• Journal of the Optical Society of Korea
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• v.20 no.4
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• pp.524-529
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• 2016

Diagnostic sensors are demanded during plasma processes. Holograms of plasma taken with laser light without a reference beam were used to monitor behaviors of charged particles produced in nitrogen plasma as a function of electrode temperature ranging between 50 and 300℃. Holograms were characterized as a function of the pixel sum and grayscale value. Pixel sum calculated in identified grayscale ranges strongly correlated with ion density and emitted light intensity measured with a langmuir probe and optical emission spectroscopy, respectively. The performance was further evaluated with data acquired as a function of N₂ and NH₃ flow rates and improved correlations were observed in the new grayscale range. The confirmed correlations indicate that a hologram is a viable means to diagnose behaviors of plasma particles such as ions. Underlying principles are discussed in view of particle and charge composing vacuum and light.

• Journal of the Korean Mathematical Society
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• v.57 no.2
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• pp.471-487
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• 2020

We find congruences modulo 32, 64 and 128 for the partition function ${\overline{PP}_o}(n)$, the number of overpartition pairs of n into odd parts, with the aid of Ramamnujan's theta function identities and some known identities of t_k(n), for k = 6, 7, where t_k(n) denotes the number of representations of n as a sum of k triangular numbers. We also find two Ramanujan-like congruences for ${\overline{PP}_o}(n)$ modulo 128.

• Communications of the Korean Mathematical Society
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• v.30 no.4
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• pp.439-446
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• 2015

The main objective of this paper is to establish certain explicit expressions for the Humbert functions ${\Phi}_2$(a, a + i ; c ; x, -x) and ${\Psi}_2$(a ; c, c + i ; x, -x) for i = 0, ${\pm}1$, ${\pm}2$, ..., ${\pm}5$. Several new and known summation formulas for ${\Phi}_2$ and ${\Psi}_2$ are considered as special cases of our main identities.

• Proceedings of the Korean Institute of Building Construction Conference
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• 2019.11a
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• pp.170-171
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• 2019

When the cement paste in concrete is exposed to high temperatures, the mechanical performance decreases due to a series of reactions inside the cement. In this study, we investigated the change of nanostructure of $C_3S$ when $C_3S$ was exposed to high temperature using pair distribution function (PDF) based on high energy X-ray scattering. As a result of X-ray diffraction, there was no significant difference when $C_3S$ was heated at $300^{\circ}C$, but most of $Ca(OH)_2$ was decomposed into CaO at $500^{\circ}C$. In addition, it was confirmed that CaO is dominant in the nanostructure when $C_3S$ is heated to $500^{\circ}C$.

• The Bulletin of The Korean Astronomical Society
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• v.43 no.2
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• pp.51.2-51.2
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• 2018

Star clusters are important in understanding star formation. In star-forming regions, the number of stars with mass forms with an initial mass function (IMF), i.e. Chabrier, Salpeter, Kroupa, etc. In our simulations, initially sub-virial fractal star clusters evolve to become surviving sub-regions in strong tidal fields. We investigate the slope of the mass function (MF) of these sub-regions with time near the Galactic centre (GC). These sub-regions would appear to have a top-heavy IMF at ~ 2 Myr. Therefore, although our star-forming region near the GC has a normal IMF, stars in surviving 'clusters' can have a top-heavy 'IMF' due to the violent environment.

• Honam Mathematical Journal
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• v.45 no.3
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• pp.542-554
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• 2023

Given a real number α, the Lagrange number of α is the supremum of all real numbers L > 0 for which the inequality |α - p/q| < (Lq²)^-1 holds for infinitely many rational numbers p/q. All Lagrange numbers less than 3 can be arranged as a set {l_p/q : p/q ∈ ℚ ∩ [0, 1]} using the Farey index. The present paper considers a function C(α) devised from Sturmian words. We demonstrate that the function C(α) contains all information on Lagrange numbers less than 3. More precisely, we prove that for any real number α ∈ (0, 1], the value C(α) - C(0) is equal to the sum of all numbers 3 - l_p/q where the Farey index p/q is less than α.

• Communications for Statistical Applications and Methods
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• v.30 no.3
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• pp.245-258
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• 2023

This study proposes a modification to the objective function of the support vector machine for the linearly non-separable case of a binary classifier y_i ∈ {-1, 1}. The modification takes into account the position of each data item x_i from its corresponding class centroid. The resulting optimization function involves the centroid mean vector, and the spread of data besides the support vectors, which should be minimized by the choice of hyper-plane β. Theoretical assumptions have been tested to derive an optimal separable hyperplane that yields the minimal misclassification rate. The proposed method has been evaluated using simulation studies and real-life COVID-19 patient outcome hospitalization data. Results show that the proposed method performs better than the classical linear SVM classifier as the sample size increases and is preferred in the presence of correlations among predictors as well as among extreme values.

• Communications of the Korean Mathematical Society
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• v.27 no.2
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• pp.257-264
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• 2012

Exton introduced 20 distinct triple hypergeometric functions whose names are $X_i$ (i = 1, ${\ldots}$, 20) to investigate their twenty Laplace integral representations whose kernels include the confluent hypergeometric functions $_0F_1$, $_1F_1$, a Humbert function ${\Psi}_1$, and a Humbert function ${\Phi}_2$. The object of this paper is to present 18 new integral representations of Euler type for the Exton hypergeometric function $X_8$, whose kernels include the Exton functions ($X_2$, $X_8$) itself, the Horn's function $H_4$, the Gauss hypergeometric function $F$, and Lauricella hypergeometric function $F_C$. We also provide a system of partial differential equations satisfied by $X_8$.

• Communications of the Korean Mathematical Society
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• v.36 no.4
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• pp.743-757
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• 2021

We consider a different version of Schwarz Lemma for λ-spirallike function of complex order at the boundary of the unit disc D. We estimate the modulus of the angular derivative of the function $\frac{zf^{\prime}(z)}{f(z)}$ from below for λ-spirallike function f(z) of complex order at the boundary of the unit disc D by taking into account the zeros of the function f(z)-z which are different from zero. We also estimate the same function with the second derivatives of the function f at the points z = 0 and z = z₀ ≠ 0. We show the sharpness of these estimates and present examples.

• Journal of Ocean Engineering and Technology
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• v.15 no.4
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• pp.92-100
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• 2001

It is very important to determine the coefficient of earth pressure at rest accurately in order to estimate the behavior of soil structure. For estimation of K/sub 0/-value depending upon the stress history of dry sand, a new type of K/sub 0/-oedeometer apparatus is devised, and the horizontal earth pressure is accurately measured. For this study, 2 types of one-cyclic K/sub 0/-Loading/unloading models have been studied experimentally using four relative densities of the sand. The results obtained in this test are as follows : K/sub on'/ the coefficient of earth pressure at - rest for virgin loading is a function of the angle of internal friction Φ' of the sand and is determined as K/sub on/=1 - 0.914 sin Φ', K/sub ou'/ the coefficient of earth pressure at rest for virgin unloading is a function of K/sub on/ and over consolidation ratio(OCR), and is determined as K/sub ou/=K/sub on/(OCR)K/sup a/. The exponent α, increases as the relative density increases. K/sub or'/ the coefficient of earth pressure at rest for virgin reloading decreases in hyperbola type as the vertical stress, σ/sub v/’, increases. And, the stress path at virgin reloading leads to the maximum prestress point, independent upon the value of the minimum unloading stress. The gradient of this curve, m/sub r/ increases as OCR increases.