A sequential injection system for the spectrophotometric determination of calcium, magnesium and alkalinity in water samples.

A sequential injection methodology for the spectrophotometric determination of calcium, magnesium and alkalinity in water samples is proposed. A single manifold is used for the determination of the three analytes, and the same protocol sequence allows the sequential determination of calcium and magnesium (the sum corresponds to the water hardness). The determination of both metals is based on their reaction with cresolphtalein complexone; mutual interference is minimized by using 8-hydroxyquinoline for the determination of calcium and ethylene glycol-bis(beta-aminoethyl ether)-N,N,N',N'-tetraacetic acid (EGTA) for the determination of magnesium. Alkalinity determination is based on a reaction with acetic acid, and corresponding color change of Bromcresol Green. Working ranges of 0.5 - 5 mg dm(-3) for Ca, 0.5 - 10 mg dm(-3) for Mg, and 10 - 100 mg HCO3- dm(-3), for alkalinity have been achieved. The results for water samples were comparable to those of the reference methods and to a certified reference water sample. RSDs lower than 5% were obtained, a low reagent consumption and a reduced volume of effluent have been accomplished. The determination rate for calcium and magnesium is 80 h(-1), corresponding to 40 h(-1) per element, while 65 determinations of alkalinity per hour could be carried out.     

Peculiarities of Adsorption of Some Polar Substances from Vapor Phase on a Microporous Clay Adsorbent

The adsorption of polar organic substances (methanol, pyridine, and acetonitrile) and water was studied from the vapor phase on microporous adsorbent prepared by the substitution of polyhydroxyaluminum ions for the sodium ions of natural montmorillonite clay. The differential isosteric heats of adsorption of these substances were calculated and analyzed in a wide range of fillings.     

Optimization of Mass Transfer Processes in the Zone of the Air Electrode of a Fuel Cell with a Solid Polymer Electrolyte

A two-dimensional mathematical model for the transport of reactants in a fuel cell with a solid polymer electrolyte is developed. The model is used for analyzing spatial distributions of the concentration of reactants and current density over the cell. The effect of the catalytic-layer activity, reactant speed, bipolar-plate geometry, thickness and porosity of current collector and/or gas-diffusion sublayer, and the reaction mixture composition on the fuel cell efficiency is estimated theoretically and experimentally.     

Generic Well-Posedness of Constrained Variational Problems Without Convexity Assumptions

In our previous work, a generic well-posedness result (with respect to variations of the integrand of the integral functional) without the convexity condition was established for a class of optimal control problems satisfying the Cesari growth condition. In this paper, we extend this generic well-posedness result to classes of constrained variational problems in which the values at the endpoints and constraint maps are also subject to variations.     

Augmented Lagrangian Algorithms Based on the Spectral Projected Gradient Method for Solving Nonlinear Programming Problems

The spectral projected gradient method SPG is an algorithm for large-scale bound-constrained optimization introduced recently by Birgin, Martínez, and Raydan. It is based on the Raydan unconstrained generalization of the Barzilai-Borwein method for quadratics. The SPG algorithm turned out to be surprisingly effective for solving many large-scale minimization problems with box constraints. Therefore, it is natural to test its perfomance for solving the sub-problems that appear in nonlinear programming methods based on augmented Lagrangians. In this work, augmented Lagrangian methods which use SPG as the underlying convex-constraint solver are introduced (ALSPG) and the methods are tested in two sets of problems. First, a meaningful subset of large-scale nonlinearly constrained problems of the CUTE collection is solved and compared with the perfomance of LANCELOT. Second, a family of location problems in the minimax formulation is solved against the package FFSQP.     

Optimality Conditions and Geometric Properties of a Linear Multilevel Programming Problem with Dominated Objective Functions

In this paper, a model of a linear multilevel programming problem with dominated objective functions (LMPPD(l)) is proposed, where multiple reactions of the lower levels do not lead to any uncertainty in the upper-level decision making. Under the assumption that the constrained set is nonempty and bounded, a necessary optimality condition is obtained. Two types of geometric properties of the solution sets are studied. It is demonstrated that the feasible set of LMPPD(l) is neither necessarily composed of faces of the constrained set nor necessarily connected. These properties are different from the existing theoretical results for linear multilevel programming problems.     

On the Existence of Solutions to Vector Quasivariational Inequalities and Quasicomplementarity Problems with Applications Break to Traffic Network Equilibria

For vector quasivariational inequalities involving multifunctions in topological vector spaces, an existence result is obtained without a monotonicity assumption and with a convergence assumption weaker than semicontinuity. A new type of quasivariational inequality is proposed. Applications to quasicomplementarity problems and traffic network equilibria are considered. In particular, definitions of weak and strong Wardrop equilibria are introduced for the case of multivalued cost functions.     

Dynamic Strategic Pricing and Speed of Diffusion

Defining speed of diffusion as the amount of time it takes to get from one penetration level to a higher one, we introduce a dynamic model in which we study the link between pricing policy, speed of diffusion, and number of competitors in the market. Our analysis shows that, in the case of strategic (oligopolistic) competition, the speed of diffusion has an important influence on the optimal pricing policy. In particular, we find that higher speeds of diffusion create an incentive to strategically interacting firms to lower their prices.     

John Hawkes (1944-2001)

In his curriculum vitae, John Hawkes lists his research interestsas geometric measure theory, probability (Lévy processes),and potential theory (probabilistic). In fact, he made significantcontributions to all three areas, and there are strong relationshipsbetween them. He used both geometric measure theory and potentialtheory as tools for his study of the trajectories of particularLévy processes, but in many cases he needed to developthe tool before it was ready to be used. We will summarise hisresearch later, but first we discuss what is known of his lifehistory.     

On division rings with algebraic commutators of bounded degree

We shall answer several questions concerning additive or multiplicative commutators in a division ring which are algebraic of bounded degree over its center.