Compactly supported positive definite radial functions View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

1995-12

AUTHORS

Zongmin Wu

ABSTRACT

We provide criteria for positive definiteness of radial functions with compact support. Based on these criteria we will produce a series of positive definite and compactly supported radial functions, which will be very useful in applications. The simplest ones arecut-off polynomials, which consist of a single polynomial piece on [0, 1] and vanish on [1, ∞). More precisely, for any given dimensionn and prescribedCk smoothness, there is a function inCk(ℝn), which is a positive definite radial function with compact support and is a cut-off polynomial as a function of Euclidean distance. Another example is derived from odd-degreeB-splines. More... »

PAGES

283

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/bf03177517

DOI

http://dx.doi.org/10.1007/bf03177517

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1051151493


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": "Fudan University", 
          "id": "https://www.grid.ac/institutes/grid.8547.e", 
          "name": [
            "Department of Mathematics, Fudan University, 200433, Shanghai, China"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Wu", 
        "givenName": "Zongmin", 
        "id": "sg:person.013222047063.60", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013222047063.60"
        ], 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "sg:pub.10.1007/bf02016334", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1025006353", 
          "https://doi.org/10.1007/bf02016334"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf02016334", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1025006353", 
          "https://doi.org/10.1007/bf02016334"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01893414", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1025705856", 
          "https://doi.org/10.1007/bf01893414"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01893414", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1025705856", 
          "https://doi.org/10.1007/bf01893414"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1006/jath.1993.1065", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1032889469"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1006/jath.1993.1059", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1037696009"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1093/imanum/13.1.13", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1059688637"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.2307/1968466", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1069673895"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "1995-12", 
    "datePublishedReg": "1995-12-01", 
    "description": "We provide criteria for positive definiteness of radial functions with compact support. Based on these criteria we will produce a series of positive definite and compactly supported radial functions, which will be very useful in applications. The simplest ones arecut-off polynomials, which consist of a single polynomial piece on [0, 1] and vanish on [1, \u221e). More precisely, for any given dimensionn and prescribedCk smoothness, there is a function inCk(\u211dn), which is a positive definite radial function with compact support and is a cut-off polynomial as a function of Euclidean distance. Another example is derived from odd-degreeB-splines.", 
    "genre": "non_research_article", 
    "id": "sg:pub.10.1007/bf03177517", 
    "inLanguage": [
      "en"
    ], 
    "isAccessibleForFree": false, 
    "isPartOf": [
      {
        "id": "sg:journal.1045108", 
        "issn": [
          "1019-7168", 
          "1572-9044"
        ], 
        "name": "Advances in Computational Mathematics", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "1", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "4"
      }
    ], 
    "name": "Compactly supported positive definite radial functions", 
    "pagination": "283", 
    "productId": [
      {
        "name": "readcube_id", 
        "type": "PropertyValue", 
        "value": [
          "f3aa88eedfe54dba44a3b84d5e8083bf8b8a377f6686be05fd9361efffe9cc76"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/bf03177517"
        ]
      }, 
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1051151493"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1007/bf03177517", 
      "https://app.dimensions.ai/details/publication/pub.1051151493"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2019-04-11T10:00", 
    "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/v90/0000000347_0000000347/records_89816_00000002.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "http://link.springer.com/10.1007%2FBF03177517"
  }
]
 

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.10.1007/bf03177517'

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/bf03177517'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/bf03177517'

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

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/bf03177517'


 

