10,873 research outputs found
The number of independent sets in a graph with small maximum degree
Let be the number of independent sets in a graph . We show
that if has maximum degree at most then
(where is vertex degree, is the number of isolated
vertices in and is the complete bipartite graph with vertices
in one partition class and in the other), with equality if and only if each
connected component of is either a complete bipartite graph or a single
vertex. This bound (for all ) was conjectured by Kahn.
A corollary of our result is that if is -regular with then with
equality if and only if is a disjoint union of copies of
. This bound (for all ) was conjectured by Alon and Kahn and
recently proved for all by the second author, without the characterization
of the extreme cases.
Our proof involves a reduction to a finite search. For graphs with maximum
degree at most the search could be done by hand, but for the case of
maximum degree or , a computer is needed.Comment: Article will appear in {\em Graphs and Combinatorics
The Role of the Family in Immigrants' Labor-Market Activity: Evidence from the United States
We use Census of Population microdata for 1980 and 1990 to examine the labor supply and wages of immigrant husbands and wives in the United States in a family context. Earlier research by Baker and Benjamin (1997) posits a family investment model in which, upon arrival, immigrant husbands invest in their human capital while immigrant wives work to provide the family with liquidity during this period. Consistent with this model, they find for Canada that immigrant wives work longer hours upon arrival than comparable natives, but, with time in Canada, they are eventually overtaken by native wives. In contrast, we find that, among immigrants to the United States, both husbands and wives work and earn less than comparable natives upon arrival, with similar shortfalls for men and women. Further, both immigrant husbands and wives have similar, positive assimilation profiles in wages and labor supply and eventually overtake both the wages and the labor supply of comparable natives.
Anisotropy effects in a mixed quantum-classical Heisenberg model in two dimensions
We analyse a specific two dimensional mixed spin Heisenberg model with
exchange anisotropy, by means of high temperature expansions and Monte Carlo
simulations. The goal is to describe the magnetic properties of the compound
(NBu_{4})_{2}Mn_{2}[Cu(opba)]_{3}\cdot 6DMSO\cdot H_{2}O which exhibits a
ferromagnetic transition at . Extrapolating our analysis on the
basis of renormalisation group arguments, we find that this transition may
result from a very weak anisotropy effect.Comment: 8 pages, 10 Postscript figure
Hiding Single Photons With Spread Spectrum Technology
We describe a proof-of-principal experiment demonstrating the use of spread
spectrum technology at the single photon level. We show how single photons with
a prescribed temporal shape, in the presence of interfering noise, may be
hidden and recovered.Comment: 4 pages, 5 figures
A DMRG Study of Low-Energy Excitations and Low-Temperature Properties of Alternating Spin Systems
We use the density matrix renormalization group (DMRG) method to study the
ground and low-lying excited states of three kinds of uniform and dimerized
alternating spin chains. The DMRG procedure is also employed to obtain
low-temperature thermodynamic properties of these systems. We consider a 2N
site system with spins and alternating from site to site and
interacting via a Heisenberg antiferromagnetic exchange. The three systems
studied correspond to being equal to and
; all of them have very similar properties. The ground state is found
to be ferrimagnetic with total spin . We find that there is
a gapless excitation to a state with spin , and a gapped excitation to
a state with spin . Surprisingly, the correlation length in the ground
state is found to be very small for this gapless system. The DMRG analysis
shows that the chain is susceptible to a conditional spin-Peierls instability.
Furthermore, our studies of the magnetization, magnetic susceptibility
and specific heat show strong magnetic-field dependences. The product
shows a minimum as a function of temperature T at low magnetic fields; the
minimum vanishes at high magnetic fields. This low-field behavior is in
agreement with earlier experimental observations. The specific heat shows a
maximum as a function of temperature, and the height of the maximum increases
sharply at high magnetic fields. Although all the three systems show
qualitatively similar behavior, there are some notable quantitative differences
between the systems in which the site spin difference, , is large
and small respectively.Comment: 16 LaTeX pages, 13 postscript figure
Disks around massive young stellar objects: are they common?
We present K-band polarimetric images of several massive young stellar
objects at resolutions 0.1-0.5 arcsec. The polarization vectors around
these sources are nearly centro-symmetric, indicating they are dominating the
illumination of each field. Three out of the four sources show elongated
low-polarization structures passing through the centers, suggesting the
presence of polarization disks. These structures and their surrounding
reflection nebulae make up bipolar outflow/disk systems, supporting the
collapse/accretion scenario as their low-mass siblings. In particular, S140
IRS1 show well defined outflow cavity walls and a polarization disk which
matches the direction of previously observed equatorial disk wind, thus
confirming the polarization disk is actually the circumstellar disk. To date, a
dozen massive protostellar objects show evidence for the existence of disks;
our work add additional samples around MYSOs equivalent to early B-type stars.Comment: 9 pages, including 2 figures, 1 table, to appear on ApJ
Low-Temperature Properties of Quasi-One-Dimensional Molecule-Based Ferromagnets
Quantum and thermal behaviors of low-dimensional mixed-spin systems are
investigated with particular emphasis on the design of molecule-based
ferromagnets. One can obtain a molecular ferromagnet by assembling molecular
bricks so as to construct a low-dimensional system with a magnetic ground state
and then coupling the chains or the layers again in a ferromagnetic fashion.
Two of thus-constructed quasi-one-dimensional bimetallic compounds are
qualitatively viewed within the spin-wave treatment, one of which successfully
grows into a bulk magnet, while the other of which ends in a singlet ground
state. Then, concentrating on the ferrimagnetic arrangement on a two-leg ladder
which is well indicative of general coupled-chain ferrimagnets, we develop the
spin-wave theory and fully reveal its low-energy structure. We inquire further
into the ferromagnetic aspect of the ferrimagnetic ladder numerically
calculating the sublattice magnetization and the magnetic susceptibility. There
exists a moderate coupling strength between the chains in order to obtain the
most ferromagnetic ferrimagnet.Comment: 10 pages, 7 figures embedded, to be published in J. Phys. Soc. Jpn.
Vol.70, No.5 (2001
Effect of FK506 in experimental organ transplantation.
FK506 is the most potent immunosuppressive agent known. Its toxicity is substantial in dogs, minor in rats, and unknown in subhuman primates. In small doses that are nontoxic even in dogs, it can be used in synergistic combination with cyclosporine, steroids, and presumably in other drugs
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