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The hot deformation behavior was probed through hot compression experiments with a range of temperature between 250 °C and 470 °C and strain rates ranging from 0.01 to 5 s−1. Simultaneously, the microstructural evolution was revealed employing electron backscatter diffraction (EBSD). Based on the hyperbolic sine function and dynamic material model, the constitutive equation was established and the critical conditions for dynamic recrystallization (DRX) were determined. The results indicate that the Z parameter (parameter temperature and strain rate compensation factor) exerts a notable influence on the hot deformation behavior and microstructure evolution. At higher lnZ values (low temperature or high strain rate) situations, the DRX volume percentage is relatively low. As ln Z decreases, the DRX process accelerates, leading to a significant rise in the fraction of high-angle grain boundaries (HAGB). Meanwhile, the main DRX mode of alloys driven by discontinuous dynamic recrystallization (DDRX), accompanied by continuous dynamic recrystallization (CDRX). The alloy undergoes complete DRX while subjected to high temperatures and rapid strain rates (450 °C, ε ˙ = 5 s - 1 , ln Z = 23.75). With increase in deformation, the texture along grain boundaries transitions gradually from the P {001} < 122 > orientation to the Brass {011} < 211 > and S {123} < 634 > orientations. [ABSTRACT FROM AUTHOR]

With the increasing number of satellites and rising user demands, the volume of satellite data transmissions is growing significantly. Existing scheduling systems suffer from unequal resource allocation and low transmission efficiency. Therefore, effectively addressing the large-scale multi-objective satellite data transmission scheduling problem (SDTSP) within a limited timeframe is crucial. Typically, swarm intelligence algorithms are used to address the SDTSP. While these methods perform well in simple task scenarios, they tend to become stuck in local optima when dealing with complex situations, failing to meet mission requirements. In this context, we propose an improved method based on the minimum angle particle swarm optimization (MAPSO) algorithm. The MAPSO algorithm is encoded as a discrete optimizer to solve discrete scheduling problems. The calculation equation of the sine function is improved according to the problem's characteristics to deal with complex multi-objective problems. This algorithm employs a minimum angle strategy to select local and global optimal particles, enhancing solution efficiency and avoiding local optima. Additionally, the objective space and solution space exhibit symmetry, where the search within the solution space continuously improves the distribution of fitness values in the objective space. The evaluation of the objective space can guide the search within the solution space. This method can solve multi-objective SDTSPs, meeting the demands of complex scenarios, which our method significantly improves compared to the seven algorithms. Experimental results demonstrate that this algorithm effectively improves the allocation efficiency of satellite and ground station resources and shortens the transmission time of satellite data transmission tasks. [ABSTRACT FROM AUTHOR]

Lately, an adaptive exponential functional link network (AEFLN) involving exponential terms integrated with trigonometric functional expansion is being introduced as a linear-in-the-parameters nonlinear filter. However, they exhibit degraded efficacy in lieu of non-Gaussian or impulsive noise interference. Therefore, to enhance the nonlinear modelling capability, here is a modified logarithmic hyperbolic sine cost function in amalgamation with the adaptive recursive exponential functional link network. In conjugation with this, a sparsity constraint motivated by a curvelet-dependent notion is employed in the suggested approach. Therefore, this paper presents an individually weighted modified logarithmic hyperbolic sine curvelet-based recursive exponential FLN (IMLSC-REF) for robust sparse nonlinear system identification. An individually weighted adaptation gain is imparted to several coefficients corresponding to the nonlinear adaptive model for accelerating the convergence rate. The weight update rule and the maximum criteria for the convergence factor are being further derived. Exhaustive simulation studies profess the effectiveness of the introduced algorithm in case of varied nonlinearity and for identifying as well as modelling the physical path of the acoustic feedback phenomenon of a behind-the-ear (BTE) hearing aid. [ABSTRACT FROM AUTHOR]

In this paper, we provide an explicit solution for the homogeneous fractional delay oscillation difference equation with an order 2d ranging from 1 to 2. This solution is achieved through the construction of discrete sine and cosine-type delayed matrix functions. Subsequently, we employ the discrete Laplace transform technique, a powerful method for handling nonhomogeneous terms, to investigate the solution of the corresponding nonhomogeneous equation. The study then delves into the Ulam-Hyerstype stabilities of the homogeneous equation, leveraging the representation of the solution. To validate the stability theory, we illustrate a numerical example. Finally, we extend our analysis by presenting an exact solution for the nonhomogeneous fractional difference equation with 1 < 2d < 2, utilizing the discrete two-parameter delayed sine and cosine-type function. [ABSTRACT FROM AUTHOR]

This paper presents a groundbreaking numerical approach, the fractional differential quadrature method (FDQM), to simulate the complex dynamics of organic polymer solar cells. The method, which leverages polynomial-based differential quadrature and Cardinal sine functions coupled with the Caputo-type fractional derivative, offers a significant improvement in accuracy and efficiency over traditional methods. By employing a block-marching technique, we effectively address the time-dependent nature of the governing equations. The efficacy of the proposed method is validated through rigorous numerical simulations and comparisons with existing analytical and numerical solutions. Each scheme's computational characteristics are tailored to achieve high accuracy, ensuring an error margin on the order of 10 − 8   or less. Additionally, a comprehensive parametric study is conducted to investigate the impact of key parameters on device performance. These parameters include supporting conditions, time evolution, carrier mobilities, charge carrier densities, geminate pair distances, recombination rate constants, and generation efficiency. The findings of this research offer valuable insights for optimizing and enhancing the performance of organic polymer solar cell devices. [ABSTRACT FROM AUTHOR]

