A bargaining set for monotonic simple games based on external and internal stability

A new bargaining set based on notions of both internal and external stability is developed in the context of endogenous coalition formation. It allows one to make an explicit distinction between within-group and outside-group deviation options. This type of distinction is not present in current bargaining sets. For the class of monotonic proper simple games, the outcomes in the bargaining set are characterized. Furthermore, it is shown that the bargaining set of any homogeneous weighted majority game contains an outcome for which the underlying coalition structure consists of a minimal winning coalition and its complement.     

Lyapunov‐type inequalities for a class of fractional boundary value problems with integral boundary conditions

In this paper, Lyapunov‐type inequalities are derived for a class of fractional boundary value problems with integral boundary conditions. As an application, we obtain a lower bound for the eigenvalues of corresponding equations.     

Approximation of the steepest descent direction for the O-D matrix adjustment problem

In this paper, a method to approximate the directions of Clarke's generalized gradient of the upper level function for the demand adjustment problem on traffic networks is presented. Its consistency is analyzed in detail. The theoretical background on which this method relies is the known property of proximal subgradients of approximating subgradients of proximal bounded and lower semicountinuous functions using the Moreau envelopes. A double penalty approach is employed to approximate the proximal subgradients provided by these envelopes. An algorithm based on partial linearization is used to solve the resulting nonconvex problem that approximates the Moreau envelopes, and a method to verify the accuracy of the approximation to the steepest descent direction at points of differentiability is developed, so it may be used as a suitable stopping criterion. Finally, a set of experiments with test problems are presented, illustrating the approximation of the solutions to a steepest descent direction evaluated numerically. Research supported under Spanish CICYT project TRA99-1156-C02-02.     

Spectroscopic and structural impact of a stem base-pair change in DNA hairpins: GTTC-ACA-GAAC versus GTAC-ACA-GTAC

Successive investigations over the last decade have revealed and confirmed a stable loop closure in a family of d-[GTAC-5Pur6N7N-GTAC] hairpins, where 5Pur6N7N is a AAA, GAG and AXC loop (X being any nucleotide). The trinucleotide loop is characterized by a well defined 5Pur-7N mispairing mode, and by upfield chemical shifts for three sugar protons of the apical nucleotide 6N. The GTTC-ACA-GAAC DNA hairpin, of interest for its likely involvement in Vibrio cholerae genome mutations, has now been investigated. The GTAC-ACA-GTAC DNA hairpin has also been studied because it is intermediate between the other structures, as it contains the loop of the hairpin under consideration and the stem of the above family. The two hairpins with the ACA loop are stable. They show the same mispairing mode and similar upfield shifts as the previous family, but GTTC-ACA-GAAC seems to be slightly less compact than any other. GTTC-ACA-GAAC is remarkable in that it exhibits a B(II) character for the phosphate-ester conformation at 8Gp9A, together with a swing of the upper hairpin into the major groove that, in particular, brings 6CH1' roughly as close to 7AH2 as to 6CH6. These unexpected structural features are qualitatively deduced from (1)H and (31)P NMR spectra, and confirmed by Raman spectroscopy. This comparative study shows that not only the loop sequence but also the stem sequence may control hairpin structures.     

On the Iterated Biclique Operator

A biclique of a graph G is a maximal induced complete bipartite subgraph of G. The biclique graph of G, denoted by , is the intersection graph of the bicliques of G. We say that a graph G diverges (or converges or is periodic) under an operator F whenever ( for some m, or for some k and , respectively). Given a graph G, the iterated biclique graph of G, denoted by , is the graph obtained by applying the biclique operator k successive times to G. In this article, we study the iterated biclique graph of G. In particular, we classify the different behaviors of when the number of iterations k grows to infinity. That is, we prove that a graph either diverges or converges under the biclique operator. We give a forbidden structure characterization of convergent graphs, which yield a polynomial time algorithm to decide if a given graph diverges or converges. This is in sharp contrast with the situsation for the better known clique operator, where it is not even known if the corresponding problem is decidable. © 2012 Wiley Periodicals, Inc. J. Graph Theory 73: 181–190, 2013     

Metal Nodes of Metal-Organic Frameworks can Activate Molecular Hydrogen

Hydrogenation of multiple bonds are among the most general and important organic reactions. Typical heterogeneous catalysts are based on transition metal nanoparticles, including noble metals. Data are presented here showing that metal nodes of MIL-101(Cr) and UiO-66 in the absence of occluded metal nanoparticles can promote hydrogenation of polarized X=Y double bonds of nitro and carbonyl groups. The catalytic activity is a function of the composition of the metal node and the organic linker. It is proposed that the reaction mechanism is based on the operation of frustrated Lewis acid/base pairs.     

Design, synthesis, and biological evaluation of platensimycin analogues with varying degrees of molecular complexity

The molecular design, chemical synthesis, and biological evaluation of two distinct series of platensimycin analogues with varying degrees of complexity are described. The first series of compounds probes the biological importance of the benzoic acid subunit of the molecule, while the second series explores the tetracyclic cage domain. The biological data obtained reveal that, while the substituted benzoic acid domain of platensimycin is a highly conserved structural motif within the active compounds with strict functional group requirements, the cage domain of the molecule can tolerate considerable structural modifications without losing biological action. These findings refine our present understanding of the platensimycin pharmacophore and establish certain structure-activity relationships from which the next generation of designed analogues of this new antibiotic may emerge.     

H2‐Fueled ATP Synthesis on an Electrode: Mimicking Cellular Respiration

ATP, the molecule used by living organisms to supply energy to many different metabolic processes, is synthesized mostly by the ATPase synthase using a proton or sodium gradient generated across a lipid membrane. We present evidence that a modified electrode surface integrating a NiFeSe hydrogenase and a F₁F₀‐ATPase in a lipid membrane can couple the electrochemical oxidation of H₂ to the synthesis of ATP. This electrode‐assisted conversion of H₂ gas into ATP could serve to generate this biochemical fuel locally when required in biomedical devices or enzymatic synthesis of valuable products.