Uniform Approximation of the Curvature of Smooth Plane Curves with the Use of Partial Fourier Sums View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2018-12

AUTHORS

Yu. N. Subbotin, N. I. Chernykh

ABSTRACT

An error bound for the approximation of the curvature of graphs of periodic functions from the class Wr for r ≥ 3 in the uniform metric is obtained with the use of the simplest approximation technique for smooth periodic functions, which is approximation by partial sums of their trigonometric Fourier series. From the mathematical point of view, the interest in this problem is connected with the specific nonlinearity of the graph curvature operator on the class of smooth functions Wr on a period or a closed interval for r ≥ 2. There are several papers on curvature approximation for plane curves in the mean-square and Chebyshev norms. In previous works, the approximation was performed by partial sums of trigonometric series (in the L2 norm), interpolation splines with uniform knots, Fejér means of partial sums of trigonometric series, and orthogonal interpolating wavelets based on Meyer wavelets (in the C∞ norm). The technique of this paper, based on the lemma, can possibly be generalized to the Lp metric and other approximation methods. More... »

PAGES

213-215

Identifiers

URI

http://scigraph.springernature.com/pub.10.1134/s0081543818090225

DOI

http://dx.doi.org/10.1134/s0081543818090225

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1112591695


Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
Incoming Citations Browse incoming citations for this publication using opencitations.net

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/2008/0101", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Pure Mathematics", 
        "type": "DefinedTerm"
      }, 
      {
        "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"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "Ural Branch of the Russian Academy of Sciences", 
          "id": "https://www.grid.ac/institutes/grid.426536.0", 
          "name": [
            "Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, 620990, Yekaterinburg, Russia"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Subbotin", 
        "givenName": "Yu. N.", 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Ural Branch of the Russian Academy of Sciences", 
          "id": "https://www.grid.ac/institutes/grid.426536.0", 
          "name": [
            "Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, 620990, Yekaterinburg, Russia"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Chernykh", 
        "givenName": "N. I.", 
        "type": "Person"
      }
    ], 
    "datePublished": "2018-12", 
    "datePublishedReg": "2018-12-01", 
    "description": "An error bound for the approximation of the curvature of graphs of periodic functions from the class Wr for r \u2265 3 in the uniform metric is obtained with the use of the simplest approximation technique for smooth periodic functions, which is approximation by partial sums of their trigonometric Fourier series. From the mathematical point of view, the interest in this problem is connected with the specific nonlinearity of the graph curvature operator on the class of smooth functions Wr on a period or a closed interval for r \u2265 2. There are several papers on curvature approximation for plane curves in the mean-square and Chebyshev norms. In previous works, the approximation was performed by partial sums of trigonometric series (in the L2 norm), interpolation splines with uniform knots, Fej\u00e9r means of partial sums of trigonometric series, and orthogonal interpolating wavelets based on Meyer wavelets (in the C\u221e norm). The technique of this paper, based on the lemma, can possibly be generalized to the Lp metric and other approximation methods.", 
    "genre": "non_research_article", 
    "id": "sg:pub.10.1134/s0081543818090225", 
    "inLanguage": [
      "en"
    ], 
    "isAccessibleForFree": false, 
    "isPartOf": [
      {
        "id": "sg:journal.1136804", 
        "issn": [
          "0081-5438", 
          "1531-8605"
        ], 
        "name": "Proceedings of the Steklov Institute of Mathematics", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "Suppl 1", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "303"
      }
    ], 
    "name": "Uniform Approximation of the Curvature of Smooth Plane Curves with the Use of Partial Fourier Sums", 
    "pagination": "213-215", 
    "productId": [
      {
        "name": "readcube_id", 
        "type": "PropertyValue", 
        "value": [
          "a6ac7380c1d0e60d7649560e5554a3f034f6b5a0dd77828bb4910fa71afc4010"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1134/s0081543818090225"
        ]
      }, 
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1112591695"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1134/s0081543818090225", 
      "https://app.dimensions.ai/details/publication/pub.1112591695"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2019-04-11T11:14", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-uberresearch-data-dimensions-target-20181106-alternative/cleanup/v134/2549eaecd7973599484d7c17b260dba0a4ecb94b/merge/v9/a6c9fde33151104705d4d7ff012ea9563521a3ce/jats-lookup/v90/0000000353_0000000353/records_45372_00000002.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "https://link.springer.com/10.1134%2FS0081543818090225"
  }
]
 

Download the RDF metadata as:  json-ld nt turtle xml License info

HOW TO GET THIS DATA PROGRAMMATICALLY:

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.10.1134/s0081543818090225'

N-Triples is a line-based linked data format ideal for batch operations.

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1134/s0081543818090225'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1134/s0081543818090225'

RDF/XML is a standard XML format for linked data.

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1134/s0081543818090225'


 

This table displays all metadata directly associated to this object as RDF triples.

