• Journal of the Korean Vacuum Society
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• v.8 no.2
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• pp.102-110
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• 1999

The LIGA X-ray exposure step was modelled into three inequalities, by assuming that the X-ray energy attenuated within a resist is deposited only in the localized range of the resist. From these inequalities, equations for the minimum and maximum exposure times required for a good quality microstructure were obtained. Also, an equation for the thickness of an X-ray mask absorber was obtained from the exposure requirement of threshold dose deposition. The calculation method of the synchrotron radiation power from a synchrotron radiation source was introduced and applied to an X-ray exposure step. A power from a synchrotron radiation source was introduced and applied to an X-ray exposure step/ A power function of photon energy, approximating the attenuation length of the representative LIGA resist, PMMA, and the mean photon energy of the XZ-rays incident upon an X-ray mask absorber were applied to the above mentioned equations. Consequently, the tendencies of the minimum and maximum exposure and with respect to mean photon energy and thick ness of PMMA was obtained. Additionally, the tendencies of the necessary thickness of PMMA and photon energy of the X-ray mask absorber with respect to thickness of PMMA and photon energy of the X-rays incident upon an X-ray mask absorber were examined. The minimum exposure time increases monotonically with increasing mean photon energy for the same total power density and is not a function of the thickness of resist. The minimum exposure time increases with increasing mean photon energy for the same total power density in the case of the general LIGA process, where the thickness of PMMA is thinner than the attenuation length of PMMA. Additionally, the minimum exposure time increases monotonically with increasing thickness of PMMA. The maximally exposable thickness of resist is proportional to the attenuation length of the resist at the mean photon energy with its proportional constant of ln $(Dd_m/D_{dv})$. The necessary thickness of a gold X-ray mask absorber due to absorption edges of gold, increases smoothly with increasing PMMA thickness ratio, and is independent of the total power density itself. The simplicity of the derived equations has made clearly understandable the X-ray exposure phenomenon and the correlation among the exposure times, the attenuation coefficient and the thickness of an X-ray mask absorber, the attenuation coefficient and the thickness of the resist, and the synchrotron radiation power density.

• Ocean Systems Engineering
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• v.3 no.1
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• pp.71-77
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• 2013

The effective tracking area of ultra short baseline (USBL) systems strongly relates to the safety of autonomous underwater vehicles (AUVs). This problem has not been studied previously. A method for determining the effective tracking area using acoustic theory is proposed. Ray acoustic equations are used to draw rays which ascertain the effective space. The sonar equation is established in order to discover the available range of the USBL system and the background noise level using sonar characteristics. The available range defines a hemisphere like enclosure. The overlap of the effective space with the hemisphere is the effective area for USBL systems tracking AUVs. Lake and sea trials show the proposed method's validity.

• Journal of Energy Engineering
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• v.16 no.1 s.49
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• pp.46-52
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• 2007

The piecewise constant angular approximation is developed to replace the conventional angular quadrature sets in the solution of the second-order, multi-dimensional $S_{N}$ neutron transport equations. The newly generated quadrature sets by this method substantially mitigate ray effects and can be used in the same manner as the conventional quadrature sets are used. The discrete-ordinates and the piecewise-constant approximations are applied to both the first-order Boltzmann and the second-order form of neutron transport equations in treating angular variables. The result is that the mitigation of ray effects is only achieved by the piecewise-constant method, in which new angular quadratures are generated by integrating angle variables over the specified region. In other sense, the newly generated angular quadratures turn out to decrease the contribution of mixed-derivative terms in the even-parity equation that is one of the second-order neutron transport equation. This result can be interpreted as the entire elimination or substantial mitigation of ray effect are possible in the simplified even-parity equation which has no mixed-derivative terms.

• East Asian mathematical journal
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• v.30 no.3
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• pp.327-334
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• 2014

In this paper, we construct extrapolated expanded mixed finite element approximations to approximate the scalar unknown, its gradient and its flux of semilinear Sobolev equations. To avoid the difficulty of solving the system of nonlinear equations, we use an extrapolated technique in our construction of the approximations. Some numerical examples are used to show the efficiency of our schemes.

