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Due to the hasty growth of digital technology, securing medical images for transmission and storage is a significant issue. Information on the texture of medical images is essential for diagnosis. Hence, protecting these content has become a great challenge in the e-Healthcare system. So, we propose a novel dynamic circular bit shifting and bit-flipping process in the diffusion phase of the image cryptosystem to provide high level protection for the medical image. In the developed framework, at first, the hyperbolic chaotic map is executed for generating three hyper chaotic series and these chaotic series are utilized for encryption process. In encryption process, primarily the secret image is confused by utilizing any two chaotic series, then the confused image is divided into blocks and each block is diffused by executing the proposed dynamic circular bit shifting and bit-flipping process which greatly increases the probability and complexity level of the developed cryptosystem. Evaluation using different medical images represents that the proposed model has robustness, high efficiency, key sensitivity and also has the ability to withstand different attacks. This has been represented using the results of security measures and statistical analysis, such as Shannon entropy (7.997), CC (< 0), NPCR (99.63 %), UACI (37.14 %), SSIM (< 0), FSIM (< 0.5), PSNR (6.88). These results prove that the developed medical crypt can efficiently provide better security for medical images utilized in real time medical application like e-Healthcare and telemedicine.

AbstractSoil-cement columns are implemented in coastal areas to improve the capacity of loose, soft, and dredged soils, reduce settlement, and mitigate liquefaction effects. Static load testing is used for quality control and the verification of design assumptions. Given the greater reliability of full-scale testing results compared to physical and numerical modeling results and the lack of a database for soil-cement columns, 42 full-scale loading records on these columns were compiled to assess the behavior of these columns and identify the most influential factor in their behavior. The database contains columns ranging in length from 5 to 19 meters with diameters ranging from 40 to 120 cm, as well as soil profiles ranging from clay to sand and mixed soil. Their behavior was evaluated using a hyperbolic relationship. The results indicate that component materials, influenced by implementation technique, in-situ soil properties, and reinforcing, more significantly influence the behavior of columns than the columns’ length. The columns are categorized into three separate groups, which are separated due to their different equivalent unconfined compressive strengths and shapes. These categories allow for the prediction of the load-displacement ratio diagram range of the column based on initial information such as the column diameter, length, and properties of in-situ soil. The upper and lower bounds of categories were validated by the loading results of five soil-cement columns implemented in Iran coastal line. [ABSTRACT FROM AUTHOR]

This work aims to provide a unique analytical model designed for calculating the magnetic field of a surface-mounted permanent magnet Vernier motor (SPMVM). The model is created utilizing the separation variable method to solve Laplace or Poisson equations of the vector magnetic potential in a quasi-Cartesian coordinate system subdomain model. The theoretical justifications for the final analytical equations of electromagnetic torque, no-load back-EMF, stator inductance, and magnetic flux density distribution are given in detail. Then the solution of the equation is expressed in the form of a hyperbolic function. Furthermore, the improved analytical method in the study is generic and can be applied to estimating the parameters of machines with different design concepts. Finally, FEM is employed as the reference for comparison between other models. Compared to the original subdomain model, the calculation results of the improved analytical model are more time-efficient and closer to those of FEM. In addition, the improved analytical method can reduce the dimension of the coefficient matrix and improve the calculation speed. The SPMVM prototype is then built to demonstrate the validity and feasibility of the improved subdomain method and serves as a guide for future SPMVM development. [ABSTRACT FROM AUTHOR]

Due to the hasty growth of digital technology, securing medical images for transmission and storage is a significant issue. Information on the texture of medical images is essential for diagnosis. Hence, protecting these content has become a great challenge in the e-Healthcare system. So, we propose a novel dynamic circular bit shifting and bit-flipping process in the diffusion phase of the image cryptosystem to provide high level protection for the medical image. In the developed framework, at first, the hyperbolic chaotic map is executed for generating three hyper chaotic series and these chaotic series are utilized for encryption process. In encryption process, primarily the secret image is confused by utilizing any two chaotic series, then the confused image is divided into blocks and each block is diffused by executing the proposed dynamic circular bit shifting and bit-flipping process which greatly increases the probability and complexity level of the developed cryptosystem. Evaluation using different medical images represents that the proposed model has robustness, high efficiency, key sensitivity and also has the ability to withstand different attacks. This has been represented using the results of security measures and statistical analysis, such as Shannon entropy (7.997), CC (< 0), NPCR (99.63 %), UACI (37.14 %), SSIM (< 0), FSIM (< 0.5), PSNR (6.88). These results prove that the developed medical crypt can efficiently provide better security for medical images utilized in real time medical application like e-Healthcare and telemedicine. [ABSTRACT FROM AUTHOR]

