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A novel structural reliability analysis method that combines the improved beluga whale optimization (IBWO) and the arctangent function‐based maximum entropy method (AMEM) is proposed in this paper. It aims to augment the accuracy of failure probability prediction in structural reliability analysis based on the traditional maximum entropy method (MEM). First, the arctangent function is introduced to avoid the effects of truncation error and numerical overflow in the traditional MEM. The arctangent function can nonlinearly transform the structural performance function defined on the infinite interval into a transformed performance function defined on the bounded interval. Subsequently, the undetermined Lagrange multipliers in the maximum entropy probability density function (MEPDF) of the transformed performance function are obtained using IBWO at a swifter convergence speed with heightened convergence accuracy. Finally, the MEPDF of the transformed performance function can be obtained by combining the IBWO and AMEM, and the structural failure probability can be predicted. The analysis of the metro bogie frame as an engineering example reveals that compared with the traditional MEM using the genetic algorithm to solve the Lagrange multipliers, the proposed method diminishes the relative error in failure probability prediction from 20.51% to only 0.09%. This method significantly enhances the prediction accuracy of failure probability. [ABSTRACT FROM AUTHOR]

In this paper, we propose an elementary proof of Niven's Theorem in which the tangent function will have a primary role. [ABSTRACT FROM AUTHOR]

This paper presents a novel polyphase-basis discrete cosine transform that can be used for challenges to observe heart rate (HR) variability and sudden changes of HR in short time. To succeed in the challenges, real-time measurement which requires a short window length is needed. As the window length decreases, however, increased main-lobe width (MLW) and sidelobe width (SLW) result errors in measuring HR. Unlike commonly used discrete Fourier transform (DFT), the proposed method is based on DCT, which improves the accuracy of measured HR even though the short window length is used for the real-time measurement of HR. We demonstrate that the DCT can give 2 times shorter MLW and SLW than the DFT can. To verify the proposed method, it is compared with well-known existing methods, arctangent demodulation and complex signal demodulation, which use the DFT. We measured HR using a 10.225-GHz continuous-wave Doppler radar. In each experiment, the window lengths of 3, 2, and 1.5 s were used to measure HR in real time. Experimental results show that the proposed method has lower mean and standard deviation of errors than the existing methods have. [ABSTRACT FROM PUBLISHER]

This paper presents a new spline prioritization optimization adaptive filter with arctangent-exponential hyperbolic cosine (SPOAF-ARC-EHC) to solve the high steady-state error in colored and/or impulsive noise environments. Different from the traditional spline adaptive filtering algorithm, the weight update of the spline prioritization optimization adaptive filter (SPOAF) is only based on the linear error, and the update of the spline control points is based on the error of the whole system. To improve the robustness of the proposed SPOAF algorithm, the linear part and the nonlinear part use independent cost functions. More specifically, we utilize the arctangent function (ARC) as the cost function for the linear part and the exponential hyperbolic cosine as the loss function for the nonlinear part. Through simulation, it is shown that the proposed algorithm significantly reduces the steady-state error compared with the existing algorithms in a colored and/or impulsive noise environment. [ABSTRACT FROM AUTHOR]

In this paper, a new class of the continuous distributions is established via compounding the arctangent function with a generalized log-logistic class of distributions. Some structural properties of the suggested model such as distribution function, hazard function, quantile function, asymptotics and a useful expansion for the new class are given in a general setting. Two special cases of this new class are considered by employing Weibull and normal distributions as the parent distribution. Further, we derive a survival regression model based on a sub-model with Weibull parent distribution and then estimate the parameters of the proposed regression model making use of Bayesian and frequentist approaches. We consider seven loss functions, namely the squared error, modified squared error, weighted squared error, K-loss, linear exponential, general entropy, and precautionary loss functions for Bayesian discussion. Bayesian numerical results include a Bayes estimator, associated posterior risk, credible and highest posterior density intervals are provided. In order to explore the consistency property of the maximum likelihood estimators, a simulation study is presented via Monte Carlo procedure. The parameters of two sub-models are estimated with maximum likelihood and the usefulness of these sub-models and a proposed survival regression model is examined by means of three real datasets. [ABSTRACT FROM AUTHOR]

