System identification is important in science and engineering. This contribution proposes a simple yet elegant scheme for identifying a fractional order dynamic system based on its observed response to a standard excitation. Our approach consists in obtaining and solving a set of simultaneous linear equations connecting the parameters to yield the desired estimates. To minimise the effect of no...

lanczos-type algorithms are well known for their inherent instability. they typically breakdown occurs when relevant orthogonal polynomials do not exist. current approaches to curing breakdown rely on jumping over the non-existent polynomials to resume computation. this may have to be used many times during the solution process. we suggest an alternative to jumping, which consists of restarting...

This paper presents a numerical matrix method based on Bernstein polynomials (BPs) for approximate the solution of a system of m-th order nonlinear Volterra integro-differential equations under initial conditions. The approach is based on operational matrices of BPs. Using the collocation points,this approach reduces the systems of Volterra integro-differential equations associated with the giv...

Algebraic integral equations is a special category of Volterra integral equations system,  that has many applications in physics and engineering. The principal aim of this paper is to serve the numerical solution of an integral algebraic equation by using the Taylor expansion method. In this method, using the Taylor expansion of the unknown function, the algebraic integral equation system becom...

We present three new methods that investigate the equalities implied by a system of linear arithmetic constraints. Implied equalities can be used to simplify linear arithmetic constraints and are valuable in the context of Nelson-Oppen style combinations of theories. The first method efficiently checks whether a system of linear arithmetic constraints implies an equality at all. In case the sys...

Consider the homogeneous equation u ′(t) = l(u)(t) for a.e. t ∈ [a, b] where l : C([a, b];R) → L([a, b];R) is a linear bounded operator. The efficient conditions guaranteeing that the solution set to the equation considered is one-dimensional, generated by a positive monotone function, are established. The results obtained are applied to get new efficient conditions sufficient for the solvabili...

We will study special solutions of the fourth, fifth and sixth Painlevé equations with generic values of parameters whose linear monodromy can be calculated explicitly. We will show the relation between Umemura’s classical solutions and our solutions.

This paper develops asymptotically pivotal structural change tests in simultaneous equations with weakly identified parameters. In former literature, Caner (2007) proposes boundedly pivotal structural change tests when there are weakly identified parameters. The tests developed in this article are new, and benefit from reparameterizing the model. This results in asymptotically pivotal tests. Si...