13,830 research outputs found
Key polynomials for simple extensions of valued fields
Let be a simple transcendental extension
of valued fields, where is equipped with a valuation of rank 1. That
is, we assume given a rank 1 valuation of and its extension to
. Let denote the valuation ring of . The purpose
of this paper is to present a refined version of MacLane's theory of key
polynomials, similar to those considered by M. Vaqui\'e, and reminiscent of
related objects studied by Abhyankar and Moh (approximate roots) and T.C. Kuo.
Namely, we associate to a countable well ordered set the are called {\bf key
polynomials}. Key polynomials which have no immediate predecessor are
called {\bf limit key polynomials}. Let .
We give an explicit description of the limit key polynomials (which may be
viewed as a generalization of the Artin--Schreier polynomials). We also give an
upper bound on the order type of the set of key polynomials. Namely, we show
that if then the set of key polynomials has
order type at most , while in the case
this order type is bounded above by , where stands
for the first infinite ordinal.Comment: arXiv admin note: substantial text overlap with arXiv:math/060519
An integrated model for computer assisted diagnosis, treatment and design of insoles for the diabetic foot
The incidence of diabetes has increased significantly in recent decades. In Germany, there is an estimate of three million diabetics and this number is growing at a rate of about 2 percent per year. In the U.S.A., the American Diabetes Association estimates that thirteen million people suffer from this condition, representing 5.2 percent of the entire population and every year, some 35 thousand patients have a lower limb amputated. In Latin America, it has been reported that the prevalence of diabetes is of the order of 14 to 20 percent, according to a research conducted by the WHO's Ad Hoc Diabetes Reporting Group. In Colombia, a study by Ashner et al concludes that the prevalence is 7 percent in both sexes
Ballistic Localization in Quasi-1D Waveguides with Rough Surfaces
Structure of eigenstates in a periodic quasi-1D waveguide with a rough
surface is studied both analytically and numerically. We have found a large
number of "regular" eigenstates for any high energy. They result in a very slow
convergence to the classical limit in which the eigenstates are expected to be
completely ergodic. As a consequence, localization properties of eigenstates
originated from unperturbed transverse channels with low indexes, are strongly
localized (delocalized) in the momentum (coordinate) representation. These
eigenstates were found to have a quite unexpeted form that manifests a kind of
"repulsion" from the rough surface. Our results indicate that standard
statistical approaches for ballistic localization in such waveguides seem to be
unappropriate.Comment: 5 pages, 4 figure
Photocurable Bioink for the Inkjet 3D Pharming of Hydrophilic Drugs.
Novel strategies are required to manufacture customized oral solid dosage forms for personalized medicine applications. 3D Pharming, the direct printing of pharmaceutical tablets, is an attractive strategy, since it allows for the rapid production of solid dosage forms containing custom drug dosages. This study reports on the design and characterization of a biocompatible photocurable pharmaceutical polymer for inkjet 3D printing that is suitable for hydrophilic active pharmaceutical ingredients (API). Specifically, hyaluronic acid was functionalized with norbornene moieties that, in the presence of poly(ethylene) glycol dithiol, Eosin Y as a photoinitiator, and a visible light source, undergoes a rapid step-growth polymerization reaction through thiol-ene chemistry. The engineered bioink was loaded with Ropinirole HCL, dispensed through a piezoelectric nozzle onto a blank preform tablet, and polymerized. Drug release analysis of the tablet resulted in 60% release within 15 min of tablet dissolution. The study confirms the potential of inkjet printing for the rapid production of tablets through the deposition of a photocurable bioink designed for hydrophilic APIs
The Odyssey Approach for Optimizing Federated SPARQL Queries
Answering queries over a federation of SPARQL endpoints requires combining
data from more than one data source. Optimizing queries in such scenarios is
particularly challenging not only because of (i) the large variety of possible
query execution plans that correctly answer the query but also because (ii)
there is only limited access to statistics about schema and instance data of
remote sources. To overcome these challenges, most federated query engines rely
on heuristics to reduce the space of possible query execution plans or on
dynamic programming strategies to produce optimal plans. Nevertheless, these
plans may still exhibit a high number of intermediate results or high execution
times because of heuristics and inaccurate cost estimations. In this paper, we
present Odyssey, an approach that uses statistics that allow for a more
accurate cost estimation for federated queries and therefore enables Odyssey to
produce better query execution plans. Our experimental results show that
Odyssey produces query execution plans that are better in terms of data
transfer and execution time than state-of-the-art optimizers. Our experiments
using the FedBench benchmark show execution time gains of at least 25 times on
average.Comment: 16 pages, 10 figure
Present Limits on the Precision of SM Predictions for Jet Energies
We investigate the impact of theoretical uncertainties on the accuracy of
measurements involving hadronic jets. The analysis is performed using events
with a Z boson and a single jet observed in collisions at
= 1.96 TeV in 4.6 of data from the Collider Detector at
Fermilab (CDF). The transverse momenta (\pt) of the jet and the boson should
balance each other due to momentum conservation in the plane transverse to the
direction of the and beams. We evaluate the dependence of the
measured \pt-balance on theoretical uncertainties associated with initial and
final state radiation, choice of renormalization and factorization scales,
parton distribution functions, jet-parton matching, calculations of matrix
elements, and parton showering. We find that the uncertainty caused by parton
showering at large angles is the largest amongst the listed uncertainties. The
proposed method can be re-applied at the LHC experiments to investigate and
evaluate the uncertainties on the predicted jet energies. The distributions
produced at the CDF environment are intended for comparison to those from
modern event generators and new tunes of parton showering.Comment: Submitted to Nucl. Instr. and Meth.
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