China
Africa
Explore chapters and articles related to this topic
CAD of Cardiovascular Diseases
Published in de Azevedo-Marques Paulo Mazzoncini, Mencattini Arianna, Salmeri Marcello, Rangayyan Rangaraj M., Medical Image Analysis and Informatics: Computer-Aided Diagnosis and Therapy, 2018
Marco A. Gutierrez, Marina S. Rebelo, Ramon A. Moreno, Anderson G. Santiago, Maysa M. G. Macedo
The behavior of stents after their introduction into the vessel is of extreme importance for monitoring patients’ stents post-introduction. The high image resolution allows IVOCT to identify the stent through a sequence of cross section acquired during the pullback, allowing a 3D reconstruction of the whole metal structure (Dubuisson et al. 2015; Unal et al. 2009; Nakao et al. 2013; Wang et al. 2014). Wang et al. (2015b) applied a method based on Bayesian network and graph searches to detect stents in 72 patients. Since the 3D reconstruction may comprise both the stent and the various tissues that constitute the blood vessel wall, some studies have developed automatic methods to segment and reconstruct the structures (stent and tissues) in three dimensions (Farooq et al. 2011; Tsantis et al. 2012; Wang et al. 2010).
Calculus on Manifolds
Published in Mattias Blennow, Mathematical Methods for Physics and Engineering, 2018
Although both the pushforward and pullback will always be defined, they may not be invertible. However, if one of them is invertible, so is the other. Any map f that induces an invertible pushforward and pullback is called an immersion of M into N. If, in addition, f itself is invertible, then it is an embedding of M in N. For any embedding, the image f(M) in N is called a submanifold of N.
Supersymmetric Theory of Stochastics:Demystification of Self-Organized Criticality
Published in Christos H. Skiadas, Charilaos Skiadas, Handbook of Applications of Chaos Theory, 2017
This is the well-known FP equation for the TPD in the Stratonovich interpretation of the white Gaussian noise. What resolves the issue here is the understanding that the temporal evolution is a stochastically averaged pullback induced by the SDE-defined maps and that the TPD in the coordinate-free setting is a top differential form.
Forward dynamics of 3D double time-delayed MHD-Voight equations
Published in Applicable Analysis, 2023
The goal of this section is to consider the forward stability of pullback attractors in Theorem 3.4. More precisely, the pullback attractor upper-converges to the global attractor of autonomous equation corresponding to (1) as the time parameter tends to positive infinity. For this purpose, we introduce the following autonomous equation: Using the Leray–Helmholtz projection to (35) yields where and satisfy the following assumptions: In addition, we can find a weak hypothesis: to replace (37). More precisely, by (37) we have
Pullback exponential attractors in nonlocal Mindlin's strain gradient porous elasticity
Published in Applicable Analysis, 2023
In this section we study the robustness (in the sense of upper semicontinuity) of the minimal pullback attractors, which is a pullback -attractor, with respect to the perturbed parameter (especially as . For this, suppose that is a family of real valued functions of real variable satisfying (5), and denote by and , respectively, the evolution process and its minimal pullback attractor with problem (2)–(4) in as given by Theorem 4.6.
Pullback
Published in Applicable Analysis, 2018
The article is divided as follows. In the next section, we introduce the GMCHNSE and its mathematical setting and we recall from [35] some results on the weak/strong solutions to the 3D GMCHNSE. The main results appear in the third and fourth sections where we prove the existence of the pullback attractors using the concept of the flattening property introduced in [36,37]. The finite fractal dimension of these pullback attractors is established in the fifth section.