segments around the boundary of the polygon are identified. The topological, metric, and complex structures of the resulting surfaces are discussed: In particular, a condition is given under which the surface has a global complex structure (i.e., is a Riemann surface). In this case, a modulus of continuity for a uniformizing map is given. The motivation for considering this construction comes from dynamical systems theory: If the modulus of continuity is uniform across a family of such constructions, each with an iteration defined on it, then it is possible to take limits in the family and hence to complete it. Such an application is briefly discussed.

Hydrogen peroxide and supercritical carbon dioxide: a new bleaching stage for Eucalyptus kraft-O(2) pulps

Kraft pulp is currently bleached largely by the elemental chlorine free (ECF) technology with oxygen, chlorine dioxide, and hydrogen as active agents. This technology brought about significant environmental improvements in relation to standard processes based on chlorine gas and hypochlorite, but there is still need for further improvements. This study presents a novel environmentally friendly bleaching stage - the so-called `hydrogen peroxide in supercritical carbon dioxide`, P((SC-CO2)) - that can be adapted to current ECF bleaching processes, with preference in cases where hydrogen peroxide is already used. In this study, the P((SC-CO2)) stage was evaluated as a replacement to the last peroxide stage of the D(EP)DP bleaching sequence and to the first peroxide stage of the D(EP)DP sequence, for an oxygen delignified eucalypt kraft-O(2) pulp. The P((SC-CO2)) stage was run with 0.5% hydrogen peroxide, at 15% consistency, 70 degrees C, and 73 bar. The reaction time was 30 min. The performances of regular P stages and the new P((SC-CO2)) stage were compared. Promising results were observed with the DEP((SC-CO2))DP sequence; the P((SC-CO2)) decreased kappa number from 2.7 to 2.1, and the hexenuronic acid groups from 17.0 to 12.4 mmol kg(-1). The P((SC-CO2)) stage showed poor performance when applied in the D(EP)DP((SC-CO2)) sequence. It is concluded that the process presents potential but requires further optimization to improve selectivity and efficiency.