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.     

Simultaneous brightness enhancement and wavelength conversion to the eye‐safe region in a high‐power diamond Raman laser

Brightness enhancement in an external cavity diamond Raman laser designed for high power conversion of a neodymium (1064 nm) laser to the eye‐safe spectral region is reported. Using a multimode input beam pulsed at 36 kHz pulse repetition frequency, 16.2 W with 40% overall conversion efficiency was obtained at the second Stokes wavelength of 1485 nm. The output beam had a quality factor of which is a factor of 2.7 times lower than that of the input beam, resulting in a higher overall brightness. The output power, brightness, and brightness enhancement obtained represent significant advances in performance for Raman lasers as well as other competing kHz‐pulsed eye‐safe technologies.     

Genetic algorithms for the 2-page book drawing problem of graphs

The minimisation of edge crossings in a book drawing of a graph is one of the important goals for a linear VLSI design, and the 2-page crossing number of a graph provides an upper bound for the standard planar crossing number. We design genetic algorithms for the 2-page drawings, and test them on the benchmark test suits, Rome graphs and Random Connected Graphs. We also test some circulant graphs, and get better results than previously presented in the literature. Moreover, we formalise three conjectures for certain kinds of circulant graphs,supported by our experimental results.     

Thermal stability of surface-esterified cellulose and its composite with polyolefinic matrix

Thermal stability of hydrophobized cellulose powders was investigated from the perspective of potential use as filler in non-polar polyolefinic matrix. The hydrophobization was done by heterogeneous esterification with three carboxylic acids which differ in chain length (3, 10 and 18 carbons). Data measured by means of thermogravimetry (TG) were recalculated according to model-free isoconversional method to construct time–temperature plots. It was demonstrated that the esterification significantly decreases thermal stability of the material, which reduces feasible processing window. Under non-oxidative atmosphere, the single-step decomposition of materials is prevailing, while the process is more complex in air. In both cases the oleic acid esters showed the lowest stability and the original cellulose was the most stable. Finally, all powders were compounded with polyethylene or polypropylene. Obtained composites were then subjected to color measurement and TG. Even though the materials were partly degraded, which was indicated by the yellowish hue of the composites, virtually no impact of the filler pyrolysis on the polymer matrix decomposition was observed, particularly in case of decanoyl esters.     

Efficient Raman frequency conversion of high‐power fiber lasers in diamond

We report high‐power frequency conversion of a Yb‐doped fiber laser using a double‐pass pumped external‐cavity diamond Raman oscillator. Pumping with circular polarization is shown to be efficient while facilitating high‐power optical isolation between the pump and Raman laser. We achieved continuous‐wave average power of 154 W with a conversion efficiency of 50.5% limited by backward‐amplified light in the fiber laser. In order to prove further scalability, we achieved a maximum steady‐state Raman‐shifted output of 381 W with 61% conversion efficiency and excellent beam quality using 10 ms pump pulses, approximately a thousand times longer than the transient thermal time‐constant. No power saturation or degradation in beam quality is observed. The results challenge the present understanding of heat deposition in Raman crystals and foreshadow prospects for reduced thermal effects in diamond than originally anticipated. We also report the first experimental evidence for stimulated Brillouin scattering in diamond.

     

γ-Fe2O3 Nanoparticles Covered with Glutathione-Modified Quantum Dots as a Fluorescent Nanotransporter

The present paper describes the synthesis, characterization, and utilization of multi-functional magnetic conjugates that integrate optical and magnetic properties in a single structure for use in many biomedical applications. Spontaneous interaction with eukaryotic cell membrane (HEK-239 cell culture) was determined using fluorescence microscopy, and fluorescence analyses. Both, differences in excitation, and emission wavelength were observed, caused by glutathione intake by cells, resulting in disintegration of core–shell structure of quantum dots, as well as adhesion of conjugate onto cell surface. When compared with quantum dots fluorescent properties, HEK-239 cells with incorporated nanoconjugate exhibited two excitation maxima (λ _ex = 430 and 390 nm). Simultaneously, application of ideal λ _ex for quantum dots (λ _ex = 430 nm), resulted in two emission maxima (λ = 740 and 750 nm). This nanoconjugate fulfills the requirements of term theranostics, because it can be further functionalized with biomolecules as DNA, proteins, peptides or antibodies, and thus serves as a tool for therapy in combination with simultaneous treatment.     

