1,884 research outputs found
Asymptotics of orthogonal polynomials via the Koosis theorem
The main aim of this short paper is to advertize the Koosis theorem in the
mathematical community, especially among those who study orthogonal
polynomials. We (try to) do this by proving a new theorem about asymptotics of
orthogonal polynomials for which the Koosis theorem seems to be the most
natural tool. Namely, we consider the case when a Szeg\"o measure on the unit
circumference is perturbed by an arbitrary measure inside the unit disk and an
arbitrary Blaschke sequence of point masses outside the unit disk
Towards a robust algorithm to determine topological domains from colocalization data
One of the most important tasks in understanding the complex spatial
organization of the genome consists in extracting information about this
spatial organization, the function and structure of chromatin topological
domains from existing experimental data, in particular, from genome
colocalization (Hi-C) matrices. Here we present an algorithm allowing to reveal
the underlying hierarchical domain structure of a polymer conformation from
analyzing the modularity of colocalization matrices. We also test this
algorithm on several model polymer structures: equilibrium globules, random
fractal globules and regular fractal (Peano) conformations. We define what we
call a spectrum of cluster borders, and show that these spectra behave
strikingly differently for equilibrium and fractal conformations, allowing us
to suggest an additional criterion to identify fractal polymer conformations
Suppression of Conductance in a Topological Insulator Nanostep Junction
We investigate quantum transport via surface states in a nanostep junction on
the surface of a 3D topological insulator that involves two different side
surfaces. We calculate the conductance across the junction within the
scattering matrix formalism and find that as the bias voltage is increased, the
conductance of the nanostep junction is suppressed by a universal factor of 1/3
compared to the conductance of a similar planar junction based on a single
surface of a topological insulator. We also calculate and analyze the Fano
factor of the nanostep junction and predict that the Fano factor saturates at
1/5, five times smaller than for a Poisson process
Global well-posedness for the critical 2D dissipative quasi-geostrophic equation
We give an elementary proof of the global well-posedness for the critical 2D
dissipative quasi-geostrophic equation. The argument is based on a non-local
maximum principle involving appropriate moduli of continuity.Comment: 7 page
Infrared catastrophe and tunneling into strongly correlated electron systems: Exact solution of the x-ray edge limit for the 1D electron gas and 2D Hall fluid
In previous work we have proposed that the non-Fermi-liquid spectral
properties in a variety of low-dimensional and strongly correlated electron
systems are caused by the infrared catastrophe, and we used an exact functional
integral representation for the interacting Green's function to map the
tunneling problem onto the x-ray edge problem, plus corrections. The
corrections are caused by the recoil of the tunneling particle, and, in systems
where the method is applicable, are not expected to change the qualitative form
of the tunneling density of states (DOS). Qualitatively correct results were
obtained for the DOS of the 1D electron gas and 2D Hall fluid when the
corrections to the x-ray edge limit were neglected and when the corresponding
Nozieres-De Dominicis integral equations were solved by resummation of a
divergent perturbation series. Here we reexamine the x-ray edge limit for these
two models by solving these integral equations exactly, finding the expected
modifications of the DOS exponent in the 1D case but finding no changes in the
DOS of the 2D Hall fluid with short-range interaction. We also provide, for the
first time, an exact solution of the Nozieres-De Dominicis equation for the 2D
electron gas in the lowest Landau level.Comment: 6 pages, Revte
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