• Journal of the Korean Mathematical Society
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• v.57 no.1
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• pp.89-111
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• 2020

In the present paper, we give some characterization of the L₂ maximal estimate for the operator P^t_a,γf(Γ(x, t)) along curve with complex time, which is defined by $$P^t_{a,{\gamma}}f({\Gamma}(x,t))={\displaystyle\smashmargin{2}{\int\nolimits_{\mathbb{R}}}}\;e^{i{\Gamma}(x,t){\xi}}e^{it{\mid}{\xi}{\mid}^a}e^{-t^{\gamma}{\mid}{\xi}{\mid}^a}{\hat{f}}({\xi})d{\xi}$$, where t, γ > 0 and a ≥ 2, curve Γ is a function such that Γ : ℝ×[0, 1] → ℝ, and satisfies Hölder's condition of order σ and bilipschitz conditions. The authors extend the results of the Schrödinger type with complex time of Bailey [1] and Cho, Lee and Vargas [3] to Schrödinger operators along the curves.

• Communications of the Korean Mathematical Society
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• v.12 no.3
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• pp.539-541
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• 1997

Let X be a smooth projective threefold. Let C be a smooth projective curve and let $f : X \to C$ be a fiber space with connected fiber S. Assume that $q_1(S) = 0$. Then we have $-X(O_C)X(O_S) \leq -X(O_X)$.

• Bulletin of the Korean Mathematical Society
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• v.34 no.4
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• pp.595-601
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• 1997

Let $C_d$ be the rational curve of degree d in $P_k ^3$ given parametrically by $x_0 = u^d, X_1 = u^{d - 1}t, X_2 = ut^{d - 1}, X_3 = t^d (d \geq 4)$. Then the defining ideal of $C_d$ can be minimally generated by d polynomials $F_1, F_2, \ldots, F_d$ such that $degF_1 = 2, degF_2 = \cdots = degF_d = d - 1$ and $C_d$ is a set-theoretically complete intersection on $F_2 = X_1^{d-1} - X_2X_0^{d-2}$ for every field k of characteristic p > 0. For the proofs we will use the notion of Grobner basis.

• Proceedings of the Korean Society For Composite Materials Conference
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• 2002.05a
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• pp.219-222
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• 2002

A new designed composite archery bow limbs are developed in this study. The characteristic F-X curve in current recurve archery bow is first studied for a reference. Based on this, a composite archery bow is designed to obtain a higher strain Energy and good vibration performance. Carbon/Epoxy prototype archery bow limbs are made from autoclaving and test on INSTRON 5567 test machine. The experimental results show that the new designed archery bow is powerful and stable.

• The Pure and Applied Mathematics
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• v.17 no.4
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• pp.389-396
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• 2010

We investigate the existence of homoclinic orbits of the following systems of $Li{\'{e}}nard$ type: $a(x)x^'=h(y)-F(x)$, $y^'$=-a(x)g(x), where $h(y)=m{\mid}y{\mid}^{p-2}y$ with m > 0 and p > 1 and a, F, 9 are continuous functions such that a(x) > 0 for all $x{\in}{\mathbb{R}}$ and F(0)=g(0)=0 and xg(x) > 0 for $x{\neq}0$. By a series of time and coordinates transformations of the above system, we obtain sufficient conditions for the positive orbits of the above system starting at the points on the curve h(y) = F(x) with x > 0 to approach the origin through only the first quadrant. The method of this paper is new and the results of this paper cover some early results on this topic.

• Journal of the Korean Mathematical Society
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• v.52 no.5
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• pp.991-1001
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• 2015

In this work we obtain conditions for nonspecial line bundles on general ${\kappa}$-gonal curves failing to be normally generated. Let L be a nonspecial very ample line bundle on a general ${\kappa}$-gonal curve X with ${\kappa}{\geq}4$ and $deg\mathcal{L}{\geq}{\frac{3}{2}}g+{\frac{g-2}{{\kappa}}}+1$. If L fails to be normally generated, then L is isomorphic to $\mathcal{K}_X-(ng^1_{\kappa}+B)+R$ for some $n{\geq}1$, B and R satisfying (1) $h^0(R)=h^0(B)=1$, (2) $n+3{\leq}degR{\leq}2n+2$, (3) $deg(R{\cap}F){\leq}1$ for any $F{\in}g^1_k $. Its converse also holds under some additional restrictions. As a corollary, a very ample line bundle $\mathcal{L}{\simeq}\mathcal{K}_X-g^0_d+{\xi}^0_e$ is normally generated if $g^0_d{\in}X^{(d)}$ and ${\xi}^0_e{\in}X^{(e)}$ satisfy $d{\leq}{\frac{g}{2}}-{\frac{g-2}{\kappa}}-3$, supp$(g^0_d{\cap}{\xi}^0_e)={\phi}$ and deg$(g^0_d{\cap}F){\leq}{\kappa}-2$ for any $F{\in}g^1_k$.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.21 no.6
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• pp.3-12
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• 2011

