Search results for: Well posedness.

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posedness.</title> <meta name="description" content="Search results for: Well posedness."> <meta name="keywords" content="Well posedness."> <meta name="viewport" content="width=device-width, initial-scale=1, minimum-scale=1, maximum-scale=1, user-scalable=no"> <meta charset="utf-8"> <link href="https://cdn.waset.org/favicon.ico" type="image/x-icon" rel="shortcut icon"> <link href="https://cdn.waset.org/static/plugins/bootstrap-4.2.1/css/bootstrap.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/plugins/fontawesome/css/all.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/css/site.css?v=150220211555" rel="stylesheet"> </head> <body> <header> <div class="container"> <nav class="navbar navbar-expand-lg navbar-light"> <a class="navbar-brand" href="https://waset.org"> <img src="https://cdn.waset.org/static/images/wasetc.png" alt="Open Science Research Excellence" title="Open Science Research Excellence" /> </a> <button class="d-block d-lg-none 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action="https://publications.waset.org/search"> <div id="custom-search-input"> <div class="input-group"> <i class="fas fa-search"></i> <input type="text" class="search-query" name="q" placeholder="Author, Title, Abstract, Keywords" value="Well posedness."> <input type="submit" class="btn_search" value="Search"> </div> </div> </form> </div> </div> <div class="row mt-3"> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Commenced</strong> in January 2007</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Frequency:</strong> Monthly</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Edition:</strong> International</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Paper Count:</strong> 6</div> </div> </div> </div> <h1 class="mt-3 mb-3 text-center" style="font-size:1.6rem;">Search results for: Well posedness.</h1> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">6</span> An Iterated Function System for Reich Contraction in Complete b Metric Space</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=R.%20Uthayakumar">R. Uthayakumar</a>, <a href="https://publications.waset.org/search?q=G.%20Arockia%20Prabakar"> G. Arockia Prabakar</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>In this paper, we introduce R Iterated Function System and employ the Hutchinson Barnsley theory (HB) to construct a fractal set as its unique fixed point by using Reich contractions in a complete b metric space. We discuss about well posedness of fixed point problem for b metric space.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Fractals" title="Fractals">Fractals</a>, <a href="https://publications.waset.org/search?q=Iterated%20Function%20System" title=" Iterated Function System"> Iterated Function System</a>, <a href="https://publications.waset.org/search?q=Compact%20set" title=" Compact set"> Compact set</a>, <a href="https://publications.waset.org/search?q=Reich%0D%0AContraction" title=" Reich Contraction"> Reich Contraction</a>, <a href="https://publications.waset.org/search?q=Well%20posedness." title=" Well posedness."> Well posedness.</a> </p> <a href="https://publications.waset.org/9997751/an-iterated-function-system-for-reich-contraction-in-complete-b-metric-space" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/9997751/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/9997751/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/9997751/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/9997751/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/9997751/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/9997751/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/9997751/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/9997751/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/9997751/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/9997751/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/9997751.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1785</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5</span> Performance Analysis of Reconstruction Algorithms in Diffuse Optical Tomography</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=K.%20Uma%20Maheswari">K. Uma Maheswari</a>, <a href="https://publications.waset.org/search?q=S.%20Sathiyamoorthy"> S. Sathiyamoorthy</a>, <a href="https://publications.waset.org/search?q=G.%20Lakshmi"> G. Lakshmi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>Diffuse Optical Tomography (DOT) is a non-invasive imaging modality used in clinical diagnosis for earlier detection of carcinoma cells in brain tissue. It is a form of optical tomography which produces gives the reconstructed image of a human soft tissue with by using near-infra-red light. It comprises of two steps called forward model and inverse model. The forward model provides the light propagation in a biological medium. The inverse model uses the scattered light to collect the optical parameters of human tissue. DOT suffers from severe ill-posedness due to its incomplete measurement data. So the accurate analysis of this modality is very complicated. To overcome this problem, optical properties of the soft tissue such as absorption coefficient, scattering coefficient, optical flux are processed by the standard regularization technique called Levenberg - Marquardt regularization. The reconstruction algorithms such as Split Bregman and Gradient projection for sparse reconstruction (GPSR) methods are used to reconstruct the image of a human soft tissue for tumour detection. Among these algorithms, Split Bregman method provides better performance than GPSR algorithm. The parameters such as signal to noise ratio (SNR), contrast to noise ratio (CNR), relative error (RE) and CPU time for reconstructing images are analyzed to get a better performance.