Explore the vast range of titles available.

In this paper, we present a new numerical methods for solving large-scale differential Sylvester matrix equations with low rank right hand sides. These differential matrix equations appear in many applications such as robust control problems, model reduction problems and others. We present two approaches based on extended global Arnoldi process. The first one is based on approximating exponential matrix in the exact solution using the global extended Krylov method. The second one is based on a low-rank approximation of the solution of the corresponding Sylvester equation using the extended global Arnoldi algorithm. We give some theoretical results and report some numerical experiments to show the effectiveness of the proposed methods compared with the extended block Krylov method given in Hached and Jbilou (Numer Linear Algebra Appl 255:e2187, 2018).

This paper introduces an innovative, adaptive Fractional Open-Circuit Voltage (FOCV) algorithm combined with a robust Improved Model Reference Adaptive Controller (IMRAC) for Maximum Power Point Tracking (MPPT) in standalone photovoltaic (PV) systems. The proposed two-stage control strategy enhances energy efficiency, simplifies system operation, and addresses limitations in conventional MPPT methods, such as slow convergence, high oscillations, and susceptibility to environmental fluctuations. The first stage dynamically estimates the Maximum Power Point (MPP) voltage using a novel adaptive FOCV method, which eliminates the need for irradiance sensors or physical disconnection of PV modules. This stage incorporates a real-time adjustment of the kv factor based on variations in PV power, ensuring precise voltage estimation. In the second stage, the IMRAC controller ensures accurate tracking of the MPP by adapting swiftly to changes in irradiance and temperature, while minimizing ripple and power loss. Validation of the proposed system was carried out using Processor-in-the-Loop (PIL) testing on an Arduino Due microcontroller, showcasing real-world applicability. Comparative analysis with state-of-the-art MPPT controllers, including P&O-PI, InC-SMC, FLC, and VS P&O Backstepping, demonstrates superior tracking efficiency exceeding 99.49% under EN 50,530 standard test conditions. The system also maintains exceptional performance with minimal efficiency loss across a wide range of temperature and irradiance variations. By combining simplicity, robustness, and sustainability, this work establishes a cutting-edge solution for standalone PV systems, paving the way for more efficient and reliable renewable energy applications.

In this paper, we propose a new numerical method based on the extended block Arnoldi algorithm for solving large-scale differential nonsymmetric Stein matrix equations with low-rank right-hand sides. This algorithm is based on projecting the initial problem on the extended block Krylov subspace to obtain a low-dimensional differential Stein matrix equation. The obtained reduced-order problem is solved by the backward differentiation formula (BDF) method or the Rosenbrock (Ros) method, the obtained solution is used to build the low-rank approximate solution of the original problem. We give some theoretical results and report some numerical experiments.

We investigate existence and regularity of solutions to unbounded elliptic problem whose simplest model is {-div[(1+uq)∇u]+u=γ∇u2/1+u1-q+f in Ω, u=0 on ∂Ω,}, where 00 and f belongs to some appropriate Lebesgue space. We give assumptions on f with respect to q and γ to show the existence and regularity results for the solutions of previous equation.

In the present paper, we investigate the controllability, observability and fractional linear-quadratic problem of a non-homogeneous continuous-time fractional dynamical system (CF-DS) using the conformable fractional derivatives (CFD). We show that the controllability is equivalent to a controllability matrix that has a full rank. We also show a relationship between controllability and fractional differential Lyapunov equation. We give some theorems for observability of continuous-time fractional dynamical system. Moreover, we found a relationship between the solution of conformable fractional differential Riccati matrix equation and the solution of another conformable fractional linear system. We also find an optimal control that minimizes a functional cost under a conformable fractional system CF-DS by using the solution of fractional differential Riccati equation. Finally, we offer some applications to illustrate the effectiveness of our results.

