• Journal of the Chungcheong Mathematical Society
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• v.26 no.4
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• pp.769-780
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• 2013

Motivated essentially by their potential for applications in a wide range of mathematical and physical problems, the log-sine and log-cosine integrals have been evaluated, in the existing literature on the subject, in many different ways. Very recently, Choi [6] presented explicit evaluations of some families of log-sine and log-cosine integrals by making use of the familiar Beta function. In the present sequel to the investigation [6], we evaluate the log-sine and log-cosine integrals involved in more complicated integrands than those in [6], by also using the Beta function.

• Bulletin of the Korean Mathematical Society
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• v.55 no.2
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• pp.599-610
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• 2018

We aim to present some formulas for Saigo hypergeometric fractional integral and differential operators involving (p, q)-extended Bessel function $J_{{\nu},p,q}(z)$, which are expressed in terms of Hadamard product of the (p, q)-extended Gauss hypergeometric function and the Fox-Wright function $_p{\Psi}_q(z)$. A number of interesting special cases of our main results are also considered. Further, it is emphasized that the results presented here, which are seemingly complicated series, can reveal their involved properties via those of the two known functions in their respective Hadamard product.

• Honam Mathematical Journal
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• v.41 no.1
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• pp.163-174
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• 2019

The veritable pursuit of this exegesis is to exhibit integrals affined with the Bessel-Struve kernel function, which are explicitly inscribed in terms of generalized (Wright) hypergeometric function and also the product of generalized (Wright) hypergeometric function with sum of two confluent hypergeometric functions. Somewhat integrals involving exponential functions, modified Bessel functions and Struve functions of order zero and one are also obtained as special cases of our chief results.

• Bulletin of the Korean Mathematical Society
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• v.32 no.1
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• pp.123-132
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• 1995

Our interest is to study the existence of positive solutions to the following elliptic system involving competing interaction $$ (1) { -\partial(x,u,\upsilon)\Delta u = uf(x,u,v) { - \psi(x,u,\upsilon)\Delta \upsilon = \upsilon g(x,u,\upsilon) { \frac{\partial n}{\partial u} + ku = 0 on \partial\Omega { \frac{\partial n}{\partial\upsilon} + \sigma\upsilon = 0 $$ in a bounded region $\Omega$ in $R^n$ with a smooth boundary, where the diffusion terms $\varphi, \psi$ are strictly positive nondecreasing function, and k, $\sigma$ are positive constants. Also we assume that the growth rates f, g are $C^1$ monotone functions. The variables u, $\upsilon$ may represent the population densities of the interacting species in problems from ecology, microbiology, immunology, etc.

• Journal of the Korean Mathematical Society
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• v.45 no.6
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• pp.1753-1767
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• 2008

Consider the nonparametric regression model $Y_{ni}\;=\;g(x_{ni})+{\epsilon}_{ni}$ ($1\;{\leq}\;i\;{\leq}\;n$), where g($\cdot$) is an unknown regression function, $x_{ni}$ are known fixed design points, and the correlated errors {${\epsilon}_{ni}$, $1\;{\leq}\;i\;{\leq}\;n$} have the same distribution as {$V_i$, $1\;{\leq}\;i\;{\leq}\;n$}, here $V_t\;=\;{\sum}^{\infty}_{j=-{\infty}}\;{\psi}_je_{t-j}$ with ${\sum}^{\infty}_{j=-{\infty}}\;|{\psi}_j|$ < $\infty$ and {$e_t$} are negatively associated random variables. Under appropriate conditions, we derive a Berry-Esseen type bound for the estimator of g($\cdot$). As corollary, by choice of the weights, the Berry-Esseen type bound can attain O($n^{-1/4}({\log}\;n)^{3/4}$).

• Bulletin of the Korean Mathematical Society
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• v.50 no.3
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• pp.761-766
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• 2013

We derive several modular equations and present their proofs based on concise algebraic computations. In addition, we establish explicit relations and formulas for some parameterizations for the theta functions ${\varphi}$ and ${\psi}$ and show some applications of the modular equations to evaluations of the cubic continued fraction and the theta function ${\psi}$.

• Proceedings of the Korean Society For Composite Materials Conference
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• 2003.10a
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• pp.141-145
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• 2003

The FBG sensors are inserted on the liners of the filament wound pressure tanks. The strains near the welding region of the liners are monitored in the hydro-pressurizing tests. The hydro-pressurizing tests consist of the proof tests at 4500 or 3300 psi and repeated test at the operating pressure, 3000 psi. The FBG sensors work well under $3000\mu\varepsilon$, but the strains calculated from the reflected signals are instable at the high strain level. The transverse compression on the sensor head results in the split of the reflected peaks, and the calculating algorism from the split peaks is not robust under the various signal condition. The FBG sensors fracture near $7500\mu\varepsilon$ level and lose their function permanently.

• Elastomers and Composites
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• v.32 no.3
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• pp.173-178
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• 1997

In this study, the ultrasonic irradiation in elevated pressure was used to alter the molecular weight and MWD of polystyrene. The high pressure reactor was filled with 0.5w/v% polystyrene solution, and then it was pressurized from 500psi to 4000psi. The ultrasound was irradiated in 10 minutes at each pressure, and the extract was collected and analyzed by GPC. Molecular weight distribution was predicted by log-normal and Schulz distribution function. The average molecular weight and polydispersity of polystyrene were decreased, as the pressure applied during the ultrasonic irradiation was increase. It was able to fractionate polymer material and control polydispersity by adjusting pressure in the ultrasonic irradiation.

• International Journal of Precision Engineering and Manufacturing
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• v.7 no.4
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• pp.57-62
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• 2006

The quality of precision spindle units (S/Us) running on rolling bearings depends strongly on their structural parameters, such as the configuration and geometry of the S/U elements and bearing preloads. When S/Us are designed, their parameters should be optimized to improve the performance characteristics. However, it is practically impossible to state perfectly a general criterion function for S/U quality. Therefore, we propose to use a multicriteria optimization based on the parameter space investigation (PSI) method We demonstrate the efficiency of the proposed method using the optimization results of high-speed S/Us.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.3
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• pp.417-428
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• 2016

We discuss and obtain some existence theorems of unique point of coincidence for two mappings satisfying ${\varphi}$-contractive conditions or ${\psi}$-${\phi}$-contractive conditions determined by semi-continuous functions on non-complete 2-metric spaces, in which the mappings do not satisfy commutativity and uniform boundedness. The obtained results generalize and improve many well-known and corresponding conclusions.