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Novel symmetric numerical methods for solving symmetric mathematical problems

International Journal of Circuits, Systems and Signal Processing 2021年 15卷 1545-1557页

作者： Ibrahimov, V.R. Mehdiyeva, G.Y.U. Yue, Xiao-Guang Kaabar, Mohammed K.A. Noeiaghdam, Samad Juraev, Davron Aslonqulovich Institute of Control Systems named after Academician A.Huseynov BakuAZ1141 Azerbaijan Computational mathematics Baku State University BakuAZ1148 Azerbaijan Department of Computer Science and Engineering School of Sciences European University Cyprus Nicosia1516 Cyprus Institute of Mathematical Sciences Faculty of Science University of Malaya Kuala Lumpur50603 Malaysia Department of Mathematics and Statistics Washington State University PullmanWA99163 United States Industrial Mathematics Laboratory Baikal School of BRICS Irkutsk National Research Technical University Irkutsk664074 Russia Department of Applied Mathematics and Programming South Ural State University Lenin Prospect 76 Chelyabinsk454080 Russia Department of Natural Science Disciplines Higher Military Aviation School of the Republic of Uzbekistan Karshi City180100 Uzbekistan

—The mathematical model for many problems is arising in different industries of natural science, basically formulated using differential, integral and integro-differential equations. The investigation of these equations is conducted with the help of numerical integration theory. It is commonly known that a class of problems can be solved by applying numerical integration. The construction of the quadrature formula has a direct relation with the computation of definite integrals. The theory of definite integrals is used in geometry, physics, mechanics and in other related subjects of science. In this work, the existence and uniqueness of the solution of above-mentioned equations are investigated. By this way, the domain has been defined in which the solution of these problems is equivalent. All proposed four problems can be solved using one and the same methods. We define some domains in which the solution of one of these problems is also the solution of the other problems. Some stable methods with the degree p © 2021, North Atlantic University Union NAUN. All rights reserved.

关键词： Integrodifferential equations

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Automatic Fault Detection in WDM-PON with Tunable Photon Counting OTDR

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Journal of Lightwave Technology 2015年第24期33卷 5025-5031页

作者： Amaral, Gustavo C. Garcia, Joaquim D. Herrera, Luis E. Y. Temporão, Guilherme P. Urban, Patryk J. Von Der Weid, Jean Pierre Center for Telecommunications Studies Pontifical Catholic University of Rio de Janeiro Rio de Janeiro22451-900 Brazil Laboratory for Applied Mathematical Programming and Statistics Pontifical Catholic University of Rio de Janeiro Rio de Janeiro22451-900 Brazil Ericsson Research Ericsson AB Stockholm164 83 Sweden

An automatic fiber-optical fault analysis system making use of a tunable photon counting optical time-domain reflectometry (OTDR) (ν-OTDR) is proposed and demonstrated in a passive optical network testbed. The employment of the 1 trend filter as a signal processing tool enables the minimization of the intrinsic coherent random noise impact on the acquired data and also an automatic identification of fiber faults. A feedback loop between an FPGA-based acquisition unit and the filter's selections yields highly accurate automatic results and minute monitoring periods with ITU-T grid DWDM tunability, spatial resolution of 6 m and a measured 32 dB dynamic range. © 1983-2012 IEEE.

关键词： Reflectometers

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