Mathematical Physics Branches: Identifying Mixed Type Equations
The article focuses on the problem of defining paradigmatic relations between definitions of certain fields in mathematical physics. The ultimate goal is to outline the hierarchical relations between the terms that can be used when searching on the mathematical resources along with additional classi...
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| Published in | Lobachevskii journal of mathematics Vol. 40; no. 7; pp. 876 - 886 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Moscow
Pleiades Publishing
01.07.2019
Springer Nature B.V |
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| Online Access | Get full text |
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| Abstract | The article focuses on the problem of defining paradigmatic relations between definitions of certain fields in mathematical physics. The ultimate goal is to outline the hierarchical relations between the terms that can be used when searching on the mathematical resources along with additional classification parameters set in secondary documents. A thesaurus entry is selected as an information model. The thesaurus was formed by analyzing the original works of classics of mathematical analysis and differential calculus, and a representative list of articles was organized for that purpose. Following the example of thesaurus on the ‘problem of mixed type equations’ domain, a way of employing formulas in a mathematical article search is proposed. The paper covers a work script of a user, who is familiar with the subject domain and deals with papers done with the help of TeX-notation. A natural document indexing mechanism is set by key words in cited secondary documents. Such an approach helps to specify the search query with mathematical notation regardless the source language. The semantic links effect is based on usage of terms from the mathematical subject domain thesaurus stored with formulas that serve as a background for a mathematical search. It results in lower level of information noise and reduced search time. |
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| AbstractList | The article focuses on the problem of defining paradigmatic relations between definitions of certain fields in mathematical physics. The ultimate goal is to outline the hierarchical relations between the terms that can be used when searching on the mathematical resources along with additional classification parameters set in secondary documents. A thesaurus entry is selected as an information model. The thesaurus was formed by analyzing the original works of classics of mathematical analysis and differential calculus, and a representative list of articles was organized for that purpose. Following the example of thesaurus on the ‘problem of mixed type equations’ domain, a way of employing formulas in a mathematical article search is proposed. The paper covers a work script of a user, who is familiar with the subject domain and deals with papers done with the help of TeX-notation. A natural document indexing mechanism is set by key words in cited secondary documents. Such an approach helps to specify the search query with mathematical notation regardless the source language. The semantic links effect is based on usage of terms from the mathematical subject domain thesaurus stored with formulas that serve as a background for a mathematical search. It results in lower level of information noise and reduced search time. |
| Author | Serebryakov, V. A. Tuchkova, N. P. Ataeva, O. M. |
| Author_xml | – sequence: 1 givenname: O. M. surname: Ataeva fullname: Ataeva, O. M. email: oli@ultimeta.ru organization: Dorodnicyn Computing Center FRC “Computer Sciences and Control”, Russian Academy of Sciences – sequence: 2 givenname: V. A. surname: Serebryakov fullname: Serebryakov, V. A. email: serebr@ultimeta.ru organization: Dorodnicyn Computing Center FRC “Computer Sciences and Control”, Russian Academy of Sciences – sequence: 3 givenname: N. P. surname: Tuchkova fullname: Tuchkova, N. P. email: tuchkova@ccas.ru organization: Dorodnicyn Computing Center FRC “Computer Sciences and Control”, Russian Academy of Sciences |
