Simultaneous Reduction and Expansion of Multidimensional Laplace Transform Kernels
Application of Laplace transforms in linear systems analysis has many well established merits. Analogously, multidimensional Laplace transforms can be employed in the analysis of nonlinear analytic systems to provide similar benefits, including explicit input-output relationships. At present, one of...
Gespeichert in:
| Veröffentlicht in: | SIAM journal on applied mathematics 1974-06, Vol.26 (4), p.753-771 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 771 |
|---|---|
| container_issue | 4 |
| container_start_page | 753 |
| container_title | SIAM journal on applied mathematics |
| container_volume | 26 |
| creator | Crum, Larry A. Heinen, James A. |
| description | Application of Laplace transforms in linear systems analysis has many well established merits. Analogously, multidimensional Laplace transforms can be employed in the analysis of nonlinear analytic systems to provide similar benefits, including explicit input-output relationships. At present, one of the most serious drawbacks to the use of multidimensional transforms lies with the difficulty in reducing multidimensional kernels during inverse transformation. Herein, simplified reduction and expansion techniques for multidimensional inverse transformation will be presented. The labor involved in their application is comparable to that of familiar inverse transformation through use of Heaviside's expansions. Examples will help to clarify the techniques. |
| doi_str_mv | 10.1137/0126067 |
| format | Article |
| fullrecord | <record><control><sourceid>jstor_proqu</sourceid><recordid>TN_cdi_proquest_journals_917594029</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><jstor_id>2099982</jstor_id><sourcerecordid>2099982</sourcerecordid><originalsourceid>FETCH-LOGICAL-c269t-14e2e77b78171cec48423bd664980c6c9f831337ccebf1f899c1fc4b6b65bc83</originalsourceid><addsrcrecordid>eNo90E1LxDAQBuAgCq4f-Ac8BC-eqpmkm2SOsqwfuCKse_BW0jSBLm1Tkxb039t1F0_DDA_Dy0vIFbA7AKHuGXDJpDoiM2A4zxTwz2MyY0zIDATiKTlLacsYgMxxRtYfdTs2g-lcGBNdu2q0Qx06arqKLr9706XdFjx9m1Rd1a37u5iGrkzfGOvoJk7Ih9jSVxc716QLcuJNk9zlYZ6TzeNys3jOVu9PL4uHVWa5xCGD3HGnVKk0KLDO5jrnoqzkFEszKy16LUAIZa0rPXiNaMHbvJSlnJdWi3Nys3_bx_A1ujQU2zDGKVkqENQcc8ZxQrd7ZGNIKTpf9LFuTfwpgBW7uopDXZO83sttGkL8Z5whoubiF0tWZjc</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>917594029</pqid></control><display><type>article</type><title>Simultaneous Reduction and Expansion of Multidimensional Laplace Transform Kernels</title><source>JSTOR Mathematics & Statistics</source><source>JSTOR Archive Collection A-Z Listing</source><source>LOCUS - SIAM's Online Journal Archive</source><creator>Crum, Larry A. ; Heinen, James A.</creator><creatorcontrib>Crum, Larry A. ; Heinen, James A.</creatorcontrib><description>Application of Laplace transforms in linear systems analysis has many well established merits. Analogously, multidimensional Laplace transforms can be employed in the analysis of nonlinear analytic systems to provide similar benefits, including explicit input-output relationships. At present, one of the most serious drawbacks to the use of multidimensional transforms lies with the difficulty in reducing multidimensional kernels during inverse transformation. Herein, simplified reduction and expansion techniques for multidimensional inverse transformation will be presented. The labor involved in their application is comparable to that of familiar inverse transformation through use of Heaviside's expansions. Examples will help to clarify the techniques.</description><identifier>ISSN: 0036-1399</identifier><identifier>EISSN: 1095-712X</identifier><identifier>DOI: 10.1137/0126067</identifier><language>eng</language><publisher>Philadelphia: Society for Industrial and Applied Mathematics</publisher><subject>Complex variables ; Electrical engineering ; Electron mass ; Integrals ; Laplace transformation ; Laplace transforms ; Linear systems ; Mass ; Polynomials ; Power series ; Research and development laboratories ; Series convergence ; Variables</subject><ispartof>SIAM journal on applied mathematics, 1974-06, Vol.26 (4), p.753-771</ispartof><rights>Copyright 1974 Society for Industrial and Applied Mathematics</rights><rights>[Copyright] © 1974 Society for Industrial and Applied Mathematics</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c269t-14e2e77b78171cec48423bd664980c6c9f831337ccebf1f899c1fc4b6b65bc83</citedby><cites>FETCH-LOGICAL-c269t-14e2e77b78171cec48423bd664980c6c9f831337ccebf1f899c1fc4b6b65bc83</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.jstor.org/stable/pdf/2099982$$EPDF$$P50$$Gjstor$$H</linktopdf><linktohtml>$$Uhttps://www.jstor.org/stable/2099982$$EHTML$$P50$$Gjstor$$H</linktohtml><link.rule.ids>314,780,784,803,832,3183,27922,27923,58015,58019,58248,58252</link.rule.ids></links><search><creatorcontrib>Crum, Larry A.</creatorcontrib><creatorcontrib>Heinen, James A.