• 대한토목학회논문집
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• 제13권5호
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• pp.29-37
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• 1993

본 논문은 추계론적 유한요소해석의 한 방법인 가중적분법의 확장에 대해서 논하였다. 가중적분법의 사용은 Deodatis에 의해서 삼각형요소로 확장되었다. 이에 의해서 2차원 문제에 대한 응답변화도를 수치적인 해석에 의해서 얻을 수 있게 되었다. 본 논문에서는 가중적분법을 일반 평면요소를 사용할 수 있도록 확장한다. 제안된 방법에 의해서 확정론적 유한요소해석에서 사용된 요소망은 추계론적 유한요소해석에서도 그대로 사용할 수 있도록 되었다. 나아가서, CST요소는 상수만을 그 요소로 가지는 변위-변형률 행렬을 가지는 특수한 경우이므로 제안된 방법을 사용할 경우 CST요소와 일반 평면 사변형 요소를 혼용하여 사용할 수 있을 것이다.

• 대한기계학회논문집
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• 제13권2호
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• pp.221-228
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• 1989

본 연구에서는 가상균열진전법과 수정 J-적분식을 연계하여 사용할 수 있는 유한요소 프로그램을 개발하고, 이 프로그램을 기존 결과가 있는 2상재료에 적응하여 타당성을 검토한 후, 다상재료의 경우에도 확장하였고, 실제 상변태가 발생하는 중수(heavy water)형 원자로 압력관(pressure tube)의 균열해석에 적용하여 보았다.

• 호남수학학술지
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• 제43권2호
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• pp.183-197
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• 2021

Recently several authors have extended the Beta function by using its integral representation. However, in many cases no expression of these extended functions in terms of classic special functions is known. In the present paper, we introduce a further extension by defining a family of functions G_r,s : ℝ^*₊ → ℂ, with r, s ∈ ℂ and ℜ(r) > 0. For given r, s, we prove that this function satisfies a second-order linear differential equation with rational coefficients. Solving this ODE, we express G_r,s as a combination of confluent hypergeometric functions. From this we deduce a new integral relation satisfied by Tricomi's function. We then investigate additional specific properties of G_r,1 which take the form of new non trivial integral relations involving exponential and error functions. We discuss the connection between G_r,1 and Stokes' first problem (or Rayleigh problem) in fluid mechanics which consists in determining the flow created by the movement of an infinitely long plate. For $r{\in}{\frac{1}{2}}{\mathbb{N}}^*$, we find additional relations between G_r,1 and Hermite polynomials. In view of these results, we believe the family of extended beta functions G_r,s will find further applications in two directions: (i) for improving our knowledge of confluent hypergeometric functions and Tricomi's function, (ii) and for engineering and physics problems.

• 대한수학회지
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• 제51권5호
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• pp.1045-1073
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• 2014

The study of the identities of symmetry for the Bernoulli polynomials arises from the study of Gauss's multiplication formula for the gamma function. There are many works in this direction. In the sense of p-adic analysis, the q-Bernoulli polynomials are natural extensions of the Bernoulli and Apostol-Bernoulli polynomials (see the introduction of this paper). By using the N-fold iterated Volkenborn integral, we derive serval identities of symmetry related to the q-extension power sums and the higher order q-Bernoulli polynomials. Many previous results are special cases of the results presented in this paper, including Tuenter's classical results on the symmetry relation between the power sum polynomials and the Bernoulli numbers in [A symmetry of power sum polynomials and Bernoulli numbers, Amer. Math. Monthly 108 (2001), no. 3, 258-261] and D. S. Kim's eight basic identities of symmetry in three variables related to the q-analogue power sums and the q-Bernoulli polynomials in [Identities of symmetry for q-Bernoulli polynomials, Comput. Math. Appl. 60 (2010), no. 8, 2350-2359].

• Kyungpook Mathematical Journal
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• 제63권1호
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• pp.11-13
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• 2023

We give a new proof for the full form of Hilbert's Nullstellensatz based on on integral extension and Noether's Normalization Lemma.

• 대한기계학회논문집
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• 제17권9호
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• pp.2138-2144
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• 1993

An integral equation representation of cracks was presented which differs from well-known "dislocation layer" representation. In this new representation, the equations are written in terms of the displacement discontinuity across the crack surfaces rather than derivatives of the displacement-discontinuity. It was shown in that the new technique is well-suited to the treatment of kinked cracks. In the present paper, this integral equation representation is coupled to the direct boundary-element method for the treatment of finite bodies containing kinked cracks. The method is demonstrated for two-dimensional finite domains but extension to three-dimensional problems would appear to be possible. The resulting approach is shown to be simple, yet very accurate. accurate.

• Selected Papers of The Society of Naval Architects of Korea
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• 제2권1호
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• pp.1-17
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• 1994

For a planar curve-sided panel with constant or linear density distributions of source or doublet in the singularity methods, Cantaloube and Rehbach show that the surface integral can be transformed into contour integral by using Stokes'formulas. As an extension of their formulations, this paper deals with a planar polygonal panel for which we derive the closed-forms of the potentials and the velocities induced by the singularity distributions. Test calculations show that the analytical evaluation of the closed-forms is superior to numerical integration (suggested by Cantaloube and Rehbach) of the contour integral. The compact and explicit expressions may produce accurate values of matrix elements of simultaneous linear equations in the singularity methods with much reduced computer time.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2002년도 하계학술대회 논문집 D
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• pp.2262-2264
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• 2002

In this paper, the integral sliding mode controller developed by Utkin is considered. It is pointed out that some theoretical consideration has to be added to that controller. Another type of integral sliding mode controller developed by Park is also considered. These integral sliding mode controllers have very important results in the extension of the robustness of sliding mode to the other linear control technique.

• 충청수학회지
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• 제9권1호
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• pp.101-106
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• 1996

In this paper, we will consider the Denjoy-Riemann integral of functions mapping a closed interval into a Banach space. We will show that a Riemann integrable function on [a, b] is Denjoy-Riemann integrable on [a, b] and that a Denjoy-Riemann integrable function on [a, b] is Denjoy-McShane integrable on [a, b].

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 1998년도 The Third Asian Fuzzy Systems Symposium
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• pp.380-386
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• 1998

In this paper we introduce the concept of fuzzy integrals for set-valued mappings, which is an extension of fuzzy integrals for single-valued functions defined by Sugeno. And we give some properties including convergence theorems on fuzzy integrals for set-valued mappings.