• Kyungpook Mathematical Journal
• /
• v.56 no.1
• /
• pp.137-146
• /
• 2016

In this paper we study the oscillation criteria for the second order nonlinear differential equation with delay and advanced arguments of the form $$([x(t)+a(t)x(t-{\sigma}_1)+b(t)x(t+{\sigma}_2)]^{\alpha})^{{\prime}{\prime}}+q(t)x^{\beta}(t-{\tau}_1)+q(t)x^{\gamma}(t+{\tau}_2)=0,\;t{\geq}t_0$$ where ${\sigma}_1$, ${\sigma}_2$, ${\tau}_1$ and ${\tau}_2$ are nonnegative constants and ${\alpha}$, ${\beta}$ and ${\gamma}$ are the ratios of odd positive integers. Examples are provided to illustrate the main results.

• Journal of the Korean Mathematical Society
• /
• v.42 no.1
• /
• pp.111-127
• /
• 2005

Let B and S be the unit ball and the unit sphere in $\mathbb{C}^n$, respectively. Let ${\sigma}$ be the normalized Lebesgue measure on S. Define the Privalov spaces $N^P(B)\;(1\;<\;p\;<\;{\infty})$ by $$N^P(B)\;=\;\{\;f\;{\in}\;H(B) : \sup_{0 where H(B) is the space of all holomorphic functions in B. Let ${\varphi}$ be a holomorphic self-map of B. Let ${\mu}$ denote the pull-back measure ${\sigma}o({\varphi}^{\ast})^{-1}$. In this paper, we prove that the composition operator $C_{\varphi}$ is metrically bounded on $N^P$(B) if and only if ${\mu}(S(\zeta,\delta)){\le}C{\delta}^n$ for some constant C and $C_{\varphi}$ is metrically compact on $N^P(B)$ if and only if ${\mu}(S(\zeta,\delta))=o({\delta}^n)$ as ${\delta}\;{\downarrow}\;0$ uniformly in ${\zeta}\;\in\;S. Our results are an analogous results for Mac Cluer's Carleson-measure criterion for the boundedness or compactness of $C_{\varphi}$ on the Hardy spaces $H^P(B)$.

• Journal of Radiation Protection and Research
• /
• v.44 no.2
• /
• pp.64-71
• /
• 2019

Background: It is very difficult to distinguish between a radioactive contamination source and background radiation from natural radionuclides in the marine environment by means of online monitoring system. The objective of this study was to investigate a statistical process for triggering abnormal level of count rate data measured from our on-line seawater radioactivity monitoring. Materials and Methods: Count rate data sets in time series were collected from 9 monitoring posts. All of the count rate data were measured every 15 minutes from the region of interest (ROI) for $^{137}Cs$ ($E_{\gamma}=661.6keV$) on the gamma-ray energy spectrum. The Shewhart ($3{\sigma}$), CUSUM, and Bayesian S-R control chart methods were evaluated and the comparative analysis of determination methods for count rate data was carried out in terms of the false positive incidence rate. All statistical algorithms were developed using R Programming by the authors. Results and Discussion: The $3{\sigma}$, CUSUM, and S-R analyses resulted in the average false positive incidence rate of $0.164{\pm}0.047%$, $0.064{\pm}0.0367%$, and $0.030{\pm}0.018%$, respectively. The S-R method has a lower value than that of the $3{\sigma}$ and CUSUM method, because the Bayesian S-R method use the information to evaluate a posterior distribution, even though the CUSUM control chart accumulate information from recent data points. As the result of comparison between net count rate and gross count rate measured in time series all the year at a monitoring post using the $3{\sigma}$ control charts, the two methods resulted in the false positive incidence rate of 0.142% and 0.219%, respectively. Conclusion: Bayesian S-R and CUSUM control charts are better suited for on-line seawater radioactivity monitoring with an count rate data in time series than $3{\sigma}$ control chart. However, it requires a continuous increasing trend to differentiate between a false positive and actual radioactive contamination. For the determination of count rate, the net count method is better than the gross count method because of relatively a small variation in the data points.

