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Parabolic geometric flows are smoothing for short time however, over long time, singularities are typically unavoidable, can be very nasty and may be impossible to classify. The idea of [CM6] and here is that, by bringing in the dynamical properties of the flow, we obtain also smoothing for large time for generic initial conditions. When combined with [
Colding, Tobias Holck +1 more
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to be published in Physical Review ...
Sakaguchi, Hidetsugu, Malomed, Boris A.
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Singular Continuous Spectrum for Singular Potentials [PDF]
We prove that Schr dinger operators with meromorphic potentials $(H_{ , }u)_n=u_{n+1}+u_{n-1}+ \frac{g( +n )}{f( +n )} u_n$ have purely singular continuous spectrum on the set $\{E: L(E)
Svetlana Jitomirskaya, Fan Yang
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We consider the statistical distribution of zeros of random meromorphic functions whose poles are independent random variables. It is demonstrated that correlation functions of these zeros can be computed analytically and explicit calculations are performed for the 2-point correlation function. This problem naturally appears in e.g.
Bogomolny, E., Gerland, U., Schmit, C.
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Two spatial regions $B$ and $R$ are hyperentangled if the generalized entropy satisfies $S_{\text{gen}}^{B\cup R}
Raphael Bousso, Arvin Shahbazi-Moghaddam
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Classical and Quantum Strings in plane waves, shock waves and spacetime singularities: synthesis and new results [PDF]
Key issues of classical and quantum strings in gravitational plane waves, shock waves and spacetime singularities are synthetically understood. This includes the string mass and mode number excitations, energy-momentum tensor, scattering amplitudes ...
Sanchez, Norma G.
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We prove that a homogeneous and isotropic universe containing a scalar field with a power-law potential, $V( )=A ^{n}$, with $00$ always develops a finite-time singularity at which the Hubble rate and its first derivative are finite, but its second derivative diverges.
Barrow, John D, Graham, Alexander AH
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Classical Collapse to Black Holes and Quantum Bounces: A Review
In the last four decades, different programs have been carried out aiming at understanding the final fate of gravitational collapse of massive bodies once some prescriptions for the behaviour of gravity in the strong field regime are provided.
Daniele Malafarina
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Power Corrections in QCD: A Matter of Energy Resolution [PDF]
We consider power-like corrections in QCD which can be viewed as power surpressed infrared singularities. We argue that the presence of these singularities depends crucially on the energy resolution.
A. H. Mueller +15 more
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Some Examples of Calculation of Massless and Massive Feynman Integrals
We show some examples of calculations of massless and massive Feynman integrals.
Anatoly V. Kotikov
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