• 대한기계학회논문집A
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• 제27권1호
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• pp.119-125
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• 2003

A way to measure the second parameter $A_2$of CT specimens is described. The displacement $\delta$$_{5}$ which is measured continuously from visual images of the lateral surface during crack growth is used to calculate the A, as a function of crack growth. The crack length is measured by DCPD(Direct Current Potential Drop) method and the J-resistance curve is determined according to ASTM standard E1737-96. To prove the validity of this method, three dimensional finite element analyses were performed, and variations of the displacements $\delta$$_{5}$ and $A_2$along the thickness were explored. As the result, it has been shown that the $\delta$$_{5}$ measured from the visual images of the lateral surface and the corresponding $A_2$can be regarded as the average through the thickness for 1T and 1/2T specimens of SA106Gr.C steel.steel.

• 한국인터넷방송통신학회논문지
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• 제15권3호
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• pp.15-24
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• 2015

Jacket 행렬은 1984년 이문호 교수에 의해 소개되어 신호처리 및 코딩이론에 사용되는 $J^{\dagger}=[J_{ik}^{-1}]^T$인 행렬로서, Galois field F에서 $J^{\dagger}$가 J의 원소별 역행렬일 때 $JJ^{\dagger}=mI_m$의 특성을 갖는 $J=[J_{ik}]$인 $m{\times}m$ 정방행렬이다. 본 논문에서는 Jacket 행렬에 의해 고유 값으로 분해될 수 있는 정방행렬 $A_{2^n}$을 제안하였다. 특히 $A_2$와 그의 확장인 $A_3$ 행렬을 가지고 쌍곡선과 쌍곡면의 성질을 수정하는데 각각 적용할 수 있음을 보였다. 특히 쌍곡선이 n배의 정보량을 갖게 되면 $A_2$ 행렬의 EVD[7]를 이용하여 최종 행렬 $A_2^n$을 쉽게 계산할 수 있다. 또한 여기서 제안한 알고리즘을 가지고 컴퓨터 그래픽에서의 응용 프로그램과 수치해석에서도 이용될 수 있음을 보였다.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제8권1호
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• pp.71-78
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• 2001

In 1984, Johnson[A bounded convergence theorem for the Feynman in-tegral, J, Math. Phys, 25(1984), 1323-1326] proved a bounded convergence theorem for hte Feynman integral. This is the first stability theorem of the Feynman integral as an $L(L_2 (\mathbb{R}^N), L_2(\mathbb{R}^{N}))$ theory. Johnson and Lapidus [Generalized Dyson series, generalized Feynman digrams, the Feynman integral and Feynmans operational calculus. Mem, Amer, Math, Soc. 62(1986), no 351] studied stability theorems for the Feynman integral as an $L(L_2 (\mathbb{R}^N), L_2(\mathbb{R}^{N}))$ theory for the functional with arbitrary Borel measure. These papers treat functionals which involve only a single integral. In this paper, we obtain the stability theorems for the Feynman integral as an $L(L_1 (\mathbb{R}^N), L_{\infty}(\mathbb{R}^{N}))$theory for the functionals which involve double integral with some Borel measures.

• 한국정보과학회논문지:시스템및이론
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• 제29권9호
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• pp.514-519
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• 2002

단백질의 구조를 예측하는 과정에 사용될 수 있는 다음 문제를 고려한다. 길이가 n이고 원소가 모두 양수인 두 배열 A, B와 양수 M이 주어질 때, A[i]＋…A[j]＋B[k]＋…B[ι]=M이 되는 부배열 쌍 A[i]＋…A[j],$1{\leq}i{\leq}j{\leq}n$과 B[k], …, B[l], $1{\leq}k{\leq}l{\leq}n$을 모두 찾으시오. 본 논문에서는 이 문제를 $Ο(n^2log n+K)$ 시간에 Ο(n) 메모리를 사용하여 해결하는 알고리즘을 제시한다. 단, K는 찾은 부배열 쌍의 수이다. 기존의 결과는$Ο(n^2log +Klog n)$ 시간과 Ο(n) 메모리였다.

• 대한수학회지
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• 제60권2호
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• pp.303-325
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• 2023

In this paper, we introduce relative Rota-Baxter systems on Leibniz algebras and give some characterizations and new constructions. Then we construct a graded Lie algebra whose Maurer-Cartan elements are relative Rota-Baxter systems. This allows us to define a cohomology theory associated with a relative Rota-Baxter system. Finally, we study formal deformations and extendibility of finite order deformations of a relative Rota-Baxter system in terms of the cohomology theory.

