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In the present paper, we give the bounds for the second Hankel determinant of the logarithmic coefficients of a certain subclass of normalized univalent functions, which we have introduced here. Relevant connections of the results, which we have presented here, with those available in the existing literature are also described briefly [ABSTRACT FROM AUTHOR]

The paper deals with the impulsive infinite-dimensional problem generated by solutions of the thermal conductivity equation under the condition of impulse ”pumping” of heat. Moments of impulses are not fixed and are determined by the amount of total heat in the system. It is proved that such a problem generates impulsive dynamical system in the space of continuous functions and its ω-limits sets are investigated. [ABSTRACT FROM AUTHOR]

In this paper, we firstly establish an identity by using the notions of quantum derivatives and integrals. Using this quantum identity, quantum Newton-type inequalities associated with convex functions are proved. We also show that the newly established inequalities can be recaptured into some existing inequalities by taking q → 1 −. Finally, we give mathematical examples of convex functions to verify the newly established inequalities. [ABSTRACT FROM AUTHOR]

A generalized autoregressive (GNAR) model fusing both linearity and nonlinearity is proposed to solve the complex nonlinear time series modeling problem. First, the mathematical model of the GNAR model is established while the mathematical mechanism and physical meaning of the GNAR model are both expounded from the two aspects of Weierstrass theory and Volterra theory. Then, an improved least squares parameter estimation method, namely robust Residuals Adjusted Least Squares (RALS) method, is introduced and its process is successionally proposed to improve the anti-outlier performance of the GNAR model. Next, the mathematical model of the computational complexity for the GNAR model is established and the complexity model is introduced into the AIC to propose an improved AIC (iAIC). Finally, a dataset containing 23 records is established and experiments are carried out. The results show that the GNAR model with RALS estimator has high fitting accuracy. The Mean Square Error (MSE) of the series predicted by the GNAR model with Least Squares (LS) estimator is 325.3% higher than that of the series predicted by the GNAR model with RALS estimator at most. The effectiveness of order determination method reaches 82.61%. Therefore, the GNAR model together with its parameter estimation method and order determination method proposed in this paper are effective. [ABSTRACT FROM AUTHOR]

This study examines Einstein's field equations in the context of general relativity, comparing five distinct methodologies: (a) vanishing complexity, (b) embedding class one or the Karmarkar condition, (c) conformally flat spacetime, (d) conformal killing symmetry, and (e) the Karmarkar scalar condition. The first four methods reveal a significant connection between two metric potentials, while the fifth method provides a coordinate-independent condition expressed in terms of structural scalars. The paper provides a comprehensive comparative analysis of a new exact solution derived by assuming a common metric function and solving the remaining metric functions through corresponding bridge equations to evaluate their effectiveness and validity. Critical parameters such as thermodynamic factors, causality conditions, stability, and mass function analysis are investigated. [ABSTRACT FROM AUTHOR]

This research paper develops a novel hybrid approach, called hybrid particle swarm optimization–teaching–learning-based optimization (hPSO-TLBO), by combining two metaheuristic algorithms to solve optimization problems. The main idea in hPSO-TLBO design is to integrate the exploitation ability of PSO with the exploration ability of TLBO. The meaning of "exploitation capabilities of PSO" is the ability of PSO to manage local search with the aim of obtaining possible better solutions near the obtained solutions and promising areas of the problem-solving space. Also, "exploration abilities of TLBO" means the ability of TLBO to manage the global search with the aim of preventing the algorithm from getting stuck in inappropriate local optima. hPSO-TLBO design methodology is such that in the first step, the teacher phase in TLBO is combined with the speed equation in PSO. Then, in the second step, the learning phase of TLBO is improved based on each student learning from a selected better student that has a better value for the objective function against the corresponding student. The algorithm is presented in detail, accompanied by a comprehensive mathematical model. A group of benchmarks is used to evaluate the effectiveness of hPSO-TLBO, covering various types such as unimodal, high-dimensional multimodal, and fixed-dimensional multimodal. In addition, CEC 2017 benchmark problems are also utilized for evaluation purposes. The optimization results clearly demonstrate that hPSO-TLBO performs remarkably well in addressing the benchmark functions. It exhibits a remarkable ability to explore and exploit the search space while maintaining a balanced approach throughout the optimization process. Furthermore, a comparative analysis is conducted to evaluate the performance of hPSO-TLBO against twelve widely recognized metaheuristic algorithms. The evaluation of the experimental findings illustrates that hPSO-TLBO consistently outperforms the competing algorithms across various benchmark functions, showcasing its superior performance. The successful deployment of hPSO-TLBO in addressing four engineering challenges highlights its effectiveness in tackling real-world applications. [ABSTRACT FROM AUTHOR]

This paper studies the assignment problem of multi product assembly jobs to days. The problem aims to minimize the amount of overtime while avoiding assembly delays for jobs that can be fragmented into smaller sub-tasks. When sequencedependent setup times are negligible, the problem considered transforms into the bin packing problem with restricted item fragmentation where jobs represent items and days stand for bins. We present a mixed integer programming model of the problem by extending earlier formulations in the literature. Computational experiments show that the mathematical model obtained optimal solutions for majority of instances tested within reasonable computation times. [ABSTRACT FROM AUTHOR]

Introduction/purpose: The study of vehicle suspension is a challenge for researchers in the field of vehicles regarding the impact of the suspension system on vehicle performances such as ride comfort, road holding, and working space. This paper presents the simulation of the Land Rover Defender 110 vehicle in the roll plane (half vehicle) in Simulink/MATLAB. The obtained results were compared with the results obtained in the ADAMS/CAR software package of the Land Rover Defender 110 simulation model previously experimentally validated. The Defender 110 vehicle has a dependent suspension system in both axles and a passive suspension type with four degrees of freedom (4 DOF). Methods: The equations of the system can be solved mathematically with a scheme in Simulink/MATLAB while half-vehicle modeling has been done in ADAMS/CAR. Results: The comparison of the vehicle characteristics obtained by the two simulation methods was done for three different scenarios, and it was noticed that there is a good correlation between them. Conclusion: It was concluded that the Defender 110 vehicle simulation model in Simulink/MATLAB is validated. The validated model can be used to perform suspension system optimization in future work [ABSTRACT FROM AUTHOR]

