10,719 research outputs found
Generalized Irreducible Divisor Graphs
In 1988, I. Beck introduced the notion of a zero-divisor graph of a
commutative rings with . There have been several generalizations in recent
years. In particular, in 2007 J. Coykendall and J. Maney developed the
irreducible divisor graph. Much work has been done on generalized
factorization, especially -factorization. The goal of this paper is to
synthesize the notions of -factorization and irreducible divisor graphs
in domains. We will define a -irreducible divisor graph for non-zero
non-unit elements of a domain. We show that by studying -irreducible
divisor graphs, we find equivalent characterizations of several finite
-factorization properties.Comment: 17 pages, 2 figures, to appear in Communications in Algebr
Generalized U-factorization in Commutative Rings with Zero-Divisors
Recently substantial progress has been made on generalized factorization
techniques in integral domains, in particular -factorization. There has
also been advances made in investigating factorization in commutative rings
with zero-divisors. One approach which has been found to be very successful is
that of U-factorization introduced by C.R. Fletcher. We seek to synthesize work
done in these two areas by generalizing -factorization to rings with
zero-divisors by using the notion of U-factorization.Comment: 16 pages, to appear in Rocky Mountain Journal of Mathematic
Tracing technological development trajectories: A genetic knowledge persistence-based main path approach
The aim of this paper is to propose a new method to identify main paths in a
technological domain using patent citations. Previous approaches for using main
path analysis have greatly improved our understanding of actual technological
trajectories but nonetheless have some limitations. They have high potential to
miss some dominant patents from the identified main paths; nonetheless, the
high network complexity of their main paths makes qualitative tracing of
trajectories problematic. The proposed method searches backward and forward
paths from the high-persistence patents which are identified based on a
standard genetic knowledge persistence algorithm. We tested the new method by
applying it to the desalination and the solar photovoltaic domains and compared
the results to output from the same domains using a prior method. The empirical
results show that the proposed method overcomes the aforementioned drawbacks
defining main paths that are almost 10x less complex while containing more of
the relevant important knowledge than the main path networks defined by the
existing method.Comment: 20 pages, 7 figure
Model-Independent Production of a Top-Philic Resonance at the LHC
We investigate the collider phenomenology of a color-singlet vector
resonance, which couples to the heaviest quarks, the top quarks, but very
weakly to the rest of the fermions in the Standard Model. We find that the
dominant production of such a resonance does not appear at the tree level -- it
rather occurs at the one-loop level in association with an extra jet.
Signatures like t anti-t plus jets readily emerge as a result of the subsequent
decay of the resonance into a pair of top quarks. Without the additional jet,
the resonance can still be produced off-shell, which gives a sizeable
contribution at low masses. The lower top quark multiplicity of the loop
induced resonance production facilitates its reconstruction as compared to the
tree level production that gives rise to more exotic signatures involving three
or even four top quarks in the final state. For all these cases, we discuss the
constraints on the resonance production stemming from recent experimental
measurements in the top quark sector. We find that the top-philic vector
resonance remains largely unconstrained for the majority of the parameter
space, although this will be scrutinized closely in the Run 2 phase of the LHC.Comment: 32 pages, 16 figure
Concordance of knots in
We establish a number of results about smooth and topological concordance of
knots in . The winding number of a knot in is
defined to be its class in . We
show that there is a unique smooth concordance class of knots with winding
number one. This improves the corresponding result of Friedl-Nagel-Orson-Powell
in the topological category. We say a knot in is slice (resp.
topologically slice) if it bounds a smooth (resp. locally flat) disk in
. We show that there are infinitely many topological concordance
classes of non-slice knots, and moreover, for any winding number other than
, there are infinitely many topological concordance classes even within
the collection of slice knots. Additionally we demonstrate the distinction
between the smooth and topological categories by constructing infinite families
of slice knots that are topologically but not smoothly concordant, as well as
non-slice knots that are topologically slice and topologically concordant, but
not smoothly concordant.Comment: 25 pages, 19 figures, final version, to appear in Journal of London
Mathematical Societ
Computed tomographic imaging characteristics of the normal canine lacrimal glands.
BackgroundThe canine lacrimal gland (LG) and accessory lacrimal gland of the third eyelid (TEG) are responsible for production of the aqueous portion of the precorneal tear film. Immune-mediated, toxic, neoplastic, or infectious processes can affect the glands directly or can involve adjacent tissues, with secondary gland involvement. Disease affecting these glands can cause keratoconjunctivitis sicca, corneal ulcers, and loss of vision. Due to their location in the orbit, these small structures are difficult to evaluate and measure, making cross-sectional imaging an important diagnostic tool. The detailed cross-sectional imaging appearance of the LG and TEG in dogs using computed tomography (CT) has not been reported to date.ResultsForty-two dogs were imaged, and the length, width, and height were measured and the volume calculated for the LGs & TEGs. The glands were best visualized in contrast-enhanced CT images. The mean volume of the LG was 0.14 cm3 and the TEG was 0.1 cm3. The mean height, width, and length of the LG were, 9.36 mm, 4.29 mm, and 9.35 mm, respectively; the corresponding values for the TEG was 2.02 mm, 9.34 mm, and 7.90 mm. LG and TEG volume were positively correlated with body weight (p < 0.05).ConclusionsContrast-enhanced CT is a valuable tool for noninvasive assessment of canine lacrimal glands
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