A new modified Adomian Decomposition Method (ADM) was utilized to obtain an analytical solution for the buckling of the nanocantilever actuators immersed in liquid electrolytes. The nanoactuators in electrolytes are subject to different nonlinear forces including ionic concentration, van der Waals, external voltage and electrochemical forces. The Duan–Rach modified Adomian decomposition method ...

First Riccati equation with matrix variable coefficients, arising in optimal and robust control approach, is considered. An analytical approximation of the solution of nonlinear differential Riccati equation is investigated using the Adomian decomposition method. An application in optimal control is presented. The solution in different order of approximations and different methods of approximat...

In this study, delay-dependent robust stability problem is investigated for uncertain neutral systems with discrete and distributed delays. By constructing an augmented Lyapunov-Krasovskii functional involving triple integral terms and taking into account the relationships between the different delays, new less conservative stability and robust stability criteria are established first using the...

We obtain an explicit Iwasawa decomposition of the symplectic matrices, complex or real, in terms of the Cholesky factorization for positive definite n×n matrices. We also provide a MATLAB program to compute the decomposition. 1. Iwasawa decomposition of the symplectic groups Let G be the real (noncompact) symplectic group [3, p.129] (the notation there is Spn), [4, p.265] G := Spn(R) = {g ∈ SL...

Low rank approximation of matrices has been well studied in literature. Singular value decomposition , QR decomposition with column pivoting, rank revealing QR factorization (RRQR), Interpolative decomposition etc are classical deterministic algorithms for low rank approximation. But these techniques are very expensive (O(n 3) operations are required for n × n matrices). There are several rando...

We obtain several asymptotic results on the powers of a square matrix associated with SVD, QR decomposition and Cholesky decomposition. 1. Yamamoto’s theorem Given X ∈ Cn×n, the eigenvalue moduli of X are always less than or equal to the spectral norm of X since ‖X‖ := max ‖v‖2=1 ‖Xv‖2 and if Xv = λv for some unit vector v, then |λ| = ‖Xv‖2 ≤ ‖X‖. So for all m ∈ N, r(X) ≤ ‖X‖ ≤ ‖X‖, where r(X) ...

In this paper we introduce a new form of decomposition of graphs, the (P, Q)-decomposition. We first give an optimal algorithm for finding the 1-decomposition of a graph which is a special case of the (P, Q)-decomposition which was first introduced in [21]. We then examine the connections between the 1-decomposition and well known forms of decomposition of graphs, namely, modular and homogeneou...