1,803 research outputs found
Combinatorics of n-point functions via Hopf algebra in quantum field theory
We use a coproduct on the time-ordered algebra of field operators to derive
simple relations between complete, connected and 1-particle irreducible n-point
functions. Compared to traditional functional methods our approach is much more
intrinsic and leads to efficient algorithms suitable for concrete computations.
It may also be used to efficiently perform tree level computations.Comment: 26 pages, LaTeX + AMS + eepic; minor corrections and modification
Combinatorics of 1-particle irreducible n-point functions via coalgebra in quantum field theory
We give a coalgebra structure on 1-vertex irreducible graphs which is that of
a cocommutative coassociative graded connected coalgebra. We generalize the
coproduct to the algebraic representation of graphs so as to express a bare
1-particle irreducible n-point function in terms of its loop order
contributions. The algebraic representation is so that graphs can be evaluated
as Feynman graphs
Generating loop graphs via Hopf algebra in quantum field theory
We use the Hopf algebra structure of the time-ordered algebra of field
operators to generate all connected weighted Feynman graphs in a recursive and
efficient manner. The algebraic representation of the graphs is such that they
can be evaluated directly as contributions to the connected n-point functions.
The recursion proceeds by loop order and vertex number.Comment: 22 pages, LaTeX + AMS + eepic; new section with alternative recursion
formula added, further minor changes and correction
Correlation of estuarine sedimentary cores based on color analysis: an example from the Algarve region (Portugal)
Coastal zones play a significant role in the regional development and have been an important area for human occupation
through time. The study of estuarine sediments applied to sea level changes had always been of extreme importance, as it
reflects the coastal line evolution, either by local, regional or global changes
Regional sea level change study based on estuarine sediment color and biogeochemistry - preliminary results
Coastal zones play a significant role in the regional development and have been an important area for human occupation through time. The study of estuarine sediments applied to sea level changes had always been of extreme importance, as it reflects the coastal line evolution, either by local, regional or global changes
An attempt to use color as a tool for high resolution correlations between estuarine sedimentary cores from Algarve (Portugal)
Nowadays, paleoenvironmental and climatological researches focus on studying shortterm
climatic changes and one of the more sensitive environments for recording those
short-term climatic variations are the high sedimentation rate of coastal regions. Accordingly,
4 estuaries from the Algarve region, south of Portugal, have been cored
in order to study sedimentary and climatic variations during recent times (c.a. 5000
yrs). For this purpose, we applied sampling and analytical techniques from deep-sea
studies, allowing the acquirement of almost continuous data profiles, as the color data
obtained with the spectrophotometer Colortron
Is it possible to use "twin cores" as a unique sedimentary record? An experimental design based on sediment color
Sedimentary cores are widely used for studying Quaternary records. However, the
amount of sediment that is available is proportional to the diameter of the core, which is rarely
bigger than 15 cm. One way to obtain more sediment is to use two cores retrieved from almost
the same location and use them as if they represent a unique sedimentary record. In the present
work, an experimental design has been applied to verify if “twin cores” from an estuary can be
considered as representing the same sedimentary record with twice the amount of sediment to
study. Because sediment can be characterized based on its color, the variables used as
replicates in the experimental design are the three Lab CIE colors acquired with a X-Rite
Colortron spectrophotometer. Sediment cores were retrieved from the upper saltmarsh of GilĂŁo
River’s estuary, southern Portugal. Twin cores, with in between distances of 50 cm, 100 cm
and 200 cm, from two different sites were analysed. Results from a nested ANOVA show that
even for the closest twin cores (50 cm apart) there is at least one color variable that shows
significant variations between the profiles of both cores. These results clearly show that “twin
cores” cannot be used as a unique sedimentary record without any previous testing, at least in
such transitional regions
Elliptic curves of large rank and small conductor
For r=6,7,...,11 we find an elliptic curve E/Q of rank at least r and the
smallest conductor known, improving on the previous records by factors ranging
from 1.0136 (for r=6) to over 100 (for r=10 and r=11). We describe our search
methods, and tabulate, for each r=5,6,...,11, the five curves of lowest
conductor, and (except for r=11) also the five of lowest absolute discriminant,
that we found.Comment: 16 pages, including tables and one .eps figure; to appear in the
Proceedings of ANTS-6 (June 2004, Burlington, VT). Revised somewhat after
comments by J.Silverman on the previous draft, and again to get the correct
page break
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