Classical soft graviton theorem rewritten

Classical soft graviton theorem gives the gravitational wave-form at future null infinity at late retarded time u for a general classical scattering. The large u expansion has three known universal terms: the constant term, the term proportional to 1/u and the term proportional to ln u/u2, whose coefficients are determined solely in terms of the momenta of incoming and the outgoing hard particles, including the momenta carried by outgoing gravitational and electromagnetic radiation produced during scattering. For the constant term, also known as the memory effect, the dependence on the momenta carried away by the final state radiation / massless particles is known as non-linear memory or null memory. It was shown earlier that for the coefficient of the 1/u term the dependence on the momenta of the final state massless particles / radiation cancels and the result can be written solely in terms of the momenta of the incoming particles / radiation and the final state massive particles. In this note we show that the same result holds for the coefficient of the ln u/u2 term. Our result implies that for scattering of massless particles the coefficients of the 1/u and ln u/u2 terms are determined solely by the incoming momenta, even if the particles coalesce to form a black hole and massless radiation. We use our result to compute the low frequency flux of gravitational radiation from the collision of massless particles at large impact parameter.

Effect of Static Bifurcation on Logical Stochastic Resonance in a Symmetric Bistable System

In previous research works, logical stochastic resonance (LSR) was reported to frequently occur in an asymmetric bistable system, where the bias parameter is the key factor to make the LSR appear. In this work, we investigate the effect of different anharmonic periodic signals on the pitchfork and saddle-node bifurcations in a symmetric bistable system. We focus on the relationship between the static bifurcation and LSR. We use both numerical and circuit simulations to analyze some interesting phenomena. Like the bias parameter, some anharmonic periodic signals also break the symmetry of the symmetric bistable system and lead to the saddle-node bifurcation. The anharmonic periodic signal with a constant term in its expanded Fourier series induces a reliable LSR in the symmetric bistable system. The key factor of LSR is the saddle-node bifurcation which implies the asymmetry of the system. Here, we replace the bias parameter by choosing an anharmonic periodic signal and make the LSR occur in a different way.

f(T) cosmology with nonzero curvature

We investigate exact and analytic solutions in [Formula: see text] gravity within the context of a Friedmann–Lemaître–Robertson–Walker background space with nonzero spatial curvature. For the power-law theory [Formula: see text] we find that the field equations admit an exact solution with a linear scalar factor for negative and positive spatial curvature. That Milne-like solution is asymptotic behavior for the scale factor near the initial singularity for the model [Formula: see text]. The analytic solution for that specific theory is presented in terms of Painlevé series for [Formula: see text]. Moreover, from the value of the resonances of the Painlevé series we conclude that the Milne-like solution is always unstable while for large values of the independent parameter, the field equations provide an expanding universe with a de Sitter expansion of a positive cosmological constant. Finally, the presence of the cosmological term [Formula: see text] in the studied [Formula: see text] model plays no role in the general behavior of the cosmological solution and the universe immerge in a de Sitter expansion either when the cosmological constant term [Formula: see text] in the [Formula: see text] model vanishes.

Success story of controlling COVID-19 in East Asia: lessons for South Asia

The novel coronavirus is an issue of life and death. The main purpose of the study is to know the East Asian success story of controlling Covid-19 and identify which strategies could be a lesson for South Asia and to examine the influence of good governance on controlling COVID-19. Total daily cases of COVID-19 are collected from March 10 to June 15 for East Asian and March 4 to June 15 for South Asian countries. ARIMA forecasting, ADF test, stability test, and diagnostic tests are applied. The minimum value of AIC and BIC shows the appropriate model is ARIMA (0, 1, 1) for both regions. In the East and South Asian model, the coefficients of the constant term are -0.759451 and 198.0155, and coefficients of MA (1) are -0.715686 and -0.339701 respectively for both regions. It's significant at a 1% significance level and support our hypotheses that the total daily cases of COVID-19 decreasing into East Asia but increasing into South Asia and prove that the South Asia region has faced a lot of difficulties to tackle COVID-19 as most of the countries have not enough government capacity, weak institutions, limited resources, narrow government reaches to the vulnerable people and corruption compare to East Asian region and no actual strategies are yet noticeable from the governments of South Asia as a result transmission increases day by day. That is why; we think that South Asian countries could take lessons from East Asian countries as these countries are more successful to control COVID-19.