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| Cites_doi | 10.1119/1.1972798 10.1002/bult.37 10.1134/S0012266116100086 10.1134/S1064562407060026 10.1002/9783527617234 10.1007/11856290_21 |
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| References | MoiseevE IMuromskijA ATuchkovaN PInternet and Mathematical Knowledge: Representation of the Equations of Mathematical Physics in the Information-Search Environment2008MoscowMAKS Press[in Russian] DemidovichB PModenovV PDifferential Equations, The School-Book2003St. PeterburgIvan Fedorov[in Russian] FranklFCauchy’s problem for partial differential equations of mixed elliptico-hyperbolic type with initial data on the parabolic lineIzv. Akad. Nauk SSSR, Ser. Mat.19448195224123720061.21604 Handbook of UDC. https://teacode.com/online/udc/. Accessed 2019. SteklovV AThe Main Problems of Mathematical Physics1983MoscowNauka0547.35004[in Russian] SobolevS LPartial Differential Equations of Mathematical Physics1966MoscowNauka10.1119/1.1972798Pergamon, Oxford, 1964 GermainPBaderRProblemes elliptiques et hyperboliques singuliers pour une equation du type mixte1952Chatillon-sous-BagneuxO.N.E.R.A.No. 60 State Rubricator of Scientific and Technical Information. http://grnti.ru/. Accessed 2019. VinogradovI MMathematical Encyclopedy1979MoscowSov. EncyclopediaVol. 2 [in Russian] Ph. Bond, The Era of Mathematics. https://epsrc.ukri.org/newsevents/pubs/era-of-maths/. Accessed 2019. BitsadzeA VEquations of Mathematical Physics1982MoscowNauka0554.35001Mir, Moscow, 1980 KoshlaykovN SGlinerE BSmirnovM MDifferential Equations of Mathematical Physics1962MoscowFizmatlit[in Russian] Lavrent’evM ABitsadzeA VTo the problem of equations of mixed typeDokl. Akad. Nauk1950703733760040.20001 Interstate Standard. System of Standards on Information, Librarianship and Publishing. Search and Disseminate of Information. http://bibliography.ufacom.ru/method/gosts/7-73/7_73.htm. Accessed 2019. Il’inV AMoiseevE IOptimization of a boundary control by a displacement at one end of a string with second end free during an arbitrary sufficiently large time intervalDokl. Math.200776806811245444110.1134/S10645624070600261151.49003 Intelligent Computer Mathematics, Proceedings of 10th International Conference, CICM 2017, Edinburgh, UK, July 17–21, 2017, Ed. by H. Geuvers, M. England, O. Hasan, F. Rabe, and O. Teschke, Vol. 18 of Lecture Notes in Artificial Intelligence (Springer, 2017). MoiseevE IMuromskiiA ATuchkovaN PInformation Search with Thesaurus in Application Area of Ordinary Differential Equations2005MoscowMAKS Press[in Russian] AramanovichI GLevinV IEquations of Mathematical Physics1969MoscowNauka[in Russian] Dewey Decimal Classification. https://www.oclc.org/en/dewey.html. Accessed 2019. BabenkoK BOn the theory of equations of mixed type1952MoscowMath. Inst. Acad. Sci. USSR TricomiFEquazioni a derivate parziali1957RomaCremonese0086.29501[in Italian] ColeT WDrakeMMathematics Databases, Encyclopedia of Library and Information Science2003New YorkMarcel Dekker17921795 CourantRHilbertDMethods of Mathematical Physics2008TorontoWiley-VCH0121.07801Vol. 2 MoiseevE ILihomanenkoT NEigenfunctions of the Tricomi problem with an inclined type change lineDiffer. Equat.20165213231330358268010.1134/S00122661161000861357.35234 BersLJohnFSchechterMPartial Differential Equations1971ProvidenceAm. Math. Soc. Mathematics Subject Classification. http://msc2010.org/mediawiki/index.php?title=MSC2010. Accessed 2019. MoiseevE IMuromslijA ATuchkovaN POn the subject area thesaurus mixed equations of mathematical physicsCEUR Workshop Proc.20182260395405 GellerstedtSFr Sur un probleme aux limites pour une equation lineaire aux derivees partielles du second ordre de type mixte1935UppsalaAlmqvist och Wiksells61.1259.02 SerebryakovV AAtaevaO MInformation model of the open personal semantic library LibmetaProceedings of the 18th All-Russia Conference on Scientific Service on the Internet, Novorossijsk, Sept. 19–24, 20162016MoscowIPM im. M. V. Keldysha RAN304313 TimoshenkoS PGoodierDTheory of Elasticity1970ColumbusMcGraw-Hill Education0266.73008 PetrowskyI GLectures on Partial Differential Equations1950Moscow, LeningradGNTLDover, New York, 1992 LurieSBelovPTuchkovaNThe application of the multiscale models for description of the dispersed compositesComput. Mater. Sci. A200436145152 SmirnovM MMixed Type Equations1970MoscowNauka[in Russian] Il’inV AMoiseevE IA nonlocal boundary value problem of the second kind for the Sturm-Liouville operatorDiffer. Uravn.198723142214319095900668.34024 VekuaI NNew Methods for Solving Elliptical Equations1948MoscowOGIZ Gostekhizdat[in Russian] VolkovV SDifferential Equations and Their Applications in Natural Science1961LeningradLeningr. Gos. Univ.