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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]

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]

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]

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]

The article describes a study of the foodborne transmission mechanisms for norovirus. It was undertaken for the U.K. Food Standards Agency and received the System Dynamics Society's 2020 "System Dynamics Applications Award". The article opens with descriptions of norovirus, the organisational context and the aims of the study. The first phase involved the construction of a large, fully formulated SD simulation model which included person‐to‐person mechanisms and, newly built, food‐related mechanisms for norovirus transmission. The group modelling process and the model structure are described. The model's existence demonstrated that enough was known about foodborne mechanisms to create an explicit and carefully documented representation that specialists recognised, understood, and accepted. Additionally, a framework for analysing the model's parameters—some currently unknown—helped organise FSA thinking on future research and potential policy levers. A second phase used mathematical analysis of a simplified SD model to assess the relative scale of the foodborne effects. In terms of contributions, this generated insights into possible sources of seasonality and insights into whether the most effective leverage points in the system lay solely within the remit of the FSA or were also within the remits of other government departments. The article closes by summarising the findings and then exploring their policy implications and recording the client's reactions to them. © 2022 The Authors. System Dynamics Review published by John Wiley & Sons Ltd on behalf of System Dynamics Society. [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]

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 paper is concerned with the well‐posedness of a diffusion–reaction system for a susceptible‐exposed‐infected‐recovered (SEIR) mathematical model. This model is written in terms of four nonlinear partial differential equations with nonlinear diffusions, depending on the total amount of the SEIR populations. The model aims at describing the spatio‐temporal spread of the COVID‐19 pandemic and is a variation of the one recently introduced, discussed, and tested in a paper by Viguerie et al (2020). Here, we deal with the mathematical analysis of the resulting Cauchy–Neumann problem: The existence of solutions is proved in a rather general setting, and a suitable time discretization procedure is employed. It is worth mentioning that the uniform boundedness of the discrete solution is shown by carefully exploiting the structure of the system. Uniform estimates and passage to the limit with respect to the time step allow to complete the existence proof. Then, two uniqueness theorems are offered, one in the case of a constant diffusion coefficient and the other for more regular data, in combination with a regularity result for the solutions. [ABSTRACT FROM AUTHOR]

In the paper "The non‐Riemannian nature of perceptual color space," the authors analyze the data of visual experiments conducted using triad of CIE L* achromatic stimuli. The statistical analysis of their results leads them to claim that the L* axis cannot be endowed with a Riemannian metric coherent with observers' responses. In this communication we provide a mathematical analysis which, in our opinion, refutes the main claim of the quoted paper. Furthermore, we raise questions on the soundness of using an achromatic perceptual coordinate to describe non‐chromatic perception. We inform about an alternative in which achromaticity emerges from the very act of observing colors (Provenzi E. SIAM J Imag Sci, 15(4):1944–1976, 2022; Berthier M, Provenzi E. Proc R Soc A, 478(2258):20210508, 2022). [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]

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]

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]

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]

The layer of protection analysis (LOPA) is a ubiquitous part of the workflow for process hazards analysis and engineered safeguard design. LOPA became popular as an extension of process hazards analysis (PHA) techniques like hazard and operability (HAZOP) studies, where a little more formality and quantification were required to help better understand the risk or to provide order‐of‐magnitude design criteria for safeguards. Even so, from its inception LOPA has suffered from limitations that are rooted in the "one‐cause, one‐consequence" paradigm to the analysis that limits the scope. This limitation can result in design errors where engineered safeguards that protect against a consequence with multiple causes can be under‐designed by looking at one cause at a time. Also, safeguards that reduce the magnitude of consequences (i.e., mitigate) instead of preventing loss of containment cannot be addressed at all without ignoring the residual consequence that exists even if the safeguard activates successfully. While some extensions of LOPA that address the issue of multiple causes are commonly used, mitigative safeguards are rarely appropriately addressed and designed using LOPA. Finally, the textual nature of the process also makes results hard to communicate to nonpractitioners. Recent research into unified hazard assessment that combines HAZOP, LOPA, and bow tie analysis has yielded techniques that elegantly address all the limitations of LOPA while also providing a graphical presentation that facilitates result communication. This paper will provide background on how unified hazard assessment yielded the techniques of quantitative bow tie analysis. The paper will also describe in detail how to implement quantitative bow tie analysis along with the mathematical concepts used for quantification of risk for multiple causes and multiple consequences inside a single bow tie diagram. The concepts will be presented using example studies that include mitigative safeguards and multiple cause scenarios. [ABSTRACT FROM AUTHOR]

