• Bulletin of the Korean Mathematical Society
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• v.59 no.1
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• pp.191-202
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• 2022

In this paper, we obtain the quantitative weighted bounds of oscillatory singular integral with rough kernel. Moreover, the quantitative weighted bounds of maximally truncated oscillatory singular integral with rough kernel are also obtained.

• Journal of the Korean Mathematical Society
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• v.46 no.3
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• pp.577-588
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• 2009

In this paper, the author studies the k-th commutators of oscillatory singular integral operators with a BMO function and phases more general than polynomials. For 1 < p < $\infty$, the $L^p$-boundedness of such operators are obtained provided their kernels belong to the spaces $L(log+L)^{k+1}(S^{n-1})$. The results of the corresponding maximal operators are also established.

• Honam Mathematical Journal
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• v.33 no.1
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• pp.1-9
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• 2011

In this paper we study oscillatory integrals with analytic homogeneous phase functions for smooth radial functions. We give their sharp asymptotic behavior in terms of spherical Newton distance.

• Journal of the Korean Society for Precision Engineering
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• v.16 no.4 s.97
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• pp.197-204
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• 1999

The boundary element method was used for studying singularities of an interface crack with contact zones. The iterative procedure is applied to estimate the contact zone size. Because the contact zone size was extremely small in a tension field, a large number of Gaussian points were used for numerical integration of the Kernels. Stress extrapolation method and J-integral were used ofr determining stress intensity factors. When the interface crack was assumed to have opened tips, oscillatory singularities appear near the tips of the interface crack. But the interface crack with contact zone which Comninou suggested had no oscillatory behavior. The contact zone size under shear loading was much larger than that under tensile. The stress intensity factors computed by stress extrapolation method were close to those of Comninou's solution. And the stress intensity factor evaluated by J-integral was similar to that by stress extrapolation method.

• Kyungpook Mathematical Journal
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• v.31 no.2
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• pp.151-154
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• 1991

• Journal of applied mathematics & informatics
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• v.40 no.1_2
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• pp.267-281
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• 2022

Herein, an algorithm for efficient evaluation of oscillatory Fourier-integrals with Jacobi-Cauchy type singularities is suggested. This method is based on the use of the traditional Clenshaw-Curtis (CC) algorithms in which the given function is approximated by the truncated Chebyshev series, term by term, and the oscillatory factor is approximated by using Bessel function of the first kind. Subsequently, the modified moments are computed efficiently using the numerical steepest descent method or special functions. Furthermore, Algorithm and programming code in MATHEMATICA^® 9.0 are provided for the implementation of the method for automatic computation on a computer. Finally, selected numerical examples are given in support of our theoretical analysis.

• Communications of the Korean Mathematical Society
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• v.18 no.4
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• pp.755-765
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• 2003

Krylov-Bogoliubov-Mitropolskii method has been extended to obtain asymptotic solution of n-th order nonlinear differential system characterized by certain non-oscillatory processes. The damping force is considered in such a manner that one of the characteristic roots of the linear system becomes small and others are in integral multiple. The method is illustrated by an example. The solutions for different initial conditions show a good agreement with those obtained by numerical method.

• Journal of Korean Society of Disaster and Security
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• v.6 no.3
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• pp.1-8
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• 2013

Based on random vibration theory, a procedure for calculating the dynamic response of the tall building to time-dependent random excitation is developed. In this paper, the fluctuating along- wind load is assumed as time-dependent random process described by the time-independent random process with deterministic function during a short duration of time. By deterministic function A(t)=1-exp($-{\beta}t$), the absolute value square of oscillatory function is represented from author's studies. The time-dependent random response spectral density is represented by using the absolute value square of oscillatory function and equivalent wind load spectrum of Solari. Especially, dynamic mean square response of the tall building subjected to fluctuating wind loads was derived as analysis function by the Cauchy's Integral Formula and Residue Theorem. As analysis examples, there were compared the numerical integral analytic results with the analysis fun. results by dynamic properties of the tall uilding.

• Kyungpook Mathematical Journal
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• v.46 no.3
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• pp.377-387
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• 2006

In this paper, we study the $L^p$ mapping properties of singular integral operators related to homogeneous mappings on product spaces with kernels which belong to $L(log^+\;L)^2$. Our results extend as well as improve some known results on singular integrals.

• Ocean and Polar Research
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• v.25 no.1
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• pp.63-74
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• 2003

The build-up of the heat field in shallow coastal water due to a point source has been investigated using an analytical solution of a time-integral form derived by extending the solutions by Holley(1969) and also presented in Harleman (1971). The uniform water depth is assumed with non-isotropic turbulent dispersion. The alongshore-flow is assumed to be uni-directional, spatially uniform and oscillatory. Due to the presence of the oscillatory alongshore-flow, the heat build-up occurs in an oscillatory manner, and the excess temperature thereby fluctuates in that course and even in the quasi-steady state. A series of calculations reveal that proper choices of the decay coefficient as well as dispersion coefficients are critical to the reliable prediction of the excess temperature field. The dispersion coefficients determine the absolute values of the excess temperature and characterize the shoreline profile, particularly within the tidal excursion distance, while the decay coefficient determines the absolute value of the excess temperature and the convergence rate to that of the quasi-steady state. Within the e-folding time scale $1/k_d$ (where $k_d$ is the heat decay coefficient), heat build-up occurs more than 90% of the quasi-steady state values in a region within a tidal excursion distance (L), while occurs increasingly less the farther we go to the downstream direction (about 80% at 1.25L, and 70% at 1.5L). Calculations with onshore and offshore discharges indicate that thermal spreading in the direction of the shoreline is reduced as the shoreline constraint which controls the lateral mixing is reduced. The importance of collecting long-term records of in situ meteorological conditions and clarifying the definition of the heat loss coefficient is addressed. Interactive use of analytical and numerical modeling is recommended as a desirable way to obtain a reliable estimate of the far-field excess temperature along with extensive field measurements.