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Diffuse%20optical%20tomography" title="Diffuse optical tomography">Diffuse optical tomography</a>, <a href="https://publications.waset.org/search?q=ill-posedness" title=" ill-posedness"> ill-posedness</a>, <a href="https://publications.waset.org/search?q=Levenberg%20Marquardt%20method" title=" Levenberg Marquardt method"> Levenberg Marquardt method</a>, <a href="https://publications.waset.org/search?q=Split%20Bregman" title=" Split Bregman"> Split Bregman</a>, <a href="https://publications.waset.org/search?q=the%20Gradient%20projection%20for%20sparse%20reconstruction." title=" the Gradient projection for sparse reconstruction."> the Gradient projection for sparse reconstruction.</a> </p> <a href="https://publications.waset.org/10004161/performance-analysis-of-reconstruction-algorithms-in-diffuse-optical-tomography" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10004161/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10004161/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10004161/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10004161/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10004161/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10004161/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10004161/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10004161/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10004161/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10004161/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10004161.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1619</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4</span> Fourier Spectral Method for Analytic Continuation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Zhenyu%20Zhao">Zhenyu Zhao</a>, <a href="https://publications.waset.org/search?q=Lei%20You"> Lei You</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>The numerical analytic continuation of a function f(z) = f(x + iy) on a strip is discussed in this paper. The data are only given approximately on the real axis. The periodicity of given data is assumed. A truncated Fourier spectral method has been introduced to deal with the ill-posedness of the problem. The theoretic results show that the discrepancy principle can work well for this problem. Some numerical results are also given to show the efficiency of the method.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Analytic%20continuation" title="Analytic continuation">Analytic continuation</a>, <a href="https://publications.waset.org/search?q=ill-posed%20problem" title=" ill-posed problem"> ill-posed problem</a>, <a href="https://publications.waset.org/search?q=regularization%20method%20Fourier%20spectral%20method" title=" regularization method Fourier spectral method"> regularization method Fourier spectral method</a>, <a href="https://publications.waset.org/search?q=the%20discrepancy%20principle." title=" the discrepancy principle."> the discrepancy principle.</a> </p> <a href="https://publications.waset.org/9760/fourier-spectral-method-for-analytic-continuation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/9760/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/9760/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/9760/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/9760/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/9760/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/9760/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/9760/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/9760/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/9760/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/9760/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/9760.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1500</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3</span> On Method of Fundamental Solution for Nondestructive Testing</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Jieer%20Wu">Jieer Wu</a>, <a href="https://publications.waset.org/search?q=Zheshu%20Ma"> Zheshu Ma</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Nondestructive testing in engineering is an inverse Cauchy problem for Laplace equation. In this paper the problem of nondestructive testing is expressed by a Laplace-s equation with third-kind boundary conditions. In order to find unknown values on the boundary, the method of fundamental solution is introduced and realized. Because of the ill-posedness of studied problems, the TSVD regularization technique in combination with L-curve criteria and Generalized Cross Validation criteria is employed. Numerical results are shown that the TSVD method combined with L-curve criteria is more efficient than the TSVD method combined with GCV criteria. The abstract goes here. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=ill-posed" title="ill-posed">ill-posed</a>, <a href="https://publications.waset.org/search?q=TSVD" title="TSVD">TSVD</a>, <a href="https://publications.waset.org/search?q=Laplace%27s%20equation" title=" Laplace's equation"> Laplace's equation</a>, <a href="https://publications.waset.org/search?q=inverse%20problem" title="inverse problem">inverse problem</a>, <a href="https://publications.waset.org/search?q=L-curve" title=" L-curve"> L-curve</a>, <a href="https://publications.waset.org/search?q=Generalized%20Cross%20Validation." title=" Generalized Cross Validation."> Generalized Cross Validation.