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

81 TRIPLES      21 PREDICATES      33 URIs      19 LITERALS      7 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/bf03177517 schema:about anzsrc-for:01
2 anzsrc-for:0101
3 schema:author N1822363bc23045f8bae0e35d231b6253
4 schema:citation sg:pub.10.1007/bf01893414
5 sg:pub.10.1007/bf02016334
6 https://doi.org/10.1006/jath.1993.1059
7 https://doi.org/10.1006/jath.1993.1065
8 https://doi.org/10.1093/imanum/13.1.13
9 https://doi.org/10.2307/1968466
10 schema:datePublished 1995-12
11 schema:datePublishedReg 1995-12-01
12 schema:description We provide criteria for positive definiteness of radial functions with compact support. Based on these criteria we will produce a series of positive definite and compactly supported radial functions, which will be very useful in applications. The simplest ones arecut-off polynomials, which consist of a single polynomial piece on [0, 1] and vanish on [1, ∞). More precisely, for any given dimensionn and prescribedCk smoothness, there is a function inCk(ℝn), which is a positive definite radial function with compact support and is a cut-off polynomial as a function of Euclidean distance. Another example is derived from odd-degreeB-splines.
13 schema:genre non_research_article
14 schema:inLanguage en
15 schema:isAccessibleForFree false
16 schema:isPartOf N9d97163dc978425d8612d209d15f24be
17 Na3c49e783cfe4c109778dedc0220d643
18 sg:journal.1045108
19 schema:name Compactly supported positive definite radial functions
20 schema:pagination 283
21 schema:productId N0f02bfafff2f4096ad010149fe2660f9
22 N5d77f0655d424e5abe921aa0f99e95c3
23 N97588dc07aa4497bb153409e826980cf
24 schema:sameAs https://app.dimensions.ai/details/publication/pub.1051151493
25 https://doi.org/10.1007/bf03177517
26 schema:sdDatePublished 2019-04-11T10:00
27 schema:sdLicense https://scigraph.springernature.com/explorer/license/
28 schema:sdPublisher N8fa3755bbed0448298b15b58984d8097
29 schema:url http://link.springer.com/10.1007%2FBF03177517
30 sgo:license sg:explorer/license/
31 sgo:sdDataset articles
32 rdf:type schema:ScholarlyArticle
33 N0f02bfafff2f4096ad010149fe2660f9 schema:name readcube_id
34 schema:value f3aa88eedfe54dba44a3b84d5e8083bf8b8a377f6686be05fd9361efffe9cc76
35 rdf:type schema:PropertyValue
36 N1822363bc23045f8bae0e35d231b6253 rdf:first sg:person.013222047063.60
37 rdf:rest rdf:nil
38 N5d77f0655d424e5abe921aa0f99e95c3 schema:name dimensions_id
39 schema:value pub.1051151493
40 rdf:type schema:PropertyValue
41 N8fa3755bbed0448298b15b58984d8097 schema:name Springer Nature - SN SciGraph project
42 rdf:type schema:Organization
43 N97588dc07aa4497bb153409e826980cf schema:name doi
44 schema:value 10.1007/bf03177517
45 rdf:type schema:PropertyValue
46 N9d97163dc978425d8612d209d15f24be schema:volumeNumber 4
47 rdf:type schema:PublicationVolume
48 Na3c49e783cfe4c109778dedc0220d643 schema:issueNumber 1
49 rdf:type schema:PublicationIssue
50 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
51 schema:name Mathematical Sciences
52 rdf:type schema:DefinedTerm
53 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
54 schema:name Pure Mathematics
55 rdf:type schema:DefinedTerm
56 sg:journal.1045108 schema:issn 1019-7168
57 1572-9044
58 schema:name Advances in Computational Mathematics
59 rdf:type schema:Periodical
60 sg:person.013222047063.60 schema:affiliation https://www.grid.ac/institutes/grid.8547.e
61 schema:familyName Wu
62 schema:givenName Zongmin
63 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013222047063.60
64 rdf:type schema:Person
65 sg:pub.10.1007/bf01893414 schema:sameAs https://app.dimensions.ai/details/publication/pub.1025705856
66 https://doi.org/10.1007/bf01893414
67 rdf:type schema:CreativeWork
68 sg:pub.10.1007/bf02016334 schema:sameAs https://app.dimensions.ai/details/publication/pub.1025006353
69 https://doi.org/10.1007/bf02016334
70 rdf:type schema:CreativeWork
71 https://doi.org/10.1006/jath.1993.1059 schema:sameAs https://app.dimensions.ai/details/publication/pub.1037696009
72 rdf:type schema:CreativeWork
73 https://doi.org/10.1006/jath.1993.1065 schema:sameAs https://app.dimensions.ai/details/publication/pub.1032889469
74 rdf:type schema:CreativeWork
75 https://doi.org/10.1093/imanum/13.1.13 schema:sameAs https://app.dimensions.ai/details/publication/pub.1059688637
76 rdf:type schema:CreativeWork
77 https://doi.org/10.2307/1968466 schema:sameAs https://app.dimensions.ai/details/publication/pub.1069673895
78 rdf:type schema:CreativeWork
79 https://www.grid.ac/institutes/grid.8547.e schema:alternateName Fudan University
80 schema:name Department of Mathematics, Fudan University, 200433, Shanghai, China
81 rdf:type schema:Organization
 




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


...