Retinal vein cannulation involves puncturing an occluded vessel on the micron scale. Even single millinewton force can cause permanent damage. An ophthalmic robot with a piezo-driven injector is precious enough to perform this delicate procedure, but the uncertain viscoelastic characteristics of the vessel makes it difficult to achieve the desired contact force without harming the retina. The paper utilizes a viscoelastic contact model to explain the mechanical characteristics of retinal blood vessels in order to tackle this issue. The uncertainty in the viscoelastic properties is considered an internal disturbance of the contact model, and an active disturbance rejection controller is then proposed to precisely control the contact force. The experimental results show that this method can precisely adjust the contact force at the millinewton level even when the viscoelastic parameters vary significantly (up to 403.8%). The root mean square (RMS) and maximum value of steady-state error are 0.32 mN and 0.41 mN. The response time below 2.51 s with no obvious overshoot.

This paper has the objective of implementing the radial rotor position control of a three-phase bearingless induction machine with split winding and optimized drive structure, using the ADRC technique. Because it is a multivariable, nonlinear, time-varying system with coupled variables, it is necessary to use advanced control strategies in order for the system to operate efficiently and with good dynamic performance. The ADRC controller considers the total disturbance composed of unmodeled dynamics, nonlinearities, uncertainties, and load variations, as a new system state, to be estimated in real-time through an extended state observer. In this mode, disturbances are compensated in real-time, eliminating regime errors and with good response to disturbances in general.

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, multivariable Fractional-Order Controller is designed for the nonlinear device. The merits of the fractional-order design include: 1) Control of multivariable nonlinearities, 2) Compensation of uncertainties, 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 design.

This study presents finite-time synchronization of chaotic fractional order systems with disturbance uncertainty and unknown time delay. First, a PID sliding surface is presented. Then, for the finite-time synchronization of the master and slave systems, a robust sliding-adaptive control method is provided. Update rules have been retrieved to estimate the system parameters by using the Lyapunov function while establishing the stability of the suggested mechanism and assuring the convergence of errors to zero. The proposed approach was used to solve the fractional order system of Gensou-Tsei with time-varying parameters, and the simulation results show that the presented approach performs well.

The Doppler band compensated by the keystone transform (KT) is limited. Therefore, it needs to be used in conjunction with the Doppler ambiguity compensation function to correct the range migration (RM) caused by maneuvering targets with Doppler ambiguity. However, the KT implemented by sinc interpolation suffers from significant performance loss at boundaries of compensation Doppler bands. Additionally, in a multi-target scenario, KT implementation methods occupy high complexity when the Doppler range of targets spans over two compensation Doppler bands. To address aforementioned issues, this study presents a variable Doppler starting point keystone transform (VDSPKT) method, where a new form of ambiguity compensation function is constructed, turning the Doppler starting point of the compensation band in KT variable. Firstly, the position of the compensation Doppler band is changed from fixed to adjustable as needed, enhancing the flexibility of KT. Crucially, the connection points of the compensation Doppler bands in sinc interpolation are reset, avoiding the performance loss at their boundaries. Also, the compensation band is adjusted to cover the narrow Doppler frequency range caused by targets, significantly improving the computational efficiency. Finally, the simulation results demonstrate that the proposed approach effectively addresses the performance degradation and high computational complexity of KT in the aforementioned scenarios, resulting in a computational load reduced by approximately 50% compared to traditional methods.

Due to the nonlinear stiffness and fractional-order damping characteristics of some real suspension systems, coupled with the presence of viscoelastic materials, fractional-order nonlinear suspension system modeling has become a focus of research in recent years. In this study, an electric oil and gas actuator based on fractional-order PID position feedback control is proposed, through which the damping coefficient of the suspension system is adjusted to realize the active control of the suspension. A fractional order PID algorithm is used to control the motor's rotational angle to realize the damping adjustment of the suspension system. In this process, the road roughness is collected by the sensors as the criterion of damping adjustment, and the particle swarm algorithm is utilized to find the optimal objective function under different road surface slopes, to obtain the optimal cornering value. According to the mathematical and physical model of the suspension system, the simulation model and the corresponding test platform of this type of suspension system are built. The simulation and experimental results show that the simulation results of the fractional-order nonlinear suspension model are closer to the actual experimental values than those of the traditional linear suspension model, and the accuracy of each performance index is improved by more than 18.5%. The designed active suspension system optimizes the body acceleration, suspension dynamic deflection, and tire dynamic load to 89.8%, 56.7%, and 73.4% of the passive suspension, respectively. Notably, the designed fractional order PID control circuit for the motor shows better control results compared to the conventional PID control circuit. This study provides an effective theoretical and empirical basis for the control and optimization of fractional-order nonlinear suspension systems.

This paper presents an approach to improve the robustness of tip-tilt controllers for fast-steering mirror (FSM)-based laser beam steering (LBS) systems in the presence of dynamic disturbances such as external shocks. To this end, we propose the addition of a disturbance observer (DOB)-based anti-shock controller in parallel to the original linear servo control loop to improve its control performance in the presence of external shocks. To increase the tip-tilt control performance against external shocks, the DOB-based control method, which is an improved control method for eliminating nonperiodic disturbances, is implemented in the original tip-tilt control system. Results indicate that the control error of the DOB-based anti-shock controller decreased, resulting in an efficient improvement in its disturbance-rejection performance.

We designed a novel growth controller regulated by feeding of an unnatural amino acid, Nε-benzyloxycarbonyl-L-lysine (ZK), using a specific incorporation system at a sense codon. This system is constructed by a pair of modified pyrrolisyl-tRNA synthetase (PylRS) and its cognate tRNA (tRNApyl). Although ZK is non-toxic for normal organisms, the growth of Escherichia coli carrying the ZK incorporation system was inhibited in a ZK concentration-dependent manner without causing rapid bacterial death, presumably due to generation of non-functional or toxic proteins. The extent of growth inhibition strongly depended on the anticodon sequence of the tRNApyl gene. Taking advantage of the low selectivity of PylRS for tRNApyl anticodons, we experimentally determined the most effective anticodon sequence among all 64 nucleotide sequences in the anticodon region of tRNApyl gene. The results suggest that the ZK-regulated growth controller is a simple, target-specific, environmental noise-resistant and titratable system. This technique may be applicable to a wide variety of organisms because the growth inhibitory effects are caused by “informational disturbance”, in which the highly conserved system for transmission of information from DNA to proteins is perturbed.

When a grid-forming (GFM) inverter is connected to a low or medium voltage weak power grid, the line impedance with resistive-inductive characteristics will cause power coupling. Typical GFM decoupling control strategies are designed under nominal line impedance parameters. However, there are deviations between the nominal line impedance and actual parameters, resulting in poor decoupling effects. Aiming at this problem, this paper proposes a power decoupling strategy based on a reduced-order extended state observer (ESO). Firstly, the power dynamic model of GFM is established based on the dynamic phasor method. Then, the model deviation and power coupling due to line impedance parameter perturbation are estimated as internal disturbances of the system, and the disturbances are compensated on the basis of typical power control strategy and virtual impedance decoupling. Good decoupling performance is obtained under different impedance parameters, improving the control strategy's robustness. Finally, the effectiveness of the proposed method is verified by the results of RT Box hardware-in-the-loop experiments.

This paper focus on the modeling and time-domain analyzing method of piecewise-smooth fractional-order circuit systems. Firstly, an analytical framework is constructed based on a generalized piecewise-smooth two-port impedance network model, which takes the topological characteristics of Dickson type switched-capacitor converters (SCCs) as examples, and considers the fractional-order characteristics of class-2 X7R ceramic capacitors, which are widely used in SCCs. Secondly, the time-domain analyzing method for such a piecewise-smooth fractional-order circuit system is developed, numerical solutions are obtained, and the influence of the fractional-order capacitor on the power conversion efficiency of the system are revealed. Finally, in order to validate the analysis, both numerical simulation and experiments are provided in the work, the results of which confirm that, the proposed fractional-order analytical framework can capture the power loss mechanism of piecewise-smooth fractional-order circuit systems more effectively than the traditional integer-order based approach, thus benefiting the design of circuit systems.

In this paper, two types of the general fractional derivatives of distributed order as well as a corresponding fractional integral of distributed type are defined and their basic properties are investigated. The general fractional derivatives of distributed order are constructed for a special class of the one-parametric Sonin kernels with a power law singularities at the origin. The conventional fractional derivatives of distributed order based on the Riemann-Liouville and the Caputo fractional derivatives are particular cases of the general fractional derivatives of distributed order introduced in this paper.

In this paper the D 3 dihedral logistic map of fractional order is introduced. The map 1 presents a dihedral symmetry D 3 . It is numerically shown that the construction and interpretation 2 of the bifurcation diagram versus the fractional order require special attention. The system stability 3 is determined and the problem of hidden attractors is analyzed. Also, analytical and numerical 4 results show that the chaotic attractor of integer order, with D 3 symmetries, looses its symmetry 5 in the fractional-order variant.

The gradient descent algorithm has become the standard algorithm for computing the extreme values of functions, but for multivariate functions this algorithm is mostly ineffective. This is because the convergence rate of each element is inconsistent in most cases. However, in this paper, we found that the gradient sign is a self-optimizing operator, ensuring that the convergence rate is consistent across all elements. This also explains, from an optimization perspective, the success of the Fast Gradient Sign Method (FGSM) in generating adversarial samples that are indistinguishable from the normal input, but can easily fool neural networks. We also found that the fractional order gradient is also self-optimizing, and that the convergence speed of this algorithm can be controlled by adjusting the order of the gradient. Experiments suggest that this algorithm not only generates adversarial samples faster than other algorithms, but that a single source image can generate many such samples. This algorithm is also more effective than others at generating adversarial samples from simple images.