Introduction/purpose: Simulated annealing is a powerful technique widely used in optimization problems. One critical aspect of using simulated annealing effectively is a proper and optimal adjustment of its parameters. This paper presents a novel approach to efficiently adjust the parameters of simulated annealing to enhance its performance and convergence speed. Methods: Since the simulated algorithm is inspired by the cooling Metropolis process, the basic idea is to simulate and analyze this process using a mathematical model. The proposed work tends to properly imitate the Metropolis cooling process in the algorithmic field. By intelligently adjusting the temperature schedule, temperature reduction and cooling rate, the algorithm optimizes the balance between exploration and exploitation, leading to improved convergence and higher-quality solutions. Results: To evaluate the effectiveness of this approach, it was applied first on a chosen sample function to be minimized, and then on some usual known optimization functions. The results demonstrate that our approach, called Optimal Adjusting of Simulated Annealing parameters (OASA), achieves superior performance compared to traditional static parameter settings and other existing approaches, showing how to well adjust the parameters of the simulated annealing algorithm to improve its efficiency in terms of solution quality and processing time. Conclusion: Adjusting the algorithm parameters could have a significant contribution in the optimization field even for other metaheuristics. [ABSTRACT FROM AUTHOR]

Exploring special multi-scroll chaotic systems is meaningful work. This paper studies an expanded multi-scroll chaotic system consisting of eight terms with one nonlinearity. It is generated by modifying the nonlinear term of the newly constructed chaotic system by a polynomial function. The unique mathematical model makes the unstable index-2 equilibria increase in four dimensions, which contributes to the number of scrolls expanding in each phase plane unidirectionally. Dynamic analysis finds that the system can yield complex nested multi-scroll attractors and has single-parameter-based synchronization control of amplitude and offset boosting behavior. Moreover, circuit implementation verifies the physical existence of the proposed system. Also, an image encryption algorithm for remote sensing images is established. Permutation and diffusion operations are performed using new pixel coordinates derived from the data of the chaotic matrix, which comes from the same position as the pixel matrix. Relevant tests suggest that the algorithm is secure and able to resist undesirable interference. • Simple multiscroll chaotic system with various signal control features is proposed. • Complex dynamics, circuit implementation of the proposed system is studied. • New chaos-based image encryption algorithm with high security is designed. [ABSTRACT FROM AUTHOR]

Fractional calculus is defined by expanded integer order integration and differentiation. In this paper, multiple mathematical models of a nonlinear dual-tank device are precisely formulated by fractional calculus. Using the accurate model, a multivariable fractional-order controller is designed for nonlinear devices. The merits of the fractional-order design include: (1) control of multivariable nonlinearities, (2) compensation of uncertainties, and (3) elimination of coupling effects. Simulations and experiments are conducted to verify the precision of the fractional order models and the effectiveness of the multivariable fractional-order control system design. [ABSTRACT FROM AUTHOR]

In this article, we will introduce the mathematical model of the diffusion process in a swelling medium that has already been modeled. The main purpose of this paper is introducing a new class of group transformations for solving the nonlinear emulsion equation. Thus, we introduce this method as the discrete group methods based on solvable class orbits. One of the crucial advantages of this method is that a transformation is sought, which reduces the equation being investigated to some standard form for which the methods of integration are known. In developing this approach, one may construct all canonical forms of solvable equations. [ABSTRACT FROM AUTHOR]

The classification of reflective modular forms is an important problem in the theory of automorphic forms on orthogonal groups. In this paper, we develop an approach based on the theory of Jacobi forms to give a full classification of 2-reflective modular forms. We prove that there are only three lattices of signature (2, n)having 2-reflective modular forms when n ≥ 14. We show that there are exactly 51 lattices of type 2U ⊕ (L-1) which admit 2-reflective modular forms and are such that L has 2-roots. We further determine all 2-reflective modular forms giving arithmetic hyperbolic 2-reflection groups. This is the first attempt to classify reflective modular forms on lattices of arbitrary level [ABSTRACT FROM AUTHOR]

Introduced by Erdős in 1950, a covering system of the integers is a finite collection of arithmetic progressions whose union is the set Z. Many beautiful questions and conjectures about covering systems have been posed over the past several decades, but until recently little was known about their properties. Most famously, the so-called minimum modulus problem of Erdős was resolved in 2015 by Hough, who proved that in every covering system with distinct moduli, the minimum modulus is at most 1016 . In this paper we answer another question of Erdős, asked in 1952, on the number of minimal covering systems. More precisely, we show that the number of minimal covering systems with exactly n elements is exp ((4√τ/3+o(1)n3/2/(logn)1/2) as n→∞, where τ=∑∞ t=1(logt+1/t)².En route to this counting result, we obtain a structural description of all covering systems that are close to optimal in an appropriate sense. [ABSTRACT FROM AUTHOR]

In this paper we relate a fundamental parameter of a random graph, its degree sequence, to a simple model of nearly independent binomial random variables. As a result, many interesting functions of the joint distribution of graph degrees, such as the distribution of the median degree, become amenable to estimation. Our result is established by proving an asymptotic formula conjectured in 1990 for the number of graphs with given degree sequence. In particular, this gives an asymptotic formula for the number of d-regular graphs for all d, as n→∞. The key to our results is a new approach to estimating ratios between point probabilities in the space of degree sequences of the random graph, including analysis of fixed points of the associated operators. [ABSTRACT FROM AUTHOR]

