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This paper derives well-posedness and asymptotic results that provide qualitative information about the behavior, mechanism and strategies used by living organisms to navigate their biological networks. Chemical driven swimming is a captivating phenomenon that is observed in various living organisms like bacteria and protozoa but the problem in weighted networks is more complex, since the equations of parabolic-parabolic Keller-Segel model coupled with incompressible Navier-Stokes equations must be reformulated in a discrete setting. The starting point is to transpose the coupled system from the Euclidean case to the connected networks with certain network-theoretic simplified approaches, which yields fruitful key results. These results not only enable the construction of global solutions but also serve as a foundation for determining information about the stability and large time behavior of the system. Then, decay rates are well established to predict important features, such as how quickly weak solutions at a given point decrease over time due to dissipative processes. Additionally, the L 1 - convergence of cell densities towards the self-similar Gaussian solution of the heat equation is well proved by time dependent scaling, which shows that the solution maintains its shape and only scales in time and space as time evolves. Finally, this paper includes many numerical tests through a recent robust numerical scheme to illustrate the theoretical results and to develop computational control and prediction of living organisms' trajectories around central nodes in networked flows. [ABSTRACT FROM AUTHOR]

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]

In this paper, a mathematical analysis of fractional order fishery model with stage structure for predator is carried out under the background of prey refuge and protected area. First, it is demonstrated that the solution exists and is unique. The paper aims to analyze predator-prey dynamics in a fishery model through the application of fractional derivatives. It is worth emphasizing that we explicitly examine how fractional derivatives affect the dynamics of the model. The existence of each equilibrium point and the stability of the system at the equilibrium point are proved. The theoretical results are proved by numerical simulation. Alternatively, allocate harvesting efforts within an improved model aimed at maximizing economic benefits and ecologically sustainable development. The ideal solution is obtained by applying Pontryagin's optimal control principle. A large number of numerical simulations show that the optimal control scheme can realize the sustainable development of the ecosystem. [ABSTRACT FROM AUTHOR]

In this paper, we present novel advancements in the theory of bicomplex hypergeometric functions and their applications. We extend the hypergeometric function to bicomplex parameters, analyse its convergence region, and define its integral and derivative representations. Furthermore, we delve into the k-Riemann–Liouville fractional integral and derivative within a bicomplex operator, proving several significant theorems. The developed bicomplex hypergeometric functions and bicomplex fractional operators are demonstrated to have practical applications in various fields. This paper also highlights the essential concepts and properties of bicomplex numbers, special functions, and fractional calculus. Our results enhance the overall comprehension and possible applications of bicomplex numbers in mathematical analysis and applied sciences, providing a solid foundation for future research in this field. [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 our paper, we propose a generalized version of the Alternating Projections Digital Hard Successive Interference Cancellation (AP-HSIC) algorithm that is capable of decoding any order of constellation M in an M-Quadrature Amplitude Modulation (QAM) system. Our approach applies to Rayleigh deep-fading Multiple-Input Multiple-Output (MIMO) channels with high-level Additive White Gaussian Noise (AWGN). It can handle various destructive phenomena without restricting the number of antenna arrays in the transmitter/receiver. Importantly, it does not rely on closed-loop MIMO feedback or the need for Channel-State Information Transmission (CSIT). We have demonstrated the effectiveness of our approach and provided a Bit Error Rate (BER) analysis for 16-, 32-, and 64-QAM modulation systems. Real-time simulations showcase the differences and advantages of our proposed algorithm compared to the Multi-Group Space-Time Coding (MGSTC) decoding algorithm and the Lagrange Multipliers Hard Successive Interference Cancellation (LM-HSIC) algorithm, which we have also developed here. Additionally, our paper includes a mathematical analysis of the LM-HSIC algorithm. The AP-HSIC algorithm is not only effective and fast in decoding, including interference cancellation computational feedback, but it can also be integrated with any Linear Processing Complex Orthogonal Design (LPCOD) technique, including Complex Orthogonal Design (COD) schemes such as high-order Orthogonal Space–Time Block Code (OSTBC) with high-order QAM symbols. [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]

