26,778 research outputs found
Algorithmic problems for free-abelian times free groups
We study direct products of free-abelian and free groups with special
emphasis on algorithmic problems. After giving natural extensions of standard
notions into that family, we find an explicit expression for an arbitrary
endomorphism of \ZZ^m \times F_n. These tools are used to solve several
algorithmic and decision problems for \ZZ^m \times F_n : the membership
problem, the isomorphism problem, the finite index problem, the subgroup and
coset intersection problems, the fixed point problem, and the Whitehead
problem.Comment: 38 page
Optimal domain of -concave operators and vector measure representation of -concave Banach lattices
Given a Banach space valued -concave linear operator defined on a
-order continuous quasi-Banach function space, we provide a description
of the optimal domain of preserving -concavity, that is, the largest
-order continuous quasi-Banach function space to which can be
extended as a -concave operator. We show in this way the existence of
maximal extensions for -concave operators. As an application, we show a
representation theorem for -concave Banach lattices through spaces of
integrable functions with respect to a vector measure. This result culminates a
series of representation theorems for Banach lattices using vector measures
that have been obtained in the last twenty years
Radiatively Generated Isospin Violations in the Nucleon and the NuTeV Anomaly
Predictions of isospin asymmetries of valence and sea distributions are
presented which are generated by QED leading photon
bremsstrahlung effects. Together with isospin violations arising from
nonperturbative hadronic sources (such as quark and target mass differences) as
well as with even a conservative contribution from a strangeness asymmetry
(), the discrepancy between the large NuTeV `anomaly' result for
and the world average of other measurements is removed.Comment: 10 pages, 2 figure
Two-photon imaging through a multimode fiber
In this work we demonstrate 3D imaging using two-photon excitation through a
20 cm long multimode optical fiber (MMF) of 350 micrometers diameter. The
imaging principle is similar to single photon fluorescence through a MMF,
except that a focused femtosecond pulse is delivered and scanned over the
sample. In our approach, focusing and scanning through the fiber is
accomplished by digital phase conjugation using mode selection by time gating
with an ultra-fast reference pulse. The excited two-photon emission is
collected through the same fiber. We demonstrate depth sectioning by scanning
the focused pulse in a 3D volume over a sample consisting of fluorescent beads
suspended in a polymer. The achieved resolution is 1 micrometer laterally and
15 micrometers axially. Scanning is performed over an 80x80 micrometers field
of view. To our knowledge, this is the first demonstration of high-resolution
three-dimensional imaging using two-photon fluorescence through a multimode
fiber
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