• Proceedings of the Korean Society of Precision Engineering Conference
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• 1997.10a
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• pp.706-709
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• 1997

Extruders are the heart of the polymer processing industry. The single most important mechanical element of a screw extruder is the screw. The proper design of the geometriy of the extruder screw is of crucial importance to the proper functioning of the extruder. If material transport instabilities occur as a result of improper screw geometry, even the most sophisticated computerized control system cannot solve the problem. For this purpose, characteristics design on helix angle of the extruder screw. This paper presents strength of the screw flight, optimum helix angle versus dimensionless down channel pressure gradient, optimum helix angle versus the power law index in simultaneous optimization, volumetric efficiency versus helix angle at various number of flights and power consumption versus helix angle in the barrel of screw extruder.

• Honam Mathematical Journal
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• v.34 no.2
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• pp.209-217
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• 2012

Convergence rates in the law of large numbers for i.i.d. random variables have been generalized by Gut[Gut, A., 1978. Marc inkiewicz laws and convergence rates in the law of large numbers for random variables with multidimensional indices, Ann. Probab. 6, 469-482] to random fields with all indices having the same power in the normalization. In this paper we generalize these convergence rates to the identically distributed and negatively associated random fields with different indices having different power in the normalization.

• Journal of The Korean Astronomical Society
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• v.24 no.1
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• pp.107-116
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• 1991

With a modern microdensitometer and POSS glass copies, we have performed an automated star counting in two colors, blue and red, over the region containing Bok globule B361. Distribution of the measured extinction values over the projected angular distance from the cloud center was approximated by a power-law, and the resulting power-law indices for the blue and red are shown to be distinctly different from each other. The difference in the power-law index indicates that the mean dust size increases towards the cloud center. Possible physical causes for such size variation are briefly discussed.

• The Bulletin of The Korean Astronomical Society
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• v.36 no.2
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• pp.54.2-54.2
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• 2011

We present a study of HII regions in M51 using HST/ACS images taken as part of the Hubble Heritage Program. We found about 19,600 HII regions in M51 with $H_{\alpha}$ luminosity in the range of $L=10^{35.5}-10^{39.0}\;erg\;s^{-1}$. The $H_{\alpha}$ luminosity function of HII regions (HII LF) in M51 is well represented by a double power law with its index ${\alpha}=-2.25{\pm}0.02$ for the bright part and ${\alpha}=-1.42{\pm}0.01$ for the faint part, separated at a break point $L=10^{37.1}\;erg\;s^{-1}$. Comparison with simulated HII LFs suggests that this break is caused by the transition of HII region ionizing sources, from low-mass clusters (including several OB stars) to more massive clusters (including several tens of OB stars). The HII LFs with L < $10^{37.1}\;erg\;s^{-1}$ are found to have different slopes for different parts in M51: the HII LF for the interarm region is steeper than those for the arm and the nuclear regions. This observed difference in HII LFs can be explained by evolutionary effects: HII regions in the interarm region are relatively older than those in the other parts of M51. The size distribution of the HII regions is fitted by a double power law with a break at D = 30 pc. The power law index for the small HII regions with 15 pc < D < 30 pc is ${\alpha}=-1.78{\pm}0.04$, whereas ${\alpha}=-5.04{\pm}0.08$ for the large HII region with 30 pc < D < 110 pc. The power law indices of the size distribution are related with those of HII LF, and the relation between the luminosities and sizes of HII regions is fitted well by $L{\propto}D^{3.04{\pm}}$.

• Journal of The Korean Astronomical Society
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• v.29 no.spc1
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• pp.99-102
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• 1996

I discuss implications of gamma-ray emission from blazars based on electron acceleration by shock waves in a relativistic jet. The number spectrum of electrons turns out to be a broken power law; while at low energies the power law index has a universal value of 2, at high energies it steepens to an index of 3 because of strong radiative cooling. This spectrum can basically reproduce the observed spectral break between X-rays and gamma-rays. I show that energetics of relativistic jets can be well explained by this model. I estimate physical quantities of the relativistic jets by comparing the prediction with observations. The results show that the jets are particle dominated and are comprised of electron-positron pairs. A connection between gamma-ray emission and radiation drag is also discussed.

