1,711 research outputs found
Colourings of cubic graphs inducing isomorphic monochromatic subgraphs
A -bisection of a bridgeless cubic graph is a -colouring of its
vertex set such that the colour classes have the same cardinality and all
connected components in the two subgraphs induced by the colour classes
(monochromatic components in what follows) have order at most . Ban and
Linial conjectured that every bridgeless cubic graph admits a -bisection
except for the Petersen graph. A similar problem for the edge set of cubic
graphs has been studied: Wormald conjectured that every cubic graph with
has a -edge colouring such that the two
monochromatic subgraphs are isomorphic linear forests (i.e. a forest whose
components are paths). Finally, Ando conjectured that every cubic graph admits
a bisection such that the two induced monochromatic subgraphs are isomorphic.
In this paper, we give a detailed insight into the conjectures of Ban-Linial
and Wormald and provide evidence of a strong relation of both of them with
Ando's conjecture. Furthermore, we also give computational and theoretical
evidence in their support. As a result, we pose some open problems stronger
than the above mentioned conjectures. Moreover, we prove Ban-Linial's
conjecture for cubic cycle permutation graphs.
As a by-product of studying -edge colourings of cubic graphs having linear
forests as monochromatic components, we also give a negative answer to a
problem posed by Jackson and Wormald about certain decompositions of cubic
graphs into linear forests.Comment: 33 pages; submitted for publicatio
Experiment K-6-03. Gravity and skeletal growth, part 1. Part 2: Morphology and histochemistry of bone cells and vasculature of the tibia; Part 3: Nuclear volume analysis of osteoblast histogenesis in periodontal ligament cells; Part 4: Intervertebral disc swelling pressure associated with microgravity
Bone area, bone electrophysiology, bone vascularity, osteoblast morphology, and osteoblast histogenesis were studied in rats associated with Cosmos 1887. The results suggest that the synchronous animals were the only group with a significantly larger bone area than the basal group, that the bone electrical potential was more negative in flight than in the synchronous rats, that the endosteal osteoblasts from flight rats had greater numbers of transitional Golgi vesicles but no difference in the large Golgi saccules or the alkaline phosphatase activity, that the perioteal vasculature in the shaft of flight rats often showed very dense intraluminal deposits with adjacent degenerating osteocytes as well as lipid accumulations within the lumen of the vessels and sometimes degeneration of the vascular wall (this change was not present in the metaphyseal region of flight animals), and that the progenitor cells decreased in flight rats while the preosteoblasts increased compared to controls. Many of the results suggest that the animals were beginning to recover from the effects of spaceflight during the two day interval between landing and euthanasia; flight effects, such as the vascular changes, did not appear to recover
Coriolis force in Geophysics: an elementary introduction and examples
We show how Geophysics may illustrate and thus improve classical Mechanics
lectures concerning the study of Coriolis force effects. We are then interested
in atmospheric as well as oceanic phenomena we are familiar with, and are for
that reason of pedagogical and practical interest. Our aim is to model them in
a very simple way to bring out the physical phenomena that are involved.Comment: Accepted for publication in European Journal of Physic
Dehydration in the tropical tropopause layer: Implications from the UARS Microwave Limb Sounder
An optically driven quantum dot quantum computer
We propose a quantum computer structure based on coupled asymmetric
single-electron quantum dots. Adjacent dots are strongly coupled by means of
electric dipole-dipole interactions enabling rapid computation rates. Further,
the asymmetric structures can be tailored for a long coherence time. The result
maximizes the number of computation cycles prior to loss of coherence.Comment: 4 figure
'I would rather die': reasons given by 16-year-olds for not continuing their study of mathematics
Improving participation rates in specialist mathematics after the subject ceases to be compulsory at age 16 is part of government policy in England. This article provides independent and recent support for earlier findings concerning reasons for non- participation, based on free response and closed items in a questionnaire with a sample of over 1500 students in 17 schools, close to the moment of choice. The analysis supports findings that perceived difficulty and lack of confidence are important reasons for students not continuing with mathematics, and that perceived dislike and boredom, and lack of relevance, are also factors. There is a close relationship between reasons for non-participation and predicted grade, and a weaker relation to gender. An analysis of the effects of schools, demonstrates that enjoyment is the main factor differentiating schools with high and low participation indices. Building on discussion of these findings, ways of improving participation are briefly suggested
Nonlinear Dynamics of Gravity Wave Driven Flows in the Solar Radiative Interior
We present results of nonlinear numerical simulations of gravity wave driven
shear flow oscillations in the equatorial plane of the solar radiative
interior. These results show that many of the assumptions of quasi-linear
theory are not valid. When only two waves are forced (prograde and retrograde)
oscillatory mean flow is maintained; but critical layers often form and are
dynamically important. When a spectrum of waves is forced, the non-linear
wave-wave interactions are dynamically important, often acting to decrease the
maintenance of a mean flow. The (in)coherence of such wave-wave interactions
must be taken into account when describing wave driven mean flows.Comment: 21 pages, 10 figures, accepted to MNRAS animations can be found at
http://www.solarphysicist.co
Physical theory of the twentieth century and contemporary philosophy
It has been shown that the criticism of Pauli as well as of Susskind and
Glogover may be avoided if the standard quantum-mechanical mathematical model
has been suitably extended. There is not more any reason for Einstein's
citicism, either, if in addition to some new results concerning Bell's
inequalities and Belifante's argument are taken into account. The ensemble
interpretation of quantum mechanics (or the hidden-variable theory) should be
preferred, which is also supported by the already published results of
experiments with three polarizers. Greater space in the text has been devoted
also to the discussion of epistemological problems and some philosophical
consequences.Comment: 12 page
Families of Small Regular Graphs of Girth 5
In this paper we obtain --regular graphs of girth 5 with fewer
vertices than previously known ones for and for any prime performing operations of reductions and amalgams on the Levi graph of
an elliptic semiplane of type . We also obtain a 13-regular graph of
girth 5 on 236 vertices from using the same technique
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