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## Numerical stabilization of the Lorenz system by a small external perturbation

### Computational Mathematics and Mathematical Physics (2006-08-01) 46: 1341-1348 , August 01, 2006

The Lorenz system perturbed by noise and its invariant measure whose density obeys the stationary Fokker-Planck equation are analyzed numerically. A linear functional of the invariant measure is considered, and its variation caused by a variation in the right-hand side of the Lorenz system is calculated. A small (in modulus) external perturbation is calculated under which the strange attractor of the Lorenz system degenerates into a stable fixed point.

## Solution of a stochastic Darcy equation by polynomial chaos expansion

### Numerical Analysis and Applications (2017-07-01) 10: 259-271 , July 01, 2017

This paper deals with solving a boundary value problem for the Darcy equation with a random hydraulic conductivity field.We use an approach based on polynomial chaos expansion in a probability space of input data.We use a probabilistic collocation method to calculate the coefficients of the polynomial chaos expansion. The computational complexity of this algorithm is determined by the order of the polynomial chaos expansion and the number of terms in the Karhunen–Loève expansion. We calculate various Eulerian and Lagrangian statistical characteristics of the flow by the conventional Monte Carlo and probabilistic collocation methods. Our calculations show a significant advantage of the probabilistic collocation method over the directMonte Carlo algorithm.

## Double degeneracy in the problem on unbounded branches of forced oscillations

### Doklady Mathematics (2008-05-04) 77: 170-174 , May 04, 2008

## Multiscale approach to computation of three-dimensional gas mixture flows in engineering microchannels

### Doklady Mathematics (2016-07-01) 94: 458-460 , July 01, 2016

A multiscale approach to computing real gas flows in engineering microchannels on high-performance computer systems in a wide range of Knudsen numbers is described. The numerical implementation of the approach combines the solution of quasigasdynamic equations and the molecular dynamics method. Following the approach, the parameters of the real gas equation of state are found at the molecular level, the kinetic gas properties are calculated, and the form of boundary conditions on the microchannel walls are determined. The technique is verified by computing several test problems. The results agree well with available theoretical and experimental data.

## On the 90th anniversary of the birthday of Academician Nikita Nikolaevich Moiseev

### Computational Mathematics and Mathematical Physics (2008-09-01) 48: 1447-1453 , September 01, 2008

## Algebrogeometric solutions of the nonlinear boundary problem on a segment for the sine-Gordon equation

### Mathematical Notes (1992-10-01) 52: 1005-1011 , October 01, 1992

## Antiproximinal convex bounded sets in the space c0(Γ) equipped with the day norm

### Mathematical Notes (2006-03-01) 79: 299-313 , March 01, 2006

We construct a convex smooth antiproximinal set in any infinite-dimensional space *c*_{0}(Γ) equipped with the Day norm; moreover, the distance function to the set is Gâteaux differentiable at each point of the complement.

## Analytical model of data transmission in the IEEE 802.16 network

### Automation and Remote Control (2009-11-18) 70: 1843-1855 , November 18, 2009

In the wireless networks controlled by the IEEE 802.16 protocol, the subscriber stations reserve the common channel using the mechanism of competitive access. Developed was an analytical model for studying the efficiency of transmission of the upward traffic in IEEE 802.16 network including the processes of channel reservation by the algorithm of multiple random access and packet transmission.

## Distributions of Poles to Painlevé Transcendents via Padé Approximations

### Constructive Approximation (2014-02-01) 39: 85-99 , February 01, 2014

A version of the Fair–Luke algorithm has been used to find the Padé approximate solutions to the Painlevé I, II, and IV equations. The distributions of poles in the complex plane are studied to check the dynamics of movable poles and the emergence of rational and truncated solutions, as well as various patterns formed by the poles. The high-order approximations allow us to check asymptotic expansions at infinity and estimate the range of asymptotic domains. The Coulomb gas interpretation of the pole ensembles is discussed in view of the patterns arising in Painlevé IV transcendents.

## Holographic relation between p-adic effective action and string field theory

### Proceedings of the Steklov Institute of Mathematics (2014-08-01) 285: 26-29 , August 01, 2014

We consider two holographically related theories. As the first (*d* + 1)-dimensional theory, we consider a model in which the (*d* + 1)-dimensional space is the direct product of ℝ^{d} and the half-axis ℝ_{+} and in which the kinetic operator has a nonlocal term induced by the nonlocal kinetic operator of the *p*-adic effective action. It turns out that the kinetic operator in the second, holographically related, *d*-dimensional theory is the kinetic operator of the string field theory effective action.