• 한국수학교육학회지시리즈A:수학교육
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• 제53권1호
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• pp.25-40
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• 2014

Mathematical concept exists in the structural form, not in the independent form. The purpose of this study is to consider the network which students actually have for the mathematical concept structure related to the properties of derivatives. First, we analyzed the properties of derivatives in 'Mathematics II' and showed the mathematical concept structure of the relations among derivatives, functions, and primitive functions as a network. Also, we investigated the understanding of high school students for the mathematical concept structure between derivatives and functions, and the structure between functions and second order derivatives when the functional formula is not given, and only the graph is given. The results showed that students mainly focus on the relation of 'function-derivatives', the thinking process for direction of derivative and the thinking style for algebra. On this basis, we suggest the educational implication that is necessary for students to build the network properly.

• 한국전산구조공학회논문집
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• 제20권6호
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• pp.779-787
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• 2007

본 연구는 계면경계에서 특이성을 갖는 이종재료 열전달문제를 효율적으로 해석할 수 있는 이동최소제곱 유한차분법을 제시한다 이동최소제곱 유한차분법은 격자망(grid)없이 절점만으로 이동최소제곱법을 이용하여 Taylor 다항식을 구성하고 차분식을 만들어 미분방정식을 직접 푼다. 초평면함수 개념에 근거한 쐐기함수를 이동최소제곱 센스(sense)로 근사식에 매입하여 쐐기거동과 미분 점프에 따른 계면경계 특성을 효과적으로 묘사하고 고속으로 미분을 근사하는 이동최소제곱 유한차분법의 강점을 발휘하도록 했다. 서로 다른 열전달계수를 갖는 이종재료 열전도문제 해석을 통해 이동최소제곱 유한차분법이 계면경계문제에서도 뛰어난 계산효율성과 해의 정확성을 확보할 수 있음을 보였다.

• Journal of Mechanical Science and Technology
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• 제14권2호
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• pp.197-206
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• 2000

A boundary integral equation method in the shape design sensitivity analysis is developed for the elasticity problems with axisymmetric non-homogeneous bodies. Functionals involving displacements and tractions at the zonal interface are considered. Sensitivity formula in terms of the interface shape variation is then derived by taking derivative of the boundary integral identity. Adjoint problem is defined such that displacement and traction discontinuity is imposed at the interface. Analytic example for a compound cylinder is taken to show the validity of the derived sensitivity formula. In the numerical implementation, solutions at the interface for the primal and adjoint system are used for the sensitivity. While the BEM is a natural tool for the solution, more generalization should be made since it should handle the jump conditions at the interface. Accuracy of the sensitivity is evaluated numerically by the same compound cylinder problem. The endosseous implant-bone interface problem is considered next as a practical application, in which the stress value is of great importance for successful osseointegration at the interface. As a preliminary step, a simple model with tapered cylinder is considered in this paper. Numerical accuracy is shown to be excellent which promises that the method can be used as an efficient and reliable tool in the optimization procedure for the implant design. Though only the axisymmetric problem is considered here, the method can be applied to general elasticity problems having interface.

• 대한수학회지
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• 제45권2호
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• pp.435-453
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• 2008

In this paper, by using q-deformed bosonic p-adic integral, we give $\lambda$-Bernoulli numbers and polynomials, we prove Witt's type formula of $\lambda$-Bernoulli polynomials and Gauss multiplicative formula for $\lambda$-Bernoulli polynomials. By using derivative operator to the generating functions of $\lambda$-Bernoulli polynomials and generalized $\lambda$-Bernoulli numbers, we give Hurwitz type $\lambda$-zeta functions and Dirichlet's type $\lambda$-L-functions; which are interpolated $\lambda$-Bernoulli polynomials and generalized $\lambda$-Bernoulli numbers, respectively. We give generating function of $\lambda$-Bernoulli numbers with order r. By using Mellin transforms to their function, we prove relations between multiply zeta function and $\lambda$-Bernoulli polynomials and ordinary Bernoulli numbers of order r and $\lambda$-Bernoulli numbers, respectively. We also study on $\lambda$-Bernoulli numbers and polynomials in the space of locally constant. Moreover, we define $\lambda$-partial zeta function and interpolation function.

• 전산구조공학
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• 제7권2호
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• pp.147-153
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• 1994

전미분 개념과 보조변수식을 사용하여 한 평면상에 투영할 수 없는 일반 형상의 축대칭 쉘 구조물에 대한 형상 설계민감도 해석방법을 개발하였다. 이 방법의 기본 개념은 대상 구조물을 여러 구간으로 나눈후, 각 구간마다에 얕은 아치나 축대칭 쉘에 사용되는 설계민감도 식을 적용하는 것이다. 그러나 기존의 설계민감도식은 투영면에 수직한 방향의 변분에 관한 것이기 때문에 각 구간 사이의 연속성을 유지하기가 곤란하므로, 이식을 확장하여 곡면의 법선 방향 변분에 관한 민감도 식을 유도하였다. 또한 개발된 방법을 원자력발전소 부품의 최적설계 문제에 적용하여 봄으로써 그 타당성과 유용성을 보였다.

