Ensuring precise electric locomotive stopping is pivotal for achieving intelligent and unmanned auxiliary transportation systems. Currently, human drivers' expertise plays a central role in the stopping process, posing challenges for automation and cargo location accuracy, particularly in coal mining. This paper focuses on achieving accurate electric locomotive stopping under diverse conditions by utilizing permanent magnet synchronous motor-driven locomotives. This technique introduces a novel stopping control method that combines a fuzzy Proportional-Integral-Derivative (F-PID) controller and a vector control model for permanent magnet synchronous motors (PMSM). After this, we design the F-PID using the PMSM technique based on the new fuzzy rules for each sub-system. In the end, extensive simulations and real-world experiments are conducted on an electric locomotive stopping test bed, which demonstrate the effectiveness of the proposed control method. From the simulation results, it confirming that the ability to achieve precise stopping under various working conditions.

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.

Abstract: — management of the Continuous Stirred Tank Reactor (CSTR) operation has proven to be a difficult undertaking due to the complex and ever-changing nature of its behavior, which is both nonlinear and dynamic, which is further compounded by its instability. Attempts have been made to use Proportional-Integral-Derivative (PID) controllers for such processes, but the performance is often poor due to the inherent limitations of the controllers. In contrast, heuristic algorithms have been employed to tune the controllers, but these methods can only provide optimal performance for a restricted range of parameter variations. This paper presents a novel approach that involves using a conventional gain scheduling PID controller in combination with a fuzzy gain scheduling (FGS) controller method to calibrate set-point weighted PID controllers for the CSTR process. The paper outlines the design of the controllers and evaluates their performance by subjecting them to varying input signals within the given bandwidth.

In the paper, a study of the performance of unmanned ground vehicle (UGV), establishes numerical simulation model of the chassis system by three-dimensional software and finite element analysis software. Based on the numerical modelling and analysis, the work focuses on study of the strength and stiffness of the vehicle's chassis and researched the distribution of stress and deformation under the extremal condition. The paper also presents an autopilot design with new cascade control system for an autonomous motion of an unmanned ground vehicle based on Proportional-Integral-Derivative (PID) and Feed-Forward (FF) control. The PID-FF controller is a part of dedicated for presented UGV used in a hybrid control system for precise control and stabilization, necessary to increase the vehicle motion stability and maneuvers precision. The hybrid PID-FF control system proposed for the ground vehicle model gives a satisfactory quality of control, while maintaining the simplicity of the control system. Presented tests performed in area of mechanical design and control analysis gives good results and proves usefulness of designed unmanned device.

In this paper, the design of a low cost portable ventilator with performance analysis have been done to solve the scarcity of respiratory ventilators for COVID-19 patients. The materials used to build the system are: DC motor, rotating disc and pneumatic piston. The system input is the patient heart beat and the output is volume of air to the patient lung with adjusted breathing rate. This ventilator adjusts the breathing rate to the patient depending on his heart beat rate. The performance analysis of this system have been done using Proportional Integral Derivative (PID) and Full State Feedback H2 controllers. Comparison of the system with the proposed controllers have been done using a step change and a random change of the patient heart beat and a promising result have been analyzed successfully.

This paper aims to unify q-derivative/q-integral and h-derivative/h-integral in a single definition, this will be called q−h-derivative/q−h-integral. These notions are further extended on finite interval [a,b] in the form of left and right q−h-derivatives and q−h-integrals. Some inequalities are studied for q−h-integrals which are directly connected with well known results. In diverse fields of science and engineering the theory based on q-derivatives/q-integrals and h-derivatives/h-integrals can be unified by using the concept of q−h-derivative/q−h-integral.

The design of a mixed-mode proportional-integral-derivative (PID) controller circuit using current-feedback operational amplifiers (CFOAs) as active components is proposed. With the same circuit topology, the proposed configuration of three CFOAs, four resistors, and two capacitors is capable of performing the PID controller in all four operation modes: namely voltage mode, trans-admittance mode, current mode, and trans-impedance mode. Numerous mathematical analyses are conducted to determine the controller performance under ideal and non-ideal conditions. Additionally, the mixed-mode second-order lowpass filter is suggested, and also used to examine the workability of the proposed mixed-mode PID controller in a feedback control structure. The proposed PID controller is implemented with the commercially available IC-type CFOA AD844, and the simulation results are presented to illustrate the functionality of the controller and its closed-loop control system.

Discretization is the process of converting a continuous function or model or equation into discrete steps. In this work, adaptive and learning methods are implemented to control DC motors that are used for actuating control surfaces of unmanned underwater vehicles. Adaptive control is a method in which the controller is designed to adapt the system with parameters which vary or are uncertain. Parameter estimation is the process of computing the parameters of a system using a model & measured data. Adaptive methods have been used in conjunction with different parameter estimation techniques. Deterministic artificial intelligence, a learning-based approach that uses the process dynamics defined by physics, is also applied to control the output of the DC motor to track a specified trajectory. This work goes further to evaluate the performance of the adaptive & learning techniques based on different discretization methods. The results are evaluated based on the absolute error mean between the output & the reference trajectory and the standard deviation of the error. The first order-hold method of discretization and surprisingly large sample time of seven tenths of a second yields over sixty percent improvement over the results presented in the prequel literature.

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

This study was conducted to develop a PID control algorithm considering viscosity for the planting depth control system of a rice transplanter using various hydraulic oils at different temperatures and to evaluate the performance of the control algorithm, and compare the performance of the PID control algorithm without considering viscosity and considering viscosity. In this study, the simulation model of the planting depth control system and a PID control algorithm were developed based on the power flow of the rice transplanter (ERP60DS). The primary PID coefficients were determined using the Ziegler–Nichols (Z–N) second method. Routh’s stability criteria were applied to optimize the coefficients. The pole and double zero points of the PID controller were also applied to minimize the sustained oscillations of the responses. The performance of the PID control algorithm was evaluated for three ISO (The International Organization for Standardization) standard viscosity grade (VG) hydraulic oils (VG 32, 46, and 68). The results show that the control algorithm considering viscosity is able to control the pressure of the proportional valve, which is associated with the actuator displacement for various types of hydraulic oils. It was noticed that the maximum pressure was 15.405 bars at 0, 20, 40, 60, 80, and 100 ℃ for all of the hydraulic oils. The settling time and steady-state errors were 0.45 s at 100 ℃ for VG 32, and 0% for all of the conditions. The maximum overshoots were found to be 17.50% at 100 ℃ for VG 32. On the other hand, the PID control algorithm without considering viscosity could not control the planting depth, because the response was slow and did not satisfy the boundary conditions. The PID control algorithm considering viscosity could sufficiently compensate for the nonlinearity of the hydraulic system and was able to perform for any of temperature-dependent viscosity of the hydraulic oils. In addition, the rice transplanter requires a faster response for accurately controlling and maintaining the planting depth. Planting depth is highly associated with actuator displacement. Finally, this control algorithm considering viscosity could be helpful in minimizing the tilting of the seedlings planted using the rice transplanter. Ultimately, it would improve the transplanter performance.

As an option to deal with the insulin-dependent disease, a recent commuted PD control strategy is designed and carefully analyzed for different clinic diabetic patients. This controller approach is mainly conceived to stabilize the glucose blood concentration in a diabetic patient around its basal value, hence avoiding extreme situations such as hypoglycemia and hyperglycemia. This control strategy receives two inputs carefully tuned to actuate when the measured variable is out of a prescribed healthy zone. Therefore, one of these variables is invoked to decrease the glucose concentration to insulin injection, and the other is employed to increase the glucose absorption, both by using a proper PD controller. According to our numerical experiments, our controller approach performs well, even when there is an external disturbance in the controlled system.

