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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 article introduces a team-based model of researchers in a specialty and investigates the manifestation of such teams in a specialty's literature. The proposed qualitative behavioral model, with its mathematical expression as a growth model, is significant because it simultaneously describes the two phenomena of collaboration and author productivity (Lotka's law) in a specialty. The model is nested: A team process models the creation of research teams and the success-breeds-success process of their production of articles, while at a lower level the productivity of authors within teams is also modeled as a success-breeds-success process. Interteam collaboration (weak ties) is modeled as random events. This simple growth model is shown to faithfully mimic six network metrics of bipartite article-author networks. The model is demonstrated on three example article collections from specialties that have a wide range of degree of collaboration: (a) a distance education collection with low collaboration degree, (b) a complex networks collection with typical collaboration degree, and (c) an atrial ablation collection with heavy collaboration degree. [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 deals with the existence of weak solutions of the system that describes the two‐phase two‐component fluid flow in porous media. Both two‐phase and possible one‐phase flow regions are taken into account. Our research is based on a global pressure, an artificial variable that allows us to partially decouple the original equations. As a second primary unknown for the system, we choose the gas pseudo‐pressure, a persistent variable which coincides with the gas pressure in the two‐phase regions while it does not have physical meaning in one‐phase flow regions, when only the liquid phase is present. This allows us to introduce an another persistent variable that is an artificial variable in one‐phase flow regions and a physical variable in two‐phase flow regions—the capillary pseudopressure. We rewrite the system's equations in a fully equivalent form in terms of the global pressure and the gas‐pseudo pressure. In order to prove the existence of weak solutions of obtained system, we also use the capillary pseudo‐pressure. By using it, we can decouple obtained equations on the discrete level. This allows us to derive the existence result for weak solutions in more tractable way. [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 purpose of the present note is to point out mathematical mistakes in some published papers on boundary value problems to prevent usage of mistaken results and methods by mathematicians. Copyright © 2013 John Wiley & Sons, Ltd. [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]

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]

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 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]

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 selective classified bibliography of symbolic computation in some areas of chemistry is provided together with some examples of computer algebra algorithms and techniques to facilitate future joint work of chemists and computer scientists. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004 [ABSTRACT FROM AUTHOR]

It is a privilege to have the chance of congratulating Professor Efron first on this wise paper, then on the richly merited International Prize, the award of which the paper commemorates, but above all on the whole body of his deeply impressive, wide-ranging contributions to our subject. One of the great masterpieces of our field, largely unread nowadays, is M.S. Bartlett's (1958) I Introduction to stochastic processes and their application i and Bartlett's influence on statistical development, at least in UK, was second only to Fisher's. Professor Efron in his theoretical papers manages with great skill and panache to combine careful mathematical discussion with judicious statistical emphasis. [Extracted from the article]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

Summary: Non‐orthogonal multiple‐access (NOMA) scheme using massive multiple‐input multiple‐output (MIMO) transmission suffers from interference between users. In this paper, we propose a novel MIMO‐NOMA framework based on space–time block code (STBC) to decrease the multiple‐access interference (MAI), when the number of users is increasing. In this paper, besides giving an analysis of network, cluster, group, and users, we first present the system model. Then, an efficient precoder and detector are designed based on interference analysis. In particular, the proposed scheme can decompose a massive MIMO‐NOMA system into multiple separated single‐input single‐output NOMA channels. Also, analytical results are developed to evaluate the performance of the system. To address the dramatic increment of power level, with the aid of the proposed algorithm, the optimal solution is achieved. Mathematical analyses for both MIMO‐NOMA and STBC are presented to design efficient precoding and detection. Finally, simulation results, based on STBC, are provided to verify the theoretical analysis to demonstrate significant capacity improvements of the massive MIMO‐NOMA. [ABSTRACT FROM AUTHOR]

This paper examines the effects of treatment on tumor‐immune dynamics based on a conceptual two‐dimensional model. In absence of treatment, this model exhibits regimes of "active" and "dormant" tumor. Increasing intensity of chemotherapy entails a significant complication of tumor‐immune interaction with parameter zones of monostability, bistability, and tristability where "active," "dormant," and "zero" tumor states can coexist. A detailed description of bifurcations, attractors, and their basins is given. Based on this mathematical analysis, we discuss efficiency of various programs of treatment combining chemotherapy and radiotherapy. [ABSTRACT FROM AUTHOR]

