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This paper introduces a novel topology for a non‐isolated bidirectional multiphase single inductor (BMPSIC) DC–DC converter. The proposed BMPSIC requires only a single inductor, irrespective of the number of arms, and features reduced volume and weight compared to the total magnetics needed for a conventional converter with similar ratings. The proposed BMPSIC advantages include a high DC voltage gain without operating on a large duty cycle, voltage stress on the power switches equal to that at the high‐voltage port, easy implementation, and a lower cost for application at high‐power densities. Furthermore, this topology requires only one current and voltage control loop. This paper thoroughly details the steady‐state operating principles of the inductor current continuous mode. It provides theoretical and mathematical analysis, including a comparative analysis of the proposed BMPSIC against earlier DC–DC converters, highlighting the superior performance and efficiency of the BMPSIC. An 8‐kW laboratory prototype, designed as a proof of concept, has been meticulously developed and tested, showcasing the performance of the converter across a broad range of load variations. The efficiency measured for the rated load exceeded 98.2% at the low‐voltage port of 250 V and the high‐voltage port of 400 V. Additionally, the article features Video S1, which illustrates the functioning of the converter. [ABSTRACT FROM AUTHOR]

Summary: Multilevel inverters are known as essential converters in renewable sources. First, in this paper, a new submodule is presented, and based on it, a new sub‐multilevel inverter is presented. The proposed sub‐multilevel inverter consists of several unidirectional and bidirectional switches and DC voltage sources. Then, the generalized topology, developed in two modular and cascaded modes, is presented to increase production levels. The proposed submodules are connected in series in the modular topology, increasing production levels. The proposed topology to produce the maximum output levels has the minimum number of IGBTs, drivers, DC voltage sources, etc. Mathematical analyses for conduction and switching losses are provided, and mathematical analyses for the number of devices and voltage across the switches are also presented. In addition to the mathematical analysis of losses, the simulation results are also presented. A general comparison of proposed topology components is presented to demonstrate their advantages. This comparison shows that the proposed topology has the minimum number of power electronic devices. In this paper, nearest level modulation is used to control the proposed topology. The simulation and experimental results of the proposed sub‐multilevel verify the performance of the proposed topology. [ABSTRACT FROM AUTHOR]

In this paper, we develop and analyze a mathematical model for spreading malaria, including treatment with transmission‐blocking drugs (TBDs). The paper's main aim is to demonstrate the impact the chosen model for demographic growth has on the disease's transmission and the effect of its treatment with TBDs. We calculate the model's control reproduction number and equilibria and perform a global stability analysis of the disease‐free equilibrium point. The mathematical analysis reveals that, depending on the model's demography, the model can exhibit forward, backward, and even some unconventional types of bifurcation, where disease elimination can occur for both small and large values of the reproduction number. We also conduct a numerical analysis to explore the short‐time behavior of the model. A key finding is that for one type of demographic growth, the population experienced a significantly higher disease burden than the others, and when exposed to high levels of treatment with TBDs, only this population succeeded in effectively eliminating the disease within a reasonable timeframe. [ABSTRACT FROM AUTHOR]

This paper proposes a new hybrid control strategy to solve the problem of bidirectional wide voltage range regulation in CLLC converters. On the (LLC) side (G2V direction), the SSSA control method is employed for voltage boost, combined with bus voltage and burst control to achieve wide voltage regulation. On the (C) side (V2G direction), the SSSA and full/half‐bridge mode switching control are used to achieve V2G direction wide voltage regulation. This hybrid control strategy also enables high conversion efficiency in both directions without the need for additional components to reduce the converter power density. This is particularly suitable for OBC applications with strict requirements for converter volume and weight. A detailed analysis with mathematical derivation, hybrid control strategy, and converter operation principles is introduced in this paper. The following subchapters supplement the converter voltage gain, soft switching implementation conditions, and design considerations. Finally, the feasibility of the proposed control strategy was verified through an experimental prototype with an input voltage ranging from 340 to 430 V to an output voltage ranging from 225 to 450 V and bidirectional rated power of 6.6/3.3 kW. This prototype achieved a maximum conversion efficiency of 97.7% in the G2V direction and 97.1% in the V2G direction. [ABSTRACT FROM AUTHOR]

