The nonlinear case

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  • 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....

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • Only in limited cases, for example, can the nonlinearities of the Navier-Stokes equations be ignored. With the addition of energy and mass transport, multiphase flows, and moving boundaries, as are present in practical applications, the complexity becomes magnified. Each chapter of this book presents an interesting approach to this complexity.

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  • BAYES ALGORITHM WITH ITERATIVE DIFFERENTIAL CORRECTION FOR NONLINEAR SYSTEMS 17.1 DETERMINATION OF UPDATED ESTIMATES We are now in a position to obtain the updated estimate for the nonlinear observation and target dynamic model cases [5, pp. 424–443]. We shall use the example of the ballistic projectile traveling through the atmosphere for definiteness in our discussion. Assume that the past measurements have " permitted us to obtain the state vector estimate Xðt À Þ at the time t À , the last time observations were made on the target. As done at the end of Section 16.

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  • The study of electromagnetic radiation (EM) can be divided into two distinct areas: full solution of Maxwell's Equations relevant to the specific boundary conditions in a special general case and into application of EM radiation that results in modern life e.g. medicine, telecommunication, electromagnetic compatibility (EMC) etc. The reader should have a specific scientific background and must be familiar with the fundamental ideas of EM theory for the first area. Basic understanding of applying the radiation techniques in modern life is needed for the second.

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  • 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. After considering these matters, some methods introduced for solving the nonlinear ICA or BSS problems are discussed in more detail.

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  • Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Global Behavior for a Diffusive Predator-Prey Model with Stage Structure and Nonlinear Density Restriction-I: The Case in Rn

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  • Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Optimal Interior Partial Regularity for Nonlinear Elliptic Systems for the Case 1

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  • In this paper we propose a new, information-based approach for modelling the dynamic evolution of a portfolio of credit risky securities. In our setup market prices of traded credit derivatives are given by the solution of a nonlinear filtering problem. The innovations approach to nonlinear filtering is used to solve this problem and to derive the dynamics of market prices. Moreover, the practical application of the model is discussed: we analyse calibration, the pricing of exotic credit derivatives and the computation of risk-minimizing hedging strategies.

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  • Computational Physics is now a multidisciplinary line of research. A long time ago, it was not like that, computers were used by physicists only in order to solve classical problems resistant to the analytical approach: One is able to model the problem at hands through, say, a set of coupled differential equations, but the analytical solution for these equations is not available. The solace is the numerical solution, and the old branch of Computational Physics consists in providing fast and precise numerical methods to be applied to these cases....

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  • This volume brings about the contemporary results in the field of discrete-time systems. It covers papers written on the topics of robust control, nonlinear systems and recent applications. Although the technical views are different, they all geared towards focusing on the up-to-date knowledge gain by the researchers and providing effective developments along the systems and control arena. Each topic has a detailed discussions and suggestions for future perusal by interested investigators.

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  • Due to the nonredundancy condition, the competitive-equilibrium contracts we derive exclude most options by assumption; in particular, nonsophisticated borrowers’ only option to change the repayment schedule will be to change it by a lot for a large fee. As is usually the case in models of nonlinear pricing, the same outcomes can also be implemented by allowing other choices, but making them so expensive that the borrower does not want to choose them.

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  • Fuzzy control is a practical alternative for a variety of challenging control applications since it provides a convenient method for constructing nonlinear controllers via the use of heuristic information. Such heuristic information may come from an operator who has acted as a “human-in-the-loop” controller for a process. In the fuzzy control design methodology, we ask this operator to write down a set of rules on how to control the process, then we incorporate these into a fuzzy controller that emulates the decision-making process of the human.

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  • NONLINEAR OBSERVATION SCHEME AND DYNAMIC MODEL (EXTENDED KALMAN FILTER) 16.1 INTRODUCTION In this section we extend the results for the linear time-invariant and timevariant cases to where the observations are nonlinearly related to the state vector and/or the target dynamics model is a nonlinear relationship [5, pp. 105– 111, 166–171, 298–300]. The approachs involve the use of linearization procedures. This linearization allows us to apply the linear least-squares and minimum-variance theory results obtained so far.

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  • Data-Reusing Adaptive Learning Algorithms In this chapter, a class of data-reusing learning algorithms for recurrent neural networks is analysed. This is achieved starting from a case of feedforward neurons, through to the case of networks with feedback, trained with gradient descent learning algorithms. It is shown that the class of data-reusing algorithms outperforms the standard (a priori ) algorithms for nonlinear adaptive filtering in terms of the instantaneous prediction error.

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