Compare of analytic and numerical solution of parametric oscillator with perturbation and its analytical solution

In this paper we deal with an approximative analytical solution of a second order differential equation with a fast time periodic modulation. We use for this type of the equation a homotopy perturbation method. The validity of this approximative solution is verified by numerical experiments, where we achieve considerable consistency of doth soliutions.

Backtracking-free Interactive Music Scores with Temporal Relations over Rythms

Another alternative to solve CSP s is to use (incomplete) local search algorithmsto find interatively an approximative solution. Local search is a metaheuristic forsolving computationally hard optimization problems. An example of local searchis adaptive search: A computational method that optimizes a problem by iterativelytrying to improve a candidate solution with regard to the problem constraints (andpossibly an optimization function). In spite of the advances in constraint solving for music compositions problems,as far as we know, there is little research on solving CSP s during real-time music interaction. In this paper we will focus on interactive scores, a formalism for thedesign of interactive scenarios closely related to constraint programming. we do not have a polynomial algorythm to solve all instances ofthe problem. Consider, for instance, the case where the durations of the temporalobjects are not singles values nor intervals, but discrete values.

Comparing metric and Palatini approaches to vector Horndeski theory

We compare cosmologic and spherically symmetric solutions to metric and Palatini versions of vector Horndeski theory. It appears that Palatini formulation of the theory admits more degrees of freedom. Specifically, homogeneous isotropic configuration is effectively bimetric, and static spherically symmetric configuration contains nonmetric connection. In general, the exact solution in metric case coincides with the approximative solution in Palatini case. The Palatini version of the theory appears to be more complicated, but the resulting nonlinearity may be useful: we demonstrate that it allows the specific cosmological solution to pass through singularity, which is not possible in metric approach.

Parametric oscillations of the mechanical systems

This paper deals with an approximative solution in the analytical form of some second order linear differential equation with time depend parameters. The analytic solution is compared with the numerical solution obtained by Runge-Kutta method and the conditions of the convergence of this analytical method are discussed.