Oscillatory behavior of higher order neutral differential equation with multiple functional delays under derivative operator

summary:In this article, we obtain sufficient conditions so that every solution of neutral delay differential equation $$\big (y(t)- \sum _{i=1}^k p_i(t) y(r_i(t))\big )^{(n)}+ v(t)G( y(g(t)))-u(t)H(y(h(t))) = f(t)$$ oscillates or tends to zero as $t\rightarrow \infty$, where, $n \ge 1$ is any positive integer, $p_i$, $r_i\in C^{(n)}([0,\infty ),\mathbb{R})$  and $p_i$ are bounded for each $i=1,2,\dots ,k$. Further, $f\in C([0, \infty ), \mathbb{R})$, $g$, $h$, $v$, $u \in C([0, \infty ), [0, \infty ))$, $G$ and $H \in C(\mathbb{R},\mathbb{R})$. The functional delays $r_i(t)\le t$, $g(t)\le t$ and $h(t)\le t$ and all of them approach $\infty$ as $t\rightarrow \infty$. The results hold when $u\equiv 0$ and $f(t)\equiv 0$. This article extends, generalizes and improves some recent results, and further answers some unanswered questions from the literature

Hot Nuclear Matter in Asymmetry Chiral Sigma Model

In the frame work of SU(2) chiral sigma model, the nuclear matter properties at zero and finite temperature have been investigated. We have analyzed the nuclear matter equation of state by varying different parameters, which agrees well with the one derived from the heavy-ion collision experiment at extreme densities and reliable realistic(DBHF) model at low density region. We have then calculated the temperature dependent asymmetric nuclear matter, also investigated the critical temperature of liquid gas phase transition and compared with the experimental data. We found that the critical temperature in our model is in the range of 14-20 MeV.Comment: 21 pages, 10 figures, to be published in Nuclear Physics

The systematic study of the influence of neutron excess on the fusion cross sections using different proximity-type potentials

Using different types of proximity potentials, we have examined the trend of variations of barrier characteristics (barrier height and its position) as well as fusion cross sections for 50 isotopic systems including various collisions of C, O, Mg, Si, S, Ca, Ar, Ti and Ni nuclei with $1\leq N/Z < 1.6$ condition for compound systems. The results of our studies reveal that the relationships between increase of barrier positions and decrease of barrier heights are both linear with increase of $N/Z$ ratio. Moreover, fusion cross sections also enhance linearly with increase of this ratio.Comment: 28 pages, 7 figures, 5 Table

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

Narrowband Searches for Continuous and Long-duration Transient Gravitational Waves from Known Pulsars in the LIGO-Virgo Third Observing Run

Isolated neutron stars that are asymmetric with respect to their spin axis are possible sources of detectable continuous gravitational waves. This paper presents a fully coherent search for such signals from eighteen pulsars in data from LIGO and Virgo's third observing run (O3). For known pulsars, efficient and sensitive matched-filter searches can be carried out if one assumes the gravitational radiation is phase-locked to the electromagnetic emission. In the search presented here, we relax this assumption and allow both the frequency and the time derivative of the frequency of the gravitational waves to vary in a small range around those inferred from electromagnetic observations. We find no evidence for continuous gravitational waves, and set upper limits on the strain amplitude for each target. These limits are more constraining for seven of the targets than the spin-down limit defined by ascribing all rotational energy loss to gravitational radiation. In an additional search, we look in O3 data for long-duration (hours-months) transient gravitational waves in the aftermath of pulsar glitches for six targets with a total of nine glitches. We report two marginal outliers from this search, but find no clear evidence for such emission either. The resulting duration-dependent strain upper limits do not surpass indirect energy constraints for any of these targets. © 2022. The Author(s). Published by the American Astronomical Society

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

Open data from the third observing run of LIGO, Virgo, KAGRA, and GEO

The global network of gravitational-wave observatories now includes five detectors, namely LIGO Hanford, LIGO Livingston, Virgo, KAGRA, and GEO 600. These detectors collected data during their third observing run, O3, composed of three phases: O3a starting in 2019 April and lasting six months, O3b starting in 2019 November and lasting five months, and O3GK starting in 2020 April and lasting two weeks. In this paper we describe these data and various other science products that can be freely accessed through the Gravitational Wave Open Science Center at https://gwosc.org. The main data set, consisting of the gravitational-wave strain time series that contains the astrophysical signals, is released together with supporting data useful for their analysis and documentation, tutorials, as well as analysis software packages

GW190814: gravitational waves from the coalescence of a 23 solar mass black hole with a 2.6 solar mass compact object

We report the observation of a compact binary coalescence involving a 22.2–24.3 Me black hole and a compact object with a mass of 2.50–2.67 Me (all measurements quoted at the 90% credible level). The gravitational-wave signal, GW190814, was observed during LIGO’s and Virgo’s third observing run on 2019 August 14 at 21:10:39 UTC and has a signal-to-noise ratio of 25 in the three-detector network. The source was localized to 18.5 deg2 at a distance of - + 241 45 41 Mpc; no electromagnetic counterpart has been confirmed to date. The source has the most unequal mass ratio yet measured with gravitational waves, - + 0.112 0.009 0.008, and its secondary component is either the lightest black hole or the heaviest neutron star ever discovered in a double compact-object system. The dimensionless spin of the primary black hole is tightly constrained to �0.07. Tests of general relativity reveal no measurable deviations from the theory, and its prediction of higher-multipole emission is confirmed at high confidence. We estimate a merger rate density of 1–23 Gpc−3 yr−1 for the new class of binary coalescence sources that GW190814 represents. Astrophysical models predict that binaries with mass ratios similar to this event can form through several channels, but are unlikely to have formed in globular clusters. However, the combination of mass ratio, component masses, and the inferred merger rate for this event challenges all current models of the formation and mass distribution of compact-object binaries

