Power Sine Research Articles

A novel asymmetric extension of power XLindley distribution: properties, inference and applications to engineering data

It is impossible to overstate the importance of using trigonometric functions appropriately in distribution theory. The main contribution of the research is to construct a flexible trigonometric extension of the power XLindley distribution. More specifically, we build an innovative two-parameter lifetime distribution known as the sine power XLindley distribution (SPXLD) using characteristics from the sine-generated family of distributions. As the main motivational fact, it provides an attractive alternative to the power Lindley, power XLindley, weighted Lindley, and extended power Lindley distributions; it may be better able to model lifetime phenomena presenting data of leptokurtic and platkurtic nature. In contrast to the increasing, decreasing, and reversed-j-shaped hazard rate function, the density exhibits asymmetric shapes with varying peakedness levels. Several significant characteristics are illustrated, including moments, the quantile function, the probability density function in series representation, the stress-strength reliability, and incomplete moments. To analyze the behavior of the suggested distribution, sixteen estimation techniques are applied, such as the maximum likelihood, percentiles, some methods of minimum distances, some methods based on minimum and maximum spacing distances, and the Kolmogorov method. After that, an extensive simulation study and the examination of two survival real datasets are used to show the viability, usefulness, and adaptability of the SPXLD. Relevant goodness of fit criteria demonstrates that the SPXLD fits several current distributions.

Color image encryption scheme combining cross-plane Zigzag scrambling and pseudo-random combination RGB component diffusion

At present, the frequency of image transmission in the network has increased many times compared with previous years, and the proportion of color images is the largest. This means that a powerful technology is needed to prevent color images from being stolen to ensure the security of transmission. The excellent characteristics of chaotic cryptography are favored by many scholars. Researchers have designed a series of color image encryption algorithms using this technology. Because of the large number of pixels in the three planes of the color image, some encryption algorithms are guaranteed in security, but the encryption efficiency is often not ideal. In order to avoid this defect as much as possible, this paper develops a new color image encryption scheme on the basis of ensuring the security of the image. First, a cross plane zigzag scrambling process is proposed, which solves the shortage of three planes scrambling separately. Secondly, the rules of pseudo-random combination of three plane pixel values are designed to improve the efficiency and unpredictability of encryption. In addition, the chaotic source selected in this paper is a new one-dimensional sine power parameter map (1D-SPPM). Experiments show that this scheme can resist classical attack types, and compared with some existing schemes, its efficiency and security are guaranteed.

Radiating power tracking based on fractional order sliding mode controller

The radiating power with sine waveform is required for modulated infrared thermography nondestructive testing. Sine voltage was applied by former authors for deriving sine power waveform. The theory mode of infrared lamp is proposed. According to numerical solution and FFT analysis, high frequency components are included in the radiating power waveform, when sine voltage is set to drive the lamp. A light intensity sensor was utilized for monitoring the real-time radiating power, and a close-loop power tracking system was constructed. Fractional order sliding mode controller was selected in the tracking system, for its robustness and flexibility property. The reachability of the controller is proved and the calculation formulas of reach time are given. In experiment, the tracking results with both PID and sliding mode controller were derived. Lower tracking overshoot and better robustness was derived through the sliding mode controller, compared with the PID counterpart.

Sine Power Lindley Distribution with Applications

Sine power Lindley distribution (SPLi), a new distribution with two parameters that extends the Lindley model, is introduced and studied in this paper. The SPLi distribution is more flexible than the power Lindley distribution, and we show that in the application part. The statistical properties of the proposed distribution are calculated, including the quantile function, moments, moment generating function, upper incomplete moment, and lower incomplete moment. Meanwhile, some numerical values of the mean, variance, skewness, and kurtosis of the SPLi distribution are obtained. Besides, the SPLi distribution is evaluated by different measures of entropy such as Rényi entropy, Havrda and Charvat entropy, Arimoto entropy, Arimoto entropy, and Tsallis entropy. Moreover, the maximum likelihood method is exploited to estimate the parameters of the SPLi distribution. The applications of the SPLi distribution to two real data sets illustrate the flexibility of the SPLi distribution, and the superiority of the SPLi distribution over some well-known distributions, including the alpha power transformed Lindley, power Lindley, extended Lindley, Lindley, and inverse Lindley distributions.

On the Accuracy of the Sine Power Lomax Model for Data Fitting

Every day, new data must be analysed as well as possible in all areas of applied science, which requires the development of attractive statistical models, that is to say adapted to the context, easy to use and efficient. In this article, we innovate in this direction by proposing a new statistical model based on the functionalities of the sinusoidal transformation and power Lomax distribution. We thus introduce a new three-parameter survival distribution called sine power Lomax distribution. In a first approach, we present it theoretically and provide some of its significant properties. Then the practicality, utility and flexibility of the sine power Lomax model are demonstrated through a comprehensive simulation study, and the analysis of nine real datasets mainly from medicine and engineering. Based on relevant goodness of fit criteria, it is shown that the sine power Lomax model has a better fit to some of the existing Lomax-like distributions.