Purpose – The inverse kinematics in robot manipulator have to handle the arctangent and arccosine function. However, the two functions are complicated and need much computation time so that it is difficult to be realized in the typical processing system. The purpose of this paper is to solve this problem by using Field Programmable Gate Array (FPGA) to speed up the computation power. Design/methodology/approach – The Taylor series expansion method is firstly applied to transfer arctangent and arccosine function to a polynomial form. And Look-Up Table (LUT) is used to store the parameters of the polynomial form. Then the behavior of the computation algorithm is described by Very high-speed IC Hardware Description Language (VHDL) and a co-simulation using ModelSim and Simulink is applied to evaluate the correctness of the VHDL code. Findings – The computation time of arctangent and arccosine function using by FPGA need only 320 and 420 ns, respectively, and the accuracy is <0.01°. Practical implications – Fast computation in arctangent and arccosine function can speed up the motion response of the real robot system when it needs to perform the inverse kinematics function. Originality/value – This is the first time such to combine the Taylor series method and LUT method in the computation the arctangent and arccosine function as well as to implement it with FPGA. [ABSTRACT FROM AUTHOR]

This paper presents a novel approach for power transformer incipient fault diagnosis through the analysis of dissolved gas in oil. The proposed approach is implemented for improving the diagnosis accuracy by dissolved gas analysis (DGA) of power transformer based on the combined use of a multi-classification algorithm self-adaptive evolutionary extreme learning machine (SaE-ELM) and a simple arctangent transform (AT). On the one hand, the SaE-ELM algorithm has the ability to approximate any nonlinear functions with its structure parameters, i.e. hidden node biases and output weights, optimized self-sufficiently. On the other hand, the AT can alter the data structure of the experiment data, which will enhance the generalization capability for SaE-ELM as well as other machine learning algorithms. Thus, the combination of SaEELM and AT can complement each other and improve the diagnosis accuracy from the aspect of both algorithm and data structure. The performances of the proposed approach are compared with that derived from ANN, SVM, and ELM methods, respectively. Experimental results with both published and power utility provided data indicate that the developed approach can significantly improve the accuracies for power transformer fault diagnosis. [ABSTRACT FROM PUBLISHER]

In this paper, we report a novel chaotic snap oscillator with one nonlinear function. Dynamic analysis of the system shows the existence of bistability. To study the time delay effects on the proposed snap oscillator, we introduce multiple time delay in the fourth state equation. Investigation of dynamical properties of the time-delayed system shows that the snap oscillator exhibits the same multistable properties as the nondelayed system. The new multistable hyperjerk chaotic system has been tested in chaos shift keying and symmetric choc shift keying modulated communication designs for engineering applications. It has been determined that the symmetric chaos shift keying modulated communication system implemented with the new chaotic system is more successful than the chaos shift keying modulation for secure communication. Also, circuit implementation of the chaotic snap oscillator with tangent function is carried out showing its feasibility. [ABSTRACT FROM AUTHOR]

Ground subsidence disasters are characterized by wide distribution, long duration, and high-intensity damage, which can cause serious damages to surface buildings, underground pipelines, aquifers, and so on. Therefore, research on the stability evaluation of ground subsidence and subsidence deformation prediction is of great significance. This paper takes ground subsidence in Fushun City, Liaoning Province, China, as a case study. Combined with data from 60 monitoring points in the subsidence areas, the final settlement deformation values of all monitoring points were obtained through an arctangent function model using non-linear curve fitting with monitoring data. The proposed model could enable the prediction of settlement deformation trends of the monitoring points. Correlation coefficients are all above 0.937, indicating the strong reliability of the prediction model. By processing the final settlement deformation predictive values of the 60 monitoring points, a final settlement contour map was drawn with the help of the Kriging interpolation method. This map could forecast the whole distribution characteristics of ground settlement deformation in the research area. Then, risk zoning can be obtained by combining the settlement rate and residual settlement deformation in the study area. The research results could provide a basis for future city construction and regional planning in Fushun City. [ABSTRACT FROM AUTHOR]