In this study, we studied the (2+1)-dimensional complex modified Korteweg-de Vries (cmKdV) system using the improved Ricatti equation method. cmKdV are nonlinear and coupled partial differential equations that arise in various fields of applied science and engineering, such as ferromagnetic materials and optical fibers. When the method is applied to cmKdV, we successfully derive exact soliton solutions that accurately describe the wave propagation behavior of the system under consideration. The obtained results include trigonometric and hyperbolic function solutions. The results obtained are concise and offer a deeper insight into the dynamics and characteristics of cmKdV. Traveling wave solitons are plotted in 2D and 3D to demonstrate the wave propagation phenomena in the cmKdV model, which are in the form of kink, bright, dark, singular solitons, and periodic solitary wave structures. The method recovers many solutions compared with the existing methods in the literature, indicating that the proposed method is a powerful and valuable approach for achieving analytical solutions to a wide range of nonlinear partial differential equations [ABSTRACT FROM AUTHOR]

Computation of end-of-primary compression for clayey soils is an important step undertaken to meet the serviceability criteria of geotechnical engineering structures. But for soils that exhibit secondary compression behaviour, computing the end-of-secondary compression values is more significant. One of the prevailing methods suggested for its computation is the cα (coefficient of secondary compression) method. However, without sufficient data, interpretation of the end-of-secondary compressions could be challenging, if not erroneous. This paper presents the computation of the end-of-secondary compression for a set of five soils from India namely Red soil, Bombay marine clay, Kuttanad clay, Cochin marine clay and Peat by conducting long-term consolidation tests to the order of 10 days for each pressure increment. A non-linear creep function was used to determine the limiting creep condition of the soils. The curves obtained are more realistic compared to the cα concept which overestimates secondary compression settlements. [ABSTRACT FROM AUTHOR]

In this article, we study the complex coupled Kuralay system (CKS), which have many applications in different field such as ferromagnetic material and fiber optics. We implement an analytical method, namely, the tanh–coth method to considered system to formulate a system of algebraic equations. Solving the obtained system, we acquire different traveling wave solutions that are expressed in term of hyperbolic tangent functions and hyperbolic cotangent functions. Also, we employ the energy balance technique to the selected model to sort out the behavior of traveling wave solutions. By this method, we obtain periodic wave solution that are expressed in term of cosine function. In order to show the graphical presentation of the acquired solitary waves solutions, 3D and 2D curve are created by selecting well-suited parametric values via Mathematica.

The work presented in this article has been motivated by the recent research going on the Hankel determinant bounds and their related consequences, as well as the techniques used previously by many different authors. We aim to establish a new subfamily of holomorphic functions connected with the hyperbolic tangent function with bounded boundary rotation. We investigate the sharp estimate of the third Hankel determinant for this newly defined family of functions. Moreover, for the defined functions family, the Krushkal inequality, the first four initial sharp bounds of the logarithmic coefficients and the sharp second Hankel determinant of the logarithmic coefficients are given.

A system with distributed parameters in its mechanical part is considered. Examples of such a system are given. The reason for taking into account the distribution of parameters in such systems is indicated. Existing methods of research and calculation of control systems are considered. The boundary value problem for a system with distributed parameters is presented. The use of a surveillance device as one of the ways to implement a control system for a system with distributed parameters is proposed. The necessity of using a closed control system and the complexity of its implementation are demonstrated. A block diagram of the control method being developed is presented. Also, transfer functions describing a system with distributed parameters are given; the mathematical calculation of the surveillance device is given as well. A method for implementing a closed control system along an intermediate coordinate for an electromechanical system with distributed parameters in the mechanical part using a surveillance device has been obtained. The surveillance device is in feedback and restores the output speed without measuring it directly. A general view of the transfer function is determined for the surveillance device. The advantages and disadvantages of the transfer function of the surveillance device and a graphical view of a simple implementation of the surveillance device with a dedicated auxiliary device in feedback are presented. An approximation that is used for systems with distributed parameters is described. Approximation conclusions are obtained. According to the parameters of the experimental installation, approximated transfer functions of the mechanical part of the system with distributed parameters without a surveillance device and with a surveillance device are obtained. The LACH of the mechanical part of the system with distributed parameters with a surveillance device and without a surveillance device for an experimental installation for the simplest case is presented, as well as a method for implementing a closed control system along an intermediate coordinate for an electromechanical system with distributed parameters in the mechanical part using a surveillance device.

