Random marginal and random removal values

We propose two variations of the non-cooperative bargaining model for games in coalitional form, introduced by Hart and Mas-Colell (Econometrica 64:357–380, 1996a). These strategic games implement, in the limit, two new NTU-values: the random marginal and the random removal values. Their main characteristic is that they always select a unique payoff allocation in NTU-games. The random marginal value coincides with the Consistent NTU-value (Maschler and Owen in Int J Game Theory 18:389–407, 1989) for hyperplane games, and with the Shapley value for TU games (Shapley in In: Contributions to the theory of Games II. Princeton University Press, Princeton, pp 307–317, 1953). The random removal value coincides with the solidarity value (Nowak and Radzik in Int J Game Theory 23:43–48, 1994) in TU-games. In large games we show that, in the special class of market games, the random marginal value coincides with the Shapley NTU-value (Shapley in In: La Décision. Editions du CNRS, Paris, 1969), and that the random removal value coincides with the equal split value.      

Polarographic behaviour of orotic acid (vitamin B13). Cathodic processes

The electroanalytical behaviour of orotic acid in cathodic processes has been studied in HClO₄, at several pH values in Britton-Robinson buffers, using DPP and CV techniques. Orotic acid undergoes three cathodic waves over the entire pH range considered. Optimum conditions for determination of orotic acid using the DPP technique are also studied.     

Structure of sodiated octa-glycine: IRMPD spectroscopy and molecular modeling

The structure of the sodiated peptide GGGGGGGG-Na⁺ or G₈-Na⁺ was investigated by infrared multiple photon dissociation (IRMPD) spectroscopy and a combination of theoretical methods. IRMPD was carried out in both the fingerprint and N—H/O—H stretching regions. Modeling used the polarizable force field AMOEBA in conjunction with the replica-exchange molecular dynamics (REMD) method, allowing an efficient exploration of the potential energy surface. Geometries and energetics were further refined at B3LYP-D and MP2 quantum chemical levels. The IRMPD spectra indicate that there is no free C-terminus OH and that several N—Hs are free of hydrogen bonding, while several others are bound, however not very strongly. The structure must then be either of the charge solvation (CS) type with a hydrogen-bound acidic OH, or a salt bridge (SB). Extensive REMD searches generated several low-energy structures of both types. The most stable structures of each type are computed to be very close in energy. The computed energy barrier separating these structures is small enough that G₈-Na⁺ is likely fluxional with easy proton transfer between the two peptide termini. There is, however, good agreement between experiment and computations in the entire spectral range for the CS isomer only, which thus appears to be the most likely structure of G₈-Na⁺ at room temperature.     

Metal-ion responsive redox polyelectrolyte multilayers

We present polyelectrolyte multilayer modified electrodes exhibiting novel chemically responsive redox behaviour due to the combination of both redox and metal-ion-ligand functionalities on the same sites.     

Yetter–Drinfeld Modules over Weak Braided Hopf Monoids and Center Categories

In this paper,we introduce several centralizer constructions in a monoidal context and establish a monoidal equivalence with the category of Yetter–Drinfeld modules over a weak braided Hopf monoid.We apply the general result to the calculus of the center in module categories.     

The Generation of Random Equilateral Polygons

Freely jointed random equilateral polygons serve as a common model for polymer rings, reflecting their statistical properties under theta conditions. To generate equilateral polygons, researchers employ many procedures that have been proved, or at least are believed, to be random with respect to the natural measure on the space of polygonal knots. As a result, the random selection of equilateral polygons, as well as the statistical robustness of this selection, is of particular interest. In this research, we study the key features of four popular methods: the Polygonal Folding, the Crankshaft Rotation, the Hedgehog, and the Triangle Methods. In particular, we compare the implementation and efficacy of these procedures, especially in regards to the population distribution of polygons in the space of polygonal knots, the distribution of edge vectors, the local curvature, and the local torsion. In addition, we give a rigorous proof that the Crankshaft Rotation Method is ergodic.     

Large time asymptotics for a modified coagulation model

We study the large time asymptotics of a simplified two species model for particles (typically molecules or cells). The particles can be in two states: A “free” state where they simply move with a given velocity or an aggregated state where they do not move anymore. We show that depending only on the strength of the interaction between particles, either all of them eventually coagulate or some may escape.     

Comparison of a subrank to a full-rank time-reversal operator in a dynamic ocean

This paper investigates the application of time-reversal techniques to the detection and ensonification of a target of interest. The focusing method is based on a generalization of time-reversal operator techniques. A subrank time-reversal operator is derived and implemented using a discrete set of transmission beams to ensonify a region of interest. In a dynamic ocean simulation, target focusing using a subrank matrix is shown to be superior to using a full-rank matrix, specifically when the subrank matrix is captured in a period shorter than the coherence time of the modeled environment. Backscatter from the point target was propagated to a vertical 64-element source-receiver array and processed to form the sub-rank time-reversal operator matrix. The eigenvector corresponding to the strongest eigenvalue of the time-reversal operator was shown to focus energy on the target in simulation. Modeled results will be augmented by a limited at-sea experiment conducted on the New Jersey shelf in April-May 2004 measured low-frequency backscattered signal from an artificial target (echo repeater).