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This paper builds a wireless precision control function waveform pulse variable speed stirring device with point-to-point data transmission between the host computer and the microcontroller, which uses a programmable STM32 microcontroller as the system controller, superimposed with a single closed-loop static differential-free speed control system and a pulse broadband modulation (PWM) system to control the DC brush motor driving the stirring paddle based on arbitrary waveform function variable speed stirring respectively. The effects of different pulse waveform stirring systems on the purification effect of Cadmium ions (Cd2+) from zinc sulfate solution were studied under the same pulse period and maximum speed. The experimental results show that when KP = 0.012 and Ti = 100, the anti-disturbance of the motor during the variable speed stirring process can be effectively improved, and the speed adjustment time is short and robust; when the Cd2+ purification rate reaches 92%, the purification time of the variable sine function stirring system is shortened by about 40% compared with that of the uniform speed stirring system, and that of the variable trapezoidal function stirring system is shortened by about 33.3% compared with that of the uniform speed stirring system. When the reaction is finished, the Cd2+ concentration is reduced to 6 mg/L by the variable sinusoidal stirring system only, and the Cd2+ concentration is lower than 10 mg/L in a shorter time compared with the time required for cadmium removal in the actual industrial production line. [ABSTRACT FROM AUTHOR]

To improve the accuracy of speed estimation strategy over a wide speed range in the sensorless speed control system of an interior permanent – magnet synchronous motor (IPMSM), a full-order adaptive observer based on a novel fast super-twisting algorithm (NFSTA-AO) is proposed. The conventional model reference adaptive system (MRAS) takes the linear compensation matrix of the unit matrix, which can only achieve speed discrimination within a certain speed range. Therefore, in this paper, a new linear compensation matrix is first derived using Popov's super stability theory, and then, a new tachograph – adaptive law is obtained. A feedback correction link is also added to the adjustable model to improve the convergence speed of the error between the reference and adjustable model outputs. To further improve the accuracy of the tachograph estimation strategy, a novel fast super-twisting algorithm (NFSTA) convergence law is introduced in place of the adaptive law in the full-order adaptive observer, combining the advantages of both algorithms. The NFSTA added the inverse hyperbolic sine function based on system state variables to the integral term of the fast super-twisting algorithm (FSTA) to effectively suppress the torque pulsation of the system. A soft switching function is also designed to replace the symbolic switching function in order to reduce the system jitter caused by the sliding mode variable structure control. The simulation experiments show that the system using the NFSTA-AO estimation strategy is more resistant to disturbances and robust; additionally, it has better dynamic following than the conventional MRAS in the presence of added load disturbances and sudden speed changes. [ABSTRACT FROM AUTHOR]

In the textile industry, selecting the optimal fabric is crucial in the design and production process. The multiple-criteria decision-making (MCDM) technique has been applied to address fabric selection problems. Because the sine trigonometry function maintains the periodicity and symmetry of the origin in nature, it satisfies the preferences of experts over multiple parameters. Considering the advantages of the sine trigonometry function, we introduce sine trigonometry Pythagorean fuzzy sets (ST-PFSs) and weighted averaging (ST-PFWA) and geometric (ST-PFWG) aggregation operators (AOs). Additionally, we propose a novel method based on ST-PFWA and ST-PFWG AOs to solve two different types of fabric selection MCDM problems. The first problem is provided by Pythagorean fuzzy numbers (PFNs), and we apply the proposed method to address the issue and conduct a comparative analysis with other PFS AOs. The second problem is offered with crisp values, and we apply a PFS linguistic term transform system to convert the values into PFNs. Then, we apply ST-PFWA and ST-PFWG AOs to settle the problem and perform a comparative analysis among different PFS linguistic terms. The complete ranking results illustrate that our proposed methodology is more efficient and reliable than previous approaches and can be used in other textile fields. [ABSTRACT FROM AUTHOR]

