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Domain adaptation is a subfield of statistical learning theory that takes into account the shift between the distribution of training and test data, typically known as source and target domains, respectively. In this context, this paper presents an incremental approach to tackle the intricate challenge of unsupervised domain adaptation, where labeled data within the target domain is unavailable. The proposed approach, OTP-DA, endeavors to learn a sequence of joint subspaces from both the source and target domains using Linear Discriminant Analysis (LDA), such that the projected data into these subspaces are domain-invariant and well-separated. Nonetheless, the necessity of labeled data for LDA to derive the projection matrix presents a substantial impediment, given the absence of labels within the target domain in the setting of unsupervised domain adaptation. To circumvent this limitation, we introduce a selective label propagation technique grounded on optimal transport (OTP), to generate pseudo-labels for target data, which serve as surrogates for the unknown labels. We anticipate that the process of inferring labels for target data will be substantially streamlined within the acquired latent subspaces, thereby facilitating a self-training mechanism. Furthermore, our paper provides a rigorous theoretical analysis of OTP-DA, underpinned by the concept of weak domain adaptation learners, thereby elucidating the requisite conditions for the proposed approach to solve the problem of unsupervised domain adaptation efficiently. Experimentation across a spectrum of visual domain adaptation problems suggests that OTP-DA exhibits promising efficacy and robustness, positioning it favorably compared to several state-of-the-art methods. [ABSTRACT FROM AUTHOR]

This paper explores the truncated M-fractional three-component coupled nonlinear Schrödinger (tc-CNLS) equation, that regulates the behavior of optical pulses in optical fibers. These equations are utilized in various scientific and engineering fields, including nonlinear fiber optics, electromagnetic field waves, and signal processing through optical fibers. The study of multi-component NLS equations has gained significant attention due to their ability to elucidate various complex physical phenomena and exhibit more dynamic structures of localized wave solutions. The freshly invented integration tools, known as the fractional modified Sardar subequation method (MSSEM) and fractional enhanced modified extended tanh-expansion method (eMETEM), are employed to ensure the solutions. The study focuses on extracting various types of optical solitons, including bright, dark, singular, bright-dark, complex, and combined solitons. Optical soliton propagation in optical fibers is currently a subject of great interest due to the multiple prospects for ultrafast signal routing systems and short light pulses in communications. In nonlinear dispersive media, optical solitons are stretched electromagnetic waves that maintain their intensity due to a balance between the effects of dispersion and nonlinearity. Furthermore, hyperbolic, periodic and exponential solutions are generated. The utilized methodology is effective in explaining fractional nonlinear partial differential equations (FNLPDEs) as it offers pre-existing solutions and additionally derives novel exact solutions by mixing outcomes from various procedures. Furthermore, we plot the visualizations of solutions by plotting 3D, 2D, and contour graphs with the corresponding parameter values. The findings of this paper can improve the understanding of the nonlinear dynamical behavior of a specific system and demonstrate the efficacy of the methodology used. We anticipate that our study will provide substantial benefits to a considerable group of engineering model experts. The findings demonstrate the efficacy, efficiency, and applicability of the computational method employed, particularly in dealing with intricate systems. [ABSTRACT FROM AUTHOR]

Bera [Line graph characterization of power graphs of finite nilpotent groups, Comm. Algebra 50(11) (2022) 4652–4668] characterized finite nilpotent groups whose power graphs and proper power graphs are line graphs. In this paper, we extend the results of above-mentioned paper to arbitrary finite groups. Also, we correct the corresponding result of the proper power graphs of dihedral groups. Moreover, we classify all the finite groups whose enhanced power graphs are line graphs. We classify all the finite nilpotent groups (except non-abelian 2-groups) whose proper enhanced power graphs are line graphs of some graphs. Finally, we determine all the finite groups whose (proper) power graphs and (proper) enhanced power graphs are the complement of line graphs, respectively. [ABSTRACT FROM AUTHOR]

This study describes an easy and cheap inkjet printing method for producing a paper-based gas sensor consisting of a composite film made of graphene oxide and poly(3,4-ethylenedioxythiophene) and poly(styrenesulfonate) (PEDOT:PSS). A glossy paper substrate is an inkjet printed with ink made by dispersing graphene oxide in a PEDOT:PSS conducting polymer solution to test its ability to detect ammonia (NH3) at ambient temperature. The presence of few-layer graphene oxide in the PEDOT:PSS copolymer and the existence of π-π interactions between graphene oxide and PEDOT:PSS are confirmed by Fourier transform infrared spectroscopy, UV–Visible spectrophotometer, and X-ray diffraction. In a small concentration range of 1–100 ppm at ambient temperature, the ink-jet printed graphene oxide-PEDOT:PSS gas sensor displays strong responsiveness and good selectivity to NH3. The study found that NH4 is a strong donor in the ammonia gas produced by a bubble system of ammonia water, with NH4 molecules being ideal candidates for molecular doping of graphene. The H2O molecule can facilitate quick desorption by converting NH3 to NH4. The interaction between graphene oxide and NH3 molecules is weak. The attained gas-sensing performance may be attributed to the increased specific surface area of graphene oxide and enhanced interactions between the sensing film and NH3 molecules via π and lone pair electron network. The NH3-sensing mechanisms of the flexible printed gas sensor are based on the competitive interaction of ammonia on the sensor, adsorption and dissociate ionization on the sensor surface. [ABSTRACT FROM AUTHOR]

Uncertainty in the master–slave model is one of the primary factors affecting the transparency of teleoperation systems, and congestion in the master–slave communication network also greatly influences the performance of the teleoperation system. This paper proposes a combined framework of adaptive and impedance control to address the uncertainty in the master–slave model and achieve smooth operation at the slave end. Building upon this linear model, an event-triggered mechanism is designed using Lyapunov functions, with dynamic online adjustment of the triggering threshold parameters. Following the completion of the aforementioned research, control objectives are established to validate the performance of the teleoperation control system proposed in this paper. Finally, simulation verification is conducted in the Matlab/Simulink environment. [ABSTRACT FROM AUTHOR]

The most promising emerging technology that can reduce the power, area and delay in digital circuits is Quantum-dot Cellular Automata (QCA) technology. The Serial Input-Serial Output (SISO) Shift Register (SR) is a basic component in digital circuits. The SISO SR can be designed using two methods in the QCA technology, directly mapping circuits from the CMOS technology and using the inherent capability of the QCA technology. This paper presents and evaluates the new n-bit QCA SISO SR that not only uses the inherent capability of QCA technology but also has a regular architecture. The proposed n-bit SISO SR is developed based on the building block, which is designed in this paper. In addition, the developed QCA SISO SR has coplanar architecture and it has the ability to correct or change data. The proposed n-bit SISO SR is evaluated for 3, 4 and 5 bits using QCADesigner-E. The results demonstrate that the designed circuits for 3-, 4- and 5-bit QCA SISO SRs require 68 (0.06 μm2), 92 (0.08μm2) and 116 (0.09μm2) cells (area), respectively. The comparison demonstrates that the developed QCA SISO SRs have advantages in comparison to other QCA SISO SR circuits. [ABSTRACT FROM AUTHOR]