In the present article, we define and investigate a new subfamily of holomorphic functions connected with the cosine hyperbolic function with bounded turning. Further some interesting results like sharp coefficients bounds, sharp Fekete-Szegö estimate, sharp $ 2^{nd} $ Hankel determinant and non-sharp $ 3^{rd} $ order Hankel determinant. Moreover, the same estimates have been investigated for 2-fold, 3-fold symmetric functions, the first four initial sharp bounds of logarithmic coefficient and sharp second Hankel determinant of logarithmic coefficients fort his defined function family.

This study is concerned with an observer-based independent joint control scheme for a coupled two-link rigid-flexible robotic manipulator considering the effects of actuator saturation and external disturbances. A distributed parameter model of the robotic manipulator system described by ordinary and partial differential equation (ODE-PDE) is derived by using Hamilton's Principle. An anti-saturation controller is developed to cope with the input saturation problem by using hyperbolic tangent and hyperbolic secant function. Considering the external disturbance, a disturbance observer is designed to estimate the external disturbance. The observer-based independent joint controller can adjust the joint angle and suppress the vibration simultaneously without the need for end-mounted actuators. The extended LaSalle's Invariance Principle is adopted to strictly prove the asymptotic stability of the robotic manipulator system. The simulation comparisons validate the effectivity of the proposed controllers and observers. [ABSTRACT FROM AUTHOR]

The work presented in this article has been motivated by the recent research going on the Hankel determinant bounds and their related consequences, as well as the techniques used previously by many different authors. We aim to establish a new subfamily of holomorphic functions connected with the hyperbolic tangent function with bounded boundary rotation. We investigate the sharp estimate of the third Hankel determinant for this newly defined family of functions. Moreover, for the defined functions family, the Krushkal inequality, the first four initial sharp bounds of the logarithmic coefficients and the sharp second Hankel determinant of the logarithmic coefficients are given. [ABSTRACT FROM AUTHOR]

In this article, we establish new travelling wave solutions for the nonlinear loaded (3+1)-dimensional version of the Benjamin-Ono equation by the functional variable method. The performance of this method is reliable and effective and the method provides the exact solitary wave solutions and periodic wave solutions. The solution procedure is very simple and the traveling wave solutions are expressed by hyperbolic functions and trigonometric functions. After visualizing the graphs of the soliton solutions and the periodic wave solutions, the use of distinct values of random parameters is demonstrated to better understand their physical features. It has been shown that the method provides a very effective and powerful mathematical tool for solving nonlinear equations in mathematical physics. [ABSTRACT FROM AUTHOR]

In the present article, we define and investigate a new subfamily of holomorphic functions connected with the cosine hyperbolic function with bounded turning. Further some interesting results like sharp coefficients bounds, sharp Fekete-Szego estimate, sharp 2nd Hankel determinant and nonsharp 3rd order Hankel determinant. Moreover, the same estimates have been investigated for 2-fold, 3-fold symmetric functions, the first four initial sharp bounds of logarithmic coefficient and sharp second Hankel determinant of logarithmic coefficients fort his defined function family. [ABSTRACT FROM AUTHOR]

Fractional calculus is a field that is currently used in the world's applications in many science and engineering fields where many models are still being developed and researched. The conformable time-fractional gives the full history of this function, which is the advantage of using fractional calculus to solve physical problems. In this study, the conformable time-fractional extended (2 + 1)-dimensional quantum Zakharov-Kuznetsov and the time-fractional modified Korteweg-de Vries equations are investigated by using the the modified exp (- Ω (ξ)) -expansion function approach. Some new prototype analytical solutions such the hyperbolic and trigonometric function solutions are successfully reached. The importance of current research is to derive new solutions using a strong analytical approach. All the reported solutions in this study have verified their corresponding model. Under the choice of suitable values of the parameters involved, the 3D and 2D to the obtained solutions are successfully plotted. [ABSTRACT FROM AUTHOR]

Locally Rotationally Symmetric (LRS) Bianchi type-I metric is examined in the presence of perfect fluid. Exact solutions of Einstein's field equations (EFE) have been studied by taking into account a hyperbolic scale factor. We observed that the model has initial singularity. It is found that the Universe approaches isotropy at late times. Through state finder pair { r , s } , it is observed that at late cosmic time, the model behaves analogous to Λ CDM model. Energy conditions of the model are studied and it is found that null energy condition (NEC), weak energy condition (WEC) and dominant energy conditions (DEC) are satisfied for our model while SEC is violated. We investigate some physically and geometrically realistic models in order to develop a viable cosmological model. [ABSTRACT FROM AUTHOR]

