• Journal for History of Mathematics
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• v.24 no.3
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• pp.23-35
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• 2011

The sphere theorem is one of the main streams in modern Riemannian geometry. In this article, we survey developments of pinching theorems from the classical one to the recent differentiable pinching theorem. Also we include sphere theorems of metric invariants such as diameter and radius with historical view point.

• The Korean Journal of Applied Statistics
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• v.17 no.3
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• pp.547-556
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• 2004

This paper consider the testing problem of variance component for the unbalanced two-way error component model with nuisance parameter. We derive the one-sided LM test statistic for testing zero individual(time) effects assuming that the other time-specific(individual) effects are present. Using the Monte Carlo experiments, the computational more demanding LR test slightly underestimates the nominal size and has the low powers relative to LM test statistic.