Stability of the solutions to a nonlinear impulsive Caputo fractional differential equation is studied using Lyapunov like functions. The derivative of piecewise continuous Lyapunov functions among the nonlinear impulsive Caputo differential equation of fractional order is defined. This definition is a natural generalization of the Caputo fractional Dini derivative of a function. Several suffic...

We study the asymptotics of solutions logistic type equations with fractional Laplacian as time goes to infinity and exponent in nonlinear part infinity. prove strong convergence energy space uniform solution an obstacle problem. As a by-product, we also cut-off property for eigenvalues Dirichlet Laplace operator perturbed by exploding potentials.

BACKGROUND Increasing evidence suggests that ultrafine particles (UFPs) may contribute to cardiorespiratory morbidity. We examined the relationship between near road UFPs and several traffic and built environment factors to identify predictors that may be used to estimate exposures in population-based studies. Black carbon (BC) was also examined. METHODS Data were collected on up to 6 occasio...

The introductory part will feature: rate of approximation of real numbers by rationals; theorems of Kronecker, Dirichlet, Liouville, Borel-Cantelli; connections with dynamical systems: circle rotations, hyperbolic flow in the space of lattices, geodesic flow on the modular survace, Gauss map (continued fractions); ergodicity, unique ergodicity, mixing, applications to uniform distribution of se...

Particulate matter (PM) such as ultrafine particulate matter (UFP) and the organic compound pollutants such as polycyclic aromatic hydrocarbon (PAH) are widespread in the environment. UFP and PAH are present in the air, and their presence may enhance their individual adverse effects on human health. However, the mechanism and effect of their combined interactions on human cells are not well und...

Ultrafine particles (UFP, particles <100 nm) are ubiquitous in ambient urban and indoor air from multiple sources and may contribute to adverse respiratory and cardiovascular effects of particulate matter (PM). Depending on their particle size, inhaled UFP are efficiently deposited in nasal, tracheobronchial, and alveolar regions due to diffusion. Our previous rat studies have shown that UFP ca...

BACKGROUND While producing good-quality analgesia, µ-opioid (MOP) receptor activation produces a number of side-effects including tolerance. Simultaneous blockade of δ-opioid (DOP) receptors has been shown to reduce tolerance to morphine. Here, we characterize a prototype bifunctional opioid H-Dmt-Tic-Gly-NH-Bzl (UFP-505). METHODS We measured receptor binding affinity in Chinese hamster ovary...

The adverse health impact of particles and ultrafine (UFP) is proven, highlighting the need measuring particle number concentration (PNC) dominated by UFP. So far, PNC had never been measured in Strasbourg urban area (France). present study on size distribution measurements an UFP-3031 analyzer was conducted during winter 2019 a background roadside multi-instrumented sites (Black Carbon, chemic...

The fractional filtration efficiency for particles ranging from 5 nm to 100 nm was estimated based on previous publications. The downstream concentration and size distribution was calculated for each of four outdoor aerosols representing both urban and rural conditions. When interpreting data expressed as the total number concentration (dp>5 nm), the studied F7filter (corresponding roughly to M...