Mock theta functions were first introduced by Ramanujan in his last paper to Hardy. Moreover, some other mock theta functions were presented in his lost notebook. It is well known that all the classical mock theta functions can be expressed by the universal mock theta functions g2(x,q) and g3(x,q). In this paper, we establish some generalized mock theta functions and express them in terms of Appell–Lerch sums. Meanwhile, we show that some of Ramanujan’s two-parameter mock theta functions are the special cases of these functions. [ABSTRACT FROM AUTHOR]

Many papers have been recently devoted to the study of the radial behavior as z → 1− of transcendental r-Mahler functions holomorphic in the open unit disk. In particular, Bell and Coons showed in 2017 that, in a generic sense, r-Mahler functions behave like (1 + o(1))C(z)/(1 − z)ρ for some ρ ∈ ℂ and C(z) is a real analytic function of z ∈ (0, 1) such that C(z) = C(zr). They did not provide a formula for C(z) which was made explicit only in a few examples of r-Mahler functions of orders 1 and 2, and for specific values of r. In this paper, we first provide an explicit expression of C(z) as an exponential of a Fourier series in the variable loglog(1/z)/log(r) for every r-Mahler function of order 1. Then, extending to a large setting a method introduced by Brent–Coons–Zudilin in 2016 to compute C(z) associated to the Dilcher–Stolarsky function (a 4-Mahler function of order 2 in ℚ[[z]]), we provide an explicit expression of C(z) for every r-Mahler function of order 2 under mild assumptions on the coefficients in ℝ(z) of the underlying r-Mahler equations. This applies in particular to the generating function of the Baum–Sweet sequence. We do the same for r-Mahler functions solutions of inhomogeneous Mahler equations of order 1. [ABSTRACT FROM AUTHOR]

Zika is a mosquito-transmitted viral disease which may spread directly by the vector or sexual transmission. Zika virus may persist in semen and urine for a long time after disappearance from the blood, those persons are known as the convalescent humans. It can also be transmitted vertically among mosquitoes. In this paper, we have considered an eight-compartment Zika model to study the effect of all the said aspects on the virus dynamics in deterministic as well as stochastic environment. In analytic part, we have computed basic reproduction number and discussed stability of different equilibria. We have shown the proposed model undergoes through transcritical bifurcation when the reproduction number is unity and validate the model with real infection data of Dominican Republic in 2016. To study the model in stochastic environments, the additive noise is taken into consideration which is formulated considering the standard Brownian white noises proportional to each class. We have obtained the condition for disease extinction and persistence in mean. All theoretical findings are justified by numerical simulations. Lastly, the paper is ended with some conclusions. [ABSTRACT FROM AUTHOR]

To further expand the application range of cold-formed steel (CFS) members in practical engineering, a novel fold-fastened multi-cellular steel wall (FMSW) was introduced and investigated in detail. The FMSWs were mechanically connected by the hook-shaped and groove-shaped regions at both ends of the single limb members, by which the assembly efficiency was greatly improved. In this paper, a total of 10 slender FMSW specimens were subjected to axial compressive loadings, and the failure mode, load–vertical displacement curves, load–lateral displacement curves, and bearing capacity of the specimens were obtained. According to the experimental results, the development and failure modes of the local-global interactive buckling of FMSWs were revealed. All specimens experienced local buckling initially, followed by global buckling, and ultimately interactive buckling. The load–displacement curves exhibited similar trends, being characterized by three stages: the elastic stage, the elastic-plastic stage, and the descending stage. Furthermore, the nonlinear ascending segment was short, indicating that the failure was sudden. By comparing the bearing capacities among specimens, it was recognized that the ultimate resistance of FMSWs could be obtained by the superposition of the cells, and the bearing capacity was rarely affected by the height-to-thickness ratio. Based on the experimental results, refined finite element (FE) models were established and the accuracy and effectiveness of the modeling method were verified. Valuable reference could be provided by the research achievements of this paper for the subsequent research of CFS built-up members and their application in practical engineering. [ABSTRACT FROM AUTHOR]

Nanoparticles have been considered in many fields such as medicine and industry due to their very small size and their special physicochemical properties. Biosynthesis of nanoparticles has advantages over other methods. This paper examines the bibliography of the relationship between nanotechnology and fungi from 1985 to 2021. Data were collected from three databases consisting of Web of Science, Scopus, and Dimensions. The number and type of documents were examined and then the analysis was continued using VOSviewer and Bibliometrix-package on the documents of the Scopus database. Analysis of 1203 documents from this database showed an upward trend in the publication in recent years. The term "Fungi" was also identified as the keyword index and India as the country with the most published documents. Future research is likely to be on using modern techniques in the study of nanoparticles as well as focusing on other genera of fungi. This paper explores the relationship between nanotechnology and fungi from 1985 to 2021. Biosynthesis offers advantages in creating nanoparticles, which are tiny particles with unique properties used in many fields. Data from three databases were analysed, indicating an increasing trend in publications in recent years. Future research is likely to focus on modern techniques to study nanoparticles and other types of fungi. [ABSTRACT FROM AUTHOR]

In this paper, we propose a verifiable multi-party secret sharing protocol based on an entanglement swapping theorem of GHZ states. In our protocol, all receivers only need to perform simple GHZ measurements to recover the secret. The quantum-safe system proposed in this paper is feasible with current quantum technologies, and we show that it is secure against both external and internal attacks. In addition, the secret sender can verify whether the secret is correctly recovered. [ABSTRACT FROM AUTHOR]

In this paper, we investigate in this paper the Type IV singular bouncing in the framework of f (R ,) theory of gravity where R and mean the curvature scalar and the Gauss–Bonnet invariant, respectively. Cosmological f (R ,) models constrained by the slow-roll evolution is reconstructed and their explicit forms are provided near the bounce and far away from it. One obtains finally two models whose stability is numerically analyzed in this work. Our results show that the stability of the reconstructed models is very affected by their parameters. The model far from the singularity recovers stability quickly than the model near the singularity. [ABSTRACT FROM AUTHOR]