Doubly salient permanent magnet machine (DSPMM), which is a branch of stator-Permanent Magnet (PM) machine, is becoming more and more attractive due to higher power density and fault-tolerant capability, better mechanical robustness, simpler rotor configuration, lower PM consumption and higher PM material utilization efficiency. Thus, it has great application potential in the fields of transportation electrification and renewable energy generation. However, due to the special doubly salient structure, PM flux-linkage and inductance have the same variation period, which would complicate the relationship between the current and torque, and bring difficulties in the modeling and control (even after Park's transformation). In order to solve these problems, this paper will develop, analyze and compare the different current waveforms which could theoretically reduce the torque ripple and the transformations which could decouple the model in the rotating stationary frame for a simplified DSPMM model neglecting the higher harmonics. Based on the mathematical analysis, this paper would provide a clear relationship between the current waveforms and the torque with the DSPMM parameters, and the possible transformation which could simplify the model and be used in the control system. [ABSTRACT FROM AUTHOR]

The increasing demand for low voltage, power efficient, high-speed analog-to-digital converters (ADCs) results in the improvement of speed and power of regenerative dynamic comparator. In this paper, a dual-tail dynamic comparator is used with two extra transistors in the latch stage. These extra transistors help in the increase of transconductance of the latch stage, which helps decrease the delay of the proposed comparator. Mathematical analysis is done for the proposed architecture; this gives the idea of reducing the delay of the comparator with an increase in the transconductance of the comparator. The simulation and layout of the proposed comparator are done on the Cadence software with 90 nm CMOS technology. This proposed design is simulated with a 2 GHz clock frequency at supply voltage of 1 V. The proposed architecture consumes a power of 39.19 μ W and a delay of 143.12 ps at 1 V supply voltage, 5 mV input difference voltage and 0.9 V common mode voltage. The Monte Carlo simulation of the proposed architecture for power, delay, power delay product (PDP) and offset is also demonstrated in this paper. Process corner analysis is done for power, delay and PDP. [ABSTRACT FROM AUTHOR]

The history of variational calculus dates back to the late 17th century when Johann Bernoulli presented his famous problem concerning the brachistochrone curve. Since then, variational calculus has developed intensively as many problems in physics and engineering are described by equations from this branch of mathematical analysis. This paper presents two non-classical, distinct methods for solving such problems. The first method is based on the differential transform method (DTM), which seeks an analytical solution in the form of a certain functional series. The second method, on the other hand, is based on the physics-informed neural network (PINN), where artificial intelligence in the form of a neural network is used to solve the differential equation. In addition to describing both methods, this paper also presents numerical examples along with a comparison of the obtained results.Comparingthe two methods, DTM produced marginally more accurate results than PINNs. While PINNs exhibited slightly higher errors, their performance remained commendable. The key strengths of neural networks are their adaptability and ease of implementation. Both approaches discussed in the article are effective for addressing the examined problems. [ABSTRACT FROM AUTHOR]

This paper explores the Apéry-like series and demonstrates the derivation of closed-form expressions using fractional calculus. We consider a variety of Apéry-like functions, which were categorized by their functional forms and coefficients by applying the Riemann–Liouville fractional integral and derivative to examine their properties across various domains. The study focuses on establishing rigorous mathematical frameworks that unveil new insights into the behaviors of these series, contributing to a deeper understanding of number theory and mathematical analysis. Key results include proofs of convergence and divergence within specified intervals and the derivation of closed-form solutions through fractional integration and differentiation. This paper also introduces a method aimed at conjecturing mathematical constants through continued fractions as an application of our results. Finally, we provide the proof of validation for three unproven conjectures of continued fractions obtained from the Ramanujan Machine. [ABSTRACT FROM AUTHOR]

