In the current study, the effects of Casimir force and squeeze film damping on pull-in instability and dynamic behavior of electrostatically actuated nano and micro electromechanical systems are investigated separately. Linear elastic membrane theory is used to model the static and dynamic behavior of the system for strip, annular and disk geometries. Squeeze film damping is modeled using nonli...

in this paper, an iterative method is proposed for solving matrix equation $sum_{j=1}^s a_jx_jb_j = e$. this method is based on the global least squares (gl-lsqr) method for solving the linear system of equations with the multiple right hand sides. for applying the gl-lsqr algorithm to solve the above matrix equation, a new linear operator, its adjoint and a new inner product are dened. it is ...

‎in this paper‎, ‎we propose two preconditioned aor iterative methods to solve systems of linear equations whose coefficient matrices are z-matrix‎. ‎these methods can be considered as improvements of two previously presented ones in the literature‎. ‎finally some numerical experiments are given to show the effectiveness of the proposed preconditioners‎.‎

In this paper, operational matrices of Riemann-Liouville fractional integration and Caputo fractional differentiation for shifted Jacobi polynomials are considered. Using the given initial conditions, we transform the fractional differential equation (FDE) into a modified fractional differential equation with zero initial conditions. Next, all the existing functions in modified differential equ...

We present a theoretical foundation for studying parametric systems of linear equations and prove an efficient algorithm for identifying all parametric values (including degenerate cases) for which the system is consistent. The algorithm gives a small set of regimes where for each regime, the solutions of the specialized systems may be given uniformly. For homogeneous linear systems, or for sys...

in this paper, a numerical solution for a system of linear fredholm integro-differential equations by means of the sinc method is considered. this approximation reduces the system of integro-differential equations to an explicit system of algebraic equations. the exponential convergence rate $o(e^{-k sqrt{n}})$ of the method is proved. the analytical results are illustrated with numerical examp...

the purpose of this paper is to show that the ideas and techniques of the classical methods of finding stability, such as the criteria of leonhard and nyquist, can be used to derive simple algorithm to verify stability. this is enhanced by evaluating the argument of the characteristic equation of a linear system in the neighbourhood of the origin of the complex plane along the imaginary axis

Given A ∈ Zm×n and b ∈ Zm, we consider the issue of existence of a nonnegative integral solution x ∈ Nn to the system of linear equations Ax = b. We provide a discrete and explicit analogue of the celebrated Farkas lemma for linear systems in Rn and prove that checking existence of integral solutions reduces to solving an explicit linear programming problem of fixed dimension, known in advance.

Fuzzy systems of linear equations play a vital role in various applications of engineering, science and finance problems. This paper proposes a new method for solving Fully Fuzzy System of Linear Equations (FFSLE) using the linear programming problem approach. There is no restriction on the elements of coefficient matrix. The proposed method is able to solve the system, when the elements of the...