• 대한수학회보
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• 제57권3호
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• pp.649-660
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• 2020

This paper proves a new regularity criterion for solutions to the Cauchy problem of the 3D Boussinesq equations via one directional derivative of the horizontal component of the velocity field (i.e., (∂_iu₁; ∂_ju₂; 0) where i, j ∈ {1, 2, 3}) in the framework of the anisotropic Lebesgue spaces. More precisely, for 0 < T < ∞, if $$\large{\normalsize\displaystyle\smashmargin{2}{\int\nolimits_o}^T}({\HUGE\left\|{\small{\parallel}{\partial}_iu_1(t){\parallel}_{L^{\alpha}_{x_i}}}\right\|}{\small^{\gamma}_{L^{\beta}_{x_{\hat{i}}x_{\bar{i}}}}+}{\HUGE\left\|{\small{\parallel}{\partial}_iu_2(t){\parallel}_{L^{\alpha}_{x_j}}}\right\|}{\small^{\gamma}_{L^{\beta}_{x_{\hat{i}}x_{\bar{i}}}}})dt<{{\infty}},$$ where ${\frac{2}{{\gamma}}}+{\frac{1}{{\alpha}}}+{\frac{2}{{\beta}}}=m{\in}[1,{\frac{3}{2}})$ and ${\frac{3}{m}}{\leq}{\alpha}{\leq}{\beta}<{\frac{1}{m-1}}$, then the corresponding solution (u, θ) to the 3D Boussinesq equations is regular on [0, T]. Here, (i, ${\hat{i}}$, ${\tilde{i}}$) and (j, ${\hat{j}}$, ${\tilde{j}}$) belong to the permutation group on the set 𝕊₃ := {1, 2, 3}. This result reveals that the horizontal component of the velocity field plays a dominant role in regularity theory of the Boussinesq equations.

• 한국윤활학회:학술대회논문집
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• 한국윤활학회 2002년도 proceedings of the second asia international conference on tribology
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• pp.459-460
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• 2002

This article discusses a diagnostics method based on models, and information theory. From an extensive system dynamics bond graph model of a gearbox [1], simulated were various cases germane to this diagnostics approach, including the response of an ideal gearbox, which functions perfectly to designer's specifications, and degraded gearboxes with tooth root cracking. By comparing these cases and constructing a signal flow analogy between the gearbox and a communication channel, Shannon' s information theory [2], including theorems, was applied to the gearbox to assess system health, in terms of ability to function.

• 대한수학회지
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• 제61권5호
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• pp.975-995
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• 2024

In this paper, we utilize Nevanlinna theory to study the existence and forms of solutions for quadratic trinomial complex partial differential-difference equations of the form aF² + 2ωFG + bG² = exp(g), where ab ≠ 0, ω ∈ ℂ with ω² ≠ 0, ab and g is a polynomial in ℂⁿ. In order to achieve a comprehensive and thorough analysis, we study the characteristics of solutions in two specific cases: one when ω² ≠ 0, ab and the other when ω = 0. Because polynomials in several complex variables may exhibit periodic behavior, a property that differs from polynomials in single complex variables, our study of finding solutions of equations in ℂⁿ is significant. The main results of the paper improved several known results in ℂⁿ for n ≥ 2. Additionally, the corollaries generalize results of Xu et al. [Rocky Mountain J. Math. 52(6) (2022), 2169-2187] for trinomial equations with arbitrary coefficients in ℂⁿ. Finally, we provide examples that endorse the validity of the conclusions drawn from the main results and their related remarks.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2008년도 학술대회
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• pp.84-91
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• 2008

Generalized hydrodynamic (GH) theory for multi-species gas and the computational models are developed for the numerical simulation of hypersonic rarefied gas flow on the basis of Eu's GH theory. The rotational non-equilibrium effect of diatomic molecules is taken into account by introducing excess normal stress associated with the bulk viscosity. The numerical model for the diatomic GH theory is developed and tested. Moreover, with the experience of developing the dia-tomic GH computational model, the GH theory is extended to a multi-species gas including 5 species; O$_2$, N$_2$, NO, O, N. The multi-species GH model includes diffusion relation due to the molecular collision and thermal phenomena. Two kinds of GH models are developed for an axisymmetric flow solver. By compar-ing the computed results of diatomic and multi-species GH theories with those of the Navier-Stokes equations and the DSMC results, the accuracy and physical consistency of the GH computational models are examined.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2008년 추계학술대회논문집
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• pp.84-91
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• 2008

Generalized hydrodynamic (GH) theory for multi-species gas and the computational models are developed for the numerical simulation of hypersonic rarefied gas flow on the basis of Eu's GH theory. The rotational non-equilibrium effect of diatomic molecules is taken into account by introducing excess normal stress associated with the bulk viscosity. The numerical model for the diatomic GH theory is developed and tested. Moreover, with the experience of developing the dia-tomic GH computational model, the GH theory is extended to a multi-species gas including 5 species; $O_2,\;N_2$, NO, O, N. The multi-species GH model includes diffusion relation due to the molecular collision and thermal phenomena. Two kinds of GH models are developed for an axisymmetric flow solver. By compar-ing the computed results of diatomic and multi-species GH theories with those of the Navier-Stokes equations and the DSMC results, the accuracy and physical consistency of the GH computational models are examined.