The variation analysis is a key tool for ensuring the high quality assembly in the process of developing the technology for manufacturing of aircraft parts. One of the main factors in variations is the deviations in the positioning procedure. This paper is devoted to the development of an approach that allows taking into account the variations during positioning and merging it with the special algorithm of contact problem solving. The impact of varied boundary conditions is incorporated into an additional vector of forces that can be interpreted as reactions to the shift of supports. The obtained results are illustrated with a case of wing-to-fuselage assembly. [ABSTRACT FROM AUTHOR]

In the theory of gene networks, the mathematical apparatus that uses dynamical systems is fruitfully used. The same is true for the theory of neural networks. In both cases, the purpose of the simulation is to study the properties of phase space, as well as the types and the properties of attractors. The paper compares both models, notes their similarities and considers a number of illustrative examples. A local analysis is carried out in the vicinity of critical points and the necessary formulas are derived. [ABSTRACT FROM AUTHOR]

This paper investigates the effects of model fidelity and parameter uncertainty on the performance of a hybrid model-based feedback-feedforward control scheme for attitude tracking of a satellite with flexible appendages. The feedforward component is an inverse model-based term produced through a computational approach known as inverse simulation (InvSim), which works by iteratively solving a discretised reference trajectory. The hybrid controller's feedback is proportional-derivative (PD) based, using body attitude and rate feedback to provide stability and robustness. Furthermore, to ensure that the flexible modes do not trigger instability, the PD control gains are tuned to give a closed-loop response that is significantly slower than the flexible modes. Additionally, excitation of the flexible modes is reduced by minimising jerk through polynomial rest-to-rest manoeuvres, following the shortest quaternion path using spherical–linear-interpolation (SLERP). The effects of the appendage flexing on attitude tracking are then compensated through the feedforward element of the hybrid controller, with performance being compared to a traditional PD tracking law. The effect of the model fidelity on the performance of the hybrid controller is investigated through the use of both rigid body and multiple-fidelity finite-element mathematical models. Additionally, the effect of uncertainties in the model parameters is investigated to determine the accuracy of the model required to obtain significant improvement in attitude tracking. It is found that in the absence of any model parameter uncertainty, the hybrid controller outperforms the PD tracking control law by at least one order of magnitude when the finite-element model is used. Increasing the number of finite elements was found to provide no significant improvement in performance, with one element being sufficient and favourable with its lower computational overhead. It was also found that to ensure good performance compared to the PD tracking controller, the uncertainty in the inertia tensor should be < 1%. Similarly, uncertainty in the first flexible modal frequency should be < 0.5 rad/s. • Inverse simulation (InvSim) used to produce model-based feedforward control. • Combined with PD feedback to improve attitude tracking. • Effects of model uncertainty and fidelity on model-based control investigated. [ABSTRACT FROM AUTHOR]

Physics-informed neural networks (PINN) architectures have been recently explored to accelerate hemodynamics simulations by leveraging mathematical models for blood flow and empirical data. In this paper, a variable separated physics-informed neural networks based on adaptive weighted loss functions (AW-vsPINN) is developed for blood flow model in arteries. In particular, sub-neural networks are proposed to separately predict the unknown scalar state variables by sharing the same input layer. The AW-vsPINN adaptively adjusts the weights of loss terms by the minmax algorithm, which will be updated synchronously along with the network parameters and can balance the contributions of different loss terms during training. The two-stage optimization is implemented to train the neural networks. Specifically, the Adam optimizer is iterated for initial steps with the learning rate generated by the inverse time decay scheduler, and then the L-BFGS optimizer continues to train until the loss converges. Numerical results illustrate that the AW-vsPINN can remarkably improve prediction accuracy and enhance the ability of generalization compared to the conventional PINN. The proposed AW-vsPINN framework has high potential in predicting the blood flow information in cardiovascular disease. [ABSTRACT FROM AUTHOR]

The two-degree-of-freedom (2-DOF) aerial manipulator is composed of a quadrotor aircraft and a 2-DOF manipulator, which significantly expands the scope of grabbing and transporting objects. After the manipulator is installed on the quadrotor, the manipulator and the load will cause serious interference to the quadrotor, resulting in difficulty of system control and even instability. This paper presents a mathematical model of the angular velocity system of the 2-DOF aerial manipulator. The model considers the influence of the manipulator and the load on the quadrotor. Based on this model, the nonlinear dynamics of the angular velocity system of the 2-DOF aerial manipulator are analyzed by solving the equilibrium points, calculating the Lyapunov exponents, analyzing the dynamic bifurcation diagram, and drawing the dynamic region distribution map. It is found that angular velocity can produce the dynamic behaviors of sink, period-doubling, and chaos under certain circumstances. By analyzing the nonlinear dynamic behaviors of the angular velocity system under different manipulator postures, different manipulator configurations, different load masses, and different load resistances, the stability of the angular velocity system is analyzed to guide the use of the aerial manipulator more safely and efficiently. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to present an easier and more efficient method for the determination of the geometry of a bevelled gear tooth. Based on a method that provides an easier way for the rack generation of involute helical gears, the mathematical model of a beveloid gear is studied. The mathematical procedure for developing two-dimensional cross-sections has been extended to three-dimensional gear models. A computer programme is developed to obtain generating and generated surfaces. The proposed algorithm is compared with the previous studies for verification and validation. The results demonstrate that the coordinates obtained from the given method are nearly the same on the start and end points of the main gear parts, such as the involute and root fillets regions. Also, between the limits, the values can be considered acceptable. A coordinate deviation of the gear profile has been observed in the mathematical model, because of the profile shift. Modifications have been developed in the equations to eliminate these cases. The main advantage of the proposed method is to obtain mathematical models without carrying out some of the calculation steps used in previous studies. Eventually, this feature will provide an easier and faster method to develop computer-aided models of the beveloid gear types. [ABSTRACT FROM AUTHOR]