</creatorcontrib><title>Simultaneous Reduction and Expansion of Multidimensional Laplace Transform Kernels</title><title>SIAM journal on applied mathematics</title><description>Application of Laplace transforms in linear systems analysis has many well established merits. Analogously, multidimensional Laplace transforms can be employed in the analysis of nonlinear analytic systems to provide similar benefits, including explicit input-output relationships. At present, one of the most serious drawbacks to the use of multidimensional transforms lies with the difficulty in reducing multidimensional kernels during inverse transformation. Herein, simplified reduction and expansion techniques for multidimensional inverse transformation will be presented. The labor involved in their application is comparable to that of familiar inverse transformation through use of Heaviside's expansions. Examples will help to clarify the techniques.</description><subject>Complex variables</subject><subject>Electrical engineering</subject><subject>Electron mass</subject><subject>Integrals</subject><subject>Laplace transformation</subject><subject>Laplace transforms</subject><subject>Linear systems</subject><subject>Mass</subject><subject>Polynomials</subject><subject>Power series</subject><subject>Research and development laboratories</subject><subject>Series convergence</subject><subject>Variables</subject><issn>0036-1399</issn><issn>1095-712X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1974</creationdate><recordtype>article</recordtype><sourceid>8G5</sourceid><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><sourceid>GUQSH</sourceid><sourceid>M2O</sourceid><recordid>eNo90E1LxDAQBuAgCq4f-Ac8BC-eqpmkm2SOsqwfuCKse_BW0jSBLm1Tkxb039t1F0_DDA_Dy0vIFbA7AKHuGXDJpDoiM2A4zxTwz2MyY0zIDATiKTlLacsYgMxxRtYfdTs2g-lcGBNdu2q0Qx06arqKLr9706XdFjx9m1Rd1a37u5iGrkzfGOvoJk7Ih9jSVxc716QLcuJNk9zlYZ6TzeNys3jOVu9PL4uHVWa5xCGD3HGnVKk0KLDO5jrnoqzkFEszKy16LUAIZa0rPXiNaMHbvJSlnJdWi3Nys3_bx_A1ujQU2zDGKVkqENQcc8ZxQrd7ZGNIKTpf9LFuTfwpgBW7uopDXZO83sttGkL8Z5whoubiF0tWZjc</recordid><startdate>19740601</startdate><enddate>19740601</enddate><creator>Crum, Larry A.</creator><creator>Heinen, James A.</creator><general>Society for Industrial and Applied Mathematics</general><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7RQ</scope><scope>7WY</scope><scope>7WZ</scope><scope>7X2</scope><scope>7XB</scope><scope>87Z</scope><scope>88A</scope><scope>88F</scope><scope>88I</scope><scope>88K</scope><scope>8AL</scope><scope>8FE</scope><scope>8FG</scope><scope>8FH</scope><scope>8FK</scope><scope>8FL</scope><scope>8G5</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>ATCPS</scope><scope>AZQEC</scope><scope>BBNVY</scope><scope>BENPR</scope><scope>BEZIV</scope><scope>BGLVJ</scope><scope>BHPHI</scope><scope>CCPQU</scope><scope>D1I</scope><scope>DWQXO</scope><scope>FRNLG</scope><scope>F~G</scope><scope>GNUQQ</scope><scope>GUQSH</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K60</scope><scope>K6~</scope><scope>K7-</scope><scope>KB.</scope><scope>L.-</scope><scope>L6V</scope><scope>LK8</scope><scope>M0C</scope><scope>M0K</scope><scope>M0N</scope><scope>M1Q</scope><scope>M2O</scope><scope>M2P</scope><scope>M2T</scope><scope>M7P</scope><scope>M7S</scope><scope>MBDVC</scope><scope>P5Z</scope><scope>P62</scope><scope>PATMY</scope><scope>PDBOC</scope><scope>PQBIZ</scope><scope>PQBZA</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><scope>PYCSY</scope><scope>Q9U</scope><scope>U9A</scope></search><sort><creationdate>19740601</creationdate><title>Simultaneous Reduction and Expansion of Multidimensional Laplace Transform Kernels</title><author>Crum, Larry A. ; Heinen, James A.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c269t-14e2e77b78171cec48423bd664980c6c9f831337ccebf1f899c1fc4b6b65bc83</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1974</creationdate><topic>Complex variables</topic><topic>Electrical engineering</topic><topic>Electron mass</topic><topic>Integrals</topic><topic>Laplace transformation</topic><topic>Laplace transforms</topic><topic>Linear systems</topic><topic>Mass</topic><topic>Polynomials</topic><topic>Power series</topic><topic>Research and development laboratories</topic><topic>Series convergence</topic><topic>Variables</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Crum, Larry A.</creatorcontrib><creatorcontrib>Heinen, James A.