Method Of Successive Approximations Research Articles

On weighted sum‐rate maximization of full‐duplex systems in presence of STAR‐RIS

AbstractReflecting intelligent surface (RIS) is one of the key enabling technologies for beyond fifth generation wireless networks to further improve coverage, spectral‐ and energy‐efficiency of wireless networks. Recently, a novel simultaneous transmission and reflection RIS (STAR‐RIS) technology is introduced which enables more degrees‐of‐freedom in simultaneously serving users in reflection and transmission regions of RIS. This paper investigates a STAR‐RIS assisted two‐user full‐duplex communication system, wherein multi‐antenna base station (BS) and single‐antenna users are subject to maximum power constraints. Firstly, weighted sum rates are computed for three well‐known STAR‐RIS protocols, e.g. energy splitting, mode selection, and time splitting. Then, for each of the cases, weighted sum rate optimization problem is investigated to find optimal resource allocations, i.e. base station's precoding and combining matrices, coefficients of STAR‐RIS, and power allocations. The optimization problem is transferred into multiple convex sub‐problems using equivalent weighted minimum mean‐square‐error forms. Also, by use of the successive convex approximation method, tunable parameters of the STAR‐RIS are optimized. Although the original problem is a non‐convex one, proposed iterative alternating technique achieves an acceptable sub‐optimal performance. Finally, performance of the system is analysed and compared to some baselines to highlight superiority of the STAR‐RIS compared to the conventional RIS schemes.

Mathematical Evaluation and Dynamic Transmissions of a Tumor Growth Model Using a Generalized Singular and Non-Local Kernel

Currently, fractional calculus plays a critical role in improving control techniques, analyzing disease transmission dynamics, and solving several other real-world problems. This research investigates the time-fractional tumor growth model using an innovative approach. The new modified fractional derivative operator employs a singular and non-local kernel, based on Atangana and Baleanu's concepts with the Caputo derivative. The tumor growth model used the newly modified fractional operator, which provided numerical simulation. With the introduction of this new operator, we provide significant analysis for the tumor growth epidemic model. We have proven the uniqueness and stability conditions of the model by utilizing Banach's fixed point theory and the Picard successive approximation method. Using the Laplace-Adomian decomposition method (LADM), we found the numerical solution to the Modified Atangana-Baleanu-Caputo derivative model. We have verified the convergence analysis of the suggested scheme. We ultimately utilize the suggested method to obtain numeric outcomes and simulations for the tumor growth model. The study investigates the effect of multiple biological variables on the transmission of tumor growth dynamics.

Cauchy Type Nonlinear Inverse Problem in a Two-Layer Cylindrical Area

Various types of protective coatings, such as ceramics, are used to increase the efficiency of metal parts that are exposed to high heat loads. Maintaining mechanical properties and acceptable thermal stresses requires temperature control for components such as turbine blades, gun barrels or combustion chambers. This paper presents a new method for controlling thermal parameters by solving a non-stationary Cauchy problem for the heat conduction equation. The solution is presented in a cylindrical two-layer area considering the variation of the thermophysical parameters of the metal and ceramic. The non-linear equation was solved by successive approximation method using differential quotients for the space and time variable. In order to regularize the ill-conditioned inverse problem, a quasi-regularization method was applied by performing an energy balance for the ceramic. Numerical calculations were carried out for different thicknesses of the ceramic layer. The temperature, heat flux density and heat transfer coefficient for the protective layer were calculated. For the same values of the heat transfer coefficient for 0.1 and 0.3 mm thick protective layers, the difference in permissible gas temperature differs by 10.5 °C.

