A high-order Absorbing Boundary Condition (ABC) is devised on an artificial boundary for time-dependent elastic waves in unbounded domains. The configuration considered is that of a two-dimensional elastic waveguide. The proposed ABC is an extension of the Hagstrom-Warburton ABC which was originally designed for acoustic waves, and is applied directly to the displacement field. The order of the...

In this paper, we study under which conditions the trajectories of a mechanical control system can track any curve on the configuration manifold. We focus on systems that can be represented as forced affine connection control systems and we generalize the sufficient conditions for tracking known in the literature. The sufficient conditions are expressed in terms of convex cones of vector fields...

We study strategies for increasing the precision in the blurring models by maintaining a complexity in the related numerical linear algebra procedures (matrixvector product, linear system solution, computation of eigenvalues etc.) of the same order of the celebrated Fast Fourier Transform. The key idea is the choice of a suitable functional basis for representing signals and images. Starting fr...

In a geometric point of view, a nonlinear control system, affine in the controls, is thought of as an affine subbundle of the tangent bundle of the state space. In deriving conditions for local controllability from this point of view, one should describe those properties of the affine subbundle that either ensure or prohibit local controllability. In this paper, second-order conditions of this ...

This paper describes a strategy for structural estimation of economic models that I will refer to as SML based on FOCs. In this approach, one uses simulated maximum likelihood (SML) to estimate the structural parameters that appear in the Euler or first order conditions (FOCs) solved by an optimizing economic agent. I will argue that the SML based on FOCs approach has certain advantages over th...

a lattice boltzmann method is applied to demonstrate the comparison results of simulating natural convection in an open end cavity using different hydrodynamic and thermal boundary conditions. the prandtl number in the present simulation is 0.71, rayleigh numbers are 104,105 and 106 and viscosities are selected 0.02 and 0.05. on-grid bounce-back method with first-order accuracy and non-slip met...

Tree theory, partitions of integer numbers, combinatorial mathematics and computer algebra are the basis for the construction of a powerful and efficient symbolic package for the derivation of Runge Kutta order conditions and principal truncation error terms.

We describe the derivation of order conditions, without restrictions on stage order, for general linear methods for ordinary differential equations. This derivation is based on the extension of Albrecht approach proposed in the context of Runge-Kutta and composite and linear cyclic methods. This approach was generalized by Jackiewicz and Tracogna to two-step Runge-Kutta methods, by Jackiewicz a...

We describe a generalization to Optimal Control of the theory of envelopes of the classical Calculus of Variations. This generalization extends our previous work, by allowing the use of \quasi-extremal" trajectories, i.e. trajectories that satisfy all the conditions of the Pontryagin Maximum Principle except for the fact that the sign of the constant 0 that appears in the Hamiltonian multiplyin...

‎second derivative general linear methods (sglms) as an extension‎ ‎of general linear methods (glms) have been introduced to improve‎ ‎the stability and accuracy properties of glms‎. ‎the coefficients of‎ ‎sglms are given by six matrices‎, ‎instead of four matrices for‎ ‎glms‎, ‎which are obtained by solving nonlinear systems of order and‎ ‎usually runge--kutta stability conditions‎. ‎in this p...