A stochastic dominance (SD) relation can be defined by two different perspectives: One from the view of distributions, and the other one from the view of expected utilities. In early days, Fishburn investigated SD from the view of distributions and we refer this perspective as Fishburn’s SD. One of his many results was the development of fractional-order SD for continuous distributions. However, discrete fractional-order SD may not be generalized directly since some properties of fractional calculus do not have a discrete counterpart. In this paper, we develop a discrete analogue of fractional-order SD from the view of distributions. We generalize the order of SD by Lizama’s fractional delta operator, show the preservation of SD hierarchy, and formulate the utility classes that are congruent with our SD relations. This work brings a message that some results of discrete SD cannot be generalized directly from continuous SD. We characterize the difference between discrete and continuous fractional-order SD, as well as the way to handle them.

This paper discusses the concept of fractional derivative with complex order from the application point of view. It is shown that a fractional derivative is hermitian, if and only if the order is real. The hermitian part of complex order derivatives behave like allpass filters with almost logarithmic phase.

In this research article we solve the problem of synchronization and anti-synchronization of chaotic systems described by discrete and time-delayed variable fractional order differential equations. To guarantee the synchronization and anti-synchronization of these systems, we use the well-known PID control theory and the Lyapunov-Krasovskii stability theory for discrete systems of variable fractional order.We illustrate the results obtained through simulation with examples, in which it can be seen that our results are satisfactory, thus achieving synchronization and anti-synchronization of chaotic systems of variable fractional order with discrete time delay.

This paper reports a new global Mittag-Leffler synchronization criterion with regard to fractional-order hyper-chaotic financial systems by designing the suitable impulsive control and the state feedback controller. The significance of this impulsive synchronization lies in the fact that the backward economic system can synchronize asymptotically with the advanced economic system under the effective impulse macroeconomic management means. Matlab LMI-toolbox is utilized to deduce the feasible solution in numerical example, which shows the effectiveness of the proposed methods. It is worth mentioning that the LMI-based criterion usually requires the activation function of the system to be Lipschitz, but the activation function in this paper is fixed and truly nonlinear, which cannot be assumed to be Lipschitz continuous. This is another mathematical difficulty overcome in this paper.

In this paper, we compare the performance between systems of ordinary and (Caputo) fractional differential equations depicting the susceptible-exposed-infectious-recovered (SEIR) models of diseases. In order to understand the origins of both approaches as mean-field approximations of integer and fractional stochastic processes, we introduce the fractional differential equations as approximations of some type of fractional nonlinear birth--death processes. Then, we examine validity of the two approaches against empirical courses of epidemics; we fit both of them to case counts of three measles epidemics that occurred during the pre-vaccination era in three different locations. While FDEs appear more flexible in fitting empirical data, our ODEs offered better fits to two out of three data sets. Important differences in transient dynamics between these modeling approaches are discussed.

DGJ (Daftardar-Gejii-Jafaris) method is used to obtain numerical solution of the third order fractional differential equation. Providing the DGJ method converges, the approximate solution is a good and effective numerical result which is close to the exact solution or the exact solution. For this,the examples of the explaning the method are presented. The proposed method is implemented for the approximation solution of the third order nonlinear fractional partial differential equations. The method was shown to be unsuitable and inconsistent for an example of a nonlinear fractional partial differential equation depend on initial-boundary value conditions. The fact that these numerical results are not consistent can be explained by the fact that the method is not convergent.

This paper is concerned with bump-less transfer of parametrized disturbance observer based controller (DOBC) with Individual Pitch Control (IPC) strategy for full load operation of wind turbine. Aerodynamic cyclic loads are reduced by tuning multivariable DOBC with the objective to reduce output power fluctuation, tower oscillation and drive-train torsion. Furthermore tower shadow and wind shear effect are also mitigated using parametrized controller. A scheduling mechanism between two DOBC is developed and tested on Fatigue, Aerodynamics, Structures, and Turbulence ( FAST) code model of National Renewable Energy Laboratory (NREL)’s 5 MW wind turbine. The closed-loop system performance is assessed by comparing the simulation results of proposed controller with a fixed gain and Linear Parameter Varying (LPV) DOBC with Collective Pitch Control (CPC) for full load operation. It is tested with step changing wind to see the behavior of the system under step change with wind shear and tower shadow (cyclic load) effects. Also turbulent wind is applied to see the smooth transition of the controllers. It can be concluded from the results that the proposed parametrized control DOBC with IPC shows smooth transition from one controller to another by interpolation. Moreover fatigue of the gear and tower due to wind shear and tower shadow effects are reduced considerably by the proposed controller as compared to collective pitch control.

In this paper, we propose to explore a nonlinear fractional mathematical model of HFMD- Hand Foot Mouth Disease with vaccinated compartment. Firstly, we prove the non negativity and boundedness for the fractional order dynamical model. The system’s existence and uniqueness are studied using the formulation of the Caputo derivative operator. The fixed-point approach was used to get results indicating the presence of at least one solution. In numerical simulation, we obtained the approximate solution by using fractional Euler method.

In this paper, the 1st level general fractional derivatives of arbitrary order are defined and investigated for the first time. We start with a generalization of the Sonin condition for the kernels of the general fractional integrals and derivatives and then specify a set of the kernels that satisfy this condition and posses an integrable singularity of power law type at the origin. The 1st level general fractional derivatives of arbitrary order are integro-differential operators of convolution type with the kernels from this set. They contain both the general fractional derivatives of arbitrary order of the Riemann-Liouville type and the regularized general fractional derivatives of arbitrary order considered in the literature so far. For the 1st level general fractional derivatives of arbitrary order, some important properties including the 1st and the 2nd fundamental theorems of Fractional Calculus are formulated and proved.

This paper first discusses a fractional-order Liu system of order as low as 2.7 and shows its chaotic characteristics by carrying out numerical simulations such as Lyapunov exponents, bifurcation diagrams and phase portraits. Then, by using the topological horseshoe theory and computer-assisted proof, the existence of chaos in the system is verified theoretically. Finally, the fractional-order system is implemented on a Field Programmable Gate Array (FPGA) and the results obtained show that the fractional-order Liu system is indeed chaotic.

The aim of this study was to investigate the physicochemical characterization and biological activities of chitosan (CH) based composite films with the incorporation of chestnut flower essential oil (CFEO). The composite films were prepared by casting method and characterized in terms of structural, morphological and mechanical properties via FT-IR, XRD, UV, SEM and TGA. The results proved the significantly increased water vapor permeability (WVP), heat resistance, antibacterial and antioxidant capabilities of CH-CFEO films. The incorporation of CH and CFEO enhanced the UV blocking, which made the film shield almost all UV light. Films with the tensile strength of 6.37 ± 0.41 MPa and elongation at break of 22.57 ± 0.35% were got with 6 mg mL-1 CFEO. Subsequently, the fruit preservation experiments also confirmed that the composite films could effectively extend the shelf life of bananas through their excellent water vapor and oxygen barrier. These desirable performances enable our newly developed composite films to be a remarkable packaging material to solve the fresh fruit preservation dilemma.

This study presents an effective control algorithm to improve the robustness of fast steering mirror (FSM)-based laser beam steering systems against dynamic disturbances such as repetitive disturbances resulting from operating conditions. A stable control system must be able to maintain the required high-precision control even when dynamic disturbances affect the FSM system. In this study, an improved control method is proposed using an internal model principle (IMP)-based nonlinear controller with a disturbance observer (DOB) for the FSM system. This IMP-based controller with DOB can attenuate the residual control error signal under dynamic disturbance conditions.

This paper assesses the behaviour of active distribution networks with high penetration of renewable energy sources when the control is performed in a centralised manner. The control assets are the on-load tap changers of transformers at the primary substation, the reactive power injections of the renewable energy sources and the active and reactive power exchanged between adjacent feeders when they are interconnected through a DC link. A scaled-down distribution network is used as testbed to emulate the behaviour of an active distribution system with massive penetration of renewable energy resources. The laboratory testbed involves hardware devices, real-time control, and communication infrastructure. Several key performance indices are adopted to assess the effects of the different control actions on the system operation. The experimental results demonstrate that the combination of control actions enables the optimal integration of a massive penetration of renewable energy.

Vibrations of blades and tower have important impact for wind turbine. This paper presents a active controller design to suppress blade edgewise vibrations under aerodynamic load and gravitational load.Treating the sum of aerodynamic load input in edgewise direction and gravitational load as unknown disturbance input,a stochastic disturbance accommodating control(SDAC) approach is proposed to design a controller which it utilizes a minimum-variance unbiased estimator(MVUE) to estimate both state and unknown input. The stability analysis proved that the proposed SDAC is bounded in mean square.In order to verify the performance of the minimum-variance unbiased estimator and the proposed SDAC, numerical simulations using Matlab/Simulink have been carried out for the National Renewable Energy Laboratory 5-MW wind turbine.Under the different circumstance which exists the random process and measure noise and noise free. It is shown that the estimation value by MVUE can tracking the real state and unknown input. The results are also compared to the traditional linear quadratic regulator(LQR) and show that the proposed stochastic disturbance accommodating control scheme can further reduce displacement in edgewise vibrations direction and the control strategy is more effective than the LQR.

Abstract The modified Bessel function (MBF) of the first kind is a fundamental special function in mathematics with applications in a large number of areas. When the order of this function is integer, it has an integral representation which includes the exponential of the cosine function. Here we generalize this MBF to include a fractional parameter, such that the exponential in the previously mentioned integral is replaced by a Mittag-Leffler function. The necessity for this generalization arises from a problem of communication in networks. We find the power series representation of the fractional MBF of the first kind, as well as some differential properties. We give some examples of its utility in graph/networks analysis and mention some fundamental open problems for further investigation.

This paper is related to the fractional view analysis of Helmholtz equations, using innovative analytical techniques. The fractional analysis of the proposed problems has been done in terms of Caputo-operator sense. In the current methodology, first, we applied the r-Laplace transform to the targeted problem. The iterative method is then implemented to obtain the series form solution. After using the inverse transform of the r-Laplace, the desire analytical solution is achieved. The suggested procedure is verified through specific examples of the fractional Helmholtz equations. The present method is found to be an effective technique having a closed resemblance with the actual solutions. The proposed technique has less computational cost and a higher rate of convergence. The suggested methods are therefore very useful to solve other systems of fractional order problems.