Chinese high-quality tea can be specially required for the appearance quality of tea leaves. Particularly, every single tea bud should be intact with the uniform length of all buds. Chinese famous tea is still widely picked by hand, due to the high breakage of tea shoots that are plucked by machines even the state-of-the-art ones. However, manual harvesting cannot fully meet large-scale tea production in recent years, leading to high labor intensity with low efficiency. It is absolutely necessary and urgent to investigate the suitable plucking machines for Chinese high-quality tea at present. Among them, the commonly-used reciprocating-cutting-type cutter was the core reason for the high tea crushing rate in the bulk tea plucking machine. As a result, the machine cannot be suitable for the high-quality tea. In this study, an optimization experiment was carried out on the structure and parameters of the cutter, in order to develop an excellent plucking tool for the high-quality tea. Firstly, the specific structure of the cutter was introduced to analyze the motion characteristics of the blade. The cutter device consisted of two blades, a double eccentric cam shaft, a driving box, and some standard units. When actuated by the motor through the shaft, the motion of the blade approximated a sine function without considering the micro deformation. The cut diagram was then drawn to determine the main factors for the high crushing rate of the machine. The results show that the main factors influencing the picking quality included the machine moving speed, speed ratio between cutter and machine, reciprocating movement stroke, and cutter tooth height, referring to the moving speed, speed ratio, stroke, and tooth height, respectively. These resulting factors interacted with each other for the complex tea plucking. Hence, comprehensive optimization was very necessary to clarify the plucking effect of every single factor, rather than the cut diagram only. Secondly, an electrical test platform was designed with the rail-type tea plucking to permit the setting of exactly the velocity values of cutting and driving needed in the experiment within a certain range. The self-propelled tea plucking machine was also designed before. The high precision values were achieved in the 0.1 (r/min) and 0.01 (m), respectively. A quadratic regression orthogonal rotary center combination test was carried out on the test platform. The nine pairs of blades were produced with different structure parameters, according to the test scheme. Then, the parameter optimization model was established with the evaluation indexes (including the integrity percentage of sprout leaves, leakage rate, and complete rate stubble roughness). The improved model was solved with the genetic algorithm (GA). The best combination of parameters was obtained for the machine as follows: the blade speed was about 0.4 m/s, the speed ratio was 1.2, the stroke was 23 mm, and the tooth height was 25 mm. The calculated integrity rate of bud and leaf was 86.89% under these conditions. Finally, the new cutter blade was developed, according to the parameter optimization. The experimental verification was achieved as follows: the integrity rate of bud and leaf was 82.6%, the leakage rate was 0.24%, and the stubble roughness was 2.8 mm, indicating better consistency with the optimized test. The integrity rate of tea picking increased by more than 20% after optimization, indicating the significantly improved quality of tea plucking. The finding can lay a sound foundation for the efficient technology mode of “machine picking and grading” during high-quality tea harvesting. This improved mode can be expected as a broad application prospect in the tea industry. The adaptive optimization of tea varieties and the dynamic process can be used further to promote the plucking tea quality during the reciprocating cutting plucking. [ABSTRACT FROM AUTHOR]

The HLS of digital filters is a complex optimization task in electronic design automation that increases the level of abstraction for designing and scheming digital circuits. The complexity of this issue attracting the interest of the researcher and solution of this issue is a big challenge for the researcher. The scientists are trying to present the various most powerful methods for this issue, but keep in mind these methods could be trapped in the complex space of this problem due to own weaknesses. Due to shortcomings of these methods, we are trying to design a new framework with the mixture of the phases of the powerful approaches for high level synthesis of digital filters in this work. This modification has been done by merging the chimp optimizer with sine cosine functions. The sine cosine phases helped in enhancing the exploitation phase of the chimp optimizer and also ignored the local optima in the search area during the searching of new shortest paths. The algorithms have been applied on 23-standard test suites and 14-digital filters for verifying the performance of the algorithms. Experimental results of single and multi-objective functions have been compared in terms of best score, best maxima, average, standard deviation, execution time, occupied area and speed respectively. Furthermore, by analyzing the effectiveness of the proposed algorithm with the recent algorithms for the HLS digital filters design, this can be concluded that the proposed method dominates the other two methods in HLS digital filters design. Another prominent feature of the proposed system in addition to the stated enhancement, is its rapid runtime, lowest delay, occupied area and lowest power in achieving an appropriate response. This could greatly reduce the cost of systems with broad dimensions while increasing the design speed. [ABSTRACT FROM AUTHOR]

The problem of finding parameters of the Schwarz–Christoffel integral for a conformal mapping of a canonical domain onto an L-shaped one is solved analytically for arbitrary geometric parameters of the domain. The unknown preimage is represented in the form of a series in powers of a small parameter with coefficients written in closed form, and an estimate for the moduli of the coefficients is obtained. We find asymptotics for the crowding effect (crowding of preimages), which is especially pronounced for elongated domains. are computing The mapping and its inverse are computed using series with closed-form coefficients, whose domains of convergence collectively cover the entire (closed) mapped domain. Combining with linear fractional mappings and the elliptic sine function yields mappings of the half-plane, disk, and rectangle onto an L-shaped domain. Numerical implementations of the constructed mappings demonstrate the high efficiency of the applied methods. [ABSTRACT FROM AUTHOR]

In this article, a family of complex Appell–Bessel functions is considered and an integral representation for this family is derived. As a consequence, cosine and sine analogs of these functions are obtained. Certain properties, including addition formulas and differential recurrence relations, are also established. Further, the degenerate complex Appell–Bessel functions are investigated, and certain results for degenerate cosine-Appell–Bessel and degenerate sine-Appell–Bessel functions are obtained. Jacobi–Anger expansions for complex Appell–Bessel functions and degenerate complex Appell–Bessel functions are explored as well. [ABSTRACT FROM AUTHOR]