Cancer caused by malignant tumor is a very common and serious disease which can lead to people towards death. However, sometimes, cancer may be controlled if the cancer cells can be infected and split by particular virus with weak pathogenicity. To give a better understanding on tumor dynamics, in this paper, we deal with a reaction–diffusion tumor model, which comes from the process of tumor therapy with oncolytic virus. Our main objective is to analyze the biological compatibility of uninfected and infected tumor cells. In addition, we are concerned with the long‐time behavior, stability, and a priori estimates for the model. The compatibility conditions show that under certain range of parameters control, the infected tumor cells can coexist with normal tumor cells or be eliminated by oncolytic virus as time goes on; in the elimination case, it implies that the organism's complete recovery is highly possible as a result of the attack of oncolytic virus. An indirect idea in calculating fixed point index is proposed; correspondingly, a new condition on coexistence is presented. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the intrinsic impact of the predator‐taxis coefficient on the formation of spatial patterns in a predator–prey system with prey social behavior subject to Neumann boundary conditions. By treating the predator‐taxis coefficient as a potential critical parameter for Turing bifurcation, we observe that the Turing pattern is fully captured by three distinct critical thresholds. Meanwhile, utilizing weakly nonlinear analysis and the amplitude equation, we establish the direction of Turing bifurcation. Our mathematical analysis reveals that the inclusion of the predator‐taxis coefficient in the predator–prey system may lead to the emergence of either subcritical or supercritical Turing bifurcation. Our numerical experiments confirm the theoretical findings and exhibit various spatial patterns with different values of predator‐taxis coefficients. [ABSTRACT FROM AUTHOR]

The inter‐turn short‐circuit fault of a power transformer has a large current in the winding, which will cause serious heating and deformation of the winding and may threaten the safety of the power transformer. Under this background, this paper proposes a scheme based on open‐delta voltage monitoring and identification of inter‐turn short circuits in power transformers. First, the mathematical modeling and analysis of the principle of inter‐turn short‐circuit monitoring of power transformers are carried out, and the mathematical expression to characterize power transformers with different short‐circuit turns are given. Second, the magnetic field distribution of the power transformer under different short‐circuit conditions, the relationship between the eigenvalue and the number of short‐circuit turns etc. are given. Finally, the experimental study verifies the correctness of the proposed scheme. [ABSTRACT FROM AUTHOR]

The security control problem for a class of unknown nonlinear systems is considered in this paper. For the nonlinear system running in the network environment, the measurement channel is subjected to hybrid attacks. Intermittent denial of service attacks and false data injection attacks are modeled as the hybrid attacks. According to the characteristics of the repetitive system, a resilient iterative learning control (ILC) algorithm under hybrid attacks is devised. Subsequently, the stability of the system is proved by mathematical derivation and theoretical analysis in the sense of mathematical expectation. The theoretical analysis results indicate that the resilient ILC algorithm can ensure the stability of the system, and the tracking error converges with the increased number of iterations. Finally, the validity of the algorithm is illustrated by numerical simulation and mobile robot simulation. [ABSTRACT FROM AUTHOR]

This paper presents a novel approach for generating structured light using a diffractive beam‐shaping element that can generate multiple beams with distinct spatial structures in the focal plane. The element is constructed by restructuring a spiral zone plate with fork gratings, providing a tunable and controllable means for generating structured light. The element can create linear and 2D arrays of various structured beams, including vortices with adjustable charge and vorticity, petallike beams, and ring‐lattice structures. To control the generation of these beams, it introduces several parameters of the fork gratings, enabling tailoring of the beam properties to specific applications. The proposed approach involves significant mathematical analysis, including the derivation of complex equations and expressions to understand the behavior of the proposed element and its impact on the generated beams. It conducts simulations and experiments to validate the mathematical analysis and demonstrate the feasibility of the proposed approach. [ABSTRACT FROM AUTHOR]