This paper describes a proposed fractional filter-based multi-scale underwater and hazy image enhancement algorithm. The proposed system combines a modified global contrast operator with fractional order-based multi-scale filters used to generate several images, which are fused based on entropy and standard deviation. The multi-scale-global enhancement technique enables fully adaptive and controlled colour correction and contrast enhancement without over exposure of highlights when processing hazy and underwater images. This in addition to illumination/reflectance estimation coupled with global and local contrast enhancement. The proposed algorithm is also compared with the most recent available state-of-the-art multi-scale fusion de-hazing algorithm. Experimental comparisons indicate that the proposed approach yields better edge and contrast enhancement results without halo effect, colour degradation and is faster and more adaptive than all other algorithms from the literature.

This paper presents an observer-based dynamic output feedback controller design procedure using Linear Matrix Inequality (LMI) optimization for second-order systems with uncertainty and persistent perturbation in the states. Using linear-quadratic criteria, cost functions are minimized in a two-stage procedure to compute optimal state feedback gains, and observer gains are coupled into a dynamic output feedback optimal controller. The LMI set used in the two stages is matrix inversion-free, a key issue for polytope formulation when uncertainty is present. The approach is tested in a mobile inverted pendulum robotic platform, and the effectiveness is verified in this underactuated and undesensed case.

In this paper, we propose an efficient numerical computation method of reduced-order controller design for linear time-invariant systems. The design problem is described by linear matrix inequalities (LMIs) with a rank constraint on a structured matrix, due to which the problem is NP-hard. Instead of the heuristic method that approximates the matrix rank by the nuclear norm, we propose a numerical projection onto the rank-constrained set based on the alternating direction method of multipliers (ADMM). Then the controller is obtained by alternating projection between the rank-constrained set and the LMI set. We show the effectiveness of the proposed method compared with existing heuristic methods, by using 95 benchmark models from the COMPLeib library.

In this paper, a two-link manipulator system stability performance is designed and analyzed using Optimal control technique. The manipulator system is highly nonlinear and unstable. The system is modelled using Lagrangian equation and linearized in upward unstable position. The closed loop system is designed using optimal sliding mode controller. The system is compared with a known PID controller with an impulse applied and disturbance torques and a promising results has been obtained.

Fractional differential equations have become a fundamental modelling approach for understanding and simulating the many aspects of nonlocality and spatial heterogeneity of complex materials and systems. Yet, while real-order fractional operators are nowadays widely adopted, little progress has been made in extending such operators to complex-order counterparts. In this work, we introduce new definitions for the complex-order fractional Laplacian, fully consistent with the theory of averaging of smooth functions over fractal sets, and present tailored spectral methods for their numerical treatment. The proposed complex-order operators exhibit a dual particle-wave behaviour, with solutions manifesting wave-like features depending on the magnitude of the imaginary part of the fractional order. Reaction-diffusion systems driven by the complex-order fractional Laplacian exhibit unique spatio-temporal dynamics, such as equilibrium of diffusion in random materials by interference of scattered waves, conduction block and highly fractionated propagation, or the generation of completely novel Turing patterns. Taken together, our results support that the proposed complex-order operators hold unparalleled capabilities to advance the description of multiscale transport phenomena in physical and biological processes highly influenced by the heterogeneity of complex media.

We consider a model of predator-prey interaction at fractional-order where the predation obeys the ratio-dependent functional response and the prey is linearly harvested. For the proposed model, we show the existence, uniqueness, non-negativity as well as the boundedness of the solutions. Conditions for the existence of all possible equilibrium points and their stability criteria, both locally and globally, are also investigated. The local stability conditions are derived using the Magtinon's theorem, while the global stability is proven by formulating an appropriate Lyapunov function. The occurance of Hopf bifurcation around the interior point is also shown analytically. At the end, we implement the Predictor-Corrector scheme to perform some numerical simulations.

This paper presents Chebyshev Type inequalities for the Riemann-Liouville variable-order fractional integral operator using two synchronous functions on the set of real numbers. It is the first result of its kind in the current literature using variable-order Riemann-Liouville fractional integral operator. Some special cases for the result obtained in the paper are discussed.

In this study, we introduce the dynamics of a Hepatitis B virus (HBV) model with the class of asymptomatic carriers and conduct a comprehensive analysis to explore its theoretical aspects and examine the crossover effect within the HBV model. To investigate the crossover behavior of the operators, we divide the study interval into two subintervals. In the first interval, the classical derivative is employed to study the qualitative properties of the proposed system, while in the second interval, we utilize the ABC fractional differential operator. Consequently, the study is initiated using the piecewise Atangana-Baleanu derivative framework for the systems. The HBV model is then analyzed to determine the existence, Hyers-Ulam (HU) stability, and disease-free equilibrium point of the model. Moreover, we showcase the application of an Adams-type predictor-corrector (PC) technique for Atangana-Baleanu derivatives and an extended Adams-Bashforth-Moulton (ABM) method for Caputo derivatives through numerical results. Subsequently, we employ computational methods to numerically solve the models and visually present the obtained outcomes using different fractional-order values. This network is designed to provide more precise information for disease modeling, considering that communities often interact with one another, and the rate of disease spread is influenced by this factor.

Lithium batteries are widely used due to their advantages such as high energy density, stable performance, low pollution, and long recyclable life. Accurate SOC estimation is important for the use of lithium batteries. To address the problem of low accuracy of SOC estimation by traditional methods, this paper proposes a joint method of fractional order robust unscented Kalman filter (FORUKF) and robust unscented Kalman filter (RUKF) to estimate SOC. The method is based on a fractional order model (FOM) that combines the unscented transformation (UT) technique, the H∞ observer and the joint estimator. Specifically, an adaptive genetic algorithm (AGA) was first used to identify the parameters of the FOM for lithium batteries and to verify the accuracy of the model. Estimation and updating of the ohmic resistance R0 and the capacity QN in the model in real-time by RUKF and then estimation of the SOC by FORUKF. Finally, the accuracy of FORUKF-RUKF was verified under the Federal Urban Driving Schedule (FUDS), US06 Highway Driving Schedule and Beijing Dynamic Stress Test (BJDST). According to the results, the FORUKF-RUKF estimated SOC was found to have better accuracy and robustness than the RUKF, FOUKF and EKF.

We presented a fractional order model to capture the transmission dynamics of Anthrax infection with a nonlinear force of infection and its long-term impacts. Analysis by the standard Fabrizio Caputo approach established the model is well-posed and investigation on the stability of the model, Anthrax-free equilibrium as connected to the basic reproduction number R0

The paper focuses on the admissibility problem of descriptor fractional-order systems (DFOSs). The alternate admissibility criteria are addressed for DFOSs with order in (0,2) which involve a non-strict linear matrix inequality (LMI) method and a strict LMI method, respectively. The forms of non-strict and strict LMIs are brand-new and distinguished with the existing literature, which fill the gaps of studies for admissibility. These approaches are available to the order in (0,2) without separating the order ranges into (0,1) and [1,2). In addition, a method involved least real decision variables in terms of strict LMIs is derived which is more convenient to process the practical solution. Three numerical examples are given to illustrate the validity of proposed results.

In the present study, nonlinear vibration of a nanobeam resting on fractional order viscoelastic Winkler-Pasternak foundaion is studied using nonlocal elasticity theory. D'Alembert principle is used to derive the governing equation and the associated boundary conditions. The approximate analytical solution is obtained by applying the multiple scales method. Detailled parametric study is conducted, the effects of variation in different parameters belonging to the application problems on the system are calculated numerically and depicted. We remark that the order and the coefficient of the fractional derivative have significant effect on the natural frequency and the amplitude of vibrations

Recently, Gohar et al. introduced a novel, local, and well-behaved fractional calculus. It possesses all the classical properties, and Its locality imposes simplicity and accuracy in modeling fractional order systems. In this article, we further develop the definitions and extend the classical properties of Gohar fractional calculus to address some of the open problems in Calculus. The fractional Gronwall's integral inequality, Taylor power series expansion, and Laplace transform are defined and applied to overcome some of the limitations in the classical integer-order calculus. The fractional Laplace transform is applied to solve Bernoulli-type logistic and Bertalanffy nonlinear fractional differential equations, and the criteria under which it can be applied to solve linear differential equations are investigated.

In the paper the new, fractional order, state space model of a heat transfer in a one- 1 dimensional metallic rod is addressed. The fractional orders of derivative along space and time 2 are not exactly known and they are described by intervals. The proposed model is the interval 3 expanding of the state space fractional model of the one dimensional heat transfer. It is expected to 4 better describe the reality because interval order of each real process is hard to estimate. Elementary 5 properties of the proposed model are analysed. Theoretical results are experimentally validated using 6 data from real experimental laboratory system.

This paper studies the finite-time synchronization problem of fractional-order stochastic memristive bidirectional associative memory neural networks (MBAMNNs) with discontinuous jumps. A novel criterion for finite-time synchronization is obtained by utilizing the properties of quadratic fractional-order Gronwall inequality with time delay and the comparison principle. This criterion provides a new approach to analyze the finite-time synchronization problem of neural networks with stochasticity. Finally, numerical simulations are provided to demonstrate the effectiveness and superiority of the obtained results.

In this study, we investigate the existence of positive solutions within a system of Riemann-Liouville fractional differential equations that incorporate the (r1,r2,r3)-Laplacian operator while being subject to three-point boundary conditions. These equations incorporate various fractional derivatives and are influenced by parameters represented as (ψ1,ψ2,ψ3). Our approach involves employing techniques such as cone expansion and compression of the functional type, in conjunction with the Leggett-Williams fixed point theorem, to establish the existence of positive solutions. To emphasize the practical significance of our findings in the realm of fractional differential equations, we provide two illustrative examples.