The main contribution of this paper is to present a simple algorithm that theoretically and numerically assesses the switching angles of an inverter operated with the SPWM technique. This technique is the most widely used for eliminating harmonics in DC-AC converters for powering motors, renewable energy applications, household appliances, etc. Unlike conventional implementations of the SPWM technique based on the analog or digital comparison of a sinusoidal signal with a triangular signal, this paper mathematically performs this comparison. It proposes a simple solution to solve the transcendental equations arising from the mathematical analysis numerically. The technique is validated by calculating the total harmonic distortion (THD) of the generated signal theoretically and numerically, and the results indicate that the calculated angles produce the same distribution of harmonics calculated analytically and numerically. The algorithm is limited to single-phase inverters with unipolar SPWM. [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]

The object of research is a vibrating plate with interchangeable working bodies developed by the authors. Vibrating plates are an integral part of small mechanization equipment and are mainly intended for layer-by-layer compaction of various materials, such as sand, gravel, bituminous mixtures, etc. Vibration compaction methods are widely used in the construction of road surfaces and other infrastructure facilities. Self-propelled vibrating slabs are also used effectively in other construction processes such as compaction, trench reinforcement, land work and laying paving slabs. They ensure effective compaction of materials due to vibration. This paper is aimed at determining the optimal equipment for compaction of materials during the construction of small objects. Analyzing the characteristics of the machines that most affect the quality of compaction, it is also necessary to evaluate their influence in specific conditions. Studies show that for each type of material, a special working body should be selected, taking into account the specific conditions and requirements for compaction, to ensure optimal quality of work. The authors seek to consider the selection of vibrating plates and their working bodies that best meet the requirements and needs of compaction of various materials on limited construction sites. The analysis of different types of working bodies for different surfaces helps to improve the compaction process and provides optimal conditions for different types of building materials, taking into account their unique properties. The paper examines the influence of the working body on the processed environment, in particular, analyzes the ability of various factors to influence the quality of material compaction. Special attention is paid to the influence of the geometry and size of the contact area on the sealing efficiency of each material type. Overall, this analysis can significantly improve material compaction strategies in the construction industry, contributing to improved construction quality. [ABSTRACT FROM AUTHOR]

This paper studies internal (or intra-)mathematical explanations, namely those proofs of mathematical theorems that seem to explain the theorem they prove. The goal of the paper is a rigorous analysis of these explanations. This will be done in two steps. First, we will show how to move from informal proofs of mathematical theorems to a formal presentation that involves proof trees, together with a decomposition of their elements; secondly we will show that those mathematical proofs that are regarded as having explanatory power all display an increase of conceptual complexity from the assumptions to the conclusion. [ABSTRACT FROM AUTHOR]

The class of generalized S D D 1 (G S D D 1 ) matrices is a new subclass of H -matrices. In this paper, we focus on the subdirect sum of G S D D 1 matrices, and some sufficient conditions to ensure that the subdirect sum of G S D D 1 matrices with strictly diagonally dominant (S D D) matrices is in the class of G S D D 1 matrices are given. Moreover, corresponding examples are given to illustrate our results. The class of generalized matrices is a new subclass of -matrices. In this paper, we focus on the subdirect sum of matrices, and some sufficient conditions to ensure that the subdirect sum of matrices with strictly diagonally dominant matrices is in the class of matrices are given. Moreover, corresponding examples are given to illustrate our results. [ABSTRACT FROM AUTHOR]

In this two-paper series, we prove the invariance of the Gibbs measure for a threedimensional wave equation with a Hartree nonlinearity. The novelty lies in the singularity of the Gibbs measure with respect to the Gaussian free field. In this paper, we focus on the dynamical aspects of our main result. The local theory is based on a paracontrolled approach, which combines ingredients from dispersive equations, harmonic analysis, and random matrix theory. The main contribution, however, lies in the global theory. We develop a new globalization argument, which addresses the singularity of the Gibbs measure and its consequences. [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]

Today, because infectious diseases have a large impact on people, control methods for all infectious diseases are crucial. In this paper, we propose a SIQR model with Crowley-Martin type incidence rate and saturated treatment. We have incorporated precautionary measures taken by the population through the saturated incidence rate. Screening of individuals who have come into contact with infected individuals is modelled. Thus, we explore a four-dimensional mathematical model to study the dynamics of the infectious diseases and their management. Stability and bifurcation analysis ofthe system is done. The Mensitivity analysis of all parameters in relation to the basic reproduction number has been performed and the theoretical results have been validated using numerical simulation. Mathematical results in this paper suggest that both government interventions and individual efforts must be incorporated to achieve better control of emerging infectious diseases in the population. [ABSTRACT FROM AUTHOR]

