Resource allocation based on cost efficiency

In this paper, we consider a resource allocation (RA) problem and develop an approach based on cost (overall) efficiency. The aim is to allocate some inputs among decision making units (DMUs) in such way that their cost efficiencies improve or stay unchanged after RA. We formulate a multi-objective linear programming problem using two different strategies. First, we propose an RA model which keeps the cost efficiencies of units unchanged. This is done assuming fixed technical and allocative efficiencies. The approach is based on the assumption that the decision maker (DM) may not have big changes in the structure of DMUs within a short term. The second strategy does not impose any restrictions on technical and allocative efficiencies. It guarantees that none of the cost efficiencies of DMUs get worse after RA, and the improvement for units is possible if it is feasible and beneficial. Two numerical examples and an empirical illustration are also provided.     

An Interactive Multiple Criteria Approach to Ranking Alternatives

In this paper we are concerned with ranking various orderings of a set of alternatives to a composite order as a multiple criteria problem. The orderings (called preference orderings) can be real preference orderings or any natural orderings. The objective is to find the most preferred order of the decision maker using the preference orderings as criteria.In principle, the problem can be formulated as a multiple objective linear programming problem using the model of Bowman and Colantoni and then solved with the interactive method proposed by Zionts and Wallenius. However, the fact that we are dealing with integer variables prohibits us from applying this approach as such. We discuss the problem formulation and propose a modified approach to that of Zionts and Wallenius for solving the problem.     

Linear differential equations with coefficients in weighted Bergman and Hardy spaces

Complex linear differential equations of the form

with coefficients in weighted Bergman or Hardy spaces are studied. It is shown, for example, that if the coefficient of belongs to the weighted Bergman space , where , for all , then all solutions are of order of growth at most , measured according to the Nevanlinna characteristic. In the case when all solutions are shown to be not only of order of growth zero, but of bounded characteristic. Conversely, if all solutions are of order of growth at most , then the coefficient is shown to belong to for all and .

Analogous results, when the coefficients belong to certain weighted Hardy spaces, are obtained. The non-homogeneous equation associated to is also briefly discussed.

     

Logic as a Science and Logic as a Theory: Remarks on Frege, Russell and the Logocentric Predicament

Since its publication in 1967, van Heijenoort??s paper, ??Logic as Calculus and Logic as Language?? has become a classic in the historiography of modern logic. According to van Heijenoort, the contrast between the two conceptions of logic provides the key to many philosophical issues underlying the entire classical period of modern logic, the period from Frege??s Begriffsschrift (1879) to the work of Herbrand, G?del and Tarski in the late 1920s and early 1930s. The present paper is a critical reflection on some aspects of van Heijenoort??s thesis. I concentrate on the case of Frege and Russell and the claim that their philosophies of logic are marked through and through by acceptance of the universalist conception of logic, which is an integral part of the view of logic as language. Using the so-called ??Logocentric Predicament?? (Henry M. Sheffer) as an illustration, I shall argue that the universalist conception does not have the consequences drawn from it by the van Heijenoort tradition. The crucial element here is that we draw a distinction between logic as a universal science and logic as a theory. According to both Frege and Russell, logic is first and foremost a universal science, which is concerned with the principles governing inferential transitions between propositions; but this in no way excludes the possibility of studying logic also as a theory, i.e., as an explicit formulation of (some) of these principles. Some aspects of this distinction will be discussed.     

Power control of optical CDMA star networks

In this paper, we apply the power control concept to optical CDMA star networks. Two approaches are considered, namely, centralized and distributed power control. Both approaches are used to optimize the optical transmit power and to maximize network capacity in terms of the number of users satisfying a target signal to interference (SIR) ratio. Centralized algorithms result in the optimum power vector while distributed algorithms are more suitable for practical system implementation and eliminate the need for a centralized control node. Both analytical and simulation results show significant improvement in the performance of the power controlled optical CDMA system. For instance, in a network of 31 nodes, a doubling of the capacity as compared to the non power control case is obtained. Furthermore, we show in the interference-limited case that the network performance is upper bounded by the number of nodes and the correlation properties of the employed code rather than network attenuation and optical fiber lengths. The concept of network partitioning is then introduced to simplify optimum power calculations. Using network partitioning, we find in the interference-limited case that the optical fibers after the star coupler are irrelevant to the optimum power evaluation.     

Simultaneous gas chromatographic determination of aliphatic C2−C20 n-carboxylic acids and their methyl esters using SE-30 and OV-351 quartz capillary columns

Summary Simultaneous determination of aliphatic C₂–C₂₀ carboxylic acids and their methyl esters was carried out using SE-30 and OV-351 quartz capillary columns with temperature programming. Complete resolution of all 36 components was achieved. On SE-30 the methyl ester and the corresponding free acid are eluted in turn, whereas on OV-351 acetic acid eluted after methyl octanoate, after which the C_n methyl ester and C_n-6 carboxylic acid (n>9) are eluted one after the other. A non-polar SE-30 column is better for long-chain acids giving sharp peaks without tailing, the analysis time of the mixture being less than 16 minutes. The weight response correction factors for compounds under optimum operating conditions are given.     

Ratio-based RTS determination in weight-restricted DEA models

This paper provides computationally efficient approaches for determining to which returns to scale (RTS) class a unit belongs in weight-restricted Data Envelopment Analysis (DEA) models. A non-traditional computational algorithm is introduced. The suggested approach is based on the calculation of certain ratios within the data set and offers obvious computational advantages over the traditional approaches involving the solution of standard DEA models. Some theorems and algorithms are given. Computational advantages of the provided results are discussed and one of the algorithms is illustrated using real world data.     

Interactive evolutionary multi-objective optimization for quasi-concave preference functions

We present a new hybrid approach to interactive evolutionary multi-objective optimization that uses a partial preference order to act as the fitness function in a customized genetic algorithm. We periodically send solutions to the decision maker (DM) for her evaluation and use the resulting preference information to form preference cones consisting of inferior solutions. The cones allow us to implicitly rank solutions that the DM has not considered. This technique avoids assuming an exact form for the preference function, but does assume that the preference function is quasi-concave. This paper describes the genetic algorithm and demonstrates its performance on the multi-objective knapsack problem.     

A contribution to the chemical aspects of precise mass spectrometric analysis or uranium

The chemical aspects of isotopic fractionation in a multiple filament thermal ionization source were investigated. Samples of uranium were loaded as nitrates, chlorides and sulphates. The dependence of measured isotopic ratios on the filament material and the chemical form of the loading solution was studied. The dependence of the formation of uranium and its oxide ions on various chemical and instrumental conditions were investigated using tungsten and rhenium filaments.