Fluorescence resonance energy transfer between green fluorescent protein and doxorubicin enabled by DNA nanotechnology

DNA nanotechnology is a rapidly growing research area, where DNA may be used for wide range of applications such as construction of nanodevices serving for large scale of diverse purposes. Likewise a panel of various purified fluorescent proteins is investigated for their ability to emit their typical fluorescence spectra under influence of particular excitation. Hence these proteins may form ideal donor molecules for assembly of fluorescence resonance emission transfer (FRET) constructions. To extend the application possibilities of fluorescent proteins, while using DNA nanotechnology, we developed nanoconstruction comprising green fluorescent protein (GFP) bound onto surface of surface active nanomaghemite and functionalized with gold nanoparticles. We took advantage of natural affinity between gold and thiol moieties, which were modified to bind DNA fragment. Finally we enclosed doxorubicin into fullerene cages. Doxorubicin intercalated in DNA fragment bound on the particles and thus we were able to connect these parts together. Because GFP behaved as a donor and doxorubicin as an acceptor using excitation wavelength for GFP (395 nm) in emission wavelength of doxorubicin (590 nm) FRET was observed. This nanoconstruction may serve as a double‐labeled transporter of doxorubicin guided by force of external magnetic force owing to the presence of nanomaghemite. Further nanomaghemite offers the possibility of using this technology for thermotherapy.     

Spectrometric and Chromatographic Study of Reactive Oxidants Hypochlorous and Hypobromous Acids and Their Interactions with Taurine

In this study, we focused on the studying of taurine complexes with phenol and sodium hypochlorite, and of taurine with sodium hypobromite by spectrometry, reverse phase chromatography and ion-exchange chromatography. The formed complexes were studied under various conditions such as temperature (10, 20, 30, 40, 50 and 60 °C), and/or time of interaction (0, 5, 10, 15, 20, 25 and 30 min). In addition, we optimized high performance liquid chromatography coupled with UV detector for detection of taurine and its complexes with the acids. Taurine–phenol–hypochlorite complex was effectively separated under isocratic elution, mobile phase water:methanol 30:70 %, v:v, flow rate 1 mL min^?1 and 55 °C. Taurine-bromamine complex was isolated under the following optimized conditions as isocratic elution, mobile phase water:methanol 85:15 % v:v, flow rate 1 mL min^?1 and 55 °C. The limits of detection (3 S/N) were estimated as 1 μM for both types of complexes, i.e. for taurine. Further, we estimated recovery in one sample of urine (male 25 years), commercially achieved energy drink and tea leaves and varied from 79 to 86 %. Further, we aimed our attention at investigating the ability of the above characterized taurine and taurine complexes to scavenge reactive oxygen species. For this purpose, an ion-exchange liquid chromatography with post-column derivatization with ninhydrin and VIS detector was used. It clearly follows from the results obtained that taurine itself reacts with peroxide more intensely than in a bound form, which can be associated with the highest signal decrease. Complexes stabilized structure taurine against peroxide radicals, resulting in slower decreasing of peak heights. The most stable was taurine complexes with phenol and hypobromite.     

A Magnetically Drivable Nanovehicle for Curcumin with Antioxidant Capacity and MRI Relaxation Properties

Curcumin possesses wide‐ranging anti‐inflammatory and anti‐cancer properties and its biological activity can be linked to its potent antioxidant capacity. Superparamagnetic maghemite (γ‐Fe₂O₃), called surface‐active maghemite nanoparticles (SAMNs) were surface‐modified with curcumin molecules, due to the presence of under‐coordinated Fe^III atoms on the nanoparticle surface. The so‐obtained curcumin‐modified SAMNs (SAMN@curcumin) had a mean size of 13±4 nm. SAMN@curcumin was characterized by transmission and scanning electron microscopy, UV/Vis, FTIR, and Mössbauer spectroscopy, X‐ray powder diffraction, bulk susceptibility (SQUID), and relaxometry measurements (MRI imaging). The high negative contrast proclivity of SAMN@curcumin to act as potential contrast agent in MRI screenings was also tested. Moreover, the redox properties of bound curcumin were probed by electrochemistry. SAMN@curcumin was studied in the presence of different electroactive molecules, namely hydroquinone, NADH and ferrocyanide, to assess its redox behavior. Finally, SAMN@curcumin was electrochemically probed in the presence of hydrogen peroxide, demonstrating the stability and reactivity of bound curcumin.