in the present study, the onset of double diffusive reaction-convection in a uid layer with viscous fluid, heated and salted from below subject to chemical equilibrium on the boundaries, has been investigated. linear and nonlinear stability analysis have been performed. for linear analysis normal mode technique is used and for nonlinear analysis minimal representation of truncated fourier serie...

This paper presents a nonlinear model of a clamped-clamped microbeam actuated by an electrostatic load with stretching and thermoelastic effects. The frequency of free vibration is calculated by discretization based on the Differential Quadrature (DQ) Method. The frequency is a complex value due to the thermoelastic effect that dissipates energy. By separating the real and imaginary parts of fr...

For a class of nonlinear systems we investigate the problem of under what conditions there exists a coordinate transformation that yields a state affine linear system up to output injection with implicit outputs. In particular, we provide necessary and sufficient conditions for time-varying linearization up to multi-output injection. We highlight that if the conditions hold, as a consequence, i...

In this paper, we establish new exact solutions for some complex nonlinear wave equations. The B"{a}cklund transformation method of Riccati equation is used to construct exact solutions of the Hamiltonian amplitude equation and the coupled Higgs field equation. This method presents a wide applicability to handling nonlinear wave equations. These equations play a very important role in mathemati...

We consider possibly stiff and implicit systems of ordinary differential equations (ODEs). The major difficulty and computational bottleneck in the implementation of fully implicit Runge–Kutta (IRK) methods resides in the numerical solution of the resulting systems of nonlinear equations. To solve those systems we show that the use of inexact simplified Newton methods is efficient. Linear syste...

A deep neural network (DNN) consists of a nonlinear transformation from an input to a feature representation, followed by a common softmax linear classifier. Though many efforts have been devoted to designing a proper architecture for nonlinear transformation, little investigation has been done on the classifier part. In this paper, we show that a properly designed classifier can improve robust...

By means of generalized Riccati transformation techniques and generalized exponential functions, we give some oscillation criteria for the nonlinear dynamic equation (p(t)x ∆ (t)) ∆ + q(t)(f • x σ) = 0, on time scales. We also apply our results to linear and nonlinear dynamic equations with damping and obtain some sufficient conditions for oscillation of all solutions.

Friction is a very old and universal issue in all mechanical systems. Since friction is non-linear, it is an ever challenging problem. Several empirical nonlinear friction models have been proposed in the technical literature. This paper does not propose any new model but it presents a new, tensor product (TP) based representation of the existing friction models which is suitable for control de...