• Communications for Statistical Applications and Methods
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• 제16권1호
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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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• 제2권1호
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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.

• 호남수학학술지
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• 제31권4호
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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].

• 대한수학회지
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• 제33권4호
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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.

• 한국미생물·생명공학회지
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• 제17권4호
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• pp.379-384
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• 1989

E. coli K-12 pgln 6가 지니는 glutamine synthetase와 반응계에 ATP 공급을 위하여 빵효모를 동시에 이용하여 glutamate로부터 glutamine의 생산이 수행되었다. Glutamine synthetase의 효소원으로서 E. coli K-12 pgln 6 생균체를 사용하였을 때, 18시간 배양 후에 11.8g/ι의 glutamine이 생산되었다(기질인 glutamate 기준으로 60%의 수율). 부분정제된 glutamine synthetase를 이용하여, 5시간 후에 19.8g/ι의 glutamine이 생산되었다. 이 양은 glutamate 기준으로 90% 수율에 해당되는 것이다.