Ontology type: schema:ScholarlyArticle
2021-10-27
AUTHORSRahul Raju Pattar, N. Uday Kiran
ABSTRACTWe investigate the behavior of the solutions of a class of certain strictly hyperbolic equations defined on (0,T]×Rn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(0,T]\times {\mathbb {R}}^n$$\end{document} in relation to a class of metrics on the phase space. In particular, we study the global regularity and decay issues of the solution to an equation with coefficients polynomially bound in x with their x-derivatives and t-derivative of order O(t-δ),δ∈[0,1),\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\text {O}(t^{-\delta }),\delta \in [0,1),$$\end{document} and O(t-1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\text {O}(t^{-1})$$\end{document} respectively. This type of singular behavior allows coefficients to be either oscillatory or logarithmically bounded at t=0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t=0$$\end{document}. We use the Planck function associated with the metric to subdivide the extended phase space and define an appropriate generalized parameter dependent symbol class. We report that the solution experiences a finite loss in the Sobolev space index in relation to the initial datum defined in the Sobolev space tailored to the metric. Our analysis suggests that an infinite loss is quite expected when the order of singularity of the first time derivative of the leading coefficients exceeds O(t-1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O(t^{-1})$$\end{document}. We confirm this by providing a counterexample. Further, using the L1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^1$$\end{document} integrability of the logarithmic singularity in t and the global properties of the operator with respect to x, we derive an anisotropic cone condition in our setting. More... »
PAGES11-45
http://scigraph.springernature.com/pub.10.1007/s11565-021-00378-2
DOIhttp://dx.doi.org/10.1007/s11565-021-00378-2
DIMENSIONShttps://app.dimensions.ai/details/publication/pub.1142180088
JSON-LD is the canonical representation for SciGraph data.
TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT
[
{
"@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json",
"about": [
{
"id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01",
"inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/",
"name": "Mathematical Sciences",
"type": "DefinedTerm"
},
{
"id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0101",
"inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/",
"name": "Pure Mathematics",
"type": "DefinedTerm"
}
],
"author": [
{
"affiliation": {
"alternateName": "Department of Mathematics and Computer Science, Sri Sathya Sai Institute of Higher Learning, Puttaparthi, Andhra Pradesh, India",
"id": "http://www.grid.ac/institutes/grid.444651.6",
"name": [
"Department of Mathematics and Computer Science, Sri Sathya Sai Institute of Higher Learning, Puttaparthi, Andhra Pradesh, India"
],
"type": "Organization"
},
"familyName": "Pattar",
"givenName": "Rahul Raju",
"id": "sg:person.012615137567.84",
"sameAs": [
"https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012615137567.84"
],
"type": "Person"
},
{
"affiliation": {
"alternateName": "Department of Mathematics and Computer Science, Sri Sathya Sai Institute of Higher Learning, Puttaparthi, Andhra Pradesh, India",
"id": "http://www.grid.ac/institutes/grid.444651.6",
"name": [
"Department of Mathematics and Computer Science, Sri Sathya Sai Institute of Higher Learning, Puttaparthi, Andhra Pradesh, India"
],
"type": "Organization"
},
"familyName": "Kiran",
"givenName": "N. Uday",
"id": "sg:person.014132532161.17",
"sameAs": [
"https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014132532161.17"
],
"type": "Person"
}
],
"citation": [
{
"id": "sg:pub.10.1007/s11868-013-0086-9",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1051094397",
"https://doi.org/10.1007/s11868-013-0086-9"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/978-3-7643-8510-1",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1020384038",
"https://doi.org/10.1007/978-3-7643-8510-1"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/s11868-017-0203-2",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1084519886",
"https://doi.org/10.1007/s11868-017-0203-2"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/978-3-642-46175-0",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1029183879",
"https://doi.org/10.1007/978-3-642-46175-0"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/s11868-018-0236-1",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1100481062",
"https://doi.org/10.1007/s11868-018-0236-1"
