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Long time energy transfer in the random Schrodinger equation
Long time energy transfer random Schrodinger equation
2015/7/14
We consider the long time behavior of solutions of the d-dimensional linear Boltzmann equation that arises in the weak coupling limit for the Schrodinger equation with a time-dependent random potentia...
Complete solution to a conjecture on the maximal energy of unicyclic graphs
Complete solution conjecture unicyclic graphs
2010/11/24
For a given simple graph $G$, the energy of $G$ denoted by $E(G)$, is defined as the sum of the absolute values of all eigenvalues of its adjacency matrix. Let $P_n^{\ell}$ be the unicyclic graph obt...
Self-energy effects in the Polchinski and Wick-ordered renormalization-group approaches
Self-energy effects Polchinski Wick-ordered renormalization-group approaches
2010/12/16
I consider treatment of the self-energy effects in the functional renormalization group (fRG) schemes, which do not rely on the one-particle irreducible functional.
The supercritical generalized KdV equation: Global well-posedness in the energy space and below
supercritical generalized KdV equation Global well-posedness energy space and below
2010/12/8
We consider the generalized Korteweg-de Vries (gKdV) equation @tu + @3 xu + μ@x(uk+1) = 0, where k ≥ 5 is an integer number and μ = ±1.In the focusing case (μ = 1), we show that if the initial data u0...
Closed surfaces with bounds on their Willmore energy
Willmore energy conformal parametrization geometric measure theory
2010/12/14
The Willmore energy of a closed surface in Rn is the integral of its squared mean curvature, and is invariant under M¨obius transformations of Rn. We show that any torus in R3 with energy at most 8π &...