The use of synchronized measurement technology leads to a more reliable and secure operation of the power system. Phasor calculation is needed for all buses where a phasor measurement unit is installed, and fast and precise estimation is necessary for accurate monitoring, protection and control. The Prony algorithm is one promising method due to its capability to estimate phasor adaptively with changing frequency. The algorithm projects the signal on $L$ exponentially damped sine functions, where $L$ is the order of the Prony. However, the order under different conditions should be adapted automatically to reduce computation time. To adaptively specify the order, the empirical mode decomposition (EMD) method is proposed in this paper to be combined with the Prony and named EMD-Prony. The EMD decomposes a signal into finite single oscillatory modes, representing the number of modes in the signal. EMD is also used as a pre-processing step to filter noise from an input signal of Prony. Therefore, EMD is proposed here as an assistant of Prony in a phasor estimation. Finally, the proposed method is tested on the benchmark signals proposed in the IEEE standard, signals obtained from a simulated power system, and measured data from a real-world power system. [ABSTRACT FROM AUTHOR]

Biological neurons can exhibit complex coexisting multiple firing patterns dependent on initial conditions. To this end, this paper presents a novel adaptive synapse-based neuron (ASN) model with sine activation function. The ASN model has time-varying equilibria with the variation of externally applied current and its equilibrium stability involves transitions between stable and unstable points through fold and Hopf bifurcations, resulting in complex distributions of attractive regions with heterogeneous multi-stability. Globally coexisting heterogeneous behaviors are studied by bifurcation diagram, phase portrait, dynamical distribution, and basin of attraction. The results show that the number of coexisting heterogeneous attractors can be up to 12, but for a simple neuron model, such a large number of coexisting heterogeneous attractors has not been reported in the relevant literature. Most interestingly, the ASN model also has riddled-like complex basins of attraction and four illustrative examples are depicted by the phase portraits with small changes of the initial conditions. Besides, the ASN model is implemented using a simple microcontroller platform, and various heterogeneous coexisting attractors are acquired experimentally to validate the numerical results. [ABSTRACT FROM AUTHOR]

This research intended to create a control strategies at each time step to optimize train regulation, and passenger flows with existing constraints to improve the regularity of headway and commercial speed on metro lines. Additionally, inevitable disturbances on the metro lines are considered as a periodic sine function, and the uncertainty of fluctuating passenger arrival flow was handled using time-varying MPC. The best solution was sought as a quadratic programming problem by using time-varying MPC to issues of train regulation and passenger flow control in which the systems were timedependent. Moreover, time-varying MPC was utilized to predict future outputs and calculate optimal inputs for the objective function. Numerical examples were provided to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Remote Sensing is the property of Editorial Office of Journal of Remote Sensing & Science Publishing Co. and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Except in trivial cases, an unknown angle is always extracted from a knowledge of its sine and cosine. These two numbers determine the angle unambiguously; and yet no universally accepted notation expresses that angle as a function of those numbers in a single statement. Some authors use "atan2" for this purpose. I argue that this name is not appropriate, and its description as a "four‐quadrant inverse tangent" is misleading. I propose two interchangeable names "sc−1,cs−1$\operatorname{sc}^{-1}, \operatorname{cs}^{-1}$" as candidates for the sought‐after function. [ABSTRACT FROM AUTHOR]

Perturbation theory has long been a very useful tool in the hands of mathematicians and physicists. The purpose of this paper is to prove some perturbation results for infinitesimal generators of fractional strongly continuous cosine families. That is, we impose sufficient conditions such that A is the infinitesimal generator of a fractional strongly continuous cosine family in a Banach space X , and B is a bounded linear operator in X , then A + B is also the infinitesimal generator of a fractional strongly continuous cosine family in X. Our results coincide with the classical ones when α = 2. Furthermore, depending on commutativity condition of linear bounded operators, we propose the elegant closed-form formulas for uniformly continuous perturbed fractional operator cosine and sine functions. Finally, we present an example in the context of one-dimensional perturbed fractional wave equation to demonstrate the applicability of our theoretical results and we give some comparisons with the existing literature. [ABSTRACT FROM AUTHOR]

Memristor is a special nonlinear element with inner state variable and can give rise to the initial-boosted dynamics in systems built with it. This paper proposes a four-dimensional (4-D) sine-modulation-based memristive system by coupling an ideal memristor into a three-dimension (3-D) linear system. Particularly, the coupling variable sampled from the 3-D linear system is first modulated by the sine function before being imported into the ideal memristor. As a result, the 4-D sine-modulation-based memristive system possesses a discrete plane equilibrium set and exhibits significant initials-boosted plane bifurcation in this plane. By means of theoretical analysis and numerical simulation, the initials-boosted coexisting attractors with extreme multistability are also uncovered. Finally, a physical circuit for the 4-D sine-modulation-based memristive system is designed and corresponding circuit simulations are executed by the Power Simulation (PSIM) software. [ABSTRACT FROM AUTHOR]