• Journal of the Korean Mathematical Society
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• v.29 no.2
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• pp.225-238
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• 1992

• Nutrition Research and Practice
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• v.15 no.1
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• pp.95-105
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• 2021

BACKGROUND/OBJECTIVES: The measurement of body composition, including muscle and fat mass, remains challenging in large epidemiological studies due to time constraint and cost when using accurate modalities. Therefore, this study aimed to develop and validate prediction equations according to sex to measure lean body mass (LBM), appendicular skeletal muscle mass (ASM), and body fat mass (BFM) using anthropometric measurement, serum creatinine level, and lifestyle factors as independent variables and dual-energy X-ray absorptiometry as the reference method. SUBJECTS/METHODS: A sample of the Korean general adult population (men: 7,599; women: 10,009) from the Korean National Health and Nutrition Examination Survey 2008-2011 was included in this study. The participants were divided into the derivation and validation groups via a random number generator (with a ratio of 70:30). The prediction equations were developed using a series of multivariable linear regressions and validated using the Bland-Altman plot and intraclass correlation coefficient (ICC). RESULTS: The initial and practical equations that included age, height, weight, and waist circumference had a different predictive ability for LBM (men: R2 = 0.85, standard error of estimate [SEE] = 2.7 kg; women: R2 = 0.78, SEE = 2.2 kg), ASM (men: R2 = 0.81, SEE = 1.6 kg; women: R2 = 0.71, SEE = 1.2 kg), and BFM (men: R2 = 0.74, SEE = 2.7 kg; women: R2 = 0.83, SEE = 2.2 kg) according to sex. Compared with the first prediction equation, the addition of other factors, including serum creatinine level, physical activity, smoking status, and alcohol use, resulted in an R2 that is higher by 0.01 and SEE that is lower by 0.1. CONCLUSIONS: All equations had low bias, moderate agreement based on the Bland-Altman plot, and high ICC, and this result showed that these equations can be further applied to other epidemiologic studies.

• Journal of the Mineralogical Society of Korea
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• v.12 no.2
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• pp.96-100
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• 1999

Effects of surface conditions (temperature and roughness) of test specimens, when measuring emissive power of far-infrared ray, have been investigated using FT-IR spectrometer. Element metal zinc (Zn) was selected in this study as representative specimen of materials consisting of simple element. The zinc specimens were heated to four temperatures, i.e., 333K, 353K, .373K, and also their surface was finished with SiC abrasive papers of 100, 220, 360, 400, 600, 800, and 1000 mesh in size. The results shows that the emissive power (W/㎡) of the far-infrared ray increases with temperature for a given roughness and its relationship may be expressed by the following equations: Yη=1.0=0.142$.$T-0.937 for η=1.0, and Yη=10=0.016$.$T-1.286 for η=10. The emissive power is also known to increase with surface roughness for a given temperature. Their relationship can be represented by the following equations: YT=313K=0.234$.$$\ell$n(η)+3.53, at 313K, YT=353K=0.234$.$$\ell$n(η)+4.02 at 353K and YT=393K=0.243$.$$\ell$n(η)+4.62 at 393K.

• Journal of the Optical Society of Korea
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• v.20 no.5
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• pp.614-622
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• 2016

In this paper, we propose a novel differential equation method for designing a total internal reflection (TIR) LED lens with double freeform surfaces. A complete set of simultaneous differential equations for the method is derived from the condition for minimizing the Fresnel loss, illumination models, Snell’s Law of ray propagation, and a new constraint on the incident angle of a ray on the light-exiting surface of the lens. The last constraint is essential to complete the set of simultaneous differential equations. By adopting the TIR structure and applying the condition for minimizing the Fresnel loss, it is expected that the proposed TIR LED lens can have a high luminous flux efficiency, even though its beam-spread angle is narrow. To validate the proposed method, three TIR LED lenses with beam-spread angles of less than 22.6° have been designed, and their performances evaluated by ray tracing. Their luminous flux efficiencies could be obviously increased by at least 35% and 5%, compared to conventional LED lenses with a single freeform surface and with double freeform surfaces, respectively.

• East Asian mathematical journal
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• v.34 no.5
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• pp.601-614
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• 2018

In this paper, we introduce an extrapolated higher order characteristic finite element method to approximate solutions of nonlinear Sobolev equations with a convection term and we establish the higher order of convergence in the temporal and the spatial directions with respect to $L^2$ norm.

• Bulletin of the Korean Mathematical Society
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• v.48 no.5
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• pp.897-915
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• 2011

In this paper, we develop a symmetric Galerkin method with interior penalty terms to construct fully discrete approximations of the solution for nonlinear Sobolev equations. To analyze the convergence of discontinuous Galerkin approximations, we introduce an appropriate projection and derive the optimal $L^2$ error estimates.