272,852 research outputs found

### Absolutely Continuous Spectrum for Random Schroedinger Operators on the Bethe Strip

The Bethe Strip of width $m$ is the cartesian product \B\times\{1,...,m\},
where \B is the Bethe lattice (Cayley tree). We prove that Anderson models on
the Bethe strip have "extended states" for small disorder. More precisely, we
consider Anderson-like Hamiltonians \;H_\lambda=\frac12 \Delta \otimes 1 + 1
\otimes A + \lambda \Vv on a Bethe strip with connectivity $K \geq 2$, where
$A$ is an $m\times m$ symmetric matrix, \Vv is a random matrix potential, and
$\lambda$ is the disorder parameter. Given any closed interval $I\subset
(-\sqrt{K}+a_{\mathrm{max}},\sqrt{K}+a_{\mathrm{min}})$, where
$a_{\mathrm{min}}$ and $a_{\mathrm{max}}$ are the smallest and largest
eigenvalues of the matrix $A$, we prove that for $\lambda$ small the random
Schr\"odinger operator $\;H_\lambda$ has purely absolutely continuous spectrum
in $I$ with probability one and its integrated density of states is
continuously differentiable on the interval $I$

### Poincare submersions

We prove two kinds of fibering theorems for maps X --> P, where X and P are
Poincare spaces. The special case of P = S^1 yields a Poincare duality analogue
of the fibering theorem of Browder and Levine.Comment: Published by Algebraic and Geometric Topology at
http://www.maths.warwick.ac.uk/agt/AGTVol5/agt-5-2.abs.html Version 5:
Statement of Theorem B corrected, see footnote p2

### Agmon-type estimates for a class of jump processes

In the limit epsilon to 0 we analyze the generators H_epsilon of families of
reversible jump processes in R^d associated with a class of symmetric non-local
Dirichlet-forms and show exponential decay of the eigenfunctions. The
exponential rate function is a Finsler distance, given as solution of a certain
eikonal equation. Fine results are sensitive to the rate function being C^2 or
just Lipschitz. Our estimates are analog to the semi-classical Agmon estimates
for differential operators of second order. They generalize and strengthen
previous results on the lattice epsilon Z^d. Although our final interest is in
the (sub)stochastic jump process, technically this is a pure analysis paper,
inspired by PDE techniques

### Solvable and/or integrable and/or linearizable N-body problems in ordinary (three-dimensional) space. I

Several N-body problems in ordinary (3-dimensional) space are introduced
which are characterized by Newtonian equations of motion (``acceleration equal
force;'' in most cases, the forces are velocity-dependent) and are amenable to
exact treatment (``solvable'' and/or ``integrable'' and/or ``linearizable'').
These equations of motion are always rotation-invariant, and sometimes
translation-invariant as well. In many cases they are Hamiltonian, but the
discussion of this aspect is postponed to a subsequent paper. We consider
``few-body problems'' (with, say, \textit{N}=1,2,3,4,6,8,12,16,...) as well as
``many-body problems'' (N an arbitrary positive integer). The main focus of
this paper is on various techniques to uncover such N-body problems. We do not
discuss the detailed behavior of the solutions of all these problems, but we do
identify several models whose motions are completely periodic or multiply
periodic, and we exhibit in rather explicit form the solutions in some cases

### The Dualizing Spectrum, II

To an inclusion topological groups H->G, we associate a naive G-spectrum. The
special case when H=G gives the dualizing spectrum D_G introduced by the author
in the first paper of this series. The main application will be to give a
purely homotopy theoretic construction of Poincare embeddings in stable
codimension.Comment: Fixed an array of typo

### A psychoanalytic concept illustrated: Will, must, may, can — revisiting the survival function of primitive omnipotence

The author explores the linear thread connecting the theory of Freud and Klein, in terms of the central significance of the duality of the life and death instinct and the capacity of the ego to tolerate contact with internal and external reality. Theoretical questions raised by later authors, informed by clinical work with children who have suffered deprivation and trauma in infancy, are then considered. Theoretical ideas are illustrated with reference to observational material of a little boy who suffered deprivation and trauma in infancy. He was first observed in the middle of his first year of life while he was living in foster care, and then later at the age of two years and three months, when he had been living with his adoptive parents for more than a year