This paper presents an analytical study of the behavior of radial free-geodesics in the Friedmann–Lemaître–Robertson–Walker (FLRW) spacetime within the Lambda Cold Dark Matter (Λ CDM) model. Using the radial free motion solutions, we provide two methods for characterizing the geodesics and defines a general formula that encapsulates all possible solutions, determined by two initial conditions. We show that the past light cone, event horizon, and particle horizon, can be considered as special cases of this overarching formula. Furthermore, the paper explores the free geodesics within the currently accepted cosmological model based on the recent Planck results, thoroughly examining the various possible geodesic scenarios. [ABSTRACT FROM AUTHOR]

With the rapid development of intelligent vehicle technology, traditional vehicle design and manufacturing methods are facing many challenges. Traditional vehicle design and manufacturing methods have problems such as high cost, long development cycle and lack of personalized design. This paper took advantage of the high degree of flexibility, rapid customization and cost savings of 3D printing technology, which can provide entirely new solutions for intelligent vehicle design. This paper mainly analyzed the application of three-dimensional (3D) printing and manufacturing technology in intelligent vehicle design. In intelligent vehicle design, 3D printing can carry out 3D printed body structure design to make parts lightweight. The displacement sensor in the intelligent sensor can measure the displacement, deformation and vibration of the body components, and detect whether the body structure exceeds the safety range, which can provide safety feedback to the owner. 3D printing technology has been involved in automotive dashboard, interior design and customization. In this paper, the effects of vehicles designed under traditional methods and vehicles designed under 3D printing manufacturing technology were compared. The research and development cycle of class A, Class B, Class C and Class D in brand 1 under traditional manufacturing was 3.85 years, 3.13 years, 4.27 years and 4.32 years respectively. The R&D (research and development) cycle of grade A, B, C and D in brand 1 under 3D printing technology was 2.43 years, 2.05 years, 1.64 years and 1.73 years respectively. Under the traditional method, the average R&D cost of different levels of vehicles in brand 1, brand 2 and brand 3 was 191,000 yuan, 20900 yuan and 227,200 yuan respectively. Under 3D printing technology, the average R&D cost of different levels of vehicles in brand 1, brand 2 and brand 3 was 132,600 yuan, 145,300 yuan and 157,500 yuan respectively. The results of this paper emphasize that the application of 3D printing manufacturing technology shortens the development cycle of intelligent vehicles, reduces the development cost, and can be customized, which can be more in line with the needs of users. [ABSTRACT FROM AUTHOR]

This document is a guest editorial from the International Journal of Uncertainty, Fuzziness & Knowledge-Based Systems. It discusses the potential of fuzzy-based systems in statistical learning theory and their ability to handle uncertainty and ambiguity in real-time data. The editorial highlights recent advancements in integrating fuzzy systems with deep learning architectures and other machine learning techniques. The special issue aims to explore the intersection of fuzzy logic and statistical learning theory and includes twelve accepted papers that investigate the capabilities of fuzzy-based systems. The document provides a brief summary of each paper, covering topics such as pop-up text recognition, alignment of laser images, knowledge graph reasoning, land use changes, 3D printing in vehicle design, defect detection in electronic components, digital management process improvement, spectrum sharing in IoV, deep clustering for time series data, anti-collision algorithms, missing data filling, and video action recognition. The guest editor expresses gratitude to the authors and reviewers for their contributions and to the Editor-in-Chief for the opportunity to curate the special issue. [Extracted from the article]

To effectively promote the efficient dissemination of sci-tech journals and improve the influence of sci-tech journals, a precise push method of sci-tech journals based on knowledge graph reasoning is proposed, using knowledge graph to build network to realize push reasoning of scientific and Technological Journals. Based on the one-way author relationship network diagram and the two-way keyword network diagram, the PageRank algorithm is used to calculate the weight of network vertices, quantitatively and accurately identify the research direction of push customers and predict customers, and realize the accurate push management of content, so as to obtain the basis for the construction of network diagram. Based on the previous article in the Journal of the information society of science and technology of China, this paper constructs a knowledge reasoning diagram, mines 52 co-author cases and 60 related papers as experimental data, and verifies the progressiveness method through customer value. According to the network diagram, the progressiveness of this method is verified. The experimental results show that the knowledge map network reasoning method proposed in this paper has high accuracy in identifying the push objects of scientific and technological journals and accurately predicting the research direction. The matching degree between the number of customers and the pushed content. Using knowledge map network can ensure the timeliness and accuracy of pushing scientific and technological journals. [ABSTRACT FROM AUTHOR]

This paper is concerned with designing algorithms for and analyzing the computational complexity of the partial vertex cover problem in trees. Graphs (and trees) are frequently used to model risk management in various systems. In particular, Caskurlu et al. in [4] have considered a system which essentially represents a tripartite graph. The goal in this model is to reduce the risk in the system below a predefined risk threshold level. It can be shown that the main goal in this risk management system can be formulated as a Partial Vertex Cover problem on bipartite graphs. In this paper, we focus on a special case of the partial vertex cover problem, when the input graph is a tree. We consider four possible versions of this setting, depending on whether or not, the vertices and edges are weighted. Two of these versions, where edges are assumed to be unweighted, are known to be polynomial-time solvable. However, the computational complexity of this problem with weighted edges, and possibly with weighted vertices, remained open. The main contribution of this paper is to resolve these questions by fully characterizing which variants of partial vertex cover remain NP-hard in trees, and which can be solved in polynomial time. In the paper, we propose two pseudo-polynomial DP-based algorithms for the most general case in which weights are present on both the edges and the vertices of the tree. One of these algorithms leads to a polynomial-time procedure, when weights are confined to the edges of the tree. The insights used in this algorithm are combined with additional scaling ideas to derive an FPTAS for the general case. A secondary contribution of this work is to propose a novel way of using centroid decompositions in trees, which could be useful in other settings as well. [ABSTRACT FROM AUTHOR]

The paper focuses on the cutting behavior of Glass Fiber Reinforced Polymer (GFRP) composites and GNP–GFRP composites that contain varying amounts of Graphene Nano Platelets (GNP). GFRP composites are increasingly being used in a variety of industrial applications due to their excellent mechanical properties, such as high strength, stiffness, and low weight. However, their machining and cutting behavior can be challenging due to the presence of the reinforcing fibers. Therefore, the study aims to investigate the machining behavior of GFRP composites and the effect of adding GNP on their cutting behavior. The effect of different parameters such as cutting speed, feed rate and reinforcement rate on cutting forces and delamination factor is investigated. In addition, the tensile strength and fatigue behavior of the composite materials with the best and worst delamination factors were also determined. Addition of up to 0.2 wt.% of GNP to GFRP composites resulted in an increase in cutting forces and delamination factor when drilling GFRP composites. While the cutting force and delamination factor decreased with the increase in cutting speed, the cutting force and delamination factor increased with the increase in the feed rate. Analysis of variance (ANOVA) was performed to determine the effects of drilling parameters and reinforcement ratio on cutting force and delamination factor according to full factorial experimental design. The most efficient factor on the cutting forces is found to be feed rate (84.97%), followed by the reinforced rate (6.48%) and cutting speed (6.13%). The most efficient factor on the delamination factor is determined to be feed rate for (44.49%), followed by the reinforced rate (29.20%) and cutting speed (21.73%). [ABSTRACT FROM AUTHOR]

