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This article describes a new method for evaluation of radial crush strength of paper cores. Based on the theory of multilayered composites, a mathematical model has been developed to calculate the value of destructive force during radial crushing of spirally shaped paper cores whose layers are made of different materials. To start calculations, it is necessary to have geometry parameters of the cores, Young's modulus and SCT of an individual component layers. [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]

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]

For decades, historians have debated the origins of Einstein's special theory of relativity. The derivation of the Lorentz Transformations given by Einstein in 1905 is studied in detail; and it is found to be mathematically inconsistent, and thus in error. Therefore, he must have been aware of the transformations at the time of writing the paper, which is an extremely minority opinion in the general literature. His attempt to rederive them starting from the synchronization condition is incorrect. Though the derivation is flawed, it does not affect many of the concepts he put forth that flow from the Lorentz Transformations. The observations given here will help resolve a long-standing dispute over the priority of the discovery of various parts of the theory. The priority, which is presently concentrated with Einstein, may need to be redistributed between Einstein, Lorentz, Poincare', Larmor, Voigt, and others. [ABSTRACT FROM AUTHOR]

The present comment concerns the correct presentation of an algorithm proposed in the above paper for the glow-curve deconvolution in the case of continuous distribution of trapping states. Since most researchers would use directly the proposed algorithm as published, they should be notified of its correct formulation during the fitting of TL glow curves of materials with continuous trap distribution using this Equation. [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]

In this paper, the Cauchy problem for the nonlinear Schrodinger system {idtu1(x,t)== ∆u1(x, t)− |u1(x, t)| p−1u1(x, t)− |u2(x, t)| p−1u1(x, t), idtu2(x, t) = ∆u2(x, t) − |u2(x, t)| p−1u2(x, t) − |u1(x, t)| p−1u2(x, t), was investigated in d space dimensions. For 1 < p ≤ 1 + 2/d, the nonexistence of asymptotically free solutions for the nonlinear Schrödinger system was proved based on mathematical analysis and scattering theory methods. The novelty of this paper was to give the proof of pseudo-conformal identity on the nonlinear Schrödinger system. The present results improved and complemented these of Bisognin, Sepúlveda, and Vera(Appl. Numer. Math. 59(9)(2009): 2285–2302), in which they only proved the nonexistence of asymptotically free solutions when d = 1, p = 3. [ABSTRACT FROM AUTHOR]

Agriculture was and remains the support of human existence, representing the backbone of the Romanian rural economy. The gross domestic product represents a macroeconomic indicator of results, being the consequence of the efficient use of resources. In this context, the authors analyze the place that agriculture holds in achieving the gross domestic product in Romania compared to the European Union, as well as its dynamics. In this sense, the share of resources in the formation of the gross domestic product in the period 2000-2022 is presented. The main research methods used for this work are: analysis, synthesis, comparison and mathematical analysis. From the analysis carried out, conclusive ideas emerge, and the article becomes even more suggestive, in that it is accompanied by tables synthesized by the authors and relevant graphics that highlight and support the assessments that the authors make in the content of this article. At the end of the paper, the authors emphasize the fact that the GDP is the most complex indicator that reflects the transformations that the Romanian economy has gone through in recent years. From the point of view of the use of resources, it can be seen that the share of the agricultural sector has registered a downward evolution, which can be largely explained by the increase in the importance of industry and the service sector in the overall national economy. [ABSTRACT FROM AUTHOR]

In this short paper, we look into a conclusion drawn by Alzalg (J Optim Theory Appl 169:32-49, 2016). We think the conclusion drawn in the paper is incorrect by pointing out three things. First, we provide a counterexample that the proposed inner product does not satisfy bilinearity. Secondly, we offer an argument why a pth-order cone cannot be self-dual under any reasonable inner product structure on $$\mathbb {R}^n$$ . Thirdly, even under the assumption that all elements operator commute, the inner product becomes an official inner product and the arbitrary-order cone can be shown as a symmetric cone, we think this condition is still unreasonable and very stringent so that the result can only be applied to very few cases. [ABSTRACT FROM AUTHOR]

Immediately following the commentary below, this previously published article is reprinted in its entirety: Cathleen Synge Morawetz, "The mathematical approach to the sonic barrier". [ABSTRACT FROM AUTHOR]

The use of the efficient score statistic in sequential monitoring procedures is reviewed and analysed. Various models that arise in applications are considered. The efficient score vector has the same optimality property as the generalized likelihood ratio, but it has a simple-structure requiring fewer estimations, and this is especially important when the data have a complicated structure. Furthermore, with the efficient score vector it is possible to detect which component of the parameter vector is different from the hypothetical or the historical value. The problems we solve here were the subjects of separate publications, but with the new methodology they are easily calculated examples. [ABSTRACT FROM PUBLISHER]

In this short paper we show that the results obtained by [N. Hussain, V. Parvaneh, B. Samet and C. Vetro, Some fixed point theorems for generalized contractive mappings in complete metric spaces, Fixed Point Theory and Applications (2015) 2015:185] can be obtained without the continuity assumption for the self mapping. [ABSTRACT FROM AUTHOR]

Ahmad et al. (2015) consider a Transmuted Kumaraswamy distribution and study certain properties of their distribution. In the title of their paper they mention characterization of this distribution, but no characterizations are presented in the paper. In the present short note we establish certain characterizations of the Transmuted Kumaraswamy in three directions. [ABSTRACT FROM AUTHOR]

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

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

• 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]

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]

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

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]

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

In theory, two extreme forms of substances exist: the pure form and the single-molecule mixture form. The latter contains a mixture of molecules with molecularly different structures. Inspired by the "chemical space" concept, in this paper, I report a study of the single-molecule mixture state that combines model construction and mathematical analysis, obtaining some interesting results. These results provide theoretical evidence that the single-molecule mixture state may indeed exist in realistic synthetic or natural polymer systems. [ABSTRACT FROM AUTHOR]

Tuberculosis (TB) is a communicable, airborne infection caused by the bacillus Mycobacterium tuberculosis. Pulmonary tuberculosis (PTB) is the most common presentation, although infection can spread anywhere to cause extra-pulmonary tuberculosis (EPTB). In this paper, a novel fractional order mathematical model is designed for the transmission dynamics of tuberculosis. Uninfected vulnerable individuals are categorized into the following: susceptible with underline ailment and susceptible without underline ailment. The research seeks to qualitatively and quantitatively analyze the proposed model and suggests comprehensive intervention measures for the control of tuberculosis among individuals with underline ailment. Some of the major highlights from the numerical investigation points out that TB vaccination is key to reducing the spread of TB among individuals with underline ailment. Furthermore, efforts to step down the spread of TB through awareness campaigns could significantly reduce the burden of the disease among individuals with co-morbidity. [ABSTRACT FROM AUTHOR]

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

The main goal of mathematical modeling and analysis of queueing systems is to understand the dynamic behavior of the underlying processes, enabling informed and intelligent management decisions. While the queueing systems with random factors have received extensive scrutiny, this paper introduces an uncertain queueing model that considers the belief degree of customer behavior. In this model, customers arrive in groups and the interarrival times and service times are treated as uncertain variables. To evaluate the performance of this proposed uncertain queueing model, the busy index and busy period are also discussed, and the analytical formulas and uncertainty distribution are derived respectively. Additionally, two numerical examples are also given to illustrate the obtained results. [ABSTRACT FROM AUTHOR]