In this article, a simplified sine cosine algorithm (SSCA) is applied to solve the optimal reactive power dispatch (ORPD) issues by estimating the control variables. This algorithm uses sine cosine functions and generates number of random solutions to obtain the best solution by fluctuating inwards or outwards. The SSCA is implemented in the ORPD problem to find the best control variables to achieve minimum power loss and maximum net savings. Furthermore, the efficacy of SSCA is validated with other recently used algorithms considering three case studies, i.e., IEEE-30, -57, and -118 bus test system. The results show that the SSCA approach finds more precise and superior ORPD solutions. A comparison among SSCA and other methods proves the robustness of SSCA to attain the solution with faster convergence. The statistical analysis is performed to justify the effectiveness of SSCA by yielding minimum operating cost and maximum net savings as compared to other techniques considered in this study. [ABSTRACT FROM AUTHOR]

In this paper, we studied a fractional-order robust backstepping control (BSC) combined with a fractional-order tracking differentiator and a fractional-order nonlinear disturbance observer for a quadrotor unmanned aerial vehicle (UAV) system. A fractional-order filtered error and a fractional-order tracking differentiator were utilized in a conventional BSC system to improve the positioning control performance of a highly coupled nonlinear quadrotor UAV system and bypass the differentiation issue of the virtual control and compensation of the transformation error in the conventional BSC design. A new fractional-order disturbance observer with the sine hyperbolic function was then proposed to enhance the estimation performance of the uncertain quadrotor UAV. Sequential comparative simulations were conducted, demonstrating that the proposed positioning controller and observer utilizing fractional-order calculus outperformed those of the conventional controller and observer systems. [ABSTRACT FROM AUTHOR]

This paper presents the handling of nonlinear system identification problem based on Volterra model. Gradient-based algorithms are generally applied to solve system identification problems. However, these algorithms have the limitation of getting trapped in the local minimum. In the presented work, a novel population-based optimization algorithm popularly known as sine cosine algorithm (SCA) is being utilized for the identification of nonlinear discrete-time system. The SCA uses mathematical sine and cosine functions for the purpose of optimization. SCA is responsible for the creation of multiple random solutions and moving them towards best solution while maintaining proper balance between the exploitation and exploration phases of optimization. The performance evaluation of the applied SCA is carried out in terms of coefficient evaluation, mean square error and convergence profile. Two different examples for nonlinear system are presented in this work so as to demonstrate the validity of the employed algorithm. Performance analysis of the proposed approach with the existing state-of-the-art algorithms proves that the SCA outperforms the other algorithms. [ABSTRACT FROM AUTHOR]

Based on the gas–solid two-phase flow theory, numerical simulation of the dust dispersion law of fully mechanized mining work under different inclination angles and comparative analysis of field-measured data show that with the increase of working face inclination, the inclination of airflow into the unmined zone increases from 25° to 50° and the maximum wind speed increases from 2.16 to 2.25 m/s after the mixing of cutting turbulent wind and system ventilation. Meanwhile, the range of high-concentration dust clusters, suspension time, lateral migration intensity, and deposition zone increase to varying degrees; dust clusters increases from 62.02 to 202.46 m3. When X < 53.96 m, the dust concentration in the sidewalk-breathing zone shows a sine function with the length of the working face, and when X ≥ 53.96 m, it satisfies the exponential decay function. Based on this, the tracking closed dust control technology is proposed. Combining the offset angle of the airflow and t the gathering position of dust mass, the wind curtain angle and air velocity are automatically controlled to ensure that the dust is restricted to one side of the cable trough. [ABSTRACT FROM AUTHOR]

In the paper, the authors find series expansions and identities for positive integer powers of inverse (hyperbolic) sine and tangent, for composite of incomplete gamma function with inverse hyperbolic sine, in terms of the first kind Stirling numbers, apply a newly established series expansion to derive a closed-form formula for specific partial Bell polynomials and to derive a series representation of generalized logsine function, and deduce combinatorial identities involving the first kind Stirling numbers. [ABSTRACT FROM AUTHOR]

In this paper we give a new form for the Hilbert integral inequality for three variables with hyperbolic sine and cosine functions. The reverse form and equivalent forms are also obtained. The constant which we obtained is the best constant. [ABSTRACT FROM AUTHOR]

