Weak convergence of quadratically Gaussian measures

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 41, No. 5, pp. 626–631, May, 1989.     

On the existence and the stability of solutions for higher-order semilinear Dirichlet problems

We investigate the existence and stability of solutions for higher-order two-point boundary value problems in case the differential operator is not necessarily positive definite, i.e. with superlinear nonlinearities. We write an abstract realization of the Dirichlet problem and provide abstract existence and stability results which are further applied to concrete problems.     

Interpolation of positive operators

We study problems of interpolation of positive linear operators in couples of ordered Banach spaces. From this viewpoint, we study couples of noncommutative spaces L ₁, L _∞ associated with weights and traces on von Neumann algebras.     

Stability of shock waves in the modified quintic complex Ginzburg-Landau equation

We consider a shock-type wave solution of the modified quintic complex Ginzburg-Landau equation and make a numerical study of its spatiotemporal stability. Discussions related to the behavior of this front wave are introduced and it is shown how the velocities of the wave can be used to collect information concerning the pattern formation in the system. Published in Neliniini Kolyvannya, Vol. 10, No. 2, pp. 270–276, April–June, 2007.     

Estimate of the concentration function for a class of additive functions

We show how methods for estimating the concentration function of the sum of independent random variables can be used to obtain estimates of the concentration function for the values of additive functions under suitable conditions. Previously obtained estimates of the concentration function are consequences of the estimate obtained in the present paper for functions from of the class under consideration.