Purpose: The buffer allocation problem (BAP) arises in the design of production systems; it involves analyzing and defining the optimal distribution of buffers within a production line. This paper presents a BAP formulation in a parallel series line from a cup sublimation process with unreliable operating conditions. The main objective of this study is to develop a new BAP solution proposal, considering the optimization of the OEE indicator used in Lean Manufacturing. Design/methodology/approach: The BAP was analyzed under an optimization approach from two different criteria: firstly, the maximization of the OEE indicator (Overall Equipment Effectiveness) utilized in Lean Manufacturing, as well as the maximization of the average production rate (Throughput). The case study involves unreliable operating conditions. Process times, and timeframes between failures and repairs, consider normal distribution functions. The evaluation method employed in the study includes the use of simulation meta-models built from experiment designs and production line simulations; on the other hand, the nonlinear GRG algorithm is used to solve the mathematical models. Findings: In the study carried out, it is shown that the OEE indicator can be affected when more buffers are allocated than necessary, hence it is important to calculate and establish the best configuration for them through an analysis such as the one proposed in this document. Research limitations/implications: The research is limited to a case study of an unreliable production line from a cup sublimation process. Practical implications: The proposed solution established in this study can be used in other production lines with configurations different from the one analyzed, considering the optimization criterion of the OEE indicator. Originality/value: Seeking that the allocation of buffers within the production line improves the OEE indicator is something new in the literature, therefore, the results achieved in this research become even more relevant. [ABSTRACT FROM AUTHOR]

The surface properties of newsprint and other paper qualities are to a great extent determined by the properties of the cellulose fibres. An appropriate description of these fibres as they appear in the paper is therefore important and can be used for quality classification and process monitoring. We suggest a model that considers the fibre geometry and appearance. It is based on a two-dimensional shot-noise process. The model is fit by minimizing a weighted least squares distance between the model-based and estimated covariance functions and this provides estimates of the fibre size, intensity and the non-uniform distribution of the fibre orientation. The model is applied to simulated and real data. [ABSTRACT FROM AUTHOR]

In modern converter-dominated power systems, total inertia is very variable and depends on the share of power generated by renewable-based converter-interfaced generation (CIG) at each specific moment. As a result, the limits required by the grid codes on the rate of change of frequency and its nadir or zenith during disturbances become challenging to achieve with conventional control approaches. Therefore, the transition to a novel control strategy of CIG with a grid-forming power converter is relevant. For this purpose, a control algorithm based on a virtual synchronous generator (VSG) is used, which simulates the properties and capabilities of a conventional synchronous generation. However, due to continuously changing operating conditions in converter-dominated power systems, the virtual inertia formed by VSG must be adaptive. At the same time, the efficiency of adaptive algorithms strongly depends on the used VSG structure. In this connection, this paper proposes an enhanced VSG structure for which the transfer function of the active power control loop was formed. With the help of it, the advantages over the conventional VSG structure were proven, which are necessary for the effective adaptive control of the VSG parameters. Then, the analysis of the impact of the VSG parameters on the dynamic response using the transient characteristics in the time domain was performed. Based on the results obtained, adaptive algorithms for independent control of the virtual inertia and the parameters of the VSG damper winding were developed. The performed mathematical modeling confirmed the reliable and effective operation of the developed adaptive control algorithms and the enhanced VSG structure. The theoretical and experimental results obtained in this paper indicate the need for simultaneous development and improvement of both adaptive control algorithms and VSG structures used for this purpose. [ABSTRACT FROM AUTHOR]

In the evolving landscape of targeted marketing, integrating deep learning (DL) and explainable AI (XAI) offers a promising avenue for enhanced customer segmentation. This paper introduces a groundbreaking approach, DeepLimeSeg, which synergizes DL methodologies with Lime-based Explainability to segment customers effectively. The approach employs a comprehensive mathematical model to harness demographic data, behavioral patterns, and purchase histories, categorizing customers into distinct clusters aligned with their preferences and needs. A pivotal component of this research is the mathematical underpinning of the DeepLimeSeg approach. The Lime-based Explainability module ensures that the segmentation results are accurate and interpretable. The mathematical rigor facilitates businesses tailoring their marketing strategies with precision, optimizing sales outcomes. To validate the efficacy of DeepLimeSeg, we employed two real-world datasets: Mall-Customer Segmentation Data and an E-Commerce dataset. A comparative analysis between DeepLimeSeg and the traditional Recency, Frequency, and Monetary (RFM) analysis is presented. The RFM analysis, grounded in its mathematical modeling, segments customers based on purchase recency, frequency, and monetary value. Our preprocessing involved computing RFM scores for each customer, followed by K-means clustering to delineate customer segments. Empirical results underscored the superiority of DeepLimeSeg over other models in terms of MSE, MAE, and R 2 metrics. Specifically, the model registered an MSE of 0.9412, indicative of its robust predictive accuracy concerning the spending score. The MAE value stood at 0.9874, signifying minimal deviation from actual values. This paper accentuates the importance of mathematical modeling in enhancing customer segmentation. The DeepLimeSeg approach, with its mathematical foundation and explainable AI integration, paves the way for businesses to make informed, data-driven marketing decisions. [ABSTRACT FROM AUTHOR]

It is simple to implement conventional current control with a proportional integral (PI) controller. However, system stability and dynamic performance are not perfect, particularly when operating under unfavorable conditions. In this paper, an improved control method is proposed by introducing a compensation unit. The compensation unit can effectively compensate the system's phase around the crossover frequency, greatly enhancing the system's phase margin and stability. It is also capable of handling weak-grid conditions. In this paper, the concept of the proposed compensation unit is explained first. Then, the corresponding mathematical model for the current control loop is built, and system bode diagrams for the conventional and proposed methods are compared. Furthermore, the effect of the parameters for the compensation unit is investigated, and an optimization method is proposed to determine optimal parameters. In addition, to handle weak-grid conditions, the proposed scheme is expanded by including the compensation unit in the grid's feed-forward loop. Finally, an experimental platform is constructed, and the experimental results are presented to validate the proposed method. [ABSTRACT FROM AUTHOR]

