• Communications of the Korean Mathematical Society
• /
• v.13 no.3
• /
• pp.525-538
• /
• 1998

Recently, a stability theorem for the Feynman integral as a bounded linear operator on$ L_2$($R^{d}$ /) with respect to measures whose positive and negative variations are in the generalized Kato class was proved. We study a stability theorem for the Feynman integral with respect to measures whose positive variations are in the class of $\sigma$-finite smooth measures and negative variations are in the generalized Kato class. This extends the recent result in the sense that the class of $\sigma$-finite smooth measures properly contains the generalized Kato class.

• Wind and Structures
• /
• v.9 no.1
• /
• pp.59-74
• /
• 2006

Vertical stabilizer plates have been found to be an effective aerodynamic measure to improve the aerodynamic stability of bridges either with an open cross section or with a streamlined box cross section in wind tunnel testings and have been adopted in some long span bridges. By taking an open deck II-shaped section and a closed box section as examples, the mechanism of vertical stabilizer plates for improving aerodynamic stability are investigated by using numerical simulation based on Random Vortex Method. It is found that vertical stabilizer plates can increase the amplitude of the heaving motion, and decrease that of the rotational motion of the bridge decks.

• Journal of the Korean Data and Information Science Society
• /
• v.23 no.1
• /
• pp.39-51
• /
• 2012

Cluster analysis has proven to be a useful tool for investigating the association structure among genes and samples in a microarray data set. We applied several cluster validation measures to evaluate the performance of clustering algorithms for analyzing microarray gene expression data, including hierarchical clustering, K-means, PAM, SOM and model-based clustering. The available validation measures fall into the three general categories of internal, stability and biological. The performance of clustering algorithms is evaluated using simulated and SRBCT microarray data. Our results from simulated data show that nearly every methods have good results with same result as the number of classes in the original data. For the SRBCT data the best choice for the number of clusters is less clear than the simulated data. It appeared that PAM, SOM, model-based method showed similar results to simulated data under Silhouette with of internal measure as well as PAM and model-based method under biological measure, while model-based clustering has the best value of stability measure.

• Journal of the Korean Mathematical Society
• /
• v.55 no.5
• /
• pp.1131-1142
• /
• 2018

A notion of measure expansivity for homeomorphisms was introduced by Morales recently as a generalization of expansivity, and he obtained many interesting dynamic results of measure expansive homeomorphisms in [8]. In this paper, we introduce a concept of weak measure expansivity for homeomorphisms which is really weaker than that of measure expansivity, and show that a diffeomorphism f on a compact smooth manifold is $C^1$-stably weak measure expansive if and only if it is ${\Omega}$-stable. Moreover we show that $C^1$-generically, if f is weak measure expansive, then f satisfies both Axiom A and the no cycle condition.

• The Transactions of The Korean Institute of Electrical Engineers
• /
• v.58 no.12
• /
• pp.2505-2510
• /
• 2009

Semiconductor processes need measurement to confirm where there are problems in quality after progresses manufacturing process. This paper suggests equipment and automatic measure sampling method that control monitoring ratio according to change point occurrence availability of process that is not measure method by the existent simple ratio rate. This paper defines measure section as ailment section, metastable section and stability section by change point standard and create statistical model of each section and developed suitable measure rate model by section. As a result, we have accomplished maximum throughput and minimum sampling number that needs to maintain constant level of quality. Proposed method minimizes load of measure process by brings production quality sophistication and decrease of process badness and lowers measure rate in stable section making perception about problem occurrence quick heightening measure rate at change point occurrence.

• Journal of the Korea Safety Management & Science
• /
• v.12 no.3
• /
• pp.101-106
• /
• 2010

The purposes of this paper are to investigate an effect of weight of material and gender on postural stability and to introduce formulas for those. There were five levels of weights 0, 9, 18, 27 and 36 kg, and two levels of genders were conducted. Eight male and five female subjects participated in this experiment, ten tests were performed for each level of weights to measure the postural stability by using the stability platform. The effect of the genders and the load on the postural stability were statistically analysed by the two way ANOVA test and the regression analysis. The ANOVA test showed that the effect of weights was statistically significant on postural stability to the both male and female subjects. And the postural stability of female subjects was better than that of male subjects. A linear regression formula for the balancing time and the load and a formula for the reduction rate postural stability and the relative load were introduced by the regression analysis.

• Physical Therapy Korea
• /
• v.19 no.3
• /
• pp.61-71
• /
• 2012

In daily activities, people often perform two or more tasks simultaneously. This is referred to as dual-tasking or multi-tasking. The purpose of this study was to examine the effects of performing dual tasks while using a mobile phone on static and dynamic postural stability. Twenty-four subjects were asked to stand on a force plate and then instructed to perform a balance task only (BT), a balance task while listening to music (BTL), a balance task while talking on the mobile phone (BTT), and a balance task while sending text messages (BTS). We used the BioRescue$^{(R)}$ to measure postural sway and limit of stability for static and dynamic postural stability. Also the star excursion balance test (SEBT) was used to measure dynamic postural stability. A one-way ANOVA with repeated measures was used to compare the effects of the BT, BTL, BTT, and BTS. The Bonferroni's post hoc test was used to determine the differences among four tasks. Carrying out the BTS significantly decreased the limit of stability compared with carrying out the BT, BTL, and BTT (p<.05). In limit of stability, total surface area of BTT was more significantly decreased than that of BT and total surface area of BTS was more decreased than that of BT, BTL and BTT (p<.05). In the SEBT, the BTS displayed significantly smaller reach distance values compared with the BT or BTL (p<.05). These findings suggest that performing the balance task while sending text message on the mobile phone decreases dynamic postural stability, whereas performing the same task while listening to music using the mobile phone does not. Therefore, it requires more attention to maintain dynamic balance while sending text messages.

• Journal of the Korean Mathematical Society
• /
• v.35 no.4
• /
• pp.999-1018
• /
• 1998

In this paper, we prove stability theorems for the operator-valued Feynman integral of certain functionals involving some Borel measures on (0, t) as a bounded linear operator from L$_1$(R) to $C_{0}$(R).

• Korean Journal of Mathematics
• /
• v.24 no.2
• /
• pp.297-305
• /
• 2016

In this paper, by using fixed point theorem, we obtain the stability of the following functional equations $$f(pr,qs)+g(ps,qr)={\theta}(p,q,r,s)f(p,q)h(r,s)\\f(pr,qs)+g(ps,qr)={\theta}(p,q,r,s)g(p,q)h(r,s)$$, where G is a commutative semigroup, ${\theta}:G^4{\rightarrow}{\mathbb{R}}_k$ a function and f, g, h are functionals on $G^2$.

• Bulletin of the Korean Mathematical Society
• /
• v.56 no.3
• /
• pp.801-813
• /
• 2019

In this paper, using the Baire category theorem we investigate the Hyers-Ulam stability problem of pexiderized Jensen functional equation $$2f(\frac{x+y}{2})-g(x)-h(y)=0$$ and pexiderized Jensen type functional equations $$f(x+y)+g(x-y)-2h(x)=0,\\f(x+y)-g(x-y)-2h(y)=0$$ on a set of Lebesgue measure zero. As a consequence, we obtain asymptotic behaviors of the functional equations.