• Ocean Systems Engineering
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• v.2 no.3
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• pp.229-238
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• 2012

We discuss the bi - stability that is possibly exhibited by a liquid free surface in a parametrically - driven two-dimensional (2D) rectangular tank with finite liquid depth. Following the method of adaptive mode ordering, assuming two dominant modes and retaining polynomial nonlinearities up to third-order, a nonlinear finite-dimensional nonlinear modal system approximation is obtained. A "continuation method" of nonlinear dynamics is then used in order to elicit efficiently the instability boundary in parameters' space and to predict how steady surface elevation changes as the frequency and/or the amplitude of excitation are varied. Results are compared against those of the linear version of the system (that is a Mathieu-type model) and furthermore, against an intermediate model also derived with formal mode ordering, that is based on a second - order ordinary differential equation having nonlinearities due to products of elevation with elevation velocity or acceleration. The investigation verifies that, in parameters space, there must be a region, inside the quiescent region, where liquid surface instability is exhibited. There, behaviour depends on initial conditions and a wave form would be realised only if the free surface was substantially disturbed initially.

• Korean Journal of Crystallography
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• v.13 no.1
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• pp.12-16
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• 2002

The complex [Ni(L)](BDC)·4H₂O (1) (L = 3,14-dimethyl-2,6,13,17-tetraazatricyclo[16,4,O/sup 1.18/,O/sup 7.12/] docosane; BDC = 1,3-benzenedicarboxylate) has been synthesized and characterized by X-ray crystallography. Compound 1 crystallizes in the orthorhombic space group Pcnb, with a = 8.764(2) , b = 17.687(2) , c = 19.475(1) , V = 3018.7(8) ³, Z = 4, R₁, (wR₂) for 2148 observed reflections of [1>2σ(I) was 0.0822 (0.2236). Compound 1 is interconnected to give a three-dimensional network through weak hydrogen-bonding interactions.

• International Journal of Aeronautical and Space Sciences
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• v.18 no.4
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• pp.614-622
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• 2017

The characteristics of aerodynamic drag for Transonic Vehicle in Evacuated Tube was investigated using computational fluid dynamics. At first, parametric study on the system was performed according to the Mach number of the vehicle's speed ($Mach_v$), evacuated pressure of the tube ($Pre_t$), and blockage ratio (BR) between the vehicle and tube via axisymmetric flow analysis; the $Mach_v$ ranged from 0.3 to 1.0. The $Pre_t$ was 100, 1,000 and 10,000 Pa and the BR was 0.1, 0.2, and 0.4. In the calculations, the aerodynamic drag of the vehicle was larger when the BR and the pressure became larger. Concerning the $Mach_v$, the drag coefficient ($C_d$) became the maximum when the $Mach_v$ was near the Kantrowitz limit and decreased, which showed the typical transonic flow pattern. Then, three dimensional flow analysis was performed by changing the $Mach_v$ from 0.3 to 1.0 and setting the BR and the $Pre_t$ as 0.34 and 100 Pa, respectively by referring the Hyperloop Alpha documentation. From the calculations, the $C_d$ from three dimensional flow simulations were somewhat larger than those of axisymmetric ones because of the eccentricity of the vehicle inside the tube. However, the pattern of $C_d$ according to the $Mach_v$ was compatible with that of axisymmetric ones.

• Bulletin of the Korean Chemical Society
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• v.26 no.8
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• pp.1260-1264
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• 2005

Three new quaternary tantalum thiophosphates, $K_{0.18}TaPS_6,\;K_{0.28}TaPS_6,\;and\;Rb_{0.09}TaPS_6$ have been synthesized by using reactive alkali metal halide fluxes and structurally characterized by single crystal X-ray diffraction techniques. The crystal structures of $K_{0.18}TaPS_6,\;K_{0.28}TaPS_6,\;and\;Rb_{0.09}TaPS_6$ contain 3-dimensional open framework anions, $[TaPS_6]^{x-}$(x = 0.09, 0.18, 0.28) with the empty channel which disordered alkali metal cations, $K^+\;and\;Rb^+$ are located in. Crystal data: $K_{0.18}TaPS_6$, tetragonal, space group$I4_1$/acd (no. 142), a=15.874(3) $\AA$, c=13.146(4) $\AA$, V=3312.7(12) ${\AA}^3$, K, Z=16, R1=0.0545. Crystal data: $K_{0.28}TaPS_6$, tetragonal, space group $I4_1$/acd (no. 142), a=15.880(2) $\AA$, c=13.134(3) $\AA$, V=3312.1(10) ${\AA}^3$, Z=16, R1=0.0562. Crystal data: $Rb_{0.09}TaPS_6$, tetragonal, space group I41/acd (no. 142), a=15.893(3) $\AA$, c=13.163(4) $\AA$, V=3324.7(15) ${\AA}^3$, Z=16, R1=0.0432.