The present paper, in the framework of a search for a computer-aided method to detect depression, deals with experimental data of various types, with their correlation, and with the way relevant information about depression delivered by different sets of data can be fused to build a unique body of knowledge about individuals' mental states facilitating the diagnosis and its accuracy. To this aim, it suggests the use of a recently introduced «limiting form» of the kinetic-theoretic language, at present widely used to describe complex systems of objects of the most diverse nature. In this connection, the paper mainly aims to show how a wide range of experimental procedures can be described as examples of this «limiting case» and possibly rendered by this description more effective as methods of prediction from experience. In particular, the paper contains a simple, preliminary application of the method to the detection of depression, to show how the consideration of statistical parameters connected with the analysis of speech can modify, at least in a stochastic sense, each diagnosis of depression delivered by the Beck Depression Inventory (BDI-II). [ABSTRACT FROM AUTHOR]

In this paper applications of curvilinear parametrizations (Serret–Frenet, Bishop) in the path following task have been considered. The parametrizations allow one to derive manipulator's equations with respect to a path. The full mathematical model of the path following task involves two groups of equations, i.e., the dynamics of the manipulator and the equations obtained from the parametrization method, connected in the cascaded system. Based on those relations two path following algorithms have been designed according to the backstepping integrator method (dedicated to the cascaded systems). Depending on the chosen parametrization method the algorithms differ in requirements and performance. In the paper an in-depth analysis comparing features of both considered methods has been presented. The parametric description of a path requires projection of a robot on the path. In this article the orthogonal projection has been taken into account. It introduces a singularity in the robot description. We have proposed a new form of the orthogonal projection constraint which allows a robot to not only approach the path, but also move along it. This novelty design is an important enhancement of the algorithms used so far. The problem of partially known dynamic parameters of a robot has also been addressed. In this paper, we have shown how to apply an adaptive controller to the path following task. Theoretical considerations have been verified with a simulation study conducted for a holonomic stationary manipulator. Achieved results emphasized why it is strongly recommended to use the algorithm version with the orthogonal singularity outside the path. Moreover, the comparative analysis results may be used to select the best curvilinear parametrization method according to the considered task requirements. [ABSTRACT FROM AUTHOR]

In this paper, we construct a more realistic mathematical model to study toxoplasmosis dynamics. The model considers two discrete time delays. The first delay is related to the latent phase, which is the time lag between when a susceptible cat has effective contact with an oocyst and when it begins to produce oocysts. The second discrete time delay is the time that elapses from when the oocysts become present in the environment to when they are able to infect. The main aim in this paper is to find the conditions under which the toxoplasmosis can disappear from the cat population and to study whether the time delays can affect the qualitative properties of the model. Thus, we investigate the impact of the combination of two discrete time delays on the toxoplasmosis dynamics. Using dynamical systems theory, we are able to find the basic reproduction number R 0 d that determines the global long-term dynamics of the toxoplasmosis. We prove that, if R 0 d < 1 , the toxoplasmosis will be eradicated and that the toxoplasmosis-free equilibrium is globally stable. We design a Lyapunov function in order to prove the global stability of the toxoplasmosis-free equilibrium. We also prove that, if the threshold parameter R 0 d is greater than one, then there is only one toxoplasmosis-endemic equilibrium point, but the stability of this point is not theoretically proven. However, we obtained partial theoretical results and performed numerical simulations that suggest that, if R 0 d > 1 , then the toxoplasmosis-endemic equilibrium point is globally stable. In addition, other numerical simulations were performed in order to help to support the theoretical stability results. [ABSTRACT FROM AUTHOR]

When developing neutralization systems for harmful agents, it is necessary to understand the mechanisms of the formation and evolution of an aerosol cloud in a closed or open space. Effective decontamination with aerosol clouds is provided by a rather high particle concentration and dispersion in an open space or on contaminated surfaces. This paper considers neutralization systems based on pulsed powder aerosol generators. It is shown that an aerosol cloud consisting of micron- and submicron-sized particles appears for several seconds after spraying. A further evolution of the aerosol cloud in a room is associated with the gravitational settling, diffusion, and coagulation of particles and their settling on the walls and ceiling. In the case of an open space or a ventilation system in a room, the evolution of the aerosol cloud is affected by the airflow. The main purpose of this paper is to determine the most important parameters and critical conditions of pulsed aerosol generation. A mathematical model is, thus, proposed for pulsed aerosol generation, and its parametric study is conducted in the most typical conditions. The purpose performance predicted by the model is the mass concentration of aerosol particles in the air and on surfaces, depending on the time of particle spraying and dispersion. [ABSTRACT FROM AUTHOR]

In general, the structures of Multi-Active Bridge (MAB) converters that can be found in the literature are usually based on voltage converters. However, in some cases, it could be interesting to have a current-fed input due to load characteristics or operation constraints. This leads to a hybrid MAB structure mixing both current-fed and voltage-fed bridges. In this paper, a new hybrid-fed, fully coupled Triple-Active Bridge (TAB) converter topology with two voltage-fed ports and one current-fed port is studied, modelled and controlled. In the first place, a generalized average model (GAM) is developed for this system. After that, a reduced-order model is elaborated in order to simplify the behavioral study and control of this coupled system. A control strategy was also proposed in this paper, based on the developed mathematical model. Simulation results using Matlab/Simulink are presented to validate this study. [ABSTRACT FROM AUTHOR]