The reciprocal method of work is used to solve the bending problems of thin plate on elastic foundation under the combined action of lateral loads and forces in middle plane of the plate. The basic system is a simply supported thin plate on elastic foundation under combined action of lateral loads and forces in the middle plane of the plate. Two expressions of the deflection surface equation of the basic system are derived, the first is the double trigonometric function, and the second is the mixture of hyperbolic function and trigonometric function. The practical systems consist of thin plates on elastic foundation constrained by different boundary conditions. The deflection surface equation of the practical system is solved by using the reciprocal method of work between the practical system and the basic system. Compared with the finite element method with ANSYS software, the solution error is less than 5%, which satisfies the requirement of maximum error. This indicates that application of the reciprocal method of work is correct for solving the problem. [ABSTRACT FROM AUTHOR]

The KPI equation is one of most well-known nonlinear evolution equations, which was first used to described two-dimensional shallow water wavs. Recently, it has found important applications in fluid mechanics, plasma ion acoustic waves, nonlinear optics, and other fields. In the process of studying these topics, it is very important to obtain the exact solutions of the KPI equation. In this paper, a general Riccati equation is treated as an auxiliary equation, which is solved to obtain many new types of solutions through several different function transformations. We solve the KPI equation using this general Riccati equation, and construct ten sets of the infinite series exact solitary wave solution of the KPI equation. The results show that this method is simple and effective for the construction of infinite series solutions of nonlinear evolution models. [ABSTRACT FROM AUTHOR]

In this work, by the introduction of a new kernel function composed of exponent functions with several parameters, and using the method of weight coefficient, Hermite-Hadamard’s inequality, and some other techniques of real analysis, a more accurate half-discrete Hilbert-type inequality including both the homogeneous and non-homogeneous cases is established. Furthermore, by introducing the Bernoulli number and the rational fraction expansion of tangent function, some special and interesting Hilbert-type inequalities and their equivalent hardy-type inequalities are presented at the end of the paper.

The aim was to evaluate the performance of the latest quantitative marker for intrathecal IgG synthesis and to compare it with other established markers used for the same purpose. We retrospectively applied Auer's and Reiber's intrathecal IgG synthesis formulae in a cohort of 372 patients under investigation for central nervous system demyelination who had undergone lumbar puncture and oligoclonal bands (OCBs) detection for demonstrating intrathecal IgG synthesis. A ROC analysis revealed Auer's formula had lower sensitivity (68%) compared to Reiber's formula (83%) and IgG index (89%), in our cohort of patients that exhibited normal to mildly elevated albumin quotients (4.48 ± 3.93). By excluding possible sources of errors, we assume that Auer's formula is less sensitive than other established tools for the "prediction" of the detection of OCBs in routine cerebrospinal fluid (CSF) analyses due to the mathematical model used. Given the ability of Reiber's hyperbolic formula to describe the blood–CSF IgG distribution across a wide range of blood–brain barrier functionality, its use and the use of similar formulae are recommended for the discrimination between CNS-derived and blood-derived molecules in clinical laboratories. [ABSTRACT FROM AUTHOR]

The Korteweg–de Vries (KDV) equation is one of the most well-known models in nonlinear physics, such as fluid physics, plasma, and ocean engineering. It is very important to obtain the exact solutions of this model in the process of studying these topics. In the present paper, using distinct function iteration relations in two ways, namely, squaring infinitely and extracting the square root infinitely, which have not been reported in other documents, we construct abundant types of new infinite-series exact solitary wave solutions using the auxiliary equation method. Most of these solutions have not been reported in previous papers. The numerical analysis of some solutions shows complex solitary wave phenomena. Some solutions can have stable solitary wave structures, while others may have singularities in certain space–time positions. The results show that the analysis model we use is very simple and effective for the construction of new infinite-series solutions and new solitary wave structures of nonlinear models. [ABSTRACT FROM AUTHOR]

Beam models are widely applied in civil engineering, transport, and industry because the beams are basic structural elements. When dealing with the high-order modes of beam in the context of applying the modal analysis method, the numerical instability issue affects the numeric simulation accuracy in many boundary conditions. There are two solutions in literature to overcome this shortcoming, namely refinement of the asymptotic form for the high order modes and reshaping the terms within the equation of the modes to eliminate the source of the numerical instability. In this paper, the numerical instability issue is signalled when the standard form of Green's function, which includes hyperbolic functions, is applied to a free-free Timoshenko length-long beam. A new way is proposed based on new set of eigenfunctions, including an exponential function, to construct a new form of Green's function. To this end, it starts from a new general form of Green's function and the characteristic equation is obtained; then, based on the boundary condition, the Green's function associated to the differential operator of the free-free Timoshenko beam is distilled. The numerical stability of the new form of the Green's function is verified in a numerical application and the results are compared with those obtained by using the standard form of the Green's function. [ABSTRACT FROM AUTHOR]