• Communications of the Korean Mathematical Society
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• v.38 no.3
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• pp.787-805
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• 2023

Let (Ω, µ) be a measure space and {τ_α}_α∈Ω be a normalized continuous Bessel family for a finite dimensional Hilbert space 𝓗 of dimension d. If the diagonal ∆ := {(α, α) : α ∈ Ω} is measurable in the measure space Ω × Ω, then we show that $$\sup\limits_{{\alpha},{\beta}{\in}{\Omega},{\alpha}{\neq}{\beta}}\,{\mid}{\langle}{\tau}_{\alpha},\,{\tau}_{\beta}{\rangle}{\mid}^{2m}\,{\geq}\,{\frac{1}{({\mu}{\times}{\mu})(({\Omega}{\times}{\Omega}{\backslash}{\Delta})}\;\[\frac{{\mu}({\Omega})^2}{\({d+m-1 \atop m}\)}-({\mu}{\times}{\mu})({\Delta})\],\;{\forall}m{\in}{\mathbb{N}}.$$ This improves 48 years old celebrated result of Welch [41]. We introduce the notions of continuous cross correlation and frame potential of Bessel family and give applications of continuous Welch bounds to these concepts. We also introduce the notion of continuous Grassmannian frames.

• The Bulletin of The Korean Astronomical Society
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• v.45 no.1
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• pp.60.2-60.2
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• 2020

In the hierarchical framework, galaxies grow through mergers and accretion. Those mechanisms leave faint features, such as stellar streams, shells and smooth stellar halos in the outskirts of galaxies. In order to search for those features in the nearby galaxies, we are conducting a KMTNet Nearby Galaxy Survey using the Korea Microlensing Telescope Network. We present a deep and wide-field imaging of NGC 5236, a barred spiral galaxy. In one-dimensional surface brightness profiles, we reach 28, 29 mag/arcsec2 in the R- and B-band, respectively. We find that the outer disk of NGC 5236 can be well described with a single exponential profile up to 17 kpc (~3.8 Reff) indicating that the excess light due to the stellar halo is not clearly detected. B-R color gradually increases towards the outskirts of the galaxy. It may reveal that stellar properties in the outskirts are marginally distinctive from those in the central part.

• Journal of the Korean Mathematical Society
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• v.55 no.2
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• pp.373-390
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• 2018

In this paper we study the small-data scattering of the d dimensional fractional $Schr{\ddot{o}}dinger$ equations with d = 2, 3, $L{\acute{e}}vy$ index 1 < ${\alpha}$ < 2 and Hartree type nonlinearity $F(u)={\mu}({\mid}x{\mid}^{-{\gamma}}{\ast}{\mid}u{\mid}^2)u$ with max(${\alpha}$, ${\frac{2d}{2d-1}}$) < ${\gamma}{\leq}2$, ${\gamma}$ < d. This equation is scaling-critical in ${\dot{H}}^{s_c}$, $s_c={\frac{{\gamma}-{\alpha}}{2}}$. We show that the solution scatters in $H^{s,1}$ for any s > $s_c$, where $H^{s,1}$ is a space of Sobolev type taking in angular regularity with norm defined by ${\parallel}{\varphi}{\parallel}_{H^{s,1}}={\parallel}{\varphi}{\parallel}_{H^s}+{\parallel}{\nabla}_{{\mathbb{S}}{\varphi}}{\parallel}_{H^s}$. For this purpose we use the recently developed Strichartz estimate which is $L^2$-averaged on the unit sphere ${\mathbb{S}}^{d-1}$ and utilize $U^p-V^p$ space argument.

• Analytical Science and Technology
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• v.18 no.5
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• pp.391-395
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• 2005

The title complex, $[Cd(N_3)_2(2-ethylimidazole)_2]$, I, has been prepared and characterized by X-ray single crystallography. The complex I crystallizes in the monoclinic system, Cc space group with a = 16.200(3), b = 12.926(3), $c=7.007(1){\AA}$, ${\beta}=102.29(3)^{\circ}$, $V=1433.7(5){\AA}^3$, Z = 4, $R_1=0.0239$ and ${\omega}R_2=0.0604$ for 1874 independent reflections. Cd(II) atom has a slightly distorted octahedral coordination geometry, with four end-on (${\mu}-1$,1) bridging azido ligands and two 2-ethylimidazole ligands bonding through nitrogen atom. The central cadmium(II) atoms are run in parallel to the c-axis and are doubly bridged with neighboring cadmium(II) atoms by the end-on (${\mu}-1$,1) bridging azido ligands. Thus, this complex has a one-dimensional zigzag chain structure in which the 2-ethylimidazole is in the cis conformation.

• Journal of the Korean Mathematical Society
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• v.34 no.3
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• pp.633-651
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• 1997

For a non-degenerate symmetric bilinear form $\sigma$ on a finite dimensional vector space E, the Jordan algebra of $\sigma$-symmetric operators has a symmetric cone $\Omega_\sigma$ of positive definite operators with respect to $\sigma$. The cone $C_\sigma$ of elements (x,y) \in E \times E with \sigma(x,y) \geq 0$ gives the compression semigroup. In this work, we show that in the sutomorphism group of the tube domain over $\Omega_\sigma$, this semigroup has a UDL and Ol'shanskii decompositions and is exactly the compression semigroup of $\Omega_sigma$.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2011.06a
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• pp.979-980
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• 2011