4,213,302 research outputs found
De-biased Populations of Kuiper Belt Objects from the Deep Ecliptic Survey
The Deep Ecliptic Survey (DES) discovered hundreds of Kuiper Belt objects
from 1998-2005. Follow-up observations yielded 304 objects with good dynamical
classifications (Classical, Scattered, Centaur, or 16 mean-motion resonances
with Neptune). The DES search fields are well documented, enabling us to
calculate the probability of detecting objects with particular orbital
parameters and absolute magnitudes at a randomized point in each orbit.
Grouping objects together by dynamical class leads, we estimate the orbital
element distributions (a, e, i) for the largest three classes (Classical, 3:2,
and Scattered) using maximum likelihood. Using H-magnitude as a proxy for the
object size, we fit a power law to the number of objects for 8 classes with at
least 5 detected members (246 objects). The best Classical slope is
alpha=1.02+/-0.01 (observed from 5<=H<=7.2). Six dynamical classes (Scattered
plus 5 resonances) are consistent in slope with the Classicals, though the
absolute number of objects is scaled. The exception to the power law relation
are the Centaurs (non-resonant with perihelia closer than Neptune, and thus
detectable at smaller sizes), with alpha=0.42+/-0.02 (7.5<H<11). This is
consistent with a knee in the H-distribution around H=7.2 as reported elsewhere
(Bernstein et al. 2004, Fraser et al. 2014). Based on the Classical-derived
magnitude distribution, the total number of objects (H<=7) in each class are:
Classical (2100+/-300 objects), Scattered (2800+/-400), 3:2 (570+/-80), 2:1
(400+/-50), 5:2 (270+/-40), 7:4 (69+/-9), 5:3 (60+/-8). The independent
estimate for the number of Centaurs in the same H range is 13+/-5. If instead
all objects are divided by inclination into "Hot" and "Cold" populations,
following Fraser et al. (2014), we find that alphaHot=0.90+/-0.02, while
alphaCold=1.32+/-0.02, in good agreement with that work.Comment: 26 pages emulateapj, 6 figures, 5 tables, accepted by A
Suppressing Curvature Fluctuations in Dynamical Triangulations
We study numerically the dynamical triangulation formulation of
two-dimensional quantum gravity using a restricted class of triangulation,
so-called minimal triangulations, in which only vertices of coordination number
5, 6, and 7 are allowed. A real-space RG analysis shows that for pure gravity
(central charge c = 0) this restriction does not affect the critical behavior
of the model. Furthermore, we show that the critical behavior of an Ising model
coupled to minimal dynamical triangulations (c = 1/2) is still governed by the
KPZ-exponents.Comment: Talk presented at LATTICE96(gravity), 3 pages, LaTeX, espcrc2.sty, 1
figur
Character Sums and Congruences with n!
We estimate character sums with n!, on average, and individually. These
bounds are used to derive new results about various congruences modulo a prime
p and obtain new information about the spacings between quadratic nonresidues
modulo p. In particular, we show that there exists a positive integer \max \{n_i |
i=1,... 7\}=O(p^{11/12+\epsilon}), and we find the asymptotic formula for the
number of such representations. Finally, we show that products of 4 factorials
represent ``almost all''residue classes modulo p, and that products of 3
factorials n_1!n_2!n_3! with \max\{n_1, n_2, n_3\}=O(p^{5/6+\epsilon})$ are
uniformly distributed modulo p.Comment: 20 pages. Trans. Amer. Math. Soc. (to appear
Subject index and checklist of history and archaeology dissertations and research essays submitted at the University of Botswana, 1976 - 1998