A Semi-Analytical numerical non-stationary creep analysis of a rotating disk made of Polyamid66 under mechanical and thermal loads

A semi-analytical numerical non-stationary creep analysis of constant and variable thickness rotating disks made of polyamide 66 under mechanical and thermal loads is presented using Mendelson’s method of successive approximation. The material properties are time, temperature, and stress-dependent, which vary along the disk’s radius due to effective stress variation and temperature distribution and are represented by Burger’s model. A non-homogeneous differential equation in terms of radial displacement with variable and time-dependent coefficients was established using equilibrium, strain-displacement, and stress-strain relations. First, the initial thermo-elastic stresses at zero time were calculated using the Galerkin method and Hermitian elements. The history of stresses and strains was then calculated using Burger’s viscoelastic model and Prandtl-Reuss relations. To validate the results, an analysis of a disk with constant thickness made of PVDF material was also carried out using the same method employed in this study. Very good agreement of the results was observed in both elastic and creep conditions. Creep analysis was performed for PA66 disks of constant and variable thickness conditions, and the results were compared together. It has been found that the radial displacements and effective stresses are increasing with time for both disks. However, effective stresses and radial displacements of variable-thickness disks are much lower than constant-thickness disks.

Robust Multi-UAV Cooperative Trajectory Planning and Power Control for Reliable Communication in the Presence of Uncertain Jammers

Unmanned aerial vehicles (UAVs) have become a promising application for future communication and spectrum awareness due to their favorable features such as low cost, high mobility, and ease of deployment. Nevertheless, the jamming resistance appears to be a new challenge in multi-UAV cooperative communication scenarios. This paper focuses on designing trajectory planning and power allocation for efficient control and reliable communication in a ground control unit (GCU)-controlled UAV network, where the GCU coordinates multi-UAV systems to execute tasks amidst multiple jammers with imperfect location and power information. Specifically, this paper formulates a nonconvex semi-infinite optimization problem to maximize the average worst-case signal-to-interference-plus-noise ratio (SINR) among multiple UAVs by designing robust flight paths and power control strategy under stringent energy and mobility constraints. To efficiently address this issue, this paper proposes a powerful iterative algorithm utilizing the S-procedure and the successive convex approximation (SCA) method. Extensive simulations validate the effectiveness of the proposed strategy.

Determination of reduced density matrices in the doubly occupied configuration interaction space: A Hellmann-Feynman theorem approach.

In this work, the Hellmann-Feynman theorem is extended within the doubly occupied configuration interaction space to enable practical calculations of reduced density matrices and expected values. This approach is straightforward, employing finite energy differences, yet remains reliable and accurate even with approximate energies from successive approximation methods. The method's validity is rigorously tested against the Richardson-Gaudin-Kitaev and reduced Bardeen-Cooper-Schrieffer models using approximate excitation energies procured from the Hermitian operator method within the same space, effectively proving the approach's reliability with median error rates for reduced density matrix calculations around 0.1%. These results highlight the procedure's potential as a practical tool for computing reduced density matrices and expected values, particularly valuable as an ad hoc method in scenarios where only system energies are easily available.

Контактная задача для трансверсально изотропного слоя с трением

It is investigated the spatial contact problem of asymmetric interaction of two punches on a transversally isotropic layer with friction forces taken into account in an unknown contact domain. The planes of isotropy are parallel to the layer faces. The friction forces are taken into account along one coordinate axis. The lower layer face is subjected to sliding support. The layer material is characterized by five independent elastic parameters. The problem is reduced to an integral equation with respect to the contact pressure with the help of a double Fourier transformation together with the Coulomb law. The anisotropy degree is characterized be three dimensionless parameters arising in the kernel of the integral equation, two of which satisfy characteristic equation. In particular cases, the integral equation coincides with those well-known for the corresponding contact problems with friction for the isotropic layer and half-space. The B.A. Galanov method is used for numerical solutions. A system of the integral equation and integral inequality is considered. A rectangle is taken which a priori contains the unknown contact domain. By introducing special nonlinear operators, the system is reduced to only one nonlinear equation of the Hammerstein type which can be solved by the successive approximations method. The contact domain is determined by nodes at which the function required is positive. The punches are taken in the form of asymmetric elliptic paraboloids. The method allows us to investigate percolation, i.e. the process of junction of the discrete contact domains due to increasing the forces applied and settlements of the punches. Calculations are made for different friction coefficients, materials and relative thicknesses of the transversally isotropic layer.