In several investigations on control systems, sliding mode control has been identified as a beneficial instrument. The system is stable due to SMC's tolerance to instabilities and model heterogeneity. Furthermore, the chattering phenomena hinders system performance and may possibly lead to disruption. This paper deals with the application of different switching functions on inverted pendulum system. Further the comparison between them has also been done. Simulation results are given to demonstrate the effectiveness of the proposed approaches. [ABSTRACT FROM AUTHOR]

• A dynamic control algorithm based on state transition is proposed for vehicle following control. • Safe and efficient steady-following state is regarded as the optimization objective. • The absolute and relative braking modes can be flexibly chosen by the follower for safety control. • The following vehicle can adjust its own behavior in safety, efficiency, and smoothness. • The synchronous control of velocity, acceleration, and inter-vehicle distance is well achieved. This study aims to improve the safety and efficiency of vehicle-following behavior through a smooth vehicle behavior adjustment process. A dynamic control algorithm based on state transition is proposed for the following vehicle to enable it to incorporate better behavioral adjustments. This algorithm organically integrates a new generalized velocity difference control with the velocity control based on hyperbolic function to exploit its advantages and avoid weaknesses. The new generalized mathematical model based on fitting function is built for vehicle-following control within the neighborhood of a safe and efficient steady-following state, outside which, the velocity control method based on hyperbolic function is used by the following vehicle to adjust its behavior. In this algorithm, the absolute and relative braking modes can be flexibly selected by the following vehicle for safety control. Then, we establish a state transition diagram and a state optimization model with the safe and efficient steady-following state as the optimization objective of the vehicle-following behavior. The simulation shows that the current or a new safe and efficient steady-following state can be maintained, recovered, or reestablished by implementing the dynamic control algorithm based on state transition, and the synchronous control of the following vehicle's velocity, acceleration, and inter-vehicle distance can be realized by the following vehicle adjusting its own behavior safely, efficiently, and smoothly. [ABSTRACT FROM AUTHOR]

In this article, we consider the existence and uniqueness of solutions for a class of initial value problems of fuzzy Caputo-Katugampola fractional differential equations and the stability of the corresponding fuzzy fractional differential equations. The discussions are based on the hyperbolic function, the Banach fixed point theorem and an inequality property. Two examples are given to illustrate the feasibility of our theoretical results. [ABSTRACT FROM AUTHOR]

We propose two motions for a snake robot to move through crowded pipes. One motion is an S-shaped twisting motion performed by the snake robot as it moves around crowded pipes in parallel to the pipes. To develop the shape of the snake robot, the S-shaped twisting motion creates large and small semicircles alternately. In the S-shaped twisting motion, lateral rolling is used to generate the robot's twisting motion along its body to maneuver among crowded pipes. The other motion is an S-shaped traveling wave motion used by the snake robot to move among crowded pipes perpendicularly to the pipes. The S-shaped traveling wave motion adds a hyperbolic shape to the snake robot by utilizing a hyperbolic function. The shape of the hyperbolic function produces a little wave in the S-shaped traveling wave motion, and the wave is transferred from the tail to the head to move ahead. In this study, we describe the design of these two motions and exhibit the results of trials in simulation and with a real snake robot to validate the effectiveness of our proposed snake robot's motion. [ABSTRACT FROM AUTHOR]

Fourteen main tree species from typical natural broad-leaved stands in the mid-subtropical zone of the Jian’ou Wanmulin Provincial Nature Reserve were studied to reveal the characteristics and provide a typical reference for the tree height diameter ratio of main broad-leaved tree species for the sustainable management of artificial, semi-natural, and natural broad-leaved forests in mid-subtropical zones. The mean tree height diameter ratio, standard deviation, variation coefficient, Mann-Whitney U test, Spearman rank correlation coefficient, exponential function, and hyperbola equation were used to analyze the characteristics of the tree height diameter ratio of the main tree species in each storey (including three strata and the whole stand). The results showed that the mean and maximum values of the tree height diameter ratio of the main tree species of typical natural broad-leaved stands in the mid-subtropical zone decreased with increasing stratum height. The mean values were significantly (P＜0.05) or extremely significantly different (P＜0.01) among each stratum. The correlation between tree height to diameter ratio and diameter at breast-height (DBH) of the main tree species in each storey showed an extremely significant negative correlation (P＜0.01). The correlation coefficients of strata Ⅰ and Ⅱ were significantly higher than those of the whole stand and stratum Ⅲ. The absolute values of the correlation coefficients were 0.806 1-0.895 3 for stratum Ⅰ, 0.788 2-0.964 3 for stratum Ⅱ, 0.419 0-0.809 1 for stratum Ⅲ, and 0.419 0-0.848 9 in the whole stand. The effects of the exponential and hyperbolic functions on the relationship between tree height diameter ratio and DBH of strata Ⅰ and Ⅱ of the main tree species were better than those of the whole stand and stratum Ⅲ. The R², Erms, and Ema of the main tree species in the whole stand and stratum Ⅲ were relatively high in the exponential function fitting, while those in strata Ⅰ and Ⅱ were relatively high in the hyperbolic fitting. The tree height to diameter ratio of the main tree species was not constant but varied with stratum and DBH. The characteristics of the tree height diameter ratio of each tree species can be expressed by the relationship curve between the tree height diameter ratio and the DBH of each stratum of the main tree species. [ABSTRACT FROM AUTHOR]

