Expert Rule Versus Majority Rule Under Partial Information, II

The main purpose of this paper is clarifying the connection between some characteristics of a deciding body and the probability of its making correct decisions. In our model a group of decision makers is required to select one of two alternatives. We assume the probabilities of the decision makers being correct are independent random variables distributed according to the same given distribution rule. This distribution belongs to a general family, containing the uniform distribution as a particular case. We investigate the behavior of the probability of the expert rule being optimal, as well as that of the majority rule, both as functions of the distribution parameter and the group size. The main result is that for any value of the distribution parameter the expert rule is far more likely to be optimal than the majority rule, especially as the deciding body becomes larger.     

Multiple ergodic theorems

Given measure preserving transformationsT ₁,T ₂,...,T _s of a probability space (X,B, μ) we are interested in the asymptotic behaviour of ergodic averages of the form $$\frac{1}{N}\sum\limits_{n = 0}^{N - 1} {T_1^n f_1 \cdot T_2^n f_2 } \cdot \cdots \cdot T_s^n f_s $$ wheref ₁,f ₂,...,f _s ?L ^∞(X,B,μ). In the general case we study, mainly for commuting transformations, conditions under which the limit of (1) inL ²-norm is ∫ _x f ₁ dμ·∫ _x f ₂ dμ...∫ _x f _s dμ for anyf ₁,f ₂...,f _s ?L ^∞(X,B,μ). If the transformations are commuting epimorphisms of a compact abelian group, then this limit exists almost everywhere. A few results are also obtained for some classes of non-commuting epimorphisms of compact abelian groups, and for commuting epimorphisms of arbitrary compact groups.     

Nanoporous Materials Can Tune the Critical Point of a Pure Substance

Molecular simulations and NMR relaxometry experiments demonstrate that pure benzene or xylene confined in isoreticular metal–organic frameworks (IRMOFs) exhibit true vapor–liquid phase equilibria where the effective critical point may be reduced by tuning the structure of the MOF. Our results are consistent with vapor and liquid phases extending over many MOF unit cells. These results are counterintuitive since the MOF pore diameters are approximately the same length scale as the adsorbate molecules. As applications of these materials in catalysis, separations, and gas storage rely on the ability to tune the properties of adsorbed molecules, we anticipate that the ability to systematically control the critical point, thereby preparing spatially inhomogeneous local adsorbate densities, could add a new design tool for MOF applications.     

Phase behavior of model lipid bilayers

We investigated the phase behavior of double-tail lipids, as a function of temperature, headgroup interaction and tail length. At low values of the head-head repulsion parameter a(hh), the bilayer undergoes with increasing temperature the transitions from the subgel phase L(c) via the flat gel phase L(beta) to the fluid phase L(alpha). For higher values of a(hh), the transition from the L(c) to the L(alpha) phase occurs via the tilted gel phase L(beta)(') and the rippled phase P(beta)('). The occurrence of the L(beta)(') phase depends on tail length. We find that the rippled structure (P(beta)(')) occurs if the headgroups are sufficiently surrounded by water and that the ripple is a coexistence between the L(c) or L(beta)(') phase and the L(alpha) phase. The anomalous swelling, observed at the P(beta)(') --> L(alpha) transition, is not directly related to the rippled phase, but a consequence of conformational changes of the tails.     

Zur Untersuchung des Wollfettes

Ohne Zusammenfassung     

Abscheidung von Kohlendioxid: Perspektiven für neue Materialien

Der stark ansteigende Kohlendioxidgehalt in der Atmosphäre ist eines der drängendsten Umweltprobleme unserer Zeit. Eine Option zur Verringerung anthropogener CO₂‐Emissionen ist die Abscheidung und Speicherung von Kohlendioxid (Carbon Capture and Storage, CCS) an Punktquellen wie Kraftwerken. Durch diese Sequestrierung steigt allerdings der Energiebedarf der Kraftwerke um 25–40 %. Wir berichten hier über die Technologien zur Abscheidung, die zur Verringerung der CO₂‐Emissionen wahrscheinlich am besten geeignet sind. Dazu zählen Postcombustion‐Verfahren, bei denen die Abscheidung nach der Verbrennung stattfindet (vor allem die CO₂/N₂‐Separation), Precombustion‐Verfahren, bei denen CO₂/H₂‐Gemische eingesetzt werden, und die Konditionierung von Erdgas (CO₂/CH₄). Der Schlüssel zu deutlichen Fortschritten sind bessere Trennmittel zur Separation. Wir werden hier aktuelle Entwicklungen und neuartige Konzepte zur CO₂‐Abtrennung durch Lösungsmittel‐Absorption, chemische und physikalische Adsorption und Membranen schildern und besonders auf Fortschritte auf dem wachsenden Gebiet Metall‐organischer Gerüste eingehen.     

Analysis methodology for 3C-PIV data of rotary wing vortices

3C-PIV data from tip vortices of either fixed-wing or rotating wing experiments are challenging from an analysis point of view. Model motion, vortex wander, spurious vectors, periodic and aperiodic effects, turbulence, and other disturbing effects are all present in the data. In most cases the vortices are not measured perpendicular to their axis as well. Engineers need time-averaged properties from the vortex in the vortex axis system for a proper modelization within simulation codes. This article describes the methods needed to deal with all the mentioned problem areas, including the conditional averaging and rotation into the vortex axis system. The methods are validated by using numerically generated vortex vector fields, and finally applied to experimental data from a hover condition of a model rotor.     

Distribution modulo 1 of some oscillating sequences,II

Sequences defined by means of polynomials and highly differentiable quasiperiodic functions are considered. It is proved that under some conditions such sequences must assume small values modulo 1, or even be dense modulo 1. Negative results, demonstrating that some differentiablity conditions are necessary, are also obtained.