An improved Vietoris sine inequality
We prove that if { a k } is a sequence of positive numbers, such that ( 2 j − 1 ) j + 1 2 j j a 2 j + 1 ≤ a 2 j ≤ 2 j − 1 2 j a 2 j − 1 for all j = 1 , 2 , … , then for all n = 1 , 2 , … , x ∈ [ 0 , π ] , ∑ k = 1 n a k sin ( k x ) ≥ 0 . An example is { a k } = { 1 , 1 2 , 1 2 , 3 4 2 , 1 3 , 5 6 3 ,...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Kwong, Man Kam [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2015 |
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| Schlagwörter: |
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| Umfang: |
14 |
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| Übergeordnetes Werk: |
Enthalten in: Cadherins in potential link between atherosclerosis and cancer - 2011, Amsterdam [u.a.] |
|---|---|
| Übergeordnetes Werk: |
volume:189 ; year:2015 ; pages:29-42 ; extent:14 |
| Links: |
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| DOI / URN: |
10.1016/j.jat.2014.08.005 |
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ELV034918647 |
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| 520 | |a We prove that if { a k } is a sequence of positive numbers, such that ( 2 j − 1 ) j + 1 2 j j a 2 j + 1 ≤ a 2 j ≤ 2 j − 1 2 j a 2 j − 1 for all j = 1 , 2 , … , then for all n = 1 , 2 , … , x ∈ [ 0 , π ] , ∑ k = 1 n a k sin ( k x ) ≥ 0 . An example is { a k } = { 1 , 1 2 , 1 2 , 3 4 2 , 1 3 , 5 6 3 , … } = { 1 , 0.5 , 0.707 , 0.530 , 0.577 , 0.481 , … } where a k = 1 / ( k + 1 ) / 2 for odd k , and ( k − 1 ) / ( k k / 2 ) , for even k . This improves the well-known Vietoris sine inequality, by relaxing the requirement that { a n } has to be a nonincreasing sequence. | ||
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10.1016/j.jat.2014.08.005 doi GBVA2015022000001.pica (DE-627)ELV034918647 (ELSEVIER)S0021-9045(14)00166-X DE-627 ger DE-627 rakwb eng 510 510 DE-600 610 VZ 630 640 610 VZ Kwong, Man Kam verfasserin aut An improved Vietoris sine inequality 2015 14 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier We prove that if { a k } is a sequence of positive numbers, such that ( 2 j − 1 ) j + 1 2 j j a 2 j + 1 ≤ a 2 j ≤ 2 j − 1 2 j a 2 j − 1 for all j = 1 , 2 , … , then for all n = 1 , 2 , … , x ∈ [ 0 , π ] , ∑ k = 1 n a k sin ( k x ) ≥ 0 . An example is { a k } = { 1 , 1 2 , 1 2 , 3 4 2 , 1 3 , 5 6 3 , … } = { 1 , 0.5 , 0.707 , 0.530 , 0.577 , 0.481 , … } where a k = 1 / ( k + 1 ) / 2 for odd k , and ( k − 1 ) / ( k k / 2 ) , for even k . This improves the well-known Vietoris sine inequality, by relaxing the requirement that { a n } has to be a nonincreasing sequence. 42A05 Elsevier 26D05 Elsevier Enthalten in Elsevier Cadherins in potential link between atherosclerosis and cancer 2011 Amsterdam [u.a.] (DE-627)ELV015738302 volume:189 year:2015 pages:29-42 extent:14 https://doi.org/10.1016/j.jat.2014.08.005 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA AR 189 2015 29-42 14 045F 510 |
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10.1016/j.jat.2014.08.005 doi GBVA2015022000001.pica (DE-627)ELV034918647 (ELSEVIER)S0021-9045(14)00166-X DE-627 ger DE-627 rakwb eng 510 510 DE-600 610 VZ 630 640 610 VZ Kwong, Man Kam verfasserin aut An improved Vietoris sine inequality 2015 14 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier We prove that if { a k } is a sequence of positive numbers, such that ( 2 j − 1 ) j + 1 2 j j a 2 j + 1 ≤ a 2 j ≤ 2 j − 1 2 j a 2 j − 1 for all j = 1 , 2 , … , then for all n = 1 , 2 , … , x ∈ [ 0 , π ] , ∑ k = 1 n a k sin ( k x ) ≥ 0 . An example is { a k } = { 1 , 1 2 , 1 2 , 3 4 2 , 1 3 , 5 6 3 , … } = { 1 , 0.5 , 0.707 , 0.530 , 0.577 , 0.481 , … } where a k = 1 / ( k + 1 ) / 2 for odd k , and ( k − 1 ) / ( k k / 2 ) , for even k . This improves the well-known Vietoris sine inequality, by relaxing the requirement that { a n } has to be a nonincreasing sequence. 42A05 Elsevier 26D05 Elsevier Enthalten in Elsevier Cadherins in potential link between atherosclerosis and cancer 2011 Amsterdam [u.a.] (DE-627)ELV015738302 volume:189 year:2015 pages:29-42 extent:14 https://doi.org/10.1016/j.jat.2014.08.005 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA AR 189 2015 29-42 14 045F 510 |