Temporal and Spatial Impacts of Land Transfer on PM2.5 Concentration in 285 Cities of China

The threat of fine particulate matter concentration (PM2.5) is increasing globally, Tackling this issue requires an accurate understanding of its trends and drivers. The article investigates the PM2.5 characteristics of 285 prefecture-level cities in China from 2000-2018 based on multiscale geographically weighted regression(MGWR), and the results show that（1）previous studies based on classical MGWR models may be somewhat unstable, while MGWR can reflect the scale of influence of different variables on the dependent variable, and its regression results are more reliable.（2）PM2.5 is very sensitive to carbon emission(CE) factors, and there is a high degree of spatial heterogeneity, and the influence scale of location is the smallest among all variables, close to the municipal scale.（3）In 2000, the constant term all, IS, OFT, CE, and LT positively affect PM2.5, while GDP (jurisdiction) and UR negatively affect PM2.5; in 2010, the constant term all, GDP (jurisdiction), IS, OFT and LT positively affect PM2.5, while UR and CE negatively affect PM2.5; in 2018 the constant term all, IS, OFT and CE factors positively affect PM2.5, and GDP (jurisdiction), UR and LT negatively affect PM2.5.

Maxwell-modified metric affine gravity

We present a gauge formulation of the special affine algebra extended to include an antisymmetric tensorial generator belonging to the tensor representation of the special linear group. We then obtain a Maxwell modified metric affine gravity action with a cosmological constant term. We find the field equations of the theory and show that the theory reduces to an Einstein-like equation for metric affine gravity with the source added to the gravity equations with cosmological constant $$\mu $$ μ contains linear contributions from the new gauge fields. The reduction of the Maxwell metric affine gravity to Riemann–Cartan one is discussed and the shear curvature tensor corresponding to the symmetric part of the special linear connection is identified with the dark energy. Furthermore, the new gauge fields are interpreted as geometrical inflaton vector fields which drive accelerated expansion.

The 4d superconformal index near roots of unity and 3d Chern-Simons theory

We consider the S3×S1 superconformal index ℐ(τ) of 4d $$ \mathcal{N} $$ N = 1 gauge theories. The Hamiltonian index is defined in a standard manner as the Witten index with a chemical potential τ coupled to a combination of angular momenta on S3 and the U(1) R-charge. We develop the all-order asymptotic expansion of the index as q = e2πiτ approaches a root of unity, i.e. as $$ \overset{\sim }{\tau } $$ τ ~ ≡ mτ+n → 0, with m, n relatively prime integers. The asymptotic expansion of log ℐ(τ) has terms of the form $$ \overset{\sim }{\tau } $$ τ ~ k, k = −2, −1, 0, 1. We determine the coefficients of the k = −2, −1, 1 terms from the gauge theory data, and provide evidence that the k = 0 term is determined by the Chern-Simons partition function on S3/ℤm. We explain these findings from the point of view of the 3d theory obtained by reducing the 4d gauge theory on the S1. The supersymmetric functional integral of the 3d theory takes the form of a matrix integral over the dynamical 3d fields, with an effective action given by supersymmetrized Chern-Simons couplings of background and dynamical gauge fields. The singular terms in the $$ \overset{\sim }{\tau } $$ τ ~ → 0 expansion (dictating the growth of the 4d index) are governed by the background Chern-Simons couplings. The constant term has a background piece as well as a piece given by the localized functional integral over the dynamical 3d gauge multiplet. The linear term arises from the supersymmetric Casimir energy factor needed to go between the functional integral and the Hamiltonian index.

Cosmological constraints on scalar field dark matter

This paper aims to put constraints on the parameters of the Scalar Field Dark Matter (SFDM) model, when dark matter is described by a free real scalar field filling the whole universe, plus a cosmological constant term. By using a compilation of 51 [Formula: see text] data and 1048 Supernovae data from Panteon, a mass range for the scalar field was obtained, [Formula: see text]eV, in good agreement with light mass axion particles. Also, we have obtained [Formula: see text], and the present dark matter density parameter [Formula: see text] at [Formula: see text] confidence level. These results are in good agreement to standard model of cosmology, showing that SFDM model is viable in describing the dark matter content of the universe.

New Estimator for AR (1) Model with Missing Observations

In this paper, new form of the parameters of AR(1) with constant term with missing observations has been derived by using Ordinary Least Squares (OLS) method, Also, the properties of OLS estimator are discussed, moreover, an extension of Youssef [18]has been suggested for AR(1) with constant with missing observations. A comparative study between (OLS), Yule-Walker (YW) and modification of the ordinary least squares (MOLS) is considered in the case of stationary and near unit root time series, using Monte Carlo simulation.