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About 10,000 papers for “Inverse problem”

Inverse Problem

Masahide Terazima, Noboru Hirota, Silvia E. Braslavsky et al. · IUPAC Standards Online · 2016

This paper presents quantities, terminology, and symbols of terms related to photothermal phenomena and used in photothermal and related spectroscopies. The terms used in the literature to describe photothermal phenomena and methods are reviewed, and a glossary of terms is given. The origins of photothermal phenomena, as well as the relations among various photothermal effects, are summarized. The listed terms cover the terminology in transient grating, transient lens, photoacoustic spectroscopy, photothermal radiometry, calorimetry, interferometry, deflection, reflection, and other related spectroscopies, which use or are related to photothermal effects.

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Inverse Problem

World scientific series on nonlinear science, series A · 2009

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Inverse Problem

2022

The wave equation solution from numerical methods produced the synthetic data in the forward problem. This solution is obtained by taking the initial assumption that the subsurface is beneficial and useful for solving the inverse problem in seismic tomography. This inverse problem will provide information for the initial model parameters that travel to obtain the next updated model till achieving the good match/minimum error between the synthetic and field seismic data. The inverse problem was also characterized differently depending on the availability of the data points and of the required estimation of the number of model parameters. The inverse problem is said to be under-determined in the case of lacking data points rather than unknown model parameters. One may need to adopt special inversion strategies like regularization and multi-scale approaches to avoid the local solutions. The regularization helps to implement the prior information and supports the need to develop the best possible method.

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The Inverse Problem

Handbook of geophysical exploration. Section 1, Seismic exploration/Handbook of geophysical exploration. Seismic exploration · 2005

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Inverse Galois problem

Pérez Caballero, David · UCrea (University of Cantabria) · 2025

En la perspectiva habitual de la teoría de Galois se parte de polinomios para describir sus grupos de automorfismos. El Problema Inverso de Galois trata de revertir este enfoque, dado un grupo se estudia si existe algún polinomio sobre el cuerpo de los racionales que lo tenga como grupo de Galois. En este trabajo fin de grado se demuestra que todo grupo abeliano finito se puede realizar como grupo de Galois dentro de una extensión ciclotómica, siguiendo los pasos que culminaron en el Teorema de Kronecker-Weber. A continuación, se elaboran polinomios cuyo grupo de Galois es el grupo simétrico utilizando la transitividad del grupo y la aparición de determinados ciclos, con el respaldo siempre del Teorema de Dedekind. La realización de los grupos alternados se logra forzando discriminantes cuadrados y empleando el Teorema de Irreducibilidad de Hilbert. Además, se exhibe la realización del grupo de los cuaterniones siguiendo una construcción clásica mediante extensiones cuadráticas en torre, aprovechando la estructura del grupo. Por último, se demuestra que los grupos diédricos son también realizables y se hace una mención a los grupos simples finitos.

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Inverse Problem Modeling

Schijndel, AWM Jos van · TU/e Research Portal (Eindhoven University of Technology) · 2009

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Inverse Piston Problem

Tatsien Li, Libin Wang · Progress in nonlinear differential equations and their applications · 2009

Suppose that a piston originally located at the origin at t = 0 moves with the speed υ p = φ(t) (t ≥ 0) in a tube whose the length is assumed to be infinite and that the gas on the right side of the piston possesses an isentropic state. In order to determine the state of the gas on the right side of this piston, in Lagrangian representation this piston problem reduces to the following mixed initial-boundary value problem for the system with the initial data and the boundary condition where τ is the specific volume, u the velocity, and p = p(τ) the pressure. For polytropic gases, where γ > 1 is the adiabatic exponent and A is a positive constant.

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Inverse Quantum Problem

Persson Mattsson, Pär · KTH Publication Database DiVA (KTH Royal Institute of Technology) · 2011

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Feynman's Inverse Problem

Adrian Kirkeby · SIAM Review · 2024

We analyze an inverse problem for water waves posed by Richard Feynman in the BBC documentary Fun to Imagine. We show that the problem can be modeled as an inverse Cauchy problem for gravity-capillary waves, conduct a detailed analysis of the Cauchy problem, and give a uniqueness proof for the inverse problem. Somewhat surprisingly, this results in a positive answer to Feynman's question. In addition, we derive stability estimates for the inverse problem for both continuous and discrete measurements, propose a simple inversion method, and conduct numerical experiments to verify our results.

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The inverse problem

Richard Beals, Percy Deift, Carlos Tomei · Mathematical surveys and monographs · 1988

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The Inverse Problem

Knut Stamnes, Jakob J. Stamnes · 2015

This chapter provides a basic introduction to the inverse problem corresponding to the forward–inverse problem. It starts by considering how to estimate the value of a single parameter because it will serve as a good introduction to the use of Bayes' theorem, and allow for a discussion of error bars and confidence intervals. The chapter provides a general formulation of the inverse problem by considering a set of measurements assembled into a measurement vector 'y' with 'N' elements, and the retrieval parameters (the unknowns) assembled into a state vector x with 'M' elements. The forward model provides the relationship between these two vectors. The chapter then focuses on model selection for making a choice between available model options based on how well a particular model fits the data. The chapter finally discusses the methods for solving nonlinear and linear inversion problems.

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The Inverse Problem

Harry A. Mavromatis · Reidel texts in the mathematical sciences · 1992

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