Objectives: The stochastic model of observation information describes the accuracy of observation information and its correlation, and also plays an important role in parameter estimation, quality control and accuracy evaluation. In the process of global navigation satellite system (GNSS) precision positioning, an accurate stochastic model is essential for improving the accuracy of float solution, enhancing the success rate of ambiguity resolution, increasing the accuracy of gross error detection, and obtaining the accurate and reliable positioning results. Methods: An optimization method for stochastic model of BeiDou navigation satellite system (BDS) is proposed by handling the properties of four classic elevation-dependent stochastic models based on the relationship between BDS satellite observation information and elevation. Firstly, the accuracy of BDS four-frequency observation information is evaluated by the simplified Helmert variance estimation method. Then, the model parameters could be fitted based on the estimated precision of observation information. Finally, the statistical characteristics of four stochastic models, including piecewise function, sine function, cosine function and exponential function, are tested by the overall test and ω-test methods. Results: The results show that the accuracy of pseudorange and carrier phase for BDS-3 satellite are related to elevation, and the correlation degree is different by GNSS observation types. The stochastic model of exponential function shows the best performance in the fitting error, the overall test and the ωtest. The maximum fitting errors of pseudorange and carrier phase are 0.029 m and 5.484 mm, respectively. The false alarm rates of the overall test for the float solution and the fixed solution are 5.1 % and 4.9 %, respectively. In addition, the maximum false alarm rates of the ω-test are 5.8 % for the pseudorange and 6.8 % for the carrier phase. Conclusions: The stochastic model of exponential function can get the shortest convergence time and the highest positioning accuracy for BDS-3 quad-frequency precise point positioning. It can also accurately describe the accuracy of BDS observation information and improve the accuracy and reliability of BDS precise positioning results. [ABSTRACT FROM AUTHOR]

This paper aims to study the measurement accuracy of Rayleigh scattering lidar (light detection and ranging) based on a ship platform and analyze the influence of the laser beam uncertainty on the temperature inversion results. Taking the ship platform roll data as a reference, the Rayleigh scattering lidar oscillating model is simplified to a sine function, and the inversion accuracy of atmospheric temperature is analyzed under different settled observation angles and different roll angles. When the settled observation angle is 0° and the roll angle amplitudes are 10°, 20°, and 30°, the maximum deviations of the temperature within the height range of 30–80 km are 3.47 K, 13.73 K, and 22.78 K, respectively, and the average deviations are 2.35 K, 9.09 K, and 12.95 K, respectively. When the observation angle is set to 30° and the roll angle amplitudes are 10°, 20°, and 30°, the maximum deviations of the temperature within the height range of 30–80 km are 11.75 K, 27.49 K, and 53.50 K, respectively, and the average deviations are 11.05 K, 13.88 K, and 16.12 K, respectively. The results of this paper show that ship platform rolling greatly influences the measurement of atmospheric temperature, which provides a certain data reference for the construction and use of Rayleigh scattering lidar in the ship platform. [ABSTRACT FROM AUTHOR]

This study introduces a subclass S q s * of starlike functions associated with the q-analogue of the sine function defined in symmetric unit disk. This article comprises the investigation of sharp coefficient bounds, and the upper bound of the third-order Hankel determinant for this class. It also includes the findings of Zalcman and generalized Zalcman conjectures for functions of this class. [ABSTRACT FROM AUTHOR]

Design multiphase heterogeneous structures in order to provide multifunctional properties has many applications in the field of material design. In this research, a new method for construction multiscale heterogeneous microstructure is presented. Using statistical correlation function, specifically, two-point correlation functions, bicontinuous two-phase structure is constructed that has solid and void phases. In order to construction the heterogeneous media, an exponentially decreasing sine function is used as autocovariance function. Then based on Schwartz P minimal surface the porous media structure, is divided into two parts; porous solid phase and void phase. From the point of view of continuity, the phases are investigated and it is observed both phases of the constructed microstructure are connected throughout the media. Using this method it is possible to construct bicontinuous multiscale microstructures that are solid and void phase in coarse scale and the solid phase can be constructed as void and solid phase in fine scale. [ABSTRACT FROM AUTHOR]

Copyright of Al-Mustansiriyah Journal of Science is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In recent years, the theory of operators got the attention of many authors due to its applications in different fields of sciences and engineering. In this paper, making use of the Bernardi integral operator, we define a new class of starlike functions associated with the sine functions. For our new function class, extended Bernardi's theorem is studied, and the upper bounds for the fourth Hankel determinant are determined. [ABSTRACT FROM AUTHOR]

In this article, I show how to calculate consistent marginal effects on the original scale of the outcome variable in Stata after estimating a linear regression with a dependent variable that has been transformed by the inverse hyperbolic sine function. The method uses a nonparametric retransformation of the error term and accounts for any scaling of the dependent variable. The inverse hyperbolic sine function is not invariant to scaling, which is known to shift marginal effects between those from an untransformed dependent variable to those of a logtransformed dependent variable, when all observations are positive. [ABSTRACT FROM AUTHOR]

In this study, the behavior of parabolic, Jacobsen, bias-corrected Jacobsen, and Quinn estimators, which are used in frequency estimation and based on three samples of discrete Fourier transform, are examined on real signals comparatively. As an alternative to these estimators, a sine function-based frequency estimator is proposed, and the root means square errors (RMSE) of the estimator are compared by performing computer simulations. It has been observed that the proposed sine-based estimator gives lower RMS errors in a wide part of the frequency range compared to other estimators. [ABSTRACT FROM AUTHOR]

