On the existence of good stationary strategies for nonleavable stochastic games

This paper discusses the problem regarding the existence of optimal or nearly optimal stationary strategies for a player engaged in a nonleavable stochastic game. It is known that, for these games, player I need not have an -optimal stationary strategy even when the state space of the game is finite. On the contrary, we show that uniformly -optimal stationary strategies are available to player II for nonleavable stochastic games with finite state space. Our methods will also yield sufficient conditions for the existence of optimal and -optimal stationary strategies for player II for games with countably infinite state space. With the purpose of introducing and explaining the main results of the paper, special consideration is given to a particular class of nonleavable games whose utility is equal to the indicator of a subset of the state space of the game.     

On the incompressible limit of inviscid compressible fluids

We consider the Euler equations of barotropic inviscid compressible fluids in a bounded domain. It is well known that, as the Mach number goes to zero, the compressible flows approximate the solution of the equations of motion of inviscid, incompressible fluids. Here we discuss, for the boundary case, the different kinds of convergence under various assumptions on the data, in particular the weak convergence in the case of uniformly bounded initial data and the strong convergence in the norm of the data space.

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Sunto Nel presente lavoro consideriamo le equazioni di Eulero per un fluido inviscido comprimibile barotropico in un dominio limitato. è ben noto che, quando il numero di Mach tende a zero, i moti comprimibili approssimano le soluzioni delle equazioni del moto relative ad un fluido inviscido incomprimibile. Qui discutiamo, per il problema al contorno, i diversi tipi di convergenza sotto differenti ipotesi sui dati, in particolare la convergenza debole nel caso di dati iniziali uniformemente limitati e la convergenza forte nella norma dello spazio dei dati.

     

Self‐Assembly of Calix[6]arene–Diazapyrenium Pseudorotaxanes: Interplay of Molecular Recognition and Ion‐Pairing Effects

The calix[6]arene wheel CX forms pseudorotaxane species with the diazapyrenium‐based axle 1? 2PF₆ in CH₂Cl₂ solution. The macrocyclic component is a heteroditopic receptor, which can complex the electron‐acceptor moiety of the axle inside its cavity and the counterions with the ureidic groups on the upper rim. The self‐assembled supramolecular species is a complex structure, which involves three components—the wheel, the axle and its counterions—that can mutually interact and affect. The stoichiometry of the resulting supramolecular complex depends on the nature and concentration of the counterions. Namely, it is observed that in dilute solution and with low‐coordinating anions the axle takes two wheels, whereas with highly coordinating anions or in concentrated solutions the complex has a 1:1 stoichiometry.     

Individual and organizational conditions for the emergence and evolution of bandwagons

What makes employees adopt a particular innovation, practice, or idea? And what makes it more likely for adoption to spread wide in an organization? This paper presents an agent-based model that simulates interactions among employees to analyze the spread of bandwagons. Agents are subject to conformity and peer pressure as well as to a two-level organizational hierarchy. In the model, perceptions of the surrounding environment depend on individual cognitive attitudes (or ‘tolerance’ to bandwagons), the level of ambiguity attached to social relationships, and organization size. Findings show that the probability of widespread diffusion (i.e., bandwagon) is dependent more on organizational size, conformity, and interactions than ambiguity and individual attitudes.     

Surface grafting and reactivity of calixarene-based receptors and pseudorotaxanes on Si(100)

The first report is given here on the anchoring on H-Si(100) of calix[4]arenes and calix[6]arene-based pseudorotaxanes, versatile building blocks for molecular devices. Covalent functionalization on Si was reached through a wet chemistry recipe, by making use of an extra-mild photochemical activation via visible light of C=C terminated anchoring arms. Our approach largely preserves the integrity of the molecular substrate, also allowing for a full monolayer of pseudorotaxane to be formed on Si(100). Molecular adhesion has been demonstrated by the presence and quantitation of XPS signals from specific elements in the molecules. AFM measurements performed on Si(100)/calix[4]arenes have revealed structures 2.3 nm high, consistent with the length of the molecule. The availability of the calix[4]arene cavity to host further species after anchoring on Si has been demonstrated by the successful complexation reaction with Cs(+) ions, resulting in a 1:1 calix/Cs(+) ratio, and with N-methyl pyridinium iodide. A pseudorotaxane species, composed of a calix[6]arene wheel derivatised with N-phenylureido groups on the upper rim and a viologen (4,4'-bipyridinium) containing axle, has been anchored on Si(100) via the C=C termination of the axle. We demonstrated the self-assembling of this pseudorotaxane covalently bound by use of XPS.     

Tuning the Fluorescence Through Reorientation of the Axle in Calix[6]arene-Based Pseudorotaxanes

This work describes a calix[6]arene-based wheel that binds, in non-polar media, a stilbazolium salt to yield a mixture of pseudorotaxane orientational isomers. The isomer's abundance ratio evolves with time and can be reversibly tuned by adjusting the temperature. The spectroscopic properties, and notably the emission spectrum, of the bound guest depend on its orientation inside the non-palindromic wheel, suggesting such a system as a switch with spectroscopic readout.     

Bayesian nonparametric predictive inference and bootstrap techniques

We address the question as to whether a prior distribution on the space of distribution functions exists which generates the posterior produced by Efron's and Rubin's bootstrap techniques, emphasizing the connection with the Dirichlet process. We also introduce a new resampling plan which has two advantages: prior opinions are taken into account and the predictive distribution of the future observations is not forced to be concentrated on observed values.     

On Slightly Compressible Ideal Flow¶in the Half-Plane

We consider the Euler equations of barotropic inviscid compressible fluids in the half-plane. It is well known that, as the Mach number goes to zero, the compressible flows approximate the solution of the equations of motion of inviscid, incompressible fluids. In 2D (two dimensions) such limit solution exists on any arbitrary time interval, with no restriction on the size of the initial data. It is then natural to expect the same for the compressible solution, if the Mach number is sufficiently small. We decompose the solution as the sum of the irrotational part, the incompressible part and the remainder, which describes the interaction between the first two components. First we study the life span of smooth irrotational solutions, i.e., the largest time interval T(?) of existence of classical solutions, when the initial data are a small perturbation of size ? from a constant state. Related to this is a decay property for the irrotational part. Then, we study the interaction between the two components and show the existence on any arbitrary time interval, for any Mach number sufficiently small. This yields the existence of smooth compressible flow on any arbitrary time interval. For the proofs we use a combination of energy and decay estimates.     

A Multi-Phase Media Formulation for Biomechanical Analysis of Periodontal Ligament*

A numerical analysis of the biomechanical response of the periodontal ligament is presented. A multi-phase media formulation is developed for representing soft tissue constitutive models, and implemented in a specific finite element code. It is possible to simulate the presence of liquid phase permeating the extra-cellular material and to interpret the consequent time-dependent behaviour due to the fluid flux through periodontal ligament. The analysis of the mobility of human upper incisor, under the application of short time transversal forces, is reported. The numerical results are compared with in vivo experimental data. The agreement of different approaches confirms the effectiveness of the proposed model for investigation of the biomechanical behaviour of periodontal ligament under application of low magnitude forces, and represents the basis for the definition of a general multi-phase constitutive model.