scholarly journals The Problem of the Non-Uniqueness of the Solution to the Inverse Problem of Recovering the Symmetric States of a Bistable Medium with Data on the Position of an Autowave Front

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 860
Author(s):  
Natalia Levashova ◽  
Alexandr Gorbachev ◽  
Raul Argun ◽  
Dmitry Lukyanenko
Keyword(s):  
Inverse Problem ◽  
Singularly Perturbed ◽  
Stable States ◽  
Uniqueness Of The Solution ◽  
Ill Posed ◽  
Symmetric States

The paper considers the question of the possibility of recovering symmetric stable states of a bistable medium in the inverse problem for a nonlinear singularly perturbed autowave equation by data given on the position of an autowave front propagating through it. It is shown that under certain conditions, this statement of the problem is ill-posed in the sense of the non-uniqueness of the solution. A regularizing approach to its solution was proposed.

scholarly journals 2D and 3D fault basis for fuel cell diagnosis by external magnetic field measurements

2017 ◽  
Vol 79 (2) ◽  
pp. 20901 ◽  
Author(s):  
Lyes Ifrek ◽  
Gilles Cauffet ◽  
Olivier Chadebec ◽  
Yann Bultel ◽  
Sébastien Rosini ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Inverse Problem ◽  
Fuel Cell ◽  
External Magnetic Field ◽  
Current Density ◽  
Field Measurements ◽  
Magnetic Field Measurements ◽  
Uniqueness Of The Solution ◽  
Ill Posed ◽  
Value Decomposition

An original approach used for the identification of faults in fuel cell stacks is presented. It is based on the 3D reconstruction of the current density from external magnetic field measurements which is an ill-posed magnetostatic linear inverse problem. A suitable and original current density and magnetic field basis are proposed in order to define both local and global faults on a fuel cell stack. The inverse problem is regularized by truncated singular value decomposition (SVD) to ensure the uniqueness of the solution.

scholarly journals Bayesian Reconstruction through Adaptive Image Notion

Proceedings ◽  
2019 ◽  
Vol 33 (1) ◽  
pp. 21
Author(s):  
Fabrizia Guglielmetti ◽  
Eric Villard ◽  
Ed Fomalont
Keyword(s):  
Inverse Problem ◽  
Image Plane ◽  
Source Distribution ◽  
Bayesian Probability ◽  
Model Parameters ◽  
Uncertain Information ◽  
Source Detection ◽  
Component Mixture ◽  
Ill Posed ◽  
Image Planes

A stable and unique solution to the ill-posed inverse problem in radio synthesis image analysis is sought employing Bayesian probability theory combined with a probabilistic two-component mixture model. The solution of the ill-posed inverse problem is given by inferring the values of model parameters defined to describe completely the physical system arised by the data. The analysed data are calibrated visibilities, Fourier transformed from the ( u , v ) to image planes. Adaptive splines are explored to model the cumbersome background model corrupted by the largely varying dirty beam in the image plane. The de-convolution process of the dirty image from the dirty beam is tackled in probability space. Probability maps in source detection at several resolution values quantify the acquired knowledge on the celestial source distribution from a given state of information. The information available are data constrains, prior knowledge and uncertain information. The novel algorithm has the aim to provide an alternative imaging task for the use of the Atacama Large Millimeter/Submillimeter Array (ALMA) in support of the widely used Common Astronomy Software Applications (CASA) enhancing the capabilities in source detection.

SENSITIVITY ANALYSIS AND IDENTIFIABILITY OF A MATHEMATICAL MODEL OF A CHEMICAL REACTION

2021 ◽  
pp. 14-18
Author(s):  
Л.Ф. Сафиуллина
Keyword(s):  
Mathematical Model ◽  
Inverse Problem ◽  
Sensitivity Analysis ◽  
Chemical Reaction ◽  
Reaction Model ◽  
Numerical Calculations ◽  
Specific Reaction ◽  
Uniqueness Of The Solution ◽  
The Mathematical Model ◽  
Kinetics Of

В статье рассмотрен вопрос идентифицируемости математической модели кинетики химической реакции. В процессе решения обратной задачи по оценке параметров модели, характеризующих процесс, нередко возникает вопрос неединственности решения. На примере конкретной реакции продемонстрирована необходимость проводить анализ идентифицируемости модели перед проведением численных расчетов по определению параметров модели химической реакции. The identifiability of the mathematical model of the kinetics of a chemical reaction is investigated in the article. In the process of solving the inverse problem of estimating the parameters of the model, the question arises of the non-uniqueness of the solution. On the example of a specific reaction, the need to analyze the identifiability of the model before carrying out numerical calculations to determine the parameters of the reaction model was demonstrated.

scholarly journals Inverse problem for Sturm-Liouville operators on a curve

2019 ◽  
Vol 50 (3) ◽  
pp. 349-359
Author(s):  
Andrey Aleksandrovich Golubkov ◽  
Yulia Vladimirovna Kuryshova
Keyword(s):  
Inverse Problem ◽  
Asymptotic Behavior ◽  
Transfer Matrix ◽  
Liouville Equation ◽  
Inverse Spectral Problem ◽  
Rectifiable Curve ◽  
Uniqueness Of The Solution ◽  
Sturm Liouville ◽  
Discontinuity Conditions ◽  
Liouville Operators

he inverse spectral problem for the Sturm-Liouville equation with a piecewise-entire potential function and the discontinuity conditions for solutions on a rectifiable curve \(\gamma \subset \textbf{C}\) by the transfer matrix along this curve is studied. By the method of a unit transfer matrix the uniqueness of the solution to this problem is proved with the help of studying of the asymptotic behavior of the solutions to the Sturm-Liouville equation for large values of the spectral parameter module.

ON THE WAY TOWARDS INCREASING THE PREDICTIVE POWER OF THE NUCLEAR MEAN FIELD THEORIES: EVALUATION OF TWO-BODY MATRIX ELEMENTS

2012 ◽  
Vol 21 (05) ◽  
pp. 1250037
Author(s):  
HERVÉ MOLIQUE ◽  
JERZY DUDEK
Keyword(s):  
Inverse Problem ◽  
Predictive Power ◽  
Mean Field ◽  
Field Theories ◽  
Matrix Elements ◽  
The Matrix ◽  
Ill Posed ◽  
Technical Issues ◽  
Numerical Precision ◽  
Mean Field Theories

In this paper we collect a number of technical issues that arise when constructing the matrix representation of the most general nuclear mean field Hamiltonian within which "all terms allowed by general symmetries are considered not only in principle but also in practice". Such a general posing of the problem is necessary when investigating the predictive power of the mean field theories by means of the well-posed inverse problem. [J. Dudek et al., Int. J. Mod. Phys. E21 (2012) 1250053]. To our knowledge quite often ill-posed mean field inverse problems arise in practical realizations what makes reliable extrapolations into the unknown areas of nuclei impossible. The conceptual and technical issues related to the inverse problem have been discussed in the above-mentioned topic whereas here we focus on "how to calculate the matrix elements, fast and with high numerical precision when solving the inverse problem" [For space-limitation reasons we illustrate the principal techniques on the example of the central interactions].

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