Image encryption is increasingly becoming an important area of research in information security and network communications, as digital images are widely used in various applications and are vulnerable to various types of attacks. In this research work, a color image cryptosystem that is based on a 3-layer permutation-substitution network (PSN) is proposed. For every layer, an encryption key and an S-box are generated and utilized. Those are based on a four-dimensional (4D) dynamical Chen system of a fractional-order, the Mersenne Twister, OpenSLL, Rule 30 Cellular Automata and Intel’s MKL. The sequential application of Shannon’s ideas of diffusion and confusion for 3 times guarantees a total distortion of any input plain image, resulting in a totally encrypted one. Apart from the excellent and comparable performance to counterpart algorithms from the literature, showcasing resistance to visual, statistical, entropy, differential, known plaintext and brute-force attacks, the proposed image cryptosystem provides an exceptionally superior performance in 2 aspects: a vast key space of 2^1658 and an average encryption rate of 3.34 Mbps. Furthermore, the proposed image cryptosystem is shown to successfully pass all the tests of the NIST SP 800 suite.

We investigate the influence of a self-propelling, out-of-equilibrium active particle on generalized elastic systems, including flexible and semiflexible polymers, fluid membranes, and fluctuating interfaces, while accounting for long-ranged hydrodynamic effects. We derive the fractional Langevin equation governing the dynamics of the active particle, as well as that of any other passive particle (or probe) bound to the elastic system. Our study explores the diffusional behavior emerging for both the active particle and a distant probe.

The Work Ability Index (WAI) is the most widely used questionnaire for the self-assessment of working ability. Because of its different applications, shorter versions, and widespread use in healthcare activities, it is worthwhile assessing its characteristics. The WAI was distributed online among the workers of a healthcare company; the results were compared with data contained in the workers' personal health records and with absence registers. 340 out of 575 workers (59.1%) participated; 6.5% of them reported poor work ability. Exploratory factor analysis indicated that the one-factor version best described the characteristics of the WAI. The scores of the complete WAI, the shorter form without the list of diseases, and the minimal one-item version (WAS) had equal distribution and were significantly correlated. The WAI score was inversely related to age and significantly lower in women than in men, but it was higher in night workers than in colleagues due to the probable effect of selective factors. The WAI score was also correlated with absenteeism, but no differences were found between males and females in the average number of absences, suggesting that cultural or emotional factors influence the self-rating of the WAI. Workers tended to overreport illnesses in the online survey compared to data collected during occupational health checks. Musculoskeletal disorders were the most frequently reported illnesses (53%). Psychiatric illnesses affected 21% of workers and had the greatest impact on work ability. Multilevel ergonomic and human factor intervention seems to be needed to recover the working capacity of healthcare workers.

Modern power systems are confronted with a spread concern on the frequency stability issue due to the widespread integration of randomly fluctuating renewable resources. To address the above concern, this work introduces a load frequency control (LFC) scheme based on a hydrogen based energy-storage unit and a parameter tuning strategy for fractional-order proportional-integral-derivative (FOPID) controller. Firstly, a two-area interconnected power system (IPS) model, including thermal, hydro, solar, wind, gas power generator, and hydrogen based energy-storage unit, is established. Then, a FOPID controller is designed for this IPS model, and an improved gradient-based optimizer (IGBO) is developed to adaptively regulate the parameters of the FOPID controllers. Finally, the effectiveness of the offered LFC scheme are tested through load disturbance and renewable energy fluctuations test scenarios, and provides comparison and robustness analysis among different schemes. The test results validated that the offered LFC scheme can effectively suppress the frequency fluctuations of IPS and has excellent robustness.

The continuing public health issue known as COVID-19 (the 2019 Novel Corona virus infection) has a global emphasis. Despite (or perhaps because of) the fact that there are significant gaps in our understanding of COVID-19 epidemiology, transmission dynamics, research methods, and management breakout poses a new kind of global hazard. The good news is that there is currently enough knowledge about the epidemic process to allow for the creation of mathematical forecasting models. We modify a conventional SEIR epidemic model to the unique dynamic compartments and epidemic features of COVID 19 as it spreads in a population with a diverse age structure. Although many US states and other nations around the world followed lockdown and reopening processes, we perform some analysis on using some techniques of the epidemic course. A new perspective of fractional calculus known as piecewise derivatives of fractional order is used to study the proposed model. Sufficient conditions are established to show the existence theory. In addition, a numerical scheme based on Newton’s polynomials is established to simulate the approximate solutions of the proposed model by using various fractional orders. Some real data results are also shown with comparison of the numerical results.

The role of fractional calculus in circuit systems has received increased attention in recent years. In order to evaluate the effectiveness of time-domain calculation methods in the analysis of fractional-order piecewise smooth circuit systems, an experimental prototype is developed and the effects of three typical calculation methods in different test scenarios are compared and studied in this paper. It is proved that Oustaloup’s rational approximation method usually overestimates the peak-to-peak current and brings in pulse-voltage phenomenon in piecewise smooth test scenarios, while the results of two iterative recurrence-form numerical methods are in good agreement with the experimental results. The study results are dedicated to provide a reference for efficiently deploying calculation methods in fractional-order piecewise smooth circuit systems. Some quantitative analysis results are concluded in this paper.

In current transportation hubs, it is a common phenomenon that passengers travel with necessary wheeled-luggage or suitcases. Due to the fact that most luggage occupies certain space within dense passenger crowds with giant mass inertia, its abnormal motions, such as drifting, frequently trig unavoidable local disturbances and turbulence in surrounding pedestrian flows, further increasing security risk. While, current researches primarily concentrate on examining the impact of luggage on crowd evacuation efficiency through scenario-based experiments and analyzing the spatial characteristics of crowd distribution in surveillance videos. There still lacks of the dynamic disturbance mechanisms and crowd stability associated with the combined motion of passengers and luggage. Therefore, this study considers the luggage-laden passenger as a deformable particle, the resulting disturbance on surrounding non-luggage passengers is analyzed and quantified into a nonlinear pressure term. Subsequently, the disturbance propagation model of passenger-luggage is developed by adapting the classical Aw-Rascle traffic flow model with incorporation of the pressure term. Simulation experiments of disturbances caused by luggage drifting and retrograding validate that the proposed propagation model aligns with real-world situations in transportation hubs. Quantitively, when luggage-laden passenger drifted left, the disturbing force of left side crowd can reach a peak of 238N in the passenger density of 3.0 p/m2, and the maximum difference between the left and right sides disturbing force can reach 153N. Furthermore, it is recommended that the proposed model can be applied to crowd flow analysis and risk assessment.

Commonly macrophages are categorized into M1 and M2 subsets. M1 macrophages are defined as inflammatory cells and may contribute to tissue injury, while, M2 macrophages play a central role in tissue remodeling and control of immune responses. It seems that the existence of these cells in graft location is effective for control of inflammation and improvement of transplantation consequences. Although the relative contribution of M2 cells in organ transplantation is not clear, the accumulation of these cells in acute and chronic injury models of transplantation was shown. In some cases, the depletion of M2 cells leads to the amelioration of disease; however in other causes, skewing the response in M2 cells leads to an augmentation of graft fibrosis and worsening of graft condition. In spite of these findings, the benefits of such strategies and their implications in human disease are not clearly understood. The purpose of this mini-review is to highlight the role of alternatively activated M2-type macrophages in the improvement or reduction of the kidney transplantation outcome.

The quality of underground space information has become a major problem that endangers the safety of underground spaces. Currently, the main methods for the high-precision and long-distance transmission of detection information are radar and optical methods. However, in practical applications, we found that the radar method has the shortcomings of large energy loss and poor anti-jamming ability, which limit the accuracy of information data transmission and distance. The optical method has the shortcomings that the weather has a great impact on its accuracy and can only be applied to static objects above ground; therefore, it has the limitation of application objects and use environment. More importantly, the current high-precision information remote detection methods are limited to the detection of overground space objects and are not applicable to the detection of various information data in underground space. In this study, we analyze the spectral properties of the fractional differential operator and find that it is suitable for studying non-linear, non-causal, and non-stationary signals. The theory of fractional calculus is applied to the field of data processing, and a mathematical model of remote transmission and high-precision detection of information based on fractional difference is established, which realizes the functions of high-precision and remote detection of information. By fusing the information data to detect the mathematical model over a long distance and with high accuracy, a mathematical model for stratum data processing used to provide long-distance and high-accuracy data was established. Through application in engineering practice, the effectiveness of this method for underground space information data detection was verified.

Gaze tracking of high-speed moving targets is a novel application mode for low Earth orbit microsatellites. In this mode, small satellites are equipped with high-resolution narrow-field-of-view video cameras for stable gaze-tracking imaging of high-speed moving targets. This paper proposes a high-precision attitude adaptive integral sliding mode control method with a feedforward compensation disturbance observer to enhance the capability of a microsatellite attitude control system for gaze tracking of high-speed moving targets. Specifically, first, we present the attitude control system model for microsatellites and the calculation method for the desired attitude of target tracking based on image feedback. Then, an adaptive integral sliding mode attitude control algorithm with a feedforward compensation disturbance observer, which meets the requirements of high-precision tracking control, is designed. The developed algorithm utilizes the disturbance observer to observe the friction torque of the flywheel and compensates for it through feedforward control. It also employs the adaptive integral sliding mode control algorithm to reduce the impact of uncertain disturbances, decrease the steady-state error of the system, and enhance the attitude control precision. Simulation experiments demonstrated that the designed disturbance observer can successfully observe the frictional disturbance torque of the flywheel. The attitude Euler angle control precision for high-speed moving target tracking reached 0.009°, and the angular velocity control precision reached 0.005°/s, validating the effectiveness of the proposed approach.