In the present paper, we consider the large scale Stein matrix equation with a low-rank constant term A X B − X + E F T = 0 . These matrix equations appear in many applications in discrete-time control problems, filtering and image restoration and others. The proposed methods are based on projection onto the extended block Krylov subspace with a Galerkin approach (GA) or with the minimization of the norm of the residual. We give some results on the residual and error norms and report some numerical experiments.

This chapter opens with the discussion of the characteristics of thermosetting resins with special reference to epoxy resin. Cure reactions of epoxy resin with a wide variety of reagents are illustrated. A detailed account on curing of epoxies with amines, mercaptanes, isocyanates, carboxylic acids, and anhydrides are explained. Different amine and anhydride curatives are mentioned with their structures. A comprehensive account on different curing methods such as thermal, microwave, and radiation are included. A very detailed explanation on wide variety of agents employed to toughen the epoxy matrix is given with special emphasis on different aspects of rubber‐modified epoxy resins. Different toughening mechanisms including their quantitative assessment are detailed. In the last part of this chapter, all other chapters are introduced.

Chitosan was reacted with four concentrations (2.5, 5, 10 and 20 mmol) of glutamic acid resulting in four types of glutamic-chitosan hydrogels (GCs), the activity of the resulted compounds on the removal of copper(II) and nickel(II) from wastewater were tested. The results indicated that by increasing glutamic acid concentration from GCs-1 to GCs-4, the efficiency of removing Cu(II) and Ni(II) were decreased, which may be due to a decrease in the pore size of the hydrogels as a result of the increased degree of crosslinking.

The primary objective of mineral exploration is to discover new mineral-rich zones within targeted regions. The fractal concentration area (C-A) and the magnetic maps are now extensively used in mineral prospecting. Unfortunately, the calculation of the reduced-to-pole (RTP) maps suffers from several drawbacks. It requires a prior knowledge of the inclination and declination of the source magnetization. It can be complicated to determine the direction of the source magnetization vector in certain conditions because of the large and significant remanent magnetization of the source if present. Furthermore, at low magnetic latitudes, the RTP computation is unstable. However, a new class of transforms known as magnitude magnetic transforms (MMTs) overcome these drawbacks. Such transforms have nonnegative distributions and exhibit significantly higher centricity with regard to the observed anomalous field. Their anomaly patterns are much less influenced by the direction of the magnetization vector than the observed total magnetic intensity. Due to these benefits, in this work, these transforms are used instead of RTP transform as a base for fractal/multifractal analysis of the magnetic signal from the Esh El Mallaha area, Eastern desert to delineate gold mineralization and hydrothermally altered and potential zones. Moreover, are used for the singularity analysis S-A in a novel integrated workflow. The results of this study show a promising approach that can be utilized globally for mineralization detection strategies.

Multifunctional membrane technology has gained tremendous attention in wastewater treatment, including oil/water separation and photocatalytic activity. In the present study, a multifunctional composite nanofiber membrane is capable of removing dyes and separating oil from wastewater, as well as having antibacterial activity. The composite nanofiber membrane is composed of cellulose acetate (CA) filled with zinc oxide nanoparticles (ZnO NPs) in a polymer matrix and dipped into a solution of titanium dioxide nanoparticles (TiO2 NPs). Membrane characterization was performed using transmission electron microscopy (TEM), field emission scanning electron microscopy (FESEM), and Fourier transform infrared (FTIR), and water contact angle (WCA) studies were utilized to evaluate the introduced membranes. Results showed that membranes have adequate wettability for the separation process and antibacterial activity, which is beneficial for water disinfection from living organisms. A remarkable result of the membranes’ analysis was that methylene blue (MB) dye removal occurred through the photocatalysis process with an efficiency of ~20%. Additionally, it exhibits a high separation efficiency of 45% for removing oil from a mixture of oil–water and water flux of 20.7 L.m−2 h−1 after 1 h. The developed membranes have multifunctional properties and are expected to provide numerous merits for treating complex wastewater.