The KPI equation is one of most well-known nonlinear evolution equations, which was first used to described two-dimensional shallow water wavs. Recently, it has found important applications in fluid mechanics, plasma ion acoustic waves, nonlinear optics, and other fields. In the process of studying these topics, it is very important to obtain the exact solutions of the KPI equation. In this paper, a general Riccati equation is treated as an auxiliary equation, which is solved to obtain many new types of solutions through several different function transformations. We solve the KPI equation using this general Riccati equation, and construct ten sets of the infinite series exact solitary wave solution of the KPI equation. The results show that this method is simple and effective for the construction of infinite series solutions of nonlinear evolution models.

Mathematical modeling of many physical process leads to nonlinear evolution equations. The investigation of traveling wave solutions of nonlinear partial differential equations plays significant role in the study of nonlinear physical phenomena. In this article, the generalized (G' =G) - expansion method using generalized wave transformation is applied to find exact traveling wave solutions of the loaded modified Zakharov-Kuznetsov(ZK) equation. The performance of the method is reliable, useful and gives more new general exact solutions than the existing methods. The travelling wave solutions are expressed by the hyperbolic functions, the trigonometric functions and the rational functions. The results emphasize the power of proposed methods in providing distinct solutions of different physical structures in nonlinear science. The graphical presentations are demonstrated for some of newly obtained solutions. It is shown that the proposed method provides a powerful mathematical tool for solving nonlinear wave equations in mathematical physics and engineering. [ABSTRACT FROM AUTHOR]

This article investigates the local fractional generalized Kadomtsev–Petviashvili equation and the local fractional Kadomtsev–Petviashvili-modified equal width equation. It presents traveling-wave transformation in a nondifferentiable type for the governing equations, which translate them into local fractional ordinary differential equations. It also investigates nondifferentiable traveling-wave solutions for certain proposed models, using an ansatz method based on some generalized functions defined on fractal sets. Several interesting graphical representations as 2D, 3D, and contour plots at some selected parameters are presented, by considering the integer and fractional derivative orders to illustrate the physical naturality of the inferred solutions. Further results are also introduced in some details. [ABSTRACT FROM AUTHOR]

Decision tree is one of the best expressive classifiers in data mining. A decision tree is popular due to its simplicity and straightforward visualization capability for all types of datasets. Decision tree forest is an ensemble of decision trees. The prediction accuracy of the decision tree forest is more than a decision tree algorithm. Constant efforts are going on to create accurate and diverse trees in the decision tree forest. In this paper, we propose Tangent Weighted Decision Tree Forest (TWDForest), which is more accurate and diverse than random forest. The strength of this technique is that it uses a more accurate and uniform tangent weighting function to create a weighted decision tree forest. It also improves performance by taking opinions from previous trees to best fit the successor tree and avoids the toggling of the root node. Due to this novel approach, the decision trees from the forest are more accurate and diverse as compared to other decision forest algorithms. Experiments of this novel method are performed on 15 well known, publicly available UCI machine learning repository datasets of various sizes. The results of the TWDForest method demonstrate that the entire forest and decision trees produced in TWDForest have high prediction accuracy of 1–7% more than existing methods. TWDForest also creates more diverse trees than other forest algorithms. [ABSTRACT FROM AUTHOR]

This brief introduces a novel cost function framework for developing robust algorithms for adaptive filtering by embedding the standard cost function into the arctangent framework. This proposed framework is called the arctangent cost function framework. Based on this, we propose an arctangent family of robust algorithms for adaptive filtering. The performance of the proposed family of algorithms is tested through simulation studies in system identification scenarios that confirm the enhanced performance achieved by the arctangent family of algorithms over standard algorithms. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we prove that, for x>0 $x>0$, 1−exp(−x2x2+1)

A chaotic system with a hyperbolic function flux-controlled memristor is designed, which exhibits conditional symmetry and attractor growing. The newly introduced cosine function keeps the polarity balance when some of the variables get polarity inversed and correspondingly conditional symmetric coexisting chaotic attractors are coined. Due to the periodicity of the cosine function, the memristive system with infinitely many coexisting attractors shows attractor growing in some special circumstances. Analog circuit experiment proves the theoretical and numerical analysis.