• Journal of the Korean Geotechnical Society
• /
• v.23 no.7
• /
• pp.87-98
• /
• 2007

A series of dilatometer test, field vane test, and $CK_0U$ triaxial test were performed for clayey soils of Busan new port site to develop the relationships between undrained shear strength and the DMT results. Normalized undrained shear strength is turned out to be $S_{u(CKU)}/{\sigma}'_v=0.30{\sim}0.35\;for\;CK_0U$ triaxial test and ${\mu}S_{u(VST)}/{\sigma}'_v=0.20{\sim}0.22$ for vane shear test. By comparing the undrained shear strength estimated from DMT indices with the results measured by in-situ vane test or $CK_0U$ triaxial test, two methods to predict the undrained shear strength from DMT results are suggested. One is based on the relationship between $S_u/{\sigma}'_v$ and horizontal stress index (KD) while another method comes from $N_c-I_D$ and $N_c-E_D$ correlation. It was observed that the method based on $N_c-I_D\;or\;N_c-E_D$ relation shows slightly better accuracy than the one based on $K_D$ although all of the methods suggested in this study provided comparable values of predicted undrained shear strength. Since the definitions of $I_D\;and\;E_D$ contain $p_1-p_0$, in which soil condition is reflected, it is believed that the prediction method using $N_c$ is capable of taking a material type into consideration.

• Journal of Astronomy and Space Sciences
• /
• v.12 no.1
• /
• pp.133-142
• /
• 1995

We studied the nonlinear estimation problem of extended Kalman filter and appled this method to LEO satellite system. Through this method the performance of extended Kalman filter was analyzed. There were certain presumption taken; J2 and atmospheric drag were simply considered in the dynamic model of LEO satellite and the system noise error of $\sigma_r$=150m, $\sigma_r$=10m/s was presumed in the observation data. As results of this simulation, the overall state estimation errors of extended Kalman filter were within the presumed error range and also the ability of performance was maximized when the condition was the state process noise Q has the 1/10 level of covariance matrix Po.

• Journal of the Korean Mathematical Society
• /
• v.49 no.3
• /
• pp.585-604
• /
• 2012

In this paper we consider the evolution of the rolling stone with a rotationally symmetric nonconvex compact initial surface ${\Sigma}_0$ under the Gauss curvature flow. Let $X:S^n{\times}[0,\;{\infty}){\rightarrow}\mathbb{R}^{n+1}$ be the embeddings of the sphere in $\mathbb{R}^{n+1}$ such that $\Sigma(t)=X(S^n,t)$ is the surface at time t and ${\Sigma}(0)={\Sigma}_0$. As a consequence the parabolic equation describing the motion of the hypersurface becomes degenerate on the interface separating the nonconvex part from the strictly convex side, since one of the curvature will be zero on the interface. By expressing the strictly convex part of the surface near the interface as a graph of a function $z=f(r,t)$ and the non-convex part of the surface near the interface as a graph of a function $z={\varphi}(r)$, we show that if at time $t=0$, $g=\frac{1}{n}f^{n-1}_{r}$ vanishes linearly at the interface, the $g(r,t)$ will become smooth up to the interface for long time before focusing.

• Journal of the Korean Chemical Society
• /
• v.26 no.4
• /
• pp.211-217
• /
• 1982

Assuming krypton molecules adsorbed on the graphite surface as a two-dimensional (2D) gas, 4th virial coefficient of the virial equation is calculated by the use of cluster integrals. The Henry's law constant, and 2nd and 3rd virial coefficients are also calculated. Adsorption isotherms calculated from this virial equation agree very satisfactorily with experimental results. The interaction energy of Kr-graphite surface is calculated assuming the pairwise additivity of Lennard-Jones(12,6) potential, and parametars therein are taken as; ${\varepsilon}_{gs}$/k = 71.1 K, ${\varepsilon}_{gg}$/k = 170 K, ${\sigma}_{gs}$ = 354 pm, and ${\sigma}_{gg}$ = 368 pm.