This paper first analyzed the shortcomings of the summative final exam methods which focuses only on final exams. Then, we showed the specific implementation of the quantitative formative assessment which includes objective results and subjective scores. Objective results include the traditional written chapter test score, online mid-term and final exam scores, whereas the subjective scores include class attendance, homework, class performance, class notes, online learning on the "Jreenity" platform, chapter mind maps, the completion of ideological and political cases, and the introduction of mathematicians. Finally, the reforming achievement of the formative assessment was summarized. [ABSTRACT FROM AUTHOR]

The Nelson–Siegel and the Svensson models are two widely used models for the term structure of interest rates. These models are quite simple and intuitive, but fitting them to market data is numerically challenging and various difficulties have been reported. In this paper, we provide a novel mathematical analysis of the fitting problem based on parametric optimization. We formulate the fitting problem as a separable nonlinear least-squares problem, in which the linear parameters can be eliminated. We provide a thorough discussion on the conditioning of the inner part of the reformulated problem and show that many of the reported difficulties encountered when solving it are inherent to the problem formulation itself and cannot be tackled by choosing a particular optimization algorithm. Our stability analysis provides novel insights that we use to show that some of the ill-conditioning can be avoided, and that a suitably chosen penalty approach can be used to address the remaining ill-conditioning. Numerical results indicate that this approach has the expected impact while being independent of any choice of a particular optimization algorithm. We further establish smoothness properties of the reduced objective function, putting global optimization methods for the reduced problem on a sound mathematical basis. [ABSTRACT FROM AUTHOR]

Yuan, Shao and Liu proved that the H-shape tree H' n = P 1,n−6 1,2;n−3 minimizes the spectral radius among all graphs with order n ≥ 9 and diameter n−4. In this paper, we achieve the spectral characterization of all graphs in the set H' = {H' n}n ≥ 8. More precisely we show that H'n is determined by its spectrum if and only if n ≠ 8, 9, 12, and detect all cospectral mates of H' 8, H' 9 and H' 12. Divisibility between characteristic polynomials of graphs turns out to be an important tool to reach our goals. [ABSTRACT FROM AUTHOR]

The concept of special functions plays an important role in mathematical analysis and physics as well. In this paper, we study some different types of the special Gamma function defined on the two-fold fuzzy complex field, where we combine the classical Gamma function with the two-fold fuzzy algebra defined on complex numbers. On the other hand, many elementary properties of this new special function will be determined in terms of theorems and proofs. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to address a class of hybrid optimal control problems constrained with hyperelasticity and constant global volume. This type of problems can intervene for example in the mechanical aspects of cardiac activity. The time deformation of the heart tissue is modeled with the elastodynamics equations dealing with the displacement field as main unknown. These equations are coupled with a pressure whose time variations are aimed to be maximized. This pressure variable corresponds to a Lagrange multiplier associated with the so-called global injectivity condition, translating the fact that the total volume of the domain remains constant. We develop an optimal control approach in a general framework that covers in particular the maximization of the variations of this pressure, and also the time the maximum is reached, defining what we call a hybrid optimal control problem. Mathematical analysis based on the $ \mathrm {L}^p $ Lp-parabolic maximal regularity is provided for the state equations and the rigorous derivation of optimality conditions. Numerical simulations for a toy-model illustrate the capacity of the approach. [ABSTRACT FROM AUTHOR]

This paper develops a new frame for non-stationary signal separation, which is a combination of wavelet transform, clustering strategy and local maximum approximation. We provide a rigorous mathematical theoretical analysis and prove that the proposed algorithm can estimate instantaneous frequencies and sub-signal modes from a blind source signal. The error bounds for instantaneous frequency estimation and sub-signal recovery are provided. Numerical experiments on synthetic and real data demonstrate the effectiveness and efficiency of the proposed algorithm. Our method based on wavelet transform can be extended to other time–frequency transforms, which provides a new perspective of time–frequency analysis tools in solving the non-stationary signal separation problem. [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]