[in Russian] SabitovK BEquations of Mathematical Physics, The School-Book for Higher School2003MoscowVysshaya Shkola[in Russian] C. N. Moore, “Mooers Law, or why some retrieval systems are used and others are not,” Bull. Assoc. Inform. Sci. Technol., №23, 22–23 (1996). https://doi.org/10.1002/bult.37 VladimirovV SEquations of Mathematical Physics1981MoscowNaukaImported Publ., 1985 R. Mayans, “The future of mathematical text: a proposal for a new internet hypertext for mathematics,” J. Digital Inform. 5 (1) (2006). https://journals.tdl.org/jodi/index.php/jodi/article/view/128/126. Accessed 2019. SveshnikovA GBogolubovA NKravtsovV VLectures on Mathematical Physics, The School-Book1993MoscowMosk. Gos. Univ.[in Russian] M. Kohlhase and I. A. Sucan, “A search engine for mathematical formulae,” in Proceedings of the Artificial Intelligence and Symbolic Computation, Lect. Notes Artif. Intell. (4120), 241–253 (2006). TikhonovA NSamarskiiA AEquations of Mathematical Physics, The School-Book19996th ed.MoscowMosk. Gos. Univ.Pergamon, Oxford, 1963 (4893_CR10) 1979 S Lurie (4893_CR27) 2004; 36 E I Moiseev (4893_CR19) 2008 N S Koshlaykov (4893_CR23) 1962 A N Tikhonov (4893_CR11) 1999 K B Sabitov (4893_CR29) 2003 S P Timoshenko (4893_CR26) 1970 S L Sobolev (4893_CR24) 1966 V A Il’in (4893_CR25) 2007; 76 K B Babenko (4893_CR36) 1952 E I Moiseev (4893_CR39) 2018; 2260 4893_CR8 I G Petrowsky (4893_CR28) 1950 I N Vekua (4893_CR34) 1948 T W Cole (4893_CR4) 2003 V S Volkov (4893_CR21) 1961 4893_CR1 4893_CR3 4893_CR2 V A Steklov (4893_CR13) 1983 A V Bitsadze (4893_CR17) 1982 4893_CR5 4893_CR7 4893_CR6 4893_CR41 V A Il’in (4893_CR18) 1987; 23 4893_CR43 4893_CR42 M M Smirnov (4893_CR16) 1970 E I Moiseev (4893_CR40) 2016; 52 V S Vladimirov (4893_CR14) 1981 F Tricomi (4893_CR30) 1957 L Bers (4893_CR31) 1971 R Courant (4893_CR15) 2008 S Gellerstedt (4893_CR32) 1935 B P Demidovich (4893_CR22) 2003 V A Serebryakov (4893_CR38) 2016 A G Sveshnikov (4893_CR12) 1993 I G Aramanovich (4893_CR20) 1969 F Frankl (4893_CR33) 1944; 8 P Germain (4893_CR37) 1952 M A Lavrent’ev (4893_CR35) 1950; 70 E I Moiseev (4893_CR9) 2005 |
| References_xml | – reference: Mathematics Subject Classification. http://msc2010.org/mediawiki/index.php?title=MSC2010. Accessed 2019. – reference: VekuaI NNew Methods for Solving Elliptical Equations1948MoscowOGIZ Gostekhizdat[in Russian] – reference: VolkovV SDifferential Equations and Their Applications in Natural Science1961LeningradLeningr. Gos. Univ.[in Russian] – reference: GellerstedtSFr Sur un probleme aux limites pour une equation lineaire aux derivees partielles du second ordre de type mixte1935UppsalaAlmqvist och Wiksells61.1259.02 – reference: SmirnovM MMixed Type Equations1970MoscowNauka[in Russian] – reference: BabenkoK BOn the theory of equations of mixed type1952MoscowMath. Inst. Acad. Sci. USSR – reference: SveshnikovA GBogolubovA NKravtsovV VLectures on Mathematical Physics, The School-Book1993MoscowMosk. Gos. Univ.