Fission track analysis is a thermochronologic method for dating rocks and reconstructing their low-temperature thermal histories. We investigate the influence of the apatite composition on the etching of fossil confined fission tracks and its consequences for the fission track method. We conducted step-etch experiments with 5.5 M HNO3 at 21 °C on samples with etch pit diameters (Dpar) spanning most of the range for natural apatites (Panasqueira: 1.60 μm; Slyudyanka: 2.44 μm; Brazil: 3.92 μm; and Bamble: 4.60 μm) to determine their apatite etch rates vR (the rate at which each lattice plane is displaced parallel to itself) as a function of crystallographic orientation (ϕ′). Our measurements revealed significant differences between the four samples. We fitted three-parameter functions, vR = a (Dpar)ϕ′eb(Dpar)ϕ′ + c, describing vR as a function of the angle to the apatite c-axis for our hexagonal samples (excluding Bamble) and Durango apatite. Both parameters a and b exhibit a linear correlation with Dpar, whereas the constant c is small (~0.1 μm/min) and its between-sample variation is negligible at the resolution of our measurements. Bamble exhibits a different, bimodal relationship between vR and ϕ′, which we fitted with a sum of two sine functions. In all cases, including Bamble, there is a striking correlation between the angular frequencies of horizontal confined tracks and the magnitude of the apatite etch rate vR perpendicular to the track axes. This result shows that the sample of confined tracks selected for measurement and modeling is to a much greater degree determined by the etching properties of the apatite sample than by geometric or subjective biases. The track etch rate vT is constant along most of the track length but varies from track to track. The mean vT correlates with Dpar, so that tracks etch to their full lengths in a shorter time in faster etching apatites. The mean rate of length increase between etch steps, vL, also correlates with Dpar. The length increments of individual tracks are however irregular. This points to an intermittent structure at the ends of the tracks. [ABSTRACT FROM AUTHOR]

This study builds upon prior research by exploring droplet oscillation dynamics for surface tension determination using a drop-on-demand high-temperature droplet generator. Computational fluid dynamics (CFD) simulations were conducted to analyse frequency shifts over time, comparing two different materials with consistent results. The findings suggest potential for developing correction factors for oscillations with larger initial deformations. Additionally, frequency shifts relative to evolving aspect ratios of droplets starting with higher initial deformations were compared. Corrective measures can be applied, particularly beneficial for short-term measurements based on image analysis with minimal overall frequency shift. Slight asymmetry in oscillation with increasing aspect ratio could be accredited to droplet cross-sectional geometry or energy availability for returning prolate droplets to a spherical state. Experimental results indicated minimal frequency shift within a measurement duration of up to 40 ms, affirming the adequacy of using a fitted sine function without a time-dependent frequency term for overall frequency determination. A dimensionless criterion can be used to filter out unsuitable droplets. A temperature-dependent surface tension trend for AlCu10 alloy consistent with literature findings is introduced. [ABSTRACT FROM AUTHOR]

Examining the ϕ 4 and ϕ 8 models within a two-dimensional framework in the flat spacetime and embracing a theory with unconventional kinetic terms, one investigates the emergence of kinks/antikinks and double-kinks/antikinks. We devote our study to obtaining the field configurations with minimal energy, i.e., solutions possessing a Bogomol'nyi–Prasad–Sommerfield's bound. Next, to accomplish our goal, we adopt non-polynomial generalizing functions, namely, hyperbolic sine and cosine functions: the first produce BPS potentials exhibiting a minimum at ϕ = 0 , facilitating the emergence of genuine double-kink-type configurations. Conversely, the second promotes the rise of kink-type solutions. [ABSTRACT FROM AUTHOR]

A novel, precise disturbance rejection dynamic inversion control algorithm has been proposed. In the high-order dynamic surface control system, an innovative approach utilizes a monotonically increasing inverse hyperbolic sine function to construct an extended state observer, which estimates the uncertain functions at each step. The monotonicity of the inverse hyperbolic sine function simplifies the system stability analysis. Additionally, being a smooth function, it avoids the disturbances caused by piecewise functions at their breakpoints in conventional observer construction, thereby enhancing system stability. The accurate prediction capability of the new observer improves the system's disturbance rejection performance. To address the inherent differential explosion phenomenon in traditional dynamic inversion control schemes, this paper ingeniously employs a tracking signal observer as a substitute for traditional filters, thus avoiding the differential explosion that may occur with first-order filters. Finally, comparative simulations were conducted to validate the effectiveness of the proposed method. The results show that both the observer and the controller possess high-gain characteristics, and the closed-loop system exhibits a fast convergence rate. [ABSTRACT FROM AUTHOR]

Seasonal regimes of stream temperatures are important for ecological health as well as for societal water use. Seasonal regimes can be captured in the annual temperature cycle (the mean temperature for each day of the year) or in summary statistics such as seasonal mean temperatures, the former of which is the focus of this work. The annual temperature cycle is often characterized as a sine function, which performs satisfactorily for most streams. However, the sine function is unable to capture major seasonal variations, particularly for colder, drier, and high‐elevation regions. Seasonal summary statistics are effective for classification but do not capture the full time series, preventing the use of lost time‐series information, and lack context for the comparison of trends, hindering distinction between different causes of similar seasonal trends. We propose an improved function called the "three‐sine model" to describe the stream annual temperature cycle with higher accuracy and demonstrate its use in two case studies. The three‐sine model uses a cosine function over the entire year coupled with two seasonal anomaly sine functions. The three‐sine model captures the stream annual temperature cycle with eight parameters, reveals distinct spatial trends, and outperforms the sinusoidal model for all elevations and 99% of streams. We conclude that this approach can support improved stream temperature analysis by capturing detailed seasonal trends in context. [ABSTRACT FROM AUTHOR]

The low-power cluster routing protocol is a significant research focus in the WSN course. The utilization of Matlab for digital modeling and teaching simulation significantly enhances the understanding of this particular subject matter. This article introduces a low-power cluster routing algorithm based on the adaptive SSA and applies it to the simulation teaching process. Firstly, the SSA is enhanced by sine and cosine functions, with the addition of an adaptive adjustment factor. Subsequently, Levy flight is incorporated into SSA to improve its ability to escape from localized extremes. Additionally, a standard normal distribution random number is introduced to increase individual diversity within the algorithm's population. Furthermore, this proposed adaptive algorithm ASSA undergoes testing for convergence accuracy and speed using standard test functions. Finally, the proposed algorithm ASSA is utilized in cluster routing algorithms and simulation teaching. This article utilizes MATLAB simulation analysis tool for modeling and visually demonstrating processes such as cluster head election, clustering, data communication, and node death in clustering algorithms. Simultaneously, it illustrates how the ASSA algorithm effectively reduces energy consumption in each round and prolongs system stability running time to students. This simulation teaching process enables students to gain a deeper and more intuitive understanding of important features such as low power consumption of nodes, system lifetime, and energy utilization; thereby enhancing teaching effectiveness. [ABSTRACT FROM AUTHOR]