Four MA dissertations and 222 BA research essays are listed alphabetically, and indexed by reference number under three subject categories-geographical area (by district, etc.), ethnic group, and a general subject index of 42 headings. All but 31 of the 226 alphabetical entries contain research solely on Botswana: the other countries being South Africa (12 entries), Zimbabwe (11), Namibia (6), Angola and Zambia (1 each). The most researched district of Botswana is Central (54 entries), followed by Kgatleng and Kweneng (25 each), North-East (24), South-East (16), Southern (9), Ngamiland (6), Chobe and Ghanzi (3 each), and Kgalagadi (2). The subject index of 29 ethnic groups ranges from Afrikaners (2 entries) and Amandebele (2) through Babirwa (7), Bakalanga (24), Bakgatla (27), Bakhalagari (4), Bakwena (21), Bangwato (19), Basarwa (5), and Batlharo (1), to Indians (3) and Ovambanderu (2). The general subject index ranges from Administration (29 entries), Agriculture (18), and Archaeology (21), through Biography (28), Cattle (7), Chieftainship (27), Class formation (7), Councils (7), Economic development (23), Education (14), and Heritage management (7), to Labour and labour migration (7), Medicine (4), Nationalism (13), Religion (15), Serfdom, servitude and slavery (7), Settlement history (19), Trade and commerce (13), Trade unions (6), and Urbanization (15). With the notable exception of one MA dissertation, there is a lack of cultural studies which may partly be attributed to research being done instead under the aegis of other departments in the Faculty of Humanities
The integral homology of of imaginary quadratic integers with non-trivial class group
We show that a cellular complex described by Floege allows to determine the
integral homology of the Bianchi groups , where is the
ring of integers of an imaginary quadratic number field \rationals[\sqrt{-m}]
for a square-free natural number . We use this to compute in the cases m =
5, 6, 10, 13 and 15 with non-trivial class group the integral homology of
, which before was known only in the cases m = 1, 2, 3, 7 and 11
with trivial class group
Graphs, Matrices, and the GraphBLAS: Seven Good Reasons
The analysis of graphs has become increasingly important to a wide range of
applications. Graph analysis presents a number of unique challenges in the
areas of (1) software complexity, (2) data complexity, (3) security, (4)
mathematical complexity, (5) theoretical analysis, (6) serial performance, and
(7) parallel performance. Implementing graph algorithms using matrix-based
approaches provides a number of promising solutions to these challenges. The
GraphBLAS standard (istc- bigdata.org/GraphBlas) is being developed to bring
the potential of matrix based graph algorithms to the broadest possible
audience. The GraphBLAS mathematically defines a core set of matrix-based graph
operations that can be used to implement a wide class of graph algorithms in a
wide range of programming environments. This paper provides an introduction to
the GraphBLAS and describes how the GraphBLAS can be used to address many of
the challenges associated with analysis of graphs.Comment: 10 pages; International Conference on Computational Science workshop
on the Applications of Matrix Computational Methods in the Analysis of Modern
Dat
Is the five-flow conjecture almost false?
The number of nowhere zero Z_Q flows on a graph G can be shown to be a
polynomial in Q, defining the flow polynomial \Phi_G(Q). According to Tutte's
five-flow conjecture, \Phi_G(5) > 0 for any bridgeless G.A conjecture by Welsh
that \Phi_G(Q) has no real roots for Q \in (4,\infty) was recently disproved by
Haggard, Pearce and Royle. These authors conjectured the absence of roots for Q
\in [5,\infty). We study the real roots of \Phi_G(Q) for a family of non-planar
cubic graphs known as generalised Petersen graphs G(m,k). We show that the
modified conjecture on real flow roots is also false, by exhibiting infinitely
many real flow roots Q>5 within the class G(nk,k). In particular, we compute
explicitly the flow polynomial of G(119,7), showing that it has real roots at
Q\approx 5.0000197675 and Q\approx 5.1653424423. We moreover prove that the
graph families G(6n,6) and G(7n,7) possess real flow roots that accumulate at
Q=5 as n\to\infty (in the latter case from above and below); and that
Q_c(7)\approx 5.2352605291 is an accumulation point of real zeros of the flow
polynomials for G(7n,7) as n\to\infty.Comment: 44 pages (LaTeX2e). Includes tex file, three sty files, and a
mathematica script polyG119_7.m. Many improvements from version 3, in
particular Sections 3 and 4 have been mostly re-writen, and Sections 7 and 8
have been eliminated. (This material can now be found in arXiv:1303.5210.)
Final version published in J. Combin. Theory
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