Thermomechanical properties and fatigue life evaluation of SnAgCu solder joints for microelectronic power module application

In this paper, a new constitutive model of SnAgCu lead-free solder, which covered the low-temperature and elevated-temperature creep properties, was constructed according to the thermomechanical property test under a wide range of temperatures (−40 to 120°C). This model was then implemented to the finite element model for simulation of the cyclic creep deformation of Sn3Ag0.5Cu solder in a chip inside the microelectronic power module (MPM). The accumulated creep strain of the solder layer was calculated and used to predict the thermo-mechanical fatigue life of the MPM. The applicability of the life prediction method was evaluated through a cross-check of the present results with that obtained by a double power model in the literature, as well as the thermo-mechanical fatigue test results. It was found that the thermo-mechanical fatigue lives, estimated by the accumulated creep strain and creep strain energy density from the established hyperbolic sine power law, are closer to the test results than that estimated by the double power law. The presented model can be seen as an improvement on the existing constitutive models of SnAgCu lead-free solder.

A 140–220-GHz Balanced Doubler With 8.7%–12.7% Efficiency

In this letter, a 140–220-GHz balanced doubler with high efficiency is presented. To implement the proposed doubler, a taper-type balun is introduced based on a metal ridge, which features an exponential and $n$ -order sine power fitting function. Such a ridge with a slot feeds the input signal to the T-type diodes with the equal magnitude and reverse phase. Then, the second harmonic can be extracted by the metal fin-line transition. To ensure the second harmonic transmitting to the output port, an air bridge across the ridge is utilized, which is close to the diodes with a quarter-wavelength ( $\lambda $ /4) of the center operated frequency $f_{c}$ . Comparing to conventional doublers, the proposed design without substrate eliminates the dielectric loss and substrate parasitic for the enhanced efficiency with an extended bandwidth. To verify the above-mentioned mechanisms, a wideband doubler is fabricated and measured, which exhibits a good efficiency from 8.7% to 12.7% at 140–220 GHz.

Quick Performance Assessment of Improved Nyquist Pulses

An explanation is proposed for the improved behavior of the improved Nyquist pulses with an asymptotic decay rate of t-2 when sampled with a timing offset. Three figures of merit that indicate the energy distribution into the sidelobes of the time response and allow a quick assessment of their performance in terms of error probability when the impulse response is sampled with a timing error have been proposed and verified on several improved Nyquist pulses reported in the literature. In order to check the validity of the proposed figures of merit a novel family of Nyquist pulses denoted as power sine was introduced. Using the proposed approach the design process was expedited as the volume of necessary calculations was significantly decreased. To explain the difference in close pulse performance a figure of merit based on limited ISI distortion was introduced.

Study of a high power sine waveguide traveling wave tube amplifier centered at 8 GHz

Performance of a 20-stage X-band sine waveguide amplifier, driven by a 40 A, 100 kV, cylindrical electron beam, is studied using numerical simulation and interpreted using Pierce's classical traveling wave tube theory. For an input signal power level of 1.8 kW, particle-in-cell simulations predict gain and bandwidth values exceeding 14 dB and 13%, respectively. For an input signal power level of 7.2 kW, particle-in-cell simulations predict gain and bandwidth values exceeding 12 dB and 15%, respectively, with output power levels exceeding 110 kW at peak gain. Also given are: an assessment of the space charge factor (Pierce's QC parameter) for the complex circuit using simulation data, and an evaluation of the harmonic contents in the beam current.

Simplified adaptive volume scattering model and scattering analysis of crops over agricultural fields using the RADARSAT-2 polarimetric synthetic aperture radar imagery

A simplified adaptive volume scattering model (SAVSM) for RADARSAT-2 polarimetric synthetic aperture radar (PolSAR), based on the n ’th power sine and cosine functions, is developed to characterize the changes in crop phenology within the growing season. A three-component model-based decomposition (TCMD) with SAVSM is also implemented with the non-negative eigenvalue decomposition. Multitemporal RADARSAT-2 data acquired in southwestern Ontario, Canada, are used for validating the proposed TCMD-SAVSM. The TCMD-SAVSM is first compared with the adaptive model-based decomposition proposed by Arii et al. in which ∇ f v is set to 0.01, demonstrating that TCMD-SAVSM not only consumes much less computing time but also the decomposed surface and double-bounce components are also more representative of the land cover reality. Using the percentage of power of the remainder matrix 0.001 as the evaluation criterion, the SAVSM achieved the best performance in corn, soybean and wheat fields compared with other popular volume scattering models (VSMs), with the highest mean and lowest standard deviation. It suggests that the SAVSM is a suitable VSM for describing seasonal changes of crop fields. Last, the decomposed surface, double-bounce and volume scattering components of wheat, soybean and corn at various growth stages are analyzed at the individual crop level, and the results demonstrate that their variations are in concert with the crop’s phenological development.

