Applications of Compact Superharmonic Functions: Path Regularity and Tightness of Capacities

We establish relations between the existence of the L{\mathcal{L}}-superharmonic functions that have compact level sets (L{\mathcal{L}} being the generator of a right Markov process), the path regularity of the process, and the tightness of the induced capacities. We present several examples in infinite dimensional situations, like the case when L{\mathcal{L}} is the Gross–Laplace operator on an abstract Wiener space and a class of measure-valued branching process associated with a nonlinear perturbation of L{\mathcal{L}}.     

Lead-free ferroelectric BaTiO3 doped-(Na0.5Bi0.5)TiO3 thin films processed by pulsed laser deposition technique

The difficulties in synthesizing phase pure BaTiO₃ doped-(Na_0.5Bi_0.5)TiO₃ are known. In this work, we reporting the optimized pulsed laser deposition (PLD) conditions for obtaining pure phase 0.92(Na_0.5Bi_0.5)TiO₃-0.08BaTiO₃, (BNT-BT_0.08), thin films. Dielectric, ferroelectric and piezoelectric properties of BNT-BT_0.08, thin films deposited by PLD on Pt/TiO₂/SiO₂/Si substrates are investigated in this paper. Perovskite structure of BNT-BT_0.08 thin films with random orientation of nanocrystallites has been obtained by deposition at 600 °C. The relative dielectric constant and loss tangent at 100 kHz, of BNT-BT_0.08 thin film with 530 nm thickness, were 820 and 0.13, respectively. Ferroelectric hysteresis measurements indicated a remnant polarization value of 22 μC/cm² and a coercive field of 120 kV/cm. The piezoresponse force microscopy (PFM) data showed that most of the grains seem to be constituted of single ferroelectric domain. The as-deposited BNT-BT_0.08 thin film is ferroelectric at the nanoscale level and piezoelectric.     

Visual software analytics for the build optimization of large-scale software systems

Visual analytics is the science of analytical reasoning facilitated by interactive visual interfaces. In this paper, we present an adaptation of the visual analytics framework to the context of software understanding for maintenance. We discuss the similarities and differences of the general visual analytics context with the software maintenance context, and present in detail an instance of a visual software analytics application for the build optimization of large-scale code bases. Our application combines and adapts several data mining and information visualization techniques in answering several questions that help developers in assessing and reducing the build cost of such code bases by means of user-driven, interactive analysis techniques.     

On a rigidity result of singularities

The aim of this note is to prove, in the spirit of a rigidity result for isolated singularities of Schlessinger see Schlessinger (Invent Math 14:17–26, 1971) or also Kleiman and Landolfi (Compositio Math 23:407–434, 1971), a variant of a rigidity criterion for arbitrary singularities (Theorem 2.1 below). The proof of this result does not use Schlessinger’s Deformation Theory [Schlessinger (Trans Am Math Soc 130:208–222, 1968) and Schlessinger (Invent Math 14:17–26, 1971)]. Instead it makes use of Local Grothendieck-Lefschetz Theory, see (Grothendieck 1968, Éxposé 9, Proposition 1.4, page 106) and a Lemma of Zariski, see (Zariski, Am J Math 87:507–536, 1965, Lemma 4, page 526). I hope that this proof, although works only in characteristic zero, might also have some interest in its own.     

Characterisation of nickel–zinc ferrite/silica nanocomposites with low ferrite concentration obtained by an improved modified sol–gel method

The paper presents a study regarding the structure, morphology and magnetic behaviour of x% (Ni_0.65Zn_0.35Fe₂O₄)/(100 − x)% SiO₂ ferrimagnetic nanocomposites for low Ni–Zn ferrite concentration (x = 5, 10, 15, 20 and 30 mass percent) obtained by an improved modified sol–gel method. The obtained gels and nanocomposites have been characterized by fast Fourier transform-infrared (FT-IR) spectrometry, X-ray diffraction (XRD), transmission electron microscopy (TEM) and magnetic measurements (MM). The addition of a supplementary quantity of diol in the synthesis, corresponding to a molar ratio EG : TEOS = 1:1, and the control of the thermal treatment applied to the precursor xerogels tetraethylortosilicate (TEOS)–metal nitrates (MN)–ethylene glycol (EG) leads to fine (~2–9 nm), almost spherical Ni–Zn ferrite nanoparticles homogenously dispersed inside the amorphous SiO₂ matrix. TEM images reveal the fine nature and the narrow size distribution of the ferrite nanoparticles. Nanoparticles diameter increases with the ferrite concentration and with the annealing temperature. For all concentrations of ferrite in SiO₂ and all annealing temperature, we have obtained Ni_0.65Zn_0.35Fe₂O₄ ferrite as single phase (proven by XRD) in the amorphous silica matrix, only after a pre-treatment of synthesized gels, at 573 K, for 3 h. The magnetic behaviour of ferrite nanoparticles in quasi-static magnetic fields is very particular, depending on the annealing temperature and the ferrite content in silica matrix. We have obtained superparamagnetic behaviour for the nanocomposites, for a concentration of 30% ferrite in SiO₂ at high annealing temperature, of 1,273 K.     

Sensitive detection of endocrine disrupters using ionic liquid--single walled carbon nanotubes modified screen-printed based biosensors

Simple and low cost biosensor based on screen-printed electrode for sensitive detection of some alkylphenols was developed, by entrapment of HRP in a nanocomposite gel based on single-walled carbon nanotubes (SWCNTs) and 1-butyl-3-methylimidazolium hexafluorophosphate ([BMIM][PF₆]) ionic liquid. Raman and FTIR spectroscopy, CV and EIS studies demonstrate the interaction between SWCNTs and ionic liquid. The nanocomposite gel, SWCNT-[BMIM][PF₆] provides to the modified sensor a considerable enhanced electrocatalytic activity toward hydrogen peroxide reduction. The HRP based biosensor exhibits high sensitivity and good stability, allowing a detection of the alkylphenols at an applied potential of −0.2 V vs. Ag/AgCl, in linear range from 5.5 to 97.7 μM for 4-t-octylphenol and respectively, between 5.5 and 140 μM for 4-n-nonylphenol, with a response time of about 5 s. The detection limit was 1.1 μM for 4-t-octylphenol, and respectively 0.4 μM for 4-n-nonylphenol (S/N = 3).     

Potential theory of infinite dimensional Lévy processes

We study the potential theory of a large class of infinite dimensional Lévy processes, including Brownian motion on abstract Wiener spaces. The key result is the construction of compact Lyapunov functions, i.e., excessive functions with compact level sets. Then many techniques from classical potential theory carry over to this infinite dimensional setting. Thus a number of potential theoretic properties and principles can be proved, answering long standing open problems even for the Brownian motion on abstract Wiener space, as, e.g., formulated by R. Carmona in 1980. In particular, we prove the analog of the known result, that the Cameron-Martin space is polar, in the Lévy case and apply the technique of controlled convergence to solve the Dirichlet problem with general (not necessarily continuous) boundary data.     

Metric properties of the nearest extended parametric fuzzy number and applications

We propose the notion of extended parametric fuzzy number, which generalizes the extended trapezoidal fuzzy number and parametric fuzzy number, discussed in some recent papers. The metric properties of the nearest extended parametric fuzzy number of a fuzzy number, proved in the present article, help us to obtain the property of continuity for the parametric approximation operator and to simplify the solving of the problems of parametric approximations under conditions.