• Nuclear Engineering and Technology
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• v.21 no.1
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• pp.32-39
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• 1989

A method for determining the optimum ideal MHD $\beta$limit and the operation conditions is presented for an axisymmetric tokamak reactor with a circular cross section. The $\beta$limit is calculated under the constraints of ideal MHD instability criteria with varying the operation conditions which depend on the toroidal current density distributions. Semiempirical laws deduced from experimental observations are used for the toroidal current density distributions. Analytic derivations of various equations required to determine the $\beta$limit are carried out from the empirical equations. Various distributions of the $\beta$limit are obtained by the numerical calculations for different distributions of the toroidal current density. The resulting values of the maximum $\beta$limited by ideal MHD instabilities are expressed by a scaling law in terms of the tokamak geometry and the safety factor.

• Journal of the Korean Data and Information Science Society
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• v.7 no.2
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• pp.289-294
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• 1996

This paper considers the limit of the ratio of two incomplete beta functions $I_{x}(p+s,q+r)\;to\;I_{x}(p,q)\;as\;p+q{\rightarrow}{\infty}$. The results show that the limits depend on r,s,x and the limit of p/(p+q).

• Journal of KSNVE
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• v.8 no.5
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• pp.821-831
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• 1998

The actual ground vibrations due to NATM and foundation blasting at Seoul(weathered rock), Pusan(weathered rock) and Youngkwang(quartz andesite) have been measured, and the data were analyzed using reliability index($\beta$) to determinate the vibration equations and the maximum charge weight for efficient blast. These were suggested with the division of ultimate limit state($\beta$=0), serviceability limit state($\beta$=1.28) and safety state($\beta$=3), respectively. The reliability index 0 mean 50% data line obtained by the least squares best-fit line. The reliability index 1.28 and 3 represent bounds below 90% and 99.9% of the data, respectively. In this study, reliability index $\beta$=1.28 with security and economy was suggested. The maximum charge weight equations for efficient blast were obtained in W=(Vc/384.90)1.5151.D3(Seoul), W=(Vc/579.82)1.4706.D3(Pusan). W=(Vc/1654.01)1.3456.D3(Youngkwang), and the blast vibration equatiions in V=385(SD)-1.98(Seoul), V=580(SD)-2.04(Pusan), V=1654(SD)-2.23(Youngkwang), respectively. From this study, inference and analysis methods of vibration equations using reliability theory were established.

• Journal of the Korean Ceramic Society
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• v.55 no.6
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• pp.590-596
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• 2018

To improve the injection behavior of brushite cement, dense ${\beta}-Ca_3(PO_4)_2$ (${\beta}-TCP$) granules were added to the starting material. The spherical ${\beta}-TCP$ granules prepared by spray-drying and subsequent sintering at $1000{\sim}1200^{\circ}C$ accounted for fractions of from 0.5 to 0.7 of the total ${\beta}-TCP$. The injection behavior was evaluated by measuring the injected mass divided by the loaded mass of paste in the syringe pump. The injected amount was increased with the increase in the fraction and sintering temperature of ${\beta}-TCP$ granules, except at $1200^{\circ}C$. The increase in the fraction of ${\beta}-TCP$ and its sintering temperature resulted in a decrease in the plastic limit, which is the volume of water required to liquefy the compact. The rest water could be utilized in the cement with the reduced plastic limit for improved injectability. The amounts of rest water assigned for powdery phase were estimated, and correlated with the injectability of paste.

• Journal of Korean Society of Steel Construction
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• v.14 no.2
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• pp.311-318
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• 2002

This paper described the ultimate strength and deformation limit of welded T-joints in cold-formed square hollow sections. Previous studies showed that the strength of a T-joint still increases with increasing deformations at a ratio of branch width to chord width (${\beta}$) of below 0.8. Therefore, the strength at a certain deformation (chord flange indentation) limit can be regarded as the ultimate strength of a T-joint. The chord flange failure modes were investigated for the ratio of branch width to chord width (${\beta}$) and the ratio of chord width to chord web thickness (B/T). Experimental results including tests done by Kato proposed a deformation limit of 3%B for $16.7{\leq}B/T{\leq}41.6$ and $0.27{\leq}{\beta}{\leq}0.8$. The strength formula of CIDECT and other researchers were compared with the test results. Finally, the strength formula based on yield-line theory was proposed.

