• Journal of the Korean Mathematical Society
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• v.59 no.2
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• pp.353-365
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• 2022

Let 𝓐 be the collection of analytic functions f defined in 𝔻 := {ξ ∈ ℂ : |ξ| < 1} such that f(0) = f'(0) - 1 = 0. Using the concept of subordination (≺), we define $$S^*_{\ell}\;:=\;\{f{\in}A:\;\frac{{\xi}f^{\prime}({\xi})}{f({\xi})}{\prec}{\Phi}_{\ell}(\xi)=1+{\sqrt{2}{\xi}}+{\frac{{\xi}^2}{2}},\;{\xi}{\in}{\mathbb{D}}\}$$, where the function 𝚽_ℓ(ξ) maps 𝔻 univalently onto the region Ω_ℓ bounded by the limacon curve (9u² + 9v² - 18u + 5)² - 16(9u² + 9v² - 6u + 1) = 0. For 0 < r < 1, let 𝔻_r := {ξ ∈ ℂ : |ξ| < r} and 𝒢 be some geometrically defined subfamily of 𝓐. In this paper, we find the largest number 𝜌 ∈ (0, 1) and some function f₀ ∈ 𝒢 such that for each f ∈ 𝒢 𝓛_f (𝔻_r) ⊂ Ω_ℓ for every 0 < r ≤ 𝜌, and $${\mathcal{L} _{f_0}}({\partial}{\mathbb{D}_{\rho})\;{\cap}\;{\partial}{\Omega}_{\ell}\;{\not=}\;{\emptyset}$$, where the function 𝓛_f : 𝔻 → ℂ is given by $${\mathcal{L}}_f({\xi})\;:=\;{\frac{{\xi}f^{\prime}(\xi)}{f(\xi)}},\;f{\in}{\mathcal{A}}$$. Moreover, certain graphical illustrations are provided in support of the results discussed in this paper.

• Current Optics and Photonics
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• v.8 no.1
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• pp.86-96
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• 2024

This research investigation employs a terahertz (THz) time-domain spectroscopy system to study the terahertz spectral characteristics of five different citrates in both solution and solid state. The citrates under examination are lithium citrate, monosodium citrate, disodium citrate, trisodium citrate, and potassium citrate. The results show that the THz absorption coefficients of the first four citrate solutions exhibit a decreasing trend with increasing concentration. However, the potassium citrate solution shows an opposite phenomenon. At the same time, the absorption coefficients of lithium citrate, trisodium citrate, and potassium citrate solutions are compared at the same concentration. The results indicate that the absorption coefficient of citrate solution increases in proportion to the increase of metal cation radius, which is explained from the perspective of the influence of metal cations on hydrogen bonds. In addition, we also study the absorption peaks of solid citrates, and characterize the formation mechanism of the absorption peaks by molecular dynamics simulations. This methodology can be further extended to the study of multitudinous salts, presenting theoretical foundations for the detection in food and medicine industries.

• Advances in Computational Design
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• v.9 no.1
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• pp.39-52
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• 2024

If the governing differential equation arising from engineering problems is treated as an analytic, continuous and derivable function, it can be expanded by one point as a series of finite numbers. For the function to be zero for each value of its domain, the coefficients of each term of the same power must be zero. This results in a recursive relationship which, after applying the natural conditions or the boundary conditions, makes it possible to obtain the values of the derivatives of the function with acceptable accuracy. The elastoplastic analysis of an inhomogeneous thick sphere of metallic materials with linear variation of the modulus of elasticity, yield stress and Poisson's ratio as a function of radius subjected to internal pressure is presented. The Beltrami-Michell equation is established by combining equilibrium, compatibility and constitutive equations. Assuming axisymmetric conditions, the spherical coordinate parameters can be used as principal stress axes. Since there is no analytical solution, the natural boundary conditions are applied and the governing equations are solved using a proposed new method. The maximum effective stress of the von Mises yield criterion occurs at the inner surface; therefore, the negative sign of the linear yield stress gradation parameter should be considered to calculate the optimal yield pressure. The numerical examples are performed and the plots of the numerical results are presented. The validation of the numerical results is observed by modeling the elastoplastic heterogeneous thick sphere as a pressurized multilayer composite reservoir in Abaqus software. The subroutine USDFLD was additionally written to model the continuous gradation of the material.

• Journal of Educational Research in Mathematics
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• v.27 no.4
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• pp.833-855
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• 2017

This study aims to reinvestigate the reason for introducing radian as a new unit to express the size of angles, what is the meaning of radian measures to use arc lengths as angle measures, and why is the domain of trigonometric functions expanded to real numbers for expressing general angles. For this purpose, it was conducted historical, mathematical and applied mathematical analyzes in order to research at multidisciplinary analysis of the radian concept. As a result, the following were revealed. First, radian measure is intrinsic essence in angle measure. The radian is itself, and theoretical absolute unit. The radian makes trigonometric functions as real functions. Second, radians should be aware of invariance through covariance of ratios and proportions in concentric circles. The orthogonality between cosine and sine gives a crucial inevitability to the radian. It should be aware that radian is the simplest standards for measuring the length of arcs by the length of radius. It can find the connection with sexadecimal method using the division strategy. Third, I revealed the necessity by distinction between angle and angle measure. It needs justification for omission of radians and multiplication relationship strategy between arc and radius. The didactical suggestions derived by these can reveal the usefulness and value of the radian concept and can contribute to the substantive teaching of radian measure.

