Introduction. Argyria is an acquired skin condition that appears after the exposure or consumption of silver, leading to blue or grey coloration of the skin and mucosa. The aim of the present work was to draw researchers’ attention to two aspects of the argyria that until now have not received enough consideration. They are: (1) the process of delivering silver compound from the gastrointestinal tract to the skin and (2) the possibility for silver chloride to participate in this process along with the silver proteinates. Methodology. Illustrative experiments included the observation of color change (visual and using UV-Vis spectrometry) under different light exposure conditions of silver chloride sol in a sweat-simulating solution, in vials and under pig skin (in direct contact). Results and Discussion. A hypothetical mechanism based on a perspiration system for delivering the silver compounds from the gastrointestinal tract to the skin for argyria was proposed. It was also proposed not to completely exclude the partial participation of silver chloride along with the silver proteinates in this process.
For the case of isotropic diffusion we consider the representation of the weighted concentration of trajectories and its space derivatives in the form of integrals (with some weights) of the solution to the corresponding boundary value problem and its directional derivative of a convective velocity. If the convective velocity at the domain boundary is degenerate and some other additional conditions are imposed, this representation allows us to construct an efficient 'random walk by spheres and balls' algorithm. When these conditions are violated, transition to modelling the diffusion trajectories by the Euler scheme is realized, and the directional derivative of velocity is estimated by the dependent testing method, using the parallel modelling of two closely-spaced diffusion trajectories. We succeeded in justifying this method by statistically equivalent transition to modelling a single trajectory after the first step in the Euler scheme, using a suitable weight. This weight also admits direct differentiation with respect to the initial coordinate along a given direction. The resulting weight algorithm for calculating concentration derivatives is especially efficient if the initial point is in the subdomain in which the coefficients of the diffusion equation are constant.¼ has the meaning of the weighted [with weight ´¡µ] concentration of diffusion trajectories starting at the point Ö. In this work, we construct the representation of the concentration Ù´¡µ and its space derivatives in £
We propose new weight modifications of a 'path* estimate for the calculation of linear functionals (Φ,/ι) of radiation intensity Φ. In the framework of the 'collision* model of a transport process we mathematically justify the estimate, including variance finiteness, in the case of the function /ι with alternating signs.We construct and justify the analogous 'time' estimate for the calculation of linear functionals of the concentration of particles moving along trajectories of multidimensional diffusion processes (the concentration of trajectories for brevity).In this paper we consider a problem of estimating the linear functionals (Φ, h) of radiation intensity Φ by new weight modifications of a 'path' estimate, which implies that the mean path of a particle in a domain is equal to the integral of radiation intensity in this domain. We use the 'collision' model of a transport process, i.e. the Markov homogeneous chain terminating with probability one. Its states are the points in the phase space of coordinate velocities at which instantaneous velocity changes occur along a random particle trajectory. In the framework of this model we mathematically justify 'path estiamates' in the case of the function h with alternating signs. Due to this justification we can study the problem of variance finiteness for the new weight modifications of the estimate as well, i.e. when an auxiliary 'nonphysicaF Markov chain is modelled and the estimate is multiplied by a special weight multiplier.We construct and justify the analogous 'time estimate' for the calculation of linear functionals of the concentration of particles moving along trajectories of multidimensional diffusion processes (the concentration of trajectories for brevity). This estimate is the trajectory time integral of a given weight function. We study the problem of the variance finiteness of this estimate and a possibility of its approximate numerical implementation by the Euler scheme. We establish a relation between the time estimate and the probabilistic representations of solutions of boundary value problems. Under certain conditions this allows us to justify the variance finiteness of the estimate if there is particle multiplication. It is shown that we can approximately calculate the first eigenvalue of a diffusion operator by the easily realizable parametric differentiation of a special weight estimate.
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