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Note on the asymptotic structure of Kerr-Schild form

The Kerr-Schild form provides a natural way of realizing the classical double copy that relates exact solutions in general relativity to exact solutions in gauge theory. In this paper, we examine the asymptotic structure of Kerr-Schild form. In Newman-Unti gauge, we find a generic solution space satisfying the Kerr-Schild form in series expansion around null infinity. The news function in the solution space is chiral and can not lead to a mass loss formula. A class of asymptotically flat complex pp-wave solutions in closed form is obtained from the solution space.

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Consensus-Based Distributed Optimization of Generation Dispatch of Multi-Area AC Systems Interconnected by DC Lines

This paper is dedicated to solving the distributed optimization of generation dispatch of multi-area AC systems interconnected by DC lines, which aims at minimizing the total generation cost while satisfying the power supply demand balance and generation capacity constraints. A novel nodal loss formula which derived from the branch active power flow equation is proposed based on phase angle and impedance to improve the system economy. A distributed algorithm based on consensus is built to solve the generation dispatch problem. It has a great effect on improving convergence effect and rate of the system. The control strategy is used on the structure of multi-area interconnection, which improves the reliability of power supply and guarantee the power quality. The study was conducted using three area AC systems interconnected by DC lines. The simulation results show that the proposed generation dispatch method is reliable in convergence. It provides an effective tool for distributed optimization of generation dispatch of multi-area AC systems interconnected by DC lines.

Predicting the winning percentage of limited-overs cricket using the pythagorean formula

The Pythagorean Win-Loss formula can be effectively used to estimate winning percentages for sporting events. This formula was initially developed by baseball statistician Bill James and later was extended by other researchers to sports such as football, basketball, and ice hockey. Although one can calculate actual winning percentages based on the outcomes of played games, that approach does not take into account the margin of victory. The key benefit of the Pythagorean formula is its utilization of actual average runs scored and actual average runs allowed. This article presents the application of the Pythagorean Win-Loss formula to two different types of limited-overs cricket formats, namely One Day International cricket (ODI) and Twenty20 cricket. The data for the application was used from the matches played by the top 10 International Cricket Council (ICC) members who participated in the 2019 ICC Cricket World Cup. For matches for which the second batting team won, runs scored were estimated by considering the remaining amount of resources, based on the Duckworth–Lewis method.

Real Capital

Preshaped by the influence of Marx, Böhm-Bawerk and modern neoclassical economics, the general opinion is that the marginal product of capital must always be positive. With the help of the “period of production” T, we define a coefficient of intertemporal substitutionψ that is always non-negative. It can also be used when the real interest rate is negative. With the help of the concept of the “waiting period” Z, we can also define an always non-negative coefficient of intertemporal substitutionγ for the household side. The “loss formula” for deviations of the rate of interest from the growth rate is one application of ψ and γ. Ω = (ψT2 + γZ2)(r − g)2/2 provides a good approximation of the relative loss Ω. Overcomplexity of the system of production leads to negative marginal returns on capital. It can be empirically presumed that the OECD plus China region is on the cusp of overcomplexity. The hypothetical natural rate of interest in the eurozone is well into the minuses. To determine the value of the real capital of the private sector in the OECD plus China region, we use a framework of data taken from the World Inequality Database (WID.world). We have supplemented the data available there with data from other sources and adapted it to our theoretical objectives. According to our estimates, private wealth in the form of real capital in the OECD plus China region comes to approximately four times total annual consumption.

A Palm-Jacobaeus Loss Formula for Multi-Service Systems with Separated Resources

This article presents a method to determine the blocking probability (non-availability) for strictly determined multi-service resources that belong to a group of multi-service resources. The dependencies obtained during the process correspond to the Palm-Jacobaeus formula derived for the group of resources servicing single-service traffic. The approach to determining the blocking probability is based on the determination of the availability of resources at the occupancy level of allocation units. The analytical results are compared with the obtained results of the simulation experiments for a number of selected parameters of multi-service groups of resources. The results of the present study indicate a high accuracy of the proposed solutions. The elaborated extension of the Palm-Jacobaeus formula can be used in the modeling of separated wireless resources in cellular networks.

Dielectric dispersion, linear and nonlinear optical properties of Li2O–WO3–B2O3: V2O5 glasses

40 Li2O–5 WO3–(55-[Formula: see text]) B2O3: [Formula: see text]V2O5 (mol%) for [Formula: see text] glasses were prepared by melt-quenching. Electric polarization was described in terms of the dielectric constant ([Formula: see text]) and loss ([Formula: see text]). Mixed conduction phenomenon was explained by redox pairs [Formula: see text] and [Formula: see text] at high temperatures. Electronic polarizability ([Formula: see text]) was determined over a range of frequencies (100[Formula: see text]Hz–100[Formula: see text]kHz) and temperatures (30–[Formula: see text]C). The change of boron coordination in the glass network was explained with the aid of temperature coefficient of polarizability ([Formula: see text]). Nonlinear susceptibility ([Formula: see text]) and optical band gap ([Formula: see text]) were studied as a function of concentration of V2O5. The highest values of [Formula: see text] and [Formula: see text] were obtained at [Formula: see text][Formula: see text]mol%. These glasses may find potential practical applications in the fields of solid-state ionics and nonlinear optics.

Temperature-dependent structure, dielectric properties of Bi0.95Ba0.05Fe0.95Ti0.05O1.3

The temperature-dependent structure and dielectric properties of Bi[Formula: see text]Ba[Formula: see text]Fe[Formula: see text] Ti[Formula: see text]O3 ceramic are studied systematically. At the temperature range of 25–800[Formula: see text]C, the cell parameters are increasing, this indicates its distorted rhombohedral [Formula: see text]3[Formula: see text] structure. A structural phase transformation from rhombohedral [Formula: see text]3[Formula: see text] to cubic Pm3[Formula: see text] is observed at 850[Formula: see text]C. The thermal expansion coefficients in the temperature range 25–700[Formula: see text]C are calculated. Meanwhile, the temperature-dependent dielectric constant ([Formula: see text]) and dielectric loss ([Formula: see text][Formula: see text]) at different frequencies are measured. This work attempts to show the thermodynamic stability and the effect of charge defects on the electric properties for doped BiFeO3 ceramics.