scholarly journals Approximation of Fresnel Integrals with Applications to Diffraction Problems

2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
M. Sandoval-Hernandez ◽  
H. Vazquez-Leal ◽  
L. Hernandez-Martinez ◽  
U. A. Filobello-Nino ◽  
V. M. Jimenez-Fernandez ◽  
...  
Keyword(s):  
Least Squares ◽  
Good Accuracy ◽  
Least Squares Method ◽  
Numerical Algorithms ◽  
Absolute Error ◽  
Fresnel Diffraction ◽  
Opaque Screen ◽  
Aperture Problem ◽  
First Case

This article introduces two approximations that allow the evaluation of Fresnel integrals without the need for using numerical algorithms. These equations accomplish the characteristic of being continuous in the same interval as Fresnel. Both expressions have been determined applying the least squares method to suitable expressions. Accuracy of equations improves as x increases; as for small values of x, it is possible to achieve an absolute error less than 8×10-5. To probe the efficiency of the equations, two case studies are presented, both applied in the optics field. The first case is related to the semi-infinite opaque screen for Fresnel diffraction. In this case study Fresnel integrals are evaluated with the proposed equations to calculate the irradiance distribution and the Cornu spiral for diffraction computations of the Fresnel diffraction; obtained results show a good accuracy. The second case is related to the double aperture problem for Fresnel diffraction.

EXPRESS: Baseline Correction Based on a Search Algorithm from Artificial Intelligence

2020 ◽  
pp. 000370282097751
Author(s):  
Xin Wang ◽  
Xia Chen
Keyword(s):  
Artificial Intelligence ◽  
Objective Function ◽  
Least Squares ◽  
Least Squares Method ◽  
Search Algorithm ◽  
Absolute Error ◽  
Search Problem ◽  
Baseline Correction ◽  
Current Spectrum ◽  
Data Points

Many spectra have a polynomial-like baseline. Iterative polynomial fitting (IPF) is one of the most popular methods for baseline correction of these spectra. However, the baseline estimated by IPF may have substantially error when the spectrum contains significantly strong peaks or have strong peaks located at the endpoints. First, IPF uses temporary baseline estimated from the current spectrum to identify peak data points. If the current spectrum contains strong peaks, then the temporary baseline substantially deviates from the true baseline. Some good baseline data points of the spectrum might be mistakenly identified as peak data points and are artificially re-assigned with a low value. Second, if a strong peak is located at the endpoint of the spectrum, then the endpoint region of the estimated baseline might have significant error due to overfitting. This study proposes a search algorithm-based baseline correction method (SA) that aims to compress sample the raw spectrum to a dataset with small number of data points and then convert the peak removal process into solving a search problem in artificial intelligence (AI) to minimize an objective function by deleting peak data points. First, the raw spectrum is smoothened out by the moving average method to reduce noise and then divided into dozens of unequally spaced sections on the basis of Chebyshev nodes. Finally, the minimal points of each section are collected to form a dataset for peak removal through search algorithm. SA selects the mean absolute error (MAE) as the objective function because of its sensitivity to overfitting and rapid calculation. The baseline correction performance of SA is compared with those of three baseline correction methods: Lieber and Mahadevan–Jansen method, adaptive iteratively reweighted penalized least squares method, and improved asymmetric least squares method. Simulated and real FTIR and Raman spectra with polynomial-like baselines are employed in the experiments. Results show that for these spectra, the baseline estimated by SA has fewer error than those by the three other methods.

Determining Harmonic Contributions Based on Reweighted Complex Least Squares Method

2013 ◽  
Vol 448-453 ◽  
pp. 2660-2666
Author(s):  
Hui Chun Hua ◽  
Xiu Fang Jia ◽  
Hai Qing An ◽  
Shao Guang Zhang
Keyword(s):  
Quality Management ◽  
Least Squares ◽  
Power Quality ◽  
Least Squares Method ◽  
Test System ◽  
Important Task ◽  
Reasonable Result ◽  
Point Of Common Coupling ◽  
Common Coupling