</creatorcontrib><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>Career & Technical Education Database</collection><collection>ABI/INFORM Collection</collection><collection>ABI/INFORM Global (PDF only)</collection><collection>Agricultural Science Collection</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>ABI/INFORM Global (Alumni Edition)</collection><collection>Biology Database (Alumni Edition)</collection><collection>Military Database (Alumni Edition)</collection><collection>Science Database (Alumni Edition)</collection><collection>Telecommunications (Alumni Edition)</collection><collection>Computing Database (Alumni Edition)</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Natural Science Collection</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>ABI/INFORM Collection (Alumni Edition)</collection><collection>Research Library (Alumni Edition)</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>Agricultural & Environmental Science Collection</collection><collection>ProQuest Central Essentials</collection><collection>Biological Science Collection</collection><collection>ProQuest Central</collection><collection>Business Premium Collection</collection><collection>Technology Collection</collection><collection>Natural Science Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Materials Science Collection</collection><collection>ProQuest Central Korea</collection><collection>Business Premium Collection (Alumni)</collection><collection>ABI/INFORM Global (Corporate)</collection><collection>ProQuest Central Student</collection><collection>Research Library Prep</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>ProQuest Business Collection (Alumni Edition)</collection><collection>ProQuest Business Collection</collection><collection>Computer Science Database</collection><collection>Materials Science Database</collection><collection>ABI/INFORM Professional Advanced</collection><collection>ProQuest Engineering Collection</collection><collection>ProQuest Biological Science Collection</collection><collection>ABI/INFORM Global</collection><collection>Agricultural Science Database</collection><collection>Computing Database</collection><collection>Military Database</collection><collection>Research Library</collection><collection>Science Database</collection><collection>Telecommunications Database</collection><collection>Biological Science Database</collection><collection>Engineering Database</collection><collection>Research Library (Corporate)</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>Environmental Science Database</collection><collection>Materials Science Collection</collection><collection>ProQuest One Business</collection><collection>ProQuest One Business (Alumni)</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection><collection>Environmental Science Collection</collection><collection>ProQuest Central Basic</collection><jtitle>SIAM journal on applied mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Crum, Larry A.</au><au>Heinen, James A.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Simultaneous Reduction and Expansion of Multidimensional Laplace Transform Kernels</atitle><jtitle>SIAM journal on applied mathematics</jtitle><date>1974-06-01</date><risdate>1974</risdate><volume>26</volume><issue>4</issue><spage>753</spage><epage>771</epage><pages>753-771</pages><issn>0036-1399</issn><eissn>1095-712X</eissn><abstract>Application of Laplace transforms in linear systems analysis has many well established merits. Analogously, multidimensional Laplace transforms can be employed in the analysis of nonlinear analytic systems to provide similar benefits, including explicit input-output relationships. At present, one of the most serious drawbacks to the use of multidimensional transforms lies with the difficulty in reducing multidimensional kernels during inverse transformation. Herein, simplified reduction and expansion techniques for multidimensional inverse transformation will be presented. The labor involved in their application is comparable to that of familiar inverse transformation through use of Heaviside's expansions. Examples will help to clarify the techniques.</abstract><cop>Philadelphia</cop><pub>Society for Industrial and Applied Mathematics</pub><doi>10.1137/0126067</doi><tpages>19</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0036-1399 |
| ispartof | SIAM journal on applied mathematics, 1974-06, Vol.26 (4), p.753-771 |
| issn | 0036-1399 1095-712X |
| language | eng |
| recordid | cdi_proquest_journals_917594029 |
| source | JSTOR Mathematics & Statistics; JSTOR Archive Collection A-Z Listing; LOCUS - SIAM's Online Journal Archive |
| subjects | Complex variables Electrical engineering Electron mass Integrals Laplace transformation Laplace transforms Linear systems Mass Polynomials Power series Research and development laboratories Series convergence Variables |
| title | Simultaneous Reduction and Expansion of Multidimensional Laplace Transform Kernels |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-10T09%3A39%3A33IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-jstor_proqu&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Simultaneous%20Reduction%20and%20Expansion%20of%20Multidimensional%20Laplace%20Transform%20Kernels&rft.jtitle=SIAM%20journal%20on%20applied%20mathematics&rft.au=Crum,%20Larry%20A.&rft.date=1974-06-01&rft.volume=26&rft.issue=4&rft.spage=753&rft.epage=771&rft.pages=753-771&rft.issn=0036-1399&rft.eissn=1095-712X&rft_id=info:doi/10.1137/0126067&rft_dat=%3Cjstor_proqu%3E2099982%3C/jstor_proqu%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=917594029&rft_id=info:pmid/&rft_jstor_id=2099982&rfr_iscdi=true |