[in Russian] – reference: SerebryakovV AAtaevaO MInformation model of the open personal semantic library LibmetaProceedings of the 18th All-Russia Conference on Scientific Service on the Internet, Novorossijsk, Sept. 19–24, 20162016MoscowIPM im. M. V. Keldysha RAN304313 – reference: Ph. Bond, The Era of Mathematics. https://epsrc.ukri.org/newsevents/pubs/era-of-maths/. Accessed 2019. – reference: Il’inV AMoiseevE IOptimization of a boundary control by a displacement at one end of a string with second end free during an arbitrary sufficiently large time intervalDokl. Math.200776806811245444110.1134/S10645624070600261151.49003 – reference: SabitovK BEquations of Mathematical Physics, The School-Book for Higher School2003MoscowVysshaya Shkola[in Russian] – reference: M. Kohlhase and I. A. Sucan, “A search engine for mathematical formulae,” in Proceedings of the Artificial Intelligence and Symbolic Computation, Lect. Notes Artif. Intell. (4120), 241–253 (2006). – reference: Handbook of UDC. https://teacode.com/online/udc/. Accessed 2019. – reference: GermainPBaderRProblemes elliptiques et hyperboliques singuliers pour une equation du type mixte1952Chatillon-sous-BagneuxO.N.E.R.A.No. 60 – reference: FranklFCauchy’s problem for partial differential equations of mixed elliptico-hyperbolic type with initial data on the parabolic lineIzv. Akad. Nauk SSSR, Ser. Mat.19448195224123720061.21604 – reference: Intelligent Computer Mathematics, Proceedings of 10th International Conference, CICM 2017, Edinburgh, UK, July 17–21, 2017, Ed. by H. Geuvers, M. England, O. Hasan, F. Rabe, and O. Teschke, Vol. 18 of Lecture Notes in Artificial Intelligence (Springer, 2017). – reference: Lavrent’evM ABitsadzeA VTo the problem of equations of mixed typeDokl. Akad. Nauk1950703733760040.20001 – reference: MoiseevE IMuromslijA ATuchkovaN POn the subject area thesaurus mixed equations of mathematical physicsCEUR Workshop Proc.20182260395405 – reference: TikhonovA NSamarskiiA AEquations of Mathematical Physics, The School-Book19996th ed.MoscowMosk. Gos. Univ.Pergamon, Oxford, 1963 – reference: ColeT WDrakeMMathematics Databases, Encyclopedia of Library and Information Science2003New YorkMarcel Dekker17921795 – reference: PetrowskyI GLectures on Partial Differential Equations1950Moscow, LeningradGNTLDover, New York, 1992 – reference: CourantRHilbertDMethods of Mathematical Physics2008TorontoWiley-VCH0121.07801Vol. 2 – reference: TimoshenkoS PGoodierDTheory of Elasticity1970ColumbusMcGraw-Hill Education0266.73008 – reference: Interstate Standard. System of Standards on Information, Librarianship and Publishing. Search and Disseminate of Information. http://bibliography.ufacom.ru/method/gosts/7-73/7_73.htm. Accessed 2019. – reference: LurieSBelovPTuchkovaNThe application of the multiscale models for description of the dispersed compositesComput. Mater. Sci. A200436145152 – reference: MoiseevE ILihomanenkoT NEigenfunctions of the Tricomi problem with an inclined type change lineDiffer. Equat.20165213231330358268010.1134/S00122661161000861357.35234 – reference: DemidovichB PModenovV PDifferential Equations, The School-Book2003St. PeterburgIvan Fedorov[in Russian] – reference: MoiseevE IMuromskiiA ATuchkovaN PInformation Search with Thesaurus in Application Area of Ordinary Differential Equations2005MoscowMAKS Press[in Russian] – reference: KoshlaykovN SGlinerE BSmirnovM MDifferential Equations of Mathematical Physics1962MoscowFizmatlit[in Russian] – reference: TricomiFEquazioni a derivate parziali1957RomaCremonese0086.29501[in Italian] – reference: Dewey Decimal Classification. https://www.oclc.org/en/dewey.html. Accessed 2019. – reference: C. N. Moore, “Mooers Law, or why some retrieval systems are used and others are not,” Bull. Assoc. Inform. Sci. Technol., №23, 22–23 (1996). https://doi.org/10.1002/bult.37 – reference: VladimirovV SEquations of Mathematical Physics1981MoscowNaukaImported Publ., 1985 – reference: BitsadzeA VEquations of Mathematical Physics1982MoscowNauka0554.35001Mir, Moscow, 1980 – reference: VinogradovI MMathematical Encyclopedy1979MoscowSov. EncyclopediaVol. 2 [in Russian] – reference: BersLJohnFSchechterMPartial Differential Equations1971ProvidenceAm. Math. Soc. – reference: State Rubricator of Scientific and Technical Information. http://grnti.ru/. Accessed 2019. – reference: MoiseevE IMuromskijA ATuchkovaN PInternet and Mathematical Knowledge: Representation of the Equations of Mathematical Physics in the Information-Search Environment2008MoscowMAKS Press[in Russian] – reference: SteklovV AThe Main Problems of Mathematical Physics1983MoscowNauka0547.35004[in Russian] – reference: Il’inV AMoiseevE IA nonlocal boundary value problem of the second kind for the Sturm-Liouville operatorDiffer. Uravn.198723142214319095900668.34024 – reference: R. Mayans, “The future of mathematical text: a proposal for a new internet hypertext for mathematics,” J. Digital Inform. 