Rate controlling mechanisms during hot deformation of Mg–3Gd–1Zn magnesium alloy: Dislocation glide and climb, dynamic recrystallization, and mechanical twinning

The flow behavior of the Mg–3Gd–1Zn (GZ31) magnesium alloy during hot working was critically analyzed and dislocation glide in the form of a viscous drag process (viscous glide) was identified as the rate controlling mechanism due to interaction of rare earth Gd atoms with the moving dislocations. Mechanical twinning was shown to significantly affect the level of flow stress at high Zener–Hollomon parameters, i.e. low forming temperatures and high strain rates. Moreover, dynamic recrystallization (DRX) was found to be another responsible phenomenon for deviation of constitutive equations from the theoretical ones, namely the deformation activation energy based on diffusivity and the pre-defined Garofalo’s type hyperbolic sine power, during high-temperature thermomechanical processing of this creep resistant light alloy.

Modulated fiber laser welding of high reflective AZ31

Power sine modulation fiber laser welding (FLW) of AZ31 magnesium alloy was conducted. When the diameter of transmission fiber and focal spot was 400 μm and 0.4 mm, respectively, the average laser powers for penetrating a 2.7-mm-thick AZ31 plate at a welding speed of 5 m/min were reduced by about 33 % by using modulated FLW. The relationship between modulation parameters (i.e., amplitude, frequency, and average laser power) and weld depth which was closely related to the transfer efficiency of laser energy was studied through partial penetration laser welding test on 8-mm-thick AZ31 plate based on quadratic regression orthogonal design. It was found that influence of power modulation on laser welding of AZ31 alloy was highly dependent on laser power density. In the low power density range, laser energy coupling efficiency could be significantly improved by combining low amplitude with high frequency or high amplitude with low frequency. With the increasing of laser power density, the optimum frequency corresponding to maximum weld depth decreased, and the positive effect of the favorable combination of high amplitude and low frequency on laser energy coupling continuously weakened. When laser power density was high enough, power modulation had hardly positive effect on weld depth and energy coupling efficiency. It was argued that improvement of energy coupling efficiency in laser welding of AZ31 by using power modulation was due to the reduction in the portion of energy lost into surroundings. Finally, laser butt welding was conducted on 2.7-mm-thick AZ31 under the condition of high beam quality and the tensile strength of both butt-welded joint and base metal that was tested.

Research on the Method of CPM Signal Phase Smoothing Based on Different Power Sine Function

Continuous phase modulation (CPM) signal has the advantages of high bandwidth efficiency, continuous phase, faster decay speed of power spectrum, constant envelope and so on, which is widely used in communication systems. The degree of the phase smoothing is one of main factors that affect the decay speed of CPM signal power spectrum. One method of smoothing CPM signal phase based on different power sine function as the frequency modulation function is proposed. We draw the phase trajectory of baseband signal and the normalized power spectrum by using the MATLAB software. The spectrum characteristics of the signal generated have great improvement compared with MSK signal, which reach the desired goal.

Design of Dual High Precision Power Signal Generator Based on AD9854

To obtain the dual high-precision numerical control signal source, and could be accurately adjusted the dual signals frequency and phase and increase the output signal power, the paper presented a method based on direct digital synthesis technology and parallel push-pull output, designed and implemented the dual channel high-precision and high power signal generator. MSP430 controlled AD9854 registers to realize frequency and phase modulation, after low-pass filter to adjust the square wave duty cycle by the DAC7612, amplitude was integrated optimization adjustment by AD9854 AD603 and power amplifier. Consideration the anti-jamming measures, the system is stable and reliable, and can output high-precision and high power sine and square wave in the 5-150kHz frequency band, signal frequency, phase, amplitude and duty cycle can numerical control. In addition, it has sweep output mode.