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10.1016/j.jat.2014.08.005 doi GBVA2015022000001.pica (DE-627)ELV034918647 (ELSEVIER)S0021-9045(14)00166-X DE-627 ger DE-627 rakwb eng 510 510 DE-600 610 VZ 630 640 610 VZ Kwong, Man Kam verfasserin aut An improved Vietoris sine inequality 2015 14 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier We prove that if { a k } is a sequence of positive numbers, such that ( 2 j − 1 ) j + 1 2 j j a 2 j + 1 ≤ a 2 j ≤ 2 j − 1 2 j a 2 j − 1 for all j = 1 , 2 , … , then for all n = 1 , 2 , … , x ∈ [ 0 , π ] , ∑ k = 1 n a k sin ( k x ) ≥ 0 . An example is { a k } = { 1 , 1 2 , 1 2 , 3 4 2 , 1 3 , 5 6 3 , … } = { 1 , 0.5 , 0.707 , 0.530 , 0.577 , 0.481 , … } where a k = 1 / ( k + 1 ) / 2 for odd k , and ( k − 1 ) / ( k k / 2 ) , for even k . This improves the well-known Vietoris sine inequality, by relaxing the requirement that { a n } has to be a nonincreasing sequence. 42A05 Elsevier 26D05 Elsevier Enthalten in Elsevier Cadherins in potential link between atherosclerosis and cancer 2011 Amsterdam [u.a.] (DE-627)ELV015738302 volume:189 year:2015 pages:29-42 extent:14 https://doi.org/10.1016/j.jat.2014.08.005 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA AR 189 2015 29-42 14 045F 510 |
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10.1016/j.jat.2014.08.005 doi GBVA2015022000001.pica (DE-627)ELV034918647 (ELSEVIER)S0021-9045(14)00166-X DE-627 ger DE-627 rakwb eng 510 510 DE-600 610 VZ 630 640 610 VZ Kwong, Man Kam verfasserin aut An improved Vietoris sine inequality 2015 14 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier We prove that if { a k } is a sequence of positive numbers, such that ( 2 j − 1 ) j + 1 2 j j a 2 j + 1 ≤ a 2 j ≤ 2 j − 1 2 j a 2 j − 1 for all j = 1 , 2 , … , then for all n = 1 , 2 , … , x ∈ [ 0 , π ] , ∑ k = 1 n a k sin ( k x ) ≥ 0 . An example is { a k } = { 1 , 1 2 , 1 2 , 3 4 2 , 1 3 , 5 6 3 , … } = { 1 , 0.5 , 0.707 , 0.530 , 0.577 , 0.481 , … } where a k = 1 / ( k + 1 ) / 2 for odd k , and ( k − 1 ) / ( k k / 2 ) , for even k . This improves the well-known Vietoris sine inequality, by relaxing the requirement that { a n } has to be a nonincreasing sequence. 42A05 Elsevier 26D05 Elsevier Enthalten in Elsevier Cadherins in potential link between atherosclerosis and cancer 2011 Amsterdam [u.a.] (DE-627)ELV015738302 volume:189 year:2015 pages:29-42 extent:14 https://doi.org/10.1016/j.jat.2014.08.005 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA AR 189 2015 29-42 14 045F 510 |
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10.1016/j.jat.2014.08.005 doi GBVA2015022000001.pica (DE-627)ELV034918647 (ELSEVIER)S0021-9045(14)00166-X DE-627 ger DE-627 rakwb eng 510 510 DE-600 610 VZ 630 640 610 VZ Kwong, Man Kam verfasserin aut An improved Vietoris sine inequality 2015 14 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier We prove that if { a k } is a sequence of positive numbers, such that ( 2 j − 1 ) j + 1 2 j j a 2 j + 1 ≤ a 2 j ≤ 2 j − 1 2 j a 2 j − 1 for all j = 1 , 2 , … , then for all n = 1 , 2 , … , x ∈ [ 0 , π ] , ∑ k = 1 n a k sin ( k x ) ≥ 0 . An example is { a k } = { 1 , 1 2 , 1 2 , 3 4 2 , 1 3 , 5 6 3 , … } = { 1 , 0.5 , 0.707 , 0.530 , 0.577 , 0.481 , … } where a k = 1 / ( k + 1 ) / 2 for odd k , and ( k − 1 ) / ( k k / 2 ) , for even k . This improves the well-known Vietoris sine inequality, by relaxing the requirement that { a n } has to be a nonincreasing sequence. 42A05 Elsevier 26D05 Elsevier Enthalten in Elsevier Cadherins in potential link between atherosclerosis and cancer 2011 Amsterdam [u.a.] (DE-627)ELV015738302 volume:189 year:2015 pages:29-42 extent:14 https://doi.org/10.1016/j.jat.2014.08.005 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA AR 189 2015 29-42 14 045F 510 |
