Quot-scheme limit of Fubini-Study metrics and Donaldson's functional for vector bundles

For a holomorphic vector bundle $E$ over a polarised K\"ahler manifold, we establish a direct link between the slope stability of $E$ and the asymptotic behaviour of Donaldson's functional, by defining the Quot-scheme limit of Fubini-Study metrics. In particular, we provide an explicit estimate which proves that Donaldson's functional is coercive on the set of Fubini-Study metrics if $E$ is slope stable, and give a new proof of Hermitian-Einstein metrics implying slope stability.

Tail distribution estimates of the mixed-fractional CEV model

The aim of this paper is to study the tail distribution of the CEV model driven by Brownian motion and fractional Brownian motion. Based on the techniques of Malliavin calculus and a result established recently in [<a href="#1">1</a>], we obtain an explicit estimate for tail distributions.

Modeling and animation of spring dynamic absorber

The investigation of the action of the spring dynamic absorber, as well as the calculation of the physical quantities of the constructed model and animation, was carried out using non-linear methods of the Runge-Kutta type. Using only three references to the right-hand side of the differential equation, a method of the third order of accuracy is constructed, as well as two-sided approximations of the second order of accuracy. An explicit estimate of the error at each point of integration is given.

Numerical assessment of the spread dynamics of the new coronavirus infection SARS-CoV-2 using multicompartmental models with distributed parameters

We propose multicompartmental models of infectious diseases dynamics for numerical study of the spread parameters of the new coronavirus infection SARS-CoV-2, which take into account the delay effects associated with the presence of the latent period of the infection, as well as the possibility of an asymptomatic course of the disease. The dynamics of the spread of COVID-19 in the Russian Federation was investigated, using these models with distributed parameters that formalize the interactions of the models’ compartments. The paper provides numerical estimates of the spread dynamics of the new coronavirus infection in various age groups of the population. We also investigate possible consequences of the mask regime and quarantine measures. We obtain an explicit estimate allowing to assess the necessary scope of these measures for the epidemy extinction.

Weak convergence of delay SDEs with applications to Carathéodory approximation

<p style='text-indent:20px;'>In this paper, we consider a fundamental class of stochastic differential equations with time delays. Our aim is to investigate the weak convergence with respect to delay parameter of the solutions. Based on the techniques of Malliavin calculus, we obtain an explicit estimate for the rate of convergence. An application to the Carathéodory approximation scheme of stochastic differential equations is provided as well.</p>

An iterative method for elliptic problems with rapidly oscillating coefficients

We introduce a new iterative method for computing solutions of elliptic equations with random rapidly oscillating coefficients. Similarly to a multigrid method, each step of the iteration involves different computations meant to address different length scales. However, we use here the homogenized equation on all scales larger than a fixed multiple of the scale of oscillation of the coefficients. While the performance of standard multigrid methods degrades rapidly under the regime of large scale separation that we consider here, we show an explicit estimate on the contraction factor of our method which is independent of the size of the domain. We also present numerical experiments which confirm the effectiveness of the method, with openly available source code.