• Journal of the Korean Mathematical Society
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• v.35 no.2
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• pp.433-447
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• 1998

We investigate coboundary conditions for two functions defined on a mixing subshift of finite type to have the same Gibbs measure. Also we find conditions for a function to be a coboundary.

• Bulletin of the Korean Mathematical Society
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• v.53 no.6
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• pp.1685-1695
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• 2016

In this article we consider Lie super-bialgebra structures on the generalized loop super-Virasoro algebra ${\mathcal{G}}$. By proving that the first cohomology group $H^1({\mathcal{G}},{\mathcal{G}}{\otimes}{\mathcal{G}})$ is trivial, we obtain that all such Lie bialgebras are triangular coboundary.

• Journal of the Korean Mathematical Society
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• v.47 no.4
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• pp.705-718
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• 2010

It gives a method to obtain a natural Lie bialgebra from a Poisson bialgebra by an algebraic point of view. Let g be a coboundary Lie bialgebra associated to a Poission Lie group G. As an application, we obtain a Lie bialgebra from a sub-Poisson bialgebra of the restricted dual of the universal enveloping algebra U(g).

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.6 no.2
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• pp.1-8
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• 2002

Let $T_{\phi}$ be a generalized Gauss transformation and $[a_1,\;a_2,\;{\cdots}]_{T_{\phi}}$ be a symbolic representation of $x{\in}[0,\;1)$ induced by $T_{\phi}$, i.e., generalized continued fraction expansion induced by $T_{\phi}$. It is shown that the distribution of relative frequency of [$k_1,\;{\cdots},\;k_n$] in $[a_1,\;a_2,\;{\cdots}]_{T_p}$ satisfies Central Limit Theorem where $k_i{\in}{\mathbb{N}}$ for $1{\leq}i{\leq}n$.

• The Mathematical Education
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• v.22 no.2
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• pp.5-12
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• 1984

Steenrod algebra $\alpha$$_{p}$(mod p) was generated for algebra on steenrod reduced powers p$^n$ and Bochstein coboudary operation $\beta$. We know the relation between them. In this thesis I have verified the theorem: (equation omitted)

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.9 no.2
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• pp.91-97
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• 2005

If ${\beta}\;>\;1$, then every non-negative number x has a ${\beta}-expansion$, i.e., $$x\;=\;{\epsilon}_0(x)\;+\;{\frac{\epsilon_1(x)}{\beta}}\;+\;{\frac{\epsilon_2(x)}{\beta}}\;+\;{\cdots}$$ where ${\epsilon}_0(x)\;=\;[x],\;{\epsilon}_1(x)\;=\;[\beta(x)],\;{\epsilon}_2(x)\;=\;[\beta(({\beta}x))]$, and so on ([x] denotes the integral part and (x) the fractional part of the real number x). Let T be a transformation on [0,1) defined by $x\;{\rightarrow}\;({\beta}x)$. It is well known that the relative frequency of $k\;{\in}\;\{0,\;1,\;{\cdots},\;[\beta]\}$ in ${\beta}-expansion$ of x is described by the T-invariant absolutely continuous measure ${\mu}_{\beta}$. In this paper, we show the mod M normality of the sequence $\{{\in}_n(x)\}$.

• Communications of the Korean Mathematical Society
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• v.39 no.1
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• pp.11-30
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• 2024

3-Lie algebras are in close relationships with many fields. In this paper we are concerned with the study of 3-Hom-Lie super algebras, the concepts of 3-Hom-Lie coalgebras and how they make a 3-Hom-Lie superbialgebras, we study the structures of such categories of algebras and the relationships between each others. We study a super twisted 3-ary version of the Yang-Baxter equation, called the super 3-Lie classical Hom-Yang-Baxter equation (3-Lie CHYBE), which is a general form of 3-Lie classical Yang-Baxter equation and prove that the superbialgebras induced by the solutions of the super 3-Lie CHYBE induce the coboundary local cocycle 3-Hom-Lie superbialgebras.