• Bulletin of the Korean Mathematical Society
• /
• v.58 no.3
• /
• pp.559-572
• /
• 2021

It is well known that every invariant harmonic function on the unit ball of the multi-dimensional complex space has the volume version of the invariant mean value property. In 1993 Ahern, Flores and Rudin first observed that the validity of the converse depends on the dimension of the underlying complex space. Later Lie and Shi obtained the analogues on the unit ball of multi-dimensional real space. In this paper we obtain the half-space analogues of the results of Liu and Shi.

• Bulletin of the Korean Mathematical Society
• /
• v.33 no.3
• /
• pp.329-334
• /
• 1996

The notion of approximate derivative was introduced by Denjoy in 1916 [3]. Khintchine [5] proved that Rolle's theorem holds for approximate derivatives and Tolstoff [8] proved that every approximate derivative is of Baire class 1 and has Darboux property. Goffman and Neugebauer [4] proved the above results of Tolstoff [8] in a different and simplified method. Also they [4] proved indirectly (via Darboux property) that approximate derivatives possess mean value property.

• Communications of the Korean Mathematical Society
• /
• v.18 no.3
• /
• pp.481-484
• /
• 2003

We will show that if U is a Bergman ball E($\alpha;\;\delta$) in $B_n\;\subset\;{\mathbb{C}_n}$ and if U has M-harmonic volume mean value property at a for all M-harmonic functions f on $\={U} $, then U must be a ball centered at the origin with $\alpha\;=\;0$.

• Bulletin of the Korean Mathematical Society
• /
• v.50 no.1
• /
• pp.263-273
• /
• 2013

A mean-value result, saying that the difference quotient of a differentiable function in a real interval is a mean value of its derivatives at the endpoints of the interval, leads to the functional equation $$\frac{f(x)-F(y)}{x-y}=M(g(x),\;G(y)),\;x{\neq}y$$, where M is a given mean and $f$, F, $g$, G are the unknown functions. Solving this equation for the arithmetic, geometric and harmonic means, we obtain, respectively, characterizations of square polynomials, homographic and square-root functions. A new criterion of the monotonicity of a real function is presented.

• Bulletin of the Korean Mathematical Society
• /
• v.47 no.4
• /
• pp.815-823
• /
• 2010

Let ${\tau}\;{\neq}\;\delta_0$ be either a power bounded radial measure with compact support on the unit disc D with $\tau(D)\;=\;1$ such that there is a $\delta$ > 0 so that ${\mid}\hat{\tau}(s){\mid}\;{\neq}\;1$ for every $s\;{\in}\;\Sigma(\delta)$ \ {0,1}, or just a radial probability measure on D. Here, we provide a decomposition of the set X = {$h\;{\in}\;L^{\infty}(D)\;{\mid}\;lim_{n{\rightarrow}{\infty}}\;h\;*\;\tau^n$ exists}. Let $\tau_1$, ..., $\tau_n$ be measures on D with above mentioned properties. Here, we prove that if $f\;{in}\;L^{\infty}(D^n)$ satisfies an invariant volume mean value property with respect to $\tau_1$, ..., $\tau_n$, then f is n-harmonic.

• Journal of Korean Institute of Industrial Engineers
• /
• v.37 no.2
• /
• pp.124-131
• /
• 2011

In this research report, we propose a heuristic algorithm with some primal recovery strategies for capacitated facility location problems (CFLP), which is a well-known combinatorial optimization problem with applications in distribution, transportation and production planning. Many algorithms employ the branch-and-bound technique in order to solve the CFLP. There are also some different approaches which can recover primal solutions while exploiting the primal and dual structure simultaneously. One of them is a MVCD (Mean Value Cross Decomposition) ensuring convergence without solving a master problem. The MVCD was designed to handle LP-problems, but it was applied in mixed integer problems. However the MVCD has been applied to only uncapacitated facility location problems (UFLP), because it was very difficult to obtain "Integrality" property of Lagrangian dual subproblems sustaining the feasibility to primal problems. We present some heuristic strategies to recover primal feasible integer solutions, handling the accumulated primal solutions of the dual subproblem, which are used as input to the primal subproblem in the mean value cross decomposition technique, without requiring solutions to a master problem. Computational results for a set of various problem instances are reported.

