# The nonlinear case

Xem 1-20 trên 46 kết quả The nonlinear case
• ### An Introduction to Nonlinearity in Control Systems

The book is intended to provide an introduction to the effects of nonlinear elements in feedback control systems. A central topic is the use of the Describing Function (DF) method since in combination with simulation it provides an excellent approach for the practicing engineer and follows on logically from a first course in classical control, such as the companion volume in this series. Some of the basic material on the topic can be found in my earlier book which is frequently referenced throughout the text....

• ### Nonlinear vibration of a pendulum with a support in harmonic motion

The nonlinear vibration of a pendulum whose support undergoes arbitrary rectilinear harmonic motion is studied. The main attention is paid to the resonant cases and the stationary vibrations. The resonant conditions are explained. The amplitude - frequency curves are plotted for various values of parameters and the stability of vibration is investigated. The rotating motion of the pendulum and its stability are also considered.

• ### Nonlinear dynamics of pipeline with liquid in a vicinity of critical flow velocities

We developed the nonlinear model of pipeline dynamics with high-speed liquid motion. On the basis of the variational methods we constructed the nonlinear discrete model and numerical algorithm for investigation of problems of dynamics and dynamical stability of pipeline. We considered examples of dynamical behavior of the system for different velocities of liquid flowing, including the case of critical velocity of flow, when loss of straight line stability of pipeline is possible.

• ### Influence of confined acoustic phonons on the nonlinear acousto-electric effect in doped semiconductor superlattices

By using a quantum kinetic equation for electrons, we have studied the Acousto-electric effects in doped semiconductor superlattice (DSSL) under the influence of confined phonon. Considering the case of the electron - acoustic phonon interaction, we have found the expressions of the nonlinear quantum acousto-electric current.

• ### Báo cáo "The dependence of the nonlinear absorption coefficient of strong electromagnetic waves caused by electrons confined in rectangular quantum wires on the temperature of the system"

The nonlinear absorption of a strong electromagnetic wave caused by confined electrons in cylindrical quantum wires is theoretically studied by using the quantum kinetic equation for electrons. The problem is considered in the case electron-acoustic phonon scattering. Analytic expressions for the dependence of the nonlinear absorption coefficient of a strong electromagnetic wave by confined electrons in rectangular quantum wires on the temperature T are obtained.

• ### On a nonlinear inverse problem in viscoelasticity

We consider an inverse problem for determining an inhomogeneity in a viscoelastic body of the Zener type, using Cauchy boundary data, under cyclic loads at low frequency. We show that the inverse problem reduces to the one for the Helmholtz equation and to the same nonlinear Calderon equation given for the harmonic case. A method of solution is proposed which consists in two steps : solution of a source inverse problem, then solution of a linear Volterra integral equation.

• ### Colombeau solutions of a nonlinear stochastic predator-prey equation

The solution of a random semilinear hyperbolic system with singular initial data is sought as a random Colombeau distribution. The product of 2 additive white noises is well tackled within the theory of random Colombeau distributions. In the special case of a random predator–prey system, the exact Colombeau solution is obtained under some assumptions when the process is driven by doubly reflected Brownian motions.

• ### On shallow water waves in a medium with time-dependent dispersion and nonlinearity coefficients

In this paper, we studied the progression of shallow water waves relevant to the variable coefficient Korteweg–de Vries (vcKdV) equation. We investigated two kinds of cases: when the dispersion and nonlinearity coefficients are proportional, and when they are not linearly dependent. In the first case, it was shown that the progressive waves have some geometric structures as in the case of KdV equation with constant coefficients but the waves travel with time dependent speed. In the second case, the wave structure is maintained when the nonlinearity balances the dispersion.

• ### FUZZY INFERENCE SYSTEM – THEORY AND APPLICATIONS

Evolution of global technologies has prompted increasing complexity of applications developed in both, the industry and the scientific research fields. These complexities are generally attributed to nonlinearities, poorly defined dynamics and absence of apriori information about the systems. Imprecision, uncertainties and vagueness in information about the system are also playing vital roles in enhancing the complexity of application.

• ### Quantitative Analysis in Financial Markets Collected papers of the New York University Mathematical Finance Seminar, Volume II

It is a pleasure to edit the second volume of papers presented at the Mathematical Finance Seminar of New York University. These articles, written by some of the leading experts in financial modeling cover a variety of topics in this field. The volume is divided into three parts: (I) Estimation and Data-Driven Models, (II) Model Calibration and Option Volatility and (III) Pricing and Hedging. The papers in the section on "Estimation and Data-Driven Models" develop new econometric techniques for finance and, in some cases, apply them to derivatives.

