where φp(s)=|s|p−2s, p > 1, ∆u(k− 1)=u(k)−u(k−1), T∈{1,2, . . .}, N+={0,1, . . . ,T}, and u :N+ →R. Throughout this paper, we will assume f :N × (0,∞)→R is continuous. As a result, our nonlinearity f (k,u) may be singular at u= 0 and may change sign. Remark 1.1. Recall a map f :N × (0,∞)→R is continuous if it is continuous as a map of the topological space N × (0,∞) into the topological space R...

A unified analytical description of the evolution of quasi-linear optical pulses and solitons in strongly dispersion-managed transmission systems is developed. Asymptotic analysis of the nonlocal equation that describes the averaged dynamics of a dispersion-managed system shows that the nonlinearity decreases for large map strength s , as O(log s/s) . The spectral intensity is found to be an in...

We consider the period-doubling and intermittency transitions in iterated nonlinear one-dimensional maps to corroborate unambiguously the validity of Tsallis’ non-extensive statistics at these critical points. We study the map xn+1 = xn + u |xn| , z > 1, as it describes generically the neighborhood of all of these transitions. The exact renormalization group (RG) fixed-point map and perturbatio...

In this note, small amplitude free vibration of a double-beam system in presence of inner layer nonlinearity is investigated. The nonlinearity is due to inner layer material and is not related to large amplitude vibration. At first, frequencies of a double-beam system with linear inner layer are studied and categorized as synchronous and asynchronous frequencies. It is revealed that the inner l...

Integral nonlinearity (INL) should be main source of ADC's harmonic distortion. The basic question is importance of dynamic INL. There are still open questions how to describe dynamic INL and if the dynamic corrections of ADC have sense. Key-Words: ADC, testing, static, dynamic, INL, hysteresis

Measurement of integral non-linearity (INL) and differential non-linearity (DNL) of an A/D converter using the histogram method incurs large test time. This test time can be a significant percentage of the total test time, especially for high resolution and low sampling-speed A/D converters. This paper describes a test methodology for measuring the INL and DNL specifications of A/D converters b...

We use residual-delay maps of observational field data for barometric pressure to demonstrate the structure of latitudinal gradients in nonlinearity in the atmosphere. Nonlinearity is weak and largely lacking in tropical and subtropical sites and increases rapidly into the temperate regions where the time series also appear to be much noisier. The degree of nonlinearity closely follows the meri...

Transmission of coherent light through photonic gratings with varying Kerr nonlinearity is modeled within a coupled-mode system derived from the Maxwell equations. The incident light waves are uniformly stable in time-dependent dynamics if the photonic grating has zero net-average Kerr nonlinearity. When the average nonlinearity is weak but nonzero, light waves exhibit oscillatory instabilities...

We consider an inverse problem of recovering a potential associated to semi-linear wave equation with quadratic nonlinearity in $ 1+1 dimensions. develop numerical scheme determine the from noisy Dirichlet-to-Neumann map on lateral boundary. The is based recent higher order linearization method employed [23]. also present approach numerically estimating two-dimensional derivatives data via Tikh...