Correlation functions of weakly inhomogeneous plasma

This article focuses on the kinetic theory of inhomogeneous plasma and explores the interaction between a high-frequency electric field and weakly inhomogeneous plasma. Particularly, it examines the impact of an external variable field on the kinetic and high-frequency properties of the plasma, including kinetic equations, correlation functions, and distribution functions of charged particles. The study derives expressions for the pair (two-particle) correlation function and the corresponding distribution function, taking into ac- count the spatial inhomogeneity of the plasma and electric field, as well as the collisions between charged particles. The results were obtained using the kinetic equation for the spatial-temporal spectral density of fluctuations and the method of successive approximations (separation of slow motions and fast oscillations). The field amplitude is considered a slowly varying function of time and coordinates. The calculations neglect the contribution of the magnetic component of the electromagnetic field, which is applicable to longitudinal electric fields. The results obtained in this article are primarily of theoretical interest, they reveal the picture of the interaction of a weakly inhomogeneous plasma with a high-frequency electric field and can be used in the construction of a kinetic theory of an inhomogeneous plasma located in high-frequency electromagnetic fields. Note that for charged particles of the same sign, the correlation function is negative, and for particles of different signs it is positive. In addition, the correlation function is exponentially small when the distance between the particles is greater than the Debye radius. In all calculations, the contribution of the magnetic component of the electromagnetic field is neglected, which is quite true for the longitudinal electric field.

ВЛИЯНИЕ ТОЧЕК ПОВОРОТА НА ЗАДЕРЖКУ РЕШЕНИЯ ВБЛИЗИ НЕУСТОЙЧИВОГО ПОЛОЖЕНИЯ РАВНОВЕСИЯ

This paper considers a system of equations consisting of three first-order equations of fast variables and one equation of a slow variable. The first approximation matrix of the system of fast variables has different eigenvalues, with one pair of complex conjugates. The eigenvalues have zeros and they are turning points. The system has an equilibrium position, and the stability of the equilibrium position is lost at a certain value of the slow variable. The problem is set to study the delay in solving a system of fast variables near an unstable equilibrium position and the influence of turning points on the delay. The delay of the solution near an unstable position is proven and the influence of turning points is clarified. The proof used geometric constructions using the level line of harmonic functions, methods of successive approximations, Laplace, stationary phase, integration by parts and comparison of infinitesimals.

Optimal planning of photovoltaic and distribution static compensators in medium-voltage networks via the GNDO approach

This research employs the generalized normal distribution optimizer (GNDO) to address the simultaneous integration of solar photovoltaic (PV) sources and distribution static compensators (D-STATCOMs) in medium-voltage distribution networks. Through a discrete-continuous codification process, the GNDO method determines the optimal locations (nodes) and capacities (sizes) of PV systems and D-STATCOMs. A power flow approach based on the successive approximations method is used to solve the power flow equations and assess the solution's technical characteristics, including voltage profiles and power injections. Using a master-slave optimization strategy, the GNDO and the power flow method are used to address the studied problem. Numerical results in the 33- and 69-bus grids demonstrate the effectiveness of the proposed approach, showing superior performance compared to the vortex search algorithm (VSA) and the sine-cosine algorithm (SCA). The results indicate reductions of approximately 35.5554% and 35.6839% when using the GNDO in both test feeders. Additionally, the GNDO reduces the computational efforts required to find solutions in both test feeders, in comparison with the VSA and the SCA. All numerical validations were performed using MATLAB 2024a.

Modeling of moisture content during baking with different approaches for effective diffusivity and evaluation of quality variables in baked potato slices.

