Kolmogorov Type Law of the Logarithm for Arrays

In this paper, we establish the analogue of Kolmogorov-type law of the logarithm for an array of independent random variables. The main methods are to develop the classic Bernstein’s and Kolmogorov’s inequality and replace the boundedness condition by conditions on the cumulant transform.     

A Non-normal-mode Marginal State of Convection in a Porous Box with Insulating End-Walls

Transport in Porous Media - The 4th order Darcy–Bénard eigenvalue problem for the onset of thermal convection in a 3D rectangular porous box is investigated. We start from a recent 2D...     

Amplification of wind waves in reservoirs of finite depth

A method for predicting the generation and amplification of waves from the zone of generation to large fetches, where infragravity waves occur in water of finite depth, is developed from a physical model of interaction between a horizontal air flow and a water surface caused by periodic formation of vortices in the viscous air layer. The model describes the origination of multiple frequencies, and the displacement of wave energy to low-frequency region over a fetch.     

Dynamics of solutions of the Cauchy problem for semilinear parabolic stochastic partial differential equations with power-law singularities

We prove a comparison theorem for bounded solutions of the Cauchy problem for stochastic partial differential equations of the parabolic type with linear leading part. The drift and diffusion coefficients have locally bounded derivatives with respect to the state variable. We use this comparison theorem to study the dynamics of solutions of an equation with an absorber and an equation with a source.     

Unique Path Partitions: Characterization and Congruences

We give a complete classification of the unique path partitions and study congruence properties of the function which enumerates such partitions.