If the nonlinearity of the motion of a piezoelectric transducer (PZT) can be described as a quadratic function, the integrated intensity of one frame in phase shift interferometry can be calculated using the Fresnel integral. For a PZT with smaller nonlinearity, the rms phase error is almost linearly proportional to the quadratic coefficient The effects of PZT nonlinearity on the three- and the...

This work deals with the focusing Nonlinear Schrödinger Equation in one dimension with pure-power nonlinearity near cubic. We consider the spectrum of the linearized operator about the soliton solution. When the nonlinearity is exactly cubic, the linearized operator has resonances at the edges of the essential spectrum. We establish the degenerate bifurcation of these resonances to eigenvalues ...

It is well-known that linear constrained model predictive control has a nonlinearity that is continuous and piecewise affine. Under certain feasibility conditions the nonlinearity may be sector bounded and shown to satisfy sufficient conditions for the existence of Zames-Falb multipliers. Thus the nonlinearity satisfies a wide class of integral quadratic constraint (IQC). Standard analysis then...

The consistent quantum theory of self-phase modulation (SPM) and cross-phase modulation (XPM) for ultrashort light pulses (USPs) in medium with electronic Kerr-nonlinearity are developed. The approach makes use of momentum operator of electrical field which takes account of the inertial behaviour of the nonlinearity. The spectrum of quantum fluctuations of squeezed-quadrature component as a fun...

We study the nonlinearity and the weight of the rotation-symmetric (RotS) functions defined by Pieprzyk and Qu [6]. We give exact results for the nonlinearity and weight of 2-degree RotS functions with the help of the semi-bent functions [2] and we give the generating function for the weight of the 3-degree RotS function. Based on the numerical examples and our observations we state a conjectur...

A computationally simple nonlinearity in the form of a threshold device for the blind separation of sub-Gaussian signals is derived. Convergence is shown to be robust, fast, and comparable to that of more complex polynomial nonlinearities. Together with the known signum nonlinearity for super-Gaussian distributions, which basically is a threshold device with the threshold set to zero, the gener...

We consider solutions to a nonlinear reaction diffusion equation when the reaction term varies randomly with respect to the spatial coordinate. The nonlinearity is either the ignition nonlinearity or the bistable nonlinearity, under suitable restrictions on the size of the spatial fluctuations. It is known that the solution develops an interface which propagates with a well-defined speed in the...

7 High-order epistasis has been observed in many genotype-phenotype maps. These multi-way inter8 actions could have profound implications for evolution and may be useful for dissecting complex 9 traits. Previous analyses have assumed a linear genotype-phenotype map, and then applied a linear 10 high-order epistasis model to dissect epistasis. The assumption of linearity has not been tested 11 i...

In permanent magnetic machines the nonlinearity due to the quadratic terms of the current makes difficulties in the control system. In order to cancel the nonlinearity, a strategy based on a pre-compensation action, which is conceived through two input partition matrices is presented. After canceling the nonlinearity a Model Predictive Control is used to obtain a positioning of the actuator. Si...

Abstract. For cryptographic systems the method of confusion and diffusion is used as a fundamental technique to achieve security. Confusion is reflected in nonlinearity of certain Boolean functions describing the cryptographic transformation. In this paper, we present two balanced boolean functions which have low Walsh spectra and high nonlinearity. In the proof of the nonlinearity, a new metho...