27,101 research outputs found
Asymptotic enumeration of incidence matrices
We discuss the problem of counting {\em incidence matrices}, i.e. zero-one
matrices with no zero rows or columns. Using different approaches we give three
different proofs for the leading asymptotics for the number of matrices with
ones as . We also give refined results for the asymptotic
number of incidence matrices with ones.Comment: jpconf style files. Presented at the conference "Counting Complexity:
An international workshop on statistical mechanics and combinatorics." In
celebration of Prof. Tony Guttmann's 60th birthda
Determination of bone mineral mass in vivo
Radiographic equipment incorporates two radiation sources, generating high-energy and low-energy beams. Recording equipment measures amount of radiation that has penetrated limb. Data are fed into computer that determines mass of the examined bone
An analogue of Ryser's Theorem for partial Sudoku squares
In 1956 Ryser gave a necessary and sufficient condition for a partial latin
rectangle to be completable to a latin square. In 1990 Hilton and Johnson
showed that Ryser's condition could be reformulated in terms of Hall's
Condition for partial latin squares. Thus Ryser's Theorem can be interpreted as
saying that any partial latin rectangle can be completed if and only if
satisfies Hall's Condition for partial latin squares.
We define Hall's Condition for partial Sudoku squares and show that Hall's
Condition for partial Sudoku squares gives a criterion for the completion of
partial Sudoku rectangles that is both necessary and sufficient. In the
particular case where , , , the result is especially simple, as
we show that any partial -Sudoku rectangle can be completed
(no further condition being necessary).Comment: 19 pages, 10 figure
Temporal fluctuations in the differential rotation of cool active stars
This paper reports positive detections of surface differential rotation on
two rapidly rotating cool stars at several epochs, by using stellar surface
features (both cool spots and magnetic regions) as tracers of the large scale
latitudinal shear that distorts the convective envelope in this type of stars.
We also report definite evidence that this differential rotation is different
when estimated from cool spots or magnetic regions, and that it undergoes
temporal fluctuations of potentially large amplitude on a time scale of a few
years. We consider these results as further evidence that the dynamo processes
operating in these stars are distributed throughout the convective zone rather
than being confined at its base as in the Sun. By comparing our observations
with two very simple models of the differential rotation within the convective
zone, we obtain evidence that the internal rotation velocity field of the stars
we investigated is not like that of the Sun, and may resemble that we expect
for rapid rotators. We speculate that the changes in differential rotation
result from the dynamo processes (and from the underlying magnetic cycle) that
periodically converts magnetic energy into kinetic energy and vice versa. We
emphasise that the technique outlined in this paper corresponds to the first
practical method for investigating the large scale rotation velocity field
within convective zones of cool active stars, and offers several advantages
over asteroseismology for this particular purpose and this specific stellar
class.Comment: 14 pages, 4 figure
Perfect countably infinite Steiner triple systems
We use a free construction to prove the existence of perfect Steiner triple systems on a countably infinite point set. We use a specific countably infinite family of partial Steiner triple systems to start the construction, thus yielding 2ℵ0 non-isomorphic perfect systems
Moving to Extremal Graph Parameters
Which graphs, in the class of all graphs with given numbers n and m of edges
and vertices respectively, minimizes or maximizes the value of some graph
parameter? In this paper we develop a technique which provides answers for
several different parameters: the numbers of edges in the line graph, acyclic
orientations, cliques, and forests. (We minimize the first two and maximize the
third and fourth.)
Our technique involves two moves on the class of graphs. A compression move
converts any graph to a form we call fully compressed: the fully compressed
graphs are split graphs in which the neighbourhoods of points in the
independent set are nested. A second consolidation move takes each fully
compressed graph to one particular graph which we call H(n,m). We show
monotonicity of the parameters listed for these moves in many cases, which
enables us to obtain our results fairly simply.
The paper concludes with some open problems and future directions
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