This article investigates certain q-analogue of the fractional Agarwal integral operator and its application to a class of polynomials and a series of functions. By utilizing various types of q-Bessel functions, the fractional q-Agarwal integral has been discussed and formulated in a series expression form involving q-shifted factorials and gamma functions. Moreover, certain results and applications of the q-Bessel theory are reported by establishing suitable forms of the fractional integral. Furthermore, the fractional Agarwal integral has been evaluated for some multiple power series formulas. Meanwhile, some desirable results involving q-generating Heine's series of the first type are provided. Over and above, certain conclusions associated with various exponential, hyperbolic sine and cosine functions are analysed. [ABSTRACT FROM AUTHOR]

This work proposes a new two-dimensional dynamical system with complete nonlinearity. This system inherits its nonlinearity from trigonometric and hyperbolic functions like sine, cosine, and hyperbolic sine functions. This system gives birth to infinite but countable coexisting attractors before and after being forced. These two megastable systems differ in the coexisting attractors' type. Only limit cycles are possible in the autonomous version, but torus and chaotic attractors can emerge after transforming to the nonautonomous version. Because of the position of equilibrium points in different attractors' attraction basins, this system can simultaneously exhibit self-excited and hidden coexisting attractors. This system's dynamic behaviors are studied using state space, bifurcation diagram, Lyapunov exponents (LEs) spectrum, and attraction basins. Finally, the forcing term's amplitude and frequency are unknown parameters that need to be found. The sparrow search algorithm (SSA) is used to estimate these parameters, and the cost function is designed based on the proposed system's return map. The simulation results show this algorithm's effectiveness in identifying and estimating parameters of the novel megastable chaotic system. [ABSTRACT FROM AUTHOR]

In the filed of remote sensing, arbitrary-oriented object detection methods has gained great attention, benefiting from the accurate detection ability of dense objects. However, the existing methods, which are designed based on ResNet, are not fast enough for real-time application. To solve this problem, our paper proposes a new fast arbitrary-oriented object detection methods based on YOLOX. First, a new head for rotational box prediction is proposed, in which a new branch is designed to extract the angle information through weighted averaging from different angles. Then, a new loss function with sine function is designed to avoid the boundary problem for rotational box prediction. The advantage of this loss is that the value of loss is also periodic which corresponds exactly to the periodicity of rotational box. Experiment results verify that the detection speed of the proposed method is fastest in comparison with the state-of-the-art methods, while maintaining the competitive detection accuracy. Code is available at . [ABSTRACT FROM AUTHOR]

The importance of statistical distributions in accurately representing real-world scenarios and aiding in educated decision-making is well recognized. Nonetheless, it is also true that the limitations of these distributions can hinder optimal fitting in certain situations. This awareness has led researchers to seek out improved and more optimal probability distributions. Based on factual motivation, this paper introduces a new probability distribution called the weighted sine generalized inverse Weibull (WSGI-Weibull) distribution. This model emerges from the amalgamation of the generalized inverse Weibull distribution and a sine-inspired probabilistic framework. Certain statistical properties, particularly those based on quantiles, of the newly introduced WSGI-Weibull distribution have been derived. An established estimation method is applied to calculate the point estimators of the WSGI-Weibull distribution, and subsequently, a simulation study is conducted. To highlight the benefits of the WSGI-Weibull distribution, two data sets sourced from the reliability and hydrology sectors are analyzed. The empirical fitting of the WSGI-Weibull distribution is evaluated against specific adversarial distributions, utilizing the two data sets as a basis for comparison. Utilizing specific evaluation tools, it has been noted that the WSGI-Weibull distribution delivers the best and most optimal fit for the reliability and hydrological data sets.

The presence of probability-driven models is highly influential in setting the stage for vital decision-making in domains including reliability, engineering, music engineering, and other closely interconnected scenarios. With a deep understanding of the consequential roles played by probability-arisen models, we have developed and implemented a new probabilistic model. This model is constructed by utilizing the sine-based function and the exponentiated Weibull distribution, and it is known as the exponent power sine exponentiated Weibull (EPSE-Weibull) distribution. Point estimators are derived for the EPSE-Weibull distribution. These estimators are then evaluated through a simulation study. The significance of the EPSE-Weibull distribution is demonstrated through the analysis of reliability and music engineering data sets. In addition to the above, we also utilize two deep learning algorithms, namely Artificial Neural Networks (ANN) and Support Vector Regression (SVR), to forecast the same data sets. The findings indicate that the ANN model consistently exhibits higher levels of accuracy, as evidenced by its lower Root Mean Square Error (RMSE) and Mean Absolute Error (MAE) values compared to the SVR model for both data sets. These findings indicate that ANN is better at capturing the fundamental patterns in the underlying data sets. In addition, visual representations, such as bar charts and line charts, further emphasize the superior performance of the ANN across both data sets.

