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"Here is a clearly written introduction to three central areas of inverse problems: inverse problems in electromagnetic scattering theory, inverse spectral theory, and inverse problems in quantum scattering theory. Inverse problems, one of the most attractive parts of applied mathematics, attempt to obtain information about structures by nondestructive measurements. Based on a series of lectures presented by three of the authors, all experts in the field, the book provides a quick and easy way for readers to become familiar with the area through a survey of recent developments in inverse spectral and inverse scattering problems."

"A study, by two of the major contributors to the theory, of the inverse scattering transform and its application to problems of nonlinear dispersive waves that arise in fluid dynamics, plasma physics, nonlinear optics, particle physics, crystal lattice theory, nonlinear circuit theory and other areas. A soliton is a localized pulse-like nonlinear wave that possesses remarkable stability properties. Typically, problems that admit soliton solutions are in the form of evolution equations that describe how some variable or set of variables evolve in time from a given state. The equations may take a variety of forms, for example, PDEs, differential difference equations, partial difference equations, and integrodifferential equations, as well as coupled ODEs of finite order. What is surprising is that, although these problems are nonlinear, the general solution that evolves from almost arbitrary initial data may be obtained without approximation. For such exactly solvable problems, the inverse scattering transform provides the general solution of their initial value problems. It is equally surprising that some of these exactly solvable problems arise naturally as models of physical phenomena. Simply put, the inverse scattering transform is a nonlinear analog of the Fourier transform used for linear problems. Its value lies in the fact that it allows certain nonlinear problems to be treated by what are essentially linear methods."

"Frontiers in Applied MathematicsInverse problems arise in a number of important practical applications, ranging from biomedical imaging to seismic prospecting. This book provides the reader with a basic understanding of both the underlying mathematics and the computational methods used to solve inverse problems. It also addresses specialized topics like image reconstruction, parameter identification, total variation methods, nonnegativity constraints, and regularization parameter selection methods.Because inverse problems typically involve the estimation of certain quantities based on indirect measurements, the estimation process is often ill-posed. Regularization methods, which have been developed to deal with this ill-posedness, are carefully explained in the early chapters of Computational Methods for Inverse Problems. The book also integrates mathematical and statistical theory with applications and practical computational methods, including topics like maximum likelihood estimation and Bayesian estimation.Several web-based resources are available to make this monograph interactive, including a collection of MATLAB m-files used to generate many of the examples and figures. These resources enable readers to conduct their own computational experiments in order to gain insight. They also provide templates for the implementation of regularization methods and numerical solution techniques for other inverse problems. Moreover, they include some realistic test problems to be used to further develop and test various numerical methods."

"This book presents current research trends in the field of underwater acoustic wave direct and inverse problems. Until very recently, little has been published concerning model-based inversions of the boundaries and material constants of finite-sized targets located either in the water column or the sediments. This text is the first to investigate inverse problems in an ocean environment with a heavy emphasis placed on the description and resolution of the forward scattering problem.Marine Acoustics: Direct and Inverse Problems emphasizes computation of Green's Functions with new material added for elastic and poro-elastic seabeds. This timely publication addresses many areas of practical interest in connection with underwater acoustical imaging including ecological survey and clean up, protection of open water harbors, offshore petroleum and gas enterprises, as well as environmental and military uses. The ocean-seabed system is an acoustic waveguide and this is the only book that treats inverse problems in a waveguide. The propagation of acoustic waves in this system is treated for various types of seabeds and the direct and inverse problems are considered in realistic ocean environments. The inverse problem is to determine the shape of an impenetrable or penetrable object, or to determine the coefficients describing the seabed. This is done by acoustically illuminating the seabed and investigating the scattered field."

"Approximate global convergence and adaptivity for coefficient inverse problems is the first book in which two new concepts of numerical solutions of multidimensional Coefficient Inverse Problems (CIPs) for a hyperbolic Partial Differential Equation (PDE) are presented. Two central questions for CIPs are addressed, how to obtain a good approximations for the exact solution without any knowledge of a small neighborhood of this solution, and how to refine it given the approximation. The book also combines analytical convergence results with recipes for various numerical implementations of developed algorithms. The developed technique is applied to two types of blind experimental data, which are collected both in a laboratory and in the field. The result for the blind backscattering experimental data collected in the field addresses a real world problem of imaging of shallow explosives."

