Conservation laws in differential geometry of plane curves and for eikonal equation and inverse problems
We derive the new conservation laws for a set ofarbitrary smooth plane curves. In these laws a solenoidal field isexpressed in terms of the Frenet unit vectors or in terms of thecurvature vectors. When curves are vector lines of an arbitrarysmooth vector field, these laws have identical form in term...
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| Autor*in: |
Megrabov, Alexander G. [verfasserIn] |
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| Format: |
E-Artikel |
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| Erschienen: |
Walter de Gruyter GmbH ; 2013 |
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| Schlagwörter: |
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| Umfang: |
28 |
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| Reproduktion: |
Walter de Gruyter Online Zeitschriften |
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| Übergeordnetes Werk: |
Enthalten in: Journal of inverse and ill-posed problems - Berlin : de Gruyter, 1993, 21(2013), 5 vom: 11. Jan., Seite 601-628 |
| Übergeordnetes Werk: |
volume:21 ; year:2013 ; number:5 ; day:11 ; month:01 ; pages:601-628 ; extent:28 |
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| DOI / URN: |
10.1515/jip-2012-0067 |
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NLEJ247091855 |
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| 520 | |a We derive the new conservation laws for a set ofarbitrary smooth plane curves. In these laws a solenoidal field isexpressed in terms of the Frenet unit vectors or in terms of thecurvature vectors. When curves are vector lines of an arbitrarysmooth vector field, these laws have identical form in terms ofthis field or its field of directions. Also, a series of vectoranalysis formulas as differential identities relating the modulusand direction of a vector field is obtained. It is based on thesegeneral formulas, the conservation laws for the kinematic seismics(geometrical optics) for a scalar time field, i.e., for thesolutions of the eikonal equation are found. Some other formulasrelating the time field and a characteristic of a medium(refractive index) are also given. In particular, we present theformula for determining an integral characteristic of a medium inthe inverse problem formulation. All the formulas obtainedoriginate from studying the differential invariants of a Lie group(an extension of the group of conformal transformations) which isrealized as the equivalence group admitted by the eikonal equationand some other equations of mathematical physics. | ||
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10.1515/jip-2012-0067 doi artikel_Grundlieferung.pp (DE-627)NLEJ247091855 DE-627 ger DE-627 rakwb Megrabov, Alexander G. verfasserin aut Conservation laws in differential geometry of plane curves and for eikonal equation and inverse problems Walter de Gruyter GmbH 2013 28 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We derive the new conservation laws for a set ofarbitrary smooth plane curves. In these laws a solenoidal field isexpressed in terms of the Frenet unit vectors or in terms of thecurvature vectors. When curves are vector lines of an arbitrarysmooth vector field, these laws have identical form in terms ofthis field or its field of directions. Also, a series of vectoranalysis formulas as differential identities relating the modulusand direction of a vector field is obtained. It is based on thesegeneral formulas, the conservation laws for the kinematic seismics(geometrical optics) for a scalar time field, i.e., for thesolutions of the eikonal equation are found. Some other formulasrelating the time field and a characteristic of a medium(refractive index) are also given. In particular, we present theformula for determining an integral characteristic of a medium inthe inverse problem formulation. All the formulas obtainedoriginate from studying the differential invariants of a Lie group(an extension of the group of conformal transformations) which isrealized as the equivalence group admitted by the eikonal equationand some other equations of mathematical physics. Walter de Gruyter Online Zeitschriften Plane curves vector fields conservation laws equivalence group differential identities eikonal equation inverse problem Enthalten in Journal of inverse and ill-posed problems Berlin : de Gruyter, 1993 21(2013), 5 vom: 11. Jan., Seite 601-628 (DE-627)NLEJ248236091 (DE-600)2041913-2 1569-3945 nnns volume:21 year:2013 number:5 day:11 month:01 pages:601-628 extent:28 https://doi.org/10.1515/jip-2012-0067 Deutschlandweit zugänglich GBV_USEFLAG_U ZDB-1-DGR GBV_NL_ARTICLE AR 21 2013 5 11 01 601-628 28 |