In this paper, the extended (3+1)-dimensional potential KP equation in fluid mechanics is studied through Hirota bilinear method. Many types of hybrid solutions, such as the lump–kink solution, lump-two kink solution and periodic lump solution are obtained by assuming different functions in the bilinear equation. The interaction solution between lump and triangular periodic wave is also derived by combining sine and cosine functions with quadratic functions. Dynamical structures of these exact solutions are depicted by presenting the corresponding three-dimensional, two-dimensional structures and density graphs. These diverse interaction solutions could be helpful for understanding physical phenomena in fluid mechanics. [ABSTRACT FROM AUTHOR]

In this study, we developed a new method for designing progressive addition-multifocus defocused freeform lenses. We used two independent meridians and achieved a smooth gradient transition of additional optical power from the center to the peripheral area of the lens, along with an asymmetric distribution of additional optical power on the nasal-temporal side of the lens. To improve the optical performance of the lenses, we developed three different designs based on the distribution of the additional optical power on the meridians. We conducted simulations and processing on the three different designs. The lenses designed using improved logistic regression and sine functions for meridian optical power distribution exhibited stable optical performance in the central focus area. They also met the design requirements for additional optical power. However, significant distortion was still observed in the peripheral region, which required further optimization. Lenses designed using piecewise linear functions for meridian optical power distribution exhibited relatively poor optical performance with significant optimization potential. Thus, combining the optical power distribution and surface-type factors for optimization is necessary. The proposed method enabled designing of defocus-free curved mirror lenses that satisfy the optical performance requirements. Thus, this method provides a new approach for the design of progressive addition lenses. [ABSTRACT FROM AUTHOR]

To address the limitations of existing gear tooth modification methods, a differentiated tooth modification method is proposed, where the modification amount of adjacent teeth varies according to a sine function. Initially, a mathematical model of the gear tooth profile varying according to a sine function is established. Then, using Adams software, a simulation analysis of the dynamic characteristics such as centroid angular acceleration, meshing force, and transmission error of gear pairs is conducted. The dynamic transmission performance of three sets of gear pairs--unmodified, normally modified, and differentially modified--is compared. Additionally, Simcenter 3D software is used to analyze the noise characteristics of these gear pairs. The results show that the differentially modified gear pairs, compared to the normally modified ones, have a maximum reduction of 2.47 % in sound power level at the fundamental meshing frequency amplitude. This proves that the differentiated modification method enhances the dynamic transmission performance of gears, offering a new method for gear vibration and noise reduction. [ABSTRACT FROM AUTHOR]

Certain methods for implementing chaotic maps can lead to dynamic degradation of the generated number sequences. To solve such a problem, we develop a method for generating pseudorandom number sequences based on multiple one-dimensional chaotic maps. In particular, we introduce a Bernoulli chaotic map that utilizes function transformations and constraints on its control parameter, covering complementary regions of the phase space. This approach allows the generation of chaotic number sequences with a wide coverage of phase space, thereby increasing the uncertainty in the number sequence generation process. Moreover, by incorporating a scaling factor and a sine function, we develop a robust chaotic map, called the Sine-Multiple Modified Bernoulli Chaotic Map (SM-MBCM), which ensures a high degree of randomness, validated through statistical mechanics analysis tools. Using the SM-MBCM, we propose a chaotic PRNG (CPRNG) and evaluate its quality through correlation coefficient analysis, key sensitivity tests, statistical and entropy analysis, key space evaluation, linear complexity analysis, and performance tests. Furthermore, we present an FPGA-based implementation scheme that leverages equivalent MBCM variants to optimize the electronic implementation process. Finally, we compare the proposed system with existing designs in terms of throughput and key space. [ABSTRACT FROM AUTHOR]

In the present study, a series of lattice structures with Gyroid minimal surfaces were meticulously designed to incorporate linear density gradients and two distinct trigonometric function-based density gradients. These advanced architectures were subsequently compared and contrasted with a uniform lattice sandwich structure. The mechanical behavior and energy absorption characteristics of the four lattice sandwich structures were rigorously investigated through a combination of experimental testing and finite element analysis (FEA). The results of this comprehensive analysis revealed that during compression, all four gradient lattice structures exhibited varying degrees of shear slip, which manifested as discernible discrepancies in their respective stress–strain curves. Relative to the uniform lattice structure, the linear gradient lattice sandwich structure exhibited an enhancement in elastic modulus by 1.69%, while the square sine function gradient lattice sandwich structure showed a significant increase of 14.45% in elastic modulus. Conversely, the square cosine function gradient lattice sandwich structure experienced a reduction in elastic modulus by 9.61%. Employing either a linear gradient or a square sine function density gradient design was found to augment the load-bearing capacity of the uniform lattice structure. Notably, when the strain in the uniform structure reached densification strain, it absorbed energy exceeding 5.842 MJ/m3, indicating superior energy absorption capabilities among the four structures examined, thus rendering it particularly suitable for applications where high energy absorption is imperative. Furthermore, finite element simulations were conducted to validate the experimental findings, and the simulation results demonstrated a high degree of correlation with the experimental data, with discrepancies less than 6%, thereby confirming the reliability of the FEA model in predicting the performance of these intricate lattice structures. [ABSTRACT FROM AUTHOR]

In this article, our objective is to define and study a new subclass of analytic functions associated with the q-analogue of the sine function, operating in conjunction with a convolution operator. By manipulating the parameter q, we observe that the image of the unit disc under the q-sine function exhibits a visually appealing resemblance to a figure-eight shape that is symmetric about the real axis. Additionally, we investigate some important geometrical problems like necessary and sufficient conditions, coefficient bounds, Fekete-Szegö inequality, and partial sum results for the functions belonging to this newly defined subclass. [ABSTRACT FROM AUTHOR]

Similarity to reality is a necessary property of models in earth sciences. Similarity information can thus possess a large potential in advancing geophysical modeling and data assimilation. We present a formalism for utilizing similarity within the existing theoretical data assimilation framework. Two examples illustrate the usefulness of utilizing similarity in data assimilation. The first, theoretical example shows changes in the accuracy of the amplitude estimate in the presence of a phase error in a sine function, where correcting the phase error prior to the assimilation reduces the degree of ill-posedness of the assimilation problem. This signifies the importance of accounting for the phase error in order to reduce the error in the amplitude estimate of the sine function. The second, real-world example illustrates that timing errors in simulated flow degrade the data assimilation performance, and that the flow gradient-informed shifting of rainfall time series improved the assimilation results with less adjusting model states. This demonstrates the benefit of utilizing streamflow gradients in shifting rainfall time series in a way to improve streamflow timing—vital information for flood early warning and preparedness planning. Finally, we discuss the implications, potential issues, and future challenges associated with utilizing similarity in hydrologic data assimilation. [ABSTRACT FROM AUTHOR]