Autonomous navigation of spacecraft necessitates innovative technologies, methods, and algorithms, particularly when orbiting in proximity of other space objects. Optimization methods are useful for autonomous spacecraft navigation, guidance, and control, but their performance is hampered by noisy multi-sensor technologies and poorly modeled system equations, and real-time on-board utilization is generally computationally burdensome. Some proposed methods use noisy sensor data to learn the optimal guidance and control solutions real-time (online), where non-iterative instantiations are preferred to reduce computational burdens. This study aims to highlight efficacy and limitations of several common methods for optimizing guidance and control while proposing a few more, where all methods are applied to the full, nonlinear, coupled equations of motion including cross-products of motion from the transport theorem. Five disparate types of optimum guidance and control algorithms are presented and compared to a classical benchmark. Comparative analysis is based on tracking errors (both states and rates), fuel usage, and computational burden. Real-time optimalization with singular switching plus nonlinear transport theorem decoupling proves superior by matching open-loop solutions to the constrained optimization problem (in terms of state and rate errors and fuel usage), while robustness is validated in the utilization of mixed, noisy state and rate sensors and uniformly varying mass and mass moments of inertia. State tracking errors are reduced one-hundred ten percent. Rate tracking errors are reduced one-hundred thirteen percent. Control utilization (e.g., fuel) is reduced eighty four percent, while computational burden in reduced ten percent simultaneously.

This paper presents the application of optimal control problem in modeling of stirred tank heater temperature control. The analysis of the open loop system shows that the system is not efficient without a controller. Linear Quadratic Gaussian (LQG) and Linear Quadratic Integral (LQI) controllers are used to increase the performance of the system. Comparison of the closed loop system with the proposed controllers have been done with Matlab/Simulink Toolbox and a promising results have been analyzed.

In this paper, a 3 DOF gyrscope position control have been designed and controlled using optimal control theory. An input torque has been given to the first axis and the angular position of the second axis have been analyzed while the third axis are kept free from rotation. The system mathematical model is controllable and observable. Linear Quadratic Integral (LQI) and Linear Quadratic State Feedback Regulator (LQRY) controllers have been used to improve the performance of the system. Comparison of the system with the proposed controllers for tracking a desired step and random angular position have been done using Matlab/Simulink Toolbox and a promising results has been analyzed.

Epilepsy is a neurological disorder that affects approximately 1% of the world's population. To diagnose and estimate the occurrence of epilepsy, the analysis of recorded brain activity is performed by a neurologist, which is not only time-consuming and tedious but also occasionally accompanied by human error. Therefore, in recent decades, researchers have aimed to unravel an approach for designing and building an automated method for diagnosing and estimating the occurrence of epilepsy. Accordingly, the present study proposed two new-fangled ways based on brain signals and a convolutional neural network (CNN). Moreover, this research implements a CNN with a sequential three-layer structure. Numerous experiments were performed, and the accuracy of estimating epilepsy using the developed methods was achieved at 95% without feedback and 97% with feedback. The proposed methods were proven to be more accurate than the previous techniques and can be employed as a physician's assistant once entering the field of operation.

Diversified techniques have been applied in many research papers for the optimization of rehabilitation robotic movements in order to maintain smoothness and accuracy. Smooth and precise control is needed necessarily for upper limb rehabilitation robotic applications having five degree of freedom. The preferred parameters which are used for the controlling were validated by mathematical model and these tuning parameters were optimized. Designing optimization algorithms to control complex physical robots has been a challenging task. In this study, a number of optimization techniques will be analyzed to determine the optimal parameters of a PID controller with a dynamic model of the upper limb rehabilitation system. For determining optimal control parameters for PID, there exists a number of tuning methods such as Zeigler Nichols and fuzzy logic which are classical methods. Swarm intelligence-based optimization algorithms are inspired by the behaviors of living things in nature. Several researchers have reported the optimal design of PID controller parameters using optimization techniques. The proposed control technique has been implemented on a 5-DOF RAX hardware and before any clinical trials, six healthy subjects went for trials under strict protocol. It has been discovered that the proposed control technique rejects the external unwanted disturbances as well as keeps the system stable under extreme perturbed and harsh conditions. In this research paper mathematical models have been validated to determine the PID parameters for the optimization. The comparative study is carried out with four different cost functions since a well-designed objective function leads to better performance of the system and indicates control design expectations. These objective functions are an integral squared error (ISE) and integral absolute error (IAE). In this research work, the effects of different cost functions on optimization techniques for controller parameters were analyzed. The performance of the controller with different cost functions has examined for robustness analysis. The cost function of particle swarm optimization, Firefly, Ant Bee Colony and Ant Colony optimization were developed for the better optimization results.

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.

We investigate the behavior of the partial derivative approach to the change of scale formula and prove relationships among the analytic Wiener integral and the analytic Feynman integral of the partial derivative for the function space integral.

The main goal of the paper is to use a generalized proportional Riemann-Liouville fractional derivative (GPRLFD) to model BAM neural networks and to study some stability properties of the equilibrium. Initially, several properties of the GPRLFD are proved such as the fractional derivative of a squared function. Also some comparison results for GPRLFD are provided. Two types of equilibrium of the BAM model with GPRLFD are defined. In connection with the applied fractional derivative and its singularity at the initial time the Mittag-Leffler exponential stability in time of the equilibrium is introduced and studied. An example is given illustrating the meaning of the equilibrium as well as its stability properties.

TThis paper delves into the extension and characterization of radial positive definite functions into non-integer dimensions. We provide a thorough investigation by employing the Riemann-Liouville fractional integral and fractional Caputo derivatives, enabling a comprehensive understanding of these functions. Additionally, we introduce a secondary characterization based on the Bernstein characterization of completely monotone functions. The practical significance of our study is showcased through an examination of the positivity of the fundamental solution of the space-fractional Bessel diffusion equation, highlighting the real-world applicability of the developed concepts. Through this work, we contribute to the broader understanding of radial positive definite functions and their utility in diverse mathematical and applied contexts.

Our aim in this paper is to establish some new Hermite-Hadamard- Mercer type integral inequalities by utilizing the fractional proportional-integral operators.For this purpose, Hermite-Hadamard-Mercer inequalities for di¤er- antiable mappings whose derivatives in absolute value are convex.

In this paper, we study the third order semilocal convergence of the Newton-like method for finding the approximate solution of nonlinear operator equations in the setting of Banach spaces. First, we discuss the convergence analysis under ω-continuity condition, which is weaker than the Lipschitz and Hölder continuity conditions. Second, we apply our approach to solve Fredholm integral equations, where the first derivative of involved operator not necessarily satisfy the Hölder and Lipschitz continuity conditions. Finally, we also prove that the R-order of the method is 2p + 1 for any p $\in$ (0,1].

This article addresses reinsurance decision making process, which involves the insurance company and the reinsurance company, and is negotiated through reinsurance intermediaries. The article proposes a decision flow to model the reinsurance design and selection process. In contrast to existing literature on pure proportional reinsurance or stop-loss reinsurance, this article focuses on the combination into Proportional-Stop-loss reinsurance design which better addresses interest of both parties. In terms of methodology, the significant contribution of the study is to incorporate Multiple Attribute Decision Making (MADM) into modelling the reinsurance selection. The Multi-Objective Decision Making (MODM) model is applied in designing reinsurance alternatives. Then MADM is applied to aid insurance companies in choosing the most appropriate reinsurance contract. To illustrate the feasibility of incorporating intelligent decision supporting system in reinsurance market, the study includes a numerical case study using simulation software @Risk in modeling insurance claims, and programming in MATLAB to realize MADM. Managerial implications could be drawn from the case study results. More specifically, when choosing the most appropriate reinsurance, insurance companies should base their decision on multiple measurements instead of single-criteria decision making models for their decisions to be more robust.

Recently, the conformable derivative and its properties have been introduced. In this paper, we propose and prove some new results on conformable Boundary Value Problems. First, we introduce a conformable version of classical Sturm´s separation, and comparison theorems. For a conformable Sturm-Liouville problem, Green's function is constructed, and its properties are also studied. In addition, we propose the applicability of the Green´s Function in solving conformable inhomogeneous linear differential equations with homogeneous boundary conditions, whose associated homogeneous boundary value problem has only trivial solution. Finally, we prove the generalized Hyers-Ulam stability of the conformable inhomogeneous boundary value problem.

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 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 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.

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.

Since the first case of 2019 novel coronavirus disease (COVID-19) detected on Jan 30, 2020, in India, the number of cases rapidly increased to 3819 cases including 106 deaths as of 5 April 2020. Taking this into account, in the present work, we are studying a Bats-Hosts-Reservoir-People transmission fractional-order COVID-19 model for simulating the potential transmission with the thought of individual social response and control measures by the government. The real data available about infectious cases from $14^{th}$ March to $26^{th}$ March 2020 is analysed and accordingly various parameters of the model are estimated or fitted. The Picard successive approximation technique and Banach's fixed point theory have been used for verification of the existence and stability criteria of the model. Numerical computations are done utilizing the iterative Laplace transform method. In the end, we illustrate the obtained results graphically. The purpose of this study is to estimate the effectiveness of preventive measures, predicting future outbreaks and potential control strategies using the mathematical model.

