Ivana Alexandrova

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Structural and functional impairments of mitochondria in brain tissues in the pathogenesis of Alzheimer’s disease (AD) cause energy deficiency, increased generation of reactive oxygen species (ROS), and premature neuronal death. However, the causal relations between accumulation of beta-amyloid (Aβ) peptide in mitochondria and mitochondrial dysfunction, as(More)
We consider scattering by short range perturbations of the semi-classical Laplacian. We prove that when a polynomial bound on the resolvent holds the scattering amplitude is a semi-classical Fourier integral operator associated to the scattering relation near a non-trapped ray. Compared to previous work, we allow the scattering relation to have more general(More)
We study the scattering amplitude for Schrödinger operators at a critical energy level, which is a unique non-degenerate maximum of the potential. We do not assume that the maximum point is non-resonant and use results by Bony, Fujiié, Ramond and Zerzeri to analyze the contributions of the trapped trajectories. We prove a semiclassical expansion of the(More)
The existence of the Laplace-Beltrami operator has allowed mathematicians to carry out Fourier analysis on Riemannian manifolds [2]. We recall that the Laplace-Beltrami operator ∆ on a compact Riemannian manifold has a discrete set of eigenvalues {λ j } ∞ j=1 , which satisfies λ j → ∞ as j → ∞. This is known as the spectrum of the Laplace-Beltrami operator.(More)
We study the semi-classical behavior of the spectral function of the Schrödinger operator with short range potential. We prove that the spectral function is a semi-classical Fourier integral operator quantizing the forward and backward Hamiltonian flow relations of the system. Under a certain geometric condition we explicitly compute the phase in an(More)
AIM To determine the possible boundaries of high-dose immunosuppressive therapy and autologous hematopoietic stem cell transplantation (HDIT-autoHSCT) for autoimmune diseases (AUDs), such as systemic lupus erythematosus (SLE), rheumatoid arthritis (RA), and multiple sclerosis (MS). SUBJECTS AND METHODS A long-term trial was conducted at one center to(More)
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