BULLETIN of L.N. Gumilyov Eurasian National University. MATHEMATICS. COMPUTER SCIENCE. MECHANICS Series最新文献

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The Informative Power of all Possible Linear Functionals and the Mean-Square Error in the Diccretization of Solutions of the Diriclet Problem for the Laplace Equation in the Circle 圆中拉普拉斯方程Diriclet问题解离散化的所有可能线性泛函的信息幂和均方误差

BULLETIN of L.N. Gumilyov Eurasian National University. MATHEMATICS. COMPUTER SCIENCE. MECHANICS Series Pub Date : 1900-01-01 DOI: 10.32523/2616-678x-2020-134-1-42-51

M. Y. Berikkhanova, K. Y. Sherniyazov

{"title":"The Informative Power of all Possible Linear Functionals and the Mean-Square Error in the Diccretization of Solutions of the Diriclet Problem for the Laplace Equation in the Circle","authors":"M. Y. Berikkhanova, K. Y. Sherniyazov","doi":"10.32523/2616-678x-2020-134-1-42-51","DOIUrl":"https://doi.org/10.32523/2616-678x-2020-134-1-42-51","url":null,"abstract":"The Dirichlet problem for the Laplace equation in the case of a circle belongs to the classical ones and in various aspects has been the subject of study in various fields of mathematics. Among them are such topics as - \"Boundary properties of analytic functions\", in the study of which powerful methods of function theories were created and honed, - The Banach problem on the existence of a basis for a class of functions consisting of continuous in a closed circle and analytic in, - Numerical methods, since this problem as a mathematical model describes many real processes. In this article, we consider the discretization problem of solutions of the Dirichlet problem for the Laplace equation in a circle from finite numerical information obtained from the boundary function as a result of applying all possible linear functionals. The optimal order of discretization error is found and the corresponding optimal operator of discretization is constructed. The problem of constructing probabilistic measures on functional classes is also considered. Probabilistic measures on the Korobov 𝐸𝑟 (0, 2𝜋) and Nikolsky 𝐻𝑟 2 (0, 2𝜋) classes are introduced. Two-sided estimates of the mean-square error of discretization the solution of the problem by operator (𝑇𝑁 𝑓) (𝛼, 𝜃) are established.","PeriodicalId":225533,"journal":{"name":"BULLETIN of L.N. Gumilyov Eurasian National University. MATHEMATICS. COMPUTER SCIENCE. MECHANICS Series","volume":"66 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125763615","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Explicit solutions of a two-dimensional integral equation of Volterr type with boundary singularity and strongly singular line when the roots of the characteristic equations are real, different and equal 具有边界奇异和强奇异线的二维Volterr型积分方程，当特征方程的根为实、异、等时的显式解

BULLETIN of L.N. Gumilyov Eurasian National University. MATHEMATICS. COMPUTER SCIENCE. MECHANICS Series Pub Date : 1900-01-01 DOI: 10.32523/bulmathenu.2021/4.1

L. Rajabova, F. M. Ahmadov

引用次数: 0

Development of a Python application for recognizing gestures from a video stream of RGB and RGBD cameras 开发一个Python应用程序，用于从RGB和RGBD摄像机的视频流中识别手势

BULLETIN of L.N. Gumilyov Eurasian National University. MATHEMATICS. COMPUTER SCIENCE. MECHANICS Series Pub Date : 1900-01-01 DOI: 10.32523/bulmathenu.2021/3.1

D.Zh. Satybaldina, N. Glazyrina, V. S. Stepanov, K. A. Kalymova

{"title":"Development of a Python application for recognizing gestures from a video stream of RGB and RGBD cameras","authors":"D.Zh. Satybaldina, N. Glazyrina, V. S. Stepanov, K. A. Kalymova","doi":"10.32523/bulmathenu.2021/3.1","DOIUrl":"https://doi.org/10.32523/bulmathenu.2021/3.1","url":null,"abstract":"Gesture recognition systems have changed a lot recently, due to the development of modern data capture devices (sensors) and the development of new recognition algorithms. The article presents the results of a study for recognizing static and dynamic hand gestures from a video stream from RGB and RGBD cameras, namely from the Logitech HD Pro Webcam C920 webcam and from the Intel RealSense D435 depth camera. Software implementation is done using Python 3.6 tools. Open source Python libraries provide robust implementations of image processing and segmentation algorithms. The feature extraction and gesture classification subsystem is based on the VGG-16 neural network architecture implemented using the TensorFlow and Keras deep learning frameworks. The technical characteristics of the cameras are given. The algorithm of the application is described. The research results aimed at comparing data capture devices under various experimental conditions (distance and illumination) are presented. Experimental results show that using the Intel RealSense D435 depth camera provides more accurate gesture recognition under various experimental conditions.","PeriodicalId":225533,"journal":{"name":"BULLETIN of L.N. Gumilyov Eurasian National University. MATHEMATICS. COMPUTER SCIENCE. MECHANICS Series","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124908242","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

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