An Euler equation is a difference or differential equation that is an intertemporal first-order condition for a dynamic choice problem. It describes the evolution of economic variables along an optimal path. It is a necessary but not sufficient condition for a candidate optimal path, and so is useful for partially characterizing the theoretical implications of a range of models for dynamic beha...

In the paper, the authors view some ordinary differential equations and their solutions from the angle of (the generalized) derivative polynomials and simplify some known identities for the Bernoulli numbers and polynomials, the Frobenius-Euler polynomials, the Euler numbers and polynomials, in terms of the Stirling numbers of the first and second kinds.

We prove the non-uniform continuity of data-to-solution map incompressible Euler equations in Besov spaces, B p , q s where parameters and considered here are such that local existence uniqueness result holds.

This work discusses issues concerning stability, tuning and dynamics of convergence of observer-based kinetics estimators. The analysis focuses on both continuous and discrete time formulations of the estimation algorithms. Concerning the former, it is shown that, with proper tuning, stability can be guaranteed, while simultaneously imposing a desired quasi-time invariant second order time resp...

Asymptotic linear stability is studied for stochastic differential equations (SDEs) that incorporate Poisson-driven jumps and their numerical simulation using theta-method discretisations. The property is shown to have a simple explicit characterisation for the SDE, whereas for the discretisation a condition is found that is amenable to numerical evaluation. This allows us to evaluate the asymp...

A transformation is derived which takes the Lorenz integrable system into the well-known Euler equations of a torque-free rigid body about a fixed point, i.e. the famous motionà la Poinsot. The proof is based on Lie group analysis applied to two third-order ordinary differential equations admitting the same two-dimensional Lie symmetry algebra. Lie's classification of two-dimensional symmetry a...

We have adapted a simple method of numerical integration to predict the equilibrium state of a population of components undergoing reversible association according to the Law of Mass Action. Its particular application is to populations of protein molecules in aqueous solution. The method is based on Euler integration but employs an adaptive step size: the time increment being reduced if it woul...

A transformation is derived which takes Lorenz integrable system into the well-known Euler equations of a free-torque rigid body with a fixed point, i.e. the famous motionà la Poinsot. The proof is based on Lie group analysis applied to two third order ordinary differential equations admitting the same two-dimensional Lie symmetry algebra. Lie's classification of two-dimensional symmetry algebr...