In this paper, we study an age-structured population model with non-local diffusion and distributed delay. By using the non-densely defined operators and extended phase spaces, we first rewrite the model into an abstract ordinary differential equation. Then we prove the existence of the solution of the model by using the operator semigroup theory. Finally, we study the spectrum of the non-densely defined operators and analyze the asymptotic behavior via asynchronous exponential growth. Our results extend the results for the age-structured population models without time delay. [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]

It is known that time delays generally make a system unstable. However, it is numerically observed that the diffusion coefficients of the Wiener processes with time-delayed feedback decrease while increasing the time delay τ. In particular, the decay of the diffusion coefficients with the form ( 1 1 + τ ) 2 has been confirmed by numerical simulations [Ando et al., Phys. Rev. E 96, 012148 (2017)]. In this paper, we present two analytical derivations for the relation ( 1 1 + τ ) 2 by dynamical system approaches using the Laplace transform and stochastic differential equations. [ABSTRACT FROM AUTHOR]

This paper investigates Parseval–Goldstein-type relationships in the framework of Lebedev–Skalskaya transforms. The research also examines the continuity properties of these transforms, along with their adjoint counterparts over weighted Lebesgue spaces. Furthermore, the behavior of Lebedev–Skalskaya transforms and their adjoint transforms in the context of weighted Lebesgue spaces is analyzed. This study aims to provide deeper insights into the functional properties and applications of these transforms in mathematical analysis. [ABSTRACT FROM AUTHOR]

A main topic in mass production of machine parts is how to increase the productivity to produce more parts in a given time while maintaining the prescribed surface quality on the machined surfaces. Novel machining procedures have been introduced to achieve this goal; however, the further development of already established and wide-spread procedures can offer simply accessible solutions. Tangential turning is a rediscovered variant of the traditional turning procedure, where a specially designed cutting tool ensures chip removal with a feed tangential to the workpiece. This process results in low surface roughness even at higher feed rates. In this paper, the achievable surface roughness is analyzed by analytical and experimental steps. In the mathematical analysis, the theoretical surface roughness is determined using the constructive geometric modelling method. The worked-out equations are validated in cutting experiments on 42CrMo4 grade steel workpieces. The theoretical and experimental analyses show that the strictly prescribed surface roughness can be achieved with high feed rates by the application of tangential turning. [ABSTRACT FROM AUTHOR]

Nonlinear Kawarada equations have been used to model solid fuel combustion processes in the oil industry. An effective way to approximate solutions of such equations is to take advantage of the finite difference configurations. Traditionally, the nonlinear term of the equation is linearized while the numerical stability of a difference scheme is investigated. This leaves certain ambiguity and uncertainty in the analysis. Based on nonuniform grids generated through a quenching-seeking moving mesh method in space and adaptation in time, this paper introduces a completely new stability analysis of the approximation without freezing the nonlinearity involved. Pointwise orders of convergence are investigated numerically. Simulation experiments are carried out to accompany the mathematical analysis to strengthen our conclusions. [ABSTRACT FROM AUTHOR]

• A chamber model considering pressure distributions of compressors is proposed. • An exhaustive mathematical model and an efficient solution method are provided. • More geometry features and compression mechanisms can be investigated. • Parametric studies are performed using the new model with good trends. Further efficiency improvements of screw compressors rely on computer modeling and mathematical analysis at the design stage. As speed and capacity increase, the uniformity assumption used in the conventional chamber model for twin-screw compressors is no longer suitable. At the same time, CFD simulations are complicated and time-consuming for design optimization. Therefore, in this paper, a chamber model considering pressure distribution is proposed, which is fast enough and more applicable. Each working unit of a screw compressor is considered a one-dimensional compressible transient flow with two moving pistons, which allow the passage of fluid. Numerical methods of the model are verified by a shock wave test. A twin-screw compressor was also simulated and the results of the chamber model were compared with the CFD results. Pressure fluctuations like those in previous experimental studies can be captured in the simulated indicator diagram. General trends with different speeds, suction ports, and wrap angles could also be recognized in the simulation results. The compression process and the influence of structural parameters on the compressor's functioning are revealed intuitively. By combining existing chamber models, the applicability of the new model can be further extended, and it is expected to be a helpful tool for compressor design. [ABSTRACT FROM AUTHOR]

