Decreasing property of ratio of two logarithmic expressions involving tangent function.
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| Title: | Decreasing property of ratio of two logarithmic expressions involving tangent function. |
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| Authors: | Qi, Feng1,2 (AUTHOR), Agarwal, Ravi Prakash3 (AUTHOR), Lim, Dongkyu4 (AUTHOR) dklim@anu.ac.kr |
| Source: | Mathematical & Computer Modelling of Dynamical Systems. Dec2025, Vol. 31 Issue 1, p1-16. 16p. |
| Subjects: | Logarithms, Tangent function, Differentiable functions, Ratio & proportion, Mathematics, Logic, Monotonic functions |
| Abstract: | In this article, the authors review three proofs of the decreasing property of the ratio of two logarithmic expressions. With the help of the monotonicity rule for the ratio of two differentiable functions, the authors provide an alternative proof of the decreasing property of the ratio of two logarithmic expressions. These logarithmic expressions involve the tangent function. [ABSTRACT FROM AUTHOR] |
| Copyright of Mathematical & Computer Modelling of Dynamical Systems is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
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| Header | DbId: egs DbLabel: Engineering Source An: 190352321 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Decreasing property of ratio of two logarithmic expressions involving tangent function. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Qi%2C+Feng%22">Qi, Feng</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Agarwal%2C+Ravi+Prakash%22">Agarwal, Ravi Prakash</searchLink><relatesTo>3</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Lim%2C+Dongkyu%22">Lim, Dongkyu</searchLink><relatesTo>4</relatesTo> (AUTHOR)<i> dklim@anu.ac.kr</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Mathematical+%26+Computer+Modelling+of+Dynamical+Systems%22">Mathematical & Computer Modelling of Dynamical Systems</searchLink>. Dec2025, Vol. 31 Issue 1, p1-16. 16p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Logarithms%22">Logarithms</searchLink><br /><searchLink fieldCode="DE" term="%22Tangent+function%22">Tangent function</searchLink><br /><searchLink fieldCode="DE" term="%22Differentiable+functions%22">Differentiable functions</searchLink><br /><searchLink fieldCode="DE" term="%22Ratio+%26+proportion%22">Ratio & proportion</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics%22">Mathematics</searchLink><br /><searchLink fieldCode="DE" term="%22Logic%22">Logic</searchLink><br /><searchLink fieldCode="DE" term="%22Monotonic+functions%22">Monotonic functions</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: In this article, the authors review three proofs of the decreasing property of the ratio of two logarithmic expressions. With the help of the monotonicity rule for the ratio of two differentiable functions, the authors provide an alternative proof of the decreasing property of the ratio of two logarithmic expressions. These logarithmic expressions involve the tangent function. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Mathematical & Computer Modelling of Dynamical Systems is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1080/13873954.2024.2449322 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 16 StartPage: 1 Subjects: – SubjectFull: Logarithms Type: general – SubjectFull: Tangent function Type: general – SubjectFull: Differentiable functions Type: general – SubjectFull: Ratio & proportion Type: general – SubjectFull: Mathematics Type: general – SubjectFull: Logic Type: general – SubjectFull: Monotonic functions Type: general Titles: – TitleFull: Decreasing property of ratio of two logarithmic expressions involving tangent function. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Qi, Feng – PersonEntity: Name: NameFull: Agarwal, Ravi Prakash – PersonEntity: Name: NameFull: Lim, Dongkyu IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 12 Text: Dec2025 Type: published Y: 2025 Identifiers: – Type: issn-print Value: 13873954 Numbering: – Type: volume Value: 31 – Type: issue Value: 1 Titles: – TitleFull: Mathematical & Computer Modelling of Dynamical Systems Type: main |
| ResultId | 1 |
