• Journal of the Korean Mathematical Society
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• v.45 no.6
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• pp.1561-1576
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• 2008

In this paper we shall prove some weighted norm inequalities of the form $${\int}_{R^n}\;|Tf(x)|^pu(x)dx\;{\leq}\;C_p\;{\int}_{R^n}\;|f(x)|^pNu(x)dx$$ for certain rough singular integral T and maximal singular integral $T^*$. Here u is a nonnegative measurable function on $R^n$ and N denotes some maximal operator. As a consequence, some vector valued inequalities for both T and $T^*$ are obtained. We shall also get a boundedness result of T on the Triebel-Lizorkin spaces.

• Journal of Ocean Engineering and Technology
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• v.18 no.1
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• pp.7-9
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• 2004

Using the solution to th contour integral of the complex logarithmic function ${\oint}_cIn(z-z_{0})dz$, the following definite integral, derived from the formula to calculate the forces exerted to n circular cylinder by the discrete vortices shed from it, has been evaluated (equation omitted)

• Transactions of the Korean Society of Mechanical Engineers A
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• v.36 no.7
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• pp.759-768
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• 2012

This paper proposes a method to determine the elastic follow-up factors for the $C(t)$-integral under secondary stress. The rate of creep crack growth for transient creep is correlated with the $C(t)$-integral. Elastic follow-up behavior, which occurs in structures under secondary loading, prevents a relaxation of stress during transient creep. Thus, both the values of $C(t)$ and creep crack growth increase as increasing elastic follow-up. An estimation solution for $C(t)$ was proposed by Ainsworth and Dean based on the reference stress method. To predict the value of $C(t)$ using this solution, an independent method to determine the elastic follow-up factors for cracked bodies is needed. This paper proposed that the elastic follow-up factors for $C(t)$ can be determined by elastic-plastic analyses using the plastic-creep analogy. Finite element analyses were performed to verify this method.

• Kyungpook Mathematical Journal
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• v.49 no.1
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• pp.155-166
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• 2009

We give a necessary and sufficient condition that a square integrable functional F(x) on Yeh-Wiener space has an integral transform $\hat{F}_{{\alpha},{\beta}}F(x)$ which is also square integrable. This extends the result by Kim and Skoug for functional F(x) in $L_2(C_0[0,T])$.

• Korean Journal of Mathematics
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• v.28 no.1
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• pp.17-30
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• 2020

In this paper, we firstly introduce the class of C^*-algebra valued symmetric spaces and utilize the same to prove our fixed point results. We furnish an example to highlight the utility of our main result. Finally, we apply our result to examine the existence and uniqueness of a solution for a system of Fredholm integral equations.

• Journal of the Chungcheong Mathematical Society
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• v.10 no.1
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• pp.17-22
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• 1997

Let B be the open unit ball in the complex space $\mathbb{C}^n$. A holomorphic function $f:B{\rightarrow}C$ which satisfies sup{(1- ${\parallel}\;{\nabla}_zf\;{\parallel}\;{\mid}z{\in}B$} < $+{\infty}$ is called Bloch type function. In this paper, we will find some integral representation of Bloch type functions.

• Korean Journal of Mathematics
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• v.27 no.2
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• pp.445-463
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• 2019

Let C[0, T] denote the space of continuous real-valued functions on [0, T]. On the space C[0, T], we introduce a Banach algebra of series of functions which are generalized Fourier-Stieltjes transforms of measures of finite variation on the product of simplex and Euclidean space. We evaluate analytic Feynman integrals of the functions in the Banach algebra which play significant roles in the Feynman integration theory and quantum mechanics.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.9
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• pp.2133-2141
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• 1995

The thermo-mechanical fatigue tests were performed on the specimens extracted from 1.5Cr-0. 67Mo-0.33V alloy. The characteristics of thermo-mechanical fatigue crack propagation were examined and reviewed in view of fracture mechanics. The results obtained from the present study are summarized as follows : (1) The propagation characteristics of isothermal low-cycle fatigue crack are dominated by .DELTA.J$_{f}$ in case of PP waveform, and .DELTA.J$_{c}$ in case of CP waveform. (II)The propagation characteristics of thermo-mechanical fatigue crack are dominated by .DELTA.J$_{c}$ for in-phase case, and by .DELTA.J$_{c}$ for out-of-phase. The present results were in good agreement with the equation of propagation law for isothermal low-cycle fatigue crack in case of thermo-mechanical fatigue.tigue.e.

• Communications of the Korean Mathematical Society
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• v.35 no.4
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• pp.1193-1202
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• 2020

We consider the integral ${{\int}_{0}^{\infty}}(\frac{sin\;x}{x})^n\;dx$ as a function of the positive integer n. We show that there exists an asymptotic series in ${\frac{1}{n}}$ and compute the first terms of this series together with an explicit error bound.

• Bulletin of the Korean Mathematical Society
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• v.53 no.5
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• pp.1531-1548
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• 2016

Let C[0, t] denote the space of real-valued continuous functions on [0, t] and define a random vector $Z_n:C[0,t]{\rightarrow}\mathbb{R}^n$ by $Z_n(x)=(\int_{0}^{t_1}h(s)dx(s),{\ldots},\int_{0}^{t_n}h(s)dx(s))$, where 0 < $t_1$ < ${\cdots}$ < $ t_n=t$ is a partition of [0, t] and $h{\in}L_2[0,t]$ with $h{\neq}0$ a.e. Using a simple formula for a conditional expectation on C[0, t] with $Z_n$, we evaluate a generalized analytic conditional Wiener integral of the function $G_r(x)=F(x){\Psi}(\int_{0}^{t}v_1(s)dx(s),{\ldots},\int_{0}^{t}v_r(s)dx(s))$ for F in a Banach algebra and for ${\Psi}=f+{\phi}$ which need not be bounded or continuous, where $f{\in}L_p(\mathbb{R}^r)(1{\leq}p{\leq}{\infty})$, {$v_1,{\ldots},v_r$} is an orthonormal subset of $L_2[0,t]$ and ${\phi}$ is the Fourier transform of a measure of bounded variation over $\mathbb{R}^r$. Finally we establish various change of scale transformations for the generalized analytic conditional Wiener integrals of $G_r$ with the conditioning function $Z_n$.