13,113 research outputs found
Degree growth of meromorphic surface maps
We study the degree growth of iterates of meromorphic selfmaps of compact
Kahler surfaces. Using cohomology classes on the Riemann-Zariski space we show
that the degrees grow similarly to those of mappings that are algebraically
stable on some birational model.Comment: 17 pages, final version, to appear in Duke Math Journa
Singular semipositive metrics in non-Archimedean geometry
Let X be a smooth projective Berkovich space over a complete discrete
valuation field K of residue characteristic zero, endowed with an ample line
bundle L. We introduce a general notion of (possibly singular) semipositive (or
plurisubharmonic) metrics on L, and prove the analogue of the following two
basic results in the complex case: the set of semipositive metrics is compact
modulo constants, and each semipositive metric is a decreasing limit of smooth
semipositive ones. In particular, for continuous metrics our definition agrees
with the one by S.-W. Zhang. The proofs use multiplier ideals and the
construction of suitable models of X over the valuation ring of K, using
toroidal techniques.Comment: 49 pages, 1 figure. Accepted in the Journal of Algebraic Geometr
Reconstructing past atmospheric circulation changes using oxygen isotopes in lake sediments from Sweden
Here we use lake sediment studies from Sweden to illustrate how Holocene-aged oxygen isotope records from lakes located in different hydrological settings, can provide information about climate change. In particular changes in precipitation, atmospheric circulation and water balance. We highlight the importance of understanding the present lake hydrology, and the relationship between climate variables and the oxygen isotopic composition of precipitation (18Op) and lake waters (18Olakewater) for interpretation of the oxygen isotopic record from the sediments (18O). Both precipitation reconstructions from northern Sweden and water balance reconstructions from south and central Sweden show that the atmospheric circulation changed from zonal to a more meridional airflow over the Holocene. Superimposed on this Holocene trend are δ18Op minima resembling intervals of the negative phase of the North Atlantic Oscillation (NAO), thus suggesting that the climate of Northern Europe is strongly influenced by atmospheric and oceanic circulation changes over the North Atlantic
Long time motion of NLS solitary waves in a confining potential
We study the motion of solitary-wave solutions of a family of focusing
generalized nonlinear Schroedinger equations with a confining, slowly varying
external potential, . A Lyapunov-Schmidt decomposition of the solution
combined with energy estimates allows us to control the motion of the solitary
wave over a long, but finite, time interval. We show that the center of mass of
the solitary wave follows a trajectory close to that of a Newtonian point
particle in the external potential over a long time interval.Comment: 42 pages, 2 figure
Boundary Conditions for Singular Perturbations of Self-Adjoint Operators
Let A:D(A)\subseteq\H\to\H be an injective self-adjoint operator and let
\tau:D(A)\to\X, X a Banach space, be a surjective linear map such that
\|\tau\phi\|_\X\le c \|A\phi\|_\H. Supposing that \text{\rm Range}
(\tau')\cap\H' =\{0\}, we define a family of self-adjoint
operators which are extensions of the symmetric operator .
Any in the operator domain is characterized by a sort
of boundary conditions on its univocally defined regular component \phireg,
which belongs to the completion of D(A) w.r.t. the norm \|A\phi\|_\H. These
boundary conditions are written in terms of the map , playing the role of
a trace (restriction) operator, as \tau\phireg=\Theta Q_\phi, the extension
parameter being a self-adjoint operator from X' to X. The self-adjoint
extension is then simply defined by A^\tau_\Theta\phi:=A \phireg. The case in
which is a convolution operator on LD, T a distribution with
compact support, is studied in detail.Comment: Revised version. To appear in Operator Theory: Advances and
Applications, vol. 13
Effects of surface forces and phonon dissipation in a three-terminal nano relay
We have performed a theoretical analysis of the operational characteristics
of a carbon-nanotube-based three-terminal nanorelay. We show that short range
and van der Waals forces have a significant impact on the characteristics of
the relay and introduce design constraints. We also investigate the effects of
dissipation due to phonon excitation in the drain contact, which changes the
switching time scales of the system, decreasing the longest time scale by two
orders of magnitude. We show that the nanorelay can be used as a memory element
and investigate the dynamics and properties of such a device
Non-equilibrium dynamics in an interacting nanoparticle system
Non-equilibrium dynamics in an interacting Fe-C nanoparticle sample,
exhibiting a low temperature spin glass like phase, has been studied by low
frequency ac-susceptibility and magnetic relaxation experiments. The
non-equilibrium behavior shows characteristic spin glass features, but some
qualitative differences exist. The nature of these differences is discussed.Comment: 7 pages, 11 figure
A theory of normed simulations
In existing simulation proof techniques, a single step in a lower-level
specification may be simulated by an extended execution fragment in a
higher-level one. As a result, it is cumbersome to mechanize these techniques
using general purpose theorem provers. Moreover, it is undecidable whether a
given relation is a simulation, even if tautology checking is decidable for the
underlying specification logic. This paper introduces various types of normed
simulations. In a normed simulation, each step in a lower-level specification
can be simulated by at most one step in the higher-level one, for any related
pair of states. In earlier work we demonstrated that normed simulations are
quite useful as a vehicle for the formalization of refinement proofs via
theorem provers. Here we show that normed simulations also have pleasant
theoretical properties: (1) under some reasonable assumptions, it is decidable
whether a given relation is a normed forward simulation, provided tautology
checking is decidable for the underlying logic; (2) at the semantic level,
normed forward and backward simulations together form a complete proof method
for establishing behavior inclusion, provided that the higher-level
specification has finite invisible nondeterminism.Comment: 31 pages, 10figure
Five-Torsion in the Homology of the Matching Complex on 14 Vertices
J. L. Andersen proved that there is 5-torsion in the bottom nonvanishing
homology group of the simplicial complex of graphs of degree at most two on
seven vertices. We use this result to demonstrate that there is 5-torsion also
in the bottom nonvanishing homology group of the matching complex on
14 vertices. Combining our observation with results due to Bouc and to
Shareshian and Wachs, we conclude that the case is exceptional; for all
other , the torsion subgroup of the bottom nonvanishing homology group has
exponent three or is zero. The possibility remains that there is other torsion
than 3-torsion in higher-degree homology groups of when and .Comment: 11 page
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