• Bulletin of the Korean Mathematical Society
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• v.61 no.3
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• pp.621-635
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• 2024

An 𝑙-regular overpartition of n is an overpartition of n with no parts divisible by 𝑙. Recently, the authors introduced a partition statistic called r_𝑙-crank of 𝑙-regular overpartitions. Let M_r𝑙(m, n) denote the number of 𝑙-regular overpartitions of n with r_𝑙-crank m. In this paper, we investigate the monotonicity property and the unimodality of M_r3(m, n). We prove that M_r3(m, n) ≥ M_r3(m, n - 1) for any integers m and n ≥ 6 and the sequence {M_r3(m, n)}_|m|≤n is unimodal for all n ≥ 14.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.40 no.8
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• pp.751-757
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• 2016

The aim of this study is to estimate the reliability of fatigue limit of the material used for crank throw components according to the staircase method. The material used for crank throw components is forged S34MnV grade steel, which is heat treated by normalizing and tempering. In this work, to predict the reliability of the design fatigue strength, axially loaded constant amplitude fatigue testing was conducted. The test specimens were loaded with an axial push/pull load with a mean stress of 0 MPa, which corresponds to a stress ratio of R=-1. The fatigue test results were evaluated by Dixon-Mood formulas. The values of mean fatigue strength and standard deviation predicted by the staircase method were 296.3 MPa and 10.6 MPa, respectively. Finally, the reliability of the fatigue limit in some selected probability of failure is predicted. The proposed method can be applied for the determination of fatigue strength for design optimization of the forged steel.