Baking is a healthier alternative to frying, since texture, color, smell, and flavor are developed, without adding oil. The objective was to estimate the moisture content in potato slices, during baking using Fick's law of diffusion to model internal moisture transport and to assess the impact on quality attributes. Moisture transport kinetics were examined at three baking temperatures of 120, 130, and 140°C. Fick's law was employed to estimate average moisture content using different methods: considering both a constant (method of slopes by subperiods, MSS; and method of successive approximations, MSA) and a variable (represented as a quadratic function of time, QFT) behavior of effective diffusivity (De). Three quality variables were analyzed: water activity (aw, dew point hygrometry), total color difference (∆E, colorimetry), and fracturability (F, universal testing machine). The diffusivity estimated with the time-varying De method provided a more realistic description of moisture migration during baking. The aw, ∆E, and F for baked potato slices ranged from 0.234 to 0.276, 17.9 to 24.6, and 5.20 to 5.49 N, respectively. These attributes imply improved stability and extended shelf life, showing typical colors and texture changes for baked snacks. These changes are linked to variations in diffusivity, influenced by the size and quantity of micropores within the food structure. This study could allow an accurate prediction of mass transfer by considering variable De, facilitating the optimization of baking conditions. PRACTICAL APPLICATION: The analysis of the moisture content using Fick's law, considering a time-varying diffusivity, enables the optimization of the baking process for foods. This helps minimize the occurrence of defective products.

Energy efficiency optimization for 6G multi-IRS multi-cell NOMA vehicle-to-infrastructure communication networks

Intelligent Reflecting Surfaces (IRS), software-controlled metasurfaces, have emerged as an upcoming sixth-generation (6G) wireless communication technology. IRS intelligently manipulates and optimizes signal propagation using a large-scale array of intelligent elements, enhancing signal coverage, increasing capacity, mitigating path loss, and combating multipath fading This work provides a new energy-efficiency model for multi-IRS-assisted multi-cell non-orthogonal multiple access (NOMA) vehicular to infrastructure communication networks. The objective is the joint optimization of the total power budget at the roadside unit (RSU), NOMA power allocation for the user equipment, and designing phase shifts for IRS in each cell to maximize the achievable energy efficiency of the system. Due to non-convexity, the original non-convex problem is first decoupled and transformed using block coordinate descent and successive convex approximation methods. Then, an efficient solution is achieved using Gradient-based and interior-point methods. We also consider two benchmark schemes: (1) NOMA power optimization at RSU with random phase shift design at IRS and (2) orthogonal multiple access power allocation with optimal phase shift design at IRS. Numerical results show the superiority of the proposed solution compared to the benchmark schemes. The proposed solution outperforms the benchmarks, demonstrating a 59.57% and 151.21% improvement over the NOMA and orthogonal schemes, respectively, at pct=2 dBm. Additionally, it shows up to a 10.43% better performance than OMA at 10 IRS elements.

Resonant solutions of the non-linear Schrödinger equation with periodic potential *

The goal is construction of stationary solutions close to non-trivial combinations of two plane waves at high energies for a periodic non-linear Schrödinger Equation in dimension two. The corresponding isoenergetic surface is described for any sufficiently large energy k 2. It is shown that the isoenergetic surface corresponding to k 2 is essentially different from that for the zero potential even for small potentials. We use a combination of the perturbative results obtained earlier for the linear case and a method of successive approximation.

Expanding the Areas of Attraction of Solutions to Singularly Perturbed Equations

In this paper, a singularly perturbed equation of the first order is considered, the concept of a region of attraction (DO) of the solution of a singularly perturbed equation to the solution of an unperturbed equation is introduced, and the existence of an OA is proved. The problem has been set about the possibility of expanding the areas of attraction of VCA solutions. It has been proven that if there is a region of attraction, then it can be expanded to the boundary of the region under consideration. In the proof, geometric constructions were used, using the level line of conjugate-harmonic functions, the method of successive approximations and methods of asymptotic estimates.

The method of successive approximations in the problem of trajectory control of observations for a multi-position measuring system with variable topology

Based on the method of successive Krylov-Chernousko approximations, a procedure for the synthesis of trajectory control of observations for a multi-position measuring system with a variable topology is obtained. Particular search procedures are applied sequentially to the trajectories of the corresponding mobile reception points. The method of successive approximations is implemented both with a partial update of the trajectory control law for observations of each of the IFR, and with a partial update of the topology during the transition from one mobile receiving point to another.