• 대한수학회지
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• 제58권3호
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• pp.553-569
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• 2021

In this paper, we present and analyze a fully discrete numerical method for solving the time-fractional diffusion wave equation: ∂^β_tu - div(a∇u) = f, 1 < β < 2. We first construct a difference formula to approximate ∂^β_tu by using an interpolation of derivative type. The truncation error of this formula is of O(△t^2+δ-β)-order if function u(t) ∈ C^2,δ[0, T] where 0 ≤ δ ≤ 1 is the Hölder continuity index. This error order can come up to O(△t^3-β) if u(t) ∈ C³ [0, T]. Then, in combinination with the linear finite volume discretization on spatial domain, we give a fully discrete scheme for the fractional wave equation. We prove that the fully discrete scheme is unconditionally stable and the discrete solution admits the optimal error estimates in the H¹-norm and L₂-norm, respectively. Numerical examples are provided to verify the effectiveness of the proposed numerical method.

• 대한수학회지
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• 제56권1호
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• pp.265-284
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• 2019

The main purpose of this paper is to investigate the q-Apostol type Frobenius-Euler numbers and polynomials. By using generating functions for these numbers and polynomials, we derive some alternative summation formulas including powers of consecutive q-integers. By using infinite series representation for q-Apostol type Frobenius-Euler numbers and polynomials including their interpolation functions, we not only give some identities and relations for these numbers and polynomials, but also define generating functions for new numbers and polynomials. Further we give remarks and observations on generating functions for these new numbers and polynomials. By using these generating functions, we derive recurrence relations and finite sums related to these numbers and polynomials. Moreover, by applying higher-order derivative to these generating functions, we derive some new formulas including the Hurwitz-Lerch zeta function, the Apostol-Bernoulli numbers and the Apostol-Euler numbers. Finally, for an application of the generating functions, we derive a multiplication formula, which is very important property in the theories of normalized polynomials and Dedekind type sums.

• 한국축산식품학회지
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• 제41권4호
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• pp.731-738
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• 2021

Herein, a novel analytical method using a high-performance liquid chromatography-fluorescence detector (HPLC/FLD) is developed for rapidly measuring an L-carnitine ester derivative in infant powdered milk. In this study, solid-phase extraction cartridges filled with derivatized methanol and distilled water were used to effectively separate L-carnitine. Protein precipitation pretreatment was carried out to remove the protein and recover the analyte extract with a high recovery (97.16%-106.56%), following which carnitine in the formula was derivatized to its ester form. Precolumn derivation with 1-aminoanthracene (1AA) was carried out in a phosphate buffer using 1-(3-dimethylaminopropyl)-3-ethylcarbodiimide hydrochloride (EDC) as the catalyst. Method validation was performed following the AOAC guidelines. The calibration curves were linear in the L-carnitine concentration range of 0.1-2.5 mg/L. The lower limit of quantitation and limit of detection of L-carnitine were 0.076 and 0.024 mg/L, respectively. The intra- and interday precision and recovery results were within the allowable limits. The results showed that our method helped reduce the sample preparation time. It also afforded higher resolution and better reproducibility than those obtained by traditional methods. Our method is suitable for detecting the quantity of L-carnitine in infant powdered milk containing a large amount of protein or starch.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제15권1호
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• pp.31-41
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• 2011

I introduce a derivative called "Snowball Currency Option" or "USDKRWSnowball Extendible At Expiry KO" which was traded once in the over-the-counter market in Korea. A snowball currency option consists of a series of maturities the payoffs at which are like those of a long position in a put option and two short position in an otherwise identical call. The strike price at each maturity depends on the exchange rate and the previous strike price so that the strike prices are random and path-dependent, which makes it difficult to find a closed form solution of the value of a snowball currency option. I analyze the payoff structure of a snowball currency option and derive an upper and a lower boundaries of the value of it in a simplified model. Furthermore, I derive a pricing formula using integral in the simplified model.

• 대한수학회보
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• 제54권6호
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• pp.1951-1967
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• 2017

We aim to introduce a further extension of a family of the extended Hurwitz-Lerch Zeta functions of two variables. We then systematically investigate several interesting properties of the extended function such as its integral representations which provide extensions of various earlier corresponding results of two and one variables, its summation formula, its Mellin-Barnes type contour integral representations, its computational representation and fractional derivative formulas. A multi-parameter extension of the extended Hurwitz-Lerch Zeta function of two variables is also introduced. Relevant connections of certain special cases of the main results presented here with some known identities are pointed out.