5 (1) (2006). https://journals.tdl.org/jodi/index.php/jodi/article/view/128/126. Accessed 2019. – reference: SobolevS LPartial Differential Equations of Mathematical Physics1966MoscowNauka10.1119/1.1972798Pergamon, Oxford, 1964 – reference: AramanovichI GLevinV IEquations of Mathematical Physics1969MoscowNauka[in Russian] – ident: 4893_CR5 – ident: 4893_CR3 – volume-title: Fr Sur un probleme aux limites pour une equation lineaire aux derivees partielles du second ordre de type mixte year: 1935 ident: 4893_CR32 – volume: 23 start-page: 1422 year: 1987 ident: 4893_CR18 publication-title: Differ. Uravn. – ident: 4893_CR1 – volume: 2260 start-page: 395 year: 2018 ident: 4893_CR39 publication-title: CEUR Workshop Proc. – volume-title: Equations of Mathematical Physics year: 1969 ident: 4893_CR20 – ident: 4893_CR7 – volume-title: Equations of Mathematical Physics year: 1981 ident: 4893_CR14 – volume: 8 start-page: 195 year: 1944 ident: 4893_CR33 publication-title: Izv. Akad. Nauk SSSR, Ser. Mat. – volume-title: Theory of Elasticity year: 1970 ident: 4893_CR26 – volume-title: Internet and Mathematical Knowledge: Representation of the Equations of Mathematical Physics in the Information-Search Environment year: 2008 ident: 4893_CR19 – volume-title: Problemes elliptiques et hyperboliques singuliers pour une equation du type mixte year: 1952 ident: 4893_CR37 – volume-title: Information Search with Thesaurus in Application Area of Ordinary Differential Equations year: 2005 ident: 4893_CR9 – start-page: 304 volume-title: Proceedings of the 18th All-Russia Conference on Scientific Service on the Internet, Novorossijsk, Sept. 19–24, 2016 year: 2016 ident: 4893_CR38 – volume-title: The Main Problems of Mathematical Physics year: 1983 ident: 4893_CR13 – volume-title: Differential Equations of Mathematical Physics year: 1962 ident: 4893_CR23 – volume-title: Partial Differential Equations year: 1971 ident: 4893_CR31 – start-page: 1792 volume-title: Mathematics Databases, Encyclopedia of Library and Information Science year: 2003 ident: 4893_CR4 – volume-title: Equations of Mathematical Physics year: 1982 ident: 4893_CR17 – volume-title: Partial Differential Equations of Mathematical Physics year: 1966 ident: 4893_CR24 doi: 10.1119/1.1972798 – volume-title: Equations of Mathematical Physics, The School-Book for Higher School year: 2003 ident: 4893_CR29 – volume-title: Equations of Mathematical Physics, The School-Book year: 1999 ident: 4893_CR11 – volume: 36 start-page: 145 year: 2004 ident: 4893_CR27 publication-title: Comput. Mater. Sci. A – ident: 4893_CR41 doi: 10.1002/bult.37 – volume-title: Differential Equations and Their Applications in Natural Science year: 1961 ident: 4893_CR21 – volume: 70 start-page: 373 year: 1950 ident: 4893_CR35 publication-title: Dokl. Akad. Nauk – volume-title: On the theory of equations of mixed type year: 1952 ident: 4893_CR36 – ident: 4893_CR2 – volume-title: Lectures on Mathematical Physics, The School-Book year: 1993 ident: 4893_CR12 – volume-title: Mathematical Encyclopedy year: 1979 ident: 4893_CR10 – volume: 52 start-page: 1323 year: 2016 ident: 4893_CR40 publication-title: Differ. Equat. doi: 10.1134/S0012266116100086 – ident: 4893_CR6 – ident: 4893_CR8 – volume-title: Mixed Type Equations year: 1970 ident: 4893_CR16 – volume: 76 start-page: 806 year: 2007 ident: 4893_CR25 publication-title: Dokl. Math. doi: 10.1134/S1064562407060026 – volume-title: Methods of Mathematical Physics year: 2008 ident: 4893_CR15 doi: 10.1002/9783527617234 – volume-title: New Methods for Solving Elliptical Equations year: 1948 ident: 4893_CR34 – volume-title: Lectures on Partial Differential Equations year: 1950 ident: 4893_CR28 – volume-title: Differential Equations, The School-Book year: 2003 ident: 4893_CR22 – ident: 4893_CR42 doi: 10.1007/11856290_21 – volume-title: Equazioni a derivate parziali year: 1957 ident: 4893_CR30 – ident: 4893_CR43 |
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