The main contribution of this paper is to formulate a robust-adaptive and stable state-space speed control strategy for DC motors. The linear-quadratic-integral (LQI) controller is utilized as the baseline controller for optimal speed-regulation, accurate reference-tracking and elimination of steady-state fluctuations in the motor’s response. To reject the influence of modelling errors, the LQI controller is augmented with a Lyapunov-based model reference adaptation system (MRAS) that adaptively modulates the controller gains while maintaining the asymptotic stability of the controller. To further enhance the system’s robustness against parametric uncertainties, the adaptation gains of MRAS online gain-adjustment law are dynamically adjusted, after every sampling interval, using smooth hyperbolic functions of motor’s speed-error. This modification significantly improves the system’s response-speed and damping against oscillations, while ensuring its stability under all operating conditions. It dynamically re-configures the control-input trajectory to enhance the system’s immunity against the detrimental effects of random faults occurring in practical motorized systems such as bounded impulsive-disturbances, modelling errors, and abrupt load–torque variations. The efficacy of the proposed control strategy is validated by conducting credible hardware-in-the-loop experiments on QNET 2.0 DC Motor Board. The experimental results successfully validate the superior tracking accuracy and disturbance-rejection capability of the proposed control strategy as compared to other controller variants benchmarked in this article.

The aim was to evaluate the performance of the latest quantitative marker for intrathecal IgG synthesis and to compare it with other established markers used for the same purpose. We retrospectively applied Auer’s and Reiber’s intrathecal IgG synthesis formulae in a cohort of 372 patients under investigation for central nervous system demyelination who had undergone lumbar puncture and oligoclonal bands (OCBs) detection for demonstrating intrathecal IgG synthesis. A ROC analysis revealed Auer’s formula had lower sensitivity (68%) compared to Reiber’s formula (83%) and IgG index (89%), in our cohort of patients that exhibited normal to mildly elevated albumin quotients (4.48 ± 3.93). By excluding possible sources of errors, we assume that Auer’s formula is less sensitive than other established tools for the “prediction” of the detection of OCBs in routine cerebrospinal fluid (CSF) analyses due to the mathematical model used. Given the ability of Reiber’s hyperbolic formula to describe the blood–CSF IgG distribution across a wide range of blood–brain barrier functionality, its use and the use of similar formulae are recommended for the discrimination between CNS-derived and blood-derived molecules in clinical laboratories.

The Korteweg–de Vries (KDV) equation is one of the most well-known models in nonlinear physics, such as fluid physics, plasma, and ocean engineering. It is very important to obtain the exact solutions of this model in the process of studying these topics. In the present paper, using distinct function iteration relations in two ways, namely, squaring infinitely and extracting the square root infinitely, which have not been reported in other documents, we construct abundant types of new infinite-series exact solitary wave solutions using the auxiliary equation method. Most of these solutions have not been reported in previous papers. The numerical analysis of some solutions shows complex solitary wave phenomena. Some solutions can have stable solitary wave structures, while others may have singularities in certain space–time positions. The results show that the analysis model we use is very simple and effective for the construction of new infinite-series solutions and new solitary wave structures of nonlinear models.

Beam models are widely applied in civil engineering, transport, and industry because the beams are basic structural elements. When dealing with the high-order modes of beam in the context of applying the modal analysis method, the numerical instability issue affects the numeric simulation accuracy in many boundary conditions. There are two solutions in literature to overcome this shortcoming, namely refinement of the asymptotic form for the high order modes and reshaping the terms within the equation of the modes to eliminate the source of the numerical instability. In this paper, the numerical instability issue is signalled when the standard form of Green’s function, which includes hyperbolic functions, is applied to a free-free Timoshenko length-long beam. A new way is proposed based on new set of eigenfunctions, including an exponential function, to construct a new form of Green’s function. To this end, it starts from a new general form of Green’s function and the characteristic equation is obtained; then, based on the boundary condition, the Green’s function associated to the differential operator of the free-free Timoshenko beam is distilled. The numerical stability of the new form of the Green’s function is verified in a numerical application and the results are compared with those obtained by using the standard form of the Green’s function.

