• Journal of the Chungcheong Mathematical Society
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• v.21 no.1
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• pp.21-28
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• 2008

In this paper, we give the Riemann-type extensions of Dunford integral and Pettis integral, C-Dunford integral and C-Pettis integral. We prove that a function f is C-Dunford integrable if and only if $x^*f$ is C-integrable for each $x^*{\in}X^*$ and prove the controlled convergence theorem for the C-Pettis integral.

• The Pure and Applied Mathematics
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• v.6 no.1
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• pp.17-25
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• 1999

In this paper, we investigate the properties of the Dunford-Schwartz integral (the integral with respect to a finitely additive measure). Though it is not equivalent to the cylinder integral, we can show that a cylinder probability v on (H, C) can be extend as a finitely additive probability measure $\hat{v}$ on a field $\hat{C}{\;}{\supset}{\;}C$ which is equivalent to the Dunford-Schwartz integral on ($H,{\;}\hat{C},{\;}\hat{v}$).

• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.5
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• pp.795-802
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• 2002

For assessing significance of a defect in a component operating at high (creeping) temperatures, accurate estimation of fracture mechanics parameter, $C^{*}$-integral, is essential. Although the J estimation equation in the GE/EPRl handbook can be used to estimate the $C^{*}$-integral when the creep -deformation behavior can be characterized by the power law creep, such power law creep behavior is a very poor approximation for typical creep behaviors of most materials. Accordingly there can be a significant error in the $C^{*}$-integral. To overcome problems associated with GE/EPRl approach, the reference stress approach has been proposed, but the results can be sometimes unduly conservative. In this paper, a new method to estimate the $C^{*}$-integral for deflective components is proposed. This method improves the accuracy of the reference stress approach significantly. The proposed calculations are then validated against elastic -creep finite element (FE) analyses for four different cracked geometries following various creep -deformation constitutive laws. Comparison of the FE $C^{*}$-integral values with those calculated from the proposed method shows good agreements.greements.

• Journal of the Korean Mathematical Society
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• v.53 no.6
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• pp.1261-1273
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• 2016

In this paper, we analyze the necessary and sufficient condition introduced in [5]: that a functional F in $L^2(C_{a,b}[0,T])$ has an integral transform ${\mathcal{F}}_{{\gamma},{\beta}}F$, also belonging to $L^2(C_{a,b}[0,T])$. We then establish the inverse integral transforms of the functionals in $L^2(C_{a,b}[0,T])$ and then examine various properties with respect to the inverse integral transforms via the translation theorem. Several possible outcomes are presented as remarks. Our approach is a new method to solve some difficulties with respect to the inverse integral transform.

• Korean Journal of Mathematics
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• v.14 no.2
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• pp.169-183
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• 2006

In this paper, we define and study the C-integral and the strong C-integral of functions mapping an interval [a,b] into a Banach space X. We prove that the C-integral and the strong C-integral are equivalent if and only if the Banach space is finite dimensional, We also consider the property of primitives corresponding to Banach-valued functions with respect to the C-integral and the strong C-integral.

• East Asian mathematical journal
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• v.23 no.2
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• pp.229-246
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• 2007

Some inequalities related to the $H{\ddot{o}}lder$ integral inequality and applications for bounding the ${\check{C}}eby{\check{s}}ev$ functional are given.

• Communications of the Korean Mathematical Society
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• v.22 no.1
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• pp.27-39
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• 2007

In this paper, we define and study the C-integral of functions mapping an interval [a,b] into a Banach space X and discuss the relations among Henstock integral, C-integral and McShane integral. We also study the Denjoy extension of the C-integral.

• Communications of the Korean Mathematical Society
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• v.21 no.1
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• pp.75-88
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• 2006

Wiener measure and Wiener measurability behave badly under the change of scale transformation. We express the analytic Feynman integral over $C_0(B)$ as a limit of Wiener integrals over $C_0(B)$ and establish change of scale formulas for Wiener integrals over $C_0(B)$ for some functionals.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.1
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• pp.83-90
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• 2010

In this paper, we prove convergence theorems for the C-integral.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.3
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• pp.607-613
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• 2009

In this paper, we define the C-integral and prove the integration by parts formula for the C-integral.