Complex diseases such as cancer are caused by changes in the Gene Regulatory Networks. Systems that model the complex dynamics of these networks along with adapting to real gene expression data are closer to reality and can help understand the creation and treatment of cancer. In this paper, for the first time, modelling of gene regulatory networks is performed using delayed nonlinear variable order fractional systems in the state space by a new tool called GENAVOS. This tool uses gene expression time series data to identify and optimize system parameters. This software has several tools for analyzing system dynamics. The results show that the nonlinear variable order fractional systems have very good flexibility in adapting to real data. We found that regulatory networks in cancer cells actually have a larger delay parameter than in normal cells. It is also possible to create chaos, periodic and quasi-periodic oscillations by changing the delay, degradation and synthesis rates. Our findings indicate a profound effect of time-varying order on these networks, which may be related to a type of cellular memory due to epigenetic and environmental factors. We showed that by changing the delay parameter and the variable order function for a normal cell system, its behavior changes and becomes quite similar to the behavior of a cancer cell. This work also confirms the effective role of the miR-17-92 cluster in the cancer cell cycle. GENAVOS is available at https://github.com/hanif-y/GENAVOS with its user guide and MATLAB codes.

In this paper it is shown that mathematical description of strain, constitutive law and dynamics obtained by direct replacement of integer order derivatives with Caputo or Riemann-Liouville fractional order partial derivatives, having integral representation on finite interval, in case of a guitar string, is nonobjective. The basic idea is that different observers, using this type of descriptions, obtain different results which cannot be reconciled, i.e. transformed into each other using only formulas that link the coordinates of the same point in two fixed orthogonal reference frames and formulas that link the numbers representing the same moment of time in two different choices of the origin of time measuring. This is not an academic curiosity! It is rather a problem: which one of the obtained results is correct?

A new method is proposed to increase rejection in microfiltration by applying membrane oscillation using a new type of microfiltration membranes with slotted pores. The oscillations applied to the membrane surface result in reducing membrane fouling and increasing separation efficiency. An exact mathematical solution of the flow in the surrounding solution outside the oscillating membrane is developed. The oscillation results in appearance of the lift velocity, which moves oil particles away from the membrane. The latter results in both reducing membrane fouling and increasing oil droplets rejection. This developed model was supported by the experimental results for oil water separation in produced water treatment. It was proven that oil droplet concentration reduced notably in the permeate due to the membrane oscillation and that applied shear rate caused by the membrane oscillation is also reduce pore blockage. New generation of microfiltration membranes with slotted pores was used in the experiments.

The Active Distribution Networks (ADNs) are Multi-Input Multi-Output (MIMO) systems with coupled dynamics which cause interactions among the control loops of the Distributed Energy Resources (DERs). This undesired effect lead to performance degradation in the voltage control. To mitigate the effects of these unavoidable coupling, the present paper proposes a systematic design procedure based on the analysis of the interaction's sources. In details, each DER is equipped with a double loop PI to control the active and reactive powers output by the Voltage Source Converter (VSC) which connects the DER to the network's node. Furthermore, to guarantee Ancillary Services (ASs), the two loops are coupled by a simple mechanism of cooperation of the active power to voltage regulation realized by a filtered droop law. To achieve voltage regulation with reduced loop interactions, the PI parameters and the filter's pulse are designed according to a two sequential steps procedure based on the (Internal Model Control) IMC technique. Simulation studies are finally presented to demonstrate that the proposed design method achieves both reduction of the loop interaction and robust voltage control in presence of model parameter uncertainty in the MIMO model.

In this paper, an adaptive proportional and integral (PI) controller for speed control of electric drives is developed. The adaptive PI controller is designed based on model reference adaptive identification and the Lyapunov function so that the system stability can be proved. To identify the inertia, the viscous friction torque coefficient, and the load torque simultaneously and smoothly, sinusoidal speed reference is usually employed. A modified motion equation considering the low-pass filter for feedback speed and the Coulomb friction torque is introduced and the relationship between the identified parameters and their actual values are clarified. A high-precision digital simulation model is built based on MATLAB/Simulink. The effectiveness of the proposed method is verified by simulations under various conditions.

Starting from the fact that one of the global control strategies of the Permanent Magnet Synchronous Motor (PMSM), namely the Direct Torque Control (DTC) type control strategy, is characterised by the fact that the inner flux and torque control loop usually uses hysteresis ON-OFF type controllers and the oscillations introduced by them have to be cancelled out by the outer speed loop controller (which is usually a PI speed controller and whose performance is good around the global operating points and for relatively small variations of the external parameters and disturbances caused in particular by the load torque variation), while retaining the advantages of the DTC strategy, this paper presents the improvement of the performance of the PMSM sensorless control system using Proportional Integrator (PI), PI Equilibrium Optimizer Algorithm (EOA), Fractional Order (FO) PI, Tilt Integral Derivative (TID) and FO Lead-Lag for constant flux, and Sliding Mode Control (SMC) and FOSMC for variable flux. The performance indicators of the control system are the usual ones: response time, settling time, overshoot, steady-state error and speed ripple, plus another one given by the fractal dimension (FD) of the PMSM rotor speed signal, and the hypothesis that the FD of the controlled signal is higher when the control system provides better performance is verified. The paper also presents the basic equations of the PMSM, based on which the synthesis of integer and fractional controllers, the synthesis of an observer for estimating the PMSM rotor speed, electromagnetic torque and stator flux are presented. The comparison of the performance of the proposed control systems and the demonstration of the parametric robustness are performed by numerical simulations in Matlab/Simulink using Simscape Electrical and Fractional Order Modelling and Control (FOMCON). Real-time control based on an embedded system using a TMS320F28379D controller demonstrates the good performance of the PMSM sensorless control system based on the DTC strategy in a complete hardware-in-the-loop (HIL) implementation.

We here investigate the dynamical behavior of a fractional-order predator-prey system with anti-predator behavior and Holling IV type functional response. First we study the non-negativity, existence, uniqueness, and boundedness of solutions to the system from a mathematical analysis perspective. Then, we analyze the stability of its equilibrium points and the possibility of bifurcations using stability analysis methods and bifurcation theory, and prove the existence of a supercritical Hopf bifurcation in the system. After providing numerical simulations to illustrate the conclusions theoretically derived, by summarizing those various analytical results obtained, we finally present three interesting conclusions that can contribute to better understanding and preservation of ecological systems.

(1) Background: The rapid expansion of 4G and 5G networks has raised public concerns about potential health risks associated with electromagnetic radiation. This study addresses these fears by investigating electromagnetic measurements in crowded squares, where human exposure is heightened. Despite rigorous scientific methodologies showing generally low levels of radiation from these technologies, public apprehension persists; (2) Methods: We conducted 496 measurements in Larissa's major squares, using a portable field strength analyzer and GIS mapping. Squares were categorized by traffic and population density; (3) Results: Low-traffic squares exhibited exposure ratios consistently below ICNIRP limits, with median values of 0.0012 and 0.00173 in non-active and active mobile phone cases, respectively. In high-traffic squares, the median exposure ratio was 0.00335 in non-active mobile phone cases, remaining below recommended limits; (4) Conclusions: These findings indicate no significant risk of electromagnetic radiation in crowded squares in Larissa, emphasizing the importance of factual communication and dispelling public misconceptions.

The uncertainty in the secondary path of an Active Noise Control (ANC) headphone affects the waterbed effect and stability of the feedback system. This study focuses on the uncertainty of the secondary path when real users wear headphones, and proposes a new uncertainty constraint based on the measured results of the secondary path transfer function under different wearing conditions of dummy head and limited subjects. This constraint and a cascaded second-order infinite impulse response filter with fixed coefficients are used to formulate a control strategic function, which is optimized by the Improved Grey Wolf Optimizer (IGWO) algorithm to obtain the optimal controller with better noise reduction performance. The proposed method and simulation model are validated based on the experimental test results. The results demonstrate that the safety factor and waterbed suppressing factor contained in the proposed uncertainty constraint ensures more stable noise reduction and effective suppression of the waterbed effect for new subjects without a priori data.

This work (in two parts) will review the recently developed predictive modeling methodology called “4th-BERRU-PM” and its applicability to energy systems as exemplified by an illustrative application to the Polyethylene-Reflected Plutonium (acronym: PERP) OECD/NEA reactor physics benchmark. The acronym 4th-BERRU-PM designates the “Fourth-Order Best-Estimate Results with Reduced Uncertainties Predictive Modeling” methodology, which yields best-estimate results with reduced uncertainties for the first fourth-order moments (mean values, covariance, skewness, and kurtosis) of the optimally predicted posterior distribution of model results and calibrated model parameters. The 4th-BERRU-PM uses the Maximum Entropy (MaxEnt) principle to incorporate fourth-order experimental and computational information, including fourth (and higher) order sensitivities of computed model responses to model parameters, thus incorporating, as particular cases, the results previously predicted by the second-order predictive modeling methodology 2nd-BERRU-PM, and vastly generalizing the results produced by extant data assimilation and data adjustment procedures. The 4th-BERRU-PM methodology encompasses the scopes of high-order sensitivity analysis (SA), uncertainty quantification (UQ), data assimilation (DA) and model calibration (MC). The application of the 4th-BERRU-PM methodology to energy systems is illustrated by means of the above-mentioned OECD/NEA reactor physics benchmark, which is modeled using the neutron transport Boltzmann equation involving 21976 imprecisely known parameters, the solution of which is representative of “large-scale computations.” The model result (“response”) of interest is the leakage of neutrons through the outer surface of this spherical benchmark, which can be computed numerically and measured experimentally. Part 1 of this work illustrates the impact of high-order sensitivities, in conjunction with parameter standard deviations of various magnitudes, on the determination of the expected value and variance of the computed response in terms of the first four moments of the distribution of the uncertain model parameters. Part 2 of this work will illustrate the capabilities of the 4th-BERRU-PM methodology for combining computational and experimental information, up to and including forth-order sensitivities and distributional moments, for producing best-estimate values for the predicted responses and model parameters while reducing their accompanying uncertainties.

In this paper, we establish the generalized Qi-type inequality involving conformable fractional integrals. The results presented here would provide extensions of those given in earlier works.

