Common fixed points for four maps in cone metric spaces

The existence of coincidence points and common fixed points for four mappings satisfying generalized contractive conditions without exploiting the notion of continuity of any map involved therein, in a cone metric space is proved. These results extend, unify and generalize several well known comparable results in the existing literature.     

Robust exponential attractors for the strongly damped wave equation with memory. II

We consider the singular limit of the semilinear strongly damped wave equation with memory in the presence of a critical nonlinearity, as the memory kernel converges to the Dirac mass at zero. We prove the existence of a robust family of regular exponential attractors in the weak energy space. Partially supported by the Italian PRIN research project 2006 Problemi a frontiera libera, transizioni di fase e modelli di isteresi. The first author has been partially supported by a research grant from the Fondazione Fratelli Confalonieri (Milano, Italy).     

Affective bases of likelihood judgments

Analyses of likelihood judgments for 515 events support the idea that the perceived likelihood of an event is partly a function of affective processes. Production of affective disturbances makes events seem unlikely. Event likelihoods also are influenced by specific kinds of people and behaviors which are involved in the events. Affective determination of likelihood is stronger when actors have institutionally‐clear identities rather than institutionally‐vague identities; indeed, affect accounts for more than half of the variance in likelihoods of events within clear institutional contexts.     

Marked fatgraph complexes and surface automorphisms

Combinatorial aspects of the Torelli–Johnson–Morita theory of surface automorphisms are extended to certain subgroups of the mapping class groups. These subgroups are defined relative to a specified homomorphism from the fundamental group of the surface onto an arbitrary group K. For K abelian, there is a combinatorial theory akin to the classical case, for example, providing an explicit cocycle representing the first Johnson homomophism with target Λ ³ K. Furthermore, the Earle class with coefficients in K is represented by an explicit cocyle.     

The bidmensional stefan problem with convection: the time dependent case

This paper considers the time dependent stefan problem with convection in the fluid phase governed by the Stokes equation, and with adherence of the fluid on the lateral boundaries: The existence of a weak solution is obtained via the introduction of a temperature dependent penalty term in the fluid flow equation, together with the application of various compactness arguments.     

A note on statistical solutions of the three-dimensional Navier–Stokes equations: The stationary case

Stationary statistical solutions of the three-dimensional Navier–Stokes equations for incompressible fluids are considered. They are a mathematical formalization of the notion of ensemble average for turbulent flows in statistical equilibrium in time. They are also a generalization of the notion of invariant measure to the case of the three-dimensional Navier–Stokes equations, for which a global uniqueness result is not known to exist and a semigroup may not be well-defined in the classical sense. The two classical definitions of stationary statistical solutions are considered and compared, one of them being a particular case of the other and possessing a number of useful properties. Furthermore, the so-called time-average stationary statistical solutions, obtained as generalized limits of time averages of weak solutions as the averaging time goes to infinity are shown to belong to this more restrictive class. A recurrent type result is also obtained for statistical solutions satisfying an accretion condition. Finally, the weak global attractor of the three-dimensional Navier–Stokes equations is considered, and in particular it is shown that there exists a topologically large subset of the weak global attractor which is of full measure with respect to that particular class of stationary statistical solutions and which has a certain regularity property.