The aim of this paper is to present new, simple and suffciently sharp bounds for arcsine and arctangent functions. Some of the bounds are computationally effcient while others are effcient to approximate the integrals ... dx and ... As a matter of interest, several other sharp and generalized inequalities for arcsin and arctan are also established which are effcient to give some known and other trigonometric inequalities. [ABSTRACT FROM AUTHOR]

Formulas of a homogeneous polyhedron's gravitational potential typically include two arctangent terms for every edge of every face and a special term to eliminate a possible facial singularity. However, the arctangent and singularity terms are equivalent to the face's solid angle viewed from the field point. A face's solid angle can be evaluated with a single arctangent, saving computation. [ABSTRACT FROM AUTHOR]

This paper presents an improved VLSI (Very Large Scale of Integration) architecture for real-time and high-accuracy computation of trigonometric functions with fixed-point arithmetic, particularly arctangent using CORDIC (Coordinate Rotation Digital Computer) and fast magnitude estimation. The standard CORDIC implementation suffers of a loss of accuracy when the magnitude of the input vector becomes small. Using a fast magnitude estimator before running the standard algorithm, a pre-processing magnification is implemented, shifting the input coordinates by a proper factor. The entire architecture does not use a multiplier, it uses only shift and add primitives as the original CORDIC, and it does not change the data path precision of the CORDIC core. A bit-true case study is presented showing a reduction of the maximum phase error from 414 LSB (angle error of 0.6355 rad) to 4 LSB (angle error of 0.0061 rad), with small overheads of complexity and speed. Implementation of the new architecture in 0.18 µm CMOS technology allows for real-time and low-power processing of CORDIC and arctangent, which are key functions in many embedded DSP systems. The proposed macrocell has been verified by integration in a system-on-chip, called SENSASIP (Sensor Application Specific Instruction-set Processor), for position sensor signal processing in automotive measurement applications. [ABSTRACT FROM AUTHOR]

This paper presents a new family of parametric Lorenz curves based on the arctan function and adding a parameter $$-\infty <\alpha <\infty $$ , $$\alpha \ne 0$$ to an initial Lorenz curve $$L_0(p),\,0\le p\le 1$$ . The particular case obtained when $$\alpha $$ tends to zero is reduced to the initial Lorenz curve $$L_0(p)$$ . The corresponding distribution functions are shown. Some inequality measures are calculated, and a method to compute the Gini index based on the use of the inverse of the Lorenz curve is proposed. Finally, an application to two well-known data sets is presented and a good fit is obtained. [ABSTRACT FROM AUTHOR]

In this paper, a simple end face type magnetic encoder has been designed. This paper analyzed the negative effect caused by the calculation method based on the arctangent arithmetic. In addition, the negative effects caused by mechanical installation are illustrated in this paper. In order to solve these problems, a angle error compensation tabulation method has been proposed, and cross-intervals linear interpolation method has been presented to eliminate the noise signal in angle compensation table. The validity of the method proposed in this paper has been verified by experimental and simulation results. The precision of this kind of magnetic encoder could reach 0.02°. [ABSTRACT FROM AUTHOR]

The sub-pixel edge detection method is widely applied in image processing to improve accuracy of measurement and recognition. Detection methods often encounter difficulties with low computational efficiency or poor robustness. To address such difficulties, a new least-squared-error-based method is proposed in this paper. First, a one-dimensional solution is derived by means of an arctangent edge model. In the two-dimensional situation, the Sobel operator and the cubic surface fitting method are used to determine the normal direction of edge. Then, two-dimensional edge detection can be transformed into a one-dimensional problem that can be solved with a one-dimensional solution. Because there is no complicated surface fitting in this least-squared-error-based method, it will provide an opportunity to ascertain quickly the accurate location of an edge. The experiment is described at the end of the paper, comparing three edge detection methods. The results indicate that the new detection approach has robustness equal to the traditional least-squared-error-based methods, while run time is much faster and very close to the moment-based methods. The above advantages indicate this approach is very suitable for on-line accurate detection. [ABSTRACT FROM AUTHOR]

