• 충청수학회지
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• 제20권3호
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• pp.269-277
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• 2007

It is shown that $f:\mathbb{R}{\rightarrow}\mathbb{R}$ satisfies the following functional inequalities (0.1) ${\mid}f(x)+f(y){\mid}{\leq}{\mid}f(x+y){\mid}$, (0.2) ${\mid}f(x)+f(y){\mid}{\leq}{\mid}2f(\frac{x+y}{2}){\mid}$, (0.3) ${\mid}f(x)+f(y)-2f(\frac{x-y}{2}){\mid}{\leq}{\mid}2f(\frac{x+y}{2}){\mid}$, respectively, then the function $f:\mathbb{R}{\rightarrow}\mathbb{R}$ satisfies the Cauchy functional equation, the Jensen functional equation and the Jensen quadratic functional equation, respectively.

• 대한원격탐사학회지
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• 제33권4호
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• pp.401-410
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• 2017

Estimation of snow depth using optical image is conducted by using correlation with Snow Cover Fraction (SCF). Various algorithms have been proposed for the estimation of snow cover fraction based on Normalized Difference Snow Index (NDSI). In this study we tested linear, quadratic, and exponential equations for the generation of snow cover fraction maps using data from the Moderate Resolution Imaging Spectroradiometer (MODIS) Aqua satellite in order to evaluate their applicability to the complex terrain of South Korea and to search for improvements to the estimation of snow depth on this landscape. The results were validated by comparison with in-situ snowfall data from weather stations, with Root Mean Square Error (RMSE) calculated as 3.43, 2.37, and 3.99 cm for the linear, quadratic, and exponential approaches, respectively. Although quadratic results showed the best RMSE, this was due to the limitations of the data used in the study; there are few number of in-situ data recorded on the station at the time of image acquisition and even the data is mostly recorded on low snowfall. So, we conclude that linear-based algorithms are better suited for use in South Korea. However, in the case of using the linear equation, the SCF with a negative value can be calculated, so it should be corrected. Since the coefficients of the equation are not optimized for this area, further regression analysis is needed. In addition, if more variables such as Normalized Difference Vegetation Index (NDVI), land cover, etc. are considered, it could be possible that estimation of national-scale snow depth with higher accuracy.

• 정보보호학회논문지
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• 제33권2호
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• pp.211-222
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• 2023

다변수 이차식 기반 암호알고리즘은 양자컴퓨터에 안전하다고 믿어지는 수학적 난제에 기반을 둔 공개키 암호알고리즘 중의 하나로 현재 사용하고 있는 공개키 암호를 대체할 수 있는 양자내성암호 중의 하나이다. NIST 양자내성암호 공모 3라운드 최종 후보 알고리즘으로 선정되었던 다변수 이차식 기반 전자서명 알고리즘 Rainbow의 다중레이어를 사용하는 구조에 대한 진화된 공격이 대두된 후에 단일 레이어를 이용하는 UOV의 구조에 관심이 집중되고 있다. 본 논문에서는 단일 레이어를 갖는 UOV 구조를 유지하면서 일차식의 특별한 구조, 희소다항식, 랜덤다항식의 다양한 조합을 통해 비밀키의 길이를 대폭 줄이고, 블록 부분 행렬의 역행렬을 이용하여 선형 시스템의 해를 구하는 방법을 적용한 효율적인 다변수 이차식 기반 전자서명 알고리즘을 제안한다. 제안한 전자서명의 안전성 분석을 통해 안전한 파라미터를 설정하고 각 파라미터에서의 키길이와 서명 길이를 비교 분석한다. 제안한 다변수 이차식 기반 전자서명 알고리즘은 서명의 길이가 양자내성 전자서명 중 가장 짧고, 기존 다변수 이차식 기반 전자서명에 비해 비밀키 길이가 최대 97%의 축소 효과를 가진다.

• 대한수학회지
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• 제38권3호
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• pp.595-611
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• 2001

Let Q(n,1) be the set of even unimodular positive definite integral quadratic forms in n-variables. Then n is divisible by 8. For A[X] in Q(n,1), the theta series $\theta$(sub)A(z) = ∑(sub)X∈Z(sup)n e(sup)$\pi$izA[X] (Z∈h (※Equations, See Full-text) the complex upper half plane) is a modular form of weight n/2 for the congruence group Γ$_1$(8) = {$\delta$∈SL$_2$(Z)│$\delta$≡()mod 8} (※Equation, See Full-text). If n$\geq$24 and A[X], B{X} are tow quadratic forms in Q(n,1), the quotient $\theta$(sub)A(z)/$\theta$(sub)B(z) is a modular function for Γ$_1$(8). Since we identify the field of modular functions for Γ$_1$(8) with the function field K(X$_1$(8)) of the modular curve X$_1$(8) = Γ$_1$(8)＼h(sup)* (h(sup)* the extended plane of h) with genus 0, we can express it as a rational function of j(sub) 1,8 over C which is a field generator of K(X$_1$(8)) and defined by j(sub)1,8(z) = $\theta$$_3$(2z)/$\theta$$_3$(4z). Here, $\theta$$_3$ is the classical Jacobi theta series.