### Muon Production in Relativistic Cosmic-Ray Interactions

Cosmic-rays with energies up to $3\times10^{20}$ eV have been observed. The
nuclear composition of these cosmic rays is unknown but if the incident nuclei
are protons then the corresponding center of mass energy is $\sqrt{s_{nn}} =
700$ TeV. High energy muons can be used to probe the composition of these
incident nuclei. The energy spectra of high-energy ($>$ 1 TeV) cosmic ray
induced muons have been measured with deep underground or under-ice detectors.
These muons come from pion and kaon decays and from charm production in the
atmosphere.
Terrestrial experiments are most sensitive to far-forward muons so the
production rates are sensitive to high-$x$ partons in the incident nucleus and
low-$x$ partons in the nitrogen/oxygen targets. Muon measurements can
complement the central-particle data collected at colliders. This paper will
review muon production data and discuss some non-perturbative (soft) models
that have been used to interpret the data. I will show measurements of TeV muon
transverse momentum ($p_T$) spectra in cosmic-ray air showers from MACRO, and
describe how the IceCube neutrino observatory and the proposed Km3Net detector
will extend these measurements to a higher $p_T$ region where perturbative QCD
should apply. With a 1 km$^2$ surface area, the full IceCube detector should
observe hundreds of muons/year with $p_T$ in the pQCD regime.Comment: 4 pages, 2 figures - To appear in the conference proceedings for
Quark Matter 2009, March 30 - April 4, Knoxville, Tennessee. Tweaked
formatting at organizers reques

### Did children’s education matter? : family migration as a mechanism of human capital investment : evidence from nineteenth century Bohemia

This paper analyzes the rural-urban migration of families in the Bohemian region of Pilsen in 1900. Using a new 1300-family dataset from the 1900 population census I examine the role of children‘s education in rural-urban migration. I find that families migrated to the city such that the educational attainment of their children would be maximized and that there is a positive correlation between family migration and children being apprentices in urban areas. The results suggest that rural-urban migration was powered not only by the exploitation of rural-urban wage gaps but also by aspirations to engage in human capital investment

### Localization for quasiperiodic Schrodinger operators with multivariable Gevrey potential functions

We consider an integer lattice quasiperiodic Schrodinger operator. The
underlying dynamics is either the skew-shift or the multi-frequency shift by a
Diophantine frequency. We assume that the potential function belongs to a
Gevrey class on the multi-dimensional torus. Moreover, we assume that the
potential function satisfies a generic transversality condition, which we show
to imply a Lojasiewicz type inequality for smooth functions of several
variables. Under these assumptions and for large coupling constant, we prove
that the associated Lyapunov exponent is positive for all energies, and
continuous as a function of energy, with a certain modulus of continuity.
Moreover, in the large coupling constant regime and for an asymptotically large
frequency - phase set, we prove that the operator satisfies Anderson
localization.Comment: 42 pages, 3 figure

### Filtered ends of infinite covers and groups

Let f:A-->B be a covering map. We say A has e filtered ends with respect to f
(or B) if for some filtration {K_n} of B by compact subsets, A - f^{-1}(K_n)
"eventually" has e components. The main theorem states that if Y is a
(suitable) free H-space, if K < H has infinite index, and if Y has a positive
finite number of filtered ends with respect to H\Y, then Y has one filtered end
with respect to K\Y. This implies that if G is a finitely generated group and K
< H < G are subgroups each having infinite index in the next, then 0 < {\tilde
e}(G)(H) < \infty implies {\tilde e}(G)(K) = 1, where {\tilde e}(.)(.) is the
number of filtered ends of a pair of groups in the sense of Kropholler and
Roller.Comment: 6 pages, to appear in Journal of Pure and Applied Algebr

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