Yttrium-86 Is a Positron Emitting Surrogate of Gadolinium for Noninvasive Quantification of Whole-Body Distribution of Gadolinium-Based Contrast Agents

Gadolinium-based contrast agents (GBCAs) are used to provide diagnostic information in clinical magnetic resonance (MR) examinations. Gadolinium (Gd) has been detected in the brain, bone and skin of patients, months and years following GBCA administration, raising concerns about long term toxicity. Despite increased scrutiny, the concentration, chemical form and fate of the retained gadolinium species remain unknown. Importantly, the whole body biodistribution and organ clearance of GBCAs is poorly understood in humans. Gadolinium lacks suitable isotopes for nuclear imaging. We demonstrate that the yttrium-86 isotope can be used as a gadolinium surrogate. We show that Gd and their analogous Y complexes have similar properties both in solution and in vivo, and that yttrium-86 PET can be used to track the biodistribution of GBCAs over a two-day period.     

Nonlocal transmission problems with fractional diffusion and boundary conditions on non-smooth interfaces

We consider a transmission problem consisting of two semilinear parabolic equations involving fractional diffusion operators of different orders in a general non-smooth setting with emphasis on Lipschitz interfaces and transmission conditions along the interface. We give a unified framework for the existence and uniqueness of strong and mild solutions, and their global regularity properties.     

Existence and Besov regularity of the density for a class of SDEs with Volterra noise

By using a simple method based on the fractional integration by parts, we prove the existence and the Besov regularity of the density for solutions to stochastic differential equations driven by an additive Gaussian Volterra process. We assume weak regularity conditions on the drift. Several examples of Gaussian Volterra noises are discussed.     

Asymptotic expansion for vector-valued sequences of random variables with focus on Wiener chaos

We develop the asymptotic expansion theory for vector-valued sequences ${\left(F_N\right)}_{N\ge 1}$ of random variables in terms of the convergence of the Stein–Malliavin matrix associated with the sequence $F_N$. Our approach combines the classical Fourier approach and the recent Stein–Malliavin theory. We find the second order term of the asymptotic expansion of the density of $F_N$ and we illustrate our results by several examples.     

SPDE with generalized drift and fractional-type noise

We consider a stochastic partial differential equation involving a second order differential operator whose drift is discontinuous. The equation is driven by a Gaussian noise which behaves as a Wiener process in space and the time covariance generates a signed measure. This class includes the Brownian motion, fractional Brownian motion and other related processes. We give a necessary and sufficient condition for the existence of the solution and we study the path regularity of this solution.     

Small D–π–A Systems with o‐Phenylene‐Bridged Accepting Units as Active Materials for Organic Photovoltaics

Donor–acceptor (D–π–A) systems that combine triarylamine donor blocks and dicyanovinyl (DCV) acceptor groups have been synthesized. Starting from the triphenylamine (TPA)? thiophene? DCV compound ( 1 ) as a reference system, various synthetic approaches have been developed for controlling the light‐harvesting properties and energy levels of the frontier orbitals in this molecule. Thus, the introduction of methoxy groups onto TPA, the replacement of one phenyl ring of TPA by a thiophene ring, or the extension of the π‐conjugating spacer group lead to the modulation of the HOMO level. On the other hand, the fusion of the DCV group onto the vicinal thiophene ring by an ortho‐phenylene bridge allows for a specific fine‐tuning of the LUMO level. The electronic properties of the molecules were analyzed by using UV/Vis spectroscopy and cyclic voltammetry and the compounds were evaluated as donor materials in basic bilayer planar heterojunction solar cells by using C₆₀ as acceptor material. The relationships between the electronic properties of the donors and the performance of the corresponding photovoltaic devices are discussed. Bilayer planar heterojunction solar cells that used reference compound 1 and C₇₀ afforded power‐conversion efficiencies of up to 3.7 %.     

A note on statistical solutions of the three-dimensional Navier–Stokes equations: The stationary case

Stationary statistical solutions of the three-dimensional Navier–Stokes equations for incompressible fluids are considered. They are a mathematical formalization of the notion of ensemble average for turbulent flows in statistical equilibrium in time. They are also a generalization of the notion of invariant measure to the case of the three-dimensional Navier–Stokes equations, for which a global uniqueness result is not known to exist and a semigroup may not be well-defined in the classical sense. The two classical definitions of stationary statistical solutions are considered and compared, one of them being a particular case of the other and possessing a number of useful properties. Furthermore, the so-called time-average stationary statistical solutions, obtained as generalized limits of time averages of weak solutions as the averaging time goes to infinity are shown to belong to this more restrictive class. A recurrent type result is also obtained for statistical solutions satisfying an accretion condition. Finally, the weak global attractor of the three-dimensional Navier–Stokes equations is considered, and in particular it is shown that there exists a topologically large subset of the weak global attractor which is of full measure with respect to that particular class of stationary statistical solutions and which has a certain regularity property.