Summary: This paper studies the finite‐time tracking problem for nonlinear impulsive differential inclusion systems with randomly varying trial lengths. First, we convert the set‐valued mapping in the differential inclusion systems to single‐valued mapping by a Steiner‐type selector. For the tracking problem of random discontinuous output trajectories, this paper defines a piecewise continuous variable by zero‐order holder to correct the tracking error of segmented continuity. Then, we introduce the average operator with forgetting factor to design three novel learning schemes, and establish convergence results by using the mathematical analysis tools such as impulsive Gronwall inequality and λ$$ \lambda $$‐norm. Finally, a numerical example verifies the validity of the theoretical results, and we compare the tracking performance of the output trajectories for different forgetting factors. [ABSTRACT FROM AUTHOR]

This paper presents an analysis of the performance of the Energy Aware Scheduling Algorithm (EASA) in a 5G green communication system. 5G green communication systems rely on EASA to manage resource sharing. The aim of the proposed model is to improve the efficiency and energy consumption of resource sharing in 5G green communication systems. The main objective is to address the challenges of achieving optimal resource utilization and minimizing energy consumption in these systems. To achieve this goal, the study proposes a novel energy‐aware scheduling model that takes into consideration the specific characteristics of 5G green communication systems. This model incorporates intelligent techniques for optimizing resource allocation and scheduling decisions, while also considering energy consumption constraints. The methodology used involves a combination of mathematical analysis and simulation studies. The mathematical analysis is used to formulate the optimization problem and design the scheduling model, while the simulations are used to evaluate its performance in various scenarios. The proposed EASM reached a 91.58% false discovery rate, a 64.33% false omission rate, a 90.62% prevalence threshold, and a 91.23% critical success index. The results demonstrate the effectiveness of the proposed model in terms of reducing energy consumption while maintaining a high level of resource utilization. [ABSTRACT FROM AUTHOR]

Zika is a flavivirus that is transmitted to humans either through the bites of infected Aedes mosquitoes or through sexual transmission. Zika has been associated with congenital anomalies, like microcephalus. We developed and analyzed the fractional‐order Zika virus model in this paper, considering the vector transmission route with human influence. The model consists of four compartments: susceptible individuals are x1(t), infected individuals are x2(t), x3(t) shows susceptible mosquitos, and x4(t) shows the infected mosquitos. The fractional parameter is used to develop the system of complex nonlinear differential equations by using Caputo and Atangana–Baleanu derivative. The stability analysis as well as qualitative analysis of the fractional‐order model has been made and verify the non‐negative unique solution. Finally, numerical simulations of the model with Caputo and Atangana Baleanu are discussed to present the graphical results for different fractional‐order values as well as for the classical model. A comparison has been made to check the accuracy and effectiveness of the developed technique for our obtained results. This investigative research leads to the latest information sector included in the evolution of the Zika virus with the application of fractional analysis in population dynamics. [ABSTRACT FROM AUTHOR]

This paper is concerned with the modeling and mathematical analysis of linear peridynamic model for arbitrary Poisson ratio's material. Based on the fundamental laws of dynamics, we re‐derive the bond‐based peridynamic model for anisotropic materials by relaxing certain assumptions. Through this process, we draw several significant conclusions, such as the relationship between the equivalent strain energy density hypothesis and the convergence of the peridynamic operator to the classical Navier operator. Additionally, the well‐posedness of time‐dependent peridynamic equations of motion is established. Finally, some necessary conditions for the material stability of anisotropic material are given. [ABSTRACT FROM AUTHOR]

About 15 years ago, a paper proposed the first integer linear programming formulation for the constrained two‐dimensional guillotine cutting problem (with unlimited cutting stages). Since then, eight other formulations followed, seven of them in the last four years. This spike of interest gave no opportunity for a comprehensive comparison between the formulations. We review each formulation and compare their empirical results over instance datasets of the literature. We adapt most formulations to allow for piece rotation. The possibility of adaptation was already predicted but not realized by the prior work. The results show the dominance of pseudo‐polynomial formulations until the point instances become intractable by them, while more compact formulations keep achieving good primal solutions. Our study also reveals a mistake in the generation of the T instances, which should have the same optima with or without guillotine cuts. We also propose hybridising a recent formulation with a prior formulation for a restricted version of the problem. The hybridisations show a reduction of about 20% of the branch‐and‐bound time thanks to the symmetries broken by the hybridisation. [ABSTRACT FROM AUTHOR]

