Cellular automata for the spreading of technologies in socio-economic systems

We introduce an agent-based model for the spreading of technological developments in socio-economic systems where the technology is mainly used for the collaboration/interaction of agents. Agents use products of different technologies to collaborate with each other which induce costs proportional to the difference of technological levels. Additional costs arise when technologies of different providers are used. Agents can adopt technologies and providers of their interacting partners in order to reduce their costs leading to microscopic rearrangements of the system. Analytical calculations and computer simulations revealed that starting from a random configuration of different technological levels a complex time evolution emerges where the spreading of advanced technologies and the overall technological progress of the system are determined by the amount of advantages more advanced technologies provide, and by the structure of the social environment of agents. We show that agents tend to form clusters of identical technological level with a power law size distribution. When technological progress arises, the spreading of technologies in the system can be described by extreme order statistics.     

Absolutely convergent Fourier series, classical function classes and Paley’s theorem

This is a survey paper on the recent progress in the study of the continuity and smoothness properties of a function f with absolutely convergent Fourier series. We give best possible sufficient conditions in terms of the Fourier coefficients of f which ensure the belonging of f either to one of the Lipschitz classes Lip(α) and lip(α) for some 0 < α ≤ 1, or to one of the Zygmund classes Zyg(α) and zyg(α) for some 0 < α ≤ 2. We also discuss the termwise differentiation of Fourier series. Our theorems generalize those by R. P. Boas Jr., J. Németh and R. E. A. C. Paley, and a number of them are first published in this paper or proved in a simpler way.     

Comparison of separation performances of amylose- and cellulose-based stationary phases in the high-performance liquid chromatographic enantioseparation of stereoisomers of β-lactams

High-performance liquid chromatographic methods were developed for the separation of the enantiomers of 19 β-lactams. The direct separations were performed on chiral stationary phases containing either amylose tris(3,5-dimethylphenylcarbamate), (Kromasil® AmyCoat? column) or cellulose tris(3,5-dimethylphenylcarbamate), (Kromasil® CelluCoat? column) as chiral selector. The different methods were compared in systematic chromatographic examinations. The separations were carried out with good selectivity and resolution. The AmyCoat? and CelluCoat? columns appear to be highly complementary. The best separations of bi- and tricyclic β-lactam stereoisomers were obtained with the AmyCoat? column, while the 4-aryl-substituted β-lactams were better separated on the CelluCoat? column. The elution sequence was determined in all cases; no general rule could be established.     

Synthesis of Vinca Alkaloids and Related Compounds. LXV. Preparation of 7-Methoxytryptamine

7-Methoxytryptamine (6a) was prepared from cheap and easily available starting materials by using the Abramovitch-Shapiro method.     

Absolute convergence of multiple Fourier series revisited

In a recent paper [4], Gogoladze and Meskhia generalized the classical results of Bernstein, Szász, Zygmund and others related to absolute convergence of single trigonometric Fourier series. Our aim is to extend these results from single to multiple Fourier series. To this effect, we introduce the notions of multiplicative moduli of continuity and that of smoothness. Multiplicative Lipschitz classes of functions in several variables, and functions of bounded s-variation in the sense of Vitali are also considered.     

A fuzzy-stochastic OWA model for robust multi-criteria decision making

All realistic Multi-Criteria Decision Making (MCDM) problems face various kinds of uncertainty. Since the evaluations of alternatives with respect to the criteria are uncertain they will be assumed to have stochastic nature. To obtain the uncertain optimism degree of the decision maker fuzzy linguistic quantifiers will be used. Then a new approach for fuzzy-stochastic modeling of MCDM problems will be introduced by merging the stochastic and fuzzy approaches into the OWA operator. The results of the new approach, entitled FSOWA, give the expected value and the variance of the combined goodness measure for each alternative. Robust decision depends on the combined goodness measures of alternatives and also on the variations of these measures under uncertainty. In order to combine these two characteristics a composite goodness measure will be defined. The theoretical results will be illustrated in a watershed management problem. By using this measure will give more sensitive decisions to the stakeholders whose optimism degrees are different than that of the decision maker. FSOWA can be used for robust decision making on the competitive alternatives under uncertainty.     

Characterization of the network properties of poly(ethylene glycol)–acrylate hydrogels prepared by variations in the ethanol–water solvent composition during crosslinking copolymerization

The characteristics of poly(ethylene glycol) (PEG)–acrylate hydrogel networks were investigated as a function of the ethanol–water solvent composition during free‐radical crosslinking copolymerization. Macromonomer (88% ω‐methoxy‐PEG–acrylate and 10% ω‐phenoxy‐PEG–acrylate) and crosslinker (2% PEG–diacrylate) concentrations were kept constant. As the copolymerization progressed, the polymer solution in 100% ethanol became increasingly turbid, indicating the development of a heterogeneous network structure. In 100% water, however, the initially turbid polymer solution became increasingly transparent as the crosslinking copolymerization progressed. All the gels were optically clear upon equilibration in water. Kinetic studies, with attenuated total reflectance‐infrared, showed a long induction period, along with a lowered reaction rate, in 100% ethanol, and a decrease in conversion with an increase in ethanol content. These results agree with the UV analysis of the sol fractions, which indicated an increase in the amounts of unreacted PEG–acrylates with an increase in the ethanol content. The gels which were formed with a high ethanol concentration exhibited lower Young's modulus and higher swelling ability, suggesting that the network structure was significantly affected by the solvent composition during free‐radical crosslinking copolymerization. From the stress–strain and swelling experiments, the Flory–Huggins interaction parameter was evaluated. The creep characteristics of the hydrogels were modeled with two Kelvin elements. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 2677–2684, 2002