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10.1515/jip-2012-0067 doi artikel_Grundlieferung.pp (DE-627)NLEJ247091855 DE-627 ger DE-627 rakwb Megrabov, Alexander G. verfasserin aut Conservation laws in differential geometry of plane curves and for eikonal equation and inverse problems Walter de Gruyter GmbH 2013 28 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We derive the new conservation laws for a set ofarbitrary smooth plane curves. In these laws a solenoidal field isexpressed in terms of the Frenet unit vectors or in terms of thecurvature vectors. When curves are vector lines of an arbitrarysmooth vector field, these laws have identical form in terms ofthis field or its field of directions. Also, a series of vectoranalysis formulas as differential identities relating the modulusand direction of a vector field is obtained. It is based on thesegeneral formulas, the conservation laws for the kinematic seismics(geometrical optics) for a scalar time field, i.e., for thesolutions of the eikonal equation are found. Some other formulasrelating the time field and a characteristic of a medium(refractive index) are also given. In particular, we present theformula for determining an integral characteristic of a medium inthe inverse problem formulation. All the formulas obtainedoriginate from studying the differential invariants of a Lie group(an extension of the group of conformal transformations) which isrealized as the equivalence group admitted by the eikonal equationand some other equations of mathematical physics. Walter de Gruyter Online Zeitschriften Plane curves vector fields conservation laws equivalence group differential identities eikonal equation inverse problem Enthalten in Journal of inverse and ill-posed problems Berlin : de Gruyter, 1993 21(2013), 5 vom: 11. Jan., Seite 601-628 (DE-627)NLEJ248236091 (DE-600)2041913-2 1569-3945 nnns volume:21 year:2013 number:5 day:11 month:01 pages:601-628 extent:28 https://doi.org/10.1515/jip-2012-0067 Deutschlandweit zugänglich GBV_USEFLAG_U ZDB-1-DGR GBV_NL_ARTICLE AR 21 2013 5 11 01 601-628 28 |
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10.1515/jip-2012-0067 doi artikel_Grundlieferung.pp (DE-627)NLEJ247091855 DE-627 ger DE-627 rakwb Megrabov, Alexander G. verfasserin aut Conservation laws in differential geometry of plane curves and for eikonal equation and inverse problems Walter de Gruyter GmbH 2013 28 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We derive the new conservation laws for a set ofarbitrary smooth plane curves. In these laws a solenoidal field isexpressed in terms of the Frenet unit vectors or in terms of thecurvature vectors. When curves are vector lines of an arbitrarysmooth vector field, these laws have identical form in terms ofthis field or its field of directions. Also, a series of vectoranalysis formulas as differential identities relating the modulusand direction of a vector field is obtained. It is based on thesegeneral formulas, the conservation laws for the kinematic seismics(geometrical optics) for a scalar time field, i.e., for thesolutions of the eikonal equation are found. Some other formulasrelating the time field and a characteristic of a medium(refractive index) are also given. In particular, we present theformula for determining an integral characteristic of a medium inthe inverse problem formulation. All the formulas obtainedoriginate from studying the differential invariants of a Lie group(an extension of the group of conformal transformations) which isrealized as the equivalence group admitted by the eikonal equationand some other equations of mathematical physics. Walter de Gruyter Online Zeitschriften Plane curves vector fields conservation laws equivalence group differential identities eikonal equation inverse problem Enthalten in Journal of inverse and ill-posed problems Berlin : de Gruyter, 1993 21(2013), 5 vom: 11. Jan., Seite 601-628 (DE-627)NLEJ248236091 (DE-600)2041913-2 1569-3945 nnns volume:21 year:2013 number:5 day:11 month:01 pages:601-628 extent:28 https://doi.org/10.1515/jip-2012-0067 Deutschlandweit zugänglich GBV_USEFLAG_U ZDB-1-DGR GBV_NL_ARTICLE AR 21 2013 5 11 01 601-628 28 |
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10.1515/jip-2012-0067 doi artikel_Grundlieferung.pp (DE-627)NLEJ247091855 DE-627 ger DE-627 rakwb Megrabov, Alexander G. verfasserin aut Conservation laws in differential geometry of plane curves and for eikonal equation and inverse problems Walter de Gruyter GmbH 2013 28 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We derive the new conservation laws for a set ofarbitrary smooth plane curves. In these laws a solenoidal field isexpressed in terms of the Frenet unit vectors or in terms of thecurvature vectors. When curves are vector lines of an arbitrarysmooth vector field, these laws have identical form in terms ofthis field or its field of directions. Also, a series of vectoranalysis formulas as differential identities relating the modulusand direction of a vector field is obtained. It is based on thesegeneral formulas, the conservation laws for the kinematic seismics(geometrical optics) for a scalar time field, i.e., for thesolutions of the eikonal equation are found. Some other formulasrelating the time field and a characteristic of a medium(refractive index) are also given. In particular, we present theformula for determining an integral characteristic of a medium inthe inverse problem formulation. All the formulas obtainedoriginate from studying the differential invariants of a Lie group(an extension of the group of conformal transformations) which isrealized as the equivalence group admitted by the eikonal equationand some other equations of mathematical physics. Walter de Gruyter Online Zeitschriften Plane curves vector fields conservation laws equivalence group differential identities eikonal equation inverse problem Enthalten in Journal of inverse and ill-posed problems Berlin : de Gruyter, 1993 21(2013), 5 vom: 11. Jan., Seite 601-628 (DE-627)NLEJ248236091 (DE-600)2041913-2 1569-3945 nnns volume:21 year:2013 number:5 day:11 month:01 pages:601-628 extent:28 https://doi.org/10.1515/jip-2012-0067 Deutschlandweit zugänglich GBV_USEFLAG_U ZDB-1-DGR GBV_NL_ARTICLE AR 21 2013 5 11 01 601-628 28 |