• Journal of Microbiology and Biotechnology
• /
• v.16 no.9
• /
• pp.1477-1480
• /
• 2006

The 63-amino-acid-encoding afsR2 is a global antibiotics-stimulating regulatory gene identified from the chromosome of Streptomyces lividans. To dissect a putative functional domain in afsR2, several afsR2-derivative deletion constructs were generated and screened for the loss of actinorhodin-stimulating capability. The afsR2-derivative construct missing a 50-bp C-terminal region significantly lost its actinorhodin-stimulating capability in S. lividans. In addition, site-directed mutagenesis on amino acid positions of #57-#61 in a 50-bp C-terminal region, some of which are conserved among known Sigma 70 family proteins, significantly changed the AfsR2's activity. These results imply that the C-terminal region of AfsR2 is functionally important for antibiotics-stimulating capability and the regulatory mechanism might be somehow related to the sigma-like domain present in the C-terminal of AfsR2.

• Bulletin of the Society of Naval Architects of Korea
• /
• v.12 no.2
• /
• pp.43-58
• /
• 1975

There are many reports on fatigue crack of metallic materials but most of them relate crack propagation rate to stress intensity factor. The problem of crack propagation is not yet clarified, especially the bridge between micro and macro phenomena In this experiment rotating bending fatigue tests have been carried out with smoothed specimen of rolled steel plates including 0.2% carbon under application of three stress conditions to investigate the slip band and the crack propagation behaviour. The results obtained are as follows; 1) The length of cracks which have grown at initial crack tips can be expressed as follows; $l=Ae^{BNr}$(A,B: constant, $N_r$: cycle ratio) $\frac{dl}{dN}=\frac{AB}{N_f}{\cdot}e^{BNr}$($N_f$:fatigue life) 2) The ratio of slipped grain number to total grain number is $S_f=7{\sigma}-5.6$-5.6{\sigma}_c$($\sigma$: stress amplitude) (${\sigma}_c$: fatigue limit) 3) When the fatigue process transfers from Stage I to Stage II, the crack which propagates into specimen changes its direction from that of the maximum shear stress to the direction of perpendicular to principal stress and this is same in the circumferential direction of specimen. the crack propagation behaviors of both sides of a crack are different each other when they approach to the grain boundary.

• Journal of Korean Society of Industrial and Systems Engineering
• /
• v.10 no.16
• /
• pp.143-147
• /
• 1987

Safety stocks constitute one of the major means of dealing with the uncertainties associated with variation in demand and lead time. Adeguate safety facilitate production activities and help to assure customers if good service on the other hand, carrying safety storks ties up working capital on goods that sit idle. The major problem of safety stocks management thus of consists of trying to achieve an optimal balance between the other carrying cost and the costs of stock shortage. Therefore, this study aims to find safety stock level of the fixed reorder quantity system and the fixed reorder cycle system of minimizing total cost when both demand and lead time are variable. (The distribution of demand and lead time is a mere assumption that follows the normal distribution) The results can be summarized as follows. i) Safety factor on the safety stock is determined by carrying cost and the costs of stock shortage: An optimal safety stick=the costs of stork shortage($C_s$) (the carrying cost($C_h$)+the costs of stock storage($C_s$). ii) The safety stock level of the fixed reorder quantity system is ($a{\;}_p\sqrt{L}{\sigma}$) under uncertainties. iii) The safety stock level of the fixed reorder cycle system is ($a{\;}_p\sqrt{R+L{\sigma}}$) under uncertain demand and constant lead time. ($a{\;}_p\sqrt{L{\sigma}_d{\;^2+{\mu}^2L{\sigma}^2}$) under demand and lead time uncertainties.