Series

摘要： Continued fractions constitute a very important subject in mathematics. Their importance lies in the fact that they have very interesting and beautiful applications in many fields in pure and applied sciences. This review article will reveal some of these applications and will reflect the beauty behind their uses in calculating roots of real numbers, getting solutions of algebraic Equations of the second degree, and their uses in solving special ordinary differential Equations such as Legendre, Hermite, and Laguerre Equations;moreover and most important, their use in physics in solving Schrodinger Equation for a certain potential. A comparison will also be given between the results obtained via continued fractions and those obtained through the use of well-known numerical methods. Advances in the subject will be discussed at the end of this review article.

摘要： Stacey loves to watch movies.She has an account for an online movie service.Stacey pays for the account every month.She can watch many movies and TV shows using this service.When Stacey really likes a show,she tells her best friend,Adam,about it.They like many of the same TV shows and movies.Stacey watches a show called Home.It''s a series.She likes it very much.

摘要： Thirty seven years after the discovery of quasicrystals, their diffraction is completely described by harmonization between the sine wave probe with hierarchic translational symmetry in a structure that is often called quasiperiodic. The diffraction occurs in geometric series that is a special case of the Fibonacci sequence. Its members are irrational. When substitution is made for the golden section τ by the semi-integral value 1.5, a coherent set of rational numbers maps the sequence. Then the square of corresponding ratios is a metric that harmonizes the sine wave probe with the hierarchic structure, and the quasi-Bragg angle adjusts accordingly. From this fact follows a consistent description of structure, diffraction and measurement.

摘要： We study a class of Dirichlet functions obtained as analytic continuation across the line of convergence of Dirichlet series which can be written as Euler products. This class includes that of Dirichlet L-functions. The problem of the existence of multiple zeros for this last class is outstanding. It is tacitly accepted, yet not proved that the Riemann Zeta function, which belongs to this class, does not possess multiple zeros. In a previous study we provided an example of Dirichlet function having double zeros, but that function is not an Euler product function. In this paper we deal with Euler product functions and by using the geometric properties of the mapping realized by these functions, we tackle the problem of the multiplicity of their zeros.

摘要： A spectral difference method is applied to get numerical solutions for a fluid-lubricated herringbone grooved journal bearing with trapezoidal grooves by previous work of the authors. However, an inexpedience in which Fourier series of the film profile does not converge at jump points of groove start or groove end in the case of rectangle groove was still remained. In the paper, an inexpedience of numerical analysis under a special case at rectangle groove is challenged to solve. As a result, for compensation of which Fourier series does not converge at jump points in a special case of rectangle groove, Fourier coefficient of fluid film thickness is proposed as taking the limit of which in a case trapezoidal groove at trapezoidal angle approaches 0.

摘要： In this study, the sliced functional time series (SFTS) model is applied to the Global, Northern and Southern temperature anomalies. We obtained the combined land-surface air and sea-surface water temperature from Goddard Institute for Space Studies (GISS), NASA. The data are available for Global mean, Northern Hemisphere mean and Southern Hemisphere means (monthly, quarterly and annual) since 1880 to present (updated through March 2019). We analyze the global surface temperature change, compare alternative analyses, and address the questions about the reality of global warming. We detected the outliers during the last century not only in global temperature series but also in northern and southern hemisphere series. The forecasts for the next twenty years are obtained using SFTS models. These forecasts are compared with ARIMA, Random Walk with drift and Exponential Smoothing State Space (ETS) models. The comparison is made on the basis of root mean square error (RMSE), mean absolute percentage error (MAPE) and the length of prediction intervals.

摘要： The purpose of this study is to apply white noise process in measuring model adequacy targeted at confirming the assumption of independence. This ensures that no autocorrelation exists in any time series under consideration, and that the autoregressive integrated moving average (ARIMA) model entertained is able to capture the linear structure in such series. The study explored the share price series of Union bank of Nigeria, Unity bank, and Wema bank obtained from Nigerian Stock Exchange from January 3, 2006 to November 24, 2016 comprising 2690 observations. ARIMA models were used to model the linear dependence in the data while autocorrelation function (ACF), partial autocorrelation function (PACF), and Ljung-Box test were applied in checking the adequacy of the selected models. The findings revealed that ARIMA(1,1,0) model adequately captured the linear dependence in the return series of both Union and Unity banks while ARIMA(2,1,0) model was sufficient for that of Wema bank. Also, evidence from ACF, PACF and Ljung-Box test revealed that the residual series of the fitted models were white noise, thus satisfying the conditions for stationarity.