An Active Sensing Principle for Haptic Interaction With Dynamical Systems

What is it inside the colorfully wrapped present? You pick it up to ear level and listen, shake it, and then listen again. To you, the basic principle of active sensing is quite clear - first absorb, then, if there is no movement or sound, shake it, and then reabsorb. We propose an extremely basic hypothesis for the active sensing of haptic interaction with dynamical systems. Our hypothesis asserts that in order to improve the efficiency of extracting information from a probed system, the sensor should act according to the following basic principle: if the probed system is passive, the sensor should be active; conversely, when the probed system is active, the sensor should be passive. We proved the proposed principle for interaction with a second-order mechanical system with the goal to enhance classification performance between two possible sine power sources. We showed that the addition of an active power source to a passive testing sensor leads to decreased sensitivity in the amplitude and frequency of the tested power source. Further, an extension of this principle is provided, presenting the conditions for reduced sensitivity to spring and damper parameters. To test its applicability for a linear system in a noisy environment, a computer simulation was performed demonstrating that classification performance improved by following the proposed principle. At last, ten subjects probed an active virtual system under either active or passive conditions. A comparison of the mean just-noticeable difference of both conditions indicated significantly better sensitivity was obtained by following the principle.

Strictly and non-strictly positive definite functions on spheres

Isotropic positive definite functions on spheres play important roles in spatial statistics, where they occur as the correlation functions of homogeneous random fields and star-shaped random particles. In approximation theory, strictly positive definite functions serve as radial basis functions for interpolating scattered data on spherical domains. We review characterizations of positive definite functions on spheres in terms of Gegenbauer expansions and apply them to dimension walks, where monotonicity properties of the Gegenbauer coefficients guarantee positive definiteness in higher dimensions. Subject to a natural support condition, isotropic positive definite functions on the Euclidean space $\mathbb{R}^3$, such as Askey's and Wendland's functions, allow for the direct substitution of the Euclidean distance by the great circle distance on a one-, two- or three-dimensional sphere, as opposed to the traditional approach, where the distances are transformed into each other. Completely monotone functions are positive definite on spheres of any dimension and provide rich parametric classes of such functions, including members of the powered exponential, Mat\'{e}rn, generalized Cauchy and Dagum families. The sine power family permits a continuous parameterization of the roughness of the sample paths of a Gaussian process. A collection of research problems provides challenges for future work in mathematical analysis, probability theory and spatial statistics.

Electrical behaviour, characteristics and properties of anodic aluminium oxide films coloured by nickel electrodeposition

Porous anodic films on 1050 aluminium substrate were coloured by AC electrodeposition of nickel. Several experiments were performed at different deposition voltages and nickel concentrations in the electrolyte in order to correlate the applied electrical power to the electrical behaviour, as well as the characteristics and properties of the coatings. The content of nickel inside the coatings reached 1.67 g/m2, depending on the experimental conditions. According to the applied AC voltage in comparison with the threshold voltage U t, the coating either acted only as a capacitor when U < U t and, when U > U t, the behaviour during the anodic and cathodic parts of the power sine wave was different. In particular, due to the semi-conducting characteristics of the barrier layer, additional oxidation of the aluminium substrate occurred during the anodic part of the electrical signal, whilst metal deposition (and solvent reduction) occurred during the cathodic part; these mechanisms correspond to the blocked and pass directions of the barrier layer/electrolyte junction, respectively.

The impact of backscatter angular dependency on reverberation levels in shallow water under downward refracting conditions

For downward refracting conditions in shallow water over a sandy bottom it was found that propagation loss was dependent on the source and receiver depth [P. D. Herstein etal., J. Acoust. Soc. Am. 92, 2302(A) (1992)]. The analysis is now extended to reverberation levels, considering the grazing angles corresponding to various source and receiver depths and both the first and second power sine of the angle dependencies of the backscattering. This is compared to a compilation of shallow water backscattering results.

The periodic solutions of certain non-linear oscillators

A method is presented for the analysis of single degree of freedom non-linear oscillators characterized by second order non-linear ordinary differential equations containing a parameter ϵ which need not be small. The method is based on expanding the solution as a sine power series. We explain our results as an application to the Duffing oscillators.

A New Family of Multivariate Distributions with Applications to Monte Carlo Studies

Abstract We consider a new class of multivariate probability distributions having representation X = RLY (p), where R is distributed as √χ 2 (p), L is the Choleski factorization of the scaling matrix Σ, and Y (p) represents an arbitrary distribution on the p-dimensional unit hypersphere. If Y (p) is uniform, then X has a multivariate normal distribution with mean 0 and covariance matrix Σ. The use of classical spherical distributions or other nonuniform distributions for Y (p) leads to interesting, controllable departures from normality that are particularly relevant to robustness studies. Their use is illustrated in a Monte Carlo investigation of the robustness of Hotelling's T 2. Variate generation routines for the cardioid, triangular, offset normal, wrapped normal, wrapped Cauchy, von Mises, power sine, Fisher, and Bingham distributions are developed.