• ### Independent Component Analysis - Chapter 17: Nonlinear ICA

This chapter deals with independent component analysis (ICA) for nonlinear mixing models. A fundamental difﬁculty in the nonlinear ICA problem is that it is highly nonunique without some extra constraints, which are often realized by using a suitable regularization. We also address the nonlinear blind source separation (BSS) problem. Contrary to the linear case, we consider it different from the respective nonlinear ICA problem.

• ### Đề tài " Global well-posedness and scattering for the energy-critical nonlinear Schr¨odinger equation in R3 "

We obtain global well-posedness, scattering, and global L10 spacetime t,x bounds for energy-class solutions to the quintic defocusing Schr¨dinger equao tion in R1+3 , which is energy-critical. In particular, this establishes global existence of classical solutions. Our work extends the results of Bourgain [4] and Grillakis [20], which handled the radial case.

• ### Root Finding and Nonlinear Sets of Equations part 5

Not as well appreciated as it ought to be is the fact that some polynomials are exceedingly ill-conditioned. The tiniest changes in a polynomial’s coefﬁcients can, in the worst case, send its roots sprawling all over the complex plane. (An infamous example due to Wilkinson is detailed by Acton [1].) Recall that a polynomial of degree n will have n roots. The roots can be real or complex, and they might not be distinct.

• ### Propagation of ultrashort pulses in nonlinear media

In this paper, a general propagation equation of ultrashort pulses in an arbitrary dispersive nonlinear medium has been used for the case of Kerr media. This equation which is called Generalized Nonlinear Schroedinger Equation usually has very complicated form and looking for its solutions is usually a very difficult task. Theoretical methods reviewed in this paper to solve this equation are effective only for some special cases.

• ### A unified krylov-bogoliubovmitropolskii method for solving hyperbolic-type nonlinear partial differential systems

The method is an extension of the unified Kry lov-Bogoliubov-Mitropolskii method , which was initially developed for un-darn ped , under-clamped and over-clamped cases of the second order ordinary different ia l equation. The methods also cover a special condition of the over-damped case in which the general solution is useless.

• ### Parametric vibration of the prismatic shaft with hereditary and nonlinear geometry

Parametric vibration of the prismatic shaft with regard of physical and geometrical nonlinearity has been inves~igated in some publications (see for example). However, that vibration in the case of hereditary has not, to author's knowledge, been examined hitherto. In this paper it will be studied by means of the asymptotic method for high order systems.

• ### Generalized diffusion theory of hydrodynamical particle migration in suspensions part 1: the case of equal densities

This paper is concerned with using the simplest model from developed general theory for modeling of particle migration in suspensions- one of the most important and complicated aspects of particle-- liquid two- phase flows, that has been observed and studied by many authors. For this purpose it is considered the motion of Newtonian fluid- rotating rigid spherical particles two- phase continuum with specialized nonlinear constitutive equations, when the particle and fluid have equal densities.

• ### Nonlinear absorption power and linewidths in quantum well with triangular potential

The analytic expression for absorption power of a strong electromagnetic waves caused by confined electrons in quantum well is obtained in the case of electron-optical phonon scattering. Nonlinear optically detected electrophonon resonance (ODEPR) effect in a specific GaAs/AlAs quantum well with triangular potential is investigated.

• ### Performance assessment of DFT-OFDM and DFT-OFDM systems in the presence of the sspa and fading channe

This paper investigates performance degradation of conventional Orthogonal Frequency Division Multiplexing (OFDM) and Discrete Wavelet Transform based OFDM (DWT-OFDM) systems when the signals are passed through a nonlinear High Power Amplifier (HPA) and fading channel. In the case of DWT-OFDM, several wavelets such as Daubechies, Symlet and Biorthogonal are evaluated.

• ### The educational Kuznets curve: A case of Nepal

Education is among the basic human needs and one of the components of well being in the modern world. Equal distribution of education is of great interest in public policy analysis. Spending in education represents substantial share of government revenue. The inequality in educational distribution represents large welfare loss. The purposes of this article are three folds. First, it calculates average years of schooling. Second, it estimates educational inequality in terms of standard deviation of schooling.