This paper provides several contributions to the mathematical analysis of subwavelength resonances in a high‐contrast medium containing N$N$ acoustic obstacles. Our approach is based on an exact decomposition formula which reduces the solution of the sound scattering problem to that of an N$N$ dimensional linear system, and characterizes resonant frequencies as the solutions to an N$N$‐dimensional nonlinear eigenvalue problem. Under a simplicity assumptions on the eigenvalues of the capacitance matrix, we prove the analyticity of the scattering resonances with respect to the square root of the contrast parameter, and we provide a deterministic algorithm allowing to compute all terms of the corresponding Puiseux series. We then establish a nonlinear modal decomposition formula for the scattered field as well as point scatterer approximations for the far‐field pattern of the sound wave scattered by N$N$ bodies. As a prerequisite to our analysis, a first part of the work establishes various novel results about the capacitance matrix and its symmetry properties, since qualitative properties of the resonances, such as the leading order of the scattering frequencies or of the corresponding far‐field pattern are closely related to its spectral decomposition. [ABSTRACT FROM AUTHOR]

Bifurcation theory has been highly popular in the analysis of mathematical models. However, stability and bifurcation analyses are only for asymptotic dynamics while applied scientists care more about transient dynamics. In this paper, we first rigorously analyze Holling–Tanner model with generalist predators who have alternative food sources, and then discuss transient dynamics via a changing environment. For a constant environment, we provide a complete bifurcation analysis with high codimension. It is shown that the highest codimension of a nilpotent cusp is 3, and the model can undergo degenerate Bogdanov–Takens bifurcation of codimension 3. Moreover, by using resultant elimination to solve the semialgebraic varieties of Lyapunov coefficients, we show that a center‐type equilibrium is a weak focus with order at most 2, and the model can exhibit Hopf bifurcation of codimension 2. Our results indicate that generalist predators can cause not only richer dynamics and bifurcations, but also the extinction of prey for some positive initial densities. Numerical simulations, including the coexistence of a limit cycle and a homoclinic cycle, tristability, two limit cycles, are presented to illustrate the theoretical results. In a changing environment, the populations start along one stable state but can track unstable states or oscillations when the system crosses a bifurcation point, and then tend to another stable state or oscillations. This tracking on transient dynamics predicts regime shifts under environmental changes. When environmental conditions vary, the populations can track unstable states in the constant environment. The rate of environmental change determines how long the system tracks an unstable state although finally the solution under environmental change is attracted to a stable steady state or limit cycle. Finally, we focus on a periodic environment and find that the populations converge to a periodic solution or an invariant torus depending on both the initial environmental capacity and the amplitude of periodic fluctuation. [ABSTRACT FROM AUTHOR]

Summary: Information‐centric network (ICN) emphasizes on content retrieval without much bothering about the location of its actual producer. This novel networking paradigm makes content retrieval faster and less expensive by shifting data provisioning into content holder rather than content owner. Caching is the feature of ICN that makes content serving possible from any intermediate device. An efficient caching is one of the primary requirements for effective deployment of ICN. In this paper, a caching approach with balanced content distribution among network devices is proposed. The selection of contents to be cached is determined through universal and computed using Zipf's law. The dynamic change in popularity of contents is also considered to take make caching decisions. For balancing the cached content across the network, every router keeps track of its neighbor's cache status. Three parameters, the proportionate distance of the router from the client (pd), the router congestion (rc), and the cache status (cs), are contemplated to select a router for caching contents. The new caching approach is evaluated in the simulated environment using ndnSIM‐2.0. Three state‐of‐the‐art approaches, Leave Copy Everywhere (LCE), centrality measures‐based algorithm (CMBA), and a probability‐based caching (probCache), are considered for comparison. The proposed method of caching shows the better performance compared to the other three protocols used in the comparison. [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]

In this paper, a new configuration of Marx generator with high‐voltage (HV) gain is presented for electroporation applications. Each module consists of one switch, one capacitor, and two diodes. The capacitors are charged in parallel with the input inductor and the input DC voltage source simultaneously; eventually, the charged capacitors are connected in series, and the HV output pulses are generated. The load is connected differently at the output stage, and there is not any switch at the output stage to generate the HV pulses. The majority of Marx generators suffer from the high number of modules to reach the desired pulse peak voltage. Due to the high‐voltage gain of the proposed topology, fewer modules are needed to achieve the desired HV pulse peak voltage. Mathematical analysis is presented along with a full design of the system components. Soft switching reduces the switching power loss in this converter, which is presented in detail. A comparative study is carried out to demonstrate the advantages of the proposed structure. Finally, simulation and experimental results are presented to validate the proposed concept. [ABSTRACT FROM AUTHOR]