Let P (x) : = a d x d + ⋯ + a 0 ∈ ℚ [ x ] , a d > 0 , be a polynomial of degree d ≥ 2. Let (x n) be a sequence of integers satisfying x n + 1 = P (x n) for all  n = 0 , 1 , 2 , ... and x n → ∞ as  n → ∞. Set α : = lim n → ∞ x n d − n . Then, under the assumption a d 1 / (d − 1) ∈ ℚ , in a recent result by [A. Dubickas, Transcendency of some constants related to integer sequences of polynomial iterations, Ramanujan J. 57 (2022) 569–581], either α is transcendental or α can be an integer or a quadratic Pisot unit with α − 1 being its conjugate over ℚ. In this paper, we study the nature of such α without the assumption that a d 1 / (d − 1) is in ℚ , and we prove that either the number α is transcendental, or α h is a Pisot number with h being the order of the torsion subgroup of the Galois closure of the number field ℚ α , a d − 1 d − 1 . Other results presented in this paper investigate the solutions of the inequality | | q 1 α 1 n + ⋯ + q k α k n + β | | < n in (n , q 1 , ... , q k) ∈ ℕ × (K ×) k , considering whether β is rational or irrational. Here, K represents a number field, and ∈ (0 , 1). The notation | | x | | denotes the distance between x and its nearest integer in ℤ. [ABSTRACT FROM AUTHOR]

Denote by h = h (− p) the class number of the imaginary quadratic field ℚ (− p) with p prime. It is well known that h = 1 for p ∈ { 3 , 7 , 1 1 , 1 9 , 4 3 , 6 7 , 1 6 3 }. Recently, all the solutions of the Diophantine equation x 2 + p s = 4 y n with h = 1 were given by Chakraborty et al. in [Complete solutions of certain Lebesgue–Ramanujan–Nagell type equations, Publ. Math. Debrecen 97(3–4) (2020) 339–352]. In this paper, we study the Diophantine equation x 2 + p s = 2 r y n in unknown integers (x , y , s , r , n) , where s ≥ 0 , r ≥ 3 , n ≥ 3 , h ∈ { 1 , 2 , 3 } and gcd (x , y) = 1. To do this, we use the known results from the modularity of Galois representations associated with Frey–Hellegoaurch elliptic curves, the symplectic method and elementary methods of classical algebraic number theory. The aim of this paper is to extend the above results of Chakraborty et al. [ABSTRACT FROM AUTHOR]

The optimization of robot controller parameters is a crucial task for enhancing robot performance, yet it often presents challenges due to the complexity of multi-objective, multi-dimensional multi-parameter optimization. This paper introduces a novel approach aimed at efficiently optimizing robot controller parameters to enhance its motion performance. While spiking neural P systems have shown great potential in addressing optimization problems, there has been limited research and validation concerning their application in continuous numerical, multi-objective, and multi-dimensional multi-parameter contexts. To address this research gap, our paper proposes the Entropy-Weighted Numerical Gradient Optimization Spiking Neural P System, which combines the strengths of entropy weighting and spiking neural P systems. First, the introduction of entropy weighting eliminates the subjectivity of weight selection, enhancing the objectivity and reproducibility of the optimization process. Second, our approach employs parallel gradient descent to achieve efficient multi-dimensional multi-parameter optimization searches. In conclusion, validation results on a biped robot simulation model show that our method markedly enhances walking performance compared to traditional approaches and other optimization algorithms. We achieved a velocity mean absolute error at least 35% lower than other methods, with a displacement error two orders of magnitude smaller. This research provides an effective new avenue for performance optimization in the field of robotics. [ABSTRACT FROM AUTHOR]

This paper identifies certain interesting mathematical problems of stochastic quantization type in the modeling of Laser propagation through turbulent media. In some of the typical physical contexts, the problem reduces to stochastic Schrödinger equation with space–time white noise of Gaussian or Poisson or Lévy type. We identify their mathematical resolution via stochastic quantization. Nonlinear phenomena such as Kerr effect can be modeled by a stochastic nonlinear Schrödinger equation in the focusing case with space–time white noise. A treatment of stochastic transport equation, the Korteweg–De Vries equation as well as a number of other nonlinear wave equations with space–time white noise is also given. The main technique is the S-transform (we will actually use the closely related Hermite transform) which converts the stochastic partial differential equation (PDE) with space–time white noise to a deterministic PDE defined on the Hida–Kondratiev white noise distribution space. We then utilize the inverse S-transform/Hermite transform known as the characterization theorem combined with the infinite-dimensional implicit function theorem for analytic maps to establish local existence and uniqueness theorems for path-wise solutions of this class of problems. The particular focus of this paper on singular white noise distributions is motivated by practical situations where the refractive index fluctuations in the propagation medium in space and time are intense due to turbulence, ionospheric plasma turbulence, marine-layer fluctuations, etc. Since a large class of PDEs, that arise in nonlinear wave propagation, have polynomial-type nonlinearities, white noise distribution theory is an effective tool in studying these problems subject to different types of white noises. [ABSTRACT FROM AUTHOR]

To address the issue of frequency stability in microgrids with limited communication resources and bandwidth, this paper proposed an event-triggered control method based on a cloud-edge collaborative architecture. Firstly, to address the limited communication resources, event-triggered detector is set up at the edge to upload state variables and update control instructions only when the frequency deviation exceeds a pre-set threshold. Secondly, a fractional-order PI–PD controller is designed at the cloud control center, which achieves higher control degrees of freedom and stronger robustness than traditional integer-order PID control schemes. Additionally, to obtain better control parameters, an optimized design method based on an improved Big Bang-Big Crunch method (BB-BC3) is proposed for the fractional-order PI–PD controller. At last, a simulation example is given to prove the validity of the proposed method. Simulation results show that compared to the integer-order PI–PD controller, the fractional-order PI–PD controller based on the BB-BC3 algorithm proposed in this paper reduces the peak value of the response curve by 5%, and shortens the setting time by 0.14 s. [ABSTRACT FROM AUTHOR]

