• Communications for Statistical Applications and Methods
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• v.16 no.1
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• pp.157-162
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• 2009

The baker transformation is an ergodic transformation defined on the half open unit square. This paper considers the limiting behavior of the partial sum process of a martingale sequence constructed from the baker transformation. We get the uniform law of large numbers for the baker transformation.

• Communications for Statistical Applications and Methods
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• v.2 no.1
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• pp.194-200
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• 1995

The baker's transformation is an ergodic transformation defined on the half open unit square. This paper considers the limiting begavior of the partial sum process of a martingale sequence constructed from the baker's transformation in the context of an invariance principle of a uniform central limit theorm.

• Honam Mathematical Journal
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• v.31 no.4
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• pp.591-599
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• 2009

For given ${\alpha},{\omega}\;{\in}\;{\mathbb{R}}$ and ${\beta}$ > 1, let $T_{{\beta},{\alpha},{\omega}}$ be the skew-product transformation on the torus, [0, 1) ${\times}$ [0, 1) defined by (x, y) ${\longmapsto}\;({\beta}x,y+{\alpha}x+{\omega})$ (mod 1). In this paper, we give a criterion of ergodicity and weakly mixing for the transformation $T_{{\beta},{\alpha},{\omega}}$ when the natural extension of the given ${\beta}$-transformation can be viewed as a generalized baker's transformation, i.e., they flatten and stretch and then cut and stack a two-dimensional domain. This is a generalization of theorems in [10].

• Journal of the Korean Mathematical Society
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• v.33 no.4
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• pp.909-928
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• 1996

In this paper, an empirical law of the iterated logarithm is investigated in the context of a stationary and ergodic martingale differences whose values taking in a measurable space.

• Microbiology and Biotechnology Letters
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• v.17 no.4
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• pp.379-384
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• 1989

Glutamine production from glutamate was carried out using glutamine synthetase from E. coli K-12 pgln 6 and baker's yeast, which supplies ATP into the reaction system through alcohol fermentation, simultaneously. With whole cells of E. coli K-12 pgln 6 as an enzyme source of glutamine synthetase, 11.8 g/ι of glutamine produced after 18-h incubation (60％ yield based on a substrate, glutamate). Using the partially purified glutamine synthetase, 19.8 git of glutamine was produced after 5-h incubation. This amount of glutamine was correspond to 90％ yield, based on substrate, glutamate.