In this paper, we use a previously developed measles model to forecast measles in Turkey for the period 1970–2021. We study the structural identifiability of the model both by hand and using software. By hand, we assume the prevalence and the total population size are given. Using software, we assume the incidence and the total population size are given. The model is structurally identifiable if one of the three parameters is fixed. We notice that Turkey has a significant change in time of the immigration rate and vaccination proportions, so we assume these two quantities are time-dependent. We fit the nonautonomous model to the measles incidences in Turkey for 1970–2021. We perform practical identifiability of the fitted model, and find that all parameters but one are practically identifiable. When fixing the unidentifiable parameter to a value derived from additional data, we obtain that all parameters are practically identifiable. [ABSTRACT FROM AUTHOR]

The growing demand for maintaining secure communication channels with the advancements in digital technologies has led to an intensified interest in designing reliable image encryption schemes. Despite various encryption schemes that have been used, some are considered to have insecurity regarding data transmission and multimedia. Motivated by this concern, this paper proposes a new color image encryption algorithm of a multi-key generation-based nD-Hyperchaotic (HC) system. The new algorithm achieves Shannon’s confusion and diffusion principles using a two S-box generation approach, where the first S-box is generated from the proposed nD-HC system and the resulting sequence is used to increase encryption complexity, while the second S-box is generated from (n + i)D-HC system. Afterward, mathematical analysis is carried out to showcase the robustness and efficiency of the proposed algorithm, as well as its resistance to visual, statistical, differential, and brute-force attacks. The proposed scheme successfully passes all NIST SP 800 suite tests. The cryptographic system demonstrated by the proposed scheme has proven to have outstanding performance through simulation tests, which indicates promising potential applicability aspects in secure and real-time image communication settings. [ABSTRACT FROM AUTHOR]

In the Internet of Things (IoT) era, Mobile Edge Computing (MEC) significantly enhances the efficiency of smart devices but is limited by battery life issues. Wireless Power Transfer (WPT) addresses this issue by providing a stable energy supply. However, effectively managing overall energy consumption remains a critical and under-addressed aspect for ensuring the network's sustainable operation and growth. In this paper, we consider a WPT-MEC network with user cooperation to migrate the double near–far effect for the mobile node (MD) far from the base station. We formulate the problem of maximizing long-term computation rates under a power consumption constraint as a multi-stage stochastic optimization (MSSO) problem. This approach is tailored for a sustainable WPT-MEC network, considering the dynamic and varying MEC network environment, including randomness in task arrivals and fluctuating channels. We introduce a virtual queue to transform the time-average energy constraint into a queue stability problem. Using the Lyapunov optimization technique, we decouple the stochastic optimization problem into a deterministic problem for each time slot, which can be further transformed into a convex problem and solved efficiently. Our proposed algorithm works efficiently online without requiring further system information. Extensive simulation results demonstrate that our proposed algorithm outperforms baseline schemes, achieving approximately 4% enhancement while maintain the queues stability. Rigorous mathematical analysis and experimental results show that our algorithm achieves  O (1 / V) , O (V)  trade-off between computation rate and queue stability. [ABSTRACT FROM AUTHOR]

This study delves into special class of generalized p-trigonometric functions, examining their connection to the established counterparts like p-cosine and p-sine functions. We here explore the new class of functions called the p-versine, p-coversine, p-haversine, and p-hacovercosine, by providing comprehensive definitions and properties. Grounded in the characteristics of p-cosine and p-sine functions, the newly proposed functions offer unique mathematical insights. Our work contributes towards a thorough understanding of these new special functions, showcasing their potential applications in diverse scientific domains, from mathematical analysis to physics and engineering. This paper contributes as a valuable resource for future applied mathematics researchers, engaging with these new mathematical functions, enhancing the ability to model complex patterns from diverse real-world applications. [ABSTRACT FROM AUTHOR]

