• 대한수학회지
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• 제44권2호
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• pp.455-466
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• 2007

The zero-distribution of the Fourier integral $${\int}^{\infty}_{-{\infty}}\;Q(u)e^{p(u)+^{izu}du$$, where P is a polynomial with leading term $-u^{2m}(m\;{\geq}\;1)$ and Q an arbitrary polynomial, is described. To this end, an asymptotic formula for the integral is established by applying the saddle point method.

• 대한수학회논문집
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• 제37권2호
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• pp.415-421
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• 2022

This paper presents a fundamental theorem of calculus, an integration by parts formula and a version of equiintegrability convergence theorem for the M_α-integral using the M_α-strong Lusin condition. In the convergence theorem, to be able to relax the condition of being point-wise convergent everywhere to point-wise convergent almost everywhere, the uniform M_α-strong Lusin condition was imposed.

• 대한수학회보
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• 제53권5호
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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 $Z_n$.

• 대한수학회논문집
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• 제29권3호
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• pp.429-437
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• 2014

Motivated by the recent investigations of several authors, in this paper we present a generalization of a result obtained recently by Choi et al. ([3]) involving hypergeometric identities. The result is obtained by suitably applying fractional calculus method to a generalization of the hypergeometric transformation formula due to Kummer.

• 한국통계학회:학술대회논문집
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• 한국통계학회 2005년도 춘계 학술발표회 논문집
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• pp.173-178
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• 2005

We derive an It${\hat{o}}$ formula for generalized functionals for the fractional Brownian sheet with arbitrary Hurst parameter ${H_1},\;H_2$ ${\epsilon}$ (0,1). As an application, we consider a stochastic integral representation for the local time of the fractional Brownian sheet.

• 대한수학회보
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• 제56권1호
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• pp.229-243
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• 2019

We use the so-called pseudoinversion of degenerate metrics technique on foliated compact null hypersurface, $M^{n+1}$, in Lorentzian manifold ${\overline{M}}^{n+2}$, to derive an integral formula involving the r-th order mean curvatures of its foliations, ${\mathcal{F}}^n$. We apply our formula to minimal foliations, showing that, under certain geometric conditions, they are isomorphic to n-dimensional spheres. We also use the formula to deduce expressions for total mean curvatures of such foliations.

• Journal of Advanced Marine Engineering and Technology
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• 제26권1호
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• pp.59-67
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• 2002

The comparison of $J_{Rice}$-resistance considering a few strength ratio in Rice J-integral formula and $J_{\delta}$-resistance curves converted from experimental CTOD using appropriate strength chosen according to strain hardening level, n=10.6 (A533B steel) and n=8.1 (BS4360 steel) is carried out. The optimal dimensionless strength ratio like the factor of revision, (see full text)reflecting strain hardening level in Rice\`s experimental formula is found out and the reliability of appropriate reference strength chosen according to strain hardening level in different materials is investigated through doing that CTOD is transformed from $J_{\delta}$-integral using relationship between J-integral and CTOD. The results are as follows; 1) The optimal factor of revision is when m equals to 3 in (see full text) for Rice's and the above optimal factor of revision multiplies by coefficient, η in Rice's experimental formula instead of n=2, 2) and the pertinent reference strength for high strain hardening material like BS4360 steel is ultimate strength, $\sigma_{u}$ and for material like A533B steel is ultimate-flow strength, $\sigma_{u-f}$. The incompatible of the behavior of both experimental J-resistance curves using Rice's formula and CTOD-resistance curves for A533B and BS4360 steel by Gordon, et al., could be corrected using the optimal factor of revision in Rice\`s and the pertinent reference strength in J=$m_{j}$${\times}$$\sigma_{i}$${\times}$CTOD.

• 충청수학회지
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• 제6권1호
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• pp.71-87
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• 1993

• 한국통계학회:학술대회논문집
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• 한국통계학회 2002년도 춘계 학술발표회 논문집
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• pp.55-60
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• 2002

We present an extension of the Wong-Zakai type approximation theorem for a multiple stochastic integral. Using a piecewise linear approximation $W^{(n)}$ of a Wiener process W, we prove that the multiple integral processes {${\int}_{0}^{t}{\cdots}{\int}_{0}^{t}f(t_{1},{\cdots},t_{m})W^{(n)}(t_{1}){\cdots}W^{(n)}(t_{m}),t{\in}[0,T]$} where f is a given symmetric function in the space $C([0,T]^{m})$, converge to the multiple Stratonovich integral of f in the uniform $L^{2}$-sense.

• 대한전기학회논문지:전력기술부문A
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• 제48권6호
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• pp.753-759
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• 1999

BPF(block pulse function) has been used widely in the system analysis and controller design. The integral operational matrix of BPF converts the system represented in the form of the differential equation into the algebraic problem. Therefore, it is important to reduce the error caused by the integral operational matrix. In this paper, a new integral operational matrix is derived from the approximating function using Lagrange's interpolation formula. Comparing the proposed integral operational matrix with another, the result by proposed matrix is closer to the real value than that by the conventional matrix. The usefulness of th proposed method is also verified by numerical examples.