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
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.] |
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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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Katalog-ID: |
ELV034918647 |
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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 |
allfields_unstemmed |
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. |
abstractGer |
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. |
abstract_unstemmed |
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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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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