Improving Learning through Application, Exploring the “Opening Method” of Taylor Formula

2021 ◽  
Vol 09 (06) ◽  
pp. 1681-1687
Author(s):  
自森 毛
Keyword(s):  
Taylor Formula ◽  
Opening Method

scholarly journals Predicting Dam Flood Discharge Induced Ground Vibration with Modified Frequency Response Function

Water ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 144
Author(s):  
Yan Zhang ◽  
Jijian Lian ◽  
Songhui Li ◽  
Yanbing Zhao ◽  
Guoxin Zhang ◽  
...  
Keyword(s):  
Frequency Response ◽  
Frequency Distribution ◽  
Response Function ◽  
Frequency Response Function ◽  
Ground Vibration ◽  
Vibration Source ◽  
Ground Vibrations ◽  
High Energies ◽  
Flood Discharge ◽  
Opening Method

Ground vibrations induced by large flood discharge from a dam can damage surrounding buildings and impact the quality of life of local residents. If ground vibrations could be predicted during flood discharge, the ground vibration intensity could be mitigated by controlling or tuning the discharge conditions by, for example, changing the flow rate, changing the opening method of the orifice, and changing the upstream or downstream water level, thereby effectively preventing damage. This study proposes a prediction method with a modified frequency response function (FRF) and applies it to the in situ measured data of Xiangjiaba Dam. A multiple averaged power spectrum FRF (MP-FRF) is derived by analyzing four major factors when the FRF is used: noise, system nonlinearity, spectral leakages, and signal latency. The effects of the two types of vibration source as input are quantified. The impact of noise on the predicted amplitude is corrected based on the characteristics of the measured signal. The proposed method involves four steps: signal denoising, MP-FRF estimation, vibration prediction, and noise correction. The results show that when the vibration source and ground vibrations are broadband signals and two or more bands with relative high energies, the frequency distribution of ground vibration can be predicted with MP-FRF by filtering both the input and output. The amplitude prediction loss caused by filtering can be corrected by adding a constructed white noise signal to the prediction result. Compared with using the signal at multiple vibration sources after superimposed as input, using the main source as input improves the accuracy of the predicted frequency distribution. The proposed method can predict the dominant frequency and the frequency bands with relative high energies of the ground vibration downstream of Xiangjiaba Dam. The predicted amplitude error is 9.26%.

Visualizing the Variance of a Random Variable

2011 ◽  
Vol 18 (01) ◽  
pp. 71-85
Author(s):  
Fabrizio Cacciafesta
Keyword(s):  
Stochastic Dominance ◽  
Mean Absolute Error ◽  
Random Variable ◽  
Absolute Error ◽  
Second Order ◽  
Taylor Formula ◽  
Order Stochastic Dominance ◽  
The Mean ◽  
Second Order Stochastic Dominance ◽  
Options Theory

We provide a simple way to visualize the variance and the mean absolute error of a random variable with finite mean. Some application to options theory and to second order stochastic dominance is given: we show, among other, that the "call-put parity" may be seen as a Taylor formula.

scholarly journals Tingkat keberlanjutan terhadap aspek pengelolaan sumur tua secara tradisional di Bojonegoro Jawa Timur

Jurnal Zona ◽  
2021 ◽  
Vol 5 (1) ◽  
pp. 1-11
Author(s):  
Ahmad Kurnain ◽  
Yusni Ikhwan Siregar ◽  
Sri Indarti ◽  
Suwondo Suwondo
Keyword(s):  
Multidimensional Scaling ◽  
Oil Wells ◽  
One Dimension ◽  
Scaling Analysis ◽  
Multidimensional Scaling Analysis ◽  
Sustainability Index ◽  
Opening Method

This study aims to determine the sustainability status of the Re-Opening Oil Wells of Bojonegoro Regency, East Java, Indonesia. The method used in this research is Multidimensional Scaling analysis which is implemented using Rap-Re-Opening Oil Wells software. Existing status of Wells Bojonegoro Re-Opening Oil Sustainability Less Sustainable with the weighting value of each dimension is 34.56%, 39.73%, 45.25%, 37.90%, 57.00%. The strategy to increase the addition of status values from the 5 dimensions of the Sustainability Index, evaluated only one dimension that is sustainable with a fairly good status. The results obtained from the improvement scenario obtained by the respective percentage figures as follows; Ecology 41.44%, Economics 61.62%, Social and Culture 45.25%, Technology 42.02%, Institutional 61, 29%. Thus the strategy to increase sustainable status can be improved by the Oil Wells Rap-Re-Opening Method.