The inflammatory phase is an important event in the skin wound healing process. The deposition of granulation tissue in the wound bed and the rebuilding of the vascular network occur as inflammation diminishes. An angiogenic component in the formation of granulation tissue is the secretion of vascular endothelial growth factor, which assists in the chemotaxis, proliferation, and replication of fibroblasts. In this paper, we develop a mathematical model of skin wound healing angiogenic factors based on inflammatory cells (macrophages and neutrophils) and mediators (interleukin 6 and interleukin 10). We highlight the importance of this process in vascular endothelial growth factor release and in the formation of new capillary tips. We used a mathematical model of partial differential equations based on the reaction‐diffusion‐advection equations. In order to calibrate the parameters, we considered an in vivo model composed by four treatments: hydroalcoholic extract and oil‐resin of Copaifera langsdorffii at 10% concentration, collagenase, and Lanette cream. Using the laboratory data for the wound edge, our mathematical model estimated the values of vascular endothelial growth factor concentration, and tips density in the center of the wound with a maximum error of 2.9%, and predicted healing time required for each treatment. The region of viability for the parameters, in the proposed model, was found through numerical simulations from the Interleukin 6 and 10 dysregulation and we obtained that, among the parameters analyzed, the greatest influencer in the dynamics of the system is the one, which represents the production of Interleukin 10 during phagocytosis. [ABSTRACT FROM AUTHOR]

The most common disadvantages of loss of excitation (LOE) impedance relay are its improper operation in the conditions of power system disturbances (PSD) and its long operation time. In this regard, to solve the mentioned problems and as a result improve the accuracy and speed of detecting the LOE events, four key variables including active power (Psg), reactive power (Qsg), load angle (δsg), and terminal voltage (Vsg) are selected, on the basis of an in‐depth theoretical‐ and simulation studies. These variables have been implemented in a precise combinational logic. In the developed LOE detection logic of this paper, the dependent parameters of Vsg and Qsg as well as Psg and δsg parameters are examined simultaneously in an AND logic cluster. If both the defined combinations detect the occurrence of LOE, the generator trip command is issued. Otherwise, the normal operation of the under‐study machine will continue. The results of the performed simulations in MATLAB/Simulink environment (2017b) during the detailed scenarios of LOE and PSD events on the IEEE 39‐bus standard system confirm the efficiency of the outlined LOE protection model. Meanwhile, its superiority from the viewpoints of accuracy, swiftness, and simplicity and cost of implementation are comprehensively compared with the other schemes. [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]

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]

In this paper, an improved time‐domain analytical method for LLC resonant converters is proposed. Unlike traditional time‐domain analytical methods, the resonant current in the dead time is derived by considering the equivalent capacitances of the switching devices and the transformer. The equivalent output capacitance of the primary‐side switch is calculated by using a two‐segment fitting approach. The equivalent capacitance of the transformer is calculated by using the six‐capacitor model. The current increment method is used to calculate the initial value of the magnetizing current and to determine the numerical calculation conditions for the proposed time‐domain expressions. Finally, the dead time ranges for zero‐voltage switching of the converter are derived based on the improved time‐domain method. Experiments were carried out with a 10 kW LLC resonant converter. The lower limit of the dead time calculated with the proposed method is closer to the experimental results than the values of two conventional methods. [ABSTRACT FROM AUTHOR]

The main target of this paper is to present an efficient method to solve a nonlinear free boundary mathematical model of prostate tumor. This model consists of two parabolics, one elliptic and one ordinary differential equations that are coupled together and describe the growth of a prostate tumor. We start our discussion by using the front fixing method to fix the free domain. Then, after employing a nonclassical finite difference and the collocation methods on this model, their stability and convergence are proved analytically. Finally, some numerical results are considered to show the efficiency of the mentioned methods. [ABSTRACT FROM AUTHOR]