This paper presents a novel phase-shift arctangent (PSA) interpolation method to improve the measurement accuracy of a planar capacitive incremental displacement sensor. Signals of planar capacitive micro-sensors acquire waveform errors, including sensitivity differences and phase-shift errors, because of static errors and dynamic disturbances. In the proposed PSA scheme, such errors are removed completely by loading a particular arctangent function. Moreover, measuring efficiency of the proposed planar capacitive sensors is improved by combining coarse measurement and fine estimation. Experiments show unanimous results to model-based fitting. When electrode length is four times the gap distance, applying the PSA interpolation method decreases waveform errors from more than 4% to 1.72%. [ABSTRACT FROM AUTHOR]

In this paper, a novel maximum power point tracking (MPPT) algorithm based on introducing a complex function for photovoltaic (PV) systems is proposed. This function is used for determination of the duty cycle of the dc–dc converter in PV systems to track the MPP in any environment and load condition. It has been suggested based on analyzing the expected behavior of converter controller. The function is formed by a two-dimensional Gaussian function and an Arctangent function. It has been shown that contrary to many algorithms that produce wrong duty cycles in abrupt irradiance changes, the proposed algorithm is able to behave correctly in these situations. In order to evaluate the performance of method, various simulations and experimental tests have been carried out. The method has been compared with some major MPPT techniques with regard to start-up, steady-state, and dynamic performance. The results reveal that the proposed method can effectively improve the dynamic performance and steady-state performance simultaneously. [ABSTRACT FROM PUBLISHER]

A new physically based model for the simulation of the imaginary part of the shear modulus-temperature (G"-T) curve of thermosets is introduced in this paper. The model is based on the modification of the G"-T equation used for thermoplastic polymers via the introduction of two new formulations regarding the calculation of the configuration probability and the velocity matrix of the examined thermosets. The formulations for the calculation of the probability of configuration and the velocity matrix of the polymer chain were modified according to the cross-linking structure of thermosets. In addition, an arctangent function is proposed to consider the effect of temperature on the mean square separation of the ends of the sub-molecules. All the parameters necessary to calibrate the model can be either estimated or experimentally derived using low-frequency dynamic mechanical analysis. The newly introduced model is based on a sound physical background, and can be used for the investigation of the effect of the molecular structure of thermosets on their loss modulus and their glass transition temperature. [ABSTRACT FROM AUTHOR]

Many special functions and analytic constants allow for a probabilistic representation in terms of inverse moments of [0, 1]-valued random variables. Under this assumption, we give fast computations of them with an explicit upper bound for the remainder term. One of the main features of the method is that the coefficients of the main term of the approximation always contain negative binomial probabilities which, in turn, can be precomputed and stored. Applications to the arctangent function, Dirichlet functions and their nth derivatives, and the Catalan, Gompertz, and Stieltjes constants are provided. [ABSTRACT FROM AUTHOR]

The maximum signal handling capability (MSHC) is an important parameter for the fiber optic interferometric sensor (FOIS) system. It is restricted by the heterodyne frequency (HF) and the digital quadrature demodulation algorithm (DQDA) in the digital heterodyne demodulation scheme. In this paper we systematically investigate the MSHC of the FOIS based on the digital heterodyne demodulation scheme through comparison of the HF-determined MSHC and DQDA-determined MSHC. When discussing the DQDA-determined MSHC, two widely used methods are included, which are arctangent and differential-cross multiply (DCM). The comparison results reveal that the arctangent-determined MSHC is 12 dB larger than the DCM-determined MSHC. The HF-determined MSHC is between the two types of DQDA-determined MSHC. If the DQDA is arctangent, the MSHC of the system is the HF-determined MSHC. If the DQDA is DCM, the MSHC of the system is the DCM-determined MSHC. Experiments are carried out and the results are consistent with the theoretical analysis. The conclusion in this paper can help us to estimate the MSHC of the FOIS system based on the digital heterodyne demodulation scheme more accurately and provide a useful guideline for the design of the FOIS system with large demodulation dynamic scale. [ABSTRACT FROM AUTHOR]

In this paper, we study the representation of π as sum of arctangents. In particular, we highlight the role of linear recurrent sequences obtaining new identities. Moreover, we provide a method in order to express π as sum of arctangents involving the Golden mean, the Lucas numbers, and more in general any quadratic irrationality. [ABSTRACT FROM AUTHOR]

