• Communications of the Korean Mathematical Society
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• v.14 no.3
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• pp.569-579
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• 1999

We consider a random measure defined by the occupation time of Brownian motion in $l_2$. If it is normalized ${\lambda}^2$log then we show that its cluster set as ${\lambda}{longrightarrow}\infty$ can be represented by Ι-function on $\sigma$-finite measure in $l_2$.

• Korean Journal of Mathematics
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• v.16 no.3
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• pp.301-307
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• 2008

Let $R_n$ be the the first return time to its initial n-word. Then the Ornstein-Weiss first return time theorem implies that log$R_n$ divided by n converges to entropy. We consider the convergence of log$R_n$ for Sturmian sequences which has the lowest complexity. In this case, we normalize the logarithm of the first return time by log n. We show that for any numbers $1{\leq}{\alpha},\;{\beta}{\leq}{\infty}$, there is a Sturmian sequence of which limsup is ${\alpha}$ and liminf is $1/{\beta}$.

• East Asian mathematical journal
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• v.24 no.1
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• pp.67-79
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• 2008

In this paper, we characterize the chaotic operator order $A\;{\gg}\;C\;{\gg}\;B$. Consequently all other possible characterizations follow easily. Some satellite theorems of the Furuta inequality are naturally given. And finally, using results of characterizing $A\;{\gg}\;C\;{\gg}\;B$, and by the Douglas's majorization and factorization theorem we are able to characterize the chaotic operator order $A\;{\gg}\;B$ in terms of operator equalities.

• Journal of the Korea Society of Computer and Information
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• v.4 no.2
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• pp.39-45
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• 1999

In this paper we will look at its cryptographic analysis for digital signature and compare it with other complexity measures such as discrete logarithm problem and factorization problem which are based on the security. The paper especially tries to computational complexity so that it can compare and checks the performance analysis, comparison of data size and processing speed through the simulation me

• Journal of the Korean Data and Information Science Society
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• v.7 no.2
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• pp.295-299
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• 1996

In this paper, optimal change times are determined for fully three-step stress accelerated life tests, which minimize the asymptotic variance for maximum likelihood estimator of logarithm of the failure rate at the usual condition and exponential distribution is given for life time data.

• Proceedings of the Korean Statistical Society Conference
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• 2003.05a
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• pp.25-30
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• 2003

We prove that the logarithm of the flow of stochastic differential equations is an element of the free Lie algebra generated by a finite set consisting of vector fields being coefficients of equations. As an application, we directly obtain a formula of the solution of stochastic differential equations given by Castell(1993) without appealing to an expansion for ordinary differential equations given by Strichartz (1987).

• Journal of applied mathematics & informatics
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• v.38 no.5_6
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• pp.601-609
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• 2020

In this paper, we introduce degenerate generalized poly-Bernoulli numbers and polynomials with (p, q)-logarithm function. We find some identities that are concerned with the Stirling numbers of second kind and derive symmetric identities by using generalized falling factorial sum.

• Korean Journal of Mathematics
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• v.24 no.2
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• pp.273-296
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• 2016

Some new trace inequalities for convex functions of self-adjoint operators in Hilbert spaces are provided. The superadditivity and monotonicity of some associated functionals are investigated. Some trace inequalities for matrices are also derived. Examples for the operator power and logarithm are presented as well.

• Communications of the Korean Mathematical Society
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• v.15 no.4
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• pp.683-689
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• 2000

The convergence rate of the expectation of the logarithm of the first return time R(sub)n with block length n has been investigated for Bernoulli processes. This idea is applied to check the randomness of the digits of the decimal expansion of $\pi$, e and √2.

• Journal of the Korean Statistical Society
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• v.17 no.1
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• pp.30-45
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• 1988

Let ${X(t) : 0 \leq t < \infty}$ be a real-valued process with stationary independent increments. In this paper, we obtain necesary and sufficint condition for there to exist a positive, nondecreasing function $\beta(t)$ so that $0 < lim sup $\mid$X(t)$\mid$/\beta(t) < \infty$ a.s. both as t tends to zero and infinity. When no such $\beta(t)$ exists we give a simple integral test for whether $lim sup $\mid$X(t)$\mid$/\beta(t)$ is zero or infinity for a given $\beta(t)$.