On localization properties of Fourier transforms of hyperfunctions

In [Adv. Math. 196 (2005) 310-345] the author introduced a new generalized function space $\mathcal U(R^k)$ which can be naturally interpreted as the Fourier transform of the space of Sato's hyperfunctions on $R^k$. It was shown that all Gelfand--Shilov spaces $S^{\prime 0}_\alpha(R^k)$ ($\alpha>1$) of analytic functionals are canonically embedded in $\mathcal U(R^k)$. While the usual definition of support of a generalized function is inapplicable to elements of $S^{\prime 0}_\alpha(R^k)$ and $\mathcal U(R^k)$, their localization properties can be consistently described using the concept of {\it carrier cone} introduced by Soloviev [Lett. Math. Phys. 33 (1995) 49-59; Comm. Math. Phys. 184 (1997) 579-596]. In this paper, the relation between carrier cones of elements of $S^{\prime 0}_\alpha(R^k)$ and $\mathcal U(R^k)$ is studied. It is proved that an analytic functional $u\in S^{\prime 0}_\alpha(R^k)$ is carried by a cone $K\subset R^k$ if and only if its canonical image in $\mathcal U(R^k)$ is carried by $K$.Comment: 21 pages, final version, accepted for publication in J. Math. Anal. App

Bistability and hysteresis in an optically injected two-section semiconductor laser

The effect of coherent single frequency injection on two-section semiconductor lasers is studied numerically using a model based on a set of delay differential equations. The existence of bistability between different continuous-wave and nonstationary regimes of operation is demonstrated in the case of sufficiently large linewidth enhancement factors

Long-range attraction between particles in dusty plasma and partial surface tension of dusty phase boundary

Effective potential of a charged dusty particle moving in homogeneous plasma has a negative part that provides attraction between similarly charged dusty particles. A depth of this potential well is great enough to ensure both stability of crystal structure of dusty plasma and sizable value of surface tension of a boundary surface of dusty region. The latter depends on the orientation of the surface relative to the counter-ion flow, namely, it is maximal and positive for the surface normal to the flow and minimal and negative for the surface along the flow. For the most cases of dusty plasma in a gas discharge, a value of the first of them is more than sufficient to ensure stability of lenticular dusty phase void oriented across the counter-ion flow.Comment: LATEX, REVTEX4, 7 pages, 6 figure

Spectrum and transition rates of the XX chain analyzed via Bethe ansatz

As part of a study that investigates the dynamics of the s=1/2 XXZ model in the planar regime |Delta|<1, we discuss the singular nature of the Bethe ansatz equations for the case Delta=0 (XX model). We identify the general structure of the Bethe ansatz solutions for the entire XX spectrum, which include states with real and complex magnon momenta. We discuss the relation between the spinon or magnon quasiparticles (Bethe ansatz) and the lattice fermions (Jordan-Wigner representation). We present determinantal expressions for transition rates of spin fluctuation operators between Bethe wave functions and reduce them to product expressions. We apply the new formulas to two-spinon transition rates for chains with up to N=4096 sites.Comment: 11 pages, 4 figure

Cosmological perturbations in SFT inspired non-local scalar field models

We study cosmological perturbations in models with a single non-local scalar field originating from the string field theory description of the rolling tachyon dynamics. We construct the equation for the energy density perturbations of the non-local scalar field and explicitly prove that for the free field it is identical to a system of local cosmological perturbation equations in a particular model with multiple (maybe infinitely many) local free scalar fields.Comment: 21 pages, no figures, v3: presentation improved, results unchanged, references adde

Global, regional, and national age-sex-specific mortality and life expectancy, 1950–2017: a systematic analysis for the Global Burden of Disease Study 2017