In this paper, a refinement of the Becker-Stark inequalities is established and a simple proof of this new inequality is given. [ABSTRACT FROM AUTHOR]

We give some sharper refinements and generalizations of inequalities related to Shafer’s inequality for the arctangent function, stated in Theorems  1, 2,  and  4 in Mortici and Srivastava, 2014, by C. Mortici and H.M. Srivastava. [ABSTRACT FROM AUTHOR]

Abstract While monitoring large-scale scenes, visual surveillance systems are often confronted with a dilemma between obtaining efficient coverage of the scene and getting sufficient resolution of the targets of interest. To alleviate the contradiction, a solution based on binocular cameras has been proposed. In the solution, an active pan–tilt–zoom (PTZ) camera and a fixed camera operate in a collaborative way by dynamically aligning their fields of view. However, due to the asymmetric camera distribution structure and fast-changing scenario, the accurate alignment is yet challenging. In this paper, a novel view aligning method is presented which introduces three reasonable and mild simplifications to transform the complex view aligning problem into a simple arctangent control function. These simplifications not only relax the restrictions of target depth and the intrinsic parameters of PTZ camera, but also constrain the relative external parameters with a coaxial structure. Meanwhile, a corresponding calibration method is designed to estimate the model parameters off-line. The proposed method was tested in comprehensive cases with relatively close target, wide-range scene and altitude variation. Both the simulation and real scene experiments demonstrate that our method outperforms other state-of-the-art methods on accuracy and effectiveness for active target tracking tasks. Highlights • We propose three simplifications which transform the complex view aligning problem into a simple arctangent control function. All the simplifications are mathematically proved through theoretical analysis. The proposed arctangent control function has better performance in some extreme cases with relatively closer targets, wide-range scene and target altitude variation. • Through the simplifications, the proposed method is not affected by the dynamic changes of the intrinsic parameters of PTZ camera when turning and zooming. So the PTZ camera can adjust its zoom ratio in real time. • A coaxial structural constraint is proposed to constrain the relative external parameters. One advantage is that we do not need to recalibrate the system when changing the monitoring scene or installation location. • The proposed method is applicable to a large variety of scenes, due to the utilization of the structural constraint instead of the scene background, vanishing points or ground plane assumption. [ABSTRACT FROM AUTHOR]

We present a new formula for pi involving nested radicals with rapid convergence. This formula is based on the arctangent function identity with argument x=2-ak-1/ak, where ak=2+2+2+⋯+2⏟ksquarerootsis a nested radical consisting of k square roots. The computational test we performed reveals that the proposed formula for pi provides a significant improvement in accuracy as the integer k increases. [ABSTRACT FROM AUTHOR]

Based on the geometry of a radial function, a sequence of approximations for arcsine, arccosine and arctangent are detailed. The approximations for arcsine and arccosine are sharp at the points zero and one. Convergence of the approximations is proved and the convergence is significantly better than Taylor series approximations for arguments approaching one. The established approximations can be utilized as the basis for Newton-Raphson iteration and analytical approximations, of modest complexity, and with relative error bounds of the order of 10 − 16 , and lower, can be defined. Applications of the approximations include: first, upper and lower bounded functions, of arbitrary accuracy, for arcsine, arccosine and arctangent. Second, approximations with significantly higher accuracy based on the upper or lower bounded approximations. Third, approximations for the square of arcsine with better convergence than well established series for this function. Fourth, approximations to arccosine and arcsine, to even order powers, with relative errors that are significantly lower than published approximations. Fifth, approximations for the inverse tangent integral function and several unknown integrals. [ABSTRACT FROM AUTHOR]

We establish an inequality by quadratic estimations; the double inequality holds for $x>0$ , where the constants $(\pi^{2} -4)^{2}$ and 32 are the best possible. [ABSTRACT FROM AUTHOR]