The present paper is concerned with a fourth‐order Allen–Cahn model with logarithmic potential and mass source that describes the process of phase separation in two‐component systems accompanied by a flux of material. The existence of a global weak solution is obtained under appropriate hypotheses on the source term. Furthermore, we study its Cahn–Hilliard limit as a small parameter goes to zero. The main difficulty in the mathematical analysis of the model lies in the presence of the source term that leads to the nonconservation of mass, contrary to the original Cahn–Hilliard theory. [ABSTRACT FROM AUTHOR]

This paper explores the dynamics analysis of a human immunodeficiency virus (HIV) model with saturated cytotoxic T lymphocyte (CTL) immune response and Beddington–DeAngelis infection rate. There are two time delays in the model to describe the time needed for infection of cell and CTL immune response generation, respectively. We obtain two thresholds and three possible equilibria from the model. By analyzing the corresponding characteristic equations, we study the stabilities of equilibrium and the effect of delays on CTL immune response. The results indicate that when immune delay is present, the steady state of equilibrium is disrupted and leads to a Hopf bifurcation. Finally, we use sensitivity analyses to show the effect of parameters on thresholds and numerical simulations to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

This paper presents a novel mathematical model for the analysis of laterally loaded floating piles embedded in a homogeneous soil layer of finite thickness. The governing equations of the soil surrounding the pile are established by treating soil as a Tajimi‐type continuum, and their solution yields a closed‐form expression that provides the lateral force developing to resist pile deflection. Accordingly, analytical expressions are obtained for the swaying, swaying‐rocking and rocking pile head stiffness, as well as for pile displacement and rotation along its length. The derived expressions are functions of parameters that have direct physical meaning, such as pile and soil elastic stiffness. As such, they pose as an attractive alternative to numerical methods for the low‐cost calibration of Winkler‐based model empirical parameters associated with small pile deflections. The presentation concludes with a parametric study focused on exploring the sensitivity of pile stiffness and deformations to the main problem parameters, and on highlighting differences in the lateral response of floating and end‐bearing piles. [ABSTRACT FROM AUTHOR]

In this paper, we propose a Leslie–Gower predator–prey model in which the predator can only be captured when its population size exceeds a critical value; the mean growth rate of the prey in the absence of the predator is subject to a semi‐saturation rate that affects its birth curve, and the interaction between the two species is defined by a Holling II predation functional with alternative food for the predator. Since the proposed model is equivalent to a Filippov system, its mathematical analysis leads to a local study of the equilibria in each vector field corresponding to the proposed model, in addition to the study of the stability of its pseudo‐equilibria located on the curve separating the two vector fields. In particular, the model could have between one and three pseudo‐equilibria and at least one limit cycle surrounding one or two inner equilibria, locally unstable points. [ABSTRACT FROM AUTHOR]

In this paper, we proposed several disturbance observer‐based matrix‐weighted consensus algorithms. A new disturbance observer is firstly designed for linear systems with unknown matched or mismatched disturbances representable as the multiplication of a known time‐varying matrix with a unknown constant vector. Under some assumptions on the boundedness and persistent excitation of the regression matrix, the disturbances can be estimated at an exponential rate. Then, a suitable compensation input is provided to compensate the unknown disturbances. Second, disturbance‐observer based consensus algorithms are proposed for matrix‐weighted networks of single‐ and double‐integrators with matched or mismatched disturbances. We show that both matched and mismatched disturbances can be estimated and actively compensated, and the consensus system uniformly globally asymptotically converges to a fixed point in the kernel of the matrix‐weighted Laplacian. Depending on the network connectivity, the system can asymptotically achieve a consensus or a cluster configuration. The disturbance‐observer based consensus design is further extended for a network of higher‐order integrators subjected to disturbances. Finally, simulation results are provided to support the mathematical analysis. [ABSTRACT FROM AUTHOR]