Dual-active bridge (DAB) converters are receiving increasing attention from researchers as a critical part of the power transmission of energy routers. However, the DAB converter generates a large backflow power in conventional control mode, and when the load is mutated, its output voltage takes longer to return to the reference value accompanied by large fluctuations. To solve the above problems, a hybrid strategy is proposed in this paper to optimize the converter. The mathematical models of the transmitted power and the backflow power were firstly derived through in-depth analysis of the DAB converter under extended-phase-shift (EPS) modulation, and the suppression of the backflow power was performed according to the improved Lagrange method utilized in the obtained results. Moreover, considering the poor dynamic characteristics of DAB converters under PI control, according to the state space average model of output voltage in the paper, a model prediction control equation is established to improve the dynamic response of the converter by predicting the output voltage value at the next moment. The simulation results verify the effectiveness of the optimization strategy presented in the text. [ABSTRACT FROM AUTHOR]

Simple Summary: The word "model" can be used with different meanings and different contexts, like a model student, clay models or a model railway. In some cases, the context can clarify exactly what is meant by "model", but sometimes several meanings of model can be present in one area. For instance, with reference to cancer research, there can be ambiguity for what is meant by model. This paper reviews the use of the word model as related to cancer research and within the specific area of the microenvironment that surrounds a cancer tumour. The review grouped different definitions of model into four categories (model organisms, in vitro models, mathematical models and computational models) and explored what is meant in each case, mentioning the advantages and disadvantages of the different models Next, a quantitative investigation of the scientific publications listed in the database of the United States National Library of Medicine was performed by counting the frequencies of use of these terms, as well as the components of the microenvironments and the organs modelled with these techniques. The Oxford English Dictionary includes 17 definitions for the word "model" as a noun and another 11 as a verb. Therefore, context is necessary to understand the meaning of the word model. For instance, "model railways" refer to replicas of railways and trains at a smaller scale and a "model student" refers to an exemplary individual. In some cases, a specific context, like cancer research, may not be sufficient to provide one specific meaning for model. Even if the context is narrowed, specifically, to research related to the tumour microenvironment, "model" can be understood in a wide variety of ways, from an animal model to a mathematical expression. This paper presents a review of different "models" of the tumour microenvironment, as grouped by different definitions of the word into four categories: model organisms, in vitro models, mathematical models and computational models. Then, the frequencies of different meanings of the word "model" related to the tumour microenvironment are measured from numbers of entries in the MEDLINE database of the United States National Library of Medicine at the National Institutes of Health. The frequencies of the main components of the microenvironment and the organ-related cancers modelled are also assessed quantitatively with specific keywords. Whilst animal models, particularly xenografts and mouse models, are the most commonly used "models", the number of these entries has been slowly decreasing. Mathematical models, as well as prognostic and risk models, follow in frequency, and these have been growing in use. [ABSTRACT FROM AUTHOR]

Polyvinyl butyral (PVB) is a thermoplastic resin commonly used as an interlayer material in laminated glass. Combined with textile fibres from worn tyres, PVB can produce a composite material with unique properties. One such property is absorption. Absorption in textile fibre composite materials refers to the ability of the material to absorb or retain moisture or other fluids. The presence of moisture or liquids can affect the properties of composite materials, such as their strength, stiffness, and dimensional stability. As a result of the physical and chemical action of the environment, corrosion of plastics occurs and manifests itself in changes in appearance, surface quality, weight, dimensions, and also in changes in other properties. This paper investigates four composite materials with different fabrics content. The aim of this paper is to propose a generalized mathematical model for absorption values so that, with different ratios of textile fibre in the material, its quality indicators are at a sufficient level. Our study will proceed from the assumption that by changing the values of the individual coefficients of the selected model based on their analysis, we will achieve the required qualitative indicators. [ABSTRACT FROM AUTHOR]

This paper presents an analysis of the effectiveness of the element interaction model in a vehicular ad hoc network (VANET). An analysis of the mathematical model and its numerical solution for the system of boundary device interactions in the traditional configuration of roadside unit (RSU) placement using single- and dual-channel connection between on-board units (OBU) and RSU is given. In addition, the model efficiency is improved using a clustering approach. The efficiency evaluation is based on calculating the percentage of unprocessed requests generated by OBUs during their mobility, the average power consumption and the magnitude of the delay in transmitting and processing the generated requests in the OBU–RSU system. The traditional and cluster models are compared. The results obtained in this paper show that each of the proposed models can be effectively implemented in mobile nodes and will significantly reduce the overall expected query processing time to improve the organization and algorithmic support of VANET. Along with this, it is shown that the developed approach allows for efficient power consumption when combining RSUs into clusters with a shared cache. The novelty of solving the problems is due to the lack of a comprehensive model that allows the distribution and prediction of the parameters and resources of the system for different computational tasks, which is essential when implementing and using V2X technology to solve the problems of complex management of VANET elements. [ABSTRACT FROM AUTHOR]

Fractional differential equations are used to construct mathematical models and can describe the characteristics of real systems. In this paper, the parameter estimation problem of a fractional Wiener system is studied by designing linear filters which can obtain smaller tunable parameters and maintain the stability of the parameters in any case. To improve the identification performance of the stochastic gradient algorithm, this paper derives two modified stochastic gradient algorithms for the fractional nonlinear Wiener systems with colored noise. By introducing the forgetting factor, a forgetting factor stochastic gradient algorithm is deduced to improve the convergence rate. To achieve more efficient and accurate algorithms, we propose a multi-innovation forgetting factor stochastic gradient algorithm by means of the multi-innovation theory, which expands the scalar innovation into the innovation vector. To test the developed algorithms, a fractional-order dynamic photovoltaic model is employed in the simulation, and the dynamic elements of this photovoltaic model are estimated using the modified algorithms. Concurrently, a numerical example is given, and the simulation results verify the feasibility and effectiveness of the proposed procedures. [ABSTRACT FROM AUTHOR]

The aim of this paper is to evaluate the feasibility of implementation of a passive safety feature in the form of an under-fuselage airbag in the rescue systems of small aircraft. The paper presents a multidisciplinary approach for the viability of the implementation. It presents the development of mathematical model for airbag performance analysis. The model is validated against the experimental data to account for various simplifications. Validated mathematical model is used to design a full-scale airbag for the chosen airplane to perform in the designed range. Weight penalty for increased safety is determined. [ABSTRACT FROM AUTHOR]