The duality is one of the most interesting properties of the Laplace and Fourier transforms associated to the integer order derivative. Here, we will generalize it for fractional derivatives and extend the results to the Mellin, Z and discrete-time Fourier transforms. The scale and nabla derivatives are used.

In the full load operating range, wind turbines typically use pitch control to maintain rotor speed and output power at their rated values to guarantee the whole system’s safety. Blade pitch actuators are subject to physical limitations and safety requirements, which imposes strict constraints on pitch angle’s amplitude and rate of change. These constraints will bring windup problem to the integral part of the pitch controller. It leads to deterioration of the pitch control system’s performance or even the instability problem, especially for large-scale turbines operating in extreme uncertain wind conditions or suffering from cyber attacks. This paper designs an anti-windup robust pitch angle control strategy to deal with pitch rate constraint issue to enhance the security of control system. First, to facilitate controller design, a filtered tracking error technique is employed to transform the nonaffine form into an affine one. Subsequently, a feedback robust controller based on UDE is developed to handle the model’s uncertainty and external disturbances. To address the issue of integral saturation in the pitch system and guarantee its safety, an elliptical bounded constraint is integrated into the designed UDE strategy. This bounded UDE controller can improve the stability of power generation quality, reduces the mechanical loads on components and enhance the whole system’s safety. Finally, the effectiveness of the proposed scheme is verified on the Wind Turbine Blockset platform in Matlab/Simulink. It can achieve better performance than the traditional method.

In this study, we construct a new Atangana-Baleanu fractional model for whooping cough disease to predict future dynamics of the disease, as well as to suggest strategies to eliminate the disease in an optimal way. We prove that the proposed model has a unique solution which is positive and bounded. To measure contagiousness of the disease, we determine the reproduction number R0 and use it to examine the local and global stability at equilibrium points that have symmetry. Through sensitivity analysis, we determine parameters of the model that are most sensitive to R0. The ultimate aim of this research is to analyze different disease prevention approaches in order to find the most suitable one. For this, we include the vaccination and quarantine compartments in the proposed model and formulate an optimal control problem to assess the effect of vaccination and quarantine rates on disease control in three distinct scenarios. Firstly, we study the impact of vaccination strategy and conclude findings with presentation of graphical results. Secondly, we examine the impact of quarantine strategy on whooping cough infection with possible elimination from the society. Lastly, we implement vaccination and quarantine strategies together to visualize their combine effect on infection control. In addition to the study of an optimal control problem, we examine the effect of fractional order on disease dynamics as well as the impact of constant vaccination and quarantine rates on disease transmission and control. We determine that the optimal control strategy with the three controls is more effective in reducing the spread of whooping cough infection. Implementation of Toufik-Atangana type numercial scheme both for the state and adjoint equations is another contribution of this article.

A new type of ordinary differential equation is introduced and discussed, namely, the time-dependent order ordinary differential equations. These equations can be solved via fractional calculus and are mapped into Volterra integral equations of second kind with singular integrable kernel. The solutions of the time-dependent order differential equations smoothly deforms solutions of the classical integer order ordinary differential equations into one-another, and can generate or remove singularities. An interesting symmetry of the solution in relation to the Riemann zeta function and Harmonic numbers was also proved.

The bilateral tempered fractional derivatives are introduced generalising previous works on the one-sided tempered fractional derivatives and the two-sided fractional derivatives. An analysis of the tempered Riesz potential is done and showed that it cannot be considered as a derivative.

This paper presents a symmetrical topology for the design of solid-state transformer, made up of power switching converters, to replace conventional bulky transformers. The proposed circuitry not only reduces the overall size but also provides power flow control with the ability to be interfaced with renewable energy resources (RESs) to fulfill the future grid requirements at consumer end. Solid state transformer provides bidirectional power flow with variable voltage and frequency operation and has the ability to maintain unity power factor, and current total harmonic distortion (THD) for any type of load within defined limits of IEEE standard. Solid State Transformer offers much smaller size as compared to that of the conventional iron core transformer. MATLAB/Simulink platform is adopted to test the validity of the proposed circuit for different scenarios by providing the simulation results evaluated at 25 kHz switching frequency.

Nowadays energy saving is a topical issue due to increasing fuel costs and this aspect is amplified by more stringent emissions regulations that impact on vehicle development. A recent study conducted by the U.S. Department of Energy shows that about five percent of the U.S. energy consumption is transmitted by fluid power equipment. Nevertheless, this study also shows that the efficiency of fluid power averages 21 percent. This offers a huge opportunity to improve the current state-of-the-art of fluid power machines, in particular to improve the energy consumption of current applications. These facts dictate a continuous strive toward improvements and more efficient solutions: to accomplish this objective a strong reduction of hydraulic losses and better control strategies of the hydraulic systems are needed. In fluid power, there exist many techniques to reduce/recover energy losses of the conventional layouts, e.g. load sensing, electrohydraulic flow matching, independent metering, etc. One of the most efficient ways to analyze these different layouts and identify the best hydraulic solution is done through virtual simulations instead of prototyping, since the latter involves higher investment costs to deliver the product into the market. However, to build a fluid power machine virtual model, some problems arise relative to different aspects, for instance: loads on actuators (both linear and rotational) are not constant and pumps are driven by a real engine whose speed depends on required torque. Furthermore, it is important to achieve higher level of detail to simulate each component in the circuit: the greater detail, the better the machine behavior is portrayed, but it obviously entails heavy impact on simulation time and computational resources. Therefore, there is a need to create mathematical model of components and systems with sufficient level of detail to easily acquire all those phenomena necessary to correctly evaluate machine performance and make modifications to the fluid power component design. In this context, a hydraulic proportional valve PVG 32 by Danfoss is taken as an object of study, its performance is analyzed with suitable mathematical model and simulation is done to observe closeness of a model to the laboratory experiment.

The polysaccharide-based chiral stationary phase (CSP) columns for high-performance liquid chromatography (HPLC) were applied in the separation of liquid crystalline racemic mixtures obtained based on (R,S)-2-octanol and were found to be highly effective in recognizing isomers of minor structural differences. The mobile phase (MP), which consists of acetonitrile (ACN)/water (H2O) at different volume ratios, was used. All measurements were made at room temperature. The order of the elution was also determined. The chromatographic parameters such as resolution - (Rs), selectivity - (α), and the number of theoretical plates, i.e., column efficiency - (N), were determined. The polysaccharide-based CSP columns have unique advantages in separation technology, and this study has shown the potential usefulness of the CSP columns in separating liquid crystalline racemic mixtures belonging to the same homologous series.

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.

Bio-based packaging materials and efficient drug delivery systems are gaining attention, carboxymethyl cellulose (CMC) is one of the most soluble cellulose derivatives, is a good candidate material due to its biocompatibility, biodegradability, and reproducibility. However, CMC-based films are lack of sufficient mechanical properties, limiting its widespread application. In this paper, the molecular interactions between CMC and additives with different molecular structures have been studied with rheological method. The additives are chitosan and cellulose derivatives including O-carboxymethylated chitosan (O-CMCh), N-2-hydroxypropyl-3-trimethylammonium-O-carboxymethyl chitosan (HTCMCh), hydroxypropyltrimethyl ammonium chloride chitosan (HACC), cellulose nanofibers (CNC), and cellulose nanofibers (CNF). The influencing factors, such as molecular structure, concentration of additives and temperature on the rheological properties were studied, which results revealed the information intermolecular interactions. Based on the rheological properties, several systems were selected to prepare films, which show very good transparency, wettability, mechanical properties, biodegradability, and cytotoxicity. These good characteristics of the selected films also proved the good biocompatibility of CMC and chitosan and cellulose derivatives. This work will provide an idea to prepare CMC-based food packaging and effective drug delivery materials with specific properties.

In this paper, we identify several relative ordering properties of the modified proportional hazard rate and modified proportional reversed hazard rate models. For this purpose, we use two well-known relative orderings, namely the relative hazard rate ordering and the relative reversed hazard rate ordering. The investigation is to see how a relative ordering between two possible base distributions for the response distributions in these models is preserved when the parameters of the underlying models are changed. We will give some examples to illustrate the results and the conditions under which they are obtained.