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We prove that if { a k } is a sequence of positive numbers, such that ( 2 j − 1 ) j + 1 2 j j a 2 j + 1 ≤ a 2 j ≤ 2 j − 1 2 j a 2 j − 1 for all j = 1 , 2 , … , then for all n = 1 , 2 , … , x ∈ [ 0 , π ] , ∑ k = 1 n a k sin ( k x ) ≥ 0 . An example is { a k } = { 1 , 1 2 , 1 2 , 3 4 2 , 1 3 , 5 6 3 , … } = { 1 , 0.5 , 0.707 , 0.530 , 0.577 , 0.481 , … } where a k = 1 / ( k + 1 ) / 2 for odd k , and ( k − 1 ) / ( k k / 2 ) , for even k . This improves the well-known Vietoris sine inequality, by relaxing the requirement that { a n } has to be a nonincreasing sequence. |
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We prove that if { a k } is a sequence of positive numbers, such that ( 2 j − 1 ) j + 1 2 j j a 2 j + 1 ≤ a 2 j ≤ 2 j − 1 2 j a 2 j − 1 for all j = 1 , 2 , … , then for all n = 1 , 2 , … , x ∈ [ 0 , π ] , ∑ k = 1 n a k sin ( k x ) ≥ 0 . An example is { a k } = { 1 , 1 2 , 1 2 , 3 4 2 , 1 3 , 5 6 3 , … } = { 1 , 0.5 , 0.707 , 0.530 , 0.577 , 0.481 , … } where a k = 1 / ( k + 1 ) / 2 for odd k , and ( k − 1 ) / ( k k / 2 ) , for even k . This improves the well-known Vietoris sine inequality, by relaxing the requirement that { a n } has to be a nonincreasing sequence. |
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We prove that if { a k } is a sequence of positive numbers, such that ( 2 j − 1 ) j + 1 2 j j a 2 j + 1 ≤ a 2 j ≤ 2 j − 1 2 j a 2 j − 1 for all j = 1 , 2 , … , then for all n = 1 , 2 , … , x ∈ [ 0 , π ] , ∑ k = 1 n a k sin ( k x ) ≥ 0 . An example is { a k } = { 1 , 1 2 , 1 2 , 3 4 2 , 1 3 , 5 6 3 , … } = { 1 , 0.5 , 0.707 , 0.530 , 0.577 , 0.481 , … } where a k = 1 / ( k + 1 ) / 2 for odd k , and ( k − 1 ) / ( k k / 2 ) , for even k . This improves the well-known Vietoris sine inequality, by relaxing the requirement that { a n } has to be a nonincreasing sequence. |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">ELV034918647</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230624015839.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">180603s2015 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1016/j.jat.2014.08.005</subfield><subfield code="2">doi</subfield></datafield><datafield tag="028" ind1="5" ind2="2"><subfield code="a">GBVA2015022000001.pica</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)ELV034918647</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(ELSEVIER)S0021-9045(14)00166-X</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">510</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">510</subfield><subfield code="q">DE-600</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">610</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">630</subfield><subfield code="a">640</subfield><subfield code="a">610</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Kwong, Man Kam</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">An improved Vietoris sine inequality</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2015</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">14</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">nicht spezifiziert</subfield><subfield code="b">zzz</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">nicht spezifiziert</subfield><subfield code="b">z</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">nicht spezifiziert</subfield><subfield code="b">zu</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">We prove that if { a k } is a sequence of positive numbers, such that ( 2 j − 1 ) j + 1 2 j j a 2 j + 1 ≤ a 2 j ≤ 2 j − 1 2 j a 2 j − 1 for all j = 1 , 2 , … , then for all n = 1 , 2 , … , x ∈ [ 0 , π ] , ∑ k = 1 n a k sin ( k x ) ≥ 0 . An example is { a k } = { 1 , 1 2 , 1 2 , 3 4 2 , 1 3 , 5 6 3 , … } = { 1 , 0.5 , 0.707 , 0.530 , 0.577 , 0.481 , … } where a k = 1 / ( k + 1 ) / 2 for odd k , and ( k − 1 ) / ( k k / 2 ) , for even k . 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