Complementary Lidstone interpolation on scattered data sets

Recently we have introduced a new technique for combining classical bivariate Shepard operators with three point polynomial interpolation operators (Dell’Accio and Di Tommaso, On the extension of the Shepard-Bernoulli operators to higher dimensions, unpublished). This technique is based on the association, to each sample point, of a triangle with a vertex in it and other ones in its neighborhood to minimize the error of the three point interpolation polynomial. The combination inherits both degree of exactness and interpolation conditions of the interpolation polynomial at each sample point, so that in Caira et al. (J Comput Appl Math 236:1691–1707, 2012) we generalized the notion of Lidstone Interpolation (LI) to scattered data sets by combining Shepard operators with the three point Lidstone interpolation polynomial (Costabile and Dell’Accio, Appl Numer Math 52:339–361, 2005). Complementary Lidstone Interpolation (CLI), which naturally complements Lidstone interpolation, was recently introduced by Costabile et al. (J Comput Appl Math 176:77–90, 2005) and drawn on by Agarwal et al. (2009) and Agarwal and Wong (J Comput Appl Math 234:2543–2561, 2010). In this paper we generalize the notion of CLI to bivariate scattered data sets. Numerical results are provided.     

Logics for belief functions on MV-algebras

In this paper we present a generalization of belief functions over fuzzy events. In particular we focus on belief functions defined in the algebraic framework of finite MV-algebras of fuzzy sets. We introduce a fuzzy modal logic to formalize reasoning with belief functions on many-valued events. We prove, among other results, that several different notions of belief functions can be characterized in a quite uniform way, just by slightly modifying the complete axiomatization of one of the modal logics involved in the definition of our formalism.     

The linear noise approximation for reaction-diffusion systems on networks

Stochastic reaction-diffusion models can be analytically studied on complex networks using the linear noise approximation. This is illustrated through the use of a specific stochastic model, which displays travelling waves in its deterministic limit. The role of stochastic fluctuations is investigated and shown to drive the emergence of stochastic waves beyond the region of the instability predicted from the deterministic theory. Simulations are performed to test the theoretical results and are analyzed via a generalized Fourier transform algorithm. This transform is defined using the eigenvectors of the discrete Laplacian defined on the network. A peak in the numerical power spectrum of the fluctuations is observed in quantitative agreement with the theoretical predictions.     

Monatomic rarefied gas as a singular limit of polyatomic gas in extended thermodynamics

We show that, in the theory of extended thermodynamics, rarefied monatomic gases can be identified as a singular limit of rarefied polyatomic gases. Under naturally conditioned initial data we prove that the system of 14 field equations for polyatomic gases in the limit has the same solutions as those of the system of 13 field equations for monatomic gases where there exists no dynamic pressure. We study two illustrative examples in the process of the limit, that is, the linear waves and the shock waves in order to grasp the asymptotic behavior of the physical quantities, in particular, of the dynamic pressure.     

An Unexpected Role of Hyaluronic Acid in Trafficking siRNA Across the Cellular Barrier: The First Biomimetic,Anionic, Non‐Viral Transfection Method

Circulating nucleic acids, such as short interfering RNA (siRNA), regulate many biological processes; however, the mechanism by which these molecules enter the cell is poorly understood. The role of extracellular‐matrix‐derived polymers in binding siRNAs and trafficking them across the plasma membrane is reported. Thermal melting, dynamic light scattering, scanning electron microscopy, and computational analysis indicate that hyaluronic acid can stabilize siRNA via hydrogen bonding and Van der Waals interactions. This stabilization facilitated HA size‐ and concentration‐dependent gene silencing in a CD44‐positive human osteosarcoma cell line (MG‐63) and in human mesenchymal stromal cells (hMSCs). This native HA‐based siRNA transfection represents the first report on an anionic, non‐viral delivery method that resulted in approximately 60 % gene knockdown in both cell types tested, which correlated with a reduction in translation levels.     

A Volume Inequality for Quantum Fisher Information and the Uncertainty Principle

Let A ₁,…,A _N be complex self-adjoint matrices and let ρ be a density matrix. The Robertson uncertainty principle

Supersonic cluster beam fabrication of metal–ionogel nanocomposites for soft robotics

Soft robotics is an emerging field targeting at the development of robotic bodies and architectures characterized by flexibility, adaptability, and motility typical of that of biological systems. The use of electroactive ionic polymer–metal nanocomposites able to reversibly deform in response to low-intensity electric fields constitutes a promising solution for the implementation of actuators into soft robots. Currently, the use of this class of nanocomposites is hampered by several drawbacks, mainly related to the mismatch between the mechanical properties of the polymer and the metallic electrodes compromising their stability and resilience upon cyclic deformation.Here, we report and discuss on the use of supersonic cluster beam implantation (SCBI) as an effective strategy for the fabrication of soft electroactive ionic polymeric nanocomposite actuators. SCBI relies on the use of supersonically accelerated beams of neutral metal nanoparticles that can be aerodynamically collimated and directed onto a polymeric target to generate thin nanostructured metal layers physically interpenetrating with the polymer.Soft electroactive actuators based on engineered ionogel and ionogel-based hybrid nanocomposites provided with monolithically integrated cluster-assembled gold electrodes will be discussed. These systems can undergo long-term bending deformation in a low-voltage regime, due to the nanostructured electrode resilience. The use of cluster-assembled nanostructured electrodes opens new opportunities for the high-throughput manufacturing of soft ionic actuators with excellent mechanical resiliency, high-performance actuation, and high durability.     

On the six-field model of fluids based on extended thermodynamics

We study the six-field model of fluids (ET6) derived from extended thermodynamics. The six fields are the mass density, the velocity, the temperature, and the dynamic pressure (nonequilibrium pressure). We present the basic system of field equations of ET6. And we elucidate its characteristic features through the studies of the singular limit from polyatomic to monatomic rarefied gases, of hydrodynamic fluctuation, and of a hard-sphere system. Open problems remained in ET6 at present are also pointed out.     

Synthesis of Copper-Based Nanostructures in Liquid Environments by Means of a Non-equilibrium Atmospheric Pressure Nanopulsed Plasma Jet

The influence of the liquid composition on the chemical and morphological properties of copper-based nanostructures synthesized by a non-equilibrium atmospheric plasma treatment is investigated and discussed. The synthesis approach is simple and environmentally friendly, employs a non-equilibrium nanopulsed atmospheric pressure plasma jet as a contactless cathode and a Cu foil as immersed anode. The process was studied using four distinct electrolyte solutions composed of distilled water and either NaCl?+?NaOH, NaCl only or NaOH only at two different concentrations, without the addition of any copper salts. CuO crystalline structures with limited impurities (e.g. Cu and Cu(OH)₂ phases) were produced from NaCl?+?NaOH containing solutions, mainly CuO and CuCl₂ structures were synthesized in the electrolyte solution containing only NaCl and no synthesis occurred in solutions containing only NaOH. Both aggregated and dispersed nanostructures were produced in the NaCl?+?NaOH and NaCl containing solutions. Reaction pathways leading to the formation of the nanostructures are proposed and discussed.     

Tin-free generation of alkyl radicals from alkyl 4-pentynyl sulfides via homolytic substitution at the sulfur atom

Homolytic substitution at the sulfur atom of beta-(phenylsulfanyl)vinyl radicals, obtained by radical reaction of benzenethiol with easily accessible alkyl 4-pentynyl sulfides, is a mild, effective, tin-free route for the generation of all types of alkyl radicals. This protocol can be employed in reductive defunctionalizations as well as cyclizations onto both electron-rich and electron-poor C-C double bonds.