48,820 research outputs found
On the threshold-width of graphs
The GG-width of a class of graphs GG is defined as follows. A graph G has
GG-width k if there are k independent sets N1,...,Nk in G such that G can be
embedded into a graph H in GG such that for every edge e in H which is not an
edge in G, there exists an i such that both endpoints of e are in Ni. For the
class TH of threshold graphs we show that TH-width is NP-complete and we
present fixed-parameter algorithms. We also show that for each k, graphs of
TH-width at most k are characterized by a finite collection of forbidden
induced subgraphs
Towards Long-endurance Flight: Design and Implementation of a Variable-pitch Gasoline-engine Quadrotor
Majority of today's fixed-pitch, electric-power quadrotors have short flight
endurance ( 1 hour) which greatly limits their applications. This paper
presents a design methodology for the construction of a long-endurance
quadrotor using variable-pitch rotors and a gasoline-engine. The methodology
consists of three aspects. Firstly, the rotor blades and gasoline engine are
selected as a pair, so that sufficient lift can be comfortably provided by the
engine. Secondly, drivetrain and airframe are designed. Major challenges
include airframe vibration minimization and power transmission from one engine
to four rotors while keeping alternate rotors contra-rotating. Lastly, a PD
controller is tuned to facilitate preliminary flight tests. The methodology has
been verified by the construction and successful flight of our gasoline
quadrotor prototype, which is designed to have a flight time of 2 to 3 hours
and a maximum take-off weight of 10 kg.Comment: 6 page
Erratum : Squeezing and entanglement delay using slow light
An inconsistency was found in the equations used to calculate the variance of
the quadrature fluctuations of a field propagating through a medium
demonstrating electromagnetically induced transparency (EIT). The decoherence
term used in our original paper introduces inconsistency under weak probe
approximation. In this erratum we give the Bloch equations with the correct
dephasing terms. The conclusions of the original paper remain the same. Both
entanglement and squeezing can be delayed and preserved using EIT without
adding noise when the decoherence rate is small.Comment: 1 page, no figur
Simultaneous Determination of the Cosmic Ray Ionization Rate and Fractional Ionization in DR21(OH)
We present a new method for the simultaneous calculation of the cosmic ray
ionization rate, zeta(H2), and the ionization fraction, chi(e), in dense
molecular clouds. A simple network of chemical reactions dominant in the
creation and destruction of HCNH+ and HCO+ is used in conjunction with observed
pairs of rotational transitions of several molecular species in order to
determine the electron abundance and the H3+ abundance. The cosmic ray
ionization rate is then calculated by taking advantage of the fact that, in
dark clouds, it governs the rate of creation of H3+. We apply this technique to
the case of the star-forming region DR21(OH), where we successfully detected
the (J=3-2) and (J=4-3) rotational transitions of HCNH+. We also determine the
C and O isotopic ratios in this source to be 12C/13C=63+-4 and 16O/18O=318+-64,
which are in good agreement with previous measurements in other clouds. The
significance of our method lies in the ability to determine N(H3+) and chi(e)
directly from observations, and estimate zeta(H2) accordingly. Our results,
zeta(H2)=3.1x10^(-18) 1/s and chi(e)=3.2x10^(-8), are consistent with recent
determinations in other objects.Comment: 22 pages, including 3 figure
Families of weighted sum formulas for multiple zeta values
Euler's sum formula and its multi-variable and weighted generalizations form
a large class of the identities of multiple zeta values. In this paper we prove
a family of identities involving Bernoulli numbers and apply them to obtain
infinitely many weighted sum formulas for double zeta values and triple zeta
values where the weight coefficients are given by symmetric polynomials. We
give a general conjecture in arbitrary depth at the end of the paper.Comment: The conjecture at the end is reformulate
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