Riemann Integral Operator for Stationary and Non-Stationary Processes
Integral operators based on the Riemann function, which transform arbitrary analytical functions into regular solutions of equations of elliptic, parabolic, and hyperbolic types of second order, are constructed. The Riemann operator method is generalized for the biaxisymmetric Helmholtz equation. A...
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| Veröffentlicht in: | Cybernetics and systems analysis 2021-11, Vol.57 (6), p.918-926 |
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| container_title | Cybernetics and systems analysis |
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| creator | Alexandrovich, I. M. Lyashko, S. I. Sydorov, M. V.-S. Lyashko, N. I. Bondar, O. S. |
| description | Integral operators based on the Riemann function, which transform arbitrary analytical functions into regular solutions of equations of elliptic, parabolic, and hyperbolic types of second order, are constructed. The Riemann operator method is generalized for the biaxisymmetric Helmholtz equation. A method for finding solutions to the above equations in analytical form is developed. In some cases, formulas for inverting integral representations of solutions are constructed. The conditions for solving the Cauchy problem for the axisymmetric Helmholtz equation are formulated. |
| doi_str_mv | 10.1007/s10559-021-00418-x |
| format | Article |
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The conditions for solving the Cauchy problem for the axisymmetric Helmholtz equation are formulated.</description><subject>Artificial Intelligence</subject><subject>Cauchy problems</subject><subject>Control</subject><subject>Differential equations</subject><subject>Elliptic functions</subject><subject>Helmholtz equations</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Operators (mathematics)</subject><subject>Processor Architectures</subject><subject>Software Engineering/Programming and Operating Systems</subject><subject>Stationary processes</subject><subject>Systems Theory</subject><issn>1060-0396</issn><issn>1573-8337</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><recordid>eNp9kclKBDEQhhtRcH0BTw2ePEQrnaWTo4jLgDjicg6Z7srQMpOMSQbGtzfagnqRECoU31cJ-avqmMIZBWjPEwUhNIGGEgBOFdlsVXtUtIwoxtrtcgYJBJiWu9V-Sq8AwKBVe9XV44BL63098Rnn0S7q6QqjzSHWruynbPMQvI3vtfV9fR88-dV6iKHDlDAdVjvOLhIefdeD6uX66vnyltxNbyaXF3ekY5xl0s06yZmyokHnsNGNEJL2XHLgIGdcONVohz1HzlolJXM9nTHBrJ7pBqRW7KA6GeeuYnhbY8rmNayjL1eaRoKkSpVSqLORmtsFmsG7kKPtyupxOXTBoxtK_0JqEFJRpYtw-kcoTMZNntt1Smby9PiXbUa2iyGliM6s4rAsv2EomM8szJiFKVmYryzMpkhslFKB_Rzjz7v_sT4AXveKpQ</recordid><startdate>20211101</startdate><enddate>20211101</enddate><creator>Alexandrovich, I. 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| source | Springer Nature - Complete Springer Journals |
| subjects | Artificial Intelligence Cauchy problems Control Differential equations Elliptic functions Helmholtz equations Mathematical analysis Mathematics Mathematics and Statistics Operators (mathematics) Processor Architectures Software Engineering/Programming and Operating Systems Stationary processes Systems Theory |
| title | Riemann Integral Operator for Stationary and Non-Stationary Processes |
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