The chromaticity of wheels with a missing spoke II

AbstractIn the previous paper, it was shown that the graph Un + 1 obtained from the wheel Wn + 1 by deleting a spoke is uniquely determined by its chromatic polynomial if n ⩾ 3 is odd. In this paper, we show that the result is also true for even n ⩾ 4 except when n = 6 in which case, the graph W given in the paper is the only graph having the same chromatic polynomial as that of U7. The relevant tool is the notion of nearly uniquely colorable graph

Chromatic equivalence classes of complete tripartite graphs

AbstractSome necessary conditions on a graph which has the same chromatic polynomial as the complete tripartite graph Km,n,r are developed. Using these, we obtain the chromatic equivalence classes for Km,n,n (where 1≤m≤n) and Km1,m2,m3 (where |mi−mj|≤3). In particular, it is shown that (i) Km,n,n (where 2≤m≤n) and (ii) Km1,m2,m3 (where |mi−mj|≤3, 2≤mi,i=1,2,3) are uniquely determined by their chromatic polynomials. The result (i), proved earlier by Liu et al. [R.Y. Liu, H.X. Zhao, C.Y. Ye, A complete solution to a conjecture on chromatic uniqueness of complete tripartite graphs, Discrete Math. 289 (2004) 175–179], answers a conjecture (raised in [G.L. Chia, B.H. Goh, K.M. Koh, The chromaticity of some families of complete tripartite graphs (In Honour of Prof. Roberto W. Frucht), Sci. Ser. A (1988) 27–37 (special issue)]) in the affirmative, while result (ii) extends a result of Zou [H.W. Zou, On the chromatic uniqueness of complete tripartite graphs Kn1,n2,n3 J. Systems Sci. Math. Sci. 20 (2000) 181–186]

A family of sure-success quantum algorithms for solving a generalized Grover search problem

This work considers a generalization of Grover's search problem, viz., to find any one element in a set of acceptable choices which constitute a fraction f of the total number of choices in an unsorted data base. An infinite family of sure-success quantum algorithms are introduced here to solve this problem, each member for a different range of f. The nth member of this family involves n queries of the data base, and so the lowest few members of this family should be very convenient algorithms within their ranges of validity. The even member {A}_{2n} of the family covers ever larger range of f for larger n, which is expected to become the full range 0 infinity.Comment: 8 pages, including 4 figures in 4 page

Affleck-Dine baryogenesis in inflating curvaton scenario with O(10−10210-10^2TeV) mass moduli curvaton

We study the Affleck-Dine (AD) baryogenesis in the inflating curvaton scenario, when the curvaton is a moduli field with O($10-10^2$TeV) mass. A moduli field with such mass is known to be free from the Polonyi problem, and furthermore its decay products can explain the present cold dark matter abundance. In our scenario, it further explains the primordial curvature perturbation and the present baryon density all together. The current observational bound on the baryon isocurvature perturbation, which severely constrains the AD baryogenesis with the original oscillating moduli curvaton scenario, is shown to put practically negligible constraint if we replace the oscillating curvaton with the inflating curvaton.Comment: 1+21pages v2: minor correction v3: included short reviews, added refs, fixed typo

Effective Lagrangian for sˉbg\bar{s}bg and sˉbγ\bar{s}b\gamma Vertices in the mSUGRA model

Complete expressions of the $\bar{s}bg$ and $\bar{s}b\gamma$ vertices are derived in the framework of supersymmetry with minimal flavor violation. With the minimal supergravity (mSUGRA) model, a numerical analysis of the supersymmetric contributions to the Wilson Coefficients at the weak scale is presented.Comment: 12 pages + 7 ps figures, Late

Search for gravitational waves from Scorpius X-1 in the second Advanced LIGO observing run with an improved hidden Markov model

We present results from a semicoherent search for continuous gravitational waves from the low-mass x-ray binary Scorpius X-1, using a hidden Markov model (HMM) to track spin wandering. This search improves on previous HMM-based searches of LIGO data by using an improved frequency domain matched filter, the J-statistic, and by analyzing data from Advanced LIGO's second observing run. In the frequency range searched, from 60 to 650 Hz, we find no evidence of gravitational radiation. At 194.6 Hz, the most sensitive search frequency, we report an upper limit on gravitational wave strain (at 95% confidence) of h095%=3.47×10-25 when marginalizing over source inclination angle. This is the most sensitive search for Scorpius X-1, to date, that is specifically designed to be robust in the presence of spin wandering. © 2019 American Physical Society

Search for Tensor, Vector, and Scalar Polarizations in the Stochastic Gravitational-Wave Background

The detection of gravitational waves with Advanced LIGO and Advanced Virgo has enabled novel tests of general relativity, including direct study of the polarization of gravitational waves. While general relativity allows for only two tensor gravitational-wave polarizations, general metric theories can additionally predict two vector and two scalar polarizations. The polarization of gravitational waves is encoded in the spectral shape of the stochastic gravitational-wave background, formed by the superposition of cosmological and individually unresolved astrophysical sources. Using data recorded by Advanced LIGO during its first observing run, we search for a stochastic background of generically polarized gravitational waves. We find no evidence for a background of any polarization, and place the first direct bounds on the contributions of vector and scalar polarizations to the stochastic background. Under log-uniform priors for the energy in each polarization, we limit the energy densities of tensor, vector, and scalar modes at 95% credibility to Ω0T<5.58×10-8, Ω0V<6.35×10-8, and Ω0S<1.08×10-7 at a reference frequency f0=25 Hz. © 2018 American Physical Society

Erratum: "A Gravitational-wave Measurement of the Hubble Constant Following the Second Observing Run of Advanced LIGO and Virgo" (2021, ApJ, 909, 218)

[no abstract available

Search for Gravitational Waves Associated with Gamma-Ray Bursts Detected by Fermi and Swift during the LIGO-Virgo Run O3b

We search for gravitational-wave signals associated with gamma-ray bursts (GRBs) detected by the Fermi and Swift satellites during the second half of the third observing run of Advanced LIGO and Advanced Virgo (2019 November 1 15:00 UTC-2020 March 27 17:00 UTC). We conduct two independent searches: A generic gravitational-wave transients search to analyze 86 GRBs and an analysis to target binary mergers with at least one neutron star as short GRB progenitors for 17 events. We find no significant evidence for gravitational-wave signals associated with any of these GRBs. A weighted binomial test of the combined results finds no evidence for subthreshold gravitational-wave signals associated with this GRB ensemble either. We use several source types and signal morphologies during the searches, resulting in lower bounds on the estimated distance to each GRB. Finally, we constrain the population of low-luminosity short GRBs using results from the first to the third observing runs of Advanced LIGO and Advanced Virgo. The resulting population is in accordance with the local binary neutron star merger rate. © 2022. The Author(s). Published by the American Astronomical Society