• The Journal of The Korea Institute of Intelligent Transport Systems
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• v.15 no.5
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• pp.108-115
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• 2016

In this paper, the array synthesis horn antenna was designed and measured a radiation power after connecting magnetron. The proposed antenna was designed on the basis of the $4{\times}4$ array synthesis horn antenna characteristics. For suppressing a back-lobe, 2 step short-stub structures were attached to synthesis horn aperture upper and lower. The designed antenna has FBR(Front to Back Ratio) of 39.7 dB. HPBW(Half Power Beam Width) of the E-plane and the H-plane are $8.86^{\circ}$ and $7.35^{\circ}$ each in the measurement. For measuring a radiation power of array antenna that use a magnetron, the waveguide adaptor was designed and connected magnetron with horn antenna. Also, microstrip line coupler that replace a dielectric material with an air gap was designed for measuring a high power. As a result, average radiation output power of the $4{\times}4$ array synthesis horn antenna that connect a four magnetrons had a 0.063W.

• Journal of the Korean Mathematical Society
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• v.44 no.1
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• pp.55-107
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• 2007

Let k be an imaginary quadratic field, h the complex upper half plane, and let $\tau{\in}h{\cap}k,\;q=e^{{\pi}i\tau}$. In this article, we obtain algebraic numbers from the 130 identities of Rogers-Ramanujan continued fractions investigated in [28] and [29] by using Berndt's idea ([3]). Using this, we get special transcendental numbers. For example, $\frac{q^{1/8}}{1}+\frac{-q}{1+q}+\frac{-q^2}{1+q^2}+\cdots$ ([1]) is transcendental.

• Bulletin of the Korean Mathematical Society
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• v.53 no.1
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• pp.21-28
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• 2016

It is known that no two of the roots of the polynomial equation (1) $$\prod\limits_{l=1}^{n}(x-r_l)+\prod\limits_{l=1}^{n}(x+r_l)=0$$, where 0 < $r_1{\leq}r_2{\leq}{\cdots}{\leq}r_n$, can be equal and all of its roots lie on the imaginary axis. In this paper we show that for 0 < h < $r_k$, the roots of $$(x-r_k+h)\prod\limits_{{l=1}\\{l{\neq}k}}^{n}(x-r_l)+(x+r_k-h)\prod\limits_{{l=1}\\{l{\neq}k}}^{n}(x+r_l)=0$$ and the roots of (1) in the upper half-plane lie alternatively on the imaginary axis.

• Journal of the Korean Mathematical Society
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• v.40 no.6
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• pp.977-998
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• 2003

Let k be an imaginary quadratic field, η the complex upper half plane, and let $\tau$ $\in$ η $textsc{k}$, p = $e^{{\pi}i{\tau}}$. In this article, using the infinite product formulas for g2 and g3, we prove that values of certain infinite products are transcendental whenever $\tau$ are imaginary quadratic. And we derive analogous results of Berndt-Chan-Zhang ([4]). Also we find the values of (equation omitted) when we know j($\tau$). And we construct an elliptic curve E : $y^2$ = $x^3$ ＋ 3 $x^2$ ＋ {3-(j/256)}x ＋ 1 with j = j($\tau$) $\neq$ 0 and P = (equation omitted) $\in$ E.

• Journal of computational fluids engineering
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• v.15 no.4
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• pp.53-59
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• 2010

Preliminary design of a ground plate, a device installed close to the aircraft model for wind tunnel test to simulate the ground effect, was performed by a numerical simulation. A two-dimensional numerical study was performed initially to decide the optimal leading edge and flap configurations. Then, three-dimensional studies were conducted to decide the optimal flap deflection angle for pressure distribution reduction since the plate and the plate supporting system generate static pressure difference between the upper and lower flow regions. Three-dimensional simulation additionally studied the effect of the clearance between the plate and the wind tunnel side wall. For the efficiency of computation, half model was simulated and a symmetric boundary condition was applied on the center plane. Based on the preliminary design, a ground plate was designed, manufactured and tested at the Korea Aerospace Research Institute(KARI) wind tunnel. The measured pressure differences versus flap deflection angle agreed well with the predicted results.

