Varieties without minimal generators

While many familiar varieties have a minimal varietal generator, i.e., a regular projective finitely presentable regular generator such that none of its retracts is a regular generator, and even a unique one, we present (a) a variety having no minimal varietal generator at all and (b) a variety having two non-isomorphic minimal varietal generators. Moreover we demonstrate that the same effects can happen with respect to a weaker notion of minimality and are common even in module categories. Received April 7, 1999; accepted in final form July 10, 2000.     

The discrete maximum principle for Galerkin solutions of elliptic problems

This paper provides an equivalent characterization of the discrete maximum principle for Galerkin solutions of general linear elliptic problems. The characterization is formulated in terms of the discrete Green’s function and the elliptic projection of the boundary data. This general concept is applied to the analysis of the discrete maximum principle for the higher-order finite elements in one-dimension and to the lowest-order finite elements on simplices of arbitrary dimension. The paper surveys the state of the art in the field of the discrete maximum principle and provides new generalizations of several results.     

A MILP approach to the optimization of banner display strategy to tackle banner blindness

The paper addresses the issue of online advertising efficiency in the context of the “banner blindness” phenomenon. We extend the traditional exposure metric of banner efficiency by allowing the effect of a banner display (exposure effect, EE) to vary depending on the sequence of pages that lead to the display. Within a user session on the given website, we assume that EE differs for a banner carried over from the previous page (low EE), from the case where the banner suddenly appears in a previously unoccupied place (high EE). This assumption implies that a banner’s efficiency can be increased by optimising its placement throughout the website’s structure; to this end, we develop a simple model framework. First, we formalize the efficiency metric based on expected total EE for a representative user, using a Markov chain model estimable from the website’s clickstream data. Next, we formulate the selection of efficient banner placement as a mixed integer linear programming problem. We consider two scenarios: (i) a static one, where banner placement is fixed throughout the day, and (ii) a dynamic one, where banner placement is allowed to vary in different time intervals in order to respond to changes in browsing patterns. Finally, we demonstrate the use of our model on an empiric case study, and analyse the effect of different parameter settings.     

Extraction of calcium and strontium into nitrobenzene by using a synergistic mixture of hydrogen dicarbollylcobaltate and tetraisopropyl methylene diphosphonate

Extraction of microamounts of calcium and strontium by a nitrobenzene solution of hydrogen dicarbollylcobaltate (H⁺B⁻) in the presence of tetraisopropyl methylene diphosphonate [T(iPr)MDP, L] has been investigated. The equilibrium data have been explained assuming that the species HL⁺, \textHL₂ ⁺ {\text{HL}}_{2}^{ + } , \textML₂^{2 +} {\text{ML}}_{2}^{2 + } and \textML₃^{2 +} {\text{ML}}_{3}^{2 + } (M²⁺ = Ca²⁺, Sr²⁺) are extracted into the organic phase. The values of extraction and stability constants of the cationic complexes in nitrobenzene saturated with water have been determined. In the considered nitrobenzene medium, it was found that the stability constants of the \textCaL_n^{2 +} {\text{CaL}}_{n}^{2 + } complexes, where n = 2, 3 and L is T(iPr)MDP, are somewhat higher than those of the corresponding complex species \textSrL_n^{2 +} {\text{SrL}}_{n}^{2 + } .     

Almost Geodesic Mappings and Projections of the Sphere

Mathematical Notes -     

Dithiols as more effective than monothiols in protecting biomacromolecules from free-radical-mediated damage: in vitro oxidative degradation of high-molar-mass hyaluronan

Oxidative stress and the resulting damage to cellular and extracellular components has been observed in a variety of degenerative processes, including degenerative joint disorders, where high-molar-mass hyaluronan (HA) is often found to be massively degraded. The present study sought to test the hypothesis that dithiols are more effective in protecting biomacromolecules from free-radicalmediated damage than monothiols. The materials/thiols tested included bucillamine (BUC), dithioerythritol (DTE), dithiothreitol (DTT) and glutathione (GSH), as a reference, for their effectiveness in protecting HA from oxidative degradation induced in vitro. Since HA degradation results in a decrease in its dynamic viscosity, rotational viscometry was applied to follow HA oxidative degradation. The free-radical-scavenging activities of the thiols tested were determined by 2,2′-azino-bis(3-ethylbenzthiazoline-6-sulphonic acid) (ABTS) and di(phenyl)-(2,4,6-trinitrophenyl)iminoazanium (DPPH) assays. It was found that all the dithiols in the concentration range tested protected HA from the oxidative degradation. On the other hand, monothiol GSH exerted protection only at high concentrations (10 μmol L^?1 and 100 μmol L^?1) and 1 μmol L^?1 of GSH even exhibited a prodegradative effect. The ABTS assay revealed free-radical scavenging activities in the following order: BUC, DTT, DTE, GSH, and that of the DPPH assay: BUC, DTE, DTT, GSH. In conclusion, it was demonstrated that dithiols may be more effective than monothiols in affording biomacromolecule protection from oxidative degradation.