Transcerebellomedullary fissure approach with special reference to the methods of dissecting the fissure

2001 ◽  
Vol 94 (2) ◽  
pp. 257-264 ◽  
Author(s):  
Toshio Matsushima ◽  
Tooru Inoue ◽  
Takanori Inamura ◽  
Yoshihiro Natori ◽  
Kiyonobu Ikezaki ◽  
...  
Keyword(s):  
Fourth Ventricle ◽  
Posterior Margin ◽  
Lateral Wall ◽  
Microsurgical Anatomy ◽  
Optimal Method ◽  
Content Type ◽  
Lateral Recess ◽  
Tela Choroidea ◽  
Opening Method ◽  
Fine Print

Object. The purpose of the present study was to refine the transcerebellomedullary fissure approach to the fourth ventricle and to clarify the optimal method of dissecting the fissure to obtain an appropriate operative view without splitting the inferior vermis. Methods. The authors studied the microsurgical anatomy by using formalin-fixed specimens to determine the most appropriate method of dissecting the cerebellomedullary fissure. While dissecting the spaces around the tonsils and making incisions in the ventricle roof, the procedures used to expose each ventricle wall were studied. Based on their findings, the authors adopted the best approach for use in 19 cases of fourth ventricle tumor. The fissure was further separated into two slit spaces on each side: namely the uvulotonsillar and medullotonsillar spaces. The floor of the fissure was composed of the tela choroidea, inferior medullary velum, and lateral recess, which form the ventricle roof. In this approach, the authors first dissected the spaces around the tonsils and then incised the taenia with or without the posterior margin of the lateral recess. These precise dissections allowed for easy retraction of the tonsil(s) and uvula and provided a sufficient view of the ventricle wall such that the deep aqueductal region and the lateral region around the lateral recess could be seen without splitting the vermis. The dissecting method could be divided into three different types, including extensive (aqueduct), lateral wall, and lateral recess, depending on the location of the ventricle wall and the extent of surgical exposure required. Conclusions. When the fissure is appropriately and completely opened, the approach provides a sufficient operative view without splitting the vermis. Two key principles of this opening method are sufficient dissection of the spaces around the tonsil(s) and an incision of the appropriate portions of the ventricle roof. The taenia(e) with or without the posterior margin of the lateral recess(es) should be incised.

scholarly journals Computational Optimization of Residual Power Series Algorithm for Certain Classes of Fuzzy Fractional Differential Equations

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Mohammad Alaroud ◽  
Mohammed Al-Smadi ◽  
Rokiah Rozita Ahmad ◽  
Ummul Khair Salma Din
Keyword(s):  
Power Series ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Optimization Technique ◽  
Fractional Power ◽  
Taylor Formula ◽  
Residual Power Series ◽  
Fractional Differential ◽  
Residual Power ◽  
Fuzzy Fractional Differential Equations

This paper aims to present a novel optimization technique, the residual power series (RPS), for handling certain classes of fuzzy fractional differential equations of order 1<γ≤2 under strongly generalized differentiability. The proposed technique relies on generalized Taylor formula under Caputo sense aiming at extracting a supportive analytical solution in convergent series form. The RPS algorithm is significant and straightforward tool for creating a fractional power series solution without linearization, limitation on the problem’s nature, sort of classification, or perturbation. Some illustrative examples are provided to demonstrate the feasibility of the RPS scheme. The results obtained show that the scheme is simple and reliable and there is good agreement with exact solution.

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