The Experts below are selected from a list of 324 Experts worldwide ranked by ideXlab platform
M. S. Osman - One of the best experts on this subject based on the ideXlab platform.
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the Unified Method for conformable time fractional schro dinger equation with perturbation terms
Chinese Journal of Physics, 2018Co-Authors: M. S. Osman, Alper Korkmaz, Hadi Rezazadeh, Mohammad Mirzazadeh, Mostafa Eslami, Qin ZhouAbstract:Abstract The present study implements the Unified Method to the conformable time fractional non linear Schr o ¨ dinger equation with perturbation terms. Reduction of the governing equation to a simpler ODE by compatible complex transform is the first step of the procedure. The predicted solutions in finite series forms of various functions satisfying some particular ODEs are substituted into the reduced form of the governing equation. The algebra is resulted in forming the explicit exact solutions in optical solitary, periodic, elliptic and soliton wave forms represented in polynomial or rational functions.
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The Unified Method for conformable time fractional Schro¨dinger equation with perturbation terms
Chinese Journal of Physics, 2018Co-Authors: M. S. Osman, Alper Korkmaz, Hadi Rezazadeh, Mohammad Mirzazadeh, Mostafa Eslami, Qin ZhouAbstract:Abstract The present study implements the Unified Method to the conformable time fractional non linear Schr o ¨ dinger equation with perturbation terms. Reduction of the governing equation to a simpler ODE by compatible complex transform is the first step of the procedure. The predicted solutions in finite series forms of various functions satisfying some particular ODEs are substituted into the reduced form of the governing equation. The algebra is resulted in forming the explicit exact solutions in optical solitary, periodic, elliptic and soliton wave forms represented in polynomial or rational functions.
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Exact Solutions of Space Dependent Korteweg-de Vries Equation by The Extended Unified Method
Journal of the Physical Society of Japan, 2013Co-Authors: Hamdy I. Abdel-gawad, Nasser S. Elazab, M. S. OsmanAbstract:Recently the Unified Method for finding traveling wave solutions of non-linear evolution equations was proposed by one of the authors a . It was shown that, this Method unifies all the Methods being used to find these solutions. In this paper, we extend this Method to find a class of formal exact solutions to Korteweg-de Vries (KdV) equation with space dependent coefficients. A new class of multiple-soliton or wave trains is obtained.
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Exact Solutions of Space Dependent Korteweg-de Vries Equation by the Extended Unified Method
viXra, 2013Co-Authors: Hamdy I. Abdel-gawad, Nasser S. Elazab, M. S. OsmanAbstract:Abstract: Recently the Unified Method for finding traveling wave solutions of non-linear evolution equations was proposed by one of the authors a. It was shown that, this Method unifies all the Methods being used to find these solutions. In this paper, we extend this Method to find a class of formal exact solutions to Korteweg-de Vries (KdV) equation with space dependent coefficients. A new class of multiple-soliton or wave trains is obtained. Keywords: Exact solution, Extended Unified Method, Korteweg-deVries equation, variable coefficients
Laura A. Viafora - One of the best experts on this subject based on the ideXlab platform.
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A Unified Method for Digital Super-Resolution and Restoration in Infrared Microscopy Imaging
IEEE Access, 2019Co-Authors: Guillermo Machuca, Sergio N. Torres, Bradley M. Ratliff, Pablo A. Gutiérrez, Anselmo Jara, Laura A. ViaforaAbstract:Infrared (IR) imaging systems are known to have a range of sensor and optical limitations that result in degraded imagery. Fixed pattern noise (FPN), resulting from pixel-to-pixel response nonuniformity, is a dominant source of error that manifests in collected imagery through the appearance of temporally and spatially correlated noise patterns that are mixed with each image. Furthermore, finite detector size coupled with imperfect system optics can introduce blurring effects and aliasing, ultimately reducing resolution in acquired images. Here, we propose a Unified Method to reduce FPN and recover high-frequency image content in IR microscopy images. The proposed Method uses regularized nonlocal means to highlight spatial features in the scene while maintaining fine textural image details. We derive an iterative optimization Method based upon a gradient descent minimization strategy that applies a Wiener deconvolution in each iteration to estimate the blur artifacts. The Method is implemented within an embedded mid-wave IR imaging system for microscopy applications. We demonstrate a reduction in FPN and blurring artifacts, achieving improved image resolution in the reconstructed images that are apparent in recovered details on scene objects.