This paper concerns the dynamic stability of the steady three‐dimensional (3‐D) wave structure of a planar normal shock front intersecting perpendicularly to a planar solid wall for unsteady potential flows. The stability problem can be formulated as a free boundary problem of a quasi‐linear hyperbolic equation of second order in a dihedral‐space domain between the shock front and the solid wall. The key difficulty is brought by the edge singularity of the space domain, the intersection curve between the shock front and the solid wall. Different from the two‐dimensional (2‐D) case, for which the singular part of the boundary is only a point, it is a curve for the 3‐D case in this paper. This difference brings new difficulties to the mathematical analysis of the stability problem. A modified partial hodograph transformation is introduced such that the extension technique developed for the 2‐D case can be employed to establish the well‐posed theory for the initial‐boundary value problem of the linearized hyperbolic equation of second order in a dihedral‐space domain. Moreover, the extension technique is improved in this paper such that loss of regularity in the a priori estimates on the shock front does not occur. Thus, the classical nonlinear iteration scheme can be constructed to prove the existence of the solution to the stability problem, which shows the dynamic stability of the steady planar normal shock without applying the Nash–Moser iteration method. [ABSTRACT FROM AUTHOR]

Summary: The intrinsic characteristics such as modular structure, filterless operation, and absence of DC‐link capacitor have made the modular multilevel converter (MMC) superior to the conventional multilevel converters. However, the submodule (SM) capacitor voltage balancing is crucial. This paper presents a voltage balance control method for MMC. The proposed method generates 2N + 1 levels (where N is the number of SMs per arm) which halves the step size of output voltage and improves the harmonic performance as compared to N + 1 level generation. It requires only one carrier per phase and no voltage and current measurements are needed for the implementation. Therefore, the proposed method makes the system cost‐effective and reduces the implementation issues related with carrier‐based methods substantially. It also alleviates the non‐uniform charge distribution problem with the phase disposition pulse width modulation (PDPWM) technique. Further, a detailed mathematical analysis is presented which enhances the understanding of balancing algorithm. In addition to this, the circulating current with 2N + 1 modulation is analyzed and a control technique is presented. The proposed voltage balancing method is simulated comprehensively in MATLAB/SIMULINK software and validated by the experimental results obtained from a laboratory prototype. [ABSTRACT FROM AUTHOR]

This paper proposes the prediction method of differential mode noise transmitted to the input power of a single‐phase inverter in a high‐frequency model. A high‐frequency equivalent circuit considering the parasitic impedance is proposed. This paper presents a method to measure the parasitic impedance included in the DC link capacitor and insulated‐gate bipolar transistor (IGBT) using a network analyser and extract the parasitic impedance included in the DC bus plate and PCB using Q3D. A mathematical analysis is proposed by applying the double integral Fourier form to the current noise sources, and a method for obtaining differential‐mode noise by analysing the impedance path is proposed. The switching of IGBT is modelled as the noise current source that reflects the pulse width modulation (PWM) duty change using the double integral Fourier form. The impedance path of differential mode noise transmitted to the input is mathematically analysed. The differential mode noise affecting the input is modelled by multiplying the impedance path and the noise source current. The validity of the proposed high‐frequency equivalent circuit and the mathematical analysis is verified by the less than 5% error in the resonant frequency of the derived differential mode noise voltage and the resonant frequency measured experimentally. [ABSTRACT FROM AUTHOR]

In this paper, a new family of non‐isolated boost dc‐dc converters with high voltage gains is proposed. The proposed boost topologies exhibit very high voltage gains at moderate duty cycles and lower switch voltage/current stresses with reduced component counts. Here, a total of four new non‐isolated boost topologies are proposed using four‐terminal PWM high‐gain switch cells with an inductor‐switch network. Among these four topologies, two converters have identical voltage gain with opposite load voltage polarities and likewise other two exhibit similar nature (i.e., equal but opposite load voltage) but have higher gain than the former topologies. The detailed operating principle, steady‐state analysis, and design methodology are presented for the proposed positive output very high‐gain converter, which can be easily extended to the rest of the topologies. An exhaustive comparison study has been presented for the proposed topologies with the existing step‐up converters to highlight their advantages. Finally, the mathematical analysis, analytical studies, and high boosting feature of the proposed positive output high‐gain boost converter are verified using a 250 W, 50 kHz prototype. The experimental results are presented for different duty cycles with fixed input voltage to verify the efficacy of the proposed structures in terms of higher boosting capability. [ABSTRACT FROM AUTHOR]