摘要： Unlike the traditional Laplace transform, the Sumudu transform of a function, when approximated as a power series, may be readily inverted using factorial-based coefficient diminution. This technique offers straightforward computational advantages for approximate range-limited numerical solutions of certain ordinary, mixed, and partial linear differential and integro-differential equations. Furthermore, discrete convolution (the Cauchy product), may also be utilized to assist in this approximate inversion method of the Sumudu transform. Illustrative examples are provided which elucidate both the applicability and limitations of this method.

摘要： pH and base saturation percentage (BSP) are two basic indexes in identifying soil types in Chinese Soil Taxonomy. Some studies proved that there is significant correlation between BSP and pH, thus it could save the cost of laboratory work if we can infer BSP directly from pH. In this study, the measured values of BSP and pH of 162 and 232 horizon samples from 48 and 55 red soil series surveyed from 2009 to 2011 in Fujian and Guangdong respectively were adopted from Soil Series Database to set up the optimal correlation model between BSP and pH. The results showed that: 1) BSP ranged from 2.30% to 94.02% with a mean of 25.07%, while pH from 3.42 to 6.91 with a mean of 4.98 for the total soil samples. 2) There were significant differences in pH between different soil types (R2 were 0.624 for Ferralosols, 0.507 for Ferrosols, 0.515 for Argosols, and 0.456 for Cambosols, p 2 were 0.580 for Quaternary red clay, 0.434 for granite, 0.642 for sandstone, and 0.712 for basalt, p 2 were 0.623 for dryland, and 0.404 for forest land, p 0), their probability density curves were mainly in flat or normal curves (y = 6.84x2 −45.86x + 81.52, R2 = 0.494, p < 0.01).

摘要： Real-time anomaly detection of massive data streams is an important research topic nowadays due to the fact that a lot of data is generated in continuous temporal processes. There is a broad research area, covering mathematical, statistical, information theory methodologies for anomaly detection. It addresses various problems in a lot of domains such as health, education, finance, government, etc. In this paper, we analyze the state-of-the-art of data streams anomaly detection techniques and algorithms for anomaly detection in data streams (time series data). Critically surveying the techniques’ performances under the challenge of real-time anomaly detection of massive high-velocity streams, we conclude that the modeling of the normal behavior of the stream is a suitable approach. We evaluate Holt-Winters (HW), Taylor’s Double Holt-Winters (TDHW), Hierarchical temporal memory (HTM), Moving Average (MA), Autoregressive integrated moving average (ARIMA) forecasting models, etc. Holt-Winters (HW) and Taylor’s Double Holt-Winters (TDHW) forecasting models are used to predict the normal behavior of the periodic streams, and to detect anomalies when the deviations of observed and predicted values exceeded some predefined measures. In this work, we propose an enhancement of this approach and give a short description about the algorithms and then they are categorized by type of pre-diction as: predictive and non-predictive algorithms. We implement the Genetic Algorithm (GA) to periodically optimize HW and TDHW smoothing parameters in addition to the two sliding windows parameters that improve Hyndman’s MASE measure of deviation, and value of the threshold parameter that defines no anomaly confidence interval [1]. We also propose a new optimization function based on the input training datasets with the annotated anomaly intervals, in order to detect the right anomalies and minimize the number of false ones. The proposed method is evaluated on the known anomaly detection benchmarks NUMENTA and Yahoo datasets with annotated anomalies and real log data generated by the National education information system (NEIS)1 in Macedonia.

摘要： 本发明公开了一种基于FOXBORD IA Ser ies系统的发电机自动并网方法，包括以下步骤：通过参数设置菜单对各个通道的参数进行设置，完成通道参数整定；通过参数设置菜单对系统参数进行设置，完成系统参数整定；通过系统对RAM和EEPROM中的参数数据进行检测，然后对用于直接合闸的光隔MOSFET继电器进行检测。本发明，通过参数设置菜单对各个通道的参数进行设置，通过参数设置菜单对系统参数进行设置，通过系统对RAM和EEPROM中的参数数据进行检测，然后对用于直接合闸的光隔MOSFET继电器进行检测，完成并网前的准备工作，然后通过系统预先设置好的参数由控制器对系统进行调整，结合和FOXBORD IA Ser i es控制系统完成发电机并网，相比于人工操作更加精准，工作效率更高。

