Pseudodifferential Operators on Spaces of Distributions Associated with Non-negative Self-Adjoint Operators

We consider Hörmander type symbols on a family of spaces associated with non-negative self-adjoint operators, and we prove boundedness of the corresponding pseudodifferential operators on both classical and non-classical Besov and Triebel–Lizorkin spaces. Consequently, this also covers the case of Sobolev spaces. As an application, we obtain boundedness of spectral multipliers on the mentioned spaces.     

The problem of sharp notch in couple-stress elasticity

The problem of sharp notch in couple-stress elasticity is considered in this paper. The problem involves a sharp notch in a body of infinite extent. The body has microstructural properties, which are assumed to be characterized by couple-stress effects. Both symmetric and anti-symmetric loadings at remote regions are considered under plane-strain conditions. The faces of the notch are considered traction free. To determine the field around the tip of the notch, a boundary-layer approach is followed by considering an expansion of the displacements in a form of separated variables in a polar coordinate system. Our analysis is in the spirit of the Knein–Williams and Karp–Karal asymptotic techniques but it is much more involved than its corresponding analysis of standard elasticity due to the complicated boundary value problem (higher-order system of governing PDEs and additional boundary conditions as compared to the standard theory). Eventually, an eigenvalue problem is formulated and this, along with the restriction of a bounded potential energy, provides the asymptotic fields. The cases of a crack and a half-space are analyzed as limit cases of the general notch problem. Certain deviations from the standard classical elasticity results are noted.     

Scalar Field Analysis over Point Cloud Data

Given a real-valued function f defined over some metric space \(\mathbb{X}\), is it possible to recover some structural information about f from the sole information of its values at a finite set \(L\subseteq\mathbb{X}\) of sample points, whose locations are only known through their pairwise distances in \(\mathbb{X}\)? We provide a positive answer to this question. More precisely, taking advantage of recent advances on the front of stability for persistence diagrams, we introduce a novel algebraic construction, based on a pair of nested families of simplicial complexes built on top of the point cloud L, from which the persistence diagram of f can be faithfully approximated. We derive from this construction a series of algorithms for the analysis of scalar fields from point cloud data. These algorithms are simple and easy to implement, they have reasonable complexities, and they come with theoretical guarantees. To illustrate the genericity and practicality of the approach, we also present some experimental results obtained in various applications, ranging from clustering to sensor networks.     

Ultrafast room temperature NH3 sensing with positively gated reduced graphene oxide field-effect transistors

Reduced graphene oxide (R-GO) under a positive gate potential (n-type conductance) exhibits an instantaneous response and fast recovery for NH(3) sensing, far superior to the performance in p-mode at zero/negative gate potential. Our findings have important implications for fast, repeatable, room temperature gas detection using graphene/R-GO.     

Micro-immunohistochemistry using a microfluidic probe

A flexible method to extract more high-quality information from tissue sections is critically needed for both drug discovery and clinical pathology. Here, we present micro-immunohistochemistry (μIHC), a method for staining tissue sections at the micrometre scale. Nanolitres of antibody solutions are confined over micrometre-sized areas of tissue sections using a vertical microfluidic probe (vMFP) for their incubation with primary antibodies, the key step in conventional IHC. The vMFP operates several micrometres above the tissue section, can be interactively positioned on it, and even enables the staining of individual cores of tissue microarrays with multiple antigens. μIHC using such a microfluidic probe is preservative of tissue samples and reagents, alleviates antibody cross-reactivity issues, and allows a wide range of staining conditions to be applied on a single tissue section. This method may therefore find broad use in tissue-based diagnostics and in research.     

How to gamble if you're in a hurry

The beautiful theory of statistical gambling, started by Dubins and Savage (for subfair games) and continued by Kelly and Breiman (for superfair games), has mostly been studied under the unrealistic assumption that we live in a continuous world, that money is indefinitely divisible and that our life is indefinitely long. Here, we study these fascinating problems from a purely discrete, finitistic and computational viewpoint, using both symbol-crunching and number-crunching (and simulation just for checking purposes).     

Palladium nanoparticle-decorated iron nanotubes hosted in a polycarbonate porous membrane: development, characterization, and performance as electrocatalysts of ascorbic acid

One-dimensional iron metallic nanotubes were prepared by electroless deposition within the pores of polycarbonate (PC) membranes. The longitudinal nucleation of the nanotubes along the pore walls was achieved by mounting the PC membrane between two halves of a U-shaped reaction tube. Palladium nanoparticles were post-deposited on the inner wall of the nanotubes. The composition, morphology, and structure of the Pd/Fe nanotubes were characterized by transmission electron microscopy, scanning electron microscopy, and inductively coupled plasma-atomic emission spectroscopy. A glassy carbon (GC) electrode modified with the free Pd/Fe bimetallic nanotubes (isolated after the dissolution of the host membranes) showed small improvement on the overpotential oxidation of ascorbic acid in comparison to the bare GC electrode. Alternatively, the Pd/Fe-polycarbonate membrane was covered with a sputtered gold thin layer of 10?nm from one side and mounted in a homemade electrochemical cell acting as the working electrode. The potential use of these functional membranes as catalytic surfaces for the electrochemical monitoring of ascorbic acid was investigated by cyclic voltammetry and amperometry. In the presence of a phosphate buffer solution, pH?7, Pd/Fe-polycarbonate membranes showed excellent electrocatalytic properties toward the oxidation of ascorbic acid even at potentials as low as 0?mV versus a Ag/AgCl reference electrode. In addition to the substantial lower overpotential, these electrodes offered selectivity over acetaminophen and uric acid, and a prolonged working stability without the need for maintenance. The electrodes were kept dry between different working days and retained their original activity for more than 1?week. Pd-polycarbonate and Fe-polycarbonate membranes were also developed for comparison purposes.     

Analysis and applications of a group contribution sPC-SAFT equation of state

A group contribution (GC) method for estimating pure compound parameters for the molecular-based perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state (EoS) is proposed in a previous work [A. Tihic, G.M. Kontogeorgis, N. von Solms, M.L. Michelsen, L. Constantinou, Ind. Eng. Chem. Res. 47 (2008) 5092–5101]. In this paper, an investigation of the predictive capability of the GC sPC-SAFT EoS through comparison of the method’s predictions for compounds with high molecular weights and several selected binary mixtures of industrial significance with experimental data such as thiols, sulphides and polynuclear aromatics is presented. Additionally, predictions of activity coefficient at infinite dilution for athermal systems are compared with the results using existing activity coefficient models. The results show that calculated pure compound parameters using the proposed GC method allow satisfactory representation of experimental data of investigated systems with the sPC-SAFT EoS. Moreover, the variety of functional groups in the available GC scheme ensures broad applications of the GC sPC-SAFT EoS.