This paper is concerned with mathematical analysis for the viscoelastic von Karman equation with memory and time‐varying delay. Based on the existence and uniqueness of the strong solution established by Galerkin method, the finite dimensional global attractor for the system without time‐varying delay has been shown by using the quasi‐stability theory. The difficulties for our desired well‐posedness are the limiting of fourth‐order derivative terms and the von Karman bracket term, which need some delicate estimates to achieve. The key point for the dynamics is to obtain the quasi‐stability for gradient system, which needs the higher regularity of trajectory especially the von Karman bracket. [ABSTRACT FROM AUTHOR]

We introduce, in this paper, a delayed hybrid epidemic model describing the evolution of heroin addiction in a given population. The main objective of our mathematical analysis will be to provide the global behavior of the solutions. To the best of our knowledge, there are no results about the global dynamics of such a model containing both age structure and distributed time delay. We will prove that our model has threshold dynamics in terms of the basic reproduction number R0$$ {R}_0 $$. It will be established that for R0≤1$$ {R}_0\le 1 $$, the addiction‐free equilibrium is globally stable and for R0>1$$ {R}_0>1 $$, the endemic equilibrium is globally stable. The theoretical results are checked numerically. Especially, we focus on the influence of the addiction rate on the population dynamic. [ABSTRACT FROM AUTHOR]

Photonic time stretch is the key enabling technology for a wide variety of instruments with unparalleled single‐shot data acquisition performance at high throughput and continuous operation. These systems have established landmark performance in spectroscopy and imaging including flow‐through microscopy, velocimetry, lidar, and other measurements. The evolution of the original time‐stretch technique into such diverse instruments and applications over the last 25 years has created the need for a unified theoretical framework. This paper represents the first step toward a universal mathematical model for time‐stretch instruments. It shows that the "stretch factor"—the fundamental performance metric—is governed by a single canonical equation in a wide range of seemingly diverse time‐stretch instruments. The paper also provides new insight into the operation of time‐stretch imaging and light scattering systems. The stretch factor is derived for time‐stretch systems that operate in temporal, spatial, angular, and Doppler domains. The analysis and mathematical tools provided here can facilitate understanding and analysis of such systems and help future developments in this field. [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]

The main purpose of this paper is mathematical analysis on time‐periodic flows of electrons and holes in semiconductors. The flows appear in a situation that alternating‐current voltages are applied to devices. In this paper, we study the drift‐diffusion model for semiconductors in a three‐dimensional bounded domain and investigate the existence and stability of time‐periodic solutions. We first derive uniform‐in‐time estimates of time‐global solutions and then prove by the relative entropy method that the difference of any two solutions decays exponentially fast as time tends to infinity. These facts enable us to show the unique existence and global stability of time‐periodic solutions. [ABSTRACT FROM AUTHOR]

In this paper, we investigate novel solutions of fractional‐order option pricing models and their fundamental mathematical analyses. The main novelties of the paper are the analysis of the existence and uniqueness of European‐type option pricing models providing to give fundamental solutions to them and a discussion of the related analyses by considering both the classical and generalized Mittag‐Leffler kernels. In recent years, the generalizations of classical fractional operators have been attracting researchers' interest globally and they also have been needed to describe the dynamics of complex phenomena. In order to carry out the mentioned analyses, we take the Laplace transforms of either classical or generalized fractional operators into account. Moreover, we evaluate the option prices by giving the models' fractional versions and presenting their series solutions. Additionally, we make the error analysis to determine the efficiency and accuracy of the suggested method. As per the results obtained in the paper, it can be seen that the suggested generalized operators and the method constructed with these operators have a high impact on obtaining the numerical solutions to the option pricing problems of fractional order. This paper also points out a good initiative and tool for those who want to take these types of options into account either individually or institutionally. [ABSTRACT FROM AUTHOR]

In this paper, we study an age‐structured reaction‐diffusion‐advection population model. First, we use a non‐densely defined operator to the linear age‐structured reaction‐diffusion‐advection population model in a patchy environment. By spectral analysis, we obtain the asynchronous exponential growth of the population model. Then we consider nonlinear death rate and birth rate, which all depend on the function related to the generalized total population, and we prove the existence of a steady state of the system. Finally, we study the age‐structured reaction‐diffusion‐advection population model in non‐autonomous situations. We give the comparison principle and prove the eventual compactness of semiflow by using integrated semigroup. We also prove the existence of compact attractors under the periodic situation. [ABSTRACT FROM AUTHOR]

