Estimation of Wind Wave Frequency Spectra by Use of the Arcsine Law

In the present study, the surface elevation of wind waves observed in laboratory and in the Bohai Sea are adopted for the estimation of the wind wave frequency spectrtm by use of the method of the arcsine law （MAL）. The traditional method uses the surface elevation to calculate the correlation and then estimate the frequency spectrum while the MAL, presented by Yu and l.an （1979）, uses the time sequence of zero-crossing points of surface elevation rather than directly the surface elevation to calculate the correlation. 66 sets of wind wave data obtained in laboratory and 420 sets of data observed in the Bohai Sea are adopted for the examination of the method introduced by Yu and Lan. Results show that the MAL can give reliable estimation of wind wave spectra. Correlation and form of spectra estimated by the MAL are similar to those estimated by the traditional method. The peak frequency and the spectral density in peak frequency by the MAL are close to those obtained by the traditional method.

The Arcsine-X Family of Distributions with Applications to Financial Sciences

The heavy-tailed distributions are very useful and play a major role in actuary and financial management problems.Actuaries are often searching for such distributions to provide the best fit to financial and economic data sets.In the current study,a prominent method to generate new distributions useful for modeling heavy-tailed data is considered.The proposed family is introduced using trigonometric function and can be named as the Arcsine-X family of distri-butions.For the purposes of the demonstration,a specific sub-model of the proposed family,called the Arcsine-Weibull distribution is considered.The max-imum likelihood estimation method is adopted for estimating the parameters of the Arcsine-X distributions.The resultant estimators are evaluated in a detailed Monte Carlo simulation study.To illustrate the Arcsine-Weibull two insurance data sets are analyzed.Comparison of the Arcsine-Weibull model is done with the well-known two parameters and four parameters competitors.The competitive models including the Weibull,Lomax,Burr-XII and beta Weibull models.Different goodness of fit measures are taken into account to determine the useful-ness of the Arcsine-Weibull and other considered models.Data analysis shows that the Arcsine-Weibull distribution works much better than competing models in financial data analysis.

Cautionary Remarks When Testing Agreement between Two Raters for Continuous Scale Measurements: A Tutorial in Clinical Epidemiology with Implementation Using R

Background: When continuous scale measurements are available, agreements between two measuring devices are assessed both graphically and analytically. In clinical investigations, Bland and Altman proposed plotting subject-wise differences between raters against subject-wise averages. In order to scientifically assess agreement, Bartko recommended combining the graphical approach with the statistical analytic procedure suggested by Bradley and Blackwood. The advantage of using this approach is that it enables significance testing and sample size estimation. We noted that the direct use of the results of the regression is misleading and we provide a correction in this regard. Methods: Graphical and linear models are used to assess agreements for continuous scale measurements. We demonstrate that software linear regression results should not be readily used and we provided correct analytic procedures. The degrees of freedom of the F-statistics are incorrectly reported, and we propose methods to overcome this problem by introducing the correct analytic form of the F statistic. Methods for sample size estimation using R-functions are also given. Results: We believe that the tutorial and the R-codes are useful tools for testing and estimating agreement between two rating protocols for continuous scale measurements. The interested reader may use the codes and apply them to their available data when the issue of agreement between two raters is the subject of interest.

基于灰色预测控制的电动舵机控制仿真研究

分析了电动舵机结构及数学模型,针对经典PID控制器在电动舵机控制中,响应速度慢,超调量明显等问题,提出了一种灰色预测控制与传统PID控制相结合的电动舵机复合控制方法。建立了电动舵机灰色模型,设计一种基于arcsin(.)函数的变换算子,来解决正弦位置信号驱动下,算法直接预测精度不足的问题,最后在MATLAB环境下进行了建模仿真。仿真结果表明:该方法能够有效降低舵机系统超调量,改善系统动态品质,且结构简单,易于在工程中实现。

Magic Numbers of the Great Pyramid: A Surprising Result

Recently attention has been drawn to the frequently observed fifth power of the golden mean in many disciplines of science and technology. Whereas in a forthcoming contribution the focus will be directed towards Fibonacci number-based helical structures of living as well as inorganic matter, in this short letter the geometry of the Great Pyramid of the ancient Egyptians was investigated once more. The surprising main result is that the ratio of the in-sphere volume of the pyramid and the pyramid volume itself is given by π⋅φ5, where φ = 0.618033987⋅⋅⋅ is nature’s most important number, the golden mean. In this way not only phase transitions from microscopic to cosmic scale are connected with φ5, also ingenious ancient builders have intuitively guessed its magic before.

arcsin (sinα)=π-α(α∈〔π/2,(3π)/2〕)的猜想和证明

劳动人事部培训就业局组织沈炎金先生等编写的全国技工学校通用教材《数学》(1985年3月北京第1版)第206页,有:"例5求下列各式的值:

D DT Theorem over square-free numbers in short interval

We study the Cesaro means related to the divisor function. We show that the DDT Theorem holds over square-free numbers in short interval, which generalizes some results established by Deshouillers-Dress-Tenenbaum and by Cui-Wu.

Discussion on several statistical problems in establishing quality standards of standard decoctions

Since 2016,a number of studies have been published on standard decoctions used in Chinese medicine.However,there is little research on statistical issues related to establishing the quality standards for standard decoctions.In view of the currently established quality standard methods for standard decoctions,an improvement scheme is proposed from a statistical perspective.This review explores the requirements for dry matter yield rate data and index component transfer data for the application of two methods specified in‘‘Technical Requirements for Quality Control and Standard Establishment of Chinese Medicine Formula Granules,"which include the average value plus or minus three times the standard deviation (■±3SD) or 70%to 130%of the average value (■±30%■).The square-root arcsine transformation method is used as an approach to solve the problem of unreasonable standard ranges of standard decoctions.This review also proposes the use of merged data to establish a standard.A method to judge whether multiple sets of standard decoction data can be merged is also provided.When multiple sets of data have a similar central tendency and a similar discrete tendency,they can be merged to establish a more reliable quality standard.Assuming that the dry matter yield rate and transfer rate conform to a binomial distribution,the number of batches of prepared slices that are needed to establish the standard decoction quality standard is estimated.It is recommended that no less than 30 batches of prepared slices should be used for the establishment of standard decoction quality standards.