Zur Problematik individueller thermodynamischer Aktivitätskoeffizienten einzelner Ionensorten in Elektrolytlösungen hoher Konzentration

On the Individual Thermodynamic Activity Coefficients of Single Ion Species in Electrolyte Solutions at High Concentrations The individual activity coefficients of the single ion species, which are produced by dissociation of aqueous electrolytes, are necessary for the thermodynamic treatment of equilibrations and processes involving electrolytes. The determination of these values is one of the basic quests of electrochemistry and a controversial topic. This problem is unsolvable using classical thermodynamics. In this paper a mathematical method is shown, which can be used to split the mean activity coefficients into the values for the individual ion species of an electrolyte. For this determination the mean activity coefficients have to be expressed in the power form of equation. The concept based on the adaptation of a product function for the concentration development of the mean activity coefficients to the experimental data and their separation into factor functions of a predefined structure, which represent the concentration development of the individual activity coefficients of the single ion species of the electrolyte. This mathematical method was used to calculate the individual activity coefficients of the single ion species of alkali chlorides, alkaline earth chlorides, alkaline earth perchlorates, hydrohalic acids and alkali hydroxides. In summary, all the calculated single ion activity coefficients are in good agreement with the expected theoretical considerations. A proportionality to the reciprocal diameter of the unhydrated cation is clearly recognizable. The calculated individual activity coefficients correspond in every case with the assumption about their size, which can be reproduced using a variety of electrochemical investigations and experiments.     

Weighted approximation of continuous functions by sequences of linear positive operators

In this work we obtain, under suitable conditions, theorems of Korovkin type for spaces with different weight, composed of continuous functions defined on unbounded regions. These results can be seen as an extension of theorems by Gadjiev in [4] and [5].     

Characterizability of the Group ^2Dp（3） by its Order Components,Where p ≥ 5 is a Prime Number Not of the Form 2^m ＋ 1

The author will prove that the group ^2Dp（3） can be uniquely determined by its order components, where p ≠ 2^m ＋ 1 is a prime number, p ≥ 5. More precisely, if OC（G） denotes the set of order components of G, we will prove OC（G） = OC（^2Dp（3）） if and only if G is isomorphic to ^2Dp（3）. A main consequence of our result is the validity of Thompson＇s conjecture for the groups under consideration.     

Majorization, range inclusion, and factorization for bounded linear operators

In this paper, relationships among the concepts, majorization, range inclusion, and factorization, are studied in a general setting for bounded linear operators. Some applications of these concepts are given.

     

A survey on the continuous nonlinear resource allocation problem

Our problem of interest consists of minimizing a separable, convex and differentiable function over a convex set, defined by bounds on the variables and an explicit constraint described by a separable convex function. Applications are abundant, and vary from equilibrium problems in the engineering and economic sciences, through resource allocation and balancing problems in manufacturing, statistics, military operations research and production and financial economics, to subproblems in algorithms for a variety of more complex optimization models. This paper surveys the history and applications of the problem, as well as algorithmic approaches to its solution. The most common techniques are based on finding the optimal value of the Lagrange multiplier for the explicit constraint, most often through the use of a type of line search procedure. We analyze the most relevant references, especially regarding their originality and numerical findings, summarizing with remarks on possible extensions and future research.     

Nonparametric inference on the difference of location parameters of correlated variables from fragmentary samples

Summary In this paper, two types of robust estimators and approximate confidence intervals for the difference of location parameters of correlated random variables are proposed and investigated when some observations are missing. It is shown that the suggested estimators are consistent and asymptotically normally distributed. In addition, the proposed approximate confidence intervals are also shown to enjoy some nice asymptotic properties.     

On the cauchy problem for a class of degenerate differential equations with Lipschitz right-hand side

This note deals with an application of the fixed point theorem for multivalued contraction mappings to the study of degenerate differential equations with Lipschitz right-hand side and with degeneration determined by a closed surjective linear operator.     

Solving nonlinear integer programs with large-scale optimization software

This paper describes recent experience in tackling large nonlinear integer programming problems using the MINOS large-scale optimization software. A technique is presented for extending the constrained search approach used in MINOS to exploring integer-feasible solutions once a continuous optimal solution is obtained. Computational experience with this approach is described for two classes of problems: quadratic assignment problems and pipeline network design problems.     

Optimal sequencing in the presence of setup times for tow/barge traffic through a river lock

Queues of tow/barges form when a river lock is rendered inoperable due to lock malfunction, a tow/barge accident or adverse lock operating conditions. In this paper, we develop model formulations that allow the queue to be cleared using a number of differing objectives. Of particular interest is the presence of different setup times between successive passages of tow/barges through the lock. Dependent on the objective chosen, we are able to show that certain ordering protocols may be used to markedly reduce the sequencing search space for N tow/barges from the order of N! to 2^N. We present accompanying linear and nonlinear integer programming formulations and carry out computational experiments on a representative set of problems.     

MONOTONIZATION IN GLOBAL OPTIMIZATION

A general monotonization method is proposed for converting a constrained programming problem with non-monotone objective function and monotone constraint functions into a monotone programming problem. An equivalent monotone programming problem with only inequality constraints is obtained via this monotonization method. Then the existing convexification and concavefication methods can be used to convert the monotone programming problem into an equivalent better-structured optimization problem.