• Journal of Korean Society of Water and Wastewater
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• v.20 no.2
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• pp.295-302
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• 2006

Over the past decades, a flocculation and/or sedimentation process have been adopted to remove pollutants from CSOs. It has been learned that major factors affecting settlement of pollutants are the particle size distribution, their settling velocities and their specific gravity. It is, therefore, a good idea to analyze the particle size distribution and settleability of CSOs pollutants in order to develop details in designing a process. Discussed in this study are pollutant characteristics of CSOs such as particle size distribution and settleability of pollutants. The power law function is applied and is found to be an effective and reliable index for expressing the particle size distribution of pollutants in CSOs. Based on the regression analysis it is observed that the derived constants of curves representing settling velocity profile are proportional to the initial concentration of particles and to the ${\beta}$-values of power law distributions.

• The Bulletin of The Korean Astronomical Society
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• v.44 no.1
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• pp.50.2-50.2
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• 2019

Understanding three-dimensional structure and parameters (e.g., radial velocity, angular width, source location and density) of coronal mass ejections (CMEs) is essential for space weather forecast. In this study, we determine CME mean density in solar corona and near the Earth. We select 38 halo CMEs, which have the corresponding interplanetary CMEs (ICMEs), by SOHO/LASCO from 2000 to 2014. To estimate a CME volume, we assume that a CME structure is a full ice-cream cone which is a symmetrical circular cone combined with a hemisphere. We derive CME mean density as a function of radial height, which are approximately fitted to power-law functions. The average of power-law indexes is about 2.1 in the LASCO C3 field of view. We also obtain power-law functions for both CME mean density at 21 solar radii and ICME mean density at 1AU, with the average power-law index of 2.6. We estimate a ratio of CME density to background density based on the Leblanc et al.(1998) at 21 solar radii. Interestingly, the average of the ratios is 4.0, which is the same as a default value used in the WSA-ENLIL model.

• Steel and Composite Structures
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• v.45 no.4
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• pp.547-554
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• 2022

This paper studies the static stability of an axially graded column with the power-law gradient varying along the axial direction. For a nonhomogeneous column with one end linked to a rotational spring and loaded by a compressive force, respectively, an Euler problem is analyzed by solving a boundary value problem of an ordinary differential equation with varying coefficients. Buckling loads through the characteristic equation with the aid of the Bessel functions are exactly given. An alternative way to approximately determine buckling loads through the integral equation method is also presented. By comparing approximate buckling loads with the exact ones, the approximate solution is simple in form and enough accurate for varying power-law gradients. The influences of the gradient index and the rotational spring stiffness on the critical forces are elucidated. The critical force and mode shapes at buckling are presented in graph. The critical force given here may be used as a benchmark to check the accuracy and effectiveness of numerical solutions. The approximate solution provides a feasible approach to calculating the buckling loads and to assessing the loss of stability of columns in engineering.

• Korean journal of applied entomology
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• v.40 no.2
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• pp.105-109
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• 2001

Dispersion pattern of the citrus red mite (CRM), Panonychus citri (McGregor) was determined to develop a monitoring method in the satsuma mandarin fields, Citrus unshiu L., in Jeju-do, during 1999 and 2000. CRM population was sampled by collecting leaves. Taylor's power law provided better description of mean-variance relationship for the dispersion indices compared to Iwao's patchiness regression. Slopes and intercepts of Taylor's power law from leaf samples did not differ among surveyed groves. Fixed-precision levels (D) of a sequential sampling plan were developed using Taylor's power law parameters generated from all motile stages of CRM in leaf sample. This sampling plan for leaf sample estimate was tested with resampling validation for sampling plan using 4 independent data sets. Resampling simulation analysis demonstrated that actual fixed-precision level values were better than desired D values of 0.20, 0.25 and 0.30. Required numbers for tree sampling at the density of more than 7 mites per tree were fewer than 18.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.14 no.11
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• pp.5930-5938
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• 2013

The sigmoid functionally graded mateiral(S-FGM) theory is reformulated using the nonlocal elatictiry of Erigen. The equation of equilibrium of the nonlocal elasticity are derived. This theory has ability to capture the both small scale effects and sigmoid function in terms of the volume fraction of the constituents for material properties through the plate thickness. Navier's method has been used to solve the governing equations for all edges simply supported boundary conditions. Numerical solutions of biaxial buckling of nano-scale plates are presented using this theory to illustrate the effects of nonlocal theory and power law index of sigmoid function on buckling load. The relations between nonlocal and local theories are discussed by numerical results. Further, effects of (i) power law index, (ii) length, (iii) nonlocal parameter, (iv) aspect ratio and (v) mode number on nondimensional biaxial buckling load are studied. To validate the present solutions, the reference solutions are discussed.