Volume 19, Issue 5

Recently it has been proposed (in a simple model study of the surface fluxes) that there is a robust mechanism linking the surface temperature and the surface wind via atmospheric angular momentum transport. The analysis of the simple model suggested that the proposed mechanism can enhance the stabilizing effect of evaporation on the surface temperature. This issue is studied here using a simple two zone hemispheric model of the atmosphere-ocean system. We relax the two critical assumptions from the above-mentioned study, namely the assumption of a constant air-sea temperature difference and constant near-surface relative humidity, respectively. It is found from the stability analysis of the model that the proposed coupling of the surface wind to the sea surface temperature together with the Clausius–Clapeyron effect of the evaporation always increases the stability of the system as is seen in the earlier studies, but the extent to which it does is diminished by new feedbacks created by the relaxed assumptions. It is also seen that this main stabilizing effect of the surface energy budget, which is related to dynamics, has a different counterpart when looking at the top of the atmosphere energy budget which is related to the radiation. Finally, it is seen that, depending on the assumptions made, quite different physics are becoming responsible for the stability of the surface temperature.

The proteasomal proteolysis is assumed to be the main pathway of protein degradation in a cell. The studies of the proteasome structure and experiments in the proteasomal proteolysis of proteins in vitro raised questions regarding details of this process. We can attempt to elucidate them by computer simulation. We propose the model of the proteasomal proteolysis process of proteins in vitro and carry out computer experiments with it. We develop an algorithm for the direct simulation of the process by the model proposed. The mathematical results obtained allow us to appreciably reduce the computing time of the direct simulation. The form of the distribution curve of the lengths of protein segments, which was obtained in the calculations, coincides with that of the experimental curve. The explanation for the form of the curve corroborates the model chosen.

Using the example of the fourth-order classical boundary value problem, we investigate one of the approaches to the construction of a posteriori estimates of the accuracy of approximate solutions. The emphasis is made on the justification of the effectiveness of the method proposed. The respective conclusions of the theoretical part of the paper are confirmed by a series of numerical experiments.

In this paper it is shown that the fast multigrid algorithm (FMA) first proposed by the author in [A. D. Javadian, Fast multigrid algorithm for quasisingular classes of elliptic problems. Russ. J. Numer. Anal. Math. Modelling (2001) 16 , No. 5, 385–408.] is applicable to the solution of a sufficiently broad family of quasisingulsar classes of diffusion problems. The optimal accuracy in the sense of the Kolmogorov N -width is attained using O (| ln ε | 3 N ) operations, where ε is the minimum value of the coefficient in the problem.

In this paper we give the results obtained by the constructed probabilistic representation of the solution to the first boundary value problem for a polyharmonic equation. It is shown that this solution is expressed by the parametric derivative of the solution to the specially constructed Dirichlet problem for the Helmholtz equation. On this basis we develop new algorithms of 'walk on a grid' and 'random walk by spheres' for the solution of a polyharmonic equation.

Using the eigenfunctions of two Sturm–Liouville problems (with the same operator of a general form but with two different versions of boundary conditions), a method for constructing these specific basis functions is developed. The corresponding expansions of smooth and piecewise smooth functions in terms of such basis lead to fast convergent series. This result makes it possible to approximate the functions of the above class by a small number of terms. We also give brief information on a method for constructing multidimensional (in particular, two-dimensional) specific basis functions with the above properties. The proposed method is based on the ideas of the author's earlier works. However, it is, in essence, a new method that has substantially improved characteristics and is mainly oriented to the approximation of piecewise smooth functions. We also consider several important special cases.