Permanent magnet synchronous motors (PMSMs) speed control has gained wide application in various fields. Specifically, there is a disadvantage that nonlinear functions in the conventional active disturbance rejection controller (ADRC) is non‐differentiable at the piecewise points. Thus, an improved nonlinear active disturbance rejection controller (NLADRC) for permanent magnet synchronous motor speed control via sine function and whale optimization algorithm (WOA), abbreviated as NLADRC‐sin‐IWOA, is proposed to overcome this drawback. Considering the unsatisfactory control effect caused by the poor active disturbance resisting ability of the traditional PMSM controllers, this paper proposes an improved NLADRC for PMSM, that reconstructs a novel differentiable and smooth nonlinear function, the novel nonlinear function grounded on primitive function by the function of inverse hyperbolic, sine, square functions, and with difference fitting approach; and designs an improved whale optimization algorithm via convergence factor nonlinear decreasing, Gaussian variation and adaptive cross strategies. The experimental results findings show that the improved NLADRC‐sin‐IWOA has the advantages of response fast, small steady‐state error and tiny overshoot. © 2024 Institute of Electrical Engineers of Japan and Wiley Periodicals LLC. [ABSTRACT FROM AUTHOR]

Physics informed neural network (PINN) demonstrates powerful capabilities in solving forward and inverse problems of nonlinear partial differential equations (NLPDEs) through combining data-driven and physical constraints. In this paper, two PINN methods that adopt tanh and sine as activation functions, respectively, are used to study data-driven solutions and parameter estimations of a family of high order KdV equations. Compared to the standard PINN with the tanh activation function, the PINN framework using the sine activation function can effectively learn the single soliton solution, double soliton solution, periodic traveling wave solution, and kink solution of the proposed equations with higher precision. The PINN framework using the sine activation function shows better performance in parameter estimation. In addition, the experiments show that the complexity of the equation influences the accuracy and efficiency of the PINN method. The outcomes of this study are poised to enhance the application of deep learning techniques in solving solutions and modeling of higher-order NLPDEs. [ABSTRACT FROM AUTHOR]

Most implicit sentiment sentences in aspect level implicit sentiment analysis lack emotional words, but there are still potential emotional clues. Current research mainly utilizes contextual information and external knowledge of text for semantic enhancement, thereby improving implicit sentiment analysis. However, in these models, the semantic correlation between words decays as the distance between the two increases, leading to weak and difficult to capture emotional cues at long distances, presenting ambiguity in emotional polarity and reducing the performance of sentiment analysis. To solve this problem, in this paper, we propose aspect-level implicit sentiment analysis model based on semantic wave and knowledge enhancement. Firstly, the semantic wave-based aspect word context information enhancement method uses the fluctuation property of semantic wave to perform weight adaptive enhancement of semantically related long-distance context information. This method essentially utilizes a sine wave function to significantly reduce the weight of words that are close but semantically unrelated, thereby allowing the weight of words that are close and semantically similar to be relatively reflected, in order to solve the problem of hiding emotional clues at long distances. Then, the implicit sentiment analysis method based on supervised contrastive pre-training is used to capture potential sentiment cues from context information and embed them into the sentence vector by weak feature learning of implicit sentiment. Finally, multi-feature interaction-based knowledge enhancement method is used to focus on the context content of sentences that are more related to background knowledge in a feature interaction way, and the information scaling factor is combined to enhance the dependency between aspect words and sentiment cues, thereby solving the problem of weak features in long-distance emotional clues and accurately identifying the emotional polarity of aspect words. The experiment shows that the model proposed in this paper has made significant improvements on the Restaurant and Laptop datasets in SemEval 2014 Task 4, with an accuracy increase of 3.38% and 4.57% in implicit emotions, respectively, achieving the best performance so far. At the same time, generalization and robustness testing experiments were conducted on the model, achieving preferable performance improvement. [ABSTRACT FROM AUTHOR]

The stress as a response to strain prescribed as a harmonic excitation is examined in both transient and steady state regime for the viscoelastic body modeled by thermodynamically consistent fractional anti‐Zener and Zener models by the use of the Laplace transform method. Assuming strain as a sine function, the time evolution of power per unit volume, previously derived as a sum of time derivative of a conserved term, which represents the rate of change of stored energy, and a dissipative term, which represents dissipated power, is investigated when expressed through the relaxation modulus and creep compliance. Further, two forms of energy and two forms of dissipated power per unit volume are examined in order to see whether they coincide. [ABSTRACT FROM AUTHOR]

In this paper, we make use of the generalized Sălăgean differential operator to define a novel class of bi-univalent functions that is associated with the generalized hyperbolic sine function in the open unit disk D. The prime goal of this paper to derive sharp coefficient bounds in open unit disk D, especially the first two coefficient bounds for the functions belong to this class . The investigation also focuses on studying the classical Fekete-Szegö functional problem for functions belong to this class. Furthermore, some known corollaries are highlighted based on the unique choices of the parameters involved in this class. [ABSTRACT FROM AUTHOR]

Full spherical views provide advantages in many applications that use visual information. Dual back-to-back fisheye cameras are receiving much attention to obtain this type of view. However, obtaining a high-quality full spherical view is very challenging. In this paper, we propose a correction step that models the relation between the pixels of the pair of fisheye images in polar coordinates. This correction is implemented during the mapping from the unit sphere to the fisheye image using the equidistant fisheye projection. The objective is that the projections of the same point in the pair of images have the same position on the unit sphere after the correction. In this way, they will also have the same position on the equirectangular coordinate system. Consequently, the discontinuity between the spherical views for blending is minimized. Throughout the manuscript, we show that the angular polar coordinates of the same scene point in the fisheye images are related by a sine function and the radial distance coordinates by a linear function. Also, we propose employing a polynomial as a geometric transformation between the pair of spherical views during the image alignment since the relationship between the matching points of pairs of spherical views is not linear, especially in the top/bottom regions. Quantitative evaluations demonstrate that using the correction step improves the quality of the full spherical view, i.e. IQ MS-SSIM, up to 7%. Similarly, using a polynomial improves the IQ MS-SSIM up to 6.29% with respect to using an affine matrix. [ABSTRACT FROM AUTHOR]