This paper presents a diagnostic method of inverter open‐switch and open‐phase faults in multiphase permanent magnet synchronous motor (PMSM) drives. First defined are adequate variables called virtual current vectors. The projection of the zero‐sequence current component on these variables was used to define two simple fault indices. High sensitivity to fault is thus induced but with a good robustness to transient states and variation of machine parameters. The mathematical development of the proposed method is provided and supported by experimental tests conducted on two prototypes of multiphase machines in the laboratory: sinusoidal and bi‐harmonic PMSMs. The experimental results confirm the effectiveness and the robustness of the proposed method and its capability to detect the single and multiple open‐switches and open‐phase faults in the electric drive. [ABSTRACT FROM AUTHOR]

The invention of doubly‐fed induction generator (DFIG) brings the wind energy one step ahead as renewable power generation. But the performance of the grid‐connected DFIGs are greatly affected by grid disturbances as their stator windings are interfaced to the grid directly. Different fault current limiters are capable of improving fault ride through capability during short circuit faults. Nonlinear controller based fault current limiters (FCLs) are superior to deal with the nonlinearity of the power systems. This paper proposes a nonlinear adaptive backstepping controller (ABSC) based capacitive bridge‐type FCL (CBFCL) to enhance the fault ride through capability of a DFIG‐based wind farm connected to a multi‐machine power system. At first, a complete modelling of the CBFCL is derived to understand its behaviour during the normal and fault period more accurately. Then, the ABSC is designed based on that dynamic model, along with the backstepping controller (BSC) and sliding mode controller (SMC) for comparison purpose. Finally, the performance of the ABSC to control the CBFCL has been analysed and verified by comparing with that of the BSC and the sliding mode controller. All the graphical and mathematical analyses favour the ABSC based CBFCL under symmetrical and asymmetrical fault (both temporary and permanent) scenarios. [ABSTRACT FROM AUTHOR]

Integration of doubly‐fed induction generator (DFIG) based wind turbines (WTs), in series‐compensated power grids, may result in a phenomenon known as sub‐synchronous control interaction (SSCI). Indeed, SSCI, created due to interaction between WTs controllers and series‐compensated power grid, may worsen damping of sub‐synchronous resonance (SSR) oscillations. This paper deals with the analytical assessment and mitigation of SSCI phenomenon in series compensated grids comprising of DFIG‐based WTs. In this way, first, theoretical and mathematical expressions and equivalent circuits regarding the SSCI phenomenon and the impacts of the RSC and GSC controls on the SSR oscillations damping are given and then a comprehensive impedance model for the DFIG‐WT at the sub‐synchronous frequency is extracted. Next, the rotor current control is modified, and an efficient approach based on the feedback linearizing technique (FLT), different from approaches presented in the related literature, is presented to mitigate the negative role of the DFIG in SSR frequencies. By mathematical analyses and developing related formula, it is shown that the proposed approach changes the impedance of the rotor circuit to infinity at the SSR frequency. This in turn results in suppression of the SSR oscillations initiated as a result of induction generator effect and SSCI phenomenon. [ABSTRACT FROM AUTHOR]

In this paper, a point‐to‐point iterative learning control strategy for a cascaded multibody high‐speed train (HST) system with model uncertainty and external disturbance is designed to address a specified given desired points tracking problem. The proposed method, which only used desired point information rather than whole trajectory information, is used to improve the multiple‐point tracking accuracy by enjoying the repetitiveness of an HST. A norm‐optimal method is employed in the ILC operating framework to analyze the HST model with parametric uncertainties and external disturbances. Both a rigorous mathematical analysis and detailed simulation results confirm the correctness and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The g‐and‐h family of distributions is a computationally efficient, flexible option to model and simulate non‐normal data. In spite of its popularity, there are several theoretical aspects of these distributions that need special consideration when they are used. In this paper some of these aspects are explored. In particular, through mathematical analysis it is shown that a popular multivariate generalization of the g‐and‐h distribution may result in marginal distributions which are no longer g‐and‐h distributed, that more than one set of (g,h) parameters can correspond to the same values of population skewness and excess kurtosis, and that multivariate generalizations of g‐and‐h distributions available in the literature are special cases of Gaussian copula distributions. A small‐scale simulation is also used to demonstrate how simulation conclusions can change when different (g,h) parameters are used to simulate data, even if they imply the same population values of skewness and excess kurtosis. [ABSTRACT FROM AUTHOR]