BACKGROUND: Assessments of age-specific mortality and life expectancy have been done by the UN Population Division, Department of Economics and Social Affairs (UNPOP), the United States Census Bureau, WHO, and as part of previous iterations of the Global Burden of Diseases, Injuries, and Risk Factors Study (GBD). Previous iterations of the GBD used population estimates from UNPOP, which were not derived in a way that was internally consistent with the estimates of the numbers of deaths in the GBD. The present iteration of the GBD, GBD 2017, improves on previous assessments and provides timely estimates of the mortality experience of populations globally. METHODS: The GBD uses all available data to produce estimates of mortality rates between 1950 and 2017 for 23 age groups, both sexes, and 918 locations, including 195 countries and territories and subnational locations for 16 countries. Data used include vital registration systems, sample registration systems, household surveys (complete birth histories, summary birth histories, sibling histories), censuses (summary birth histories, household deaths), and Demographic Surveillance Sites. In total, this analysis used 8259 data sources. Estimates of the probability of death between birth and the age of 5 years and between ages 15 and 60 years are generated and then input into a model life table system to produce complete life tables for all locations and years. Fatal discontinuities and mortality due to HIV/AIDS are analysed separately and then incorporated into the estimation. We analyse the relationship between age-specific mortality and development status using the Socio-demographic Index, a composite measure based on fertility under the age of 25 years, education, and income. There are four main methodological improvements in GBD 2017 compared with GBD 2016: 622 additional data sources have been incorporated; new estimates of population, generated by the GBD study, are used; statistical methods used in different components of the analysis have been further standardised and improved; and the analysis has been extended backwards in time by two decades to start in 1950. FINDINGS: Globally, 18·7% (95% uncertainty interval 18·4–19·0) of deaths were registered in 1950 and that proportion has been steadily increasing since, with 58·8% (58·2–59·3) of all deaths being registered in 2015. At the global level, between 1950 and 2017, life expectancy increased from 48·1 years (46·5–49·6) to 70·5 years (70·1–70·8) for men and from 52·9 years (51·7–54·0) to 75·6 years (75·3–75·9) for women. Despite this overall progress, there remains substantial variation in life expectancy at birth in 2017, which ranges from 49·1 years (46·5–51·7) for men in the Central African Republic to 87·6 years (86·9–88·1) among women in Singapore. The greatest progress across age groups was for children younger than 5 years; under-5 mortality dropped from 216·0 deaths (196·3–238·1) per 1000 livebirths in 1950 to 38·9 deaths (35·6–42·83) per 1000 livebirths in 2017, with huge reductions across countries. Nevertheless, there were still 5·4 million (5·2–5·6) deaths among children younger than 5 years in the world in 2017. Progress has been less pronounced and more variable for adults, especially for adult males, who had stagnant or increasing mortality rates in several countries. The gap between male and female life expectancy between 1950 and 2017, while relatively stable at the global level, shows distinctive patterns across super-regions and has consistently been the largest in central Europe, eastern Europe, and central Asia, and smallest in south Asia. Performance was also variable across countries and time in observed mortality rates compared with those expected on the basis of development. INTERPRETATION: This analysis of age-sex-specific mortality shows that there are remarkably complex patterns in population mortality across countries. The findings of this study highlight global successes, such as the large decline in under-5 mortality, which reflects significant local, national, and global commitment and investment over several decades. However, they also bring attention to mortality patterns that are a cause for concern, particularly among adult men and, to a lesser extent, women, whose mortality rates have stagnated in many countries over the time period of this study, and in some cases are increasing

Search for single production of vector-like T quarks decaying into Ht or Zt in pp collisions at s√ = 13 TeV with the ATLAS detector

This paper describes a search for the single production of an up-type vector-like quark (T) decaying as T → Ht or T → Zt. The search utilises a dataset of pp collisions at s√ = 13 TeV collected with the ATLAS detector during the 2015–2018 data-taking period of the Large Hadron Collider, corresponding to an integrated luminosity of 139 fb−1. Data are analysed in final states containing a single lepton with multiple jets and b-jets. The presence of boosted heavy resonances in the event is exploited to discriminate the signal from the Standard Model background. No significant excess above the Standard Model expectation is observed, and 95% CL upper limits are set on the production cross section of T quarks in different decay channels. The results are interpreted in several benchmark scenarios to set limits on the mass and universal coupling strength (κ) of the vector-like quark. For singlet T quarks, κ values above 0.53 are excluded for all masses below 2.3 TeV. At a mass of 1.6 TeV, κ values as low as 0.35 are excluded. For T quarks in the doublet scenario, where the production cross section is much lower, κ values above 0.72 are excluded for all masses below 1.7 TeV, and this exclusion is extended to κ above 0.55 for low masses around 1.0 TeV

