• Journal of the Korea Institute of Information and Communication Engineering
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• v.16 no.5
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• pp.989-998
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• 2012

A ratio type of capacitance measurement circuit is proposed to measure an extremely small value of the fF capacitance on this paper. This measurement circuit is formed with a switched-capacitor integrator, a comparator, and logic circuit blocks to control the switches. It converts the measured ratio value between the known value of on-chip capacitor and the unknown value of capacitor to the digital signal. The fF capacitance with minimized error can be obtained by calculating this ratio. This proposed circuit is designed with standard CMOS $0.18{\mu}m$ process, and various HSpice simulations prove that this capacitance measurement circuit is able to measure the capacitance under 5fF with less than ${\pm}0.3%$ error rate.

• Communications of the Korean Mathematical Society
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• v.9 no.4
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• pp.881-889
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• 1994

Let ($X, \Beta, \mu$) be a measure space with the $\sigma$-algebra $\Beta$ and the probability measure $\mu$. Throughouth this article set equalities and inclusions are understood as being so modulo measure zero sets. A transformation T defined on a probability space X is said to be measure preserving if $\mu(T^{-1}E) = \mu(E)$ for $E \in B$. It is said to be ergodic if $\mu(E) = 0$ or i whenever $T^{-1}E = E$ for $E \in B$. Consider the sequence ${x, Tx, T^2x,...}$ for $x \in X$. One may ask the following questions: What is the relative frequency of the points $T^nx$ which visit the set E\ulcorner Birkhoff Ergodic Theorem states that for an ergodic transformation T the time average $lim_{n \to \infty}(1/N)\sum^{N-1}_{n=0}{f(T^nx)}$ equals for almost every x the space average $(1/\mu(X)) \int_X f(x)d\mu(x)$. In the special case when f is the characteristic function $\chi E$ of a set E and T is ergodic we have the following formula for the frequency of visits of T-iterates to E : $$ lim_{N \to \infty} \frac{$\mid${n : T^n x \in E, 0 \leq n $\mid$}{N} = \mu(E) $$ for almost all $x \in X$ where $$\mid$\cdot$\mid$$ denotes cardinality of a set. For the details, see [8], [10].

• Journal of the Chungcheong Mathematical Society
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• v.20 no.3
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• pp.333-342
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• 2007

Suppose that ${\mu}$ is a finite positive Borel measure on the unit ball $B{\subset}C^n$. The boundary of B is the unit sphere $S=\{z:{\mid}z{\mid}=1\}$. Let ${\sigma}$ be the rotation-invariant measure on S such that ${\sigma}(S)=1$. In this paper, we will show that if $sup_{{\zeta}{\in}S}\;{\int}_{B}\;P(z,{\zeta})d{\mu}(z)$<${\infty}$ where $P(z,{\zeta})$ is the Poission-Szeg$\ddot{o}$ kernel for B, then ${\mu}$ is a Carleson measure. We will also show that if $sup_{{\zeta}{\in}S}\;{\int}_{B}\;P(z,{\zeta})d{\mu}(z)$<${\infty}$, then the operator T such that T(f) = P[f] is compact as a mapping from $L^p(\sigma)$ into $L^p(B,d{\mu})$.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.9 no.2
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• pp.71-75
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• 2009

The purpose of this paper is to prove a Jensen type inequality for Choquet integrals with respect to a non-additive measure which was introduced by Choquet [1] and Sugeno [20]; $$\Phi((C)\;{\int}\;fd{\mu})\;{\leq}\;(C)\;\int\;\Phi(f)d{\mu},$$ where f is Choquet integrable, ${\Phi}\;:\;[0,\;\infty)\;\rightarrow\;[0,\;\infty)$ is convex, $\Phi(\alpha)\;\leq\;\alpha$ for all $\alpha\;{\in}\;[0,\;{\infty})$ and ${\mu}_f(\alpha)\;{\leq}\;{\mu}_{\Phi(f)}(\alpha)$ for all ${\alpha}\;{\in}\;[0,\;{\infty})$. Furthermore, we give some examples assuring both satisfaction and dissatisfaction of Jensen type inequality for the Choquet integral.

• Journal of the Korean Mathematical Society
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• v.56 no.5
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• pp.1387-1401
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• 2019

Consider a finite measure space (${\Omega}$, ${\Sigma}$, ${\mu}$) and a Banach space $X({\mu})$ consisting of (equivalence classes of) real measurable functions defined on ${\Omega}$ such that $f{\chi}_A{\in}X({\mu})$ and ${\parallel}f{\chi}_A{\parallel}{\leq}{\parallel}f{\parallel}$, ${\forall}f{\in}({\mu})$, $A{\in}{\Sigma}$. We prove that if it satisfies the subsequence property, then it is an ideal of measurable functions and has an equivalent norm under which it is a Banach function space. As an application we characterize norms that are equivalent to a Banach function space norm.