Aiming at the poor transient convergence and real-time performance of the horizontal vibration state variables of the high-speed elevator car system, and the low control accuracy and stability, this paper proposes an adaptive control strategy to ensure the transient response of the elevator car system. First, a prescribed preset transient performance function is introduced into the controller design to control the variation range of the state variables and ensure the steady transient performance of the elevator car; Second, representing the information of observation error/control error through algebraic operations, designing an adaptive law based on e-correction, estimating unknown parameters in the elevator car system, and achieving online parameter updates; Then, using neural networks to learn and compensate for unknown dynamics in the elevator car system, and solving the online estimation problem of neural network weights through adaptive laws, so that the tracking error and weight estimation error converge to a tight set near zero; Finally, using MATLAB/SIMULINK to compare and analyze the four control algorithms of passive control, PID control, adaptive control based on gradient descent method and transient response adaptive control proposed in this paper under two different rail excitations: Random excitation and pulse excitation. The simulation results show that the adaptive control strategy proposed in this paper effectively suppresses the horizontal vibration of the elevator car, makes the state variables have faster convergence speed and smaller convergence error, and ensures the stable and transient performance of the elevator car system. [ABSTRACT FROM AUTHOR]

A charge and discharge management scheme is proposed. The stored electric energy in distributed storage devices will converge to the consistent. The consistency of the stored electric energy of the devices helps to maintain the maximum load capacity and maximum consumption capacity of distributed storage devices. The charging and discharging process is constructed as a time-varying optimization problem, and the proposed algorithm can respond to the time-varying parameters of the distributed storage devices in real time. The time-varying neurodynamic algorithms can obtain time-varying optimal solution trajectories to give the optimal charging and discharging strategy in real time. In addition, the proposed approach in this paper focuses on the privacy protection of device data. Each device can calculate the power of discharging or charging by communicating with the partially connected nodes. Numerical simulations of the proposed scheme in the paper are given to verify the effectiveness of the scheme. Numerical simulations show that our scheme can make the electric energy stored in each storage device converge and maintain the maximum load capacity or maximum consumption capacity of the whole distributed storage device. [ABSTRACT FROM AUTHOR]

Confronted with the fast social development, the speed of garbage generation has increased. Therefore, from every aspect, especially staying green and healthy, it is urgent and vital to ensure accurate and stable garbage classification. In the field of garbage classification, household garbage has a large volume and the classification process still requires manual intervention. Besides, most of the current studies focus on industrial waste and medical waste, while the existing studies on household garbage are not effective enough. Furthermore, these studies are mostly trained and validated in self-built datasets, making the experimental results insufficiently representative and severely limiting the development of research. Aiming to facilitate the study of household garbage classification, this paper proposes a simple yet effective network model (FConvNet) to improve classification performance. In this paper, an effective convolution block with fused convolution is designed to enhance the potential correlation of the features in the spatial dimension, and then a lightweight symmetric structure is constructed to infer more information about the feature representation. The experiments on public datasets have justified the effectiveness of FConvNet with accuracy rates of 95%, 95% and 97%, achieving better performance on public datasets compared to baselines. Additionally, an online system based on the WeChat mini program framework is designed to provide convenient household garbage classification services and enable the collection of uploaded images to perform model optimizations. [ABSTRACT FROM AUTHOR]

This research paper introduces a novel approach to deriving traveling wave solutions (TWSs) for the Caputo-fractional Klein–Gordon equations. This research presents a distinct methodological advancement by introducing TWSs of a particular time-fractional partial differential equation, utilizing a non-local fractional operator, specifically the Caputo derivative. To achieve our goal, a novel transformation is considered, that converts a time-fractional partial differential equation into fractional ordinary differential equations, enabling analytical solutions through various analytical methods. This paper employs the homotopy analysis method to achieve the target objectives. To demonstrate the efficiency and applicability of the proposed transform and method, two examples are discussed and analyzed in figures. [ABSTRACT FROM AUTHOR]

The collective motions are studied using a recently created pseudopotential and some elastic constants. This paper involves the calculations of the collective motions like phonon dispersion curves (PDCs) for longitudinal and transverse frequencies (ωL and ωT), longitudinal sound velocity (vl), transverse sound velocity (vt), isothermal bulk modulus (B), modulus of rigidity (G), Young’s modulus (Y), Poisson’s ratio (σ), Debye temperature (θD) of some monovalent (Na), divalent (Mg) and polyvalent liquid metals (Al, Pb, Bi). This investigation is based upon the theory of pseudopotential of second-order approach via the equations of Hubbard and Beeby (HB). g(r) The pair correlation function is calculated from the different mean spherical approximation (MSA), one-component plasma (OCP) and optimized random phase approximation (ORPA) structure factors employed in this work. Three different types of local field correction (screening) functions proposed by Hartree (H), Taylor (T) and Nagy (N) are utilized in this paper. The current findings are found to be in qualitative accord with experimental and theoretical data. [ABSTRACT FROM AUTHOR]

This paper introduces a nonconvex ℓ1−2-analysis model: minx(∥D∗x∥ 1 −∥D∗x∥ 2)s.t. Ax = y, where A is a measurement matrix and D is a tight frame. Our main motivation is to generalize the sparse recovery via ℓ1 − ℓ2 minimization to this new model. As a nonconvex model, it is well known that its global minimizer and local minimizer are usually inconsistent. This paper provides a type of null space property (NSP) characterization which are necessary and sufficient conditions for the measurement matrix A such that a vector x can be recovered from Ax with a tight frame D via ℓ1−2-analysis local minimization, or any vector x can be uniformly recovered from Ax with a tight frame D via ℓ1−2-analysis minimization locally and globally. [ABSTRACT FROM AUTHOR]

This paper reviews Holevo’s contributions to quantum information theory during the 20 century. At that time, he mainly studied three topics, classical-quantum channel coding, quantum estimation with Craméro–Rao approach and quantum estimation with the group covariant approach. This paper addresses these three topics. [ABSTRACT FROM AUTHOR]

The prediction of price trends in the stock market has always been a hot research topic in the financial field. However, due to the high instability and volatility of stock prices, it is very difficult to accurately predict stock trends. How to remove the noise of stock data, extract effective features, and pursue maximum value returns has always been a challenge. This paper proposes a hybrid model (DWT-DQN) that combines discrete wavelet transform with deep reinforcement learning to improve the accuracy and return rate of stock predictions. First, the model captures price fluctuation information on different scales by performing discrete wavelet transformation on the difference between long- and short-term moving averages of stock prices, and well extracts the changing characteristics of stock price data in the time domain and frequency domain. Then the feature data are input into the built DQN network for model training. The network can select the optimal trading action based on market status and historical experience and returns. At the same time, during the data sampling process, an attention mechanism is introduced to allow the model to further learn in the direction of maximizing returns. Through testing and verification on SSEC, HSI, NDX and SPX data sets, experiments show that the hybrid model proposed in this paper has excellent performance in terms of accuracy and return rate. [ABSTRACT FROM AUTHOR]

