Transfer of electronic excitation energy in partially disordered polymer chain

A new form of the generalized master equation for electronic excitation transfer in a partially disordered polymer chain was derived. Within this equation, in order to differentiate the transfer in ordered parts of the partially disordered polymer chain, we decomposed the memory function of electronic excitation into several parts. These parts are memory functions associated with various types of subdynamics of electronic excitation. The partially disordered polymer chain where the disorder is caused by conformational defects is discussed.     

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.     

Glycogen as a Biodegradable Construction Nanomaterial for in vivo Use

It is demonstrated that glycogen as a biodegradable and inexpensive material coming from renewable resources can be used as a carrier for the construction of in vivo imaging nanoagents. The model system considered is composed of glycogen modified with gadolinium and fluorescent labels. Systematic studies of properties of these nanocarriers by a variety of physical methods and results of in vivo tests of biodegradability are reported. This represents, to the authors' best knowledge, the first such use of glycogen.

     

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.     

Experimental and theoretical studies of the optimisation of fluorescence from near-infrared dye-doped silica nanoparticles

There is substantial interest in the development of near-infrared dye-doped nanoparticles (NPs) for a range of applications including immunocytochemistry, immunosorbent assays, flow cytometry, and DNA/protein microarray analysis. The main motivation for this work is the significant increase in NP fluorescence that may be obtained compared with a single dye label, for example Cy5. Dye-doped NPs were synthesised and a reduction in fluorescence as a function of dye concentration was correlated with the occurrence of homo-Förster resonance energy transfer (HFRET) in the NP. Using standard analytical expressions describing HFRET, we modelled the fluorescence of NPs as a function of dye loading. The results confirmed the occurrence of HFRET which arises from the small Stokes shift of near-infrared dyes and provided a simple method for predicting the optimum dye loading in NPs for maximum fluorescence. We used the inverse micelle method to prepare monodispersed silica NPs. The NPs were characterised using dynamic light scattering, UV spectroscopy, and transmission electron microscopy (TEM). The quantum efficiency of the dye inside the NPs, as a function of dye loading, was also determined. The fluorescent NPs were measured to be approximately 165 times brighter than the free dye, at an optimal loading of 2% (w/w). These experimental results were in good agreement with model predictions.

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Figure The change in nanoparticle fluorescence versus increased dye loading modelled using homo-Förster resonance energy transfer.

     

Synthesis of (pentacarbonyl)tungstate(−1) and (pentacarbonyl)molybdate(−1) dinucleotides

New methods for preparation of metallo dinucleotides with transition metals directly bonded to phosphorus are presented. (Pentacarbonyl)tungstate(−1) and (pentacarbonyl)molybdate(−1) dimers are prepared by the reaction of dinucleotide-H-phosphonate with M(CO)₅(THF) (M = W, Mo). These syntheses can be completed in solution or on solid-phase.     

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.