The concepts of fractional calculus and the related techniques have been gaining momentum in circuit system fields, and an increasing body of evidence suggests that fractional-order characteristics are widely distributed in electronic components. In this paper, we consider the fractional characteristics of non-solid aluminum electrolytic capacitors and focus on the nonlinear dynamic characteristics of peak-current-mode controlled (PCMC) dc-dc boost converters with such components. In the work, we establish a piecewise smooth non-commensurate fractional-order model to describe the converter, in which the fractional-order equivalent impedance model of capacitors is adopted and the detailed control loop is considered. In order to analyze the converter, we use the fractional Adams-Bashforth-Moulton typed method (F-ABM) and stroboscopic map technique to obtain the time-domain solutions and the bifurcation diagram. The results of bifurcation diagrams indicate that, with the change of different parameters, the converter enters chaotic state through period doubling bifurcation. In order to provide empirical evidence for the nonlinear dynamic analysis, we consider both circuit-level simulation and experiments in the work, the results of which further confirm the results of theoretical analysis.

In this paper, we have established Hermite-Hadamard inequalities for r-preinvex functions via fractional integrals.

This research focuses on the Hopf bifurcation occurring at a singular point with high-order degeneracy in a class of three-dimensional systems. Based on center manifold theorem, by expanding the technique for determining singular point values of degenerate singularities in two-dimensional systems, the formal series method to determine the singular point values at the high-order degenerate critical point is discussed. Furthermore, a class of specific three-dimensional differential systems with high-order degenerate singularities is explored. By computing the singular point values and determining center conditions, we proved that a minimum of 5 small-amplitude limit cycles in the vicinity of the origin. This research provides new perspectives on the center problem and limit cycle bifurcation in high-dimensional systems with high-order degenerate singular points.

In this paper, a horizontally moving suspended mass pendulum base is designed and controlled using robust control theory. H infinity optimal loop shaping with first and second order desired loop shaping function controllers are used to improve the performance of the system using Matlab/Simulink Toolbox. Comparison of the H infinity optimal loop shaping with first and second order desired loop shaping function controllers for the proposed system have been done to track the desired angular position of the pendulum using step and sine wave input signals and a promising result has been obtained succesfully.

Local polynomial smoother (LPS) is a weighted local least-squares nonparametric method. It provides a local Taylor series fit of the data at any location and can be directly used in a differential equation to provide a numerical scheme. In this article, we introduce this new nonparametric idea based on local polynomial smoother, for acquiring the numerical solution of the Bagley-Torvik fractional-order differential equations. Furthermore, this paper will present a numerical comparison with some methods, such as legendre operational matrix and pseudo-spectral method. The efficiency and accuracy of the LPS method are demonstrated by two numerical examples.

An active power dispatch method for a microgrid (MG) with multi-type loads, renewable energy sources (RESs) and distributed energy storage devices (DESDs) is the focus of this paper. The MG operates in a grid-connected model, and distributed power sources contribute to the service for load demands. The outputs of multiple DESDs are controlled to optimize the active power dispatch. Our goal with optimization is to reduce the economic cost under time-of-use (TOU) price, and to adjust the excessively high or low load rate of distributed transformers (DTs) caused by the peak-valley demand and load uncertainties. To simulate a practical environment, the stochastic characteristics of multi-type loads are formulated. The transition matrix of system state is provided. Then, a finite-horizon Markov decision process (FHMDP) model is established to describe the dispatch optimization problem. A learning-based technique is adopted to search the optimal joint control policy of multiple DESDs. Finally, simulation experiments are performed to validate the effectiveness of the proposed method, and the fuzzification analysis of the method is presented.

In this paper, we prove the existence of three solutions for a $p$-Kirchhoff problem with $\psi$-Hilfer fractional derivative. To be more precise, we use the variational method and we prove that the associated functional energy admits a critical point in each of the three constructed sets, these critical points are weak solutions for a studied problem. Moreover, by definition of these sets, one of these solutions is positive, the second is negative, and the third one change sign. At the end of this work, we present an example to validate our main results.

Silicon Photomultipliers find applications across various fields. One potential Silicon Photomultiplier application domain is neutrino telescopes, where they may enhance the angular resolution. However, the elevated dark count rate associated with Silicon Photomultipliers represents a significant challenge to their widespread utilization. To address this issue, it is proposed to use Silicon Photomultipliers and Photomultiplier Tubes together. The Photomultiplier Tubes signals would serve as a trigger to mitigate the dark count rate, thereby preventing undue saturation of the available bandwidth. This paper presents an investigation into a fast and resource-efficient method for filtering Silicon Photomultiplier dark count rate. A low-resource and fast coincident filter has been developed, which removes the Silicon Photomultiplier dark count rate by using as trigger the Photomultiplier Tube input signals. The architecture of the coincidence filter, together with the first results obtained, which validate the effectiveness of this method are presented.

Recovery of forest after logging can be tested in many ways: the presence of particular species of fauna or flora, the similarity of the biodiversity of the recovering forest to that on neighbouring areas of undisturbed forest; or the characteristics of soils and streams whose conditions may have drastically changed during logging. Three cases of rainforest recovery after logging and clearance from Australia and Borneo exhibit different starting and different goals for recovery. Faunal indicators of recovery vary with size and with species dependence of the rainforest. Endemic forest species may have difficulty in recovering. Tree species richness and abundance may recover in two decades, but canopy closure takes longer. Compacted soils may retain low infiltration capacities for many decades. This diversity in recovery rates is confirmed when compared with those used elsewhere. Because the starting points for recovery vary, from damage by tropical cyclones and landslides, to clearance for shifting cultivation, pasture or agriculture, to post-logging conditions, universal indicators may be inappropriate. The desired endpoints of recovery also range from a “wilderness” state to a National Park for human enjoyment, biodiversity preservation, safeguarding rights of traditional forest-dwelling peoples, or a second round of selective logging.

For many engineering applications it is sufficient to use the concept of simple materials. However, higher gradients of the kinematic variables are taken into account to model materials with internal length scales as well as to describe localization effects using gradient theories in finite plasticity or fluid mechanics. In many approaches length scale parameter have been introduced that are related to a specific micro structure. An alternative approach is possible, if a thermodynamically consistent framework is used for material modelling as shown in the present contribution. However, even if sophisticated and thermodynamically consistent material models can be established there are still not yet standard experiments to determine higher order material constants. In order to contribute to this ongoing discussion system identification based on the method of self-adaptive filtering is proposed in this paper. To evaluate the effectiveness of this approach it has been applied to second-order gradient materials considering longitudinal vibrations. Based on thermodynamically consistent models that have been solved numerically it has been possible to prove that system identification based on self-adaptive filtering can be used effectively for both narrow-band and broadband signals in the field of second-order gradient materials. It has also been found that the differences identified for simple materials and gradient materials allow for condition monitoring and detection of gradient effects in the material behavior.

This paper analyzes and compares models for predicting average magnet losses in interior permanent-magnet motors with fractional-slot concentrated windings due to harmonics in the armature reaction (assuming sinusoidal phase currents). Particularly, loss models adopting different formulations and solutions to the Helmholtz equation to solve for the eddy currents are compared to a simpler model relying on an assumed eddy-current distribution. Boundaries in terms of magnet dimensions and angular frequency are identified (numerically and using an identified approximate analytical expression) to aid the machine designer whether the more simple loss model is applicable or not. The assumption of a uniform flux-density variation (used in the loss models) is also investigated for the case of V-shaped and straight interior permanent magnets. Finally, predicted volumetric loss densities are exemplified for combinations of slot and pole numbers common in automotive applications.

Noise reduction is the major issue in the loudspeaker for the application of the musical instruments and related areas. In this paper, a noise disturbance control of a loudspeaker with optimal and robust controllers has been done successfully. The noise of the loudspeaker has been analyzed by simply track a reference cone displacement with the actual cone displacement. Static output feedback and H infinity optimal loop shaping controllers have been used to compare the actual and reference cone displacements by using a sine wave and random cone displacement signals and a promising results have been analyzed.

This paper proposes an innovative mechatronic piezo-actuated module to control vibrations in modern machine tools. Vibrations represent one of the main issues that compromise seriously the quality of the workpiece. The active vibration control (AVC) device is composed by a host part integrated with sensors and actuators synchronized by a regulator, able to make a self-assessment and adjust to the environmental alteration. This study presents the mechatronic model based on the kinematic and dynamic analysis of the AVC device. To ensure a real time performance, a H2-LQG controller has been developed and validated by simulations involving machine tool, PZT actuator and controller models. The Hardware-in-the-loop (HIL) architecture is adopted to control and attenuate the vibrations. A set of experimental tests has been performed to validate the AVC module on a commercial machine tool. The feasibility of the real time vibration damping is demonstrated and the simulation accuracy is evaluated.

Sea cucumber peptides are small molecular peptides with biological function obtained from fresh sea cucumber as feedstock, which were hydrolyzed by protease, separated ,and purified. As the main product of sea cucumber refinement, it more accurately expresses the nutritional effect of sea cucumber and has a wide range of potential applications. It has been demonstrated that sea cucumber has a certain value-added effect on bone mineral density regulation, but the differences in bone mineral density regulation of extracts from different parts of sea cucumber and the techniques contributing to the efficient isolation of bone sea cucumber peptides have not been reported. Firstly, the aim of this study was to reveal the differences in osteogenic activities of enzymatic peptides from three major parts of sea cucumber: the body wall, the egg protein, and the intestinal protein. Then, the bone-enhancing sea cucumber peptides were isolated based on the characteristics of the dif-ferences in molecular weight distribution, hydrophilicity, and ionisation degree of sea cucumber, and to explore the possible mechanisms of their action. The findings indicated that sea cucumber peptides extracted from three distinct sites exhibited a dose-dependent enhancement of osteoblast proliferation and differentiation. Upon evaluating the three methods of sea cucumber peptide separation based on molecular weight distribution, hydrophilicity, and ionization, it was observed that the fraction isolated by hydrophobicity and

The pharmacological effects of the fruiting body of Ophiocordyceps sinensis (Os) exerted antioxidant, anti-virus, and immunomodulatory, whereas the anti-inflammatory effects and active components of Os mycelial submerged culture (OMSC) are not known. This study aimed to investigate the active compounds in the fermented liquid (FLOS), hot water (WEOS), and 50-95% (EEOS-50, EEOS-95) ethanol extracts of OMSC and their anti-inflammatory effects and potential mechanisms in LPS-stimulated microglial BV2 cells. The results demonstrated that all of the OMSC extracts could inhibit NO production in BV2 cells. EEOS-95 exhibited the strongest inhibitory effects (41 % inhibitory ability at 500 µg/mL), and its ergosterol, GABA, total phenolic, and total flavonoid contents were significantly higher than those of the other extracts (18.60, 18.60, 2.28, and 2.14 mg/g, p < 0.05, respectively). EEOS-95 also has a strong inhibitory ability against IL-6, IL-1β and TNF-α with IC50 of 617, 277 and 507 µg/mL, respectively, which is higher than that of 1 mM melatonin. The anti-inflammatory mechanism of EEOS-95 seems to be associated with up-regulation of PPAR-γ/Nrf-2/HO-1 antioxidant-related expression and down-regulation of NF-κB/COX-2/iNOS pro-inflammatory expression signaling. Therefore, we hypothesized that EEOS-95 can prevent neurodegenerative diseases, but the effect on the application in vivo should be further investigated.