],
"type": "CreativeWork"
}
],
"datePublished": "2021-10-27",
"datePublishedReg": "2021-10-27",
"description": "We investigate the behavior of the solutions of a class of certain strictly hyperbolic equations defined on (0,T]\u00d7Rn\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$(0,T]\\times {\\mathbb {R}}^n$$\\end{document} in relation to a class of metrics on the phase space. In particular, we study the global regularity and decay issues of the solution to an equation with coefficients polynomially bound in x with their x-derivatives and t-derivative of order O(t-\u03b4),\u03b4\u2208[0,1),\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\text {O}(t^{-\\delta }),\\delta \\in [0,1),$$\\end{document} and O(t-1)\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\text {O}(t^{-1})$$\\end{document} respectively. This type of singular behavior allows coefficients to be either oscillatory or logarithmically bounded at t=0\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$t=0$$\\end{document}. We use the Planck function associated with the metric to subdivide the extended phase space and define an appropriate generalized parameter dependent symbol class. We report that the solution experiences a finite loss in the Sobolev space index in relation to the initial datum defined in the Sobolev space tailored to the metric. Our analysis suggests that an infinite loss is quite expected when the order of singularity of the first time derivative of the leading coefficients exceeds O(t-1)\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$O(t^{-1})$$\\end{document}. We confirm this by providing a counterexample. Further, using the L1\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$L^1$$\\end{document} integrability of the logarithmic singularity in t and the global properties of the operator with respect to x, we derive an anisotropic cone condition in our setting.",
"genre": "article",
"id": "sg:pub.10.1007/s11565-021-00378-2",
"inLanguage": "en",
"isAccessibleForFree": false,
"isPartOf": [
{
"id": "sg:journal.1136062",
"issn": [
"0430-3202",
"1827-1510"
],
"name": "Annali dell' Universit\u00e0 di Ferrara",
"publisher": "Springer Nature",
"type": "Periodical"
},
{
"issueNumber": "1",
"type": "PublicationIssue"
},
{
"type": "PublicationVolume",
"volumeNumber": "68"
}
],
"keywords": [
"phase space",
"extended phase space",
"class of metrics",
"hyperbolic equations",
"order of singularity",
"first time derivative",
"Cauchy problem",
"singular coefficients",
"Sobolev spaces",
"global regularity",
"time derivative",
"singular behavior",
"initial data",
"logarithmic singularity",
"global properties",
"cone condition",
"finite loss",
"infinite loss",
"symbol classes",
"equations",
"Planck function",
"singularity",
"X derivatives",
"space",
"T derivatives",
"solution",
"integrability",
"class",
"coefficient",
"metrics",
"operators",
"counterexamples",
"regularity",
"Rn",
"problem",
"space index",
"order",
"properties",
"behavior",
"function",
"relation",
"derivatives",
"respect",
"conditions",
"analysis",
"data",
"types",
"issues",
"loss",
"setting",
"index"
],
"name": "Strictly hyperbolic Cauchy problems on Rn with unbounded and singular coefficients",
"pagination": "11-45",
"productId": [
{
"name": "dimensions_id",
"type": "PropertyValue",
"value": [
"pub.1142180088"
]
},
{
"name": "doi",
"type": "PropertyValue",
"value": [
"10.1007/s11565-021-00378-2"
]
}
],
"sameAs": [
"https://doi.org/10.1007/s11565-021-00378-2",
"https://app.dimensions.ai/details/publication/pub.1142180088"
],
"sdDataset": "articles",
"sdDatePublished": "2022-05-20T07:38",
"sdLicense": "https://scigraph.springernature.com/explorer/license/",
"sdPublisher": {
"name": "Springer Nature - SN SciGraph project",
"type": "Organization"
},
"sdSource": "s3://com-springernature-scigraph/baseset/20220519/entities/gbq_results/article/article_907.jsonl",
"type": "ScholarlyArticle",
"url": "https://doi.org/10.1007/s11565-021-00378-2"
}
]
Download the RDF metadata as: json-ld nt turtle xml License info
JSON-LD is a popular format for linked data which is fully compatible with JSON.
curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/s11565-021-00378-2'
N-Triples is a line-based linked data format ideal for batch operations.
curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/s11565-021-00378-2'
Turtle is a human-readable linked data format.
curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s11565-021-00378-2'
RDF/XML is a standard XML format for linked data.
curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s11565-021-00378-2'
This table displays all metadata directly associated to this object as RDF triples.