Summary: The modular‐multilevel converter (MMC) faces the problem of second order ripples in the sub‐module DC capacitor voltage during the low frequency operation at the load side. To sort out this problem, this paper demonstrates a three‐phase modified MMC that includes a novel circuit placed between upper and lower arms of each phase, where load is connected through proposed circuit. The aim of the proposed circuit is to reduce the magnitude of the ripples in each sub‐module's DC capacitor voltage; moreover, it also uses a less number of components compared with the conventional circuits. In order to keep the capacitor voltage at its rated value and to prevent the development of common mode voltage, the proposed circuit uses the high frequency‐based power transfer control channel for balancing power between the upper or top and lower or bottom arms. Furthermore, the mathematical analysis, operating principle, and proposed control is explained in detail for the conventional MMC and modified MMC. The simulation results have been obtained for the modified MMC with resistive load by using MATLAB and Simulink. An experimental test results have been verified with simulation results for the modified MMC topology. [ABSTRACT FROM AUTHOR]

Summary: Optical millimeter‐wave generation is a predominant approach for the generation of high‐quality carrier signals for future wireless transmissions. This paper proposes an optical frequency 12‐tupling millimeter‐wave generation scheme using three cascaded‐MZMs assisted by polarization multiplexing for carrier suppression. A three‐stage MZM architecture produces the desired sixth‐order sidebands along with the undesired carrier signal. The proper adjustment of polarization direction and angle of polarization rotation lead to the effective suppression of the undesired optical carrier signal. A comprehensive mathematical analysis has been accomplished to evaluate the system's performance, and the obtained results are also validated through simulation findings. The derived results demonstrate that the proposed system is capable of operating over a broad modulation index range extending from 1.5 to 4.5, thereby relaxing the stringent requirements for a constant modulation index. The proposed system generates high‐purity mm‐wave signals with an OSSR of 62.06 dB and an RFSSR of 54.79 dB at a modulation index of 2.6. Moreover, it is also validated that even if the system parameters like modulation index, polarizer rotation angle, and phase difference among RF driving signals deviate from their ideal values to a certain degree, the system performance remains acceptable. The involvement of polarization technique, omission of wavelength‐dependent devices, and a large modulation index operating range make this methodology readily appealing for implementation in radio‐over‐fiber transmissions. [ABSTRACT FROM AUTHOR]

This special issue of the Journal Mathematical Methods in the Applied Sciences on the topic of Modelling, Analysis, and Applications is devoted to the development of mathematical modelling, analysis, and applications, from theoretical and numerical perspectives, involving different applied sciences and engineering. It collects invited contributions, from selected quality full papers submitted to the International Conference on Mathematical Analysis and Applications in Science and Engineering (ICMA2SC2022). The conference took place in Porto, Portugal in 27–29 June 2022 (https://www.isep.ipp.pt/Page/ViewPage/ICMASC). [ABSTRACT FROM AUTHOR]

Summary: In this paper, a new light‐emitting diode (LED) driver based on full‐bridge series resonant converter (SRC) is presented. In the proposed converter LED, load is placed in between DC source and the input side of the full‐bridge inverter which reduces the rectifier components of the SRC. The proposed converter reduces the number of diodes used for rectification and ensures zero voltage switching of the power switches which improves the efficiency of the converter. LED lamp current is regulated with phase‐shift pulse width modulation (PWM) of full‐bridge. Lamp illumination is controlled with PWM dimming. The operation and mathematical analysis of LED driver is presented. To validate the proposed concept, a 40‐W laboratory prototype is developed. Experimental results are presented. Peak efficiency of 93% is obtained. [ABSTRACT FROM AUTHOR]

In this paper, we measured the electrical potential distribution of surface dielectric barrier discharges (SDBD) caused by alternating voltage in synthetic air and nitrogen using the Pockels effect. It was shown that different potential distributions of filament thickness and length are generated in synthetic air and nitrogen. A filament analysis based on mathematical morphology was performed to quantify the geometric characteristics of the filaments produced in each gas atmosphere. The results show that the discharge filament thickness and the entropy in the filament direction depend on the oxygen ratio and the magnitude of the applied voltage. [ABSTRACT FROM AUTHOR]

This paper presents a mathematical model for the analysis of axially‐loaded end‐bearing piles embedded in a two‐layer elastic soil deposit. The governing equations of the soil layers surrounding the pile are cast by means of a Tajimi‐type continuum formulation, and this allows deriving a closed‐form expression that provides the frictional stresses that develop at the soil‐pile interface. The pile is treated as two virtual one‐dimensional elastic rods, and pile displacements are obtained by solving a system of linear equations that results from considering the boundary and continuity conditions. This results in improved efficiency compared to existing Tajimi‐based solutions for piles in layered soil, at no expense of accuracy. The model is used to study the effect of the relative stiffness of the soil layers on the serviceability behavior of axially‐loaded piles, and drawn conclusions of practical importance. [ABSTRACT FROM AUTHOR]