To address the issue of suboptimal spectral purity in Direct Digital Frequency Synthesis (DDFS) within resource-constrained environments, this paper proposes an optimized DDFS technique based on cubic Hermite interpolation. Initially, a DDFS hardware architecture is implemented on a Field-Programmable Gate Array (FPGA); subsequently, essential interpolation parameters are extracted by combining the derivative relations of sine and cosine functions with a dual-port Read-Only Memory (ROM) structure using the cubic Hermite interpolation method to reconstruct high-fidelity target waveforms. This approach effectively mitigates spurious issues caused by amplitude quantization during the DDFS digitalization process while reducing data node storage units. Moreover, this paper introduces single-quadrant ROM compression technology to further diminish the required storage space. Experimental results indicate that, compared to traditional DDFS methods, the optimization scheme proposed in this work achieves a ROM resource compression ratio of 1792:1 and a 14-bit output Spurious-Free Dynamic Range (SFDR) of −88.134 dBc, effectively enhancing amplitude quantization precision and significantly lowering spurious levels. This significantly improves amplitude quantization precision and reduces spurious levels. The proposed scheme demonstrates notable advantages in both spectral performance and resource utilization efficiency, making it highly suitable for resource-constrained embedded systems and high-performance applications such as radar and communication systems. [ABSTRACT FROM AUTHOR]

The presence of probability-driven models is highly influential in setting the stage for vital decision-making in domains including reliability, engineering, music engineering, and other closely interconnected scenarios. With a deep understanding of the consequential roles played by probability-arisen models, we have developed and implemented a new probabilistic model. This model is constructed by utilizing the sine-based function and the exponentiated Weibull distribution, and it is known as the exponent power sine exponentiated Weibull (EPSE-Weibull) distribution. Point estimators are derived for the EPSE-Weibull distribution. These estimators are then evaluated through a simulation study. The significance of the EPSE-Weibull distribution is demonstrated through the analysis of reliability and music engineering data sets. In addition to the above, we also utilize two deep learning algorithms, namely Artificial Neural Networks (ANN) and Support Vector Regression (SVR), to forecast the same data sets. The findings indicate that the ANN model consistently exhibits higher levels of accuracy, as evidenced by its lower Root Mean Square Error (RMSE) and Mean Absolute Error (MAE) values compared to the SVR model for both data sets. These findings indicate that ANN is better at capturing the fundamental patterns in the underlying data sets. In addition, visual representations, such as bar charts and line charts, further emphasize the superior performance of the ANN across both data sets. [ABSTRACT FROM AUTHOR]

Copulas are helpful in studying joint distributions of two variables, in particular, whenconfounders are unobserved. However, most conventional copulas cannot model joint distributions where one variable does not increase or decrease in the other in a monotonic manner. For instance, suppose that two variables are linearly positively correlated for one type of unit and negatively for another type of unit. If the type is unobserved, we can observe only a mixture of both types. Seemingly, one variable tends to take either a high or low value (or a middle value) when the other variable is small (large), or vice versa. To address this issue, I consider an overlooked copula with trigonometric functions (Chesneau [2021, Applied Mathematics , 1(1), pp. 3–17]) thatI name the "normal mode copula." I apply the copula to a dataset about government formation and duration to demonstrate that the normal mode copula has better performance than other conventional copulas. [ABSTRACT FROM AUTHOR]

The overtaking process for autonomous vehicles must prioritize both efficiency and safety, with safe distance being a crucial parameter. To address this, we propose an automatic overtaking path planning method based on minimal safe distance, ensuring both maneuvering efficiency and safety. This method combines the steady movement and comfort of the constant velocity offset model with the smoothness of the sine function model, creating a mixed-function model that is effective for planning lateral motion. For precise longitudinal motion planning, the overtaking process is divided into five stages, with each stage's velocity and travel time calculated. To enhance the control system, the model predictive control (MPC) algorithm is applied, establishing a robust trajectory tracking control system for overtaking. Numerical simulation results demonstrate that the proposed overtaking path planning method can generate smooth and continuous paths. Under the MPC framework, the autonomous vehicle efficiently and safely performs automatic overtaking maneuvers, showcasing the method's potential to improve the performance and reliability of autonomous driving systems. [ABSTRACT FROM AUTHOR]

Introduction: The ability of transgenic plants to respond to sudden environmental pollution accidents has become viable. Nonetheless, there is a dearth of research regarding the mechanism by which transgenic plants degrade organic pollutants. Hence, this study aimed to elucidate the process of organic pollutant degradation by plants, offering theoretical support for the application of transgenic plant emergency phytoremediation technology. Methods: In this investigation, we developed a 3D-QSAR pharmacophore model to represent the collective impact of plant resistance and phytodegradation. This was achieved by employing integrated effect values following treatment with a sine function approach. Moreover, we have undertaken an inaugural exploration of the coregulatory mechanism involved in plant resistance and pollutant degradation within plants. Additionally, we applied virtual molecular modification techniques for analysis and validation, striving for a more indepth understanding of the molecular-level enhancement mechanism related to the degradation of pollutants within plant organisms. Results and discussion: The mechanism analysis results of the Hypo 1 pharmacophore model were verified, indicating that hydrophobic characteristics affect the resistance and degradation of PCBs in plants, significantly affecting the degradation effect of pollutants in plants. [ABSTRACT FROM AUTHOR]

Sine cosine algorithm (SCA) is a recently developed meta-heuristic method based on the characteristics of sine and cosine functions. However, SCA algorithm may suffer premature convergence in solving complex optimization problems. To mitigate this limitation, a modified SCA (MSCA) is developed to achieve an effective balance between exploration and exploitation. Specifically, the conversion parameter can be configured adaptively by using the individual fitness information in the evolution process to guide the individual search behavior. After that, an inertia weight is embedded in the position updating equation to further improve the search accuracy and accelerate the convergence speed. The performance of MSCA algorithm is investigated on 13 benchmark functions and the chaotic time series prediction problem. Experimental results demonstrate that MSCA algorithm is more effective than the other optimization methods. [ABSTRACT FROM AUTHOR]