</a> </p> <a href="https://publications.waset.org/5950/on-method-of-fundamental-solution-for-nondestructive-testing" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/5950/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/5950/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/5950/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/5950/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/5950/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/5950/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/5950/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/5950/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/5950/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/5950/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/5950.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1475</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">2</span> Algorithm for Reconstructing 3D-Binary Matrix with Periodicity Constraints from Two Projections</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=V.%20Masilamani">V. Masilamani</a>, <a href="https://publications.waset.org/search?q=Kamala%20Krithivasan"> Kamala Krithivasan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>We study the problem of reconstructing a three dimensional binary matrices whose interiors are only accessible through few projections. Such question is prominently motivated by the demand in material science for developing tool for reconstruction of crystalline structures from their images obtained by high-resolution transmission electron microscopy. Various approaches have been suggested to reconstruct 3D-object (crystalline structure) by reconstructing slice of the 3D-object. To handle the ill-posedness of the problem, a priori information such as convexity, connectivity and periodicity are used to limit the number of possible solutions. Formally, 3Dobject (crystalline structure) having a priory information is modeled by a class of 3D-binary matrices satisfying a priori information. We consider 3D-binary matrices with periodicity constraints, and we propose a polynomial time algorithm to reconstruct 3D-binary matrices with periodicity constraints from two orthogonal projections.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=3D-Binary%20Matrix%20Reconstruction" title="3D-Binary Matrix Reconstruction">3D-Binary Matrix Reconstruction</a>, <a href="https://publications.waset.org/search?q=Computed%20Tomography" title=" Computed Tomography"> Computed Tomography</a>, <a href="https://publications.waset.org/search?q=Discrete%20Tomography" title=" Discrete Tomography"> Discrete Tomography</a>, <a href="https://publications.waset.org/search?q=Integral%20Max%20Flow%20Problem." title=" Integral Max Flow Problem."> Integral Max Flow Problem.</a> </p> <a href="https://publications.waset.org/9296/algorithm-for-reconstructing-3d-binary-matrix-with-periodicity-constraints-from-two-projections" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/9296/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/9296/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/9296/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/9296/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/9296/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/9296/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/9296/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/9296/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/9296/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/9296/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/9296.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">4896</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1</span> Electromagnetic Imaging of Inhomogeneous Dielectric Cylinders Buried in a Slab Mediumby TE Wave Illumination</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Chung-Hsin%20Huang">Chung-Hsin Huang</a>, <a href="https://publications.waset.org/search?q=Chien-Ching%20Chiu"> Chien-Ching Chiu</a>, <a href="https://publications.waset.org/search?q=Chun%20Jen%20Lin"> Chun Jen Lin</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The electromagnetic imaging of inhomogeneous dielectric cylinders buried in a slab medium by transverse electric (TE) wave illumination is investigated. Dielectric cylinders of unknown permittivities are buried in second space and scattered a group of unrelated waves incident from first space where the scattered field is recorded. By proper arrangement of the various unrelated incident fields, the difficulties of ill-posedness and nonlinearity are circumvented, and the permittivity distribution can be reconstructed through simple matrix operations. The algorithm is based on the moment method and the unrelated illumination method. Numerical results are given to demonstrate the capability of the inverse algorithm. Good reconstruction is obtained even in the presence of additive Gaussian random noise in measured data. In addition, the effect of noise on the reconstruction result is also investigated. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Slab%20Medium" title="Slab Medium">Slab Medium</a>, <a href="https://publications.waset.org/search?q=Unrelated%20Illumination%20Method" title=" Unrelated Illumination Method"> Unrelated Illumination Method</a>, <a href="https://publications.waset.org/search?q=TEWave%20Illumination" title=" TEWave Illumination"> TEWave Illumination</a>, <a href="https://publications.waset.org/search?q=Inhomogeneous%20Cylinders." title=" Inhomogeneous Cylinders."> Inhomogeneous Cylinders.</a> </p> <a href="https://publications.waset.org/2516/electromagnetic-imaging-of-inhomogeneous-dielectric-cylinders-buried-in-a-slab-mediumby-te-wave-illumination" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/2516/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a 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