In this paper, we extend the modulating functions method to estimate the state and the unknown input of a linear time-varying system defined by a linear differential equation. We first estimate the unknown input by taking a truncated Jacobi orthogonal series expansion with unknown coefficients which can be estimated by the modulating functions method. Then, we estimate the state by using extend...

Kautz series allow orthogonal series expansion of finiteenergy signals defined on a semi-infinite axis. The Kautz series consists of orthogonalized exponential functions or sequences. This series has as free parameters an ordered set of poles, each pole associated with an exponential function or sequence. For reasons of approximation and compact representation (coding), an appropriate set of or...

significance and objectives. A practical problem when integrating systems of linear ordinary differential equations, is that if we wish to sample the solution for a different value of an inherent parameter, then we must re-integrate. This is particularly inefficient when we want to accurately sample the solution over a continuous widespread set of parameter values. Though continuity methods res...

We propose a simple but effective method for enriching dictionary definitions with images based on image searches. Various query expansion methods using synonyms/hypernyms (or related words) are evaluated. We demonstrate that our method is effective in obtaining highprecision images that complement dictionary entries, even for words with abstract or multiple meanings.

in this paper we present a diferent proof of a well known asymptotic estimate for Laplace integrals. The novelty of our approach is that it emphasizes, and rigorously justifies, the appealing heuristic method of Laplace. As a bonus, we also obtain a simple and short proof of Watson’s Lemma. Let a be an element of the extended real number set [−∞,∞]. If lim x−→a f(x)/g(x) = 1 we write f(x) ∼ g(x...

The exp((-?(?))-expansion method is used as the first time to investigate the wave solution of a nonlinear the space-time nonlinear fractional PKP equation, the space-time nonlinear fractional SRLW equation, the space-time nonlinear fractional STO equation and the space-time nonlinear fractional KPP equation. The proposed method also can be used for many other nonlinear evolution equations.

This work investigated the effects of iodine on copper/functionalized carbon nanotubes (Cu/f-CNT) that were used in coating 1350 Aluminum Alloy wires, using process electrophoretic exposure with a solution copper sulfate and iodine, under an electrical current 1.2 A voltage 10 V. The Al@Cu/f-CNT was characterized by Scanning Electron Microscopy Secondary mode, X-ray Diffraction Raman spectrosco...