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Meyer-Vietoris type formula for determinants of elliptic differential operators
Abstract For a closed codimension one submanifold Γ of a compact manifold M, let MΓ be the manifold with boundary obtained by cutting M along Γ. Let A be an elliptic differential operator on M and BExpand
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Global wellposedness of KdV in $H^{-1}({\mathbb T},{\mathbb R})$
By the inverse method we show that the Korteweg–de Vries equation (KdV) ∂tv(x,t)=-∂x3v(x,t)+6v(x,t)∂xv(x,t)x∈T,t∈R)Hβ(T,R)β≥−1.
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Microlocal dispersive smoothing for the Schrödinger equation
This paper establishes a connection between the microlocal smoothness of solutions of the initial value problem for Schrodinger's equation and the global behavior of bicharacteristics of theExpand
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The Defocusing NLS Equation and Its Normal Form
The theme of this monograph is the nonlinear Schrodinger equation. This equation models slowly varying wave envelopes in dispersive media and arises in various physical systems such as water waves,Expand
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The Miura map on the line
Abstract. We study relations between properties of the Miura map r ↦ → q = B(r) = r ′ + r2 and Schrodinger operators Lq = −d2 /dx2 + q where r and q are real-valued functions or distributionsExpand
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Scattering and inverse scattering for steplike potentials in the Schrödinger equation
On etudie les problemes avant et inverses dans la theorie de la diffusion de l'equation de Schrodinger: −y″+ν(x)y=k 2 y, x∈R avec des potentiels en echelon ν(x) qui sont asymptotiques a differentesExpand
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TX Task: Automatic Detection of Focus Organisms in Biomedical Publications
In biomedical information extraction (IE), a central problem is the disambiguation of ambiguous names for domain specific entities, such as proteins, genes, etc. Expand
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Estimates for Periodic and Dirichlet Eigenvalues of the Schrödinger Operator
Consider the Schrodinger equation $-y' + Vy = \lambda y$ for a complex-valued potential V of period 1 in the weighted Sobolev space $H^w$ of 2-periodic functions $f : \mathbb R \rightarrow \mathbbExpand
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Refined analytic torsion
Given an acyclic representation $\alpha$ of the fundamental group of a compact oriented odd-dimensional manifold, which is close enough to an acyclic unitary representation, we define a refinementExpand
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Estimates for Periodic and Dirichlet Eigenvalues of the Schrödinger Operator with Singular Potentials
Abstract In this paper, the periodic and the Dirichlet problems for the Schrodinger operator −(d2/dx2)+V are studied for singular, complex-valued potentials V in the Sobolev space H−αper[0, 1] (0⩽αExpand
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