In recent years, queuing systems with batch service are emerging as powerful and flexible mathematical models in different frameworks. In this paper, we consider a single server queuing system with Poissonian arrivals, infinite buffers, and a constant batch size b. This paper addresses a little-studied optimization problem, namely the existence of an optimal arrival rate that minimizes the average sojourn time. Unlike the classical M / M / 1 queue, for any batch size b, the problem admits a non-trivial solution that can be found by solving a polynomial equation of degree b + 1 . Since, in general, only numerical solutions are available, a simple first-order approximation is also derived and the corresponding deviations (in terms of input rate and sojourn time) are calculated. In more detail, it is shown that the approximation improves as the batch size increases and, in any case, the relative error for the average sojourn time is less than 0.34%. Finally, the paper provides new theoretical results about the asymptotic service rate in the equivalent birth–death process, highlighting how it depends on all queue parameters. [ABSTRACT FROM AUTHOR]

Aiming at the penetration problem of high-speed vehicles against a modified proportional guidance interceptor, a three-dimensional mathematical model of attack–defense confrontation between the high-speed vehicle and the interceptor is established in this paper. The modified proportional navigation guidance law of the interceptor is included in the model, and control constraints, pitch angle velocity constraints, and dynamic delay are introduced. Then, the performance index of the optimal penetration of high-speed vehicles is established. Under the condition of considering the 180-degree BTT control, the analytical solutions of the optimal speed roll angle and the optimal overload of high-speed vehicles are obtained according to symmetric Hamilton principle. The simulation results show that the overload switching times of high-speed vehicles to achieve optimal penetration are N − 1, where N is the modified proportional guidance coefficient of the interceptor. When the maximum speed roll angle velocity is [60, 90] degrees per second, the penetration effect of high-speed vehicles is good. Finally, the optimal penetration guidance law proposed in this paper can achieve a miss distance of more than 5 m when the overload capacity ratio is 0.33. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to efficiently find the number and optimal placement of BTSs in the coverage area such that the implementation cost is minimized, while the user's traffic in the corresponding area and the channel interference constraints are satisfied. Design/methodology/approach: An integer linear mathematical model has been proposed to assign all customer points to transceiver-based stations. The objective function has been assumed to minimize fixed costs while considering a penalty for reducing interference. An optimization solver has been applied to solve the model. Findings: The proposed mathematical model was compared to another existing model in the literature from three points of view: coverage cost, construction costs, and running time. The results indicated that the proposed model has the appropriate efficiency to find solutions to real practical problems. In more detail, the proposed model succeeded to find solutions with less coverage or construction cost in a shorter time, compared with the model in literature, which has been referred to as the SSH model in the paper. However, there have been some samples in which the SSH model overtakes the proposed model in one or two mentioned aspects for comparison. Research limitations/implications: The limitation of this study is that the channel model was considered based on the simple free space path loss model, while the real channel model based on the environmental effects can be suggested for future work. Another important issue is that for BTS localization design, knowing the status of the real environment leads to the proper design in such networks. Social/practical implications: BTS localization is the most important issue in mobile networks' design. In a practical situation, there is not any software available to design a mobile network in the corresponding coverage area. Therefore, this paper can help communication engineers to implement the proposed approach in a real environment. Originality/value: In this paper, the problem of the optimal location of transceiver-based stations (BTS) in different models in the coverage area has been addressed such that the implementation cost is minimized, while the user's traffic in the corresponding area and the channel interference constraints are satisfied. This has not been considered in the literature. Any of the existing models focus on one aspect to optimize, such as maximizing the coverage, minimizing the interference, and minimizing coverage or construction costs. The novelties of the proposed model are twofold: i) two goals were considered in the objective function, i.e., minimizing construction costs and minimizing interference. Since interference with full coverage is unavoidable, the model added a penalty to the objective function to reduce the interference as much as possible; and ii) it was assumed that there is more than one single type BTS, any of which has different power, radius, and capacity. This makes the model more real and indeed more complicated to solve. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of moisture in the transformer insulation system. The author proposed that apart from the temperature, the uneven aging of cellulose insulation may have a substantial effect on moisture distribution. The main goal of the research was to check the influence of the degree of aging of winding paper on moisture distribution by taking into account temperature distribution. New paper and paper at three different stages of aging were tested. The obtained results confirmed the hypothesis it was proven that the uneven aging of insulation may enhance moisture distribution in the insulation system. [ABSTRACT FROM PUBLISHER]

Abstract: In a previous work, a moisture diffusion coefficient for non-impregnated transformer insulation paper was proposed, which is useful for analysing the moisture dynamics in electrical power transformer insulation during its construction stage. This diffusion coefficient was determined using a set of experimental drying curves obtained in a thermogravimetric analyzer and an optimization process that employs genetic algorithms. The expression for the moisture diffusion coefficient proposed in that previous work is dependent on the temperature, insulation thickness and average moisture concentration. The use of average moisture concentration is not common in diffusion models. In this paper, a new expression for the moisture diffusion coefficient is proposed in which the dependence on average moisture has been substituted by a dependence on the local concentration. This new expression was obtained that is more suitable for diffusion models. To obtain that expression, the same experimental data used in the previous study have been used, but the genetic algorithm’s optimization process was modified. In this paper, a description of the applied procedure is detailed, and the new proposed expression is presented. Finally, a comparison between both equations, the one dependent on average moisture and the one dependent on the local moisture, is performed using a drying diffusion model implemented in a finite element commercial software package. [Copyright &y& Elsevier]