• Communications for Statistical Applications and Methods
• /
• v.3 no.2
• /
• pp.275-282
• /
• 1996

A life distribution F with survival function $\overline{F}$=1-F, finite mean $\mu$ and mean residual life m(t) is said to be NBUE(NWUE) if m(t)$\leq$($\geq$) .$\mu$ for t$\geq$0. This NBUE property can equivalently be characterized by the fact that $\varphi$(u)$\geq$($\leq$)u for 0$\leq$u$\leq$1, where $\varphi$(u) is the scaled total-time-on test transform of F. A generalization of the NBUE properties is that there is a value of p such that $\varphi$(u)\geq.u$ for 0$\leq$u$\leq$p and $\varphi$(u)\leq$$\leq$u$\leq$1, or vice versa. This means that we have a trend change in the NBUE property. In this paper we point out an error of Klefsjo's paper (1988). He erroneously takes advantage of trend change point of failure rate to calculate the empirical test size and power in lognormal distribution. We solves the trend change point of mean residual lifetime and recalculate the empirical test size and power of Klefsjo (1988) in mocensoring case.

• Journal of Environmental Science International
• /
• v.10 no.2
• /
• pp.129-133
• /
• 2001

The purpose of this study is to examine the property of climatological environment using the daily mean meteorological data measured at the serveral meteorological observatory for 30years(1961~1990). It was found that the distribution of discomfort index tended to mainly depend on the geographical situation in the same season. Major portions of Korea were subjected to continental except for some seaside districts. The discomfort index have a large(small) value in summer(winter) season. And there is a short interval(1 or 2 months) between summer and winter season in Korea.

• Proceedings of the Korean Nuclear Society Conference
• /
• 1997.10a
• /
• pp.244-250
• /
• 1997

The mean time to failure (MTTF) expressing the mean value of the system life is a measure of system effectiveness. To estimate the remaining life of component and/or system, the dynamic mean time to failure concept is suggested. It is the time-dependent Property depending on the status of components. The Kalman filter is used to estimate the reliability of components using the on-line information (directly measured sensor output or device-specific diagnostics in the intelligent sensor) in form of the numerical value (state factor). This factor considers the persistency of the fault condition and confidence level in measurement. If there is a complex system with many components, each calculated reliability's or components are combined, which results in the dynamic MTTF or system. The illustrative examples are discussed. The results show that the dynamic MTTF can well express the component and system failure behaviour whether any kinds of failure are occurred or not.

• Korean Journal of Veterinary Research
• /
• v.30 no.4
• /
• pp.525-532
• /
• 1990

The values of blood composition were analyzed by age, season, and sex from Chejuhorse in Korea. The results obtained were summarized as follow; 1. The values of white blood cell(WBC), packed cell volume(PCV), mean corpuscular volume (MCV), and mean corpuscular hemoglobin concentration(MCHC) were significantly different between age. The WBC value was decreased with the progress of age and the PCV value was lower in the early age of 1,2 to 3 years than in the higher age of 4 to 5, and over 6 years. 2. The mean value of MCV was increased with the progress of age but the adverse was true in MCHC. 3. In the case of seasons, the values of red blood cell(RBC), WBC, hemoglobin(Hb) PCV, MCV, mean corpuscular hemoglobin(MCH), MCHC, globulin(Glo), albumin/globulin(A/G) ratio, inorganic phosphorus(Pi), cholesterol(Chol), and chlorine(Cl) showed significant differences. The number of RBC was not varied from winter to summer but decreased in autumn. The number of WBC was high in summer and autumn, but low in winter and spring. 4. The values of MCV were high in autumn and winter, but low in spring and summer. 5. The values of MCH and MCHC were similar in spring and summer, but strikingly increased in autumn. 6. The values of Glo and A/G ratio were negatively correlated with the season; The value of A/G ratio was lowest in summer but no differences were observed in spring, autumn and winter. On the other hand, the value of Glo was highest in summer but no differences were observed in spring, autumn, and winter. 7. The values of Pi, Chol, and CI were high in summer and winter, but low in spring and autumn. 8. The values of RBC, MCV, and MCH were significantly different between sex. The value of the RBC count in male was higer than the female, but the adverse is true in MCV, and MCH.