In this paper, we present some generalizations and improvements of a new integral inequality from the 29th IMC in 2022. Some applications of our new results are also provided. [ABSTRACT FROM AUTHOR]

For polynomials, local connectivity of Julia sets is a much‐studied and important property. Indeed, when the Julia set of a polynomial of degree d⩾2$d\geqslant 2$ is locally connected, the topological dynamics can be completely described as a quotient of a much simpler system: angle d$d$‐tupling on the circle. For a transcendental entire function, local connectivity is less significant, but we may still ask for a description of the topological dynamics as the quotient of a simpler system. To this end, we introduce the notion of docile functions (Definition 1.1): a transcendental entire function with bounded postsingular set is docile if it is the quotient of a suitable disjoint‐type function. Moreover, we prove docility for the large class of geometrically finite transcendental entire functions with bounded criticality on the Julia set. This is an analogue of the local connectivity of Julia sets for geometrically finite polynomials, first proved by Douady and Hubbard, and extends previous work of the second author and of Mihaljević for more restrictive classes of entire functions. We deduce a number of further results, concerning bounded Fatou components and the local connectivity of Julia sets. In particular, we show that the Julia set of the sine function is locally connected, answering a question raised by Osborne. [ABSTRACT FROM AUTHOR]

Visual tracking is one of the pre-eminent tasks in several computer vision applications. Particle filter (PF) is extensively used in visual tracking for intelligent surveillance system applications, hugely significant. But the re-sampling procedure of PF will result in sample impoverishment, which will affect the precision of tracking simultaneously. In this paper, a new tracking technique, called Trigonometric Particle Filter (TPF), based on PF optimized by Sine Cosine Algorithm (SCA), which contains trigonometric sine and cosine functions, is proposed. An enhanced method for improving the number of target particles used in a Sine Cosine Algorithm for trigonometric particle filter includes SCA ahead of the re-sampling step. This step ensures a more extensive particle set Achievement of the proposed TPF tracker is inspected and assessed on Visual Tracker Benchmark (VOT) databases. The proposed TPF tracker is compared with evolutionary-based methods like the Spider monkey optimization assisted PF (SMO-PF), Firefly algorithm-based PF (FAPF) method, Particle swarm optimization-based PF (PSO-PF) and Particle filter, recent four correlation filter-based trackers, and also with other ten state-of-the-art tracking methods. We demonstrate that visual tracking using TPF delivers additional consistent and proficient tracking outcomes than compared trackers. • A new tracking technique, called TPF, based on PF optimized by SCA, is proposed. • The SCA replaces the normal re-sampling process and improves the PF. • TPF compared with evolutionary-based approaches and 10 other leading-edge methods. • TPF visual tracking is more consistent and proficient than other trackers. [ABSTRACT FROM AUTHOR]

In this article, we extensively study a family of distributions using the trigonometric function. We add an extra parameter to the sine transformation family and name it the alpha-sine-G family of distributions. Some important functional forms and properties of the family are provided in a general form. A specific sub-model alpha-sine Weibull of this family is also introduced using the Weibull distribution as a parent distribution and studied deeply. The statistical properties of this new distribution are investigated and intended parameters are estimated using the maximum likelihood, maximum product of spacings, least square, weighted least square, and minimum distance methods. For further justification of these estimates, a simulation experiment is carried out. Two real data sets are analyzed to show the suggested model’s application. The suggested model performed well compares to some existing models considered in the study.

This article proposes using in-phase and quadrature frequency-shift keying (IQFSK) modulation for low-power optical wireless communications (OWC). IQFSK independently leverages both cosine and sine basis functions to enhance the system's spectral efficiency (SE). It uses only the odd harmonic frequencies for these basis functions, allowing the clipping of negative amplitude excursions without losing information, making the waveform compatible with OWC The work presents optimal maximum likelihood and low-complexity sub-optimal detection mechanisms for IQFSK. The proposed scheme is analyzed analytically and with numerical simulations. The simulation and analytical results indicate that the proposed scheme is more energy-efficient, can attain a better energy and SE trade-off by exploiting the frame structure of the waveform, and has a lower minimum squared Euclidean distance relative to other state-of-the-art FSK-based counterparts, thus establishing it as one of the most efficient FSK approaches for low-power OWCs. [ABSTRACT FROM AUTHOR]

In this paper, we first introduced the notion of θ -hyperbolic sine distance functions on a metric space and studied their properties. We investigated the existence and uniqueness of fixed points for some classes of single-valued mappings defined on a complete metric space and satisfying contractions involving the θ -hyperbolic sine distance function. [ABSTRACT FROM AUTHOR]

