This paper deals with almost sure and moment exponential stability of a class of predictorcorrector methods applied to the stochastic differential equations of Itô-type. Stability criteria for this type of methods are derived. The methods are shown to maintain almost sure and moment exponential stability for all sufficiently small timesteps under appropriate conditions. A numerical experiment f...

The exact controllability to the origin for linear evolution control equation is considered.The problem is investigated by its transformation to infinite linear moment problem. Conditions for the existence of solution for infinite linear moment problem has been obtained. The obtained results are applied to the zero controllability for control evolution equations.

We establish the non-singular Hasse Principle for pairs of diagonal quartic equations in 22 or more variables. Our methods involve the estimation of a certain entangled two-dimensional 21 moment of quartic smooth Weyl sums via a novel cubic moment of Fourier coefficients.

In lecture 29, we introduced the Euler angles as a framework for formulating and solving the equations for conservation of angular momentum. We applied this framework to the free-body motion of a symmetrical body whose angular momentum vector was not aligned with a principal axis. The angular moment was however constant. We now apply Euler angles and Euler’s equations to a slightly more general...

We consider the moment-closure approach to transport equations which arise in Mathematical Biology. We show that the negative L2-norm is an entropy in the sense of thermodynamics, and it satisfies an H-theorem. With an L2-norm minimization procedure we formally close the moment hierarchy for the first two moments. The closure leads to semilinear Cattaneo systems, which are closely related to da...