摘要： 本发明公开了一种基于FOXBORD IA Ser ies系统的空预器间隙调整装置自动调节方法，涉及自动调节技术领域，本发明通过将各个扇形板控制箱的远方/就地切换旋钮，打到远方位实现自动调整功能当旋钮打到远方位时，运行人员可通过对应扇形板控制箱切换手自动的操作方式，操作系统会针对不同的操作方式，智能控制逻辑对间隙信号和电流信号进行综合判断，对扇形板位置进行控制最后系统可以自动检测内部的多种故障并将故障分为两类分别对待，新的操作系统有效的较少了运行人员的操作步序，降低了空预器的漏风率，有效的规避了人为误操作的可能，大大提高了设备安全运行指数及锅炉效率，解决了因采取过于繁琐的老系统而导致的人工误操作，影响机组产能的现象。

摘要： 本发明提供了一种S7-200PLC与I/A？Series的数据线，包括：通信线缆，通信线缆中设置RS232-RS485转换模块，转换模块将通信线缆分为RS232通信线缆和RS485通信线缆；RS232通信线缆的端部连接25孔串口母头，用于插接I/A？Series系统的25针公头，RS485通信线缆的端部连接9针串口公头，用于插接S7-200PLC的9孔母头；在RS232-RS485转换模块的内部设置有RS232-RS485转换电路，RS232-RS485转换电路包括电源电路、RS232电平转换电路和RS485电路。从而为S7-200PLC与I/A？Series系统进行基于Modbus协议的通信提供专用数据线，设计简单，采用元件少，成本低，还具有抗干扰能力强，使用方便的特点。

摘要： 本实用新型提供了一种S7-200PLC与I/A Series的数据线，包括：通信线缆，通信线缆中设置RS232-RS485转换模块，转换模块将通信线缆分为RS232通信线缆和RS485通信线缆；RS232通信线缆的端部连接25孔串口母头，用于插接I/A Series系统的25针公头，RS485通信线缆的端部连接9针串口公头，用于插接S7-200PLC的9孔母头；在RS232-RS485转换模块的内部设置有RS232-RS485转换电路，RS232-RS485转换电路包括电源电路、RS232电平转换电路和RS485电路。从而为S7-200PLC与I/A Series系统进行基于Modbus协议的通信提供专用数据线，设计简单，采用元件少，成本低，还具有抗干扰能力强，使用方便的特点。

摘要： 本发明涉及一种Xboxseries手柄辅助装置及其使用方法，属于Xboxseries手柄技术领域。其主要针对现有的通过扣装或者捆绑的方式连接在Xboxseries设备上，同时支持改建，使得Xboxseries也能跟精英手柄一样有更多的扩展按键但这些设备无一例外的都是有线设备，这样就让本是无线设备的Xboxseries为了使用背键变成了有线设备，放弃了本身的灵活性来获得了更多的扩展键的问题，提出如下技术方案：包括手柄与辅助柄，所述手柄背面开设有电池槽，所述辅助柄上固定设置有连接座，所述连接座上设有与电池槽内壁相固定的连接机构。本发明可以让没有背键的Xboxseries手柄拥有四颗背键的同时，还能与主机设备无线通信，四颗扩展按键不仅支持改建，同时支持一键宏功能。

摘要： 本发明公开了一种基于E3.series的电路图快速设计方法，S1：利用E3.series工具进行电路图设计，建立原理图设计页面，根据电路图的规模，选择所需的页面特性；S2：将电路图包含的各分支电缆图设置为E3.seriesp格式；S3：所述E3.seriesp格式的分支电缆图作为所述电路图的一部分，设置各分支电缆图在电路图的关系；S4：将所述各E3.seriesp格式的分支电缆图导入所述电路图，为各分析电缆图建立关系；S5：调整信号格式间距并设置信号关系流向；并构建电路图系统。改善了重复性工作的现状，提高了设计的准确性，缩短了绘图周期，大大节约了设计师时间，保证电气系统工作顺利进行。

摘要： 本实用新型公开了一种兼容xbox series x/s的主机底座结构，包括主机座，主机座包括第一底座、第二底座、剪刀架和安装块，第一底座内壁顶部的一侧和第二底座内壁顶部的一侧均固定连接有安装块，其中一个安装块的底部安装有剪刀架，剪刀架的一侧与另外一个安装块的底部连接，第一底座内壁底部的一侧开设有卡槽，第二底座内壁的中部固定连接有限位板，限位板底部的一侧固定连接有卡条，第一底座内壁顶部的两边角和第二底座内壁顶部的两边角均安装有散热扇，本实用新型一种兼容xbox series x/s的主机底座结构，设置第一底座、第二底座和剪刀架，能同时适用2款主机，降低了用户成本，同时操作方便安全，能很好的满足用户需求，提高用户使用体验。