Search for excited τ-leptons and leptoquarks in the final state with τ-leptons and jets in pp collisions at s√ = 13 TeV with the ATLAS detector

A search is reported for excited τ-leptons and leptoquarks in events with two hadronically decaying τ-leptons and two or more jets. The search uses proton-proton (pp) collision data at s√ = 13 TeV recorded by the ATLAS experiment during the Run 2 of the Large Hadron Collider in 2015–2018. The total integrated luminosity is 139 fb−1. The excited τ-lepton is assumed to be produced and to decay via a four-fermion contact interaction into an ordinary τ-lepton and a quark-antiquark pair. The leptoquarks are assumed to be produced in pairs via the strong interaction, and each leptoquark is assumed to couple to a charm or lighter quark and a τ-lepton. No excess over the background prediction is observed. Excited τ-leptons with masses below 2.8 TeV are excluded at 95% CL in scenarios with the contact interaction scale Λ set to 10 TeV. At the extreme limit of model validity where Λ is set equal to the excited τ-lepton mass, excited τ-leptons with masses below 4.6 TeV are excluded. Leptoquarks with masses below 1.3 TeV are excluded at 95% CL if their branching ratio to a charm quark and a τ-lepton equals 1. The analysis does not exploit flavour-tagging in the signal region

Measurement of the cross-sections of the electroweak and total production of a Zγ pair in association with two jets in pp collisions at √s = 13 TeV with the ATLAS detector

This Letter presents the measurement of the fiducial and differential cross-sections of the electroweak production of a Zγ pair in association with two jets. The analysis uses 140 fb−1 of LHC proton–proton collision data taken at √s = 13 TeV recorded by the ATLAS detector during the years 2015–2018. Events with a Z boson candidate decaying into either an e+e− or μ+μ− pair, a photon and two jets are selected. The electroweak component is extracted by requiring a large dijet invariant mass and by using the information about the centrality of the system and is measured with an observed and expected significance well above five standard deviations. The fiducial pp → Zγ jj cross-section for the electroweak production is measured to be 3.6 ± 0.5 fb. The total fiducial cross-section that also includes contributions where the jets arise from strong interactions is measured to be 16.8+2.0 −1.8 fb. The results are consistent with the Standard Model predictions. Differential cross-sections are also measured using the same events and are compared with parton-shower Monte Carlo simulations. Good agreement is observed between data and predictions

Search for heavy Higgs bosons with flavour-violating couplings in multi-lepton plus b-jets final states in pp collisions at 13 TeV with the ATLAS detector

A search for new heavy scalars with flavour-violating decays in final states with multiple leptons and b-tagged jets is presented. The results are interpreted in terms of a general two-Higgs-doublet model involving an additional scalar with couplings to the top-quark and the three up-type quarks (ρtt, ρtc, and ρtu). The targeted signals lead to final states with either a same-sign top-quark pair, three top-quarks, or four top-quarks. The search is based on a data sample of proton-proton collisions at √s = 13 TeV recorded with the ATLAS detector during Run 2 of the Large Hadron Collider, corresponding to an integrated luminosity of 139 fb−1. Events are categorised depending on the multiplicity of light charged leptons (electrons or muons), total lepton charge, and a deep-neural-network output to enhance the purity of each of the signals. Masses of an additional scalar boson mH between 200 − 630 GeV with couplings ρtt = 0.4, ρtc = 0.2, and ρtu = 0.2 are excluded at 95% confidence level. Additional interpretations are provided in models of R-parity violating supersymmetry, motivated by the recent flavour and (g − 2)μ anomalies