The use of logistic regression models in data analysis and machine learning has expanded in recent years and has become the primary preference of researchers in risk assessment studies across a wide range of scientific fields. From the assessment of credit risk in financial institutions to the estimation of risk factors for traffic accidents or the identification of etiological factors for chronic diseases. All logistic models are natural extensions of the simple binary model, and their interpretation is based on it. Using the data of a cross-sectional study on the risk factors of traffic collisions, the two main extended models of logistic techniques, multinomial and ordinal logistic regression, are presented in the article in detail. Emphasis is placed on the use of ordinal regression since the outcome variable of the collision data is defined as ordinal measurement reflecting a latent continuous scale.

High efficacy LED lamps combined with adaptive lighting control and greenhouse integrated photovoltaics (PV) could enable the concept of year-round cultivation and become a feasible option even in the harsh climate of the Nordic countries. Meteorological satellite data of this region was analyzed in a parametric study to evaluate the potential of these technologies. The generated maps showed monthly average temperatures fluctuating from -20°C to 20°C throughout the year. The natural photoperiod and light intensity also changed drastically, resulting in monthly average daily light integral (DLI) levels ranging from 45-50 mol·m-2·d-1 in summer and contrasting with 0-5 mol·m-2·d-1 during winter. To compensate, growth room cultivation independent from outdoor conditions could be used in winter. Depending on the efficacy of the lamps, the electricity required for sole-source lighting at 300 µmol·m-2·s-1 for 16 hours would be between 1.4 and 2.4 kWh·m-2·d-1. Greenhouses with supplementary lighting could help start the cultivation earlier in spring and extend it further into autumn. The energy required for lighting highly depends on several factors such as the natural light transmittance, the light threshold settings and the lighting control protocol, resulting in electric demands between 0.6 and 2.4 kWh·m-2·d-1. Integrating PV on the roof or wall structures of the greenhouse could offset some of this electricity, with specific energy yields ranging from 400 to 1120 kWh·kWp-2·yr-1 depending on the region and system design.

The material derivative is important in continuum physics. This Letter shows that the expression $\frac{d }{dt}=\frac{\partial }{\partial t}+(\bm v\cdot \bm \nabla)$, used in most literature and textbooks, is incorrect. The correct expression $ \frac{d (:)}{dt}=\frac{\partial }{\partial t}(:)+\bm v\cdot [\bm \nabla (:)]$ is formulated. The solution existence condition of Navier-Stokes equation has been proposed from its form-solution, the conclusion is that "\emph{The Navier-Stokes equation has a solution if and only if the determinant of flow velocity gradient is not zero, namely $\det (\bm \nabla \bm v)\neq 0$.}"

Autonomous differential equations of fractional order and non-singular kernel are solved. While solutions can be obtained through numerical, graphical, or analytical solutions, we seek an implicit analytical solution.

This contribution considers an improved control scheme for three-phase two-stage grid-tied photovoltaic (PV) power system based on integral sliding mode control (ISMC) theory. The proposed control scheme consists of maximum power point tracking (MPPT), DC-Link voltage regulation and grid currents synchronization. A modified voltage-oriented maximum power point tracking (VO-MPPT) method based on ISMC theory is proposed for design of an enhanced MPPT under irradiation changes. Moreover, a novel DC-Link voltage control based on ISMC theory is proposed in order to achieve good regulation of DC-Link voltage over its reference. To inject the generated PV power into the grid with high quality, a voltage oriented control based on space vector modulation (SVM) and ISMC (VOC-ISMC-SVM) has been developed to control the grid currents synchronization. Numerical simulations are performed in Matlab/SimulinkTM environment in order to evaluate the proposed control strategy. In comparison with conventional control scheme, the developed control strategy provides an accurate MPP tracking with less power oscillation as well as a fast and an accurate DC-Link regulation under climatic conditions variations. Moreover, the transfer of the extracted power into the grid is achieved with high quality.

In the last years, a recent growing line of research has been developed with fruitful results by using fractional and conformable derivatives in the iterative procedures of classical methods for solving nonlinear equations. In that sense, the use of conformable derivatives has shown better behavior than fractional ones, not only in the theory, but also in the practice. In this work, we adapt the approximation of conformable derivatives in order to design the first conformable derivative-free iterative schemes to solve nonlinear equations: a Steffensen’s type method and a Secant type method; the latter with memory. Convergence analysis is made, preserving the order of classical cases, and the numerical performance is studied in order to confirm the results in the theory. It is shown that these methods can present some numerical advantages versus their classical partners, with wide sets of converging initial estimations.

We show the tensor properties of joint probabilities on a Riemannian parametric manifold. Initially we develop a binary data matrix for parameter measurements of a large number of particles confining in a closed system in order to retrieve the joint probability densities of related parameters. By introducing a new generalized inner product as a multilinear operation on dual basis of parametric space, we extract the set of joint probabilities and prove them to meet contravariant tensor properties in a general Riemannian parametric space. We show these contravariant tensors reduce to classical ordinary partial derivatives definition in ordinary Euclidean parametric space. Finally we prove by a theorem that symmetrized iterative contravariant derivative of cumulative probability function on Riemannian manifold gives the set of joint probabilities in those manifold. We bring some examples for compatibility with physical tensors.

In this manuscript a new approach into analyzing the local stability of equilibrium points of non-linear Caputo fractional planar systems is shown. It is shown that the equilibrium points of such systems can be a stable focus or unstable focus. In addition, it is proposed that previous results regarding the stability of equilibrium points have been incorrect, the results here attempt to correct such results. Lastly, it is proposed that a Caputo fractional planar system cannot undergo a Hopf bifurcation, contrary to previous results prior. Though, it is shown that such systems can undergo a Hopf bifurcation (topologically).

Recently, Shehata et al. [37] introduced the r+1Rs(B;C; z) matrix function and established some properties. The aim of this study established to devote and derive certain basic properties including analytic properties, recurrence matrix relations, dierential properties, new integral representations, k- Beta transform, Laplace transform, fractional k-Fourier transform, fractional integral properties, the k-Riemann{Liouville and k-Weyl fractional integral and derivative operators an extended version of r+1Rs;k matrix function. We establish its relationships with other well known special matrix functions which have some particular cases in the context of three parametric Mittag-Leer matrix function, k- Konhauser and k-Laguerre matrix polynomials. Finally, some special cases of the established formulas are also discussed.

In option pricing, we often deal with options whose payoffs depend on multiple factors such as foreign exchange rates, stocks, etc. Usually, it leads to a knowledge of the joint distributions and complicated integration procedures. The paper develops an alternative approach that converts the option pricing problem to a dual one and presents a solution to the problem in the optional semimartingale setting. The paper contains several examples which illustrate results in terms of the parameters of models and options.

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.

Sirtuins are a family of Class III epigenetic modifying enzymes involved in regulating cellular processes through the removal of acetyl groups from proteins. They rely on NAD+ as a coenzyme in contrast with classical HDACs (Class I, II, and IV) that depends on Zn+ for their activation, linking their function to cellular energy levels. There are seven mammalian sirtuin isoforms (SIRT1-7), each located in different subcellular compartments. Sirtuins act as master regulators of cellular homeostasis, responding to changes in nutrient availability and energy status. They play vital roles in diverse physiological and pathological conditions, making them promising therapeutic targets for various diseases, including cancer, neurodegenerative disorders, and metabolic diseases. High levels of SIRT6 are involved in the cancer progression of many tumor types and our previous studies revealed that sirtuin 6 was highly expressed in NSCLC cells and its inhibition potentially favored apoptosis and cell cycle arrest. Sirt6 emerged as a promising target and inhibitors of natural and synthetic sources are highly warranted. Imidazole derivatives are often investigated as sirtuin regulators due to their ability to interact with the binding site and modulate their activity. Imidazole bestows many possible substitutions on its ring and neighboring atoms, to design and synthesize derivatives with specific target selectivity and improved pharmacokinetic properties, optimizing drug development. We recently developed imidazole-based derivatives that potentially inhibited classical HDAC enzymes. Therefore, we evaluated the Sirtuin inhibition activity of our in-house compound comprised of imidazole derivatives and the strongest inhibition was observed with Ethyl 2-[5-(4-chlorophenyl)-2-methyl-1-H-Imidazole-4-yl) acetate against Sirt6 by in-silico and protein expression studies. Our results suggested that Ethyl 2-[5-(4-chlorophenyl)-2-methyl-1-H-Imidazole-4-yl) acetate could be a potential novel sirt6 inhibitor.

