Dixmier classes on generalized Segal–Bargmann–Fock spaces

We give criteria for the membership of Toeplitz operators and products of Hankel operators, with symbols of a certain type, in the Dixmier class, and formulas for their Dixmier trace, on a variety of weighted Segal–Bargmann–Fock spaces on the complex plane.     

Weak subgroupoid lattices

The aim of the paper is a characterization of the lattice of all weak subgroupoids of a partial groupoid. It also extends to arbitrary finite algebras Pióro’s result saying that the weak subgroupoid lattice of a finite commutative groupoid G in which g·h ≠ g (for all g, h ∈ G) uniquely determines its subgroupoid lattice.     

Dixmier trace and the Fock space

We give criteria for products of Toeplitz and Hankel operators on the Fock (Segal–Bargmann) space to belong to the Dixmier class, and compute their Dixmier trace. Along the road, analogous results for the Weyl pseudodifferential operators are also obtained.     

Strongly dominating sets of reals

We analyze the structure of strongly dominating sets of reals introduced in Goldstern et al. (Proc Am Math Soc 123(5):1573–1581, 1995). We prove that for every ${\kappa < \mathfrak{b}}$ κ < b a ${\kappa}$ κ -Suslin set ${A\subseteq{}^\omega\omega}$ A ? ω ω is strongly dominating if and only if A has a Laver perfect subset. We also investigate the structure of the class l of Baire sets for the Laver category base and compare the σ-ideal of sets which are not strongly dominating with the Laver ideal l ⁰.     

Quantitative Dunford–Pettis property

We investigate possible quantifications of the Dunford–Pettis property. We show, in particular, that the Dunford–Pettis property is automatically quantitative in a sense. Further, there are two incomparable mutually dual stronger versions of a quantitative Dunford–Pettis property. We prove that L¹$L^1$ spaces and C(K)$C\left(K\right)$ spaces possess both of them. We also show that several natural measures of weak non-compactness are equal in L¹$L^1$ spaces.     

Characterization and surface-enhanced Raman spectral probing of silver hydrosols prepared by two-wavelength laser ablation and fragmentation

A four step Ag foil laser ablation-Ag nanoparticle fragmentation procedure in ultrapure water was carried out both under argon and in air. Pulses of a high power Nd/YAG laser were used for laser ablation (1064 nm) and for the three step Ag hydrosol treatment in the absence of Ag foil in the sequence 1064-532-1064 nm. Transmission electron microscopy (TEM) and surface plasmon (SP) extinction spectra provide evidence of Ag nanoparticle fragmentation in the second and third step of the procedure carried out under argon. While polydispersity of Ag hydrosol increases in the second step, both the polydispersity and the mean size of the nanoparticles are reduced in the third step. Qualitative and quantitative surface-enhanced Raman scattering (SERS)/surface-enhanced resonance Raman scattering (SERRS) spectral probing of systems with Ag hydrosols and the selected adsorbates at 514.5 nm excitation shows that Ag hydrosols obtained in the second step of the preparation procedure carried out in air are the most suitable substrates for SERS/SERRS experiments performed at this excitation wavelength.     

Study of optical properties and biocompatibility of DLC films characterized by sp3 bonds

Optical and biomedical properties of diamond-like carbon (DLC) films of various sp², sp³ bonds were studied. The layers were prepared by pulsed laser deposition (PLD) for laser energy densities from 4 J?cm^?2 to 14 J?cm^?2. The percentage of sp² and sp³ bonds was calculated using X-ray photoelectron spectroscopy (XPS). In dependence on density the films contained up to 70 % of sp³ bonds. Optical properties were measured using spectroscopic ellipsometry in region from 250 nm to 1000 nm (n=2.6–2.7; k=0.07–0.25) and by transmission measurement (from 200 nm to 1100 nm). The adhesion and growth of human fibroblasts and keratinocytes of DLC films were tested in vitro.     

Dynamic Mechanical and Dielectric Properties of Ethylene Vinyl Acetate/Carbon Nanotube Composites

A comparative study of the dielectric and mechanical properties of ethylene vinyl acetate copolymer (EVA) filled with various concentrations of pristine and modified carbon nanotubes is reported. The surface of the carbon nanotubes was modified with 4-(2-(cholesteryloxycarboxy)ethyl) phenyl to improve the interaction of the filler with the block copolymer matrix. The improved interaction and the better dispersion of the modified carbon nanotubes (mMWCNTs) were demonstrated by a detailed study of the EVA molecular mobility through dynamic mechanical analysis and broadband dielectric relaxation spectroscopy. The storage modulus of the nanocomposite with 6 wt.% of mMWCNTs at ?50°C was enhanced by 103%, whereas for the nanocomposite with the same amount of unmodified filler, the storage modulus was only enhanced by 76% compared to the pure elastomeric matrix. This difference is more pronounced in the rubbery region in which the storage moduli were increased by 117% and 48% for the composite with the modified and unmodified fillers, respectively. The morphologies of the nanocomposites were studied with scanning and transmission electron microscopies to demonstrate the dispersion of the mMWCNTs within the EVA matrix.