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