• 한국가스학회지
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• 제10권4호
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• pp.29-33
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• 2006

화학공정 설계에서 공정의 위험성 판단은 중요한 부분이다. 실제 화학공정에 사용되는 가연성 물질의 화재 및 폭발 위험성을 판단하는 인화점에 대한 예측은 그 방법 중의 하나이다. 본 연구에서는 2성분계 가연성 물질의 인화점에 대한 실험 자료를 이용하여 다변량 통계 분석법(partial least squares(PLS), quadratic partial least squares(QPLS))을 이용하여 2성분계 혼합물의 인화점을 예측하였고, 기존의 Raoult의 법칙과 Van Laar 식에 의한 예측값과 비교해 보았다.

• Advances in Computational Design
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• 제5권4호
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• pp.397-416
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• 2020

Functionally graded material (FGM) illustrates a novel class of composites that consists of a graded pattern of material composition. FGM is engineered to have a continuously varying spatial composition profile. Current work focused on buckling analysis of beam made of stepwise linear and quadratic graded material in axial direction subjected to axial span-load with piecewise function and rested on shear layer based on classical beam theory. The various boundary and natural conditions including simply supported (S-S), pinned - clamped (P-C), axial hinge - pinned (AH-P), axial hinge - clamped (AH-C), pinned - shear hinge (P-SHH), pinned - shear force released (P-SHR), axial hinge - shear force released (AH-SHR) and axial hinge - shear hinge (AH-SHH) are considered. To the best of the author's knowledge, buckling behavior of this kind of Euler-Bernoulli beams has not been studied yet. The equilibrium differential equation is derived by minimizing total potential energy via variational calculus and solved analytically. The boundary conditions, natural conditions and deformation continuity at concentrated load insertion point are expressed in matrix form and nontrivial solution is employed to calculate first buckling loads and corresponding mode shapes. By increasing truncation order, the relative error reduction and convergence of solution are observed. Fast convergence and good compatibility with various conditions are advantages of the proposed method. A MATLAB code is provided in appendix to employ the numerical procedure based on proposed method.

• 한국전산구조공학회논문집
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• 제17권4호
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• pp.351-363
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• 2004

비보존력을 받는 보-부재의 질량행렬, 탄성강도행릴, circulatory비보존력의 방향변화로 인한 load correction강도행력, 그리고 Winkler 및 Pasternak지반강도행렬을 고려한 운동방정식을 유도하고 divergence 및 flutter에 의한 안정성 해석을 수행한다. 또한 내적 및 외적 감쇠계수를 운동방정식에 포함시킴으로써 감쇠효과를 고려하고, 2차 고유치문제의 해법(quadratic eigen problem solution)을 적용하여 flutter에 미치는 영향을 조사한 후, Beck's column, Leipholz's column 및 Hauger's column에 대하여 비보존력의 방향파라미터 ${\alpha}$에 대한 임계하중의 영향, 내적 및 외적 감쇠계수 및 Winkler 및 Pasternak지반에 의한 임계하중의 영향을 각각 조사한다.

• Journal of Mechanical Science and Technology
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• 제17권3호
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• pp.457-466
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• 2003

In this paper, the numerical finite element formulations were derived for the linearized Navier-Stokes' equations with assumptions of two-dimensional incompressible, homogeneous viscous fluid field, and small oscillation and the FAMD (Fluid Added Mass and Damping) code was developed for practical applications calculating the fluid added mass and damping. In formulations, a fluid domain is discretized with C$\^$0/-type quadratic quadrilateral elements containing eight nodes using a mixed interpolation method, i.e., the interpolation function for the velocity variable is approximated by a quadratic function based on all eight nodal points and the interpolation function for the pressure variable is approximated by a linear function based on the four nodal points at vertices. Using the developed code, the various characteristics of the fluid added mass and damping are investigated for the concentric cylindrical shell and the actual hexagon arrays of the liquid metal reactor cores.

• 한국세라믹학회지
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• 제36권10호
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• pp.1022-1034
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• 1999

A relation between composition and properties of Na2O-Al2O3-SiO2 glasses was investigated with application of the extreme vertical design. Properties investigated in this study include glass transition temperature density refractive index thermal expansion electrical conductivity bending strength and hardness, Most of the quadratic models fitted on property data were statistically significant. The properties estimated from the fitted equation agreed well with the measured properties. The estimated properties were compared with those reported by other investigators. Additional composition except for those of extreme vertices were needed to yield a slightly better result for the simple system such as a temary system. In addition an optimal composition on each property could be calculated by using optimization technique on result obtained from the fitted quadratic models.

• 대한수학회보
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• 제41권3호
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• pp.541-557
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• 2004

In this paper we prove the Hyers-Ulam-Rassias stability by considering the cases that the approximate remainder ${\varphi}$ is defined by (x * y) ＋ (x * $y^{-1}$) - 2 (x) - 2 (y) =<${\varphi}$(x,y), (x*y*z)＋ (x)＋ (y)＋ (z)－ (x*y)－ (y*z)－ (z*x)＝${\varphi}$(x, y, z), where (G,*) is a group, X is a real or complex Hausdorff topological vector space, and is a function from G into X.