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Brain Connectivity Mapping and Analysis Using Diffusion MRI
Published in Troy Farncombe, Krzysztof Iniewski, Medical Imaging, 2017
Brian G. Booth, Ghassan Hamarneh
Two other model-free approaches have also gained traction in the dMRI community. First, the diffusion orientation transform (DOT) shares similarities with q-ball imaging as both are based on the earlier q-space approach. In contrast, DOT assumes diffusion decays exponentially along the radial direction and uses this assumption to perform the Fourier transform in (19.4) using fewer DWI samples [79]. The DOT diffusion ODF is then obtained by analytically integrating the resulting PDF along the radial direction.
Well-posedness and asymptotic stability results for a viscoelastic plate equation with a logarithmic nonlinearity
Published in Applicable Analysis, 2020
Mohammad M. Al-Gharabli, Aissa Guesmia, Salim A. Messaoudi
The logarithmic nonlinearity is of much interest in physics, since it appears naturally in inflation cosmology and supersymmetric filed theories, quantum mechanics and nuclear physics [24,25]. This type of problems has applications in many branches of physics such as nuclear physics, optics and geophysics [26–28]. Birula and Mycielski [27,29] studied the following problem: which is a relativistic version of logarithmic quantum mechanics and can also be obtained by taking the limit for the p-adic string equation [30,31]. In [32], Cazenave and Haraux considered and established the existence and uniqueness of the solution for the Cauchy problem. Gorka [28] used some compactness arguments and obtained the global existence of weak solutions, for all to the initial-boundary value problem (8) in the one-dimensional case. Bartkowski and Gorka [26] proved the existence of classical solutions and investigated the weak solutions for the corresponding one-dimensional Cauchy problem for Equation (8). Hiramatsu et al. [33] introduced the following equation: to study the dynamics of Q-ball in theoretical physics and presented a numerical study. However, there was no theoretical analysis for the problem. In [34], Han proved the global existence of weak solutions, for all to the initial boundary value problem (9) in .