On Toeplitz-type Operators Related to Wavelets

Let G be the “ax + b”-group with the left invariant Haar measure dν and ψ be a fixed real-valued admissible wavelet on . The structure of the space of Calderón (wavelet) transforms inside is described. Using this result some representations, properties and the Wick calculus of the Calderón-Toeplitz operators T _α acting on whose symbols a = a(ζ) depend on for are investigated. This paper was supported by Grant VEGA 2/0097/08.     

Microstructural PALS study of regulated dimethacrylates: Thiol‐ versus β‐allyl sulfone‐based networks

Radical photocuring of multifunctional (meth)acrylates is lacking control over the irregular chain growth process yielding highly crosslinked, inhomogeneous networks. Chain transfer agents (CTAs, e.g., thiols or β‐allyl sulfones) have been widely used to modify this curing process, thus reducing shrinkage stress and increasing the toughness of the formed photopolymers. Resulting photopolymer networks exhibit higher bulk density, lower crosslinking density, and narrow glass transitions. Consequently, a more homogeneous network structure was postulated for those networks. Whereas macroscopic properties of the modified final materials have already been studied, herein the microstructural arrangement of such modified networks has also been evaluated with the help of positron annihilation lifetime spectroscopy (PALS). A more homogenous network structure with a decreased average free‐volume void size was confirmed for CTA‐based dimethacrylate networks. A sharper distribution of the ortho‐positronium (o‐Ps) lifetime, mainly for the β‐allyl sulfone‐based photopolymers, hints toward a more regulated network structure. Moreover, the combination of PALS, DMTA, density and swelling experiments elucidates relations between void formation, crosslinking density and macroscopic characteristics such as shrinkage stress and mechanical properties. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 2476–2484     

Microfluidic tool based on the antibody-modified paramagnetic particles for detection of 8-hydroxy-2'-deoxyguanosine in urine of prostate cancer patients

Guanosine derivatives are important for diagnosis of oxidative DNA damage including 8-hydroxy-2'-deoxyguanosine (8-OHdG) as one of the most abundant products of DNA oxidation. This compound is commonly determined in urine, which makes 8-OHdG a good non-invasive marker of oxidation stress. In this study, we optimized and tested the isolation of 8-OHdG from biological matrix by using paramagnetic particles with an antibody-modified surface. 8-OHdG was determined using 1-naphthol generated by alkaline phosphatase conjugated with the secondary antibody. 1-Naphthol was determined by stopped flow injection analysis (SFIA) with electrochemical detector using a glassy carbon working electrode and by stationary electrochemical detection using linear sweep voltammetry. A special modular electrochemical SFIA system which needs only 10 μL of sample including working buffer for one analysis was completely designed and successfully verified. The recoveries in different matrices and analyte concentration were estimated. Detection limit (3 S/N) was estimated as 5 pg/mL of 8-OHdG. This method promises to be very easily modified to microfluidic systems as "lab on valve". The optimized method had sufficient selectivity and thus could be used for determination of 8-OHDG in human urine and therefore for estimation of oxidative DNA damage as a result of oxidation stress in prostate cancer patients.     

On the Energy Dissipation Rate of Solutions to the Compressible Isentropic Euler System

In this paper we extend and complement the results in Chiodaroli et al. (Global ill-posedness of the isentropic system of gas dynamics, 2014) on the well-posedness issue for weak solutions of the compressible isentropic Euler system in 2 space dimensions with pressure law p(ρ) = ρ ^γ , γ ≥ 1. First we show that every Riemann problem whose one-dimensional self-similar solution consists of two shocks admits also infinitely many two-dimensional admissible bounded weak solutions (not containing vacuum) generated by the method of De Lellis and Székelyhidi (Ann Math 170:1417–1436, 2009), (Arch Ration Mech Anal 195:225–260, 2010). Moreover we prove that for some of these Riemann problems and for 1 ≤ γ < 3 such solutions have a greater energy dissipation rate than the self-similar solution emanating from the same Riemann data. We therefore show that the maximal dissipation criterion proposed by Dafermos in (J Diff Equ 14:202–212, 1973) does not favour the classical self-similar solutions.     

Weak Characterizations of Stochastic Integrability and Dudley’s Theorem in Infinite Dimensions

In this paper we consider stochastic integration with respect to cylindrical Brownian motion in infinite-dimensional spaces. We study weak characterizations of stochastic integrability and present a natural continuation of results of van Neerven, Weis and the second named author. The limitation of weak characterizations will be demonstrated with a nontrivial counterexample. The second subject treated in the paper addresses representation theory for random variables in terms of stochastic integrals. In particular, we provide an infinite-dimensional version of Dudley’s representation theorem for random variables and an extension of Doob’s representation for martingales.     

Vertical symbols,Toeplitz operators on weighted Bergman spaces over the upper half-plane and very slowly oscillating functions

Extending a recent result of Herrera Yañez, Maximenko and Vasilevski, we provide a further step in the structural analysis of algebras generated by Toeplitz operators on weighted Bergman spaces over the upper half-plane. We show that the set of “spectral” functions corresponding to Toeplitz operators generated by bounded vertical symbols is dense in the C^?$C^{?}$-algebra of very slowly oscillating functions on the positive half-line.