On some characterization of probability distributions in Hilbert spaces

Summary The aim of this paper is to prove the following theorem about characterization of probability distributions in Hilbert spaces:Theorem. — Let x₁, x₂, …, x_n be n (n≥3) independent random variables in the Hilbert spaceH, having their characteristic functionals f_k(t) = E[e^i(t,x _k)], (k=1, 2, …, n): let y₁=x₁ + x_n, y₂=x₂ + x_n, …, y_n−1=x_n−1 + x_n. If the characteristic functional f(t₁, t₂, …, t_n−1) of the random variables (y₁, y₂, …, y_n−1) does not vanish, then the joint distribution of (y₁, y₂, …, y_n−1) determines all the distributions of x₁, x₂, …, x_n up to change of location.     

Anisotropy Spectra of the Solvent-Sensitive Fluorophore 4-Dimethylamino-4′-Cyanostilbene in the Presence of Light Quenching

We examined the emission wavelength-dependent anisotropies of the solvent-sensitive fluorophore 4-dimethylamino-4-cyanostilbene (DCS) under conditions of light quenching by polarized time-delayed quenching pulses. Illumination on the long-wavelength side of the emission spectrum with time-delayed light pulses resulted in a progressive decrease in the emission anisotropy as the observation wavelength increased toward the stimulating wavelength. The anisotropy changes of DCS were most wavelength dependent when spectral relaxation occurred during the excited-state lifetime. Light quenching of DCS in a low-viscosity solvent revealed no wavelength-dependent anisotropies. Control measurements using a solvent-insensitive fluorophore did not show any wavelength-dependent anisotropy with light quenching. The data for DCS can be explained by a model which allows wavelength-selective quenching of the long-wavelength emission formed by time-dependent spectral relaxation. These results indicate that polarized light quenching can be used to study systems which display multiple emissions and/or time-dependent spectral shifts.     

Effects of reprocessing of oxobiodegradable and non-degradable polyethylene on the durability of recycled materials

The use of plastics is steadily increasing in our daily lives, and plastics are the fastest-growing component of the waste stream. Although the efficiency of plastic recycling is increasing, plastics are often seen as a permanent environmental problem because of littering. The introduction of oxobiodegradable polyolefins (OBDs), containing prodegradant additives, is considered to be a way to reduce this problem by enabling the fast degradation of plastics in the environment. The prodegradant additives form radicals that attack the polymer chains, causing chain scissions and generation of low molecular mass oxidation products that can be consumed by microorganisms. There is, however, a concern that the prodegradant additives will present a problem if OBD materials end up in the conventional plastic recycling streams. The present study therefore highlights the impact of mixing OBD materials with conventional polyolefins to evaluate the impact on the remaining service life of the recyclates.The study included the use of two different OBDs, mixed in different proportions (10% and 20%) in a conventional polyethylene. The remaining service life of the mixtures was evaluated by monitoring the reduction in tensile strain after exposure to thermo-oxidative degradation at 70 °C, compared with a pure polyethylene. The impact of stabilizer content in the mixtures was also evaluated together with the effect of mixing partially degraded OBDs into the recyclate.The results show that the incorporation of minor fractions of OBD materials in the existing recycling streams will not create a severe effect on the service life of the recyclates as long as the polymer mixture possesses a reasonable degree of stabilization.     

Roughened silver electrodes for use in metal-enhanced fluorescence

Roughened silver electrodes are widely used for surface-enhanced Raman scattering (SERS). We tested roughened silver electrodes for metal-enhanced fluorescence. Constant current between two silver electrodes in pure water resulted in the growth of fractal-like structures on the cathode. This electrode was coated with a monolayer of human serum albumin (HSA) protein that had been labeled with a fluorescent dye, indocyanine green (ICG). The fluorescence intensity of ICG-HSA on the roughened electrode increased by approximately 50-fold relative to the unroughened electrode, which was essentially non-fluorescent and increased typically two-fold as compared to the silver anode. No fractal-like structures were observed on the anode. Lifetime measurements showed that at least part of the increased intensity was due to an increased radiative decay rate of ICG. In our opinion, the use of in situ generated roughened silver electrodes will find multifarious applications in analytical chemistry, such as in fluorescence based assays, in an analogous manner to the now widespread use of SERS. To the best of our knowledge this is the first report of roughened silver electrodes for metal-enhanced fluorescence.     

Properties of coatings on RFID p-Chips that support plasmonic fluorescence enhancement in bioassays

Microtransponders (RFID p-Chips) derivatized with silver island film (SIF) have previously seen success as a platform for the quantification of low-abundance biomolecules in nucleic acid based assays and immunoassays. In this study, we further characterized the morphology of the SIF as well as the polymer matrix enveloping it by scanning electron microscopy (SEM). The polymer was a two-layer silane-based matrix engulfing the p-Chip and SIF. Through a series of SEM and confocal fluorescence microscopy experiments, we found the depth of the polymer matrix to be 1–2?μm. The radiative effects of the SIF/polymer layer were assessed by fluorescence lifetime imaging (FLIM) of p-Chips coated with the polymer to which a fluorophore (Alexa Fluor 555) was conjugated. FLIM images showed an 8.7-fold increase in fluorescence intensity and an increased rate of radiative decay, the latter of which is associated with improved photostability and both of which are linked to plasmonic enhancement by the SIF. Plasmonic enhancement was found to extend uniformly across the p-Chip and, interestingly, to a depth of about 1.2?μm. The substantial depth of enhancement suggests that the SIF/polymer layer constitutes a three-dimensional matrix that is accessible to solvent and small molecules such as fluorescent dyes. Finally, we confirmed that no surface-enhanced Raman scattering is seen from the SIF/polymer combination. The analysis provides a possible mechanism by which the SIF/polymer-coated p-Chips allow a highly sensitive immunoassay and, as a result, leads to an improved bioassay platform.     

Multi-Photon Sensitized Excitation of Near Infrared Emitting Lanthanides

Near infrared (NIR) multi-photon excitation of the NIR-emitting lanthanides neodymium (Nd³⁺) and ytterbium (Yb³⁺) sensitized by a fluorescein-linked chelator was demonstrated. Because tissues display minimal absorbance near the excitation wavelength of 800 nm, and because the lanthanides display long decay times, these results suggest the use of Nd³⁺ and Yb³⁺ as luminescent probes in tissues with multi-photon excitation.     

Emerging biomedical and advanced applications of time-resolved fluorescence spectroscopy

Time-resolved fluorescence spectroscopy is presently regarded as a research tool in biochemistry, biophysics, and chemical physics. Advances in laser technology, the development of long-wavelength probes, and the use of lifetime-based methods, are resulting in the rapid migration of timeresolved fluorescence to the clinical chemistry lab, the patient's bedside, and even to the doctor's office and home health care. Additionally, time-resolved imaging is now a reality in fluorescence microscopy and will provide chemical imaging of a variety of intracellular analytes and/or cellular phenomena. Future horizons of state-of-the-art spectroscopy are also described. Two photon-induced fluorescence provides an increased information content to time-resolved data. Two photoninduced fluorescence, combined with fluorescence microscopy and time-resolved imaging, promises to provide detailed three-dimensional chemical imaging of cells. Additionally, it has recently been demonstrated that the pulses from modern picosecond lasers can be used to quench and/or modify the excited-state population by stimulated emission since the stimulated photons are directed along the quenching beam and are not observed. The phenomenon of light quenching should allow a new class of multipulse time-resolved fluorescence experiments, in which the excited-state population is modified by additional pulses to provide highly oriented systems.