Determining harmonic contribution quantitatively at the point of common coupling is an important task for power quality management. Outliers and influential points could have strong influences on regressors. This paper puts forward a method named reweighted complex least squares to eliminate or reduce the influences to ensure the robustness of the regression. The method can improve precision of the equivalent harmonic impedance and it can get a more reasonable result in harmonic contribution determination than previous methods. A case study based on the IEEE 14-bus test system was conducted, which shows the validity of the proposed method.

scholarly journals Econometric Analysis of the Impact of the Intensity of Transboundary Activities on the Level of Economic Complexity: The Case Study of European Countries

REGIONOLOGY ◽  
2019 ◽  
Vol 27 (4) ◽  
pp. 602-632 ◽  
Author(s):  
Ksenia Yu. Voloshenko ◽  
Tatiana E. Drok
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Global Market ◽  
Econometric Analysis ◽  
European Countries ◽  
Economic Complexity ◽  
Interaction Factor ◽  
Foreign Trade Turnover ◽  
The Impact

Introduction. Development of countries, regions and individual ecosystems occurs in the paradigm of innovative and technological change, the crucial element being the production knowledge and competencies. Their ranging in terms of transforming the complexity of the products that the country exports has been embodied and developed in the approach of economic complexity. However, insufficient attention is paid to the study of economic complexity in the context of transboundary processes that impact the development of territories. The objective of this study is to measure the impact of the intensity of transboundary relations on the change in economic complexity through the case study of European countries using the indicators of transboundary specialization of foreign trade turnover. Materials and Methods. The study employed the methods of econometric analysis. Information from the UN Comtrade database, as well as from the special resources for analyzing the economic complexity of countries, the Atlas of Economic Complexity and the Observatory of Economic Complexity, was used as the source data for calculations and measurements. Results. European countries have been classified into 3 subpanels based on Gaussian mixture distributions. The intensity of the impact of the transboundary activities on the complexity of the economy has been identified employing the panel cointegration method based on the constructed models (the combined model and models with fixed and random effects), which were supplemented by data analysis using the fully modified least squares method and the dynamic least squares method. Long-term interdependence between economic complexity and the intensity of transboundary activities has been identified. Discussion and Conclusion. It has been established that the influence of the transboundary interaction factor weakens as the economic complexity increases and under certain conditions it has a negative impact. The revealed dependence is due to the increasing role of global processes rather than the transboundary ones as the economy becomes more complex and more oriented towards the global market. The research findings contribute to further development of the Theory of Economic Complexity; they significantly expand the practical scope of its application, play an important role in understanding and further research on the opportunities and limitations for the development of territories differing in the transboundary cooperation intensity.

scholarly journals Does Temperature Affect COVID-19 Transmission?

2020 ◽  
Vol 8 ◽  
Author(s):  
Aly Zein Elabdeen Kassem
Keyword(s):  
Least Squares ◽  
Inverse Relationship ◽  
Least Squares Method ◽  
Linear Least Squares ◽  
First Case ◽  
Non Linear ◽  
Time Periods ◽  
The Impact ◽  
First Time

This study utilizes the non-linear least squares method to estimate the impact of temperature on COVID-19 cases per million in forty-three countries, divided into three groups as follows: the first group is composed of thirteen countries that announced the first COVID-19 cases in January 2020, while the second and third groups contain thirteen and seventeen countries, respectively, that witnessed the pandemic for the first time in February and March of the same year. This relationship was measured after four time periods from the date of reporting the first case until April 1, April 15, May 15, and July 8, 2020. The results show an inverse relationship between COVID-19 cases per million and the temperature in the studies of the four-time periods for the three-country groups. These results were only significant statistically (p < 0.1) after 110.8, 164.8 days on average from the beginning of the pandemic in the case of “January” countries.

scholarly journals PROSPEK KELAYAKAN PENGEMBANGAN BUDIDAYA IKAN NILA DI KOLAM AIR TENANG DI KECAMATAN SINJAI BORONG KABUPATEN SINJAI

2019 ◽  
Vol 2 (1) ◽  
pp. 12-17
Author(s):  
Jamaluddin Saleh ◽  
Sutia Budi ◽  
Suryawati Salam
Keyword(s):  
Least Squares ◽  
Trend Analysis ◽  
Sampling Method ◽  
Swot Analysis ◽  
Least Squares Method ◽  
Technical Aspects ◽  
Purposive Sampling ◽  
Calm Water ◽  
Production Trend

