Results 1 to 10 of about 807,904 (288)
On triangle inequalities of correlation-based distances for gene expression profiles [PDF]
BMC Bioinformatics, 2023 Background Distance functions are fundamental for evaluating the differences between gene expression profiles. Such a function would output a low value if the profiles are strongly correlated—either negatively or positively—and vice versa.
Jiaxing Chen +4 more
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Pre-Metric Spaces Along with Different Types of Triangle Inequalities
Axioms, 2018 The T 1 -spaces induced by the pre-metric spaces along with many forms of triangle inequalities are investigated in this paper. The limits in pre-metric spaces are also studied to demonstrate the consistency of limit concept in the induced ...
Hsien-Chung Wu, Wu Hsien-Chung
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Properties of distance spaces with power triangle inequalities [PDF]
Karpatsʹkì Matematičnì Publìkacìï, 2016 Metric spaces provide a framework for analysis and have several very useful properties. Many of these properties follow in part from the triangle inequality.
D. Greenhoe
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Operator inequalities via the triangle inequality [PDF]
Journal of Mathematical Inequalities, 2022 This article improves the triangle inequality for complex numbers, using the Hermite-Hadamard inequality for convex functions. Then, applications of the obtained refinement are presented to include some operator inequalities. The operator applications include numerical radius inequalities and operator mean inequalities.
Sababheh, Mohammad +2 more
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Reverse triangle inequalities for potentials [PDF]
Journal of Approximation Theory, 2009 We study the reverse triangle inequalities for suprema of logarithmic potentials on compact sets of the plane. This research is motivated by the inequalities for products of supremum norms of polynomials. We find sharp additive constants in the inequalities for potentials, and give applications of our results to the generalized polynomials.
Igor E. Pritsker, Edward B. Saff
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Open-Source Large Language Models and AI Health Equity: A Health Service Triangle Model Perspective [PDF]
Journal of Medical Internet ResearchThis study explores the role of open-source large language models (LLMs) in promoting artificial intelligence (AI) health equity from the perspective of the health service triangle model.
Shaolong Wu +8 more
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On Sharp Triangle Inequalities in Banach Spaces II
Journal of Inequalities and Applications, 2010 Sharp triangle inequality and its reverse in Banach spaces were recently showed by Mitani et al. (2007). In this paper, we present equality attainedness for these inequalities in strictly convex Banach spaces.
Kichi-Suke Saito, Ken-Ichi Mitani
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Proc. ACM Manag. DataApproximate Nearest Neighbor Search (ANNS) is a critical problem in vector databases. Cluster-based index is utilized to narrow the search scope of ANNS, thereby accelerating the search process. Due to its scalability, it is widely employed in real-world
Kang Chen, Amélie Chi Zhou
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Ceva's triangle inequalities [PDF]
Mathematical Inequalities & Applications, 2014 18 pages, 11 ...
Bényi, Árpád, Ćurgus, Branko
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Correction: On triangle inequalities of correlation-based distances for gene expression profiles [PDF]
BMC Bioinformatics, 2023 Jiaxing Chen +4 more
doaj +2 more sources