We have derived alternative closed-form formulas for the trigonometric series over sine or cosine functions when the immediate replacement of the parameter appearing in the denominator with a positive integer gives rise to a singularity. By applying the Choi–Srivastava theorem, we reduce these trigonometric series to expressions over Hurwitz's zeta function derivative. [ABSTRACT FROM AUTHOR]

In this paper, by means of the Faà di Bruno formula, with the help of explicit formulas for partial Bell polynomials at specific arguments of two specific sequences generated by derivatives at the origin of the inverse sine and inverse cosine functions, and by virtue of two combinatorial identities containing the Stirling numbers of the first kind, the author establishes power series expansions for real powers of the inverse cosine (sine) functions and the inverse hyperbolic cosine (sine) functions. By comparing different series expansions for the square of the inverse cosine function and for the positive integer power of the inverse sine function, the author not only finds infinite series representations of the circular constant π and its real powers, but also derives several combinatorial identities involving central binomial coefficients and the Stirling numbers of the first kind. [ABSTRACT FROM AUTHOR]

The research investigated the tooth backlash influences the error in seedling picking trajectories of the gear train SPM. First, a sine function and the sum of random errors are taken into account is utilized to fit the tooth backlash of the firstly and secondary transmissions. Additionally, the analysis established the relationship between the fitting parameters and the tooth backlash of the firstly and secondary transmissions, in order to determine the appropriate fitting parameters. Next, the relationship between the tooth backlash of the firstly and secondary transmission in the seedling picking mechanism (SPM) and the x, y coordinates, as well as the velocity and acceleration of the seedling needle tip (SNT), is examined. This analysis is based on the error and movement variance of the coordinate and kinematic parameters of SNT. The results indicate that the tooth backlash of the firstly transmission has a more significant influence on the error of the seedling picking trajectory compared to the tooth backlash of the secondary transmission. When the tooth backlash of the noncircular gear in the firstly transmission reaches its maximum value of 0.24 mm, the x and y coordinates of the SNT can reach maximum values of 1 and 3.5 mm. The test of the jumping of the needle tip and idling trajectory description indicated that noncircular gears with larger tooth backlash exhibit higher positional jumping at the tip of the seedling needle. [ABSTRACT FROM AUTHOR]

Statistical modeling of the practical data sets is a useful method that guides researchers to make decisions under uncertainty in applied sectors. To date, a rich number of probability distributions have appeared that have been developed in different ways and implemented in different fields. A vast literature of the available distributions have been constructed by adding new additional parameters, varying from one to eight. This specific piece of the research work also prompts a new probabilistic model, namely, the weighted sine flexible-Weibull distribution. The weighted sine flexible-Weibull distribution consists of the flexible Weibull extension model and a sine-oriented methodology. For the weighted sine flexible-Weibull distribution, the quartile-based properties are derived. Besides these properties, the estimators for the new model are also derived. The estimation part of the weighted sine flexible-Weibull distribution is further extended by conducting a simulation study. Finally, the weighted sine flexible-Weibull distribution is illustrated by considering the injury rate in logistics and public transport systems that are reported after the safety factors are considered. Based on several evaluation criteria, it is established that the weighted sine flexible-Weibull distribution provides the optimal fitting to the injury rate data.

Probability-arisen models play a considerable role in preparing a crucial stage for decision-making concerning reliability, engineering, and more closely related scenarios. Bearing in mind the consequential roles of probability-arisen models, we introduce and implement a new probabilistic model that has arisen by using the sine function, namely, the sine very flexible Weibull (SVF-Weibull) distribution. The proposed SVF-Weibull distribution is a result of a combination of the very flexible Weibull distribution with the sine-based strategy. For the SVF-Weibull distribution, point estimates are obtained. The assessment of the point estimates of the SVF-Weibull distribution is done via a simulation study. Finally, the consequential role of the SVF-Weibull distribution, illustrated by considering reliability and music engineering data sets. Furthermore, we implement some machine learning tools for predicting the reliability and music engineering data sets. The performances of the machine learning tools are assessed across many hidden variables. Our findings suggest that the artificial neural network method is more optimal than other methods for predicting the reliability and music engineering data sets.

Abstract The aim of this paper is to introduce two new subclasses R sin m ( ℑ ) $\mathcal{R}_{\sin }^{m}(\Im )$ and R sin ( ℑ ) $\mathcal{R}_{\sin }(\Im )$ of analytic functions by making use of subordination involving the sine function and the modified sigmoid activation function ℑ ( v ) = 2 1 + e − v $\Im (v)=\frac{2}{1+e^{-v}}$ , v ≥ 0 $v\geq 0$ in the open unit disc E. Our purpose is to obtain some initial coefficients, Fekete–Szego problems, and upper bounds for the third- and fourth-order Hankel determinants for the functions belonging to these two classes. All the bounds that we will find here are sharp. We also highlight some known consequences of our main results.

In engineering practice, dynamic vibration absorber is an effective method to control vibration of beam structure. The mathematical model of beam coupled with spring–mass systems under elastic edge constraints is established in this paper. In addition to Fourier cosine series, supplementary sine functions are introduced to represent the displacement function of the beam. The spring–mass system is considered by increasing degrees of freedom when constructing the mass matrix and stiffness matrix. The efficiency of solving equivalent mass is greatly improved in the comparison with FEM, which is important when designing dynamic vibration absorber. Subsequently, we conduct parametric analysis of the control effect about the dynamic vibration absorber based on the current mathematical model. The procedure of designing distributed dynamic vibration absorber of beam structure under various boundary condition is also presented. To verify the validity of the current mathematical model and design procedure, a cantilever beam experiment was conducted. The findings presented in the current research may be useful for researchers in the process of multi-line spectrum vibration control of beam structure. [ABSTRACT FROM AUTHOR]

