This paper deals with state estimation of micro tunable capacitor subjected to nonlinear electrostatic force. For this end a nonlinear observer has been designed for state estimation of the structure.  Necessary and sufficient conditions for construction of the observer are presented. Stability of the observer is checked using Lyapunov theorem. Observer design is based on converting of differen...

in this paper, we have proposed a new iterative method for finding the solution of ordinary differential equations of the first order. in this method we have extended the idea of variational iteration method by changing the general lagrange multiplier which is defined in the context of the variational iteration method.this causes the convergent rate of the method increased compared with the var...

We propose an effective and light-weight learning algorithm, Symplectic Taylor Neural Networks (Taylor-nets), to conduct continuous, long-term predictions of a complex Hamiltonian dynamic system based on sparse, short-term observations. At the heart our algorithm is novel neural network architecture consisting two sub-networks. Both are embedded with terms in form series expansion designed symm...

There are several important observations to make about this definition. (i) The definition says that, for each fixed n, ∑n m=0 amx m becomes a better and better approximation to f(x) as x gets smaller. As x → 0, ∑m=0 amx approaches f(x) faster than x tends to zero. (ii) The definition says nothing about what happens as n → ∞. There is no guarantee that for each fixed x, ∑n m=0 amx m tends to f(...

1 Overview We begin by recalling the Rolle’s Theorem.1 Using this result, we shall derive the Lagrange Form of the Taylor’s Remainder Theorem. Subsequently, we shall derive several mathematical inequalities as a corollary of this result. For example, 1. We shall use the Taylor’s Remainder Theorem to upper and lower bound exponential functions using polynomials. 2. We shall use the Taylor’ Remai...

In this chapter, we extend the first-order NOM to higher order by using a Taylor series expansion. The is special case of NOM. can be derived two methods, one weighted expansion, and other minimization operator energy functional for For quadratic functional, residual, tangent stiffness matrix nonlocal strong form. section on numerical examples, applied current method problems formulated form we...

The paper aims to obtain exact analytical solution of linear nonhomogeneous space-time fractional order partial differential equation by improved Adomian decomposition method coupled with Taylor expansion series. these equations are in series form may have rapid convergence a closed-form solution. effectiveness and sharpness this is shown obtaining the suitable initial conditions (ICs). With he...

Optical parametric chirped pulse amplification (OPCPA) is one of the most powerful techniques for generating high-energy femtosecond laser pulses. Many efforts were devoted to get spectral-band amplification able to support sub-10-fs pulses. In the optical parametric amplification (OPA), broad gain bandwidths can be obtained if the wave-vectors mismatch, ∆k, slowly increases when the signal fre...

In this paper, we continue our study that began in recent papers [2] and [3] concerning a simple yet effective Taylor series expansion method to approximate a solution of integral equations. The method is applied to Volterra integral equation of the second kind as well as to systems of Volterra equations. The results obtained in this paper improve significantly the results reported in recent pa...

Thus we can apply any optimization algorithm to solve this minimization problem and obtain a method for solving (1.1). At the point, let us consider the steepest descent method and select any initial guess x0. With xk available we try to find the direction along which φ(x) decreases most rapidly starting from xk and compute the next point xk+1 by minimizing φ(x) in this direction. By Taylor ser...