A survey of uncertainty principles and some signal processing applications

The goal of this paper is to review the main trends in the domain of uncertainty principles and localization, highlight their mutual connections and investigate practical consequences. The discussion is strongly oriented towards, and motivated by signal processing problems, from which significant advances have been made recently. Relations with sparse approximation and coding problems are emphasized.     

Associative and preassociative functions

We investigate the associativity property for functions of multiple arities and introduce and discuss the more general property of preassociativity, a generalization of associativity which does not involve any composition of functions.     

A Characterization of Barycentrically Preassociative Functions

We provide a characterization of the variadic functions which are barycentrically preassociative as compositions of length-preserving associative string functions with one-to-one unary maps. We also discuss some consequences of this characterization.     

Characterizing topological and dynamical properties of complex networks without border effects

The properties of complex networks are highly influenced by border effects frequently found as a consequence of the finite nature of real-world networks as well as network sampling. Therefore, it becomes critical to devise effective means for sound estimation of network topological and dynamical properties while avoiding these types of artifacts. In the current work, an algorithm for minimization of border effects is proposed and discussed, and its potential is illustrated with respect to two real-world networks, namely bone canals and air transportation.     

A finite element approximation for a class of degenerate elliptic equations

In this paper we exhibit a finite element method fitting a suitable geometry naturally associated with a class of degenerate elliptic equations (usually called Grushin type equations) in a plane region, and we discuss the related error estimates.

     

Self assembly of anastomosis-like superstructures in fatty acid/guanidine hydrochloride aqueous dispersions

A mixture between 1% sodium myristate and guanidine hydrochloride at a molar ratio of 1 in water forms a gel of membranes below a phase transition of ca. 21 °C and a viscous limpid and isotropic solution above. As observed by both TEM and AFM, we report the formation of interconnected superstructures in that latter phase. Those assemblies exhibit a size of ca. 4–40 nm width and several tens of μm length with unexpected disconnections and re-connections between them having the appearance of an anastomosis-like superstructure.     

Component-Mode Synthesis Method Variants in the Dynamics of Coupled Structures

The component-mode synthesis method is usually adopted in order to reduce the number of degrees-of-freedom of structures composed of two or more substructures without loosing the main physical characteristics of the whole structure. Many approaches of this method have been proposed in the literature. These approaches differ from each other for the boundary conditions which are imposed at the interface of the two substructures. In this paper four variants of interface boundary conditions are examined. For each set of conditions a suitable coordinate transformation, compatible with the conditions at the boundary degrees-of-freedom between the two substructures, is presented. Moreover, in the numerical applications a comparison between the four component-mode synthesis variants here proposed with respect to the same variants proposed in the literature is presented. The better accuracy of the proposed approach is shown.     

Thermodynamic study of functionalized calix[n]arene and resorcinol[n]arene monolayers spreaded at an aqueous pendant drop

The behavior of insoluble calix[n]arene and resorcinol[n]arene derivatives monolayers were studied through the use of a constant surface Langmuir balance based on Axisymmetric Drop Shape Analysis (ADSA). In each case, a stable monolayer was obtained and different transitions (induced for lateral compression) could be identified. Thermodynamic parameters were computed through two dimensional Clausius–Clayperon equations and used to valuate the monolayer stability. A noticeable reduction of thermodynamic parameters occurred at highly tested temperatures (328 and 338 K) for those compounds that had hydrocarbon tails or benzene rings attached to one side of macrocyclic rim. Such fact was related to a monolayer rearrangement where the macrocyclic ring changed from a parallel to a perpendicular orientation. In this orientation the hydrophobic interactions between hydrocarbon chains and benzene rings were maximized. At highly temperature, where vigorous molecular motion existed, those interactions were superior to the stabilization effect through hydrogen bond.     

Low-cost speckle interferometry for measuring 3D deformation fields: Hardware and software

In the present paper the authors propose a portable and low-cost speckle interferometer for evaluating 3D deformation fields. The interferometer was designed and realized with the aim of carrying out measurements on small areas, hence it can be used to approach problems characterized by displacement field with highly localized gradients, such as the strain relief occurring in residual stress evaluation or the displacements which arise around notches or crack tips. The costs of the experimental equipment were reduced by employing laser diodes as light sources, a PZT actuator designed and calibrated by the authors and a control electronics realized on purpose. Moreover the configuration which was adopted allows further saving on optical components. The experimental results reported at the end of the paper, and obtained by a specimen subjected to 3D rigid body motions, show a high repeatability and accuracy. Furthermore the experimental results have shown that the geometry of the optical setup implies the variation of the sensitivity vectors on the inspected area, but this effect can be evaluated (analytically and/or experimentally) and taken into account in order to increase the accuracy of the measurements.