This paper introduces an innovative composite sliding mode control strategy tailored for large-scale system, specifically tackling the intricate task of formulating a sliding mode control law for singularly perturbed systems. This paper delineates the development of a composite controller by dissecting it into subsystem controllers for both ‘slow’ and ‘fast’ subsystems, exploring its effectiveness in managing matched bounded external disturbances within the context of large-scale system. While sliding mode control proves to be a robust solution for handling uncertainty and disturbances, its inherent complexity and discontinuous characteristics pose significant challenges in crafting designs suitable for singularly perturbed systems. [ABSTRACT FROM AUTHOR]

Path planning is an essential subproblem of autonomous robots’ navigation. Reaching a given goal pose or covering the available space are typical navigation missions, that require different planning approaches. We focus on such problems in this paper, where a goal pose must be reached by a wheeled autonomous ground vehicle in challenging situations, i.e. in complex environments with limited free space. Many path-planning methods are available, from which the sampling-based approaches gained the highest interest due to their computational efficiency. However, the performance of such methods degrades if the free space is limited and narrow passages have to be crossed on the way to the goal. Finding real-time planning methods to deliver high-quality paths in such situations is challenging. This paper aims to take steps toward solving this problem. On the one hand, an approach is presented to characterize free space narrowness and the difficulty of planning tasks. This can be used as a tool to compare planning queries and evaluate the performance of planning methods from the perspective of their sensitivity to environmental narrowness. On the other hand, an improved variant of our previously proposed RTR planner, an incremental sampling-based path-planning method, is introduced that exhibits good performance even in narrow and difficult planning situations. It is shown by simulations that it outperforms the popular RRT and RRT* planners in terms of running time and path quality, and that it is less sensitive to the narrowness of the environment where the planning task has to be solved. [ABSTRACT FROM AUTHOR]

In previous works, we have proven that there are local tetrads in four-dimensional curved Lorentzian spacetimes that can be written in terms of two kinds of local structures, the skeletons and the gauge vectors. These tetrads diagonalize locally and covariantly the stress–energy tensors for systems of differential equations of the Einstein–Maxwell kind in the Abelian electromagnetic case, or of the Einstein–Maxwell–Yang-Mills kind when non-Abelian Yang–Mills fields are included, along with suitable Yang–Mills stress–energy tensors. Under local Lorentz transformations, these new tetrads conserve their skeleton-gauge vector structure. In this short paper, we will prove that given any general unit orthogonal tetrad in spacetime, we will be able to construct a new tetrad in the skeleton-gauge vector form. We will prove a theorem stating that the original orthonormal tetrad can be constructed or reexpressed with this same local tetrad skeleton-gauge vector structures. The theorems proved in this paper will enable the demonstration of new results in group isomorphism theorems in the future. [ABSTRACT FROM AUTHOR]

The real world is full of uncertainties, which we require appropriate mathematical structures to model and handle them. One such structure is the soft set, which can be combined with various algebraic and topological structures. The paper discusses how soft sets and hyperstructures can be combined to create new soft structures that can handle uncertainty and imprecision in algebraic structures. Soft sets are mappings from parameters to subsets of a universal set, and they can model fuzzy concepts. Hyperstructures are generalizations of classical algebraic structures, where the composition of two elements is a set instead of a single element. They can capture complex and diverse phenomena that cannot be modeled by single-valued operations. The paper gives examples of soft structures, such as soft polygroups, soft topological polygroups, soft topological soft polygroups and their applications in mathematics and science. The paper aims to show the usefulness and versatility of soft structures in dealing with uncertainty and imprecision in algebraic structures. We will define the concept of soft topological soft polygroups and examine its characteristics. [ABSTRACT FROM AUTHOR]

In this paper, we study a class of conformal metric deformations in the quasi-radial coordinate parametrizing the three-sphere in the conformally compactified Minkowski spacetime S1 × S3. Prior to reduction of the associated Laplace–Beltrami operators to a Schrödinger form, a corresponding class of exactly solvable potentials (each one containing a scalar and a gradient term) is found. In particular, the scalar piece of these potentials can be exactly or quasi-exactly solvable, and among them we find the finite range confining trigonometric potentials of Pöschl–Teller, Scarf and Rosen–Morse. As an application of the results developed in the paper, the large compactification radius limit of the interaction described by some of these potentials is studied, and this regime is shown to be relevant to a quantum mechanical quark deconfinement mechanism. [ABSTRACT FROM AUTHOR]

The 21st century is an era of rapid development of high-tech industry. Through continuous collection and sharing of data, IoT technology connected by things has penetrated into every aspect of human life. Modern organizations find that they increasingly rely on knowledge and information sharing and interconnection to enhance their innovation and development capabilities. Therefore, this paper studies the strategic decision-making of knowledge sharing among employees on the IoT platform drawing on evolutionary game theory, this paper constructs a three-party game model composed of "organization-knowledge sharers-knowledge seekers" from the perspective of stakeholders, and discusses the strategic choice of organization and employee behavior under the dynamic decision mechanism and when the game reaches equilibrium and stability. Moreover, this paper uses MATLAB 2016a to simulate the model. The results show that under the premise of higher organizational rewards, synergistic benefits, high-shared extra income, knowledge-sharing preferences, incentive preferences of the organization, the system is easier to reach the ideal state. With the smaller cost of sharing and incentive, organization and employees are more willing to be motivators and sharers, while the incentive degree of organization should be controlled within a reasonable range. This paper can provide specific theoretical and practical guidance for the practice of organizational knowledge management. [ABSTRACT FROM AUTHOR]