Penelitian ini bertujuan untuk mengetahui tingkat kelayakan dan prospek pengembangan budidaya ikan nila di kolam air tenang di Kecamatan Sinjai Borong Kabupaten Sinjai. Populasi dalam penelitian ini adalah pembudidaya ikan nila di kolam air tenang  yang ada di Kecamatan Sinjai Borong Kabupaten Sinjai yaitu sebanyak 163 orang pembudidaya, sampelnya sebanyak 30 orang responden ditentukan dengan menggunakan metode purposive sampling berdasarkan pengetahuan dan pengalaman dalam pengelolaan usaha pembesaran ikan nila di kolam air tenang. Data yang yang diperoleh dianalisis dari aspek teknis, aspek finansial, dianalisis dengan analisis  SWOT dan analisis trend produksi menggunakan metode kuadrat terkecil. Hasil penelitian menunjukkan bahwa dari aspek teknis layak untuk dikembangkan, aspek finansial tidak layak untuk kelayakan investasi dan Analisis SWOT menunjukkan pada posisi dapat dipertahankan untuk dikembangkan dengan memanfaatkan peluang yang ada dengan meminimalkan ancaman dan kelemahan. Hasil analisis trend menunjukkan bahwa produksi ikan nila memiliki kecenderungan terus meningkat meskipun tidak signifikan.   This research is a case study that aims to determine the level of feasibility and prospects for the development of tilapia aquaculture in calm water ponds in Sinjai Borong Sub-District, Sinjai Regency. The population in this study were tilapia fish farmers in calm water ponds in Sinjai Borong District, Sinjai Regency, as many as 163 farmers, the sampel of 30 respondent was determined using a purposive sampling method based on knowledge and experience in managing of tilapia enlargement business in calm water ponds. The study was conducted in June to July 2019. The data obtained were analyzed from technical aspects, analyzed by SWOT analysis and production trend analysis using the least squares method. The results showed that from the technical aspects feasible to be developed, the financial aspects were not feasible for investment feasibility and the SWOT analysis showed that position could be maintained to be developed by utilizing existing opportunities by minimizing threats and weaknesses. The results of ternd analysis show the tilapia  production has a tendency to increase even though it is not significant.

Detection Method of Optical Fiber Connector Internal Parts Based on Machine Vision

2014 ◽  
Vol 568-570 ◽  
pp. 483-488 ◽  
Author(s):  
Bao Hua Shi ◽  
Ya Hui Wei
Keyword(s):  
Image Analysis ◽  
Machine Vision ◽  
Optical Fiber ◽  
Least Squares ◽  
Detection Method ◽  
Least Squares Method ◽  
Detection Threshold ◽  
Absolute Error ◽  
Optical Fiber Connector ◽  
Outside Diameter

Technology of machine vision is used to measure the inside and outside diameter and concentricity of the optical fiber connector internal parts without contact. The image is got by million-pixel industrial camera. Then the image gets pretreatment, such as, grayscale transformation, binarization, smoothing, etc. Appropriate detection threshold is found by the image analysis. The edge of parts is found by the circular probe method. Inside and outside diameter and concentricity of parts are obtained by using the edge of the data through the least squares method. Experiment of 6.4 mm diameter parts, absolute error is less than one pixel. The largest error is less than 0.05 mm compared with the manual measurements and can meet the measurement requirements.

scholarly journals Least Squares Method and Empirical Modeling: A Case Study in a Mexican Manufacturing Firm

10.5772/63151 ◽  
2016 ◽  
Author(s):  
Raúl Hernández-Molinar ◽  
Roberto Sarmiento-Rebeles ◽  
César F. Méndez-Barrios
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Empirical Modeling ◽  
Manufacturing Firm

‘Least squares’ method—theorem or law?

1980 ◽  
Vol 59 (9) ◽  
pp. 8
Author(s):  
D.E. Turnbull
Keyword(s):  
Least Squares ◽  
Least Squares Method
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