A mathematical model is presented for the optimisation of an Electromagnetic Halbach Array (EHA) for wireless power transfer. The mathematical model is based on Biot‐Savart's law of magnetic field in a current‐carrying square loop. The model is validated through static electromagnetic simulations in ANSYS Maxwell and found to be accurate and effective when predicting the magnetic field within the EHA box. To verify the analytical and simulation results, an EHA was fabricated, and experimental verification was carried out. The results show that the mathematical model can be widely used in the analysis and design optimisation of EHAs of any size and with diverse parameters in the case of single‐layer square spiral planar coils. [ABSTRACT FROM AUTHOR]

The voltage‐source virtual synchronous generator is a grid‐forming type power electronic control technology and is able to support converters that have the ability of inertial, primary frequency and voltage regulation. Firstly, the authors build the small‐signal model of the voltage‐source virtual synchronous generator and conventional converters, compare and analyse the characteristics of the high‐frequency resonance modes, the results show that the voltage‐source virtual synchronous generator has almost the same high‐frequency resonance characteristics as the conventional converter. Secondly, the different control parameters and power grid strength that affect the high‐frequency resonance characteristic are analysed with eigenvalue, and the mechanism of voltage‐source VSG that caused high‐frequency resonance is derived. The leading factor that causes high‐frequency resonance is power grid strengths, and the authors proposed introducing virtual impedance into the front‐end channel of the current inner loop control strategy to suppress resonance for the voltage‐source virtual synchronous generator based on the theoretical analysis with the small‐signal model and eigenvalue analysis. In addition, the electromagnetic transient simulation model and RT‐LAB controller‐in‐loop platform are built, and the simulation and experiment results indicate the effectiveness of the virtual impedance control strategy. [ABSTRACT FROM AUTHOR]

An approach is presented to employ two different types of converters in bridgeless configuration for supply side power factor enhancement of the system. The isolated single‐stage electric vehicle battery charger uses two different converters in a bridgeless configuration to extract the advantages of both converters for supply‐side power factor enhancement. For the negative and positive semi‐cycles of the supply voltage, the power factor‐enhanced asymmetrical alternating current–direct current converter utilises a fourth order single‐ended primary‐inductor converter and a second order buck‐boost converter, respectively. The use of single‐ended primary‐inductor converter and buck‐boost converter in bridgeless configuration reduces the net order of the system with respect to conventional bridgeless‐single‐ended primary‐inductor converter schemes. The buck‐boost converter also needs the supply‐side filter to eradicate the unwanted harmonics in the supply current which increases the order of the system. The usage of both converters presents many benefits like input inductance of the single‐ended primary‐inductor converter can be utilised as a filtering element with a capacitor for the buck‐boost converter. The anti‐parallel diode conduction operation of both switches facilitates the elimination of extra reverse feed diodes (generally used in bridgeless schemes). The single‐stage charger itself comes with the benefit of elimination of extra stages and thus the losses associated with it. The presented charger also witnesses the elimination of the rectifier due to usage of bridgeless configuration. The isolated single‐stage electric vehicle battery charger is also garnished with electrical isolation which adds to the safety standard of the system. To attain power factor enhancement, the asymmetrical alternating current–direct current converter functions in discontinuous current conduction mode in the present work. The elimination of extra‐stages (with respect to two stage charger), a filter, a rectifier, two extra reverse‐feeding diodes, one voltage sensor, one current sensor (with respect to continuous current conduction mode), and electrical isolation not only makes the system compact and safer but also makes the system cheaper. Elaborated mathematical modelling and stability analysis of the presented alternating current–direct current converter using a pole‐zero map and bode plot have been included in the article. The prototype and MATLAB/Simulink model of isolated single‐stage electric vehicle battery charger system with discontinuous current conduction mode control has been built and results of both prototype and MATLAB/Simulink are deployed to verify isolated single‐stage electric vehicle battery charger system's performance during dynamic and steady‐state conditions. [ABSTRACT FROM AUTHOR]