Raphaèle Herbin - One of the best experts on this subject based on the ideXlab platform.
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A Unified approach to Mimetic Finite Difference, Hybrid Finite Volume and Mixed Finite Volume Methods
Mathematical Models and Methods in Applied Sciences, 2010Co-Authors: Jérôme Droniou, Robert Eymard, Thierry Gallouët, Raphaèle HerbinAbstract:We investigate the connections between several recent Methods for the discretization of anisotropic heterogeneous diffusion operators on general grids. We prove that the Mimetic Finite Difference scheme, the Hybrid Finite Volume scheme and the Mixed Finite Volume scheme are in fact identical up to some slight generalizations. As a consequence, some of the mathematical results obtained for each of the Methods (such as convergence properties or error estimates) may be extended to the Unified common framework. We then focus on the relationships between this Unified Method and nonconforming Finite Element schemes or Mixed Finite Element schemes. We also show that for isotropic operators, on particular meshes such as triangular meshes with acute angles, the Unified Method boils down to the well-known efficient two-point flux Finite Volume scheme.
Shaher Momani - One of the best experts on this subject based on the ideXlab platform.
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Analytic solutions for a modified fractional three wave interaction equations with conformable derivative by Unified Method
Alexandria Engineering Journal, 2020Co-Authors: Adeeb G. Talafha, Sahar M. Alqaraleh, Mohammed Al-smadi, Samir Hadid, Shaher MomaniAbstract:Abstract The present work implements the Unified Method to a class of fractional partial differential systems corresponding to modified fractional three wave interaction equations (FTWIEs). The fractional derivative of the three waves envelopes is considered under the conformable sense. The conformable FTWIEs is derived in the (3 + 1) dimensions under the conformable time-fractional derivative of order α ∈ ( 0 , 1 ] based on a modification of the Lax-pair created by Zakharov-Manakov which includes three-dimensional velocity vector dotted with the usual del operator. Then, the Unified Method for creating solutions for nonlinear evolution FTWIEs is applied. Subsequently, a systematic algorithm is used to obtain an infinite set of exact rational solutions to the novel constructed system. By randomly selecting the special values for the parameters, three-dimensional graphs are also given for different patterns. The obtained solutions might play an essential role in many other nonlinear evolution equations that occur in the fields of engineering and mathematical physics.
Guillermo Machuca - One of the best experts on this subject based on the ideXlab platform.
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A Unified Method for Digital Super-Resolution and Restoration in Infrared Microscopy Imaging
IEEE Access, 2019Co-Authors: Guillermo Machuca, Sergio N. Torres, Bradley M. Ratliff, Pablo A. Gutiérrez, Anselmo Jara, Laura A. ViaforaAbstract:Infrared (IR) imaging systems are known to have a range of sensor and optical limitations that result in degraded imagery. Fixed pattern noise (FPN), resulting from pixel-to-pixel response nonuniformity, is a dominant source of error that manifests in collected imagery through the appearance of temporally and spatially correlated noise patterns that are mixed with each image. Furthermore, finite detector size coupled with imperfect system optics can introduce blurring effects and aliasing, ultimately reducing resolution in acquired images. Here, we propose a Unified Method to reduce FPN and recover high-frequency image content in IR microscopy images. The proposed Method uses regularized nonlocal means to highlight spatial features in the scene while maintaining fine textural image details. We derive an iterative optimization Method based upon a gradient descent minimization strategy that applies a Wiener deconvolution in each iteration to estimate the blur artifacts. The Method is implemented within an embedded mid-wave IR imaging system for microscopy applications. We demonstrate a reduction in FPN and blurring artifacts, achieving improved image resolution in the reconstructed images that are apparent in recovered details on scene objects.