• Korean Management Science Review
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• v.24 no.1
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• pp.77-90
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• 2007

Taguchi assumed that a product characteristic has the uniform distribution in its preventive maintenance limit when deriving the expected loss generated by the quality deviation. But it is reasonable to assume that a product characteristic has the normal distribution than the uniform distribution. On this paper, we first find the optimum inspection interval and the optimum preventive maintenance limit under the truncated triangular distribution. Secondly we use the beta-general distribution and compare with the truncated triangular distribution. By using the numerical examples, we find the optimum inspection interval and the optimum preventive maintenance limit under their distributions. As a result, we find that the beta-general distribution gives the best solution and easy calculation.

• Journal of the Korean Society for Railway
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• v.5 no.1
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• pp.48-54
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• 2002

This research estimated decreased vibration level as quantitative according to change of track system on Seoul Subway Line No. 1 from existing ballasted track system(Pandrol type clip) to concrete track system(Youbgdan type isolation rubber clip). Following change to concrete system, vibration level at tunnel floor decreased between 4-8dB(V). Vibration equations suggested in this paper consider the velocity of train and can estimate quantitative vibration response. These are divided by ultimate limit state($\beta$=0), serviceability limit state($\beta$=1.28) and safety state($\beta$=3), respectively. The reliability index, $\beta$=0, means 50％ data line obtained by least squares best-fit line. The reliability index $\beta$=1.28 and 3 represent boundaries below 90％ and 99.9％ respectively.

• Bulletin of the Korean Mathematical Society
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• v.42 no.2
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• pp.359-367
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• 2005

Let A be a Banach algebra, we say that A has the strongly double limit property (SDLP) if for each bounded net $(a_\alpha)$ in A and each bounded net $(a^{\ast}\;_\beta)\;in\;A^{\ast},\;lim_\alpha\;lim_\beta=lim_\beta\;lim_\alpha$ whenever both iterated limits exist. In this paper among other results we show that if A has the SDLP and $A^{\ast\ast}$ is (n - 2)-weakly amenable, then A is n-weakly amenable. In particular, it is shown that if $A^{\ast\ast}$ is weakly amenable and A has the SDLP, then A is weakly amenable.

• Bulletin of the Korean Mathematical Society
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• v.36 no.1
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• pp.139-146
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• 1999

It is known that a right nilpotent congruence $\beta$ on a finite algebra A is also left nilpotent [3]. The question on whether the left nilpotency class of $\beta$ in less than or equal to the right nilpotency class of $\beta$is still open. In this paper we find an upper limit for the left nilpotency class of $\beta$. In addition, under the assumption that 1 $\in$ typ{A}, we show that $(\beta]^k=[\beta)^k$ for all k$\geq$1. Thus the left and right nilpotency classes of $\beta$ are the same in this case.

• Journal of Korean Society of Steel Construction
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• v.16 no.3 s.70
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• pp.315-324
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• 2004

This study performs a yield line analysis of welded T-joints in cold-formed Square Hollow Sections (SHS) with the branch in axial compression. The existing yield line models proposed by Koto, Packer, Zhao, and CIDECT and the proposed yield line model of the previous study are compared, using the existing test results of welded T-joints in cold-formed SHS. The yield line model suggested in the previous paper, which is based on the simplified yield line analysis, is reviewed to evaluate its application limit on cold-formed SHS T-joints. In the proposed model, the round corner of the cold-formed SHS section and weld size are taken into account. Finally, the validity range of yield line analysis is determined by observing the actual failure modes and comparing the test value with the analysis value, set as ${\beta}^{\prime}{\leq}0.8$ where ${\beta}^{\prime}=0.8$, ${\beta}^{\prime}=b_1^{\prime}/b_0^{\prime}$, $b_1{^{\prime}}=b_1+t_0$ and $b_0{^{\prime}}=b_0-t_0$.