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Here we define and prove some properties of the semi-classical wavefront set. We also define and study semi-classical Fourier integral operators and prove a generalization of Egorov's Theorem to manifolds of different dimensions.

We consider scattering by general compactly supported semi-classical perturbations of the Euclidean Laplace-Beltrami operator. We show that if the suitably cutoff resolvent of the Hamiltonian quantizes a Lagrangian relation on the product cotangent bundle, the scattering amplitude quantizes the natural scattering relation. In the case when the resolvent is… (More)

- A. V. Avetisyan, A. N. Samokhin, I. Y. Alexandrova, R. A. Zinovkin, R. A. Simonyan, N. V. Bobkova
- Biochemistry (Moscow)
- 2016

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)

- Ivana Alexandrova
- Asymptotic Analysis
- 2006

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)

- Ivana Alexandrova, Jean-François Bony, Thierry Ramond
- Asymptotic Analysis
- 2008

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)

We compute the scattering amplitude for Schrödinger operators at a critical energy level, corresponding to the maximum point of the potential. We follow [30], using Isozaki-Kitada's representation formula for the scattering amplitude, together with results from [5] in order to analyze the contribution of trapped trajectories.

- S V Makarov, V A Rossiev, +5 authors Yu L Minaev
- Terapevticheskiĭ arkhiv
- 2016

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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