Singular stochastic equations on Hilbert spaces: Harnack inequalities for their transition semigroups

We consider stochastic equations in Hilbert spaces with singular drift in the framework of [G. Da Prato, M. Röckner, Singular dissipative stochastic equations in Hilbert spaces, Probab. Theory Related Fields 124 (2) (2002) 261-303]. We prove a Harnack inequality (in the sense of [F.-Y. Wang, Logarithmic Sobolev inequalities on noncompact Riemannian manifolds, Probab. Theory Related Fields 109 (1997) 417-424]) for its transition semigroup and exploit its consequences. In particular, we prove regularizing and ultraboundedness properties of the transition semigroup as well as that the corresponding Kolmogorov operator has at most one infinitesimally invariant measure μ (satisfying some mild integrability conditions). Finally, we prove existence of such a measure μ for noncontinuous drifts.     

Harnack inequality and continuity of solutions to quasi-linear degenerate parabolic equations with coefficients from Kato-type classes

For a general class of divergence type quasi-linear degenerate parabolic equations with measurable coefficients and lower order terms from nonlinear Kato-type classes, we prove local boundedness and continuity of solutions, and the intrinsic Harnack inequality for positive solutions.     

Asymptotic Log-Harnack inequality and applications for stochastic systems of infinite memory

The asymptotic log-Harnack inequality is established for several kinds of models on stochastic differential systems with infinite memory: non-degenerate SDEs, neutral SDEs, semi-linear SPDEs, and stochastic Hamiltonian systems. As applications, the following properties are derived for the associated segment Markov semigroups: asymptotic heat kernel estimate, uniqueness of the invariant probability measure, asymptotic gradient estimate (hence, asymptotically strong Feller property), as well as asymptotic irreducibility.     

High rate production of antihydrogen

We show that antihydrogen production is the dominant process when mixing antiprotons and positrons in the ATHENA apparatus, and that the initial production rate exceeds 300 Hz, decaying to 30 Hz within 10 s. A fraction of 65% of all observed annihilations is due to antihydrogen.     

The Cellular Interactions of PEGylated Gold Nanoparticles: Effect of PEGylation on Cellular Uptake and Cytotoxicity

Poly(ethylene glycol) (PEG) is frequently used to coat various medical nanoparticles (NPs). As PEG is known to minimize NP interactions with biological specimens, the question remains whether PEGylated NPs are intrinsically less toxic or whether this is caused by reduced NP uptake. In the present work, the effect of gold NP PEGylation on uptake by three cell types is compared and evaluated the effect on cell viability, oxidative stress, cell morphology, and functionality using a multiparametric methodology. The data reveal that PEGylation affects cellular NP uptake in a cell‐type‐dependent manner and influences toxicity by different mechanisms. At similar intracellular NP numbers, PEGylated NPs are found to yield higher levels of cell death, mostly by induction of oxidative stress. These findings reveal that PEGylation significantly reduces NP uptake, but that at similar functional (= cell‐associated) NP levels, non‐PEGylated NPs are better tolerated by the cells.     

Modelling the behavior of the positron plasma temperature in antihydrogen experimentation

Antihydrogen is now routinely produced at CERN by overlapping clouds of positrons and antiprotons. The mechanisms responsible for antihydrogen formation (radiative capture and the three-body reaction) are both dependent on the temperature of the positrons (T _e ), though with a different weight. Here we present a simple model of the behavior of the positron temperature based on the main processes involved during antihydrogen synthesis, namely: antiproton–positron collisions, positron heating due to plasma expansion and cooling via the emission of synchrotron radiation. The time evolution of T _e has been simulated by changing the relevant parameters of the mechanisms involved in order to highlight the importance of the different (competing) effects.     

Finite stopping time problems and rheometry of Bingham fluids

It is shown that steady channel, simple shear and Couette flows of a Bingham fluid come to rest in a finite amount of time, if either the applied pressure falls below a critical value, or the moving boundaries are brought to rest. An explicit formula for a bound on the finite stopping time in each case is derived. This bound depends on the density, the viscosity, the yield stress, a new geometric constant, and the least eigenvalue of the second order linear differential operator for the interval under consideration.     

Hydrothermal preparation of CuGaS2 crystallites with different morphologies

The CuGaS₂ crystallites with different morphologies were prepared at 160 °C through hydrothermal process by using CuCl, GaCl₃ solution, and thiourea as source materials. The samples were characterized by means of X-ray powder diffraction, element analysis, transmission electron microscopy, and photoluminescence (PL). In present route, as-prepared CuGaS₂ crystallites displayed spherical and whisker-like nanoparticles and snowflake-like micrometer particles. Room temperature PL spectrum of the snowflake-like crystallites exhibits a weak emission band at 540 nm and a broad strong emission band at 735 nm. The role that the reaction media played in the morphologies of the CuGaS₂ crystallites was investigated, and a possible reaction mechanism was proposed.     

Electronic subband of single Siδ-doped GaAs structures

We have theoretically investigated the subband structure of single Si δ -doped GaAs inserted into a quantum well at T =  0 K. We will discuss the influence of the δ -doping concentration, the δ -layer thickness and diffusion of donor impurities. The spread of the impurities are taken into account in two different models: (i) a uniform distribution and (ii) a nonuniform distribution. In this paper, the nonuniform distribution is different from the Gaussian distribution use of other authors. The electronic structures have been calculated by solving the Schrödinger and Poisson equations self-consistently. We thus find the confining potential, the subband energies and their eigen envelope functions, the subband occupations and Fermi energy.     

Martingale property of empirical processes

It is shown that for a large collection of independent martingales, the martingale property is preserved on the empirical processes. Under the assumptions of independence and identical finite-dimensional distributions, it is proved that a large collection of stochastic processes are martingales essentially if and only if the empirical processes are also martingales. These two results have implications on the testability of the martingale property in scientific modeling. Extensions to submartingales and supermartingales are given.