Minimal Impact One-Dimensional Arrays
In this contribution, we consider the problem of finding the minimal Euclidean distance between a given converging decreasing one-dimensional array X in (<b>R<sup>+</sup></b>)<b><sup>∞</sup></b> and arrays of the form <inline-formula> <math di...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-05-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/5/811 |
| _version_ | 1797567767204855808 |
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| author | Leo Egghe Ronald Rousseau |
| author_facet | Leo Egghe Ronald Rousseau |
| author_sort | Leo Egghe |
| collection | DOAJ |
| description | In this contribution, we consider the problem of finding the minimal Euclidean distance between a given converging decreasing one-dimensional array X in (<b>R<sup>+</sup></b>)<b><sup>∞</sup></b> and arrays of the form <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>A</mi> <mi>a</mi> </msub> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <munder> <mrow> <munder> <mrow> <mi>a</mi> <mo>,</mo> <mi>a</mi> <mo>,</mo> <mo>…</mo> <mo>,</mo> <mi>a</mi> </mrow> <mo>︸</mo> </munder> <mo>,</mo> <mo> </mo> <mn>0</mn> <mo>,</mo> <mn>0</mn> <mo>,</mo> <mo> </mo> <mo>…</mo> </mrow> <mrow> <mi>a</mi> <mo> </mo> <mi>t</mi> <mi>i</mi> <mi>m</mi> <mi>e</mi> <mi>s</mi> </mrow> </munder> </mrow> <mo>)</mo> </mrow> </mrow> </semantics> </math> </inline-formula>, with <i>a</i> being a natural number. We find a complete, if not always unique, solution. Our contribution illustrates how a formalism derived in the context of research evaluation and informetrics can be used to solve a purely mathematical problem. |
| first_indexed | 2024-03-10T19:47:12Z |
| format | Article |
| id | doaj.art-eb93950ae24d49c18413cb099d2bfc8d |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T19:47:12Z |
| publishDate | 2020-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-eb93950ae24d49c18413cb099d2bfc8d2023-11-20T00:44:44ZengMDPI AGMathematics2227-73902020-05-018581110.3390/math8050811Minimal Impact One-Dimensional ArraysLeo Egghe0Ronald Rousseau1University of Hasselt, 3500 Hasselt, BelgiumFaculty of Social Sciences, University of Antwerp, 2020 Antwerpen, BelgiumIn this contribution, we consider the problem of finding the minimal Euclidean distance between a given converging decreasing one-dimensional array X in (<b>R<sup>+</sup></b>)<b><sup>∞</sup></b> and arrays of the form <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>A</mi> <mi>a</mi> </msub> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <munder> <mrow> <munder> <mrow> <mi>a</mi> <mo>,</mo> <mi>a</mi> <mo>,</mo> <mo>…</mo> <mo>,</mo> <mi>a</mi> </mrow> <mo>︸</mo> </munder> <mo>,</mo> <mo> </mo> <mn>0</mn> <mo>,</mo> <mn>0</mn> <mo>,</mo> <mo> </mo> <mo>…</mo> </mrow> <mrow> <mi>a</mi> <mo> </mo> <mi>t</mi> <mi>i</mi> <mi>m</mi> <mi>e</mi> <mi>s</mi> </mrow> </munder> </mrow> <mo>)</mo> </mrow> </mrow> </semantics> </math> </inline-formula>, with <i>a</i> being a natural number. We find a complete, if not always unique, solution. Our contribution illustrates how a formalism derived in the context of research evaluation and informetrics can be used to solve a purely mathematical problem.https://www.mdpi.com/2227-7390/8/5/811generalized h-indexgeneralized g-indexminimization problem |
| spellingShingle | Leo Egghe Ronald Rousseau Minimal Impact One-Dimensional Arrays Mathematics generalized h-index generalized g-index minimization problem |
| title | Minimal Impact One-Dimensional Arrays |
| title_full | Minimal Impact One-Dimensional Arrays |
| title_fullStr | Minimal Impact One-Dimensional Arrays |
| title_full_unstemmed | Minimal Impact One-Dimensional Arrays |
| title_short | Minimal Impact One-Dimensional Arrays |
| title_sort | minimal impact one dimensional arrays |
| topic | generalized h-index generalized g-index minimization problem |
| url | https://www.mdpi.com/2227-7390/8/5/811 |
| work_keys_str_mv | AT leoegghe minimalimpactonedimensionalarrays AT ronaldrousseau minimalimpactonedimensionalarrays |