136 TRIPLES
22 PREDICATES
81 URIs
68 LITERALS
6 BLANK NODES
Subject | Predicate | Object | |
---|---|---|---|
1 | sg:pub.10.1007/s11565-021-00378-2 | schema:about | anzsrc-for:01 |
2 | ″ | ″ | anzsrc-for:0101 |
3 | ″ | schema:author | Nc44d719954f0421c90fe0fcf746ffd27 |
4 | ″ | schema:citation | sg:pub.10.1007/978-3-642-46175-0 |
5 | ″ | ″ | sg:pub.10.1007/978-3-7643-8510-1 |
6 | ″ | ″ | sg:pub.10.1007/s11868-013-0086-9 |
7 | ″ | ″ | sg:pub.10.1007/s11868-017-0203-2 |
8 | ″ | ″ | sg:pub.10.1007/s11868-018-0236-1 |
9 | ″ | schema:datePublished | 2021-10-27 |
10 | ″ | schema:datePublishedReg | 2021-10-27 |
11 | ″ | schema:description | We investigate the behavior of the solutions of a class of certain strictly hyperbolic equations defined on (0,T]×Rn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(0,T]\times {\mathbb {R}}^n$$\end{document} in relation to a class of metrics on the phase space. In particular, we study the global regularity and decay issues of the solution to an equation with coefficients polynomially bound in x with their x-derivatives and t-derivative of order O(t-δ),δ∈[0,1),\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\text {O}(t^{-\delta }),\delta \in [0,1),$$\end{document} and O(t-1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\text {O}(t^{-1})$$\end{document} respectively. This type of singular behavior allows coefficients to be either oscillatory or logarithmically bounded at t=0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t=0$$\end{document}. We use the Planck function associated with the metric to subdivide the extended phase space and define an appropriate generalized parameter dependent symbol class. We report that the solution experiences a finite loss in the Sobolev space index in relation to the initial datum defined in the Sobolev space tailored to the metric. Our analysis suggests that an infinite loss is quite expected when the order of singularity of the first time derivative of the leading coefficients exceeds O(t-1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O(t^{-1})$$\end{document}. We confirm this by providing a counterexample. Further, using the L1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^1$$\end{document} integrability of the logarithmic singularity in t and the global properties of the operator with respect to x, we derive an anisotropic cone condition in our setting. |
12 | ″ | schema:genre | article |
13 | ″ | schema:inLanguage | en |
14 | ″ | schema:isAccessibleForFree | false |
15 | ″ | schema:isPartOf | N35b1e6a9a66a469dac42afd3bc7ad406 |
16 | ″ | ″ | N722402d4bfae467f9180e555faaddeeb |
17 | ″ | ″ | sg:journal.1136062 |
18 | ″ | schema:keywords | Cauchy problem |
19 | ″ | ″ | Planck function |
20 | ″ | ″ | Rn |
21 | ″ | ″ | Sobolev spaces |
22 | ″ | ″ | T derivatives |
23 | ″ | ″ | X derivatives |
24 | ″ | ″ | analysis |
25 | ″ | ″ | behavior |
26 | ″ | ″ | class |
27 | ″ | ″ | class of metrics |
28 | ″ | ″ | coefficient |
29 | ″ | ″ | conditions |
30 | ″ | ″ | cone condition |
31 | ″ | ″ | counterexamples |
32 | ″ | ″ | data |
33 | ″ | ″ | derivatives |
34 | ″ | ″ | equations |
35 | ″ | ″ | extended phase space |
36 | ″ | ″ | finite loss |
37 | ″ | ″ | first time derivative |
38 | ″ | ″ | function |
39 | ″ | ″ | global properties |
40 | ″ | ″ | global regularity |
41 | ″ | ″ | hyperbolic equations |
42 | ″ | ″ | index |
43 | ″ | ″ | infinite loss |
44 | ″ | ″ | initial data |
45 | ″ | ″ | integrability |
46 | ″ | ″ | issues |
47 | ″ | ″ | logarithmic singularity |
48 | ″ | ″ | loss |
49 | ″ | ″ | metrics |
50 | ″ | ″ | operators |
51 | ″ | ″ | order |
52 | ″ | ″ | order of singularity |
53 | ″ | ″ | phase space |
54 | ″ | ″ | problem |
55 | ″ | ″ | properties |
56 | ″ | ″ | regularity |
57 | ″ | ″ | relation |
58 | ″ | ″ | respect |
59 | ″ | ″ | setting |
60 | ″ | ″ | singular behavior |
61 | ″ | ″ | singular coefficients |
62 | ″ | ″ | singularity |
63 | ″ | ″ | solution |
64 | ″ | ″ | space |
65 | ″ | ″ | space index |
66 | ″ | ″ | symbol classes |
67 | ″ | ″ | time derivative |
68 | ″ | ″ | types |
69 | ″ | schema:name | Strictly hyperbolic Cauchy problems on Rn with unbounded and singular coefficients |
70 | ″ | schema:pagination | 11-45 |