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10.1515/jip-2012-0067 doi artikel_Grundlieferung.pp (DE-627)NLEJ247091855 DE-627 ger DE-627 rakwb Megrabov, Alexander G. verfasserin aut Conservation laws in differential geometry of plane curves and for eikonal equation and inverse problems Walter de Gruyter GmbH 2013 28 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We derive the new conservation laws for a set ofarbitrary smooth plane curves. In these laws a solenoidal field isexpressed in terms of the Frenet unit vectors or in terms of thecurvature vectors. When curves are vector lines of an arbitrarysmooth vector field, these laws have identical form in terms ofthis field or its field of directions. Also, a series of vectoranalysis formulas as differential identities relating the modulusand direction of a vector field is obtained. It is based on thesegeneral formulas, the conservation laws for the kinematic seismics(geometrical optics) for a scalar time field, i.e., for thesolutions of the eikonal equation are found. Some other formulasrelating the time field and a characteristic of a medium(refractive index) are also given. In particular, we present theformula for determining an integral characteristic of a medium inthe inverse problem formulation. All the formulas obtainedoriginate from studying the differential invariants of a Lie group(an extension of the group of conformal transformations) which isrealized as the equivalence group admitted by the eikonal equationand some other equations of mathematical physics. Walter de Gruyter Online Zeitschriften Plane curves vector fields conservation laws equivalence group differential identities eikonal equation inverse problem Enthalten in Journal of inverse and ill-posed problems Berlin : de Gruyter, 1993 21(2013), 5 vom: 11. Jan., Seite 601-628 (DE-627)NLEJ248236091 (DE-600)2041913-2 1569-3945 nnns volume:21 year:2013 number:5 day:11 month:01 pages:601-628 extent:28 https://doi.org/10.1515/jip-2012-0067 Deutschlandweit zugänglich GBV_USEFLAG_U ZDB-1-DGR GBV_NL_ARTICLE AR 21 2013 5 11 01 601-628 28 |
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Conservation laws in differential geometry of plane curves and for eikonal equation and inverse problems |
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We derive the new conservation laws for a set ofarbitrary smooth plane curves. In these laws a solenoidal field isexpressed in terms of the Frenet unit vectors or in terms of thecurvature vectors. When curves are vector lines of an arbitrarysmooth vector field, these laws have identical form in terms ofthis field or its field of directions. Also, a series of vectoranalysis formulas as differential identities relating the modulusand direction of a vector field is obtained. It is based on thesegeneral formulas, the conservation laws for the kinematic seismics(geometrical optics) for a scalar time field, i.e., for thesolutions of the eikonal equation are found. Some other formulasrelating the time field and a characteristic of a medium(refractive index) are also given. In particular, we present theformula for determining an integral characteristic of a medium inthe inverse problem formulation. All the formulas obtainedoriginate from studying the differential invariants of a Lie group(an extension of the group of conformal transformations) which isrealized as the equivalence group admitted by the eikonal equationand some other equations of mathematical physics. |
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We derive the new conservation laws for a set ofarbitrary smooth plane curves. In these laws a solenoidal field isexpressed in terms of the Frenet unit vectors or in terms of thecurvature vectors. When curves are vector lines of an arbitrarysmooth vector field, these laws have identical form in terms ofthis field or its field of directions. Also, a series of vectoranalysis formulas as differential identities relating the modulusand direction of a vector field is obtained. It is based on thesegeneral formulas, the conservation laws for the kinematic seismics(geometrical optics) for a scalar time field, i.e., for thesolutions of the eikonal equation are found. Some other formulasrelating the time field and a characteristic of a medium(refractive index) are also given. In particular, we present theformula for determining an integral characteristic of a medium inthe inverse problem formulation. All the formulas obtainedoriginate from studying the differential invariants of a Lie group(an extension of the group of conformal transformations) which isrealized as the equivalence group admitted by the eikonal equationand some other equations of mathematical physics. |
| abstract_unstemmed |