Extinction coefficient is the base parameter of visibility measurement, its measurement error determines the accuracy of the visibility meter. In the paper, the error sources are analyzed, and a new optical structure is proposed by adding the optical compensator. For the new structure, the measurement model based on boundary constraints is provided to reduce measure errors. Based on the new model, use an improved algorithm to solve the error convergence problem. The new algorithm use exponent arctangent function as base function, three parameters i, j and k control the contour of the function. With simulation tool, the optimization values are obtained. The experimental results show that the extinction coefficient relative error is reduced by 18% in the entire measurement region, the fluctuations of the relative error is reduced to 7.3%. [ABSTRACT FROM AUTHOR]

In an almost unreferenced article, Fitzhugh Carmichael (1928), writing of the period around the First World War, noted that “during the past twelve years many economic series have undergone what appears to be a permanent change in level.” These are prescient words that are widely applicable today. Carmichael noted that the then-standard practice of linear detrending was inappropriate in the presence of what we would now call “structural breaks”; as a result he proposed a method that would not only model a nonlinear trend, but would be suitable for situations where the transition from one regime to another was smooth. This study establishes the precedence of Carmichael’s ideas, re-examines his methods, and solves the problems that he thought would hinder wider applications of his approach, which has since become a central part of contemporary nonlinear econometric methods and for which Carmichael should be given credit. [ABSTRACT FROM PUBLISHER]

As one of the state-of-the-art grid voltage synchronization techniques, Quasi-type-1 structure based phase locked loop (QT1-PLL) achieves an excellent detection performance when only odd-order harmonics needs to be eliminated by Moving average filter (MAF). Nonetheless, when it is necessary for MAF to eliminate the fundamental negative sequence component, more delay will be introduced to the PLL, reducing its stability. The transient response speed of QT1-PLL needs to be reduced to ensure stability, which may be unacceptable for grid-connected power converters. To deal with this situation, this paper proposes a cascaded filtering stage with small delay. The suggested filtering stage is composed of second-order lead compensator, notch filter, first-order lead compensator and MAF, which is integrated in QT1-PLL. Compared with the traditional QT1-PLL, the proposed PLL has faster transient response speed and higher detection accuracy. The simulation and experimental results verify the effectiveness of the suggested filtering stage.

The behavior of nonlinear dissipative 2-DOF mechanical systems in the vicinity of resonance is studied in this paper. Namely, the free resonance vibrations of a spring–mass–pendulum system and the forced resonance vibrations of a 2-DOF dissipative system containing a nonlinear absorber are considered. A reduced system stated with respect to the system energy, the arctangent of the vibration amplitudes ratio, and the phase difference, is obtained and analyzed. The nonlinear normal mode approach is used in this analysis. Conditions for vibration energy localization are discussed. [ABSTRACT FROM AUTHOR]

Abstract: Complex-valued sparse reconstruction is conventionally solved by transforming it into real-valued problems. However, this method might not work efficiently and correctly, especially when the size of the problem is large, or the mutual coherence is high. In this paper, we present a novel algorithm called the arctangent regularization (ATANR), which can handle the complex-valued problems of large size and high mutual coherence directly. The ATANR is implemented with the iterative least squares (IRLS) framework, and accelerated by the dimension reduction and active set selection steps. Further, we summarize and analyze the common properties of a penalty kernel which is suitable for sparse reconstruction. The analyses show that the key difference, between the arctangent kernel and the ℓ1 norm, is that the first order derivative of ATANR is close to zero for a nonzero variable. This will make ATANR less sensitive to the regularization parameter λ than ℓ1 regularization methods. Finally, lots of numerical experiments validate that ATANR usually has better performance than the conventional ℓ1 regularization methods, not only for the random signs ensemble, but also for the sensing matrix with high mutual coherence, such as the resolution enhancement case. [Copyright &y& Elsevier]

Abstract: An arctangent (AT) based adaptive algorithm for a first-order complex adaptive IIR notch filter (CANF) is proposed in this paper. The objective of this work is to overcome some drawbacks including slow convergence speed and high sensitivity to impulsive noise of the previous gradient and nongradient based adaptive algorithms. The proposed AT algorithm employs the ratio of output to regressor signal as an error criterion where the arctangent value of such a ratio is employed to adjust the filter parameter. It is found that the proposed algorithm provides not only high speed convergence but also high impulsive noise robustness. Moreover, very low bias of the frequency estimate is also obtained. In addition, difference equation for the convergence in the mean and coarse stability bound in mean sense are derived. Computer simulations are conducted to show the performance of the proposed AT algorithm. [Copyright &y& Elsevier]