In this paper, we compile the fractional power series method and the Laplace transform to design a new algorithm for solving the fractional Volterra integro-differential equation. For that, we assume the Laplace power series (LPS) solution in terms of power q=1m,m∈Z+, where the fractional derivative of order α=qγ for which γ∈Z+. This assumption will help us to write the integral, the kernel, and the nonhomogeneous terms as a LPS with the same power. The recurrence relations for finding the series coefficients can be constructed using this form. To demonstrate the algorithm's accuracy, the residual error is defined and calculated for several values of the fractional derivative. Two strongly nonlinear examples are discussed to provide the efficiency of the algorithm. The algorithm gains powerful results for this kind of problem. Under Caputo meaning the obtained results are illustrated numerically, and graphically. Geometrically, the behavior of the solution declares that the changing of the fractional derivative parameter values' in their domain alters the style of the attained solution in a symmetrical meaning and fully coinciding to the ordinary derivative value'. From these simulations, the results report that the recommended novel algorithm is a straightforward, accurate, and superb tool to generate analytic-approximate solutions for Integral, and integro-differental equations of fractional order.

The fractional derivatives are a generalization the derivatives of integer order and find applications in studying memory processes in various scientific fields. Numerical methods are used to solve and analyze fractional models of real world problems. In this paper, we consider an approximation of the Caputo fractional derivative and its asymptotic formula, whose generating function is the polylogarithmic function. In the paper, we prove the convergence of the approximation and derive an estimate for the error and order. We consider an application of the approximation for the construction of finite difference schemes for numerical solution of the two-term ordinary fractional differential equation and the time-fractional Black-Scholes equation for option pricing. The properties of the approximation are used to prove the convergence of the methods used for numerical solution of the fractional differential equations. The theoretical results for the error and order of the methods are illustrated by the results of numerical experiments.

Intelligent ship technology is currently an international research hotspot, and model predictive control is widely used in the path-tracking control of intelligent vehicles. To construct an intelligent ship anti-disturbance path-tracking control method, firstly, an environmental disturbance model was constructed with the actual meteorological data of the target sea area. Secondly, the Fossen ship equation of motion is linearized and discretized as the ship motion model. Thirdly, the expression of the prediction equation is derived from the ship motion model. Fourthly, the cost function is constructed by using the polar diameter and polar angle values of the ship. Fifth, the power function in the cost function is replaced with an exponential function to obtain an improved cost function. Sixthly, according to the Lyapunov theory and the MPC terminal constraint theory, the stability of the improved cost function is verified. Seventh, different test paths are set up, the environmental disturbance model is taken as the external disturbance, the ship motion model, the prediction equation, and the improved cost function are used to design the anti-disturbance path-tracking control algorithm according to the model prediction control idea for simulation experiments. Finally, different MATLAB simulation results show that the improved cost function can resist disturbance of the external wave, current, and wind, and effectively track the target path. Therefore, this study provides a reference for improving the navigation safety of ship path-tracking.

In contemporary construction, the prevalence of vibration serviceability issues in lightweight and slender structures has become increasingly common, owing to advancements in building materials and construction methods. While these structures often meet the criteria for ultimate limit states, they can still elicit complaints due to excessive vibrations induced by human activity. To address this challenge, the Integral Resonant Control (IRC) technique has emerged as a favored approach for actively damping vibrations in various systems. This study introduces a fresh perspective on implementing a multi-input multi-output (MIMO) IRC scheme for active vibration control (AVC) specifically tailored for pedestrian structures utilizing inertial mass actuators. Building upon a common framework and design methodology outlined in previous research, this work presents a novel application of MIMO IRC for AVC. The designed controller is rigorously tested and implemented on a laboratory floor structure to validate its efficacy.

Brucellosis is a multi-system infectious disease that exhibits with various manifestations and complications. Neurobrucellosis is a rare but serious presentation of brucellosis that can be discovered in every stages of the disease. Laboratory tests and physical examination and patient history are generally the basis for diagnosing the disease. It has both insidious and prolonged clinical course of the disease and long-term therapies. Also the most common pattern of exhibition is subacute or chronic. We reported a case of young female who had history of painless weakness in the right lower limb (proximal and distal) that started gradually and had progressed over the time, and after a month she felt weakness in the left lower limb with the same pattern. Lumbosacral Magnetic resonance imaging (MRI) with and without contrast was shown evidence of enhancement thickening of caudal equina ventral roots. Brucella antigen titer was positive, the result was 1/160. And other clinical tests were normal. Patient treated with Intravenous injection (IV) Rifampicin and Intravenous Cotrimoxazole. patient was discharged with good health and continuinng all two medications for 5 months. The descision was taken to report this case as a result of entire respond in patient’s illness after a enduring disease. Neurobrucellosis is a treatable disease in which it would be better to consider a high indication of suspicion. Due to if ignored, it may cause significant morbidity and mortality.

The objective of this study was to carry out the extraction and characterization of chitin and chitosan from the exoskeletons of the Farfantepenaeus californiensis species of shrimp, as well as its application in the formulation of polymeric films plasticized with glycerol used in the process of food packaging. The characterization of the extracted polymer was made by Fourier transform infrared spectroscopy (FTIR), Scanning electron microscopy (SEM), and physicochemical analysis of chitin and chitosan, resulting in a theoretical performance of 29.33% and 16.46%, respectively. In terms of quality, it was determined that the extracted chitosan had a molecular weight of 1.10 x105 g/mol and a deacetylation degree of 80.23%, which classifies it as a low-molecular weight chitosan, suitable for food packaging. It was shown that the extracted chitosan is fit for the production of the films by using the casting method, presenting a tension resistance of 1 MPa. The Antibacterial analysis was carried out using Staphylococcus aureus (S. aureus) and Escherichia coli (E. coli), bacterial models commonly found in food. The results showed an effective inhibition capability of the polymeric materials. Overall, the results for both chitosan and the films indicate a high potential for application in the food packaging sector.

Efficient traffic flow management at intersections is vital for optimizing urban transportation networks. This paper presents a comprehensive approach to refining traffic flow by analyzing the capacity of roads and integrating fuzzy logic-based traffic light control systems. We were examining the capacity of roads connecting intersections, considering factors such as road vehicle capacity, vehicle speed, and traffic flow volume, through detailed mathematical modelling and analysis. Control is determined by the maximum capacity of each road segment, providing valuable insights into traffic flow dynamics. Building upon this capacity and flow analysis, the research introduces a novel Intelligent Traffic Light Controller (ITLC) system based on fuzzy logic principles. By incorporating real-time traffic data and lever-aging fuzzy logic algorithms, our ITLC system dynamically adjusts traffic light timings to optimize vehicle flow at two intersections. The paper discusses the de-sign and implementation of the ITLC system, highlighting its adaptive capabilities in response to changing traffic conditions. Simulation results are presented, demonstrating effectiveness of the ITLC system in improving traffic flow and re-ducing congestion at intersections. Furthermore, this research provides an analysis of the mathematical models used to calculate road capacity, offering insights into the underlying principles of traffic flow optimization. Through the simulation, we have validated accuracy and reliability of our controller.

Functional connectivity (FC) is a potential candidate that can increase the performance of brain-computer interfaces (BCIs) in the elderly because of its compensatory role in neural circuits. However, it is difficult to decode FC by current machine learning techniques because of a lack of its physiological understanding. To investigate the suitability of FC in BCI for the elderly, we propose the decoding of lower- and higher-order FCs using a convolutional neural network (CNN) in six cognitive-motor tasks. The layer-wise relevance propagation (LRP) method describes how age-related changes in FCs impact BCI applications for the elderly compared to younger adults. Seventeen younger (24.5±2.7 years) and twelve older (72.5±3.2 years) adults were recruited to perform tasks related to hand-force control with or without mental calculation. CNN yielded a six-class classification accuracy of 75.3% in the elderly, exceeding the 70.7% accuracy for the younger adults. In the elderly, the proposed method increases the classification accuracy by 88.3% compared to the filter-bank common spatial pattern (FBCSP). LRP results revealed that both lower- and higher-order FCs were dominantly overactivated in the prefrontal lobe depending on task type. These findings suggest a promising application of multi-order FC with deep learning on BCI systems for the elderly.