The fractional derivative with nonsingular kernel has been widely used to many physical fields which was shown to offer a new insight into the mathematical modeling of natural phenomena. In this paper, we first study the well‐posedness and regularity of the multidimensional variable‐order time‐fractional reaction–diffusion equation with Caputo–Fabrizio fractional derivative and then present and analyze a Galerkin finite element approximation to the proposed model based on the proved smoothing properties of the solutions. To improve the computational efficiency of the variable‐order Caputo–Fabrizio derivative, we approximate the kernel of the fractional derivative by the K‐term truncation of its Taylor expansion at a fixed fractional order to develop a fast evaluation scheme which significantly reduces the memory requirement from O(N) to O(K) and the computational complexity from O(N2) to O(K2N) where N refers to the number of time steps. We accordingly develop a fast Galerkin finite element method to the proposed model. Numerical experiments are carried out to substantiate the theoretical findings and to show the performance of the fast method. [ABSTRACT FROM AUTHOR]

Tyshkovskiy and Panchin have recently published a commentary on our paper in which they outline several "points of disagreement with the Segreto/Deigin hypothesis." As our paper is titled "The genetic structure of SARS‐CoV‐2 does not rule out a laboratory origin," points of disagreement should provide evidence that rules out a laboratory origin. However, Tyshkovskiy and Panchin provide no such evidence and instead attempt to criticize our arguments that highlight aspects of SARS‐CoV‐2 that could be consistent with the lab leak hypothesis. Strikingly, Tyshkovskiy and Panchin's main point of criticism is based on a false premise that we have claimed RaTG13 to be a direct progenitor of SARS‐CoV‐2, and their other points of criticism are either not valid, based on flawed mathematical analysis, or are unrelated to our hypotheses. Thus, the genetic structure of SARS‐CoV‐2 remains consistent with both natural or laboratory origin, which means that both the zoonotic and the lab leak hypothesis need to be investigated equally thoroughly. [ABSTRACT FROM AUTHOR]

Retransmission in optical burst switching networks is a solution to recover data loss by retransmitting the dropped burst. The ingress node temporarily stores a copy of the complete burst and sends it each time it receives a retransmission request from the core node. Some retransmission schemes have been suggested, but uncontrolled retransmission often increases the network load, consumes more bandwidth, and consequently, increases the probability of contention. Controlled retransmission is therefore essential. This paper proposes a new controlled retransmission scheme for loss recovery, where the available bandwidth of wavelength channels and the burst lifetime are referred to as network conditions to determine whether to transmit a dropped burst. A retrial queue‐based analysis model is also constructed to validate the proposed retransmission scheme. The simulation and analysis results show that the controlled retransmission scheme is more efficient than the previously suggested schemes regarding byte loss probability, successful retransmission rate, and network throughput. [ABSTRACT FROM AUTHOR]

This paper presents an analytical modelling technique based on modified winding function and co‐energy analysis, for characterisation of synchronous reluctance machines, in conjunction with a hybrid algorithm for mapping of the machine's operating point on BH curve and the corresponding performance parameters in non‐linear magnetic condition. The model successfully provides the mean torque and the torque profiles of a synchronous reluctance motor as a function of input current and load‐angle in the magnetic linear and non‐linear conditions. The obtained results of this proposed model are compared with finite‐element‐analysis (FEA) based commercial design software Simcentre‐MAGNET. The comparison proves this model's capability to estimate the machine's performance parameters with considerable accuracy from an already established design analysis technique, FEA. The proposed modelling technique requires only a fraction of simulation runtime when compared to other design analysis techniques. Considering the accuracy of this modelling technique and the least requirement of computation resources and simulation time, this model can be used as an initial iterative‐design tool for mass personalised, additively manufactured electrical machines where rapidness of the iterative design analysis tool is of paramount importance. [ABSTRACT FROM AUTHOR]