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1.
We obtain solutions of new extremal problems of the geometric theory of functions of a complex variable related to estimates
for the inner radii of nonoverlapping domains. Some known results are generalized to the case of open sets.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 10, pp. 1313–1321, October, 2007. 相似文献
2.
We study applications of the theory of quadratic differentials to the solution of new extremal problems of nonoverlapping
domains with free poles on rays and generalize known results to a certain class of open sets.
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Translated from Neliniini Kolyvannya, Vol. 10, No. 4, pp. 435–442, October–December, 2007. 相似文献
3.
The first goal of this paper is to prove multiple asymptotic results for a time-discrete and space-continuous polymer model of a random walk in a random potential. These results include: existence of deterministic free energy density in the infinite-volume limit for every fixed asymptotic slope, concentration inequalities for free energy implying a bound on its fluctuation exponent, and straightness estimates implying a bound on the transversal fluctuation exponent. The culmination of this program is almost sure existence and uniqueness of polymer measures on one-sided infinite paths with given endpoint and slope, and interpretation of these infinite-volume Gibbs measures as thermodynamic limits. Moreover, we prove that marginals of polymer measures with the same slope and different endpoints are asymptotic to each other. The second goal of the paper is to develop ergodic theory of the Burgers equation with positive viscosity and random kick forcing on the real line without any compactness assumptions. Namely, we prove a one force–one solution principle, using the infinite-volume polymer measures to construct a family of stationary global solutions for this system, and proving that each of those solutions is a one-point pullback attractor on the initial conditions with the same spatial average. This provides a natural extension of the same program realized for the inviscid Burgers equation with the help of action minimizers that can be viewed as zero temperature limits of polymer measures. © 2018 Wiley Periodicals, Inc. 相似文献
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We study extremal problems for domains with free poles that belong to ray systems of points.
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Translated from Neliniini Kolyvannya, Vol. 8, No. 3, pp. 298–303, July–September, 2005. 相似文献
7.
Gurbatov S. N. Vyugin P. N. Deryabin M. S. Kasyanov D. A. Kurin V. V. Tyurina A. V. Bakhtin V. K. 《Acoustical Physics》2021,67(3):237-244
Acoustical Physics - The paper presents the experimental and theoretical studies of diffraction effects in intense acoustic beams diffracted by a narrow circular aperture in a screen. The... 相似文献
8.
A. K. Bakhtin 《Ukrainian Mathematical Journal》2007,59(12):1800-1818
We study extremal problems of the geometric theory of functions of a complex variable. Sharp upper estimates are obtained
for the product of inner radii of disjoint domains and open sets with respect to equiradial systems of points.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 12, pp. 1601–1618, December, 2007. 相似文献
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