We derive the new conservation laws for a set ofarbitrary smooth plane curves. In these laws a solenoidal field isexpressed in terms of the Frenet unit vectors or in terms of thecurvature vectors. When curves are vector lines of an arbitrarysmooth vector field, these laws have identical form in terms ofthis field or its field of directions. Also, a series of vectoranalysis formulas as differential identities relating the modulusand direction of a vector field is obtained. It is based on thesegeneral formulas, the conservation laws for the kinematic seismics(geometrical optics) for a scalar time field, i.e., for thesolutions of the eikonal equation are found. Some other formulasrelating the time field and a characteristic of a medium(refractive index) are also given. In particular, we present theformula for determining an integral characteristic of a medium inthe inverse problem formulation. All the formulas obtainedoriginate from studying the differential invariants of a Lie group(an extension of the group of conformal transformations) which isrealized as the equivalence group admitted by the eikonal equationand some other equations of mathematical physics. |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">NLEJ247091855</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20220820030151.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">220814s2013 xx |||||o 00| ||und c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1515/jip-2012-0067</subfield><subfield code="2">doi</subfield></datafield><datafield tag="028" ind1="5" ind2="2"><subfield code="a">artikel_Grundlieferung.pp</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)NLEJ247091855</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Megrabov, Alexander G.</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Conservation laws in differential geometry of plane curves and for eikonal equation and inverse problems</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="b">Walter de Gruyter GmbH</subfield><subfield code="c">2013</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">28</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">We derive the new conservation laws for a set ofarbitrary smooth plane curves. In these laws a solenoidal field isexpressed in terms of the Frenet unit vectors or in terms of thecurvature vectors. When curves are vector lines of an arbitrarysmooth vector field, these laws have identical form in terms ofthis field or its field of directions. Also, a series of vectoranalysis formulas as differential identities relating the modulusand direction of a vector field is obtained. It is based on thesegeneral formulas, the conservation laws for the kinematic seismics(geometrical optics) for a scalar time field, i.e., for thesolutions of the eikonal equation are found. Some other formulasrelating the time field and a characteristic of a medium(refractive index) are also given. In particular, we present theformula for determining an integral characteristic of a medium inthe inverse problem formulation. All the formulas obtainedoriginate from studying the differential invariants of a Lie group(an extension of the group of conformal transformations) which isrealized as the equivalence group admitted by the eikonal equationand some other equations of mathematical physics.</subfield></datafield><datafield tag="533" ind1=" " ind2=" "><subfield code="f">Walter de Gruyter Online Zeitschriften</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Plane curves</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">vector fields</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">conservation laws</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">equivalence group</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">differential identities</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">eikonal equation</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">inverse problem</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Journal of inverse and ill-posed problems</subfield><subfield code="d">Berlin : de Gruyter, 1993</subfield><subfield code="g">21(2013), 5 vom: 11. Jan., Seite 601-628</subfield><subfield code="w">(DE-627)NLEJ248236091</subfield><subfield code="w">(DE-600)2041913-2</subfield><subfield code="x">1569-3945</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:21</subfield><subfield code="g">year:2013</subfield><subfield code="g">number:5</subfield><subfield code="g">day:11</subfield><subfield code="g">month:01</subfield><subfield code="g">pages:601-628</subfield><subfield code="g">extent:28</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1515/jip-2012-0067</subfield><subfield code="z">Deutschlandweit zugänglich</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_U</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-1-DGR</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_NL_ARTICLE</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">21</subfield><subfield code="j">2013</subfield><subfield code="e">5</subfield><subfield code="b">11</subfield><subfield code="c">01</subfield><subfield code="h">601-628</subfield><subfield code="g">28</subfield></datafield></record></collection>
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