Related papers: Quasi-Lie schemes and Emden--Fowler equations
Conventional finite-difference schemes for solving partial differential equations are based on approximating derivatives by finite-differences. In this work, an alternative theory is proposed which view finite-difference schemes as…
A recent development of the studies on classical and quasi-classical properties of supersymmetric quantum mechanics in Witten's version is reviewed. First, classical mechanics of a supersymmetric system is considered. Solutions of the…
Computational feasibility of turbulent reacting flows hinges on the reduction of large chemical kinetics systems to smaller more manageable reaction sets. Recently, several sophisticated reduction techniques have been developed but they…
Mechanisms that stabilize quasicrystals are much discussed but not finally resolved. We confirm the random tiling hypothesis and its predictions in a fully atomistic decagonal quasicrystal model by calculating the free energy and the phason…
In this contribution, a new class of lattice Boltzmann schemes is introduced and studied. These schemes are presented in a framework that generalizes the multiple relaxation times method of d'Humi\`eres. They extend also the Geier's…
We consider structural equation modeling (SEM) with latent variables for diffusion processes based on high-frequency data. We derive the quasi-likelihood estimators for parameters in the SEM. The goodness-of-fit test based on the…
We study, from a purely quantitative point of view, the quasi-steady-state assumption for the fundamental mathematical model of the general enzymatic reaction: we re-establish, on a rigorous basis, certain already known results and we…
While not generally a conservation law, any symmetry of the equations of motion implies a useful reduction of any second-order equationto a first-order equation between invariants, whose solutions (first integrals) can then be integrated by…
The general conditions under which the quadratic, uniform and monotonic convergence in the quasilinearization method of solving nonlinear ordinary differential equations could be proved are formulated and elaborated. The generalization of…
This article provides a survey of recent research efforts on the application of quasi-Monte Carlo (QMC) methods to elliptic partial differential equations (PDEs) with random diffusion coefficients. It considers, and contrasts, the uniform…
In this paper we give necessary and sufficient conditions for the existence of solutions to quasilinear equations of Lane--Emden type with measure data on a Carnot group $\mathbb G$ of arbitrary step. The quasilinear part involves operators…
We study the stability of quantum motion of classically regular systems in presence of small perturbations. Onthe base of a uniform semiclassical theory we derive the fidelity decay which displays a quite complexbehaviour, from Gaussian to…
We construct a family of quasigraded Lie algebras that coincide with the deformations of the loop algebras in "principal" gradation and admit Kostant-Adler-Symes scheme. Using them we obtain new Volterra coupled systems and modified Toda…
Some simple examples from quantum physics and control theory are used to illustrate the application of the theory of Lie systems. We will show, in particular, that for certain physical models both of the corresponding classical and quantum…
A Lie system is a system of differential equations admitting a superposition rule, i.e., a function describing its general solution in terms of any generic set of particular solutions and some constants. Following ideas going back to the…
Within the Large Eddy Simulation framework, we propose a methodology based on the Lie theory to derive symmetry-preserving turbulence models. We apply this methodology to the incompressible Navier-Stokes equations.} These models explicitly…
Dynamic properties of fermionic systems, like contollability, reachability, and simulability, are investigated in a general Lie-theoretical frame for quantum systems theory. Observing the parity superselection rule, we treat the fully…
Assuming that quantum mechanics is obeyed exactly after averaging over hidden variables, and considering models that obey both the hypotheses of free will and locality, we establish the form of all possible hidden-variable models that…
Time-dependent frequency harmonic oscillators (TDFHO's) are studied through the theory of Lie systems. We show that they are related to a certain kind of equations in the Lie group SL(2,R). Some integrability conditions appear as conditions…
We introduce families of quasi-rectifiable vector fields and study their geometric and algebraic aspects. Then, we analyse their applications to systems of partial differential equations. Our results explain, in a simpler manner, previous…