This paper proposes an algorithm and hardware realization of generalized chaotic systems using fractional calculus and rotation algorithms. Enhanced chaotic properties, flexibility, and controllability are achieved using fractional orders, a multi-scroll grid, a dynamic rotation angle(s) in two- and three-dimensional space, and translational parameters. The rotated system is successfully utilized as a Pseudo-Random Number Generator (PRNG) in an image encryption scheme. It preserves the chaotic dynamics and exhibits continuous chaotic behavior for all values of the rotation angle. The Coordinate Rotation Digital Computer (CORDIC) algorithm is used to implement rotation and the Grünwald–Letnikov (GL) technique is used for solving the fractional-order system. CORDIC enables complete control and dynamic spatial rotation by providing real-time computation of the sine and cosine functions. The proposed hardware architectures are realized on a Field-Programmable Gate Array (FPGA) using the Xilinx ISE 14.7 on Artix 7 XC7A100T kit. The Intellectual-Property (IP)-core-based implementation generates sine and cosine functions with a one-clock-cycle latency and provides a generic framework for rotating any chaotic system given its system of differential equations. The achieved throughputs are 821.92 Mbits/s and 520.768 Mbits/s for two- and three-dimensional rotating chaotic systems, respectively. Because it is amenable to digital realization, the proposed spatially rotating translational fractional-order multi-scroll grid chaotic system can fit various secure communication and motion control applications. [ABSTRACT FROM AUTHOR]

The Föppl‐von Kármán equations describing deformation of flexible thin plates are established on the basis of moderately large‐deflection and small rotation angle. For many years, the equations have been regarded as a classical and effective model used for the analysis of flexible thin plate problems, and at the same time, this model has also been constantly evolving and improving. The improvements for the model, however, come mainly from properties of materials perspective, but seldom from the deformation of plate perspective. In this study, we revisit Föppl‐von Kármán equations from the viewpoint of deformation concerning rotation angle. A new form for the classical equations without a small‐rotation‐angle assumption is derived, for the first time, by giving up the basic assumption that the sine function of the rotation angle equals to the first‐order derivative of the corresponding displacement, thus improving the governing equations while enhancing the nonlinearity. The abandonment of the small‐rotation‐angle assumption reveals such a fact that the second‐order derivative of displacement in classical equations originates from the curvature and twist of plates. Due to the complexity of the equations derived, its perturbation solution is obtained under cylindrical bending with two opposites fully fixed. Results indicate that via cylindrical bending, a two‐dimensional plate or membrane problem is easily associated with a one‐dimensional beam or cable problem. Results also show that the abandonment of the small‐rotation‐angle assumption will contribute to the free development of the deflection curve rotation of the plate, while at the same time, the deflection value will tend to decrease to agree with the deformation of the plate. [ABSTRACT FROM AUTHOR]

The launch angle I i in the denominator of the square root in Eq. (6) or (7) can be that of either rock according to Eq. (3). Since the difference of sine functions is squared, we can write the two sine functions in either order inside the square brackets. Draw a straight line of length I r i = 25 m from the launch to the landing points, inclined at angle I i to the horizontal, as sketched below. [Extracted from the article]

Raman spectroscopy, widely used for material analysis, has formed an extensive spectral library. In practical applications, it is usually necessary to preprocess Raman spectroscopy of the target material and then identify the material through spectral-library comparisons. Baseline correction is an important step during pre-processing and it usually requires a special algorithm. However, it demands time and high-level professional skill, confining Raman spectroscopy to laboratories rather than large-scale applications. Therefore, to improve its efficiency and take advantage of the big data in the spectral library, this paper proposes a simple data-augmented deep learning method to achieve Raman spectroscopy recognition without baseline correction. In this method, a simple mathematical baseline (linear or sine function) is added to the spectrum in the database to complete data augmentation. Its training set is used to train the deep learning model. The trained deep-learning model can identify 20 minerals with 100% accuracy without additional baseline correction. Therefore, the method is effective for rapid and direct recognition of Raman spectra. [ABSTRACT FROM AUTHOR]

The objective of economic load dispatch (ELD) is to minimize the overall cost of generation under the premises of meeting the load demand and satisfying different operational constraints. A new improved Arithmetic Optimization Algorithm (AOA) based on elementary function disturbance was proposed to solve ELD problems. Math optimizer accelerated (MOA) and math optimizer probability (MOP) are two important parameters in the original AOA. Ten six elementary functions were adopted, which are sine function, tangent function, hyperbolic secant function, power function, hyperbolic cosecant function and arc-cosine function. Adding the disturbance generated by six elementary functions respectively on the original MOA and MOP parameters can effectively balance the exploration and exploitation ability of AOA, enhance the global search ability, avoid falling into local optimization, and improve the convergence speed of AOA. Then the original AOA was compared with 6 variants by using 23 benchmark functions in CEC-2005, and selected the best improved method. Next, some intelligent optimization algorithms with better performance in optimizing CEC-2005 benchmark functions are adopted to carry out the simulation experiments with the improved AOA to verify its superiority. Finally, three ELD problem cases including valve point effect, prohibited operation area, transmission loss and other factors are selected with a total demand of 1263 MW, 2500 MW and 10,500 MW respectively. The AOA based on elementary function disturbance was used to solve these three ELD problems. Experimental results show that the proposed AOA has the best performance in solving ELD problems. [ABSTRACT FROM AUTHOR]