71 | ″ | schema:productId | N9f6d5c6d2c304e04a309a2284b9e139b |
72 | ″ | ″ | Nf5cf015b3eb8459488224428b51f5085 |
73 | ″ | schema:sameAs | https://app.dimensions.ai/details/publication/pub.1142180088 |
74 | ″ | ″ | https://doi.org/10.1007/s11565-021-00378-2 |
75 | ″ | schema:sdDatePublished | 2022-05-20T07:38 |
76 | ″ | schema:sdLicense | https://scigraph.springernature.com/explorer/license/ |
77 | ″ | schema:sdPublisher | N3d326bf057b94e7aa2f903a7d1335e41 |
78 | ″ | schema:url | https://doi.org/10.1007/s11565-021-00378-2 |
79 | ″ | sgo:license | sg:explorer/license/ |
80 | ″ | sgo:sdDataset | articles |
81 | ″ | rdf:type | schema:ScholarlyArticle |
82 | N35b1e6a9a66a469dac42afd3bc7ad406 | schema:volumeNumber | 68 |
83 | ″ | rdf:type | schema:PublicationVolume |
84 | N3d326bf057b94e7aa2f903a7d1335e41 | schema:name | Springer Nature - SN SciGraph project |
85 | ″ | rdf:type | schema:Organization |
86 | N722402d4bfae467f9180e555faaddeeb | schema:issueNumber | 1 |
87 | ″ | rdf:type | schema:PublicationIssue |
88 | N9f6d5c6d2c304e04a309a2284b9e139b | schema:name | doi |
89 | ″ | schema:value | 10.1007/s11565-021-00378-2 |
90 | ″ | rdf:type | schema:PropertyValue |
91 | Nbee587423adb44828243743f8dbbf561 | rdf:first | sg:person.014132532161.17 |
92 | ″ | rdf:rest | rdf:nil |
93 | Nc44d719954f0421c90fe0fcf746ffd27 | rdf:first | sg:person.012615137567.84 |
94 | ″ | rdf:rest | Nbee587423adb44828243743f8dbbf561 |
95 | Nf5cf015b3eb8459488224428b51f5085 | schema:name | dimensions_id |
96 | ″ | schema:value | pub.1142180088 |
97 | ″ | rdf:type | schema:PropertyValue |
98 | anzsrc-for:01 | schema:inDefinedTermSet | anzsrc-for: |
99 | ″ | schema:name | Mathematical Sciences |
100 | ″ | rdf:type | schema:DefinedTerm |
101 | anzsrc-for:0101 | schema:inDefinedTermSet | anzsrc-for: |
102 | ″ | schema:name | Pure Mathematics |
103 | ″ | rdf:type | schema:DefinedTerm |
104 | sg:journal.1136062 | schema:issn | 0430-3202 |
105 | ″ | ″ | 1827-1510 |
106 | ″ | schema:name | Annali dell' Università di Ferrara |
107 | ″ | schema:publisher | Springer Nature |
108 | ″ | rdf:type | schema:Periodical |
109 | sg:person.012615137567.84 | schema:affiliation | grid-institutes:grid.444651.6 |
110 | ″ | schema:familyName | Pattar |
111 | ″ | schema:givenName | Rahul Raju |
112 | ″ | schema:sameAs | https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012615137567.84 |
113 | ″ | rdf:type | schema:Person |
114 | sg:person.014132532161.17 | schema:affiliation | grid-institutes:grid.444651.6 |
115 | ″ | schema:familyName | Kiran |
116 | ″ | schema:givenName | N. Uday |
117 | ″ | schema:sameAs | https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014132532161.17 |
118 | ″ | rdf:type | schema:Person |
119 | sg:pub.10.1007/978-3-642-46175-0 | schema:sameAs | https://app.dimensions.ai/details/publication/pub.1029183879 |
120 | ″ | ″ | https://doi.org/10.1007/978-3-642-46175-0 |
121 | ″ | rdf:type | schema:CreativeWork |
122 | sg:pub.10.1007/978-3-7643-8510-1 | schema:sameAs | https://app.dimensions.ai/details/publication/pub.1020384038 |
123 | ″ | ″ | https://doi.org/10.1007/978-3-7643-8510-1 |
124 | ″ | rdf:type | schema:CreativeWork |
125 | sg:pub.10.1007/s11868-013-0086-9 | schema:sameAs | https://app.dimensions.ai/details/publication/pub.1051094397 |
126 | ″ | ″ | https://doi.org/10.1007/s11868-013-0086-9 |
127 | ″ | rdf:type | schema:CreativeWork |
128 | sg:pub.10.1007/s11868-017-0203-2 | schema:sameAs | https://app.dimensions.ai/details/publication/pub.1084519886 |
129 | ″ | ″ | https://doi.org/10.1007/s11868-017-0203-2 |
130 | ″ | rdf:type | schema:CreativeWork |
131 | sg:pub.10.1007/s11868-018-0236-1 | schema:sameAs | https://app.dimensions.ai/details/publication/pub.1100481062 |
132 | ″ | ″ | https://doi.org/10.1007/s11868-018-0236-1 |
133 | ″ | rdf:type | schema:CreativeWork |
134 | grid-institutes:grid.444651.6 | schema:alternateName | Department of Mathematics and Computer Science, Sri Sathya Sai Institute of Higher Learning, Puttaparthi, Andhra Pradesh, India |
135 | ″ | schema:name | Department of Mathematics and Computer Science, Sri Sathya Sai Institute of Higher Learning, Puttaparthi, Andhra Pradesh, India |
136 | ″ | rdf:type | schema:Organization |