Coalition formation in the presence of continuing conflict

This paper studies endogenous coalition formation in a rivalry environment where continuing conflict exists. A group of heterogeneous players compete for a prize with the probability of winning for a player depending on his strength as well as the distribution of strengths among his rivals. Players can pool their strengths together to increase their probabilities of winning as a group through coalition formation. The players in the winning coalition will compete further until one individual winner is left. We show that in any equilibrium there are only two coalitions in the initial stage of the contest. In the case of three players, the equilibrium often has a coalition of the two weaker players against the strongest. The equilibrium coalition structure with four players mainly takes one of the two forms: a coalition of the three weaker players against the strongest or a coalition of the weakest and strongest players against a coalition of the remaining two. Our findings imply that the rivalry with the possibility of coalition formation in our model exhibits a pattern of two-sidedness and a balance of power. We further study the impact of binding agreements by coalition members on equilibrium coalition structures. Our analysis sheds some light on problems of temporary cooperation among individuals who are rivals by nature.     

The (signless) Laplacian spectral radius of unicyclic and bicyclic graphs with <Emphasis Type="Italic">n</Emphasis> vertices and <Emphasis Type="Italic">k</Emphasis> pendant vertices

In this paper, the effects on the signless Laplacian spectral radius of a graph are studied when some operations, such as edge moving, edge subdividing, are applied to the graph. Moreover, the largest signless Laplacian spectral radius among the all unicyclic graphs with n vertices and k pendant vertices is identified. Furthermore, we determine the graphs with the largest Laplacian spectral radii among the all unicyclic graphs and bicyclic graphs with n vertices and k pendant vertices, respectively.     

How well does Poisson-Boltzmann implicit solvent agree with explicit solvent? A quantitative analysis

We have quantitatively studied the performance of a finite-difference Poisson-Boltzmann implicit solvent with respect to the TIP3P explicit solvent in a range of systems of biochemical interest. An overall agreement was found between the tested implicit and explicit solvents for hydrogen-bonding/salt-bridging dimers and peptide monomers and dimers of different conformations and different lengths. These comparative analyses also indicate a good transferability of empirically optimized parameters for the implicit solvent from small training molecules to large testing peptides. However, deviations between the two tested solvents are also apparent. Specifically, a consistent deviation was observed when hydrogen-bonding or salt-bridging dimers are within 4-6 A. The deviation reaches a maximum at about 5.5 A, the so-called water-bridging distance. The tested implicit solvent, even with optimized parameters, cannot capture the subtle fluctuation in the distance-dependent reaction field energy profiles, although smoothed profiles can still be obtained and are in overall agreement with those in the explicit solvent. Interestingly, the same mechanism underlining the above discrepancy is also responsible for the larger deviations of certain peptide conformations, such as parallel beta-strand dimers. It is likely that the observed discrepancy may cause improper conformational distributions in simulations with the implicit solvent when hydrogen-bonding or salt-bridging interactions are crucial, such as secondary structure populations in proteins. Validation of the implicit solvent with optimized parameters in dynamics simulations will be the next step to study the influences of the observed discrepancy at biological conditions.     

Quenching of IR luminescence of erbium, neodymium, and ytterbium beta-diketonate complexes by ligand C-H and C-D bonds

The effect of CH and CD quenching on the luminescence lifetime of Er(3+) Nd(3+) and Yb(3+) in the Cs[Ln(HFA)(4)] system has been quantified, and we have shown that for Er(3+) ions the quenching is dominated by the nearest neighbor CH oscillators, whereas for Nd(3+) ions the roles of more distant CH oscillators and nearest neighbor CD oscillators are important.     

Facile preparation of hierarchically porous carbon using diatomite as both template and catalyst and methylene blue adsorption of carbon products

Hierarchically porous carbons were prepared using a facile preparation method in which diatomite was utilized as both template and catalyst. The porous structures of the carbon products and their formation mechanisms were investigated. The macroporosity and microporosity of the diatomite-templated carbons were derived from replication of diatom shell and structure-reconfiguration of the carbon film, respectively. The macroporosity of carbons was strongly dependent on the original morphology of the diatomite template. The macroporous structure composed of carbon plates connected by the pillar- and tube-like macropores resulted from the replication of the central and edge pores of the diatom shells with disk-shaped morphology, respectively. And another macroporous carbon tubes were also replicated from canoe-shaped diatom shells. The acidity of diatomite dramatically affected the porosity of the carbons, more acid sites of diatomite template resulted in higher surface area and pore volume of the carbon products. The diatomite-templated carbons exhibited higher adsorption capacity for methylene blue than the commercial activated carbon (CAC), although the specific surface area was much smaller than that of CAC, due to the hierarchical porosity of diatomite-templated carbons. And the carbons were readily reclaimed and regenerated.     

Rational orthogonal bases satisfying the Bedrosian identity

We develop a necessary and sufficient condition for the Bedrosian identity in terms of the boundary values of functions in the Hardy spaces. This condition allows us to construct a family of functions such that each of which has non-negative instantaneous frequency and is the product of two functions satisfying the Bedrosian identity. We then provide an efficient way to construct orthogonal bases of L ²(ℝ) directly from this family. Moreover, the linear span of the constructed basis is norm dense in L ^p (ℝ), 1 < p < ∞. Finally, a concrete example of the constructed basis is presented.     

Band-limited refinable functions for wavelets and framelets

Extending band-limited constructions of orthonormal refinable functions, a special class of periodic functions is used to generate a family of band-limited refinable functions. Characterizations of Riesz bases and frames formed by integer shifts of these refinable functions are obtained. Such families of refinable functions are employed to construct band-limited biorthogonal wavelet bases and biframes with desirable time-frequency localization.     

Automorphism group and representation of a twisted multi-loop algebra

Let G be the complexification of the real Lie algebra so（3） and A = C[t1^±1, t2^±1] be the Lau-ent polynomial algebra with commuting variables. Let L：（t1, t2, 1） = G c .A be the twisted multi-loop Lie algebra. Recently we have studied the universal central extension, derivations and its vertex operator representations. In the present paper we study the automorphism group and bosonic representations ofL（t1, t2, 1）.