Resource Allocation for UAV-RIS-Assisted NOMA-Based URLLC Systems

This work focuses on maximizing the sum rate of ultra-reliable low-latency communication (URLLC) systems by leveraging unmanned aerial vehicle-mounted reconfigurable intelligent surface (UAV-RIS) to provide short packet services for users based on the non-orthogonal multiple access (NOMA) protocol. To optimize the sum rate of system, a joint optimization is performed with respect to the power allocation, UAV position, decoding order, and RIS phase shifts. As the original problem is a non-convex integer optimization problem, it is challenging to obtain the optimal solution. Therefore, approximate solutions are derived using successive convex approximation (SCA), slack variables, and penalty-based methods. The simulation results demonstrate the superiority of the proposed resource allocation algorithm compared with the benchmark algorithm with orthogonal multiple access (OMA) scheme. In addition, this work emphasizes the performance gap between the proposed communication system and the traditional Shannon communication system in terms of throughput and the performance capacity sacrificed to achieve lower latency.

Successive approximation method to solve nonlinear fuzzy Fredholm integral equations using NC rules

Successive approximation method to solve nonlinear fuzzy Fredholm integral equations using NC rules

On the application of some fixed-point techniques to Fredholm integral equations of the second kind

It is known that the global convergence of the method of successive approximations is obtained by means of the Banach contraction principle. In this paper, we study the global convergence of the method by means of a technique that uses auxiliary points and, as a consequence of this study, we obtain fixed-point type results on closed balls. We apply the study to nonlinear Fredholm integral equations of the second kind.

To plasma electrons motion theory in high-frequency fields

The article is dedicated to the kinetic theory of plasma, where the problem of interaction of high-frequency electric fields with weakly non-uniform plasma is investigated using kinetic equations with binary collision integrals for plasma particles. A new methodology for determining the expression of the averaged highfrequency pressure force is proposed based on solving the kinetic equation and using the method of successive approximations (separation of slow motions and fast oscillations) under the limiting conditions. An expression for the averaged quasi-potential force is derived based on the kinetic equation for the electron distribution function in weakly inhomogeneous magnetoactive plasma, taking into account electrons collisions with fixed ions and the presence of a longitudinally inhomogeneous high-frequency electric field using wellknown methods of theoretical and mathematical physics, such as successive approximations, averaging over the effective field oscillation period, and integration over trajectories. The amplitude of the field is a slowly varying function in both time and space coordinates. The obtained expression allows us to estimate the influence of collisions of plasma particles on the Miller force, and under limiting conditions it coincides with the known expressions for the high-frequency pressure force derived from the equation of plasma electrons motion in high-frequency fields. In all calculations, the contribution of the magnetic component of the electromagnetic field is neglected, which is quite justified for the longitudinal electric field.

A multi-objective PSO for DC microgrids: Efficient battery management to minimize energy losses and operating costs

This article addresses the challenge of battery energy management in a Direct Current (DC) Microgrid (MG) with distributed photovoltaic generators working at their highest power point. This study adopted a multi-objective approach whose main goals is to reduce energy losses and operating costs. To mathematically model this problem, we used Multi-Objective Mixed-Integer Nonlinear Programming (MOMINLP) that incorporated two conflicting objective functions that minimize — at the same time — the energy losses and operating costs of DC MGs. To solve this problem, we followed a master–slave approach. Two multi-objective algorithms were used in the master stage: the Multi-Objective Particle Swarm Optimizer (MOPSO) and the Multi-Objective Lion Ant Optimizer (MOALO). The slave stage applied an hourly load flow analysis employing the method of Successive Approximations (SAs). To validate our methodology, the 33-bus test feeder was adapted by incorporating specific data on generated power and electricity demand from a specific region in Colombia. These data (obtained from the local network operator) are projections of electricity demand for an average day in the region under analysis. The methodology was implemented in the MATLAB environment, and each algorithm was run 100 times to assess standard deviations, maximum reductions, average reductions, and processing times. The two algorithms were compared to identify which one exhibited the best performance when they solved the problem examined here. The results proved that the MOPSO was the most effective approach in terms of minimizing operating costs and significantly reducing energy losses compared to the benchmark scenario.