Battery Management System (BMS) functions to monitor individual cell in a battery pack and its crucial task is to maintain stability throughout the battery pack. The BMS is responsible for maintaining the safety of the battery as well as not to harm the user or environment. The parameters that are to be monitored in a battery are Voltage, Current and Temperature. With the collected data, BMS carefully monitors the charging–discharging behavior of the battery particularly in the Lithium-ion (Li-ion) batteries in which charging and discharging behavior are completely different. This paper proposes a real-time IOT connected deep learning algorithm for estimation of State-of-Charge (SoC) of Li-ion batteries. This paper provides unique objectives and congruence between model-based conventional methods and state-of-the-art deep learning algorithm, specifically Feed Forward Neural Network (FNN) which is nonRecurrent. This paper also highlights the advantages of Internet-of-Things (IoT) connected deep learning algorithm for estimation of State-of-Charge of Li-ion batteries in Hybrid Electric Vehicles (HEVs) and Electric Vehicles (EVs). The major advantage of the proposed method is that the Artificial Intelligence (AI)-based techniques aim to bring the estimation error less than 2% at a low cost and time without the model of the battery, at par with conventional method of Extended Kalman Filter (EKF) which is the best ever practical estimation theory. Another advantage of the proposed method is that in an abnormal condition (i.e., Unsafe Temperature) the IF This Then That (IFTTT) IoT mobile application interfaced with BMS through ThingSpeak cloud, sends a notification alert to the battery expert or to the user prior to an emergency. Finally, the real-time data of the battery parameters are collected through ThingSpeak cloud platform for future research and analysis. [ABSTRACT FROM AUTHOR]

Accurately predicting the maximum temperature is essential for studying human comfort, ecological environment development and social progress. However, traditional prediction methods are inefficient and inaccurate when dealing with large volumes of meteorological data. To tackle these challenges, this paper introduces an integrated approach, the ARIMA–LSTM–XGBoost model, which combines the strengths of autoregressive integrated moving average (ARIMA), long short-term memory network (LSTM) and eXtreme Gradient Boosting (XGBoost) to predict the maximum temperature. The proposed model enhances the prediction accuracy and convergence rate through techniques like MAPE reciprocal weight (MAPE-RW) and Schedule Sampling. Additionally, the model selects the best performing model using the early stopping method. This paper compares and analyzes the prediction results of the ARIMA, LSTM, XGBoost and ARIMA–LSTM–XGBoost models. The experimental results indicate that the ARIMA–LSTM–XGBoost model proposed in this paper achieves superior prediction accuracy, performance, and confidence. The ARIMA–LSTM–XGBoost model shows a Root-Mean-Squared Error (RMSE) of 1.381, significantly outperforming the ARIMA model (3.828), LSTM model (3.360) and XGBoost model (1.422). The coefficient of determination ( R 2) is 0.977, surpassing the values of 0.905 for the ARIMA model, 0.922 for the LSTM model and 0.910 for the XGBoost model. The ARIMA–LSTM–XGBoost model also exhibits a higher confidence level compared to the individual models. [ABSTRACT FROM AUTHOR]

The low-light image enhancement task aims to improve the visibility of information in the dark to obtain more data and utilize it, while also improving the visual quality of the image. In this paper, we propose a dual cross-attention multi-stage embedding network (DCMENet) for fast and accurate enhancement of low-light images into high-quality images with high visibility. The problem that enhanced images tend to have more noise in them, which affects the image quality, is improved by introducing an attention mechanism in the encoder–decoder structure. In addition, the encoder–decoder can focus most of its attention on the dark areas of the image and better attend to the detailed features in the image that are obscured by the dark areas. In particular, the poor performance of the Transformer when the dataset size is small is solved by fusing the CNN-Attention and Transformer in the encoder. Considering the purpose of the low-light image enhancement task, we raise the importance of recovering image detail information to the same level as reconstructing the lighting. For features such as texture details in images, cascade extraction using spatial attention and pixel attention can reduce the model complexity while the performance is also improved. Finally, the global features obtained by the encoder–decoder are fused into the shallow feature extraction structure to reconstruct the illumination while guiding the network for the focused extraction of information in the dark. The proposed DCMENet achieves the best results in both objective quality assessment and subjective evaluation, while for the computer vision tasks working in low-light environments as well, the enhanced images using the DCMENet proposed in this paper show the best performance. [ABSTRACT FROM AUTHOR]

The discovery of the Jones polynomial made an important connection between quantum physics and knot theory. Kauffman and Lomonaco introduced the knot mosaic system to define the quantum knot system for the purpose of representing an actual physical quantum system. This paper is inspired by an open question about the knot mosaic enumeration suggested by them. A knot m × n-mosaic is an m × n array of 11 mosaic tiles representing a knot diagram by adjoining properly. The total number Dm×n of knot m × n-mosaics, which indicates the dimension of the Hilbert space of the quantum knot system, is known to grow in a quadratic exponential rate. Recently, Oh et al. developed the state matrix recursion method producing the exact enumeration of knot mosaics, which uses a recursion formula of state matrices. Furthermore, they showed the existence of the knot mosaic constant δ =limm,n→∞(Dm×n) 1 mn and found its upper and lower bounds in a series of papers. The latest upper bound was obtained through two new concepts: quasimosaics and cling mosaics. As a sequel to this research program, we adjust the state matrix recursion method to handle cling mosaics inside a quasimosaic, which is called the progressive state matrix recursion method. This method provides recursive matrix-relations producing a sharper bound of the knot mosaic constant: 4 ≤ δ ≤ 4.1035507⋯. [ABSTRACT FROM AUTHOR]

The possibility of the existence of multiquark hadrons made of 4-quarks for mesons and 5-quarks for baryons was predicted by Gell-Mann [Phys. Lett. 8, 214 (1964)]. The renewed interest for the search for exotic pentaquark states was initiated by the paper by Diakonov, Petrov, and Polyakov [Z. Phys. A 359, 305 (1997)]. The 2003 experimental reports on the observation of Θ + pentaquark with u u d d s ̄ quark content created a great excitement and many following experiments have reported its observation [K. H. Hicks, Eur. Phys. J. H 37, 1 (2012)]. After high-statistics experiments at JLab, which did not confirm previous claims by the CLAS collaboration, the community concluded that the Θ + pentaquark either does not exist at all or has an extremely small cross-section, making it currently unobserved. There were different review papers on this subject, questioning the existence of Θ + or trying to explain the reasons why reaching a conclusion based on production experiments is challenging [M. Amaryan, Eur. Phys. J. Plus 137, 684 (2022)]. To address the challenge of minimal 3-body final states, a formation experiment with a projectile-kaon beam is proposed. In the following, we discuss how the Θ + could be observed in the K L p → Θ + → K + n reaction in the KLF experiment at JLab [M. Amaryan et al. [KLF Collaboration], arXiv:2008.08215 [nucl-ex]]. [ABSTRACT FROM AUTHOR]