• Journal of the Korean Mathematical Society
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• v.33 no.2
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• pp.235-247
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• 1996

Many numerical computations in science and engineering can only be solved approximately since the available infomation is partial. For instance, for problems defined ona space of functions, information about f is typically provided by few function values, $N(f) = [f(x_1), f(x_2), \ldots, f(x_n)]$. Knwing N(f), the solution is approximated by a numerical method. The error between the true and the approximate solutions can be reduced by acquiring more information. However, this increases the cost. Hence there is a trade-off between the error and the cost.

• Communications of the Korean Mathematical Society
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• v.11 no.3
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• pp.695-706
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• 1996

In the control system $ \dot{x} = f(t,x(t)) + g(t,x(t))\dot{u}, x(0) = \bar{x}, t \in [0,T], $ this paper shows that the map from u with $L^1(m)$-topology to $x_u$ with $L^1(\mu)$-topology is Lipschitz continuous where f is $C^1$, $\mu$ is the Stieltjes measure derived from the function g which is not smooth in the variable t and $x_u$ is the solution of the above system corresponding to u under the assumption that $\dot{u}$ is bounded.

• Communications of the Korean Mathematical Society
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• v.18 no.4
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• pp.677-685
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• 2003

Let M be the vector space of all real S-measurable functions defined on a measure space (X, S, $\mu$). In this paper, we investigate some topological structure of T on M. Indeed, (M, T) becomes a topological vector space. Moreover, if $\mu$, is ${\sigma}-finite$, we can define a complete invariant metric on M which is compatible with the topology T on M, and hence (M, T) becomes a F-space.

• Journal of the Korean Home Economics Association
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• v.31 no.1
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• pp.181-192
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• 1993

This study was undertaken to investigate the factorial structure of clothing purchase motives, and to examine the relationship between clothing purchase motives, self-concept, and post-purchase clothing satisfaction of males. Questionnaire was comprised of three sections: 25 Likert type statements of clothing purchase motive measure; post-purchase clothing satisfaction measure; and three self-concepts measure(physical, personal, and social self-concept). For the measurement of self-concepts, a portion of‘Self-Concept Scale’by Wonshik Chung was used. Samples were 312 male white collar workers in Seoul, whose age were ranged from 20 to 39. the data were analyzed using factor analysis, Cronbach's alpha reliability coefficient, Pearson's correlation coefficient, and multiple regression analysis. The results of the study were the followings: 1. Six factors of clothing purchase motives derived by factor analysis. 21 items having a factor loading of ± .40 or higher were given consideration in the interpretation of each factor: F.1‘clothing dsign’; F.2‘fashion and impulsive buying’, F.3‘clothing utility’; F.4‘others influence’: F.5‘financial margin’; F.6‘clothing’2. Male consumers perceived the purchase motive of‘clothing design’to be the most important,‘clothing deficiency’the second important, and‘others influence’the least important. 3. Physical, personal, and social self-concept had positive relations to the purchase motive of‘clothing design’and negative relations to the‘clothing deficiency’. Physical self-concept had negative relation to the motive of‘others influence’. 4. Male consumers high in physical, personal, and social self-concept had more positive attitude in the evaluation of post-purchase clothing satisfaction. 5. Post-purchase clothing satisfaction was influenced most by the purchase motive of‘clothing design’, and next by physical self-concept, and age. Age of subjects had negative relation to post-purchase clothing satisfaction. The explanatory power of the 3 variables was 19.9%.

• Journal of the Korea Society for Simulation
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• v.18 no.4
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• pp.185-195
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• 2009

As most systems get more complicated, system analysis using simulation has been taken notice of. One of the core parts of simulation analysis is validation of a simulation model, and we can identify how well the simulation model represents the real system with this validation process. The difference between input data of two systems has an effect on the comparison between a simulation model and a real system at validation stage, and the result with such difference is not enough to ensure high credibility of the model. Accordingly, in this paper, we construct a model based on Trace-driven simulation which uses identical input data with the real system. On the other hand, to validate a model by each class, not by an unique statistic, we validate the model using a metric transformed from F-measure which estimates performance of a classifier in data mining field. Finally, this procedure enables precise validation process of a model, and it helps modification by offering feedback at the validation phase.