Global burden and strength of evidence for 88 risk factors in 204 countries and 811 subnational locations, 1990–2021: a systematic analysis for the Global Burden of Disease Study 2021

Background: Understanding the health consequences associated with exposure to risk factors is necessary to inform public health policy and practice. To systematically quantify the contributions of risk factor exposures to specific health outcomes, the Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) 2021 aims to provide comprehensive estimates of exposure levels, relative health risks, and attributable burden of disease for 88 risk factors in 204 countries and territories and 811 subnational locations, from 1990 to 2021. Methods: The GBD 2021 risk factor analysis used data from 54 561 total distinct sources to produce epidemiological estimates for 88 risk factors and their associated health outcomes for a total of 631 risk–outcome pairs. Pairs were included on the basis of data-driven determination of a risk–outcome association. Age-sex-location-year-specific estimates were generated at global, regional, and national levels. Our approach followed the comparative risk assessment framework predicated on a causal web of hierarchically organised, potentially combinative, modifiable risks. Relative risks (RRs) of a given outcome occurring as a function of risk factor exposure were estimated separately for each risk–outcome pair, and summary exposure values (SEVs), representing risk-weighted exposure prevalence, and theoretical minimum risk exposure levels (TMRELs) were estimated for each risk factor. These estimates were used to calculate the population attributable fraction (PAF; ie, the proportional change in health risk that would occur if exposure to a risk factor were reduced to the TMREL). The product of PAFs and disease burden associated with a given outcome, measured in disability-adjusted life-years (DALYs), yielded measures of attributable burden (ie, the proportion of total disease burden attributable to a particular risk factor or combination of risk factors). Adjustments for mediation were applied to account for relationships involving risk factors that act indirectly on outcomes via intermediate risks. Attributable burden estimates were stratified by Socio-demographic Index (SDI) quintile and presented as counts, age-standardised rates, and rankings. To complement estimates of RR and attributable burden, newly developed burden of proof risk function (BPRF) methods were applied to yield supplementary, conservative interpretations of risk–outcome associations based on the consistency of underlying evidence, accounting for unexplained heterogeneity between input data from different studies. Estimates reported represent the mean value across 500 draws from the estimate's distribution, with 95% uncertainty intervals (UIs) calculated as the 2·5th and 97·5th percentile values across the draws. Findings: Among the specific risk factors analysed for this study, particulate matter air pollution was the leading contributor to the global disease burden in 2021, contributing 8·0% (95% UI 6·7–9·4) of total DALYs, followed by high systolic blood pressure (SBP; 7·8% [6·4–9·2]), smoking (5·7% [4·7–6·8]), low birthweight and short gestation (5·6% [4·8–6·3]), and high fasting plasma glucose (FPG; 5·4% [4·8–6·0]). For younger demographics (ie, those aged 0–4 years and 5–14 years), risks such as low birthweight and short gestation and unsafe water, sanitation, and handwashing (WaSH) were among the leading risk factors, while for older age groups, metabolic risks such as high SBP, high body-mass index (BMI), high FPG, and high LDL cholesterol had a greater impact. From 2000 to 2021, there was an observable shift in global health challenges, marked by a decline in the number of all-age DALYs broadly attributable to behavioural risks (decrease of 20·7% [13·9–27·7]) and environmental and occupational risks (decrease of 22·0% [15·5–28·8]), coupled with a 49·4% (42·3–56·9) increase in DALYs attributable to metabolic risks, all reflecting ageing populations and changing lifestyles on a global scale. Age-standardised global DALY rates attributable to high BMI and high FPG rose considerably (15·7% [9·9–21·7] for high BMI and 7·9% [3·3–12·9] for high FPG) over this period, with exposure to these risks increasing annually at rates of 1·8% (1·6–1·9) for high BMI and 1·3% (1·1–1·5) for high FPG. By contrast, the global risk-attributable burden and exposure to many other risk factors declined, notably for risks such as child growth failure and unsafe water source, with age-standardised attributable DALYs decreasing by 71·5% (64·4–78·8) for child growth failure and 66·3% (60·2–72·0) for unsafe water source. We separated risk factors into three groups according to trajectory over time: those with a decreasing attributable burden, due largely to declining risk exposure (eg, diet high in trans-fat and household air pollution) but also to proportionally smaller child and youth populations (eg, child and maternal malnutrition); those for which the burden increased moderately in spite of declining risk exposure, due largely to population ageing (eg, smoking); and those for which the burden increased considerably due to both increasing risk exposure and population ageing (eg, ambient particulate matter air pollution, high BMI, high FPG, and high SBP). Interpretation: Substantial progress has been made in reducing the global disease burden attributable to a range of risk factors, particularly those related to maternal and child health, WaSH, and household air pollution. Maintaining efforts to minimise the impact of these risk factors, especially in low SDI locations, is necessary to sustain progress. Successes in moderating the smoking-related burden by reducing risk exposure highlight the need to advance policies that reduce exposure to other leading risk factors such as ambient particulate matter air pollution and high SBP. Troubling increases in high FPG, high BMI, and other risk factors related to obesity and metabolic syndrome indicate an urgent need to identify and implement interventions. Funding: Bill & Melinda Gates Foundation