Huperzine A is an herbal reversible inhibitor of Acetylcholinesterase (AChE). A molecular docking analysis on Huperzine A molecule has been carried out to understand its structure, conformational flexibility, intermolecular interaction and the binding affinity in the active site of AChE enzyme. Further, the charge density distribution of huperzine A molecule (lifted from the active site of AChE) was determined from the high level quantum chemical calculations coupled with charge density analysis. The binding affinity of Huperzine A towards AChE was calculated from the molecular docking; the lowest docked energy is -8.46 kcal/mol. In the active site, huperzine A molecule interacts with acyl binding pocket-Phe330 of AChE, that is, the bicyclo ring group of huperzine A forms an intermolecular interaction with the oxygen atom of main chain of the amino acid residue Phe330 at the distances 3.02 and 3.25 Å respectively. On the other hand, a gas phase study on huperzine A molecule also performed using HF and DFT (B3LYP) methods with the basis set 6-311G**. The molecular structure, conformation, and the charge density distribution of huperzine A molecule in the gas phase have determined using quantum chemical calculations and the charge density analysis. The comparative studies between the gas phase and the active site forms of huperzine A molecule, explicitly reveals the degree of conformational modification and the charge density redistribution of huperzine A when present in the active site. The dipole moment of the molecule in the active site is 6.85 D, which is slightly higher than its gas phase value (5.91 D). The electrostatic potential (ESP) surface of active site molecule clearly shows the strong electronegative and positive ESP regions of the molecule, which are the expected strong reactive locations of the molecule.

Asymptotic theories for fractional cointegrations have been extensively studied in the context of time series data, with numerous empirical studies and tests developed. However, most of the previously developed testing procedures for fractional cointegration were primarily designed for time series data. This paper proposes a generalized residual-based test for fractionally cointegrated panels with fixed effects. The test development is based on bivariate panel series with the regressor assumed to be fixed across cross-sectional units. The proposed test procedure accommodates any integration order between [0,1], and it is asymptotically normal under the null hypothesis. Monte Carlo experiments demonstrate that the test exhibits better size and power compared to a similar residual-based test across varying sample sizes.

Obesity is related to the establishment of chronic inflammation and metabolic diseases, but it can be positively influenced by the regular practice of physical activity. The study aimed to compare the anthropometric, metabolic, and inflammatory parameters of physically active Military Police Officers (MPOs) with those who are less physically active. Sixty male MPOs, low activity (n=28) and physically active (n=32) participated. The following parameters were measured: plasma cytokine levels, C-reactive protein (CRP) levels, circulating glucose triglyceride (TAG) and high-density lipoprotein cholesterol (HDL-C) levels, and plasma glutamic oxalacetate transaminase (GOT), glutamic-pyruvate transaminase (GPT), and gamma-glutamyl transferase (GGT) activities. The physically active group presented lower body fat and reduced TAG and IL-8 levels compared to the low activity group. Moreover, a negative correlation between SPE and SBP, DBP, BPM was detected for the physically active group (p<0.05) but not in the low activity group. Furthermore, the physically active group's work time (WT) values were not correlated with the important metabolic markers SBP, DBP, BPM, GLU, TAG (p>0.05) but could be in the low activity group (p<0.05). These findings highlight the fundamental protective role of physical activity in controlling body composition, subclinical inflammation, and cardiovascular risk in MPOs.

: This paper presents a comparison between direct integer orders or classical model reference adaptive control (IO-DMRAC) versus its fractional orders counterpart (FO-DMRAC) applied to the F-16 aircraft longitudinal model pitch rate control. A substantial improvement is achieved when using fractional order adaptive control, since, in addition to performance indices, such as Integral Square-Error criterion (ISE) and Integral Square-Input criterion (ISU) being lower, the oscillations of the system output (pitch rate) in the transient period, are eliminated. Moreover, it is the first attempt in literature of adaptive control that a FO-DMRAC is applied to the pitch rate control of an aircraft. A F-16 short-period model, whose relative degree is equal to 1 (n^*=1) is analyzed by mean of simulations with good results. A FO-DMRAC is designed, for a specific operating flight conditions and compared with its IO-DMRAC counterpart. Furthermore, the boundedness of all signals, including the internal ones ω(t) are assured.

We monitored the water quality and hydrological conditions of a horizontal subsurface constructed wetland (HSSF-CW) in Beijing, China, for 2 years. We simulated the area rate constant and the temperature coefficient with the first-order kinetic model. We examined the relationships between the nitrogen (N) removal rate, N load, seasonal variations in the N removal rate, and environmental factors, such as the area rate constant, temperature, and dissolved oxygen (DO). The effluent ammonia (NH₄⁺-N) and nitrate (NO₃⁻-N) concentrations were significantly lower than the influent concentrations (p<0.01, n=38). The NO₃⁻-N load was significantly correlated with the removal rate (R²=0.9566, p<0.01), but the NH^₄+-N load was not correlated with the removal rate (R²=0.0187, p>0.01). The area rate constants of NO₃⁻-N and NH₄⁺-N at 20 °C were 27.01±26.49 and 16.63±10.58 m∙yr⁻¹, respectively. The temperature coefficients for NO₃⁻-N and NH₄⁺-N were estimated at 1.0042 and 0.9604, respectively. The area rate constants for NO₃⁻-N and NH₄⁺-N were not correlated with temperature (p>0.01). The NO₃⁻-N area rate constant was correlated with the corresponding load (R²=0.9625, p<0.01). The NH₄⁺-N area rate was correlated with DO (R²=0.6922, p<0.01), suggesting that the factors that influenced the N removal rate in this wetland met Liebig's law of the minimum.

This paper proposes a definition of fractional line integral, generalising the concept of fractional definite integral. The proposal replicates the properties of the classic definite integral, namely the fundamental theorem of integral calculus. It is based on the concept of fractional anti-derivative used to generalise the Barrow formula. To define the fractional line integrals the Gr\"unwald-Letnikov and Liouville directional derivatives are introduced and their properties described. The integral is defined first for broken line paths and afterwards to any regular curve

Power series expansions are useful in approximation theory and mathematical physics. The manuscript presents several types of fractional Taylor expansions of sufficiently smooth functions. This is achieved by employing an incremental regularization procedure to the computation of the derivative. The series are constructed in an algorithmic way, which allows for its implementation in computer algebra systems.

Open source software such as OpenDSS has given a lot of help to distribution network researchers and educators. With high penetration of distributed renewable energy resources into distribution network, tradition distribution steady state analysis software such as OpenDSS is faced with difficulty in handling distributed generators. Three-phase distributed generators are often modeled in sequence frame while unbalanced distribution network are usually modeled in phase frame. So a load flow in sequence-phase coupled frame is proposed to handle models described in both frames. Voltage controlled DGs which are difficult to cope with in OpenDSS are handled in proposed program. The steady state analysis platform is programmed with open source Modelica language and the main aim of this paper is to introduce an open source platform for active distribution network steady analysis include load flow and short circuit analysis which can be easily adopted and improved by other educators and researchers.

During public health events, Active Mobility (walking and cycling) plays an important role in securing residents' travel. To enhance the resilience of urban transportation, this article integrates the travel environment elements for walking and cycling and constructs a travel environment for Active Mobility evaluation index system. This article uses survey data from the main urban area of Harbin in the context of the COVID-19 pandemic in May 2022, and combines the Gradient Boosting Decision Tree (GBDT) and Impact-Asymmetry Analysis (IAA) methods to analyze the satisfaction of the travel environment for Active Mobility. It proposes strategies for optimizing the travel environment for Active Mobility, ensuring residents' travel during public health events, guiding them to adopt Active Mobility, and improving urban transportation resilience. This research shows that Active Mobility can enhance urban transportation resilience. In addition, there are differences in resident demand for walking and cycling environments in the travel environment for Active Mobility. Residents are more concerned about the comfort of the walking environment, while they prioritize the convenience of the cycling environment.

Tropical forest and savanna biomes are pivotal in the functioning of the Earth system. Tropical forests are one of the largest terrestrial biosphere carbon pools, whereas savannas exchange carbon between the biosphere and atmosphere via frequent and extensive landscape fires. Both are biodiverse and under increasing threat due to land clearing and anthropogenic climate change. Reliable mapping of tropical forest and savanna is essential to provide understanding of how anthropogenic impacts are affecting the extent of these biomes. Using Google Maps satellite imagery, we manually classified 24,239 random points as forest, savanna, or anthropogenic landscapes within the tropics. Because fire and climate are correlated, we developed separate geospatial models to rank the importance of climate, topography, and human influence on vegetation present. This modelling confirmed that those areas with more fires had lower probabilities of tropical forest, that forest was most likely in areas with high mean annual rainfall with little seasonal variation in precipitation, and that anthropogenic factors disrupt this environmental predictability. We found there were environments where tropical forest and savanna were equally probable are geographically restricted. These relationships suggest that future drier climates projected under anthropogenic climate change, combined with clearing and burning that have reduced tropical forest extent to a subset of its theoretical distribution, will lead to irreversible loss of tropical forests. Our modelling provides global mapping that can be used track further changes to distribution of rainforests.

The study of vegetation community and structural change has been central to ecology for over a century, yet how disturbances reshape the physical structure of forest canopies remains relatively unknown. Moderate severity disturbance including fire, ice storms, insect and pathogen outbreaks, affects different canopy strata and plant species, which may give rise to variable structural outcomes and ecological consequences. Terrestrial lidar (light detection and ranging) offers an unprecedented view of the interior arrangement and distribution of canopy elements, permitting the derivation of multidimensional measures of canopy structure that describe several canopy structural traits with known linkages to ecosystem functioning. We used lidar-derived canopy structural measured within a machine learning framework to detect and differentiate among various disturbance agents, including moderate severity fire, ice storm damage, age-related senescence, hemlock woolly adelgid, beech bark disease, and chronic acidification. We found that disturbance agents such as fire and ice storms primarily affected the amount and position of vegetation within canopies, while acidification, pathogen and insect infestation, and senescence altered canopy arrangement and complexity. Only two of the six disturbance agents significantly reduced leaf area, indicating that this commonly quantified canopy feature is insufficient to characterize many moderate severity disturbances. Rather, measures of canopy structure, including those that describe multidimensional change, are needed to characterize disturbance at moderate severities because structural changes from these events are spatially and quantitatively variable. Our findings suggest that standard disturbance detection methods, such as optical based remote sensing platforms, may currently be limited in their ability to detect, differentiate, and characterize disturbance. Further, we conclude that a more broadly inclusive definition of ecological disturbance that incorporates multiple aspects of canopy structure change will improve the modeling, detection, and prediction of functional implications of moderate severity disturbance.