• 대한수학회논문집
• /
• 제14권3호
• /
• pp.569-579
• /
• 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
• /
• 제16권3호
• /
• pp.301-307
• /
• 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
• /
• 제24권1호
• /
• pp.67-79
• /
• 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.

• 한국컴퓨터정보학회논문지
• /
• 제4권2호
• /
• pp.39-45
• /
• 1999

본 논문은 디지털서명을 위한 암호화 기법의 분석과 이산대수 문제와 소인수 분해와 같이 계산 복잡도의 어려움에 안전성의 근거를 둔 암호방식을 비교한다. 특히 계산량에 의한 성분분석과 데이터 크기 비교 및 처리속도를 시뮬레이션에 의해 비교, 검토하였다.

• Journal of the Korean Data and Information Science Society
• /
• 제7권2호
• /
• pp.295-299
• /
• 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.

• 한국통계학회:학술대회논문집
• /
• 한국통계학회 2003년도 춘계 학술발표회 논문집
• /
• pp.25-30
• /
• 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
• /
• 제38권5_6호
• /
• pp.601-609
• /
• 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
• /
• 제24권2호
• /
• pp.273-296
• /
• 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.

• 대한수학회논문집
• /
• 제15권4호
• /
• pp.683-689
• /
• 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
• /
• 제17권1호
• /
• pp.30-45
• /
• 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 $\beta(t)$.