The development of biosensors with high sensitivity and low-detection limits provides a new direction for medical and personal care. Graphene and graphene derivatives have been used to prepare various types of biosensors due to their excellent sensing performance (e.g. high specific surface area, extraordinary electronic properties, electron transport capabilities and ultrahigh flexibility). This perspective review focuses on graphene-based biosensors for quantitative detection of cancer related biomarkers such as DNA, miRNA, small molecules and proteins by integrating with different signal outputting approaches including fluorescent, electrochemistry, surface plasmon resonance, surface enhanced Raman scattering etc. The article also discussed their challenges and potential solutions along with future prospects.

The constant news about the corona virus is scary. It is not possible to separate treatment for Cancer due to COVID-19. An effective treatment comparison strategy is needed. We need to have a handy tool to understand cancer progression in this unprecedented scenario. Linking different events of cancer progression is the need of the hour. It is a methodological challenge. We provide the solutions to overcome the issue with interval between two consecutive events in motivating head and neck cancer (HNC) data.

In the paper, the authors consider the generating functions of the Hermite polynomials and their squares, present explicit formulas for higher order derivatives of the generating functions of the Hermite polynomials and their squares, which can be viewed as ordinary differential equations or derivative polynomials, find differential equations that the generating functions of the Hermite polynomials and their squares satisfy, and derive explicit formulas and recurrence relations for the Hermite polynomials and their squares.

We present a method using contour integration to derive definite integrals and their associated infinite sums which can be expressed as a special function. We give a proof of the basic equation and some examples of the method. The advantage of using special functions is their analytic continuation which widens the range of the parameters of the definite integral over which the formula is valid. We give as examples definite integrals of logarithmic functions times a trigonometric function. In various cases these generalizations evaluate to known mathematical constants such as Catalan’s constant and π

In the paper, the author presents explicit and unified expressions for a sequence of improper integrals in terms of the beta functions and the Wallis ratios. Hereafter, the author derives integral representations for the Catalan numbers originating from combinatorics.

Censoring occurs when complete follow-up time information is unavailable for patients enrolled in a clinical study. The process is considered to be informative (nonignorable) if the likelihood function for the censoring model cannot be partitioned into a set of response parameters that are independent of the censoring parameters. In such cases, estimated survival time probabilities may be biased, prompting the need for special statistical methods to remedy the situation. The problem is especially salient when censoring is skewed toward the early phase of a study. In this paper, we describe a method to impute censored follow-up times using a counting process method.

The Fourier Continuous Derivative ($D_C$) offers a unique perspective on fractional differentiation grounded in the theory of Fourier series. This approach has the potential to address problems across various disciplines, including physics, engineering, and mathematics. The primary insight underpinning this approach is that a convex function defined on $\mathbb{Z}$ retains its convexity on $\mathbb{R}$. This paper delves into the Fourier Continuous Derivative, compares it with traditional fractional derivatives, and outlines its possible real-world applications, such as modeling viscoelastic materials, solving wave equations, and financial data analysis.

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.

Pulsed-field gradient (PFG) diffusion experiments can be used to measure anomalous diffusion in many polymer or biological systems. However, it is still complicated to analyze PFG anomalous diffusion, particularly the finite gradient pulse width (FGPW) effect. In practical applications, the FGPW effect may not be neglected such as in clinical diffusion magnetic resonance imaging (MRI). Here, two significantly different methods are proposed to analyze PFG anomalous diffusion: the effective phase shift diffusion equation (EPSDE) method and an observing the signal intensity at the origin method. The EPSDE method describes the phase evolution in virtual phase space, while the method to observe the signal intensity at the origin describes the magnetization evolution in real space. However, these two approaches give the same general PFG signal attenuation including FGPW effect, which can be numerically evaluated by a direct integration method. The direct integration method is fast and without overflow. It is a convenient numerical evaluation method for Mittag-Leffler function type PFG signal attenuation. The methods here provide a clear view of spin evolution under field gradient, and their results will help the analysis of PFG anomalous diffusion.

Recently, different extensions of the fractional derivative operator are found in many research papers. The main aim of this paper is to establish an extension of the extended Caputo fractional derivative operator. The extension of an extended fractional derivative of some elementary functions derives by considering an extension of beta function which includes the Mittag-Leffler function in the kernel. Further, an extended fractional derivative of some familiar special functions, the Mellin transforms of newly defined Caputo fractional derivative operator and the generating relations for extension of extended hypergeometric functions also presented in this study.

The main objective of this present paper is to introduce further extension of extended Caputo fractional derivative operator and establish the extension of an extended fractional derivative of some known elementary functions. Also, we investigate the extended fractional derivative of some familiar special functions, the Mellin transforms of newly defined Caputo fractional derivative operator and generating relations for extension of extended hypergeometric functions.

Several commerical quantum computers are now available that offer Hybrid Classical-Quantum computing. Application is made to a classical-quantum model of human neocortex, Statistical Mechanics of Neocortical Interactions (SMNI), which has had its applications published in many papers since 1981. However, this project only uses Classical (super-)computers. Since 2015, PATHINT, has been used as a numerical algorithm for folding path-integrals. Applications in several systems in several disciplines has generalized been from 1 dimension to N dimensions, and from classical to quantum systems, qPATHINT. Papers have applied qPATHINT to neocortical interactions and financial options. The classical space described by SMNI applies nonlinear nonequilibrium multivariate statistical mechanics to synaptic neuronal interactions, while the quantum space described by qPATHINT applies synaptic contributions from Ca2+ waves generated by astrocytes at tripartite neuron-astrocyte-neuron sites. Previous SMNI publications since 2013 have calculated the astrocyte Ca2+ wave synaptic interactions from a closed-form (analytic) expression derived by the author. However, more realistic random shocks to the Ca2+ waves from ions entering and leaving these wave packets should be included using qPATHINT between electroencephalographic (EEG) measurements which decohere the quantum wave packets. This current project extends calculations to multiple scales of interaction between classical events and expectations over the Ca2+ quantum processes to include these random shocks to fit EEG data to the SMNI model, with previous analytic forms for the quantum processes replaced by qPATHINT. The classical-quantum system is fit using the author's Adaptive Simulated Annealing (ASA) importance-sampling optimization code. Gaussian Quadratures are used for numerical calculation of momenta expectations of the astrocyte processes that contribute to SMNI synaptic interactions. This project demonstrates how some hybrid classical-quantum systems may be calculated using only classical (super-)computers. Recent calculations also are reported using the closed-form expression, with and without shocks.

Background: There is little clarity in the application of content related to improper integrals in university students, due to the absence of meaning, which prevents them from making a connection with everyday problem situations. Methods: we designed a mathematical modelling proposal where a specific situation involving the instrumentation, use and application of this type of integrals is experimented and solved with a population of engineering students, who learn to use them. Results: The importance of using mathematical modelling as a didactic-dynamic resource is highlighted because it helps students to reach an understanding of real situations involving improper integrals in different contexts. Conclusions: Despite the numerous errors detected in the students, this strategy made it possible to demonstrate the development of advanced mathematical thinking skills in young people.

Hybrid Classical-Quantum computing has already arrived at several commercial quantum computers, offered to researchers and businesses. Here, application is made to a classical-quantum model of human neocortex, Statistical Mechanics of Neocortical Interactions (SMNI), which has had its applications published in many papers since 1981. However, this project only uses Classical (super-)computers. Since 2015, a path-integral algorithm, PATHINT, used previously to accurately describe several systems in several disciplines, has been generalized from 1 dimension to N dimensions, and from classical to quantum systems, qPATHINT. Published papers have described the use of qPATHINT to neocortical interactions and financial options. The classical space described by SMNI applies nonlinear nonequilibrium multivariate statistical mechanics to synaptic neuronal interactions, while the quantum space described by qPATHINT applies synaptic contributions from Ca2+ waves generated by astrocytes at tripartite neuron-astrocyte-neuron sites. Previous SMNI publications since 2013 have calculated the astrocyte Ca2+ wave synaptic interactions from a closed-form (analytic) expression derived by the author. However, more realistic random shocks to the Ca2+ waves from ions entering and leaving these wave packets should be included using qPATHINT between electroencephalographic (EEG) measurements which decohere the quantum wave packets. This current project extends calculations to multiple scales of interaction between classical events and expectations over the Ca2+ quantum processes to include these random shocks in previous codes used to fit EEG data to the SMNI model, that included the analytic forms for the quantum processes but now replaced by qPATHINT. The author's Adaptive Simulated Annealing (ASA) importance-sampling optimization code is used for fitting the combined classical-quantum system. Gaussian Quadratures is used for numerical calculation of momenta expectations of the astrocyte processes that contribute to SMNI synaptic interactions. This project thereby demonstrates how some hybrid classical-quantum systems may be calculated quite well using only classical (super-)computers.

