We use an X-ray stacking technique to investigate the evolution of the mean X-ray luminosity of ∼21,000 red galaxies at 0.3 ≤ z < 0.9 as a function of their stellar mass and redshift. The red galaxies are selected from the 9.3 deg 2 Boötes field of the NOAO Deep Wide-Field Survey (NDWFS). The mean X-ray luminosity is an order of magnitude larger than we would expect from stellar sources alone and therefore must be primarily due to AGN emission. The X-ray luminosities (L x ≈ 10 41 ergs s −1) imply that these must be sources with relatively low accretion rates and/or accretion efficiencies onto their central super-massive black hole (SMBH). The mean X-ray luminosity increases significantly as a function of optical luminosity and stellar mass, implying that more massive galaxies have higher nuclear accretion rates than lower mass galaxies. We calculate that the mean X-ray luminosity evolves as (1 + z) 3.3±1.5. This suggests a global decline in the mean AGN activity of normal early-type galaxies from z ∼ 1 to the present. If accreting at typical AGN efficiencies, SMBHs within red galaxies accreted an insignificant proportion of their mass in this time.

National Optical Astronomy Observatory

Cubic B-spline approximation for linear stochastic integro-differential equation of fractional order

In this paper, a potentially useful new method based on the Gegenbauer wavelet expansion, together with operational matrices of fractional integral and block-pulse functions, is proposed in order to solve the Bagley–Torvik equation. The Gegenbauer wavelets are generated here by dilation and translation of the classical orthogonal Gegenbauer polynomials. The properties of the Gegenbauer wavelets and the Gegenbauer polynomials are first presented. These functions and their associated properties are then employed to derive the Gegenbauer wavelet operational matrices of fractional integrals. The operational matrices of fractional integrals are utilized to reduce the problem to a set of algebraic equations with unknown coefficients. Illustrative examples are provided to demonstrate the validity and applicability of the method presented here.

An Application of the Gegenbauer Wavelet Method for the Numerical Solution of the Fractional Bagley-Torvik Equation

Discrete spline methods for solving two point fractional Bagley-Torvik equation

Fractional calculus became a vital tool in describing many phenomena appeared in physics, chemistry as well as engineering fields. Analytical solution of many applications, where the fractional differential equations appear, cannot be established. Therefore, cubic polynomial spline-function-based method combined with shooting method is considered to find approximate solution for a class of fractional boundary value problems (FBVPs). Convergence analysis of the method is considered. Some illustrative examples are presented.

/pdf/the-use-of-cubic-splines-in-the-numerical-solution-of-1gk5pdchar.pdf

The Use of Cubic Splines in the Numerical Solution of Fractional Differential Equations

Fractional differential equations are widely applied in physics, chemistry as well as engineering fields. Therefore, approximating the solution of differential equations of fractional order is necessary. We consider the quadratic polynomial spline function based method to find approximate solution for a class of boundary value problems of fractional order. We derive a consistency relation which can be used for computing approximation to the solution for this class of boundary value problems. Convergence analysis of the method is discussed. Four numerical examples are included to illustrate the practical usefulness of the proposed method.

Quadratic spline solution for boundary value problem of fractional order

Most power system planners are interested in the savings of electrical power consumption. Various references demonstrate that the highest consumed power is by the lighting systems standing around 19% of worldwide energy consumption. This article presents novel design methodology leading to maximizing revenue due to savings in electrical energy consumption through energy efficient installations. This hybrid methodology is built by combining benefits of the two traditional lighting design methods (lumen and specific connected load methods). This results in developing a new mathematical and applicable model with many advantages such as: high accuracy, fast calculations and most economical design. This proposed methodology is supported by MATLAB® package to shorten the long time consumed by conventional procedures and simplify the complex manual calculations. The hybrid method verifies its effectiveness and efficiency for achieving the maximum savings in energies and costs through the detailed discussion of case studies. A comparison with traditional designs will be introduced to ensure the achieved savings in costs leading to high quality and efficiency of power systems. By practically applying this new hybrid technique particularly for the Egyptian residential and commercial sectors, the system is expected to achieve a huge savings in consumed lighting energies and costs, which can reach 4489.433415 million E£ \"≈ 280.5895 million $ \"USD\"\" each year. The presented case studies give accurate and promising results for the proposed methodology as a new trend in energy and money saving system, which is verified by implementing two case studies and comparing with results from DIALux program. The results of the proposed methodology are very effective compared with that of conventional methods for marked benchmarking features and validation. MATLAB® simulation results of the proposed technique are implemented to verify its feasibility for any activity. © 2020 The Author(s). Published by solarlits.com. This is an open access article under the CC BY license (https://creativecommons.org/licenses/by/4.0/).

/pdf/a-new-trend-for-indoor-lighting-design-based-on-a-hybrid-lsj83hp623.pdf

A New Trend for Indoor Lighting Design Based on A Hybrid Methodology

Recently, a large number of applied problems have been formu- lated on fractional dierential equations. Analytical solution of many applica- tions, where the fractional dierential equations appear, cannot be established. Therefore, quintic polynomial spline function is considered to find approximate solution for a class of two point fourth order integro-dierenti al equation of fractional order. Convergence analysis of the method is considered. Some il- lustrative examples are included to demonstrate the practical usefulness of the proposed method.

Spline solution for fourth order fractional integro-differential equations

In this paper, a theoretical treatment of the stability behavior of the zero solution of nonlinear damped oscillator in the vectorial case is investigated. We study the sufficient conditions for the boundedness of solution of the nonlinear damped vectorial oscillator and the conditions for the stability of the zero solution to be uniformly stable as well as asymptotically stable.

/pdf/stability-behavior-of-the-zero-solution-for-nonlinear-damped-2qvl2q6pc9.pdf

Stability Behavior of the Zero Solution for Nonlinear Damped Vectorial Second Order Differential Equation

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