In this paper, we construct and analyze a mathematically reasonable and simplest population dynamics model based on Mark Granovetter’s idea for the spread of a matter (rumor, innovation, psychological state, etc.) in a population. The model is described by a one-dimensional difference equation. Individual threshold values with respect to the decision-making on the acceptance of a spreading matter are distributed throughout the population ranging from low (easily accepts it) to high (hardly accepts). Mathematical analysis on our model with some general threshold distributions (uniform; monotonically decreasing/increasing; unimodal) shows that a critical value necessarily exists for the initial frequency of acceptors. Only when the initial frequency of acceptors is beyond the critical, the matter eventually spreads over the population. Further, we give the mathematical results on how the equilibrium acceptor frequency depends on the nature of threshold distribution. [ABSTRACT FROM AUTHOR]

Along with the significant growth of applications and facilities provided by the Internet of Things (IoT) in recent years, security challenges and related issues to privacy become considerable interest of researchers. On the other hand, the de facto IoT routing protocol for low-power and lossy networks called RPL is vulnerable to various types of routing attacks. Many researchers have investigated RPL security solutions focusing on effective detection of prevalent and destructive routing attacks such as blackhole attack, selective forwarding attack, rank attack and so on. Recent studies are proposing trust-based mechanisms with the aim of replacing traditional cryptography-based operations with lightweight security models in order to cover the inherent challenges of IoT devices, including energy and computational limitations. Therefore, in this paper, focusing on the problem of RPL vulnerability against well-known routing attacks, we have proposed a trust-based attack detection model, which investigates traffic behavior in different attack scenarios and detects malicious nodes relying on behavior deviation exactly at the same time as the start of any attack activity. Expected behavior is predicted by our learning model trained from the historical routing behavior pattern, using recurrent neural networks as a powerful deep learning method, which leads to attack detection with high-level accuracy and precision. Both mathematical analysis and simulation results on multiple RPL attack scenarios show clearly that the proposed trust-based defense mechanism is an effective approach capable of timely and precisely detection of routing behavior pattern deviation of malicious nodes exactly at the start time of the attack occurrence, which leads to attack detection and attacker identification based on trust scores extracted from the detected fluctuations between expected and real routing behavior patterns. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel protection scheme for N-qubit Greenberger–Horne–Zeilinger (GHZ) states against amplitude damping noise, using unilateral operations. The key innovation lies in the implementation of local operations on a single qubit, irrespective of the total number of qubits, thereby significantly reducing the operational complexity and resource requirements compared to existing methods. The scheme involves a unilateral rotation to transform the GHZ state into a less vulnerable configuration before exposing it to noise, followed by a weak measurement and another unilateral rotation to recover the initial state. We provide a comprehensive mathematical analysis of the proposed unilateral protection scheme, deriving expressions for both fidelity and success probability. The practical feasibility of our scheme is demonstrated through simulations using the Qiskit SDK, in which we provide the corresponding quantum circuit for performing the partial weak measurement used in our scheme. Comparative analysis with pioneer protection schemes reveals a substantial enhancement in success probability and fidelity for both GHZ and generalized GHZ states, emphasizing the superiority of the proposed approach. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel system integrating reconfigurable intelligent surfaces (RISs) with cognitive radio (CR) technology, presenting a forward-looking solution aligned with the evolving standards of 6G and beyond networks. The proposed RIS-assisted CR networks operate with a base station (BS) transmitting signals to two users, the primary user (PU) and secondary user (SU), through direct and reflected signal paths, respectively. Our mathematical analysis focuses on deriving expressions for SU in the RIS-assisted CR system, validated through Monte Carlo simulations. The investigation covers diverse aspects, including the impact of the signal-to-noise ratio (SNR), power allocations, the number of reflected surfaces, and blocklength variations. The results provide nuanced insights into RIS-assisted CR system performance, highlighting its sensitivity to factors like the number of reflectors, fading severity, and correlation coefficient. Careful parameter selection, such as optimizing the configuration of reflectors, is shown to prevent a complete outage, showcasing the system's robustness. Additionally, the work suggests that the optimization of reflectors configuration can significantly enhance overall system performance, and RIS-assisted CR systems outperform reference schemes. This work contributes a thorough analysis of the proposed system, offering valuable insights for efficient performance evaluation and parameter optimization in RIS-assisted CR networks. [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 is devoted to studying constraint minimizers for a class of elliptic equations with two nonlocal terms. Using the methods of constrained variation and energy estimation, we analyze the existence, non-existence, and limit behavior of minimizers for the related minimization problem. Our work extends and enriches the study of bi-nonlocal problems. [ABSTRACT FROM AUTHOR]