In this article, we introduce a relatively new concept of multi-valued (θ;R)-contractions and utilize the same to prove some xed point results for a new class of multi-valued mappings in metric spaces endowed with an amorphous binary relation. Illustrative examples are also provided to exhibit the utility of our results proved herein. Finally, we utilize some of our results to investigate the existence and uniqueness of a positive solution for the integral equation of Volterra type.

In this study, we investigate spectral structure of conformable Sturm-Liouville problems and with this end, we obtain representation of solutions under different initial conditions and asymptotic formulas for eigenfunctions, eigenvalues, norming constants and normalized eigenfunctions. Consequently, we prove the existence of infinitely many eigenvalues. Also, we compare the solutions with graphics with different orders, different eigenvalues, different potentials and so, we observe the behaviors of eigenfunctions. We give an application to the α-orthogonality of eigenfunctions and reality of eigenvalues for conformable Sturm-Liouville problems defined by [15] in the last section.

In this paper, we investigate an analytical solution of a class of nonlinear fractional integro-differential equation base on a generalized fractional power series expansion. The fractional derivatives are described in the conformable's type. The new approach is a modified form of the well-known Taylor series expansion. The illustrative examples are presented to demonstrate the accuracy and effectiveness of the proposed method

The use of salt rock for underground radioactive waste disposal facilities requires a comprehensive analysis of creep-damage process in salt rock. A computer-controlled creep setup is employed to carry out a creep test of salt rock lasted as long as 359 days under a constant uniaxial stress. The AE space-time evolution and energy releasing characteristics during creep test are studied in the meantime. A new creep-damage model is proposed on the basis of fractional derivative by combining the AE statistical regularity. It indicates that the AE data in non-decay creep process of salt rock can be divided into three stages. Furthermore, the parameters of new creep-damage model are determined by Quasi-Newton method. The fitting analysis suggests that the creep-damage model based on fractional derivative in this paper provides a precise description of full creep regions in salt rock.

Pollution caused by copper is one of the key factors of environment contamination. As one of heavy metals, copper is hard to decompose in nature, the biological enrichment of which may lead to severe damage to health. Cu²⁺ detection, thus, possesses a bright application prospect both in environment protection and in human health. In this paper, a dual-functional fluorescence-magnetic composite nano-platform has been designed to sensitively detect, meanwhile capture and remove Cu²⁺ in the solution of water and ethanol (1:1, v/v). The core-shell structure nanoparticle synthesized by using Fe₃O₄ as core and SiO₂ as shell, is covalently bonded with rhodamine derivatives on the silica layer to construct the nano-platform. The emission is increased upon the addition of Cu²⁺, showing fluorescence turn on effect for the detection, and the limit of detection which was as low as 1.68 nM. Meanwhile, Cu²⁺ ions are captured by the coordination with rhodamine derivatives, and can be removable with the help of magnetic field.

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.

Background: Previous papers have developed a statistical mechanics of neocortical interactions (SMNI) fit to short-term memory and EEG data (Ingber, 2018). Adaptive Simulated Annealing (ASA) was used for all fits to data. A numerical path-integral for quantum systems, qPATHINT, was used. Objective: The quantum path-integral for Calcium ions was used to derive a closed-form analytic solution at arbitrary time. The quantum effects is parameterized here, whereas the previous 2018 paper applied a nominal ratio of 1/2 to these effects. Method: Methods of mathematical-physics for optimization and for path integrals in classical and quantum spaces are used. The quantum path-integral is used to derive a closed-form analytic solution at arbitrary time, and is used to calculate interactions with classical-physics SMNI interactions among scales. Results: The mathematical-physics and computer parts of the study are successful, in that three cases with Subjects (blind to this author) after 1,000,000 visits to the cost function gave: Subject-07 = 0.04, Subject-08 = 0.55, and Subject-09 = 1.00. All other 9 Subjects gave 0.

Background: Since circa 1980, a model of neocortical interactions, Statistical Mechanics of Neocortical Interactions (SMNI) has been successful in calculating many experimental phenomena, including fits to electroencephalographic (EEG) data in attention tasks, using an importance-sampling code Adaptive Simulated Annealing (ASA). The SMNI model is developed in the context of classical path-integrals, which affords intuitive insights as well as direct numerical benefits, e.g., using the effective Action as a a cost/objective function for parameter fits to data. Objective: Previous authors have fit affective EEG data to neural-network models. This project seeks to use models based on physics and biology to fit this same data. Previous work showed improvements in fits to EEG for attention states; this project extends these methods to affective states. Method: Path integrals are used in both classical and quantum contexts. Classical path integrals are used to define a cost/objective function to fit data, and quantum path integrals are used to derive a closed-form analytic expression for Ca-ion waves in the presence of a magnetic vector potential which is generated by highly synchronous neuronal firings which give rise to EEG. ASA is used to fit EEG data. Results: The mathematical-physics and computer parts of the study are successful, in that cost/objective functions used to fit EEG data using these models are consistent with previous work published by other authors. However, since the SMNI model includes these quantum effects, this is another reason to continue examining these issues. The results here are consistent, not better, than previous work using neural-network models, albeit only one parameter was used here, instead of multiple filters and kernels used previously on such data. Conclusion: Although these quantum effects are highly speculative, explicit calculations have shown them to be consistent with experimental data, at least to date. The current supercomputer project extends this model to affective/emotion data. Results from several authors using neural-network approaches at individual electrode sites show some predictive capabilities; the results given here are consistent with these other results. However, since the SMNI model includes these quantum effects, this is another reason to continue examining these issues.

Methods of path integrals are used to develop multi-factor probabilities of bid-ask variables for use in high-frequency trading (HFT). Adaptive Simulated Annealing (ASA) is used to fit the nonlinear forms so developed to a day of BitMEX tick data. Maxima algebraic code is used to develop the path integral codes into C codes, and sampling code is used for the fitting process. After these fits, the resultant C code is very fast and useful for forecasting upcoming ask, bid, midprice, etc., when narrow and wide windows of incoming data are used. A bonus is the availability of canonical momenta indicators (CMI) useful to forecast direction and strengths of these variables.

This paper establishes a real integral representation of the reciprocal $\Gamma$ function in terms of a regularized hypersingular integral. The equivalence with the usual complex representation is demonstrated. A regularized complex representation along the usual Hankel path is derived.

In this work we study the recently developed parametrized partition function formulation and show how we can infer the thermodynamic properties of fermions based on numerical simulation of bosons and distinguishable particles at various temperatures. In particular, we show that in the three dimensional space defined by energy, temperature and the parameter characterizing parametrized partition function, we can map the energies of bosons and distinguishable particles to fermionic energies through constant-energy contours. We apply this idea to both noninteracting and interacting Fermi systems and show it is possible to infer the fermionic energies at all temperatures, thus providing a practical and efficient approach to obtain thermodynamic properties of large fermion systems with numerical simulation. As an example, we present energies for up to 50 noninteracting fermions and up to 20 interacting fermions at all temperatures and show good agreement with the analytical result for noninteracting case.

In this present paper, we deal with the generalized (k, s)-fractional integral and differential operators recently defined by Nisar et al. and obtain some generalized (k, s)-fractional integral and differential formulas involving the class of a function as its kernels. Also, we investigate a certain number of their consequences containing the said function in their kernels.