Abstract: This paper proposes a relatively simple yet highly effective thresholding method based on the template matching idea. A reference template is first produced by sampling edge pixels of an input gray level image. A series of input patterns are sequentially obtained by extracting the boundaries of objects in the binary version of gray level image, where the binary images are sequentially generated by thresholding the input gray level image with each possible gray level from 0 to 255. A newly proposed arctangent Hausdorff distance (AHD) measure is applied to estimate an input pattern E opt that is most similar to the reference template. The binary image corresponding to the input pattern E opt is then regarded as the final thresholding result. Experimental results show that the segmentation quality of the proposed approach surpasses 11 existing thresholding methods. [Copyright &y& Elsevier]

In this paper, we investigate the monotonicity of the functions

In this paper, a new class of the continuous distributions is established via compounding the arctangent function with a generalized log-logistic class of distributions. Some structural properties of the suggested model such as distribution function, hazard function, quantile function, asymptotics and a useful expansion for the new class are given in a general setting. Two special cases of this new class are considered by employing Weibull and normal distributions as the parent distribution. Further, we derive a survival regression model based on a sub-model with Weibull parent distribution and then estimate the parameters of the proposed regression model making use of Bayesian and frequentist approaches. We consider seven loss functions, namely the squared error, modified squared error, weighted squared error, K-loss, linear exponential, general entropy, and precautionary loss functions for Bayesian discussion. Bayesian numerical results include a Bayes estimator, associated posterior risk, credible and highest posterior density intervals are provided. In order to explore the consistency property of the maximum likelihood estimators, a simulation study is presented via Monte Carlo procedure. The parameters of two sub-models are estimated with maximum likelihood and the usefulness of these sub-models and a proposed survival regression model is examined by means of three real datasets.

The number of phase wraps in an image can be either reduced, or completely eliminated, by transforming the image into the frequency domain using a Fourier transform, and then shifting the spectrum towards the origin. After this, the spectrum is transformed back to the spatial domain using the inverse Fourier transform and finally the phase is extracted using the arctangent function. However, it is a common concern that the spectrum can be shifted only by an integer number, meaning that the phase wrap reduction is often not optimal. In this paper we propose an algorithm than enables the spectrum to be frequency shifted by a rational number. The principle of the proposed method is confirmed both by using an initial computer simulation and is subsequently validated experimentally on real fringe patterns. The technique may offer in some cases the prospects of removing the necessity for a phase unwrapping process altogether and/or speeding up the phase unwrapping process. This may be beneficial in terms of potential increases in signal recovery robustness and also for use in time-critical applications. [ABSTRACT FROM AUTHOR]

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For a time-homogenous one-dimensional diffusion processX(t), we investigate the distribution of the first instant, after a given timer, at whichX(t) exceeds its maximum in the interval [0,r], generalizing a result of Papanicolaou, holding for Brownian motion. [ABSTRACT FROM PUBLISHER]

We propose a new model of gravity containing Arctan function in the Lagrangian. We show here that this model satisfies fifth force constraint unlike a similar model in 2013 by Kruglov. In addition to this, we carry out the fixed point analysis as well as comment on the existence of curvature singularity in this model. The cosmological evolution for this gravity model is also analyzed in the Friedmann-Robertson-Walker (FRW) background. To understand observational significance of the model, cosmological parameters are obtained numerically and compared with those of Lambda cold dark matter (CDM) model. We also scrutinize the model with supernova data. We apply diagnostic given by Sahni et al. in 2008 to the model. Using this diagnostic, we detect the distinction between cosmic evolution caused by the model and CDM. We find best-fit parameter values of the model using baryon acoustic oscillations data. [ABSTRACT FROM AUTHOR]