In this work, we offer a set of appropriate conditions for the approximate controllability of second‐order impulsive neutral stochastic integro‐differential evolution inclusions with infinite delay. We validate the major conclusions using concepts from the cosine function, sine function, and the fixed point method. The discussion then shifts to nonlocal second‐order stochastic integro‐differential systems. Finally, we give a theoretical application to help our conversation be more successful. [ABSTRACT FROM AUTHOR]

Here, we develop escape criteria for pc(z) = sin(z n)−az +c, a, c ∈ C, n ≥ 2, exploiting four different iterations of fixed point theory to explore various Mandelbrot sets which are different than the classical Mandelbrot set . Our concern is to utilize the lesser number of iterations that are necessary to attain the fixed point of the transcendental complex-valued sine function. Further, we investigate the effect of variables on the shape, size, color, and dynamics of fractals. Noticeably, some of the obtained fractals symbolize the Swastika (a symbol of spirituality and divinity in Indian religions), Shivling (an abstract representation of the Hindu God Shiva), flowers, spiders, butterflies, Rangoli (made mainly in the festive season in India), art on glass, and so on. Interestingly, the higher-order Mandelbrot set in Picard-orbit has a resemblance to Corona-virus. [ABSTRACT FROM AUTHOR]

In the paper, the authors establish a general inequality for the hyperbolic functions, extend the newly-established inequality to trigonometric functions, obtain some new inequalities involving the inverse sine and inverse hyperbolic sine functions, and apply these inequalities to the Neuman–Sándor mean and the first Seiffert mean. [ABSTRACT FROM AUTHOR]

Geometric error is an important error source of machine tools. Quick, accurate, and convenient measurement of machine tool geometric errors is an urgent need to improve the accuracy of machine tools. Based on the ballbar's circular trajectory test principle, this paper proposes a machine tool error identification method based on a collection of sine functions. Based on the multi-body system theory and the homogeneous coordinate transformation method, a mathematical model of the circular path error and geometric error of the machine tool with 3 axes is established. Using a collection of sine functions to fit geometric errors has a higher fitting accuracy than traditional polynomial function fitting methods. By designing five circular motion trajectories of the same radius with different centers in the test area, and assuming that each geometric error is a collection of sine functions, a parametric identification model for machine tool geometric errors based on the circular trajectory is derived. The particle swarm algorithm is used to search and solve the various parameters of the sine function collection, and finally, 9 linear errors and 5 angular errors of the machine tool are obtained. In order to verify the effectiveness of the method, simulation and test comparison experiments were carried out. The experimental results show that 4 linear errors and 1 angular error of the machine tools can be effectively obtained. The verification experiment results show that, compared with the measurement results of the laser interferometer, the maximum deviation of the measurement and identification results proposed in this paper is within 2.5 μm. [ABSTRACT FROM AUTHOR]

A novel memristor-based multi-scroll hyperchaotic system is proposed. Based on a voltage-controlled memristor and a modulating sine nonlinear function, a novel method is proposed to generate the multi-scroll hyperchaotic attractors. Firstly, a multi-scroll chaotic system is constructed from a three-dimensional chaotic system by designing a modulating sine nonlinear function. Then, a voltage-controlled memristor is introduced into the above-designed multi-scroll chaotic system. Thus, a memristor-based multi-scroll hyperchaotic system is generated, and this hyperchaotic system can produce various coexisting hyperchaotic attractors with different topological structures. Moreover, different number of scrolls and different topological attractors can be obtained by varying the initial conditions of this system without changing the system parameters. The Lyapunov exponents, bifurcation diagrams and basins of attraction are given to analyze the dynamical characteristics of the multi-scroll hyperchaotic system. Besides, the field programmable gate array (FPGA) based digital implementation of the memristor-based multi-scroll hyperchaotic system is carried out. The experimental results of the FPGA-based digital circuit are displayed on the oscilloscope. [ABSTRACT FROM AUTHOR]

Hyperchaotic complex behaviors often occur in nature. Some chaotic behaviors are harmful, while others are beneficial. As for harmful behaviors, we hope to transform them into expected behaviors. For beneficial behaviors, we want to enhance their chaotic characteristics. Aiming at the harmful hyperchaotic complex system, a tracking controller was designed to produce the hyperchaotic complex system track common expectation system. We selected sine function, constant, and complex Lorenz chaotic system as target systems and verified the effectiveness by mathematical proof and simulation experiments. Aiming at the beneficial hyperchaotic complex phenomenon, this paper extended the hyperchaotic complex system to the fractional order because the fractional order has more complex dynamic characteristics. The influences order change and parameter change on the evolution process of the system were analyzed and observed by MATLAB simulation. [ABSTRACT FROM AUTHOR]

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