• Journal of the Korean Mathematical Society
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• v.45 no.5
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• pp.1379-1391
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• 2008

Let k be an imaginary quadratic field, ${\eta}$ the complex upper half plane, and let ${\tau}{\in}{\eta}{\cap}k,\;q=e^{{\pi}{i}{\tau}}$. For n, t ${\in}{\mathbb{Z}}^+$ with $1{\leq}t{\leq}n-1$, set n=${\delta}{\cdot}2^{\iota}$(${\delta}$=2, 3, 5, 7, 9, 13, 15) with ${\iota}{\geq}0$ integer. Then we show that $q{\frac}{n}{12}-{\frac}{t}{2}+{\frac}{t^2}{2n}{\prod}_{m=1}^{\infty}(1-q^{nm-t})(1-q^{{nm}-(n-t)})$ are algebraic numbers.

• Honam Mathematical Journal
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• v.31 no.4
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• pp.463-478
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• 2009

Let k be an imaginary quadratic field, ℌ the complex upper half plane, and let ${\tau}{\in}k{\cap}$ℌ, q = exp(${\pi}i{\tau}$). And let n, t be positive integers with $1{\leq}t{\leq}n-1$. Then $q^{{\frac{n}{12}}-{\frac{t}{2}}+{\frac{t^2}{2n}}}{\prod}^{\infty}_{m=1}(1-q^{nm-t})(1-q^{nm-(n-t)})$ is an algebraic number [10]. As a generalization of this result, we find several infinite series and products giving algebraic numbers using Ramanujan's $_{1{\psi}1}$ summation. These are also related to Rogers-Ramanujan continued fractions.

• Communications of the Korean Mathematical Society
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• v.16 no.4
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• pp.585-594
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• 2001

Let η be the complex upper half plane, let h($\tau$) be a cusp form, and let $\tau$ be an imaginary quadratic in η. If h($\tau$)$\in$$\Omega$( $g_{2}$($\tau$)$^{m}$ $g_{3}$ ($\tau$)$^{ι}$with $\Omega$the field of algebraic numbers and m. l positive integers, then we show that h($\tau$) is integral over the ring Q[h/$\tau$/n/)…h($\tau$+n-1/n)] (No Abstract.see full/text)

• Journal of the Korean Mathematical Society
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• v.58 no.1
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• pp.109-122
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• 2021

In this paper, we consider the problem of finding the hypersurface Mn in the Euclidean (n + 1)-space ℝn+1 that satisfies an equation of mean curvature type, called singular minimal hypersurface equation. Such an equation physically characterizes the surfaces in the upper half-space ℝ+3 (u) with lowest gravity center, for a fixed unit vector u ∈ ℝ3. We first state that a singular minimal cylinder Mn in ℝn+1 is either a hyperplane or a α-catenary cylinder. It is also shown that this result remains true when Mn is a translation hypersurface and u is a horizantal vector. As a further application, we prove that a singular minimal translation graph in ℝ3 of the form z = f(x) + g(y + cx), c ∈ ℝ - {0}, with respect to a certain horizantal vector u is either a plane or a α-catenary cylinder.

• The korean journal of orthodontics
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• v.47 no.6
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• pp.353-364
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• 2017

Objective: The objective of this study was to investigate the effects of miniscrew-assisted rapid palatal expansion (MARPE) on changes in airflow in the upper airway (UA) of an adult patient with obstructive sleep apnea syndrome (OSAS) using computational fluid-structure interaction analysis. Methods: Three-dimensional UA models fabricated from cone beam computed tomography images obtained before (T0) and after (T1) MARPE in an adult patient with OSAS were used for computational fluid dynamics with fluid-structure interaction analysis. Seven and nine cross-sectional planes (interplane distance of 10 mm) in the nasal cavity (NC) and pharynx, respectively, were set along UA. Changes in the cross-sectional area and changes in airflow velocity and pressure, node displacement, and total resistance at maximum inspiration (MI), rest, and maximum expiration (ME) were investigated at each plane after MARPE. Results: The cross-sectional areas at most planes in NC and the upper half of the pharynx were significantly increased at T1. Moreover, airflow velocity decreased in the anterior NC at MI and ME and in the nasopharynx and oropharynx at MI. The decrease in velocity was greater in NC than in the pharynx. The airflow pressure in the anterior NC and entire pharynx exhibited a decrease at T1. The amount of node displacement in NC and the pharynx was insignificant at both T0 and T1. Absolute values for the total resistance at MI, rest, and ME were lower at T1 than at T0. Conclusions: MARPE improves airflow and decreases resistance in UA; therefore, it may be an effective treatment modality for adult patients with moderate OSAS.