Regular population monotonic allocation schemes

The paper introduces a refinement of the notion of population monotonic allocation scheme, called regular population monotonic allocation scheme (regularpmas). This refinement is based on economic situations in which players may have to select new partners from a set of potential players and in which there exist certain capacity constraints. A sufficient condition for the existence of a regularpmas is given. For the class of games with regularpmas, we prove that the core coincides with the Davis and Maschler and the Mas-Colell bargaining sets.     

The influence of slits on sound transmission through a lightweight partition

In this paper the influence on sound reduction index of the length and the depth of sound leaks at the perimeter of lightweight partitions was examined. It was shown that the most important decrease on sound reduction index is caused by the first slit between lightweight partition and one of the structural members. When the length of the slit is increased, the decrease on sound reduction index is less significative. Calculated results show the same effects as measured ones.     

Structure and electrochemical behaviour of 4,7-diazaheptyl-trimethoxy-silane and vinyl-trialkoxy-silane adsorbed at silver surface

Novel self-assembled monolayers were obtained on silver using 4,7-diazaheptyl-trimethoxy-silane (SiN) and vinyl-trialkoxy-silane (SiVA, where the alkyl group is 3,6,9,12,15,18,21,24,27,30,33,36,39,42,45,48,51,54,57,60-eicozaoxa- hexaheptaconan). It was shown that thus modified metal surface was protected against electrooxidation. A densely packed monolayer remained stable and did not desorb from the Ag electrode on the potential cycling. The structure of SiN and SiVA as well as their complexes with Li⁺ cations were calculated and visualised by the AM1d and PM5 semi-empirical methods.     

Dielectric relaxation analysis of starch oligomers and polymers with respect to their chain length

Starch belongs to the polyglucan group. This type of polysaccharide shows a broad β-relaxation process in dielectric spectra at low temperatures, which has its molecular origin in orientational motions of sugar rings via glucosidic linkages. This chain dynamic was investigated for α(1,4)-linked starch oligomers with well-defined chain lengths of 2, 3, 4, 6, and 7 anhydroglucose units (AGUs) and for α(1,4)-polyglucans with average degrees of polymerization of 5, 10, 56, 70, and so forth (up to 3000; calculated from the mean molecular weight). The activation energy (E_a) of the segmental chain motion was lowest for dimeric maltose (E_a = 49.4 ± 1.3 kJ/mol), and this was followed by passage through a maximum at a degree of polymerization of 6 (E_a = 60.8 ± 1.8 kJ/mol). Subsequently, E_a leveled off at a value of about 52 ± 1.5 kJ/mol for chains containing more than 100 repeating units. The results were compared with the values of cellulose-like oligomers and polymers bearing a β(1,4)-linkage. Interestingly, the shape of the E_a dependency on the chain length of the molecules was qualitatively the same for both systems, whereas quantitatively the starch-like substances generally showed higher E_a values. Additionally, and for comparison, three cyclodextrins were measured by dielectric relaxation spectroscopy. The ringlike molecules, with 6, 7, and 8 α(1,4)-linked AGUs, showed moderately different types of dielectric spectra. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 188–197, 2004     

A nucleophilic substitution reaction in microemulsions based on either an alcohol ethoxylate or a sugar surfactant

A nucleophilic substitution reaction between 4-tert-butylbenzyl bromide and a series of iodide salts has been performed in oil-in-water microemulsions based on either a fatty alcohol ethoxylate or a sugar surfactant. The reaction kinetics was compared with the kinetics of the same reaction performed in a microhomogeneous reaction medium, d-MeOH. Previous results showing a particularly high reactivity in the microemulsion based on the fatty alcohol ethoxylate was confirmed. It was shown that in both microemulsions the reaction rate was almost independent of the choice of counterion to iodide. This indicates that complexation of the cation with the surfactant headgroup, which, in particular, could have taken place with surfactants containing oligooxyethylene chains (a “crown ether effect”), seems not to be of importance.

¹²⁷I NMR studies, as well as quadrupole splitting experiments performed by ²H NMR, indicate that there is a certain accumulation of iodide at the oil–water interface of the microemulsions. It is difficult to draw any quantitative conclusions in this respect, however.

The results obtained in this study, combined with results from previous investigations of the same reaction, indicate that the unexpectedly high reactivity obtained in the microemulsion based on a surfactant containing an oligooxyethylene headgroup is most probably due to the nucleophile being poorly solvated when present in the headgroup layer of such a microemulsion. Poorly solvated anions are known to be highly reactive nucleophiles.     

Artificial boundary conditions for Petrovsky systems of second order in exterior domains and in other domains of conical type

The approximation of solutions to boundary value problems on unbounded domains by those on bounded domains is one of the main applications for artificial boundary conditions. Based on asymptotic analysis, here a new method is presented to construct local artificial boundary conditions for a very general class of elliptic problems where the main asymptotic term is not known explicitly. Existence and uniqueness of approximating solutions are proved together with asymptotically precise error estimates. One class of important examples includes boundary value problems for anisotropic elasticity and piezoelectricity. Copyright © 2004 John Wiley & Sons, Ltd.