ABSTRACT Using seismic attributes such as coherence and curvature to characterise faults not only can improve the efficiency of seismic interpretation but also can expand the capability to detect faults. The coherence and curvature have been widely applied to characterising faults for years. These two methods detect faults based on the similarity of seismic waveforms and shapes of the reflectors, respectively, and they are complementary to each other and both have advantages and disadvantages in fault characterisation. A recent development in fault characterisation based on reflector shapes has been the use of the rate of change of curvature. Through an application to the seismic data from Western Tazhong of the Tarim Basin, China, it was demonstrated that the rate of change of curvature is more capable of detecting subtle faults having quite small throws and heaves. However, there often exist multiple extreme values indicating the same fault when applying the rate of change of curvature, which significantly degrades the signal-to-noise ratio of the computation result for multiple extrema interfering with each other. To resolve this problem, we propose the use of a linear combination of arctangent and proportional functions as the directrix of a cylindrical surface to fit the fault model and calculate its third derivative, which can then be used to characterise the fault. Through an application to the 3D seismic data from Western Tazhong of the Tarim Basin, the results show that the proposed method not only retains the same capability to detect subtle faults having small throws as the curvature change rate but also greatly improves the signal-to-noise ratio of the calculated result. [ABSTRACT FROM AUTHOR]

We improved classic retinal modeling to alleviate the adverse effect of complex illumination on face recognition and extracted robust image features. Our improvements on classic retinal modeling included three aspects. First, a combined filtering scheme was applied to simulate functions of horizontal and amacrine cells for accurate local illumination estimation. Second, we developed an optimal threshold method for illumination classification. Finally, we proposed an adaptive factor acquisition model based on the arctangent function. Experimental results on the combined Yale B; the Carnegie Mellon University poses, illumination, and expression; and the Labeled Face Parts in the Wild databases show that the proposed method can effectively alleviate illumination difference of images under complex illumination conditions, which is helpful for improving the accuracy of face recognition and that of facial feature point detection. ©2016SPIE and IS&T[DOI: 10.1117/1.JEI.25.4.043028] [ABSTRACT FROM AUTHOR]

This work presents a wireless system that operates in the 2.4 GHz ISM band for concurrently sensing the vital signs and positions of multiple individuals. Characterized by low complexity and high accuracy, the proposed system consists of two main parts. One is a self-injection-locked (SIL) tag carried by a subject, which emits a sinusoidal frequency-modulated (SFM) signal with vital sign information. The other is a group of injection-locked (IL) I/Q receivers, which performs arctangent demodulation of the SFM signal to obtain the position information without using RF reference signals, and simultaneously extracts the vital sign information of the subject. In the experiment, the system is capable of sensing multiple individuals based on frequency division multiple access (FDMA) technique. Moreover, fidgeting effect on the detection of vital signs has been greatly reduced by a spectral product approach. Accordingly, it is demonstrated that the experimental prototype provides accurate information about the vital signs and positions of different individuals in an indoor environment. [ABSTRACT FROM AUTHOR]

A simulation program with integrated circuit emphasis (SPICE) circuit model of voltage excitation fluxgate was proposed. It used the arctangent function to describe the hysteresis loop of fluxgate core, the excitation and measurement coils of the fluxgate were equivalent to a circuit model that contains a kind of non‐linear time‐varying inductance. Moreover, the expression of non‐linear time‐varying inductance has been given, which resolved fluxgate modelling itself into solving non‐homogeneous ordinary differential equations with variable coefficient, and then the authors used HSPICE to solve the differential equations. The input and output characteristics of the dual‐core fluxgate were simulated by this SPICE model. The results show that the model can better simulate the input and output characteristics of actual fluxgate, which verifies the validity of the model. [ABSTRACT FROM AUTHOR]

The article presents a new family of disparity measures based on the trigonometric tan−1 function. A subset of members from the proposed disparity family are shown to have excellent robustness properties against both inliers and outliers and are competitive with other popular disparities such as the Hellinger distance and the symmetric chi‐square. The most notable thing about the presented disparity is that the strong robustness properties of the corresponding minimum distance estimators are attained in spite of predictions to the contrary by not just the first order influence function but also the second order influence function. This demonstrates the limitation of even the second order influence analysis in predicting the robustness properties of a disparity. Several examples and numerical studies illustrate the aforementioned property. Copyright © 2018 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]