This paper was focused on the solvability of a class of doubly critical sub-Laplacian problems on the Carnot group : Here, , , , , and . By means of variational techniques, we extended the arguments developed in [1]. In addition, we also established the existence result for the subelliptic system which involved sub-Laplacian and critical homogeneous terms. [ABSTRACT FROM AUTHOR]

Lithium metal anodes (LMAs) have been considered the ultimate anode materials for next-generation batteries. However, the uncontrollable lithium dendrite growth and huge volume expansion that can occur during charge and discharge seriously hinder the practical application of LMAs. Metal-organic framework (MOF) materials, which possess the merits of huge specific surface area, excellent porosity, and flexible composition/structure tunability, have demonstrated great potential for resolving both of these issues. This article first explores the mechanism of lithium dendrite formation as described by four influential models. Subsequently, based on an indepth understanding of these models, we propose potential strategies for utilizing MOFs and their derivatives to suppress lithium dendrite growth. We then provide a comprehensive review of research progress with respect to various applications of MOFs and their derivatives to suppress lithium dendrites and inhibit volume expansion. The paper closes with a discussion of perspectives on future modifications of MOFs and their derivatives to achieve stable and dendrite-free lithium metal batteries. [ABSTRACT FROM AUTHOR]

This paper presents the mathematical and physical analysis, as well as distinct types of exact wave solutions, of an important fluid flow dynamics model called the truncated M-fractional (1+1)-dimensional nonlinear Estevez–Mansfield–Clarkson (EMC) equation. This model is used to explain waves in shallow water, fluid dynamics, and other areas. We obtain kink, bright, singular, and other types of exact wave solutions using the modified extended direct algebraic method and the improved (G ′ / G) -expansion method. Some solutions do not exist. These solutions may be useful in different areas of science and engineering. The results are represented as three-dimensional, contour, and two-dimensional graphs. Stability analysis is also performed to check the stability of the corresponding model. Furthermore, modulation instability analysis is performed to study the stationary solutions of the corresponding model. The results will be helpful for future studies of the corresponding system. The methods used are easy and useful. [ABSTRACT FROM AUTHOR]

We consider in this paper the general properties of laminates designed to be isotropic in extension and in bending and with a coupling between the in- and out-of-plane responses. In particular, we analyze the mathematical properties of the tensors describing the elastic and thermal behavior and the mechanical consequences of these properties. The polar formalism for planar tensors is used in this study. By this approach, it is easy to put in light some interesting, qualitative, mechanical, and mathematical facts concerning coupled isotropic laminates and to appreciate the fundamental differences, from the mathematical and mechanical point of view, between hybrid laminates, i.e., composed by layers of different materials, and laminates made of identical plies. [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]

• Mathematical and physical analyses of the introduced problem. • Reporting a serious error in an important dimensionless parameter. • Indicating that the reported numerical results are completely erroneous. This is a comment on the paper [Optics and Laser Technology 128 (2020) 106233; https://doi.org/10.1016/j.optlastec.2020.106233 ] titled "Exact coupled solution for photothermal semiconducting beams using a refined multi-phase-lag theory". Herein, we report a serious error in an important dimensionless parameter employed in the problem, revealing that the defined parameter is dimensional and wrong. Accordingly, all given numerical results are based on this serious mistake, and are completely erroneous. [ABSTRACT FROM AUTHOR]