• Journal of the Korean Society for Marine Environment & Energy
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• v.17 no.3
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• pp.167-173
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• 2014

In this work, based on the blade element-momentum theory (BEMT), we proposed the geometry of a lab-scale horizontal axis tidal turbine with a diameter of 80cm, which can demonstrate the maximum power coefficient, and investigated the effect of blade pitch angle increase on the power coefficient. For validation of the computed power coefficients by the BEMT, we also computed the power coefficient using the computational fluid dynamics (CFD) for each case. For the CFD, 15 times of the turbine radius was used for the length and diameter of the computational domain, and the open boundary condition was prescribed at the boundary of the computational domain. The maximum power coefficients of the turbine acquired by the BEMT and CFD were about 48%, showing a good agreement. Both of the power coefficients computed by the BEMT and CFD tended to decrease when the blade pitch angle increases. The two power coefficients for a given tip-speed ratio were in good agreement. Through the present study, we have confirmed that we can trust the proposed geometry and the computed power coefficients based on the BEMT.

• Transactions of the Korean Society of Mechanical Engineers
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• v.11 no.6
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• pp.1001-1004
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• 1987

In this study mathematical properties of variational solution and solution of the boundary integral equation of the linear elasticity problem are studied. It is first reviewed that a variational solution for the three-dimensional linear elasticity problem exists in the Sobolev space [ $H^{1}$(.OMEGA.)]$^{3}$ and, then, it is shown that a unique solution of the boundary integral equation is identical to the variational solution in [ $H^{1}$(.OMEGA.)]$^{3}$. To represent the boundary integral equation, the Green's formula in the Sobolev space is utilized on the solution domain excluding a ball, with small radius .rho., centered at the point where the point load is applied. By letting .rho. tend to zero, it is shown that, for the linear elasticity problem, boundary integral equation is valid for the variational solution. From this fact, one can obtain a numerical approximatiion of the variational solution by the boundary element method even when the classical solution does not exist.exist.

• Journal of The Institute of Information and Telecommunication Facilities Engineering
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• v.2 no.1
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• pp.52-62
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• 2003

In this paper, photonic bandgap(PBG) bandstop filters which are composed of periodically etched circles in the ground plane show good microwave characteristics with the harmonic suppression on stopband. The PBG structures were analyzed using a finite-difference time-domain(FDTD) simulation and experimental measurement. The FDTD technique is used because it can simulate arbitrary 3-D structures and provide broadband frequency response. The analysis results are presented it is the same that only one row of etched circles and 2-dimension three rows of etched circles. And we show the PBG resonator characteristics between etched circles using field pattern and frequency characteristics as functions of etched circle number n, etched circle radius r and period a.

• Weed & Turfgrass Science
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• v.6 no.1
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• pp.28-31
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• 2017

The mutation rate of proline in the position 197 (Pro197) in acetohydroxy acid synthase (AHAS) is highest among sulfonylurea (SU) herbicide-resistance mutants. Therefore, it is significant to investigate the resistance mechanism for the mutation and to develop the herbicides specific to the mutants. SU herbicide resistance mechanism of the mutants, 197Ser, 197Thr and 197Ala, in AHAS were targeted for designing new SU-herbicide. We did molecular dynamics (MD) simulation for understanding SU herbicide-resistance mechanisms of AHAS mutants and designed new herbicides with docking and MD evaluations. We have found that mutation to 197Ala and 197Ser enlarged the entrance of the active site, while 197Thr contracted. Map of the root mean square derivation (RMSD) and radius gyrations (Rg) revealed the domain indicating the conformations for herbicide resistant. Based on the enlarging-contracting mechanism of active site entrance, we designed new herbicides with substitution at the heterocyclic moiety of a SU herbicide for the complementary binding to the changed active site entrances of mutants, and designed new herbicides. We confirmed that our screened new herbicides bonded to both AHAS wild type and mutants with higher affinity, showing more stable binding conformation than the existing herbicides.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.27 no.9
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• pp.1209-1219
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• 2003

The dynamic behaviors of the single vortex interacting with $CH_4-Air$ jet diffusion flame are investigated numerically. The numerical method is based on a predict-corrector scheme for a low Mach number flow. A two-step global reaction mechanism is adopted as a combustion model. Studies are conducted in fixed initial velocities for the three cases according as where $CO_2$ is added; (1) without dilution, (2) dilution in fuel stream and (3) dilution in oxidizer stream. A single vortex is generated by an axisymmetric jet, which is made by an impulse of a cold fuel when a flame is developed entirely in a computational domain. The simulation shows that $CO_2$ dilution in fuel stream results in somewhat larger vortex radius, and greater amount of entrainment of surrounding fluid than in other cases. Thus, the dilution of $CO_2$ in fuel stream enhances the mixing in single vortex and increases the stretching of the flame surface. The budgets of the vorticity transport equation are examined to reveal the mechanism of vortex formation when $CO_2$ is added. It is found that, in the case of $CO_2$ dilution in fuel stream, the vortex destruction due to volumetric expansion and the vortex production due to baroclinic torque are more dominant than in other cases.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.27 no.2
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• pp.101-107
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• 2016

This paper presents the characteristics of a double-cone broadband antenna with compact and three-dimensional structure that can be used in UWB system. The theoretical analysis is conducted using a finite difference time domain(FDTD) method. The parameters are the radius, a height of broadband double-cone antennas with shorting plate, and the number of plates on a ground plane. This paper examines influence of structural parameters on return loss. The results show that a condition for an optimum structure of broadband double-cone antennas with shorting plate exists. It also shows that the broadband double-cone antennas with shorting plate have radiation patterns similar to those of a dipole antenna. To verify the theoretical analysis, computed results are compared to experimental results.