The present article develops mathematical modeling of Rayleigh wave propagation in a medium under the influence of inhomogeneity parameter associated with means of elementary transcendental functions. The equations of motion and constitutive relations have been taken forward to produce the frequency equation. With the help of suitable potential functions and appropriate mathematical treatment, displacement components have been derived. Furthermore, by means of intrinsic boundary conditions, the frequency equation has been achieved in terms of the inhomogeneity function and its derivative. The inhomogeneity function has been later considered as a hyperbolic, logarithmic, and exponential function. Variation of phase velocity for these fundamental functions, as well as their compositions, has been shown graphically. A comparison between various inhomogeneity parameters and their influences on phase velocity has been discussed and demonstrated through graphs. As an outcome, a significant effect of inhomogeneity parameters on Rayleigh wave propagation has been observed which finds its applications towards the synthesis of biomaterials, property enhancement, wave mechanics, civil engineering, and mechanical engineering. [ABSTRACT FROM AUTHOR]

In applied sciences it is always useful to improve the catalogue of definite integrals available in tables. This present paper is a compendium of definite integrals involving a hyperbolic quotient function expressed in terms of the Lerch function. A substantial portion of the results are new. [ABSTRACT FROM AUTHOR]

In this paper, we establish an interesting chain of sharp inequalities involving Toader-Qi mean, exponential mean, logarithmic mean, arithmetic mean and geometric mean. This greatly improves some existing results. [ABSTRACT FROM AUTHOR]

Global orbits connect the saddle points in an infinite period through the homoclinic and heteroclinic types of manifolds. Different from the periodic movement analysis, it requires special strategies to obtain expression of the orbit and detect the associated profound dynamic behaviors, such as chaos. In this paper, a global dynamic frequency method is applied to detect the homoclinic and heteroclinic bifurcation of the complicated nonlinear systems. The so-called dynamic frequency refers to the newly introduced frequency that varies with time t, unlike the usual static variable. This new method obtains the critical bifurcation value as well as the analytic expression of the orbit by using a standard five-step hyperbolic function-balancing procedure, which represents the influence of the higher harmonic terms on the global orbit and leads to a significant reduction of calculation workload. Moreover, a new homoclinic manifold analysis maps the periodic excitation onto the target global manifold that transfers the chaos discussion of non-autonomous systems into the orbit computation of the general autonomous system. That strategy unifies the global bifurcation analysis into a standard orbit approximation procedure. The numerical simulation results are shown to compare with the predictions. [ABSTRACT FROM AUTHOR]

In this article, we study the complex coupled Kuralay system (CKS), which have many applications in different field such as ferromagnetic material and fiber optics. We implement an analytical method, namely, the tanh – coth method to considered system to formulate a system of algebraic equations. Solving the obtained system, we acquire different traveling wave solutions that are expressed in term of hyperbolic tangent functions and hyperbolic cotangent functions. Also, we employ the energy balance technique to the selected model to sort out the behavior of traveling wave solutions. By this method, we obtain periodic wave solution that are expressed in term of cosine function. In order to show the graphical presentation of the acquired solitary waves solutions, 3D and 2D curve are created by selecting well-suited parametric values via Mathematica. • Nonlinear Kuralay System is considered. • Implementation of tanh-coth and energy balance method. • Bright, periodic and singular solitons are studied. [ABSTRACT FROM AUTHOR]

The hyperbolic cosine function with high-order errors can be utilized to improve the accuracy of adaptive filters. However, when initial weight errors are large, the hyperbolic cosine-based adaptive filter (HCAF) may be unstable. In this paper, a novel normalization based on the logarithmic hyperbolic cosine function is proposed to achieve the stabilization for the case of large initial weight errors, which generates a logarithmic HCAF (LHCAF). Actually, the cost function of LHCAF is the logarithmic hyperbolic cosine function that is robust to large errors and smooth to small errors. The transient and steady-state analyses of LHCAF in terms of the mean-square deviation (MSD) are performed for a stationary white input with an even probability density function in a stationary zero-mean white noise. The convergence and stability of LHCAF can be therefore guaranteed as long as the filtering parameters satisfy certain conditions. The theoretical results based on the MSD are supported by the simulations. In addition, a variable scaling factor and step-size LHCAF (VSS-LHCAF) is proposed to improve the filtering accuracy of LHCAF further. The proposed LHCAF and VSS-LHCAF are superior to HCAF and other robust adaptive filters in terms of filtering accuracy and stability. [ABSTRACT FROM AUTHOR]

This article investigates the local fractional generalized Kadomtsev–Petviashvili equation and the local fractional Kadomtsev–Petviashvili-modified equal width equation. It presents traveling-wave transformation in a nondifferentiable type for the governing equations, which translate them into local fractional ordinary differential equations. It also investigates nondifferentiable traveling-wave solutions for certain proposed models, using an ansatz method based on some generalized functions defined on fractal sets. Several interesting graphical representations as 2D, 3D, and contour plots at some selected parameters are presented, by considering the integer and fractional derivative orders to illustrate the physical naturality of the inferred solutions. Further results are also introduced in some details.