In this paper, Kudryashov and modified Kudryashov methods are implemented for the first time to compute new exact traveling wave solutions of the space-time fractional (3+1)-dimensional Calogero–Bogoyavlenskii–Schiff (CBS) equation and Calogero–Bogoyavlenskii–Schiff and Bogoyavlensky Konopelchenko (CBS-BK) equation. With the help of wave transformation, the aforementioned fractional differential equations are converted into nonlinear ordinary differential equations. The purpose of this paper is to devise novel exact solutions for the space-time-fractional (3+1)-dimensional CBS and the space-time-fractional CBS-BK equations by utilizing the Kudryashov and modified Kudryashov techniques. The solutions, thus, acquired are demonstrated in figures by choosing appropriate values for the parameters. The solutions derived take the form of various wave patterns, including the kink type, the anti-kink type and the singular kink wave solutions. The obtained solutions are indeed beneficial to analyze the dynamic behavior of fractional CBS and CBS-BK equations in describing the interesting physical phenomena and mechanisms. The obtained solutions are entirely new and can be considered as a generalization of the existing results in the ordinary derivative case. The techniques presented here are very simple, efficacious and plausible and hence can be employed to attain new exact solutions for fractional PDEs. [ABSTRACT FROM AUTHOR]

This paper studies the task of vision-based MAV-catching-MAV, where a catcher MAV (micro aerial vehicle) can detect, localize, and pursue a target MAV autonomously. Since it is challenging to develop detectors that can effectively detect unseen MAVs in complex environments, the main novelty of this paper is to propose a real-to-sim-to-real approach to address this challenge. In this method, images of real-world environments are first collected. Then, these images are used to construct a high-fidelity simulation environment, based on which a deep-learning detector is trained. The merit of this approach is that it allows efficient automatic collection of large-scale and high-quality labeled datasets. More importantly, since the simulation environment is constructed from real-world images, this approach can effectively bridge the sim-to-real gap, enabling efficient deployment in real environments. Another contribution of this paper lies in the successful implementation of a fully autonomous vision-based MAV-catching-MAV system including proposed estimation and pursuit control algorithms. While the previous works mainly focused on certain aspects of this system, we developed a completely autonomous system that integrates detection, estimation, and control algorithms on real-world robotic platforms. [ABSTRACT FROM AUTHOR]

This paper presents full-scale observations of wind-induced vibrations on a 140m high cylindrical reinforced concrete tower under non-stationary and strong wind conditions. The vibration responses of the tower in two planar orthogonal axes and rotation, in conjunction with wind speed and direction data, have been utilized to extract the response characteristics. The primary focus is on discussing the correlation of wind-induced responses in three components: Along-wind, across-wind, and torsion. Throughout the varying levels of oscillation, the tower’s responses clearly exhibit correlations among these components. The correlation coefficients between along-wind and across-wind responses, as well as along-wind and torsional responses, remain negligible across the entire dataset. In contrast, during intense oscillations, there is a near-perfect correlation between the across-wind and torsional responses. Furthermore, the probability density functions (PDFs) of the response components under strong wind conditions significantly deviate from the Gaussian distribution and closely resemble the Cauchy distribution. The joint PDFs also indicate that the along-wind response is statistically independent of the other response components, while the across-wind response correlates well with the torsion, as indicated by the non-Gaussian distribution. This paper also includes distinct observations regarding dominant oscillating frequencies, torsional amplitudes, and vertical vibration amplitudes. The importance of this research lies in its examination of the relationship between different response components, a crucial aspect in understanding how structures behave under wind loading. By emphasizing the need for full-scale measurements, this study aims to provide valuable validation for previous theoretical and experimental research findings. [ABSTRACT FROM AUTHOR]

This paper considers the possibility that abstract thinking and advanced synthesis skills might encourage extraterrestrial civilizations to accept communication with mankind on Earth. For this purpose, a notation not relying upon the use of alphabet and numbers is proposed, in order to denote just some basic geometric structures of current physical theories: vector fields, 1-form fields, and tensor fields of arbitrary order. An advanced civilization might appreciate the way here proposed to achieve a concise description of electromagnetism and general relativity, and hence it might accept the challenge of responding to our signals. The abstract symbols introduced in this paper to describe the basic structures of physical theories are encoded into black and white bitmap images that can be easily converted into short bit sequences and modulated on a carrier wave for radio transmission. [ABSTRACT FROM AUTHOR]

Phantom attractors in nonlinear systems under additive stochastic excitation have been recently discovered. This paper uncovers the existence of phantom attractors in a single-degree-of-freedom smooth nonlinear equation, which characterizes the vibration of an inextensible beam subjected to lateral stochastic excitation. It also elucidates that the stochastic averaging method, in this context, may lead to qualitatively erroneous probability density functions, identified as one of the reasons why these attractors were previously overlooked. The study then proceeds to analyze the formation process of the phantom attractor and the critical noise intensity associated with it. Subsequently, the key nonlinear term related to the emergence of phantom attractors is identified by observing whether the system still exhibits phantom attractors after the corresponding nonlinear terms are removed. It is revealed that in this system, the presence of phantom attractors is closely linked to the inertia nonlinearity of the hardening type. The system investigated in this paper is simpler compared to previously identified systems capable of generating phantom attractors. This simplicity aids in facilitating research focused on unraveling the general principles behind the formation of phantom attractors. [ABSTRACT FROM AUTHOR]

In this paper, we prove a new extremal property of the Reuleaux triangle: it maximizes the Cheeger constant among all bodies of (same) constant width. The proof relies on a fine analysis of the optimality conditions satisfied by an optimal Reuleaux polygon together with an explicit upper bound for the inradius of the optimal domain. As a possible perspective, we conjecture that this maximal property of the Reuleaux triangle holds for the first eigenvalue of the p -Laplacian for any p ∈ (1 , + ∞) (this paper covers the case p = 1 whereas the case p = + ∞ was already known). [ABSTRACT FROM AUTHOR]

The time-varying delay is a peculiar phenomenon that occurs in almost all systems. It can cause numerous problems and instability during system operation. In this paper, the time-varying delay is considered in both the states and input vectors, which is a significant distinction between the proposed method here and previous algorithms. Furthermore, the time-varying delay is unknown but bounded. To address this issue, the Razumikhin approach is applied to the proposed method, as it incorporates a Lyapunov function with the original non-augmented state space of the system models, in contrast to the Krasovskii formula. Moreover, the Razumikhin method performs better and avoids the inherent complexity of the Krasovskii method, particularly when dealing with large delays and disturbances. For achieving output stabilization, the model predictive control (MPC) is designed for the system. The considered system in this paper is an interval type-2 (IT2) fuzzy T-S model, which provides a more accurate estimation of the dynamic model of the system. The online optimization problems are solved using linear matrix inequalities (LMIs), which reduces the computational burden and online computational costs compared to offline and non-LMI approaches. Finally, an example is provided to illustrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]