• 대한수학회보
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• 제41권2호
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• pp.347-357
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• 2004

In this note we will find out the general solution and investigate the generalized Hyers-Ulam-Rassias stability for the cubic functional equation f(3$\chi$+y) + f($3\chi$-y) = $3f(\chi$+ y) + $3f(\chi$-y) + ($48f(\chi)$ on abelian groups.

• 한국전산유체공학회지
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• 제3권2호
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• pp.1-8
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• 1998

We make use of cubic B-spline interpolation function in two cases: heat conduction and fluid flow problems. Cubic B-spline test function is employed because it is superior to approximation of linear and non-linear problems. We investigated the accuracy of the numerical formulation and focused on the position of the breakpoints within the computational domain. When the domain is divided by partitions of equal space, the results show poor accuracy. For the case of a heat conduction problem this partition can not reflect the temperature gradient which is rapidly changed near the wall. To correct the problem, we have more grid points near the wall or the region which has a rapid change of variables. When we applied the unequally spaced breakpoints, the results show high accuracy. Based on the comparison of the linear problem, we extended to the highly non-linear fluid flow problems.

• 대한수학회논문집
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• 제17권4호
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• pp.741-754
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• 2002

In this paper we present an error bound for cubic spline approximation of conic section curve. We compare it to the error bound proposed by Floater [1]. The error estimating function proposed in this paper is sharper than Floater's at the mid-point of parameter, which means the overall error bound is sharper than Floater's if the estimating function has the maximum at the midpoint.

• 방송공학회논문지
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• 제17권5호
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• pp.756-764
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• 2012

HEVC의 화면내 예측은 AIP와 화면내 평할화를 사용하여 예측 화소의 값을 결정하는데, 최종적으로 예측 화소값은 참조 화소들 사이에서 1차 방정식의 형태를 가지고 계산된다. 이는 참조 화소들의 값의 차이가 큰 경우 성능을 기대하기 어렵다. 본 논문에서는 현재 HEVC의 화면내 예측에서 사용되는 1차 함수 형태의 보간 방법 외에 DCT-IF 및 3차 함수를 사용하는 적응적 예측 방법을 제안한다. 2개 이상의 참조 화소들의 주파수 성분을 이용하는 DCT-IF를 사용하고, 또한 3차 함수의 형태를 이용하여 보간하므로 기존의 1차 함수를 이용하는 것보다 예측 화소값을 정확하게 결정한다. 3차함수는 1차함수보다 기울기가 더 크다. 따라서, 3차 함수는 예측 단위내의 에지에서 활용되어진다. HM6.0에서 부호화 시간은 3%, 복호화 시간은 1%의 증가를 보였고, 평균 BD-rate가 휘도 신호 Y에서 0.4%, 색차 신호 U, V에서 0.3%, 0.3% 감소되었다. 이를 통해 DCT-IF와 3차 함수, 그리고 기존의 방법을 적응적으로 사용할 경우 부호화 성능이 향상됨을 알 수 있다.

• 한국전산유체공학회지
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• 제14권4호
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• pp.67-77
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• 2009

This paper is a continuation of a recent development on the Hermite-based divergence-free element method and deals with a non-isothermal fluid flow driven by the buoyancy force in a square cavity with temperature difference across the two sides. Two Hermite functions are considered for numerical computations in this paper. One is a cubic function and the other is a quartic function. The degrees-of-freedom of the cubic Hermite function are stream function and its first and second derivatives for the velocity field, and temperature and its first derivatives for the temperature field. The degrees-of-freedom of the quartic Hermite function include two second derivatives and one cross derivative of the stream function in addition to the degrees-of-freedom of the cubic stream function. This paper presents a brief review on the Hermite based divergence-free basis functions and its finite element formulations for the buoyancy driven flow. The present algorithm does not employ any upwinding or a stabilization term. However, numerical values and contour graphs for major flow variables showed good agreements with those by De Vahl Davis[6].

• Communications for Statistical Applications and Methods
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• 제9권2호
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• pp.555-563
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• 2002

This paper discusses cubic equations in general saddlepoint approximations. Exact roots are found for various cases by trigonometric identities, the root which is appropriate for the general saddlepoint approximations is selected and discussed, and the defective cases in which the general saddlepoint approximations cannot be used are found.

• 대한수학회보
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• 제44권2호
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• pp.309-313
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• 2007

By applying ideas from [M. S. Moslehian, et al., Norms of operators in $X_{\lambda}$ spaces, Appl. Math. Lett. (2007), doi:10.1016/j.aml.2006. 11.009], we investigate the norm of the cubic operator on the function space $X_{\lambda}$.

• Journal of applied mathematics & informatics
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• 제18권1_2호
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• pp.329-337
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• 2005

This paper is to establish a functional equation satisfied by the generating function for counting rooted cubic c-nets and then to determine the parametric expressions of the equation directly. Meanwhile, the explicit formulae for counting rooted cubic c-nets are derived immediately by employing Lagrangian inversion with one or two parameters. Both of them are summation-free and in which one is just an answer to the open problem (8.6.5) in [1].

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2000년도 가을 학술발표회논문집
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• pp.355-360
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• 2000

This paper presents properties of piecewise cubic B-spline function and Rayleigh-Ritz method to compute the smallest eigenvales. In order to compute the smallest eigenvalues, Rayleigh quotient approach is used and four different types of finite element approximating functions corresponding to the statical deflection curve, spanned by the linearly independent set of piecewise cubic B-spline functions with equally spaced 5 knots from a partion of [0, 1], each satisfying homogeneous boundary conditions with constraining effects are used to compute the smallest eigenvalues for a Sturm-Lionville boundary equations of u"＋ λ²u＝0, u(0.0)＝u(0.0)＝0, 0≤x≤1.0.

• Kyungpook Mathematical Journal
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• 제49권3호
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• pp.435-450
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• 2009

On page 366 of his lost notebook [15], Ramanujan recorded a cubic continued fraction and several theorems analogous to Rogers-Ramanujan's continued fractions. In this paper, we derive several general formulas for explicit evaluations of Ramanujan's cubic continued fraction, several reciprocity theorems, two formulas connecting V (q) and V ($q^3$) and also establish some explicit evaluations using the values of remarkable product of theta-function.