Bargaining and membership

In coalitional games in which the players are partitioned into groups, we study the incentives of the members of a group to leave it and become singletons. In this context, we model a non-cooperative mechanism in which each player has to decide whether to stay in her group or to exit and act as a singleton. We show that players, acting myopically, always reach a Nash equilibrium.     

Large deviations for hitting times of a random walk in random environment on a strip

We consider a random walk in random environment on a strip, which is transient to the right. The random environment is stationary and ergodic. By the constructed enlarged random environment which was first introduced by Goldsheid （2008）, we obtain the large deviations conditioned on the environment （in the quenched case） for the hitting times of the random walk.     

Hochschild Cohomology and the Derived Class of m-Cluster Tilted Algebras of Type \mathbb{A}

In this paper, we characterize all the finite dimensional algebras that are derived equivalent to an m?cluster tilted algebra of type $\mathbb{A}$ . These algebras are gentle, and we show that the derived class of such an algebra is completely determined by the rank of its Grothendieck group and the dimension of its first Hochschild cohomology group.     

Dynamics of Weighted Composition Operators

We study the dynamic behaviour of weighted composition operators on the space of holomorphic functions on a simply connected plane domain and endowed with the compact open topology. Any such operator is weakly supercyclic if and only if it is topologically mixing and, when the weight is bounded, if and only if the operator has a hypercyclic subspace. We also provide conditions on the symbols that ensure the operator to be Devaney-chaotic and to have a frequently hypercyclic subspace.     

Symmetrization for linear and nonlinear fractional parabolic equations of porous medium type

We establish symmetrization results for the solutions of the linear fractional diffusion equation _∂tu+(−Δ)^σ/2u=f${\partial }_{t}u+{(-\mathrm{\Delta })}^{\sigma /2}u=f$ and its elliptic counterpart hv+(−Δ)^σ/2v=f$hv+{(-\mathrm{\Delta })}^{\sigma /2}v=f$, h>0$h>0$, using the concept of comparison of concentrations. The results extend to the nonlinear version, _∂tu+(−Δ)^σ/2A(u)=f${\partial }_{t}u+{(-\mathrm{\Delta })}^{\sigma /2}A(u)=f$, but only when the nondecreasing function A:_R+→_R+$A:{\mathbb{R}}_{+}\to {\mathbb{R}}_{+}$ is concave. In the elliptic case, complete symmetrization results are proved for B(v)+(−Δ)^σ/2v=f$B(v)+{(-\mathrm{\Delta })}^{\sigma /2}v=f$ when B(v)$B(v)$ is a convex nonnegative function for v>0$v>0$ with B(0)=0$B(0)=0$, and partial results hold when B is concave. Remarkable counterexamples are constructed for the parabolic equation when A is convex, resp. for the elliptic equation when B   is concave. Such counterexamples do not exist in the standard diffusion case σ=2$\sigma =2$.     

On proximal gradient method for the convex problems regularized with the group reproducing kernel norm

We consider a class of nonsmooth convex optimization problems where the objective function is the composition of a strongly convex differentiable function with a linear mapping, regularized by the group reproducing kernel norm. This class of problems arise naturally from applications in group Lasso, which is a popular technique for variable selection. An effective approach to solve such problems is by the proximal gradient method. In this paper we derive and study theoretically the efficient algorithms for the class of the convex problems, analyze the convergence of the algorithm and its subalgorithm.     

Fatty Acid Carboxylate‐ and Anionic Surfactant‐Controlled Delivery Systems That Use Mesoporous Silica Supports

We report the preparation of a MCM‐41 mesoporous material that contains the dye [Ru(bipy)₃]Cl₂ (bipy=bipyridine) inside the mesopores and functionalised with suitable binding groups at the entrance of the pores. Solids S1 – S3 were obtained by the reaction of the mesoporous material with N‐methyl‐N′‐propyltrimethoxysilylimidazolium chloride, N‐phenyl‐N′‐[3‐(trimethoxysilyl)propyl]thiourea, or N‐phenyl‐N′‐[3‐(trimethoxysilyl)propyl]urea, respectively. A study of the dye delivery of these systems in buffered water (pH 7.0, 2‐[4‐(2‐hydroxyethyl)piperazin‐1‐yl]ethanesulfonic acid (HEPES), 10^?3 mol dm^?3) in the presence of a family of carboxylate ions was carried out. In the interaction of the anions with the surface of the solids, the response depends on the characteristics of the binding groups (i.e., imidazolium, urea and thiourea) at the pore outlets and their specific interaction with the corresponding anion. The interaction of long‐chain carboxylate ions with the binding sites at the surface of the solids resulted in a remarkable inhibition of the delivery of the dye. This inhibition was observed clearly for the dodecanoate anion, whereas the octanoate, decanoate, cholate, deoxycholate, glycodeoxycholate and taurocholate anions induced a certain pore blockage that varied according to the solid studied. The interaction of smaller anions, such as acetate, butanoate, hexanoate and octanoate, with the solids had no effect on the dye release process. The possible use of the gating system for the chromo‐fluorogenic detection of anionic surfactants through selective dye delivery inhibition was also explored. Molecular dynamic simulations that use force‐field methods have been made to theoretically study the capping carboxylate mechanism. The calculations are in agreement with the experimental results, thus allowing a representation of the dye delivery inhibition in the presence of long‐chain carboxylate ions.     

Cooperative recognition of Cu<Superscript>2+</Superscript> based on amino acids tethered benzothiadiazoyl-bistriazoles

Fluoroionophoric properties of benzothiadiazoyl-bistriazoyl amino acids derivatives toward metal ions were investigated by UV-Vis and fluorescence spectroscopy. Our results show that the watersoluble lysine derivative 2 exhibited a significant selectivity toward Cu²⁺ in “on-off” type response in buffer solution at pH 7.4.