Digital twins are an emerging technology that could be harnessed for the digitalization of the industry. Steel industry systems contain a large number of electro-hydraulic components, as proportional valves. An input-output model for a novel water proportional cartridge valve is derived from physical modelling based on fluid mechanics, dynamics, and electrical principles. The valve is a two-stage valve with two 2/2-way water proportional valves as the pilot stage and a marginally stable poppet-type cartridge valve as the main valve. The orifice equation, which is based on Bernoulli principles, is approximated by a polynomial which makes parameter estimation easier and makes modelling possible without measuring pressure of the varying control volume situated in the pilot stage part of the valve. Data were collected when the valve was operating as a component in a closed-loop system as part of a press-mill machine in a steel manufacturing plant. Parameter estimation was made by convex optimization with physical constraints to overcome problems caused by poor system excitation. For comparison, a simple linear model was derived and the least squares method used for parameter estimation. A thorough estimation of the parameters relative errors is presented. The model contains 5 parameters related to the design parameters of the valve. The modelled position output is in good agreement with experimental data for training and test data. The model can be used for real time monitoring of the valve’s status by the model parameters. One of the model parameters varies linearly with production cycles. Thus, aging of the valve can be monitored.

In this study, long-term mortality effects associated with exposure to PM10, PM2.5, BC (black carbon), and NOx were analyzed in a cohort in southern Sweden during the period from 1991‒2016. Participants (those residing in Malmö, Sweden, born between 1923‒1950) were randomly recruited from 1991‒1996. At enrollment, 30,438 participants underwent a health screening, which consisted of questionnaires about lifestyle and diet, a clinical examination, and blood sampling. Mortality data were retrieved from the Swedish national cause of death register. The modeled concentrations of PM10 (particles with an aerodynamic diameter smaller than or equal to 10 µm), PM2.5 (particles with an aerodynamic diameter smaller than or equal to 2.5 µm), BC (black carbon), and NOx (nitrogen oxides) at the cohort participants' home addresses were used to assess air pollution exposure. Cox proportional hazard models were used to estimate the associations between long-term exposure to PM10, PM2.5, BC, and NOx and the time until death among the participants during the period from 1991‒2016. The hazard ratios (HRs) associated with an interquartile range (IQR) increase in each air pollutant were calculated based on the exposure lag windows of the same year (lag0), 1‒5 years (lag1‒5), and 6‒10 years (lag6‒10). Three models were used with varying adjustments for possible confounders including both single-pollutant estimates and two-pollutant estimates. With adjustments for all covariates, the HRs for PM10, PM2.5, BC, and NOx in the single-pollutant models at lag1‒5 were 1.06 (95% CI: 1.02‒1.11), 1.01 (95% CI: 0.95‒1.08), 1.07 (95% CI: 1.04‒1.11), and 1.11 (95% CI: 1.07‒1.16) per IQR increase, respectively. The HRs were in most cases decreased by the inclusion of a larger number of covariates in the models. The most robust associations were shown for NOx, with statistically significant positive HRs in all models. An overall conclusion is that road traffic-related pollutants had a significant association with mortality in the cohort.

This paper focuses on a joint model to analyse longitudinal proportion and survival data. After transforming the longitudinal proportional data by a logit function, we adopt a partially linear mixed-effect model for it, in which nonlinear function of time is fitted via using B-splines technique and a centered Dirichlet Process Mixture Model (CDPMM) is specified for a general distribution of random effects. The survival data is assumed to a Cox proportional hazard model, the sharing random effects joint model is developed for the two types of data. Combining the Gibbs sampler and the Metropolis-Hastings algorithm, we propose a Bayesian Lasso (BLasso) method to simultaneously estimate unknown parameters and select important covariates. Simulation studies are conducted to investigate the finite sample performance of the proposed methods. An example from the MA.5 research experiment is used to illustrate the proposed methodologies.

This article deals with the conformable double Laplace transforms and their some properties with examples and also the existence Condition for the conformable double Laplace transform is studied. Finally, in order to obtain the solution of nonlinear fractional problems, we present a modified conformable double Laplace that we call conformable double Laplace decomposition methods (CDLDM). Then, we apply it to solve, Regular and singular conformable fractional coupled burgers equation illustrate the effectiveness of our method some examples are given.

The fungus Xylaria sp. Z184, harvested from the leaves of Fallopia convolvulus (L.) Á. Löve, has been isolated for the first time. Chemical investigation of the methanol extract of this strain’s culture broth led to the discovery of three new pyranone derivatives fallopiaxylaresters A-C (1–3) and a new bisabolane-type sesquiterpenoid named fallopiaxylarol A (4), along with the first complete set of spectroscopic data for the previously-reported pestalotiopyrone M (5). Known pyranone derivatives (6–11), sesquiterpenoids (12–14), isocoumarin derivatives (15–17), and an aromatic allenic ether (18) were co-isolated. Their structures were elucidated by the interpretation of HRESIMS, 1D, 2D NMR spectroscopy and quantum chemical computation method. The antimicrobial, anti-inflammatory, and α-glucosidase inhibitory activities of selected compounds and crude extract were evaluated in vitro. The extract inhibited nitric oxide (NO) production induced by lipopolysaccharide (LPS) in murine RAW264.7 macrophage cells, with an inhibition rate of 77.28 ± 0.82% at a concentration of 50 μg/mL. The compounds 5, 7 and 8 displayed weak antibacterial activity against Staphylococcus areus subsp. aureus at a concentration of 100 μM.

The classical limit definition of a derivative is expressed in a more general form. The general form includes two arbitrary functions of the parameter for which the limit is calculated. A special case of the general form, which includes scaling and translational symmetry transformations of the limiting parameter, is also discussed. The errors in using the classical definition and the generalized form are calculated for small values of the limiting parameter. The derivatives of some known functions are proven using the new definition. For some well-known functions, a suitable selection of the generalized form may introduce simplicity in calculating the derivatives.

Based on the marine natural products piperafizine B, X334 and our previously reported compound 4m, fourteen novel 3,6-diunsaturated 2,5-diketopiperazine (2,5-DPK) derivatives (1-2, 4-6, 8-16), together with two known ones (3 and 7), were designed and synthesized as anticancer agents against cell lines A549 and Hela. The MTT assay results showed that the derivatives 6, 8-12 and 15 had moderate to good anticancer capacities with the IC50 values ranging from 0.7 to 8.9 μM. Among them, compound 11 with naphthalen-1-ylmethylene and 2-methoxybenzylidene functions at the 3- and 6-positions of 2,5-DPK ring, respectively, displayed good inhibitory activities to both cancer cells A549 (IC50 = 1.2 μM) and Hela (IC50 = 0.7 μM). It could also induce apoptosis and obviously block the cell cycle progression at G2/M phase in both cells at 1.0 μM. The electron withdrawing functions might not be favorable for the derivatives with high anticancer activities. Additionally, compared to piperafizine B and X334, these semi-N-alkylated derivatives have high liposolubilities (> 1.0 mg•mL-1). Compound 11 can be further developed aiming to the discovery of novel anticancer candidate.

The quest for accurate and more efficient methods for solving periodic/oscillatory problems is gaining more attention in recent time. This paper presents the construction and implementation of a family of exponentially–fitted Obrechkoff methods. A single–step Obrechkoff method involving terms up to the fourth derivatives was used as the base method. We also present the stability and convergence properties of the constructed family of methods. Two numerical examples were use to illustrate the performance of the constructed methods.

In this paper we use the conformable fractional derivative to discuss some fractional linear differential equations with constant coefficients. By applying some similar arguments to the theory of ordinary differential equations, we establish a sufficient condition to guarantee the reliability of solving constant coefficient fractional differential equations by the conformable Laplace transform method. Finally, we analyze the analytical solution for a class of fractional models associated with Logistic model, Von Foerster model and Bertalanffy model is presented graphically for various fractional orders and solution of corresponding classical model is recovered as a particular case.

Amplitudes of quantum transitions containing time zigzags are considered. The discussion is carried out in the framework of the Minkowski metric and the standard quantum mechanics without adding new postulates. We argue that time zigzags are not suppressed at the quantum level, but their contribution to the amplitude is zero. The result is valid for a single particle and a non-interacting scalar field.