66 TRIPLES      20 PREDICATES      27 URIs      19 LITERALS      7 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1134/s0081543818090225 schema:about anzsrc-for:01
2 anzsrc-for:0101
3 schema:author Ned3340a5b62142fabb08205973294c5f
4 schema:datePublished 2018-12
5 schema:datePublishedReg 2018-12-01
6 schema:description An error bound for the approximation of the curvature of graphs of periodic functions from the class Wr for r ≥ 3 in the uniform metric is obtained with the use of the simplest approximation technique for smooth periodic functions, which is approximation by partial sums of their trigonometric Fourier series. From the mathematical point of view, the interest in this problem is connected with the specific nonlinearity of the graph curvature operator on the class of smooth functions Wr on a period or a closed interval for r ≥ 2. There are several papers on curvature approximation for plane curves in the mean-square and Chebyshev norms. In previous works, the approximation was performed by partial sums of trigonometric series (in the L2 norm), interpolation splines with uniform knots, Fejér means of partial sums of trigonometric series, and orthogonal interpolating wavelets based on Meyer wavelets (in the C∞ norm). The technique of this paper, based on the lemma, can possibly be generalized to the Lp metric and other approximation methods.
7 schema:genre non_research_article
8 schema:inLanguage en
9 schema:isAccessibleForFree false
10 schema:isPartOf N1bd223c75334458ba43528cc92a37069
11 N371dc797625e429f8188ae066c856e5b
12 sg:journal.1136804
13 schema:name Uniform Approximation of the Curvature of Smooth Plane Curves with the Use of Partial Fourier Sums
14 schema:pagination 213-215
15 schema:productId N67eb126559db4a799653afe633c52144
16 N7be3c2329e2b43fea1525d0f9373bdf8
17 Na5246e783dbf4529a0662a70e12d0d18
18 schema:sameAs https://app.dimensions.ai/details/publication/pub.1112591695
19 https://doi.org/10.1134/s0081543818090225
20 schema:sdDatePublished 2019-04-11T11:14
21 schema:sdLicense https://scigraph.springernature.com/explorer/license/
22 schema:sdPublisher Nf8eee007903f4d12bcf7b6d4210e2405
23 schema:url https://link.springer.com/10.1134%2FS0081543818090225
24 sgo:license sg:explorer/license/
25 sgo:sdDataset articles
26 rdf:type schema:ScholarlyArticle
27 N058b6e768fbd4077b2eed7aa80c93cf1 rdf:first N9921a4df93fe4c6d9523a6217d87e455
28 rdf:rest rdf:nil
29 N1bd223c75334458ba43528cc92a37069 schema:issueNumber Suppl 1
30 rdf:type schema:PublicationIssue
31 N1dec6cb50c2248e6ba7d38b2a5af751a schema:affiliation https://www.grid.ac/institutes/grid.426536.0
32 schema:familyName Subbotin
33 schema:givenName Yu. N.
34 rdf:type schema:Person
35 N371dc797625e429f8188ae066c856e5b schema:volumeNumber 303
36 rdf:type schema:PublicationVolume
37 N67eb126559db4a799653afe633c52144 schema:name doi
38 schema:value 10.1134/s0081543818090225
39 rdf:type schema:PropertyValue
40 N7be3c2329e2b43fea1525d0f9373bdf8 schema:name readcube_id
41 schema:value a6ac7380c1d0e60d7649560e5554a3f034f6b5a0dd77828bb4910fa71afc4010
42 rdf:type schema:PropertyValue
43 N9921a4df93fe4c6d9523a6217d87e455 schema:affiliation https://www.grid.ac/institutes/grid.426536.0
44 schema:familyName Chernykh
45 schema:givenName N. I.
46 rdf:type schema:Person
47 Na5246e783dbf4529a0662a70e12d0d18 schema:name dimensions_id
48 schema:value pub.1112591695
49 rdf:type schema:PropertyValue
50 Ned3340a5b62142fabb08205973294c5f rdf:first N1dec6cb50c2248e6ba7d38b2a5af751a
51 rdf:rest N058b6e768fbd4077b2eed7aa80c93cf1
52 Nf8eee007903f4d12bcf7b6d4210e2405 schema:name Springer Nature - SN SciGraph project
53 rdf:type schema:Organization
54 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
55 schema:name Mathematical Sciences
56 rdf:type schema:DefinedTerm
57 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
58 schema:name Pure Mathematics
59 rdf:type schema:DefinedTerm
60 sg:journal.1136804 schema:issn 0081-5438
61 1531-8605
62 schema:name Proceedings of the Steklov Institute of Mathematics
63 rdf:type schema:Periodical
64 https://www.grid.ac/institutes/grid.426536.0 schema:alternateName Ural Branch of the Russian Academy of Sciences
65 schema:name Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, 620990, Yekaterinburg, Russia
66 rdf:type schema:Organization
 




Preview window. Press ESC to close (or click here)


...