A hashing function that maps arbitrary messages directly onto curve points (MapToPoint) has non-negligible complexity in pairing-based cryptosystems. Unlike elliptic curve cryptosystems, pairing-based cryptosystems require the hashing function in ternary fields. Barreto et al. observed that it is more advantageous to hash the message to an ordinate instead of an abscissa. So, they significantly improved the hashing function by using a matrix with coefficients of the abscissa. In this paper, we improve the method of Barreto et al. by reducing the matrix. Our method requires only 44% memory of the previous result. Moreover we can hash a message onto a curve point 2~3 times faster than Barreto's Method.

• Tribology and Lubricants
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• v.38 no.3
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• pp.84-92
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• 2022

In Part I, developed was a method to obtain the stress field due to an edge dislocation that locates in an elastic half plane beneath the contact edge of an elastically similar square wedge. Essential result was the corrective functions which incorporate a traction free condition of the free surfaces. In the sequel to Part I, features of the corrective functions, F_kij,(k = x, y;i,j = x,y) are investigated in this Part II at first. It is found that F_xxx(ŷ) = F_xyx(ŷ) where ŷ = y/η and η being the location of an edge dislocation on the y axis. When compared with the corrective functions derived for the case of an edge dislocation at x = ξ, analogy is found when the indices of y and x are exchanged with each other as can be readily expected. The corrective functions are curve fitted by using the scatter data generated using a numerical technique. The algebraic form for the curve fitting is designed as F_kij(ŷ) = $\frac{1}{\hat{y}^{1-{\lambda}}I+yp}$$\sum_{q=0}^{m}{\left}$$\left[A_q\left(\frac{\hat{y}}{1+\hat{y}} \right)^q \right]$ where λ_I=0.5445, the eigenvalue of the adhesive complete contact problem introduced in Part I. To investigate the exponent of F_kij, i.e.(1 - λ_I) and p, Log|F_kij|(ŷ)-Log|(ŷ)| is plotted and investigated. All the coefficients and powers in the algebraic form of the corrective functions are obtained using Mathematica. Method of analyzing a surface perpendicular crack emanated from the complete contact edge is explained as an application of the curve-fitted corrective functions.

• Journal of Korean Society for Quality Management
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• v.51 no.4
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• pp.481-496
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• 2023

Purpose: The main theme of this study is to derive a profit curve by a cubic cost function for nonlinear CVP analysis. According to the analytical approach to derive a nonlinear profit function in this study, it is possible with only the existing cost structure to calculate the profit maximization and downtime point sales unlike the classical CVP analysis. Furthermore, the profit curve by the mathematical model of this study could serve as a tool to quantify the qualitative evaluation of each stage of the industry life cycle. Methods: This study followed the mathematical approach from the cubic cost function model of microeconomics, and using real data of the Bank of Korea Results: The nonlinear profit function suggested by this study is as follows; ${\pi}(x)=-a\left(x-\frac{f}{1-v}\right)^3+(1-v)x-k$ where $a=\frac{1}{3}v\left(\frac{(1-v)}{f}\right)^2,k=f-a\left(1-\frac{f}{1-v \right)^3$ Conclusion: The process and results of this study would be able to contribute not only in practice of nonlinear CVP analysis required in the management accounting or financial management, but also in cost theory of microeconomics. Also, since the life cycle of all industries in Korea was verified to the growth or mature stage, decision makers should pay careful attention to determining life cycle stages and consider the profit curve by the average variable cost ratio over multi periods.

• Journal of the Korean Crystal Growth and Crystal Technology
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• v.9 no.1
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• pp.1-5
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• 1999

The rare-earth ions ($R^{3+}$, R=Nd, Er) doped $CaF_{2}$ layers have been grown on $CaF_{2}$ (111) substrate by molecular beam epitaxy. The surface structure and the crystallinity of $CaF_{2}:R^{3+}$ layers depending on the doping concentration of $R^{3+}$ and layer thickness were studied by reflection high-energy electron diffraction (RHEED). In aspect of application as buffer layer in semiconductor-related hybrid structure, the lattice displacement between $CaF_{2}:R^{3+}$ layers and $CaF_{2}$ (111) substrate was investigated by X-ray rocking curve analysis.