Hybrid Classical-Quantum computing has already arrived at several commercial quantum computers, offered to researchers and businesses. Here, applications are made to a model of financial options, Statistical Mechanics of Financial Markets (SMFM). These applications were published in many papers since the 1980's. This project only uses Classical (super-)computers to include quantum features of these models. Since 1989, an optimization code, Adaptive Simulated Annealing (ASA), has been to fit parameters in such models. Since 2015, a path-integral algorithm, PATHINT, used previously to accurately describe several systems in several disciplines, has been generalized from 1 dimension to N dimensions, and from classical to quantum systems, qPATHINT. Published papers have described the use of qPATHINT to neocortical interactions and financial options. The classical space by SMFM applies nonlinear nonequilibrium multivariate statistical mechanics to fit parameters in conditional short-time probability distributions, while the quantum space described by qPATHINT deals specifically with quantum systems, e.g., quantum money. This project thereby demonstrates how some hybrid classical-quantum systems may be calculated quite well using only classical (super-)computers.

Integral atmospheric dispersion models are used widely for flammable hazard and its risk analysis. There is a widespread belief that flammable distances from these models are conservative when flammable ranges are calculated using the 0.5 lower flammability limits (LFL) concentration threshold. This is erroneous. This paper traces through the development of these models and the research that led to the Birch Guidance. It shows that the 0.5 LFL is a necessary factor to transform the results of dispersion models designed for environmental assessment to applications to flammable hazard assessment in quiescent conditions. Current applications do not take account of turbulence due to wind, large and small obstructions, etc. A set of simple guidance is given in the paper to manage flammable hazards based on results from atmospheric dispersion models, including topics for future research.

Background: Forecasting nonlinear stochastic systems most often is quite difficult, without giving in to temptations to simply simplify models for the sake of permitting simple computations. Objective: Here, two basic algorithms, Adaptive Simulated Annealing (ASA) and path-integral codes PATHINT/PATHTREE (and their quantum generalizations qPATHINT/qPATHTREE) are offered to detail such systems. Method: ASA and PATHINT/PATHTREE have been effective to forecast properties in three disparate disciplines in neuroscience, financial markets, and combat analysis. Applications are described for COVID-19. Results: Results of detailed calculations have led to new results and insights not previously obtained. Conclusion: These 3 applications give strong support to a quite generic application of these tools to stochastic nonlinear systems.

Agricultural intensification is considered essential for meeting growing demand for food and biomass for energy and material purposes. Intensifying grasslands is a so-far under-represented although promising option, given their large land area and relatively low management levels. This study quantifies the bioenergy potential from intensifying temporary grasslands in Europe and the integral greenhouse gas emission effects in 2030. We first conduct a literature review of intensification options for European grasslands and then apply the environmental impact assessment model MITERRA-Europe to implement the key intensification option of using multi-species grass mixtures. The results show that 853 kha (or 8%) of temporary grassland could be made sustainably available for additional biomass production. This can be translated into a bioethanol potential of 23 PJ/yr and an emission mitigation potential of 5.8 Mt CO2-eq/yr (if conventional grass mixture from surplus temporary grassland is used for energy) or 72 PJ/yr and 4.0 Mt CO2-eq/yr (if surplus temporary grassland is used for grassy energy crops). Although the bioenergy potential is limited, the intensification measure’s key advantage is that it results in a better environmental performance of temporary grasslands. This makes it a key option for sustainably producing bioenergy in areas with high shares of temporary grasslands.

Background: Forecasting nonlinear stochastic systems most often is quite difficult, without giving in to temptations to simply simplify models for the sake of permitting simple computations. Objective: Here, two basic algorithms, Adaptive Simulated Annealing (ASA) and path-integral codes PATHINT/PATHTREE (and their quantum generalizations qPATHINT/qPATHTREE) are offered to detail such systems. Method: ASA and PATHINT/PATHTREE have been effective to forecast properties in three disparate disciplines in neuroscience, financial markets, and combat analysis. Applications are described for COVID-19. Results: Results of detailed calculations have led to new results and insights not previously obtained. Conclusion: These 3 applications give strong support to a quite generic application of these tools to stochastic nonlinear systems.

In this paper, inspired by Jleli and Samet [journal of inequalities and applications 38 (2014) 2 1–8] we introduce two new classes of auxiliary functions and utilize the same to define (q, y)R-weak 3 contractions. Utilizing (q, y)R-weak contractions, we prove some fixed point theorems in the setting 4 of relational metric spaces. We employ some examples to substantiate the utility of our newly proved 5 results. Finally, we apply one of our newly proved results to ensure the existence and uniqueness of 6 solution of a Volterra-type integral equation.

According to the fact that the low convergence level on the complete elliptic integral of the first kind for the modulus which having values approach to one. In this paper we propose novelty of the complete elliptic integral consists of the new infinite series. We apply the scheme of iteration by substituting the common modulus with own modulus function into the new infinite series. We obtained so many new exact formulas of the complete elliptic integral derived from this method correspond to the number of iteration order. On the other hand, it has been also obtained a lot of new modulus functions rather than common used previously. The calculation results show that the number of significant figures of the new infinite series of the complete elliptic integral of the first kind is increased more and more. It means more fastly convergent would be obtained comparison values with the previous infinite series.

The connection of two phenomena - non-conservative friction forces and dissipation-induced instability can lead to many interesting engineering problems. The paper studies general material-dependent damping influence on dynamical instability of disc brake systems leading to brake squeal. The effect of general damping is demonstrated on a minimal and complex model of a disc brake. A complex system including material-dependent damping is defined in the commercial finite element software. The finite element model validated by experimental data on the brake-disc test bench is used to compute the influence of a pad and a disc damping variations on system stability by complex eigenvalue analysis. Analyzes show a significant sensitivity of the experimentally verified unstable mode of the system to the ratio of the damping between the disc and the friction material components.

In this paper, we work with a diffusion-perturbed risk model comprising a surplus generating process and an investment return process. The investment return process is of standard Black-Scholes type, that is, it comprises a single risk-free asset that earns interest at a constant rate and a single risky asset whose price process is modelled by a geometric Brownian motion. Additionally, the company is allowed to purchase noncheap proportional reinsurance priced via the expected value principle. Using the Hamilton-Jacobi-Bellman approach, we derive a second-order Volterra integrodifferential equation which we transform into a linear Volterra integral equation of the second kind. We proceed to solve this integral equation numerically using the block-by-block method for the optimal reinsurance retention level that minimizes the ultimate ruin probability. The numerical results based on light- and heavy-tailed distributions show that proportional reinsurance and investments play a vital role in enhancing the survival of insurance companies. But the ruin probability exhibits sensitivity to the volatility of the stock price.

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.

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.

NAD⁺ is known classically as a metabolite that participates in catabolic and anabolic pathways throughout the metabolism that is taught to students in introductory biochemistry courses. However, non-classical studies starting over a decade ago found that NAD⁺ is also involved in higher order functions, in part because of its involvement in the activation of SIRTs and the support of the mitochondrial unfolded protein response. Many studies since have suggested that NAD⁺ is involved in an extensive spectrum of human pathologies, including neurodegenerative disorders, cardiomyopathy, obesity, and diabetes, Further, healthy aging and longevity appear to be closely related to NAD⁺ and its related metabolites, including NAR and NMN. Together, these studies show that this system has value as a dietary supplement to improve general health overall, as well as mitigating specific disease conditions. Accordingly, many are now recommending the consumption of materials in this system as dietary supplements. Nicotinamide riboside (NAR) appears to have special value in this regard. It appears to be better tolerated than other molecules in this system, as well as better pharmacodynamics and greater potency. Unfortunately, NAR is a reactive molecule, often unstable during its manufacturing, transport, and storage. Indeed, HPLC analyses of many commercial samples of NAR shows that they contain substantial amounts of material that are not, in fact, NAR. In some of these commercial preparations, NAR is a minority component. Therefore, more stable derivatives of NAR that are easily converted upon consumption into NAR are therefore desired. Recently work related to prebiotic chemistry provided the borate derivative of NAR. NARB is considerably more stable than NAR itself. However, immediately upon consumption, the borate dissociates from NARB, and is lost in the body through dilution and binding to other species, notably carbohydrates such as fructose and glucose. The NAR left behind is expected to behave pharmacologically in ways identical to NAR itself. This review provides a comprehensive summary (through Q1 of 2023) of literature that makes the case for the consumption of NAR as a dietary supplement. It then summarizes the challenges of delivering quality NAR to consumers using standard synthesis, manufacture, shipping, and storage approaches. It concludes by outlining the advantages of NAR-borate in these processes.