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2000
Some integral inequalities of the following type are proved: Suppose \(f\) has a continuous \(n\)th order derivative on \([a,b]\); \(f^{(i)}(a)\geq 0\) and \(f^{(n)}(x)\geq n!\) for all \(x\in [a,b]\) and \(0\leq i\leq n-1\). Then \[ \int^b_a [f(x)]^{n+2} dx\geq \Biggl[\int^b_a f(x) dx\Biggr]^{n+ 1}. \] An open problem is also stated.
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Some integral inequalities of the following type are proved: Suppose \(f\) has a continuous \(n\)th order derivative on \([a,b]\); \(f^{(i)}(a)\geq 0\) and \(f^{(n)}(x)\geq n!\) for all \(x\in [a,b]\) and \(0\leq i\leq n-1\). Then \[ \int^b_a [f(x)]^{n+2} dx\geq \Biggl[\int^b_a f(x) dx\Biggr]^{n+ 1}. \] An open problem is also stated.
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An overview of real‐world data sources for oncology and considerations for research
Ca-A Cancer Journal for Clinicians, 2022Lynne Penberthy +2 more
exaly
The mechanisms of integral membrane protein biogenesis
Nature Reviews Molecular Cell Biology, 2021Ramanujan Shankar Hegde, Robert J Keenan
exaly
Solving integral equations in free space with inverse-designed ultrathin optical metagratings
Nature Nanotechnology, 2023Andrea Cordaro, Andrea Alu
exaly