• 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.

• Communications of the Korean Mathematical Society
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• v.34 no.2
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• pp.383-390
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• 2019

In this paper, we discuss special polynomials involving exponential distribution, which is related to life testing. We derive some identities of special polynomials such as the symmetric property, recurrence formula and so on. In addition, we investigate explicit properties of special polynomials by using their derivative and integral.

• Communications of the Korean Mathematical Society
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• v.37 no.2
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• pp.567-574
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• 2022

We use convolution techniques to define certain classes of starlike functions which are associated with Lommel operator. Some inclusion results are investigated. It is also shown that these classes are invariant under Bernardi integral operator.

• Communications of the Korean Mathematical Society
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• v.36 no.3
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• pp.485-494
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• 2021

In this article, we prove the existence of a solution to some classes of integral equations of generalized convolution type generated by the Kontorovich-Lebedev (K) transform, the Laplace (𝓛) transform and the Fourier (F) transform in some appropriate function spaces and represent it in a closed form.

• Bulletin of the Korean Mathematical Society
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• v.48 no.3
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• pp.655-672
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• 2011

Let $C^r$[0,t] be the function space of the vector-valued continuous paths x : [0,t] ${\rightarrow}$ $R^r$ and define $X_t$ : $C^r$[0,t] ${\rightarrow}$ $R^{(n+1)r}$ and $Y_t$ : $C^r$[0,t] ${\rightarrow}$ $R^{nr}$ by $X_t(x)$ = (x($t_0$), x($t_1$), ..., x($t_{n-1}$), x($t_n$)) and $Y_t$(x) = (x($t_0$), x($t_1$), ..., x($t_{n-1}$)), respectively, where 0 = $t_0$ < $t_1$ < ... < $t_n$ = t. In the present paper, with the conditioning functions $X_t$ and $Y_t$, we introduce two simple formulas for the conditional expectations over $C^r$[0,t], an analogue of the r-dimensional Wiener space. We establish evaluation formulas for the analogues of the analytic Wiener and Feynman integrals for the function $G(x)=\exp{{\int}_0^t{\theta}(s,x(s))d{\eta}(s)}{\psi}(x(t))$, where ${\theta}(s,{\cdot})$ and are the Fourier-Stieltjes transforms of the complex Borel measures on ${\mathbb{R}}^r$. Using the simple formulas, we evaluate the analogues of the conditional analytic Wiener and Feynman integrals of the functional G.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.13 no.9
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• pp.827-835
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• 2001

In this study, condensation heat transfer characteristics were conducted with special heat transfer tubes of SH-C type. Experiments were carried out the saturated vapor temperature of 334K and the wall subcooling of 1.5-4.5K. The refrigerant was R-113 and the enhanced tubes used in the present study were SH-CDR, SH-CYR and SH-CHR. The experimental results showed that the condensation heat transfer coefficients of SH-C type tubes were about 23-66% higher than those of a low integral-fin tube. It was visualized that the condensed liquid on the outer surface of SH-C type tubes flowed continuously down unlike a low integral-fin tube and a plain tube, due to a 3-D extending fin on the outer surface of SH-C type tubes. As a result, the thermal resistance of the condensed liquid decreased and the heat transfer coefficient increased. Also, the enhancement ratio of SH-CDR tube was the highest, and it was about 9-11 times as compared to that of a plain tube.

• Honam Mathematical Journal
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• v.42 no.2
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• pp.301-318
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• 2020

In this paper, we introduce and study the concept of hyperbolic type convexity functions and their some algebraic properties. We obtain Hermite-Hadamard type inequalities for this class of functions. In addition, we obtain some refinements of the Hermite-Hadamard inequality for functions whose first derivative in absolute value, raised to a certain power which is greater than one, respectively at least one, is hyperbolic convexity. Moreover, we compare the results obtained with both Hölder, Hölder-İşcan inequalities and power-mean, improved-power-mean integral inequalities.

• Journal of the Korean Chemical Society
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• v.22 no.3
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• pp.117-127
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• 1978

Slater type orbitals, located at two different points A and B, are expressed in a common coordinate system by expanding the spherical harmonics and the radial part of these orbitals in terms of the reference point A. Master formulas for two center overlap integrals are derived, using the general expansion formulas of slater type atomic orbitals. Two center overlap integrals for $CH_4,\;H_2O,\;NH_3,\;C_2H_6\;and\;PH_3$molecules are evaluated, using master formulas for two center overlap integrals. The results are in agreement with those of two center overlap integrals of Mulliken.

• The Transactions of the Korean Institute of Electrical Engineers C
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• v.51 no.8
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• pp.375-381
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• 2002

A rigorous analysis of a broad wall slot array is presented. The slot is longitudinal and offset from the center line in the rectangular waveguide. Pertinent integral equations are developed, taking into account finite wall thickness. The mothed of moment with entire basis function is used to solve a pair of coupled-integral equations, derived from the electromagnetic boundary conditions using modified Green's function, to find the tangential electric field on the upper and lower surfaces of the slot. Numerical results for resonant length and scattering parameters of the slots are Presented over a range of offset. Computed results are compared with experimental result.

• Journal of Mechanical Science and Technology
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• v.14 no.1
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• pp.11-18
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• 2000

Fracture toughness JIC and KIC tests were performed on A516 Gr70 carbon steel plate at the temperature ranging from -$160^{\circ}C$ to $600^{\circ}C$, and test results were analyzed according to ASTM E 813 and ASTM E 399. Unloading compliance J-integral tests were performed on 1TCT specimens. The relation between the $J_{IC}$ value and the test temperature was obtained. It was concluded that the temperature ranging from $-15^{\circ}C$ to $600^{\circ}C$ is the upper shelf region of ductile-brittle transition temperature, and in this temperature range, fracture toughness $J_{IC}$ values decreased with increasing temperature. The ductile brittle transition temperature of the material may be around $-30^{\circ}C$. In the region near $-30^{\circ}C$, the tendency of $J_{IC}$ to decrease with decreasing temperature was significant.