"This book presents a methodology based on inverse problems for use in solutions for fault diagnosis in control systems, combining tools from mathematics, physics, computational and mathematical modeling, optimization and computational intelligence. This methodology, known as fault diagnosis – inverse problem methodology or FD-IPM, unifies the results of several years of work of the authors in the fields of fault detection and isolation (FDI), inverse problems and optimization. The book clearly and systematically presents the main ideas, concepts and results obtained in recent years. By formulating fault diagnosis as an inverse problem, and by solving it using metaheuristics, the authors offer researchers and students a fresh, interdisciplinary perspective for problem solving in these fields. Graduate courses in engineering, applied mathematics and computing also benefit from this work."

"Inverse limits with set-valued functions are quickly becoming a popular topic of research due to their potential applications in dynamical systems and economics. This brief provides a concise introduction dedicated specifically to such inverse limits. The theory is presented along with detailed examples which form the distinguishing feature of this work. The major differences between the theory of inverse limits with mappings and the theory with set-valued functions are featured prominently in this book in a positive light. "

"Data lifetime biasanya digunakan peneliti untuk mengetahui tingkat survival atau tingkat kegagalan suatu objek. Distribusi Weibull merupakan distribusi probabilitas yang sering digunakan untuk memodelkan data lifetime. Namun, distribusi Weibull hanya dapat memodelkan data lifetime dengan tingkat kegagalan atau hazard rate yang monoton. Sehingga dibutuhkan distribusi baru yang dapat memodelkan data lifetime dengan karakteristik tingkat kegagalan atau hazard rate yang beragam. Distribusi inverse Weibull adalah distribusi hasil transformasi inverse dari distribusi Weibull. Distribusi inverse Weibull merupakan distribusi yang dapat memodelkan data lifetime dengan hazard rate monoton (turun) maupun  non-monoton (upside-down bathtub shaped). Namun, untuk membuat kepadatan fleksibel dengan berbagai macam bentuk diperlukan generalisasi dari distribusi ini dengan menambahkan suatu parameter shape. Distribusi generalized inverse Weibull merupakan generalisasi dari distribusi inverse Weibull yaitu yang dibentuk dengan memangkatkan fungsi distribusi inverse Weibull dengan suatu parameter baru. Distribusi generalized inverse Weibull memiliki 2 parameter shape dan 1 parameter scale sehingga distribusi ini dapat menggambarkan shape dari fungsi hazard yang lebih beragam. Pada  skripsi ini, akan dibahas mengenai pembentukan distribusi inverse Weibull dan pembentukan distribusi generalized inverse Weibull, serta fungsi kepadatan probabilitas, fungsi distribusi, fungsi survival, fungsi hazard, dan karakteristik-karakteristik dari kedua distribusi tersebut. Penaksiran parameter dari distribusi generalized inverse Weibull menggunakan metode maksimum likelihood.

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Lifetime data is usually used by researchers to determine the level of survival or failure rate of an object. Weibull distribution is a probability distribution that is often used to model the lifetime data. However, the Weibull distribution is only used to model the lifetime data with monotone failure rate or monotone hazard rate. So that, a new distribution is needed to model the lifetime data with varying characteristics of failure rates or hazard rates. Inverse Weibull distribution is a distribution that is formed from the inverse transformation of the Weibull distribution. Inverse Weibull distribution is a continued distribution which can model lifetime data with a monotone hazard rate (constant, increase, and decrease) or non-monotone hazard rate (upside-down bathtub shaped). However, to make a density flexible with wide variety of shapes the generalizations from this distribution are needed by adding a shape parameter. Generalized inverse Weibull distribution is derived from generalization of inverse Weibull distribution that is formed by raising the inverse Weibull distribution function with a new parameter. Generalized inverse Weibull distribution has two shape parameters and one scale parameter. So, this distribution can describe a more diverse shapes of hazard function. In this skripsi, we will discuss how to construct inverse Weibull distribution and Generalized inverse Weibull distribution, and probability distribution function, cumulative distribution function, survival function, hazard function, and characteristics of these distributions. Parameter estimation of the generalized inverse Weibull distribution is using the maximum likelihood method."