Probability-arisen models play a considerable role in preparing a crucial stage for decision-making concerning reliability, engineering, and more closely related scenarios. Bearing in mind the consequential roles of probability-arisen models, we introduce and implement a new probabilistic model that has arisen by using the sine function, namely, the sine very flexible Weibull (SVF-Weibull) distribution. The proposed SVF-Weibull distribution is a result of a combination of the very flexible Weibull distribution with the sine-based strategy. For the SVF-Weibull distribution, point estimates are obtained. The assessment of the point estimates of the SVF-Weibull distribution is done via a simulation study. Finally, the consequential role of the SVF-Weibull distribution, illustrated by considering reliability and music engineering data sets. Furthermore, we implement some machine learning tools for predicting the reliability and music engineering data sets. The performances of the machine learning tools are assessed across many hidden variables. Our findings suggest that the artificial neural network method is more optimal than other methods for predicting the reliability and music engineering data sets. [ABSTRACT FROM AUTHOR]

Statistical modeling of the practical data sets is a useful method that guides researchers to make decisions under uncertainty in applied sectors. To date, a rich number of probability distributions have appeared that have been developed in different ways and implemented in different fields. A vast literature of the available distributions have been constructed by adding new additional parameters, varying from one to eight. This specific piece of the research work also prompts a new probabilistic model, namely, the weighted sine flexible-Weibull distribution. The weighted sine flexible-Weibull distribution consists of the flexible Weibull extension model and a sine-oriented methodology. For the weighted sine flexible-Weibull distribution, the quartile-based properties are derived. Besides these properties, the estimators for the new model are also derived. The estimation part of the weighted sine flexible-Weibull distribution is further extended by conducting a simulation study. Finally, the weighted sine flexible-Weibull distribution is illustrated by considering the injury rate in logistics and public transport systems that are reported after the safety factors are considered. Based on several evaluation criteria, it is established that the weighted sine flexible-Weibull distribution provides the optimal fitting to the injury rate data. [ABSTRACT FROM AUTHOR]

The Priestley–Taylor model of the Jet Propulsion Laboratory (PT-JPL) evapotranspiration (ET) model is relatively simple and has been widely used based on meteorological and satellite data. However, soil moisture (SM) constraints include a vapor pressure deficit (VPD) that causes large uncertainty. In this study, we proposed a PT-SinRH model by introducing a sine function of air relative humidity (RH) to replace RHVPD to characterize SM constraints, which can improve the accuracy of ET estimations. The PT-SinRH model is validated by eddy covariance (EC) data from 2000–2020. These data were collected by AmeriFlux at 28 sites on the conterminous United States (CONUS), and the land cover types of the sites vary from croplands to wetlands, grasslands, shrub lands and forests. The validation results from daily scale-based on-site and satellite data inputs showed that the PT-SinRH model estimates fit the observations with a coefficient of determination (R2) of 0.55, root-mean-square error (RMSE) of 17.5 W/m2, bias of −1.2 W/m2 and Kling–Gupta efficiency (KGE) of 0.70. Additionally, the PT-SinRH model based on reanalysis and satellite data inputs has an R2 of 0.49, an RMSE of 20.3 W/m2, a bias of −8.6 W/m2 and a KGE of 0.55. The PT-SinRH model showed better accuracy when using the site-measured meteorological data than when using reanalysis meteorological data as inputs. Additionally, compared with the PT-JPL model, the results demonstrate that our approach, i.e., PT-SinRH, improved ET estimates, increasing the R2 and KGE by 0.02 and decreasing the RMSE by about 0.6 W/m2. This simple but accurate method permits us to investigate the decadal variation in regional ET over the land. [ABSTRACT FROM AUTHOR]

The degradation state of a bearing can be monitored effectively by using a wear indicator (WI). A WI curve having smoothness and monotonicity can lay a good foundation for predicting the remaining useful life of the bearing. Most traditional models for bearing WI construction, such as time–frequency indicators and signal decomposition, are complicated; for example, some WI construction models need several models to select from, and their fusion depends on the manual experience of engineers. For example, single and mixed traditional time–frequency indicators, such as the root mean square (RMS), Kurtosis, multiple time–frequency domain fusion. However, the mentioned-above time–frequency domain indicators are difficult to adaptively reflect the operating status of the equipment when the operating conditions of the mechanical system change. Some signal decomposition models are combined with other models and rely on manual experience to extract WI, such as the selection of effective intrinsic mode function components function, parameter setting of empirical mode decomposition and ensemble empirical mode decomposition model, etc. Deep learning models, such as stacked auto encoder (SAE) and convolution neural network, have been widely used in bearing health monitoring and WI construction, because its powerful learning and feature extraction capabilities of multiple hidden layer structures. But these deep learning models are designed to use output labels. Particularly when the data volume is large, it requires manpower, material resources, and experienced engineers to label the data, or it is difficult to label and distinguish the categories of data samples. Therefore, to solve these problems and eliminate the need for manual labor, such as labeling data and selecting models for fusion, we propose using SAE without an output label layer to extract WI from original signals directly. However, an extracted WI curve without good monotonicity (Mon) will result in a poor remaining useful life prediction accuracy. To improve the monotonicity of the extracted WI and reduce the complexity of the WI construction model, we propose an unsupervised enhanced SAE without an output layer, named SINSAE, by adding a sine function of an average value which is calculated form start time to current at each hidden layer to eliminate concussion. Moreover, to demonstrate that our proposed model is better than other models, such as the RMS, Kurtosis, multiple time–frequency domain fusion, SAE, SAE without an output layer, and signal decomposition models, the Mon indicator in this study is used to compare the monotonicity of the extracted WI. Lastly, the results of our experiments using different bearing datasets and various working conditions show that the smoothness and monotonicity of the WI curve extracted by the SINSAE is better than that of other models. Moreover, compared to the traditional commonly used single and multiple time–frequency domain indicators, supervised deep learning and basic unsupervised deep models, the unsupervised SINSAE model can increase the Mon indicators from [0.1, 0.8], [0.02, 0.1], [0.1, 0.8] to above 0.9, respectively. [ABSTRACT FROM AUTHOR]