This paper elucidates the question whether bubble effect can possibly take place in the insulation of OIP (Oil Impregnated Paper) type of bushings. The investigations were performed on a bushing insulation model and indicated to a possibility that the effect may occur. Presence of metallic screens in the insulation does not limit the development of gas bubbling; they only force the motion of water vapor bubbles along the model axis. The temperature dependence of bubble initiation on the water content in paper part of the bushing insulation is similar to the presented earlier in literature characteristics for bubbling in main insulation of power transformers. The possibility of bubble effect occurrence may explain the relatively frequent cases of transformer bushing failures. [ABSTRACT FROM PUBLISHER]

Abstract: Availability analysis has been an important issue in the design field of any Industrial system as the system structure has become more complicated. Also, the system availability is affected by many factors such as design, manufacturing, installation, etc., and so it may be extremely difficult to model, analyze and predict the failure behavior of the system. The purpose of this paper is to develop a new approach for computing various performance measures, namely reliability, availability, MTBF (mean time between failures), ENOF (expected number of failures), failure rate and repair time, for any industrial system. In the proposed approach, the failure rates and repair times of all constituent components are obtained using genetic algorithms and then various performance measures are computed using fuzzy lambda–tau methodology. Washing system, the major part of paper industry is the subject of study. The interactions among the working components are modeled using Petri nets. Failure and repair rates are represented using triangular fuzzy numbers as they allow expert opinion, linguistic variables, operating conditions, uncertainty and imprecision in reliability information to be incorporated into system model. Based on calculated reliability parameters, a structured framework has been developed that may help the maintenance engineers to analyze and predict the system behavior. [Copyright &y& Elsevier]

Abstract: This paper proposes the concept and the technology of social networking federation as a paradigm where information on various social network systems can be seamlessly integrated in order to provide users a uniform and semantic view of their social connections. Such a uniformly fused social network provides a single point of access where all information with respect to one’s social networks can be queried and reasoned about. The goal of the research is to establish a foundation of integrating and assimilating information within multiple social network systems. We designed a reference model of social networking federation system in this paper, as well as some prototype application to demonstrate its paradigm. We believe our work would provide a novel vision of future online social network. [Copyright &y& Elsevier]

This paper studies gas allocation problem in the iron and steel production. Gas allocation problem is a multi-objective optimization problem with complex constraints. A gas allocation problem is mathematically modeled with high dimension, non-linear and complex constraint features. The intelligent optimization algorithms have certain advantages in solving such model. An improved Differential Evolution algorithm based on individual quality evaluation is proposed to solve the above model. The results show multiple gas allocation schemes are provided when all constraints are met, and all optimization objectives of some schemes are better than then manual gas allocation scheme. [ABSTRACT FROM AUTHOR]

Paper is a stochastic network of fibres, water and additives, and in that sense it may be envisaged as a composite material. Since fibres are much longer than the thickness of the paper sheet, the network is planar and almost two-dimensional. The two-dimensional structure governs many paper properties but the three-dimensional porous structure is also important. Insight into the structural changes that take place when paper is compressed in the paper machine may be gained by modelling and simulation of its viscoelastoplastic behaviour. The present work describes a mathematical model based on the cellular solids theory, characterising the nonlinear rheologic behaviour of the material. This approach results in an unsteady state problem and the resulting set of ODEs is solved by means of the DLSODES subroutine, which uses an integrator based in the Gear method. Experiments were conducted on a laboratory-scale dynamic press in order to validate the mechanical model. [Copyright &y& Elsevier]

We describe new ESS models of density regulation driven by genic selection to explain the cyclical dynamics of a social system that exhibits a rock-paper-scissors (RPS) set of three alternative strategies. We tracked changes in morph frequency and fitness of Lacerta vivipara and found conspicuous RPS cycles. Morphs of Uta and Lacerta exhibited parallel survival-performance trade-offs. Frequency cycles in both species of lizards are driven by genic selection. In Lacerta, frequency of each allele in adult cohorts had significant impacts on juvenile recruitment, similar to mutualistic, altruistic, and antagonistic relations of RPS alleles in Uta. We constructed evolutionarily stable strategy (ESS) models in which adults impact juvenile recruitment as a function of self versus nonself color recognition. ESS models suggest that the rapid 4-year RPS cycles exhibited by Lacerta are not possible unless three factors are present: behaviors evolve that discriminate self versus nonself morphs at higher rates than random, self- versus non-self-recognition contributes to density regulation, and context-dependent mate choice evolves in females, which choose sire genotypes to enhance progeny survival. We suggest genic selection coupled to density regulation is widespread and thus fundamental to theories of social system evolution as well as theories of population regulation in diverse animal taxa. [ABSTRACT FROM AUTHOR]

A. V. Hill's 1938 paper ‘The heat of shortening and the dynamic constants of muscle’ is an enduring classic, presenting detailed methods, meticulous experiments, and the model of muscle contraction that now bears Hill's name. Pairing a simulation based on Hill's model with a reading of his paper allows students to follow his thought process to discover key principles of muscle physiology and gain insight into how to develop quantitative models of physiological processes. In this article, the experience of the author using this approach in a graduate biomedical engineering course is outlined, along with suggestions for adapting this approach to other audiences. [ABSTRACT FROM AUTHOR]

In order to complete the broadband simulation model of power transformer, and establish a systematic and complete model for studying fast transient interaction between transformer and power system, the frequency dependent characteristics of dielectric losses in power transformer were investigated. Several typical insulation structures in power transformers were considered and measuring techniques determined to study the dielectric losses. Frequency dependent dielectric losses in the range of 10-107 Hz were measured by a dielectric spectroscopy analyzer produced by Novocontrol. The characteristics of insulating papers and pressboard measured in the air and after immersing in the mineral oil were compared. Based on the dielectric relaxation theory, the number of dielectric relaxation was determined according to the measured data, and four typical model functions were adopted to fit the data and the consistency of fitting by these functions were compared and physical explanations of fitting parameters were described. Finally, a quantitative description of frequency dependent characteristics of insulation losses was proposed for improving the transformer simulation model. [ABSTRACT FROM PUBLISHER]