• Korean Journal of Materials Research
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• v.11 no.3
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• pp.207-214
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• 2001

Silica glass is a core material for optical fiber in optical telecommunications, but its centrosymmetry eliminates the second order nonlinearity. But it is experimentally well known that the space charge polarization induces the Second Harmonic Generation (SHG) when a strong DC voltage is applied to silica glass for a long period of time with metal blocking electrodes. In this report, the results of a theoretical calculation of the nonlinear optical property caused by the space charge polarization, and a model of a numerical analysis to predict the small chance in nonlinear optical property as functions of time and space are provided. Assuming that amorphous silica is a solid state electrolyte and sodium ion is the only mobile charge carrier, 'Finite Difference Method' was employed for modeling of numerical analysis. The distributions of the concentration of sodium ion and electric field as functions of a normalized length of the specimen and a normalized applied voltage were simulated.

• The KSFM Journal of Fluid Machinery
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• v.7 no.2 s.23
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• pp.7-13
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• 2004

In an attempt to solve multiobjective optimization problems, weighted sum method is most widely used for the advantage that a designer can consider the relative significance of each object functions by weight values but it can be highly sensitive to weight vector and occasionally yield a deviated optimum from the relative weighting values designer designated because the multiobjective function has the form of simple sum of the product of the weighting values and the object functions in traditional approach. To search the design solution agree well to the designer's weighting values, we proposed new multiobjective function which was the functional of each normalized objective functions and considered to find the design solution comparing the distance between the characteristic line and the ideal optimum. In this study, proposed multiobjective function was applied to design high efficiency and low noise axial flow fan and the result shows this approach is effective for the case that the quality of the design can be highly affected by the designer's subjectiveness represented as weighting values in multiobjective design optimization process.

• Journal of Advanced Navigation Technology
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• v.18 no.1
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• pp.78-83
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• 2014

In this paper, the solutions of TM (transverse magnetic) scattering problems by perfectly conducting strip grating on two dielectric layers are analyzed by applying the FGMM (Fourier Galerkin moment method) as a numerical method. For the TM scattering problem, the induced surface current density is expected to the very high value at both edges of the strip, then the induced surface current density on the strip is expanded in a series of the multiplication of the functions of appropriate edge boundary condition and the Chebyshev polynomials of the first kind. The numerical results are obtained for the magnitude of induced current density, the normalized reflected power and transmitted power. The numerical results using proposed functions were improved the convergence faster than existing exponential functions, and the numerical results shown the good agreement compared to those of the existing papers.

• Journal of Mechanical Science and Technology
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• v.20 no.3
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• pp.426-434
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• 2006

The impact of leakage was incorporated into the transfer functions of the complex head and discharge. The impedance transfer functions for the various leaking pipeline systems were also derived. Hydraulic transients could be efficiently analyzed by the developed method. The simulation of normalized pressure variation using the method of characteristics and the impulse response method shows good agreement to the condition of turbulent flow. The leak calibration could be performed by incorporation of the impulse response method with Genetic Algorithm (GA) and Harmony Search (HS). The objective functions for the leakage detection can be made using the pressure-head response at the valve, or the pressure-head or the flow response at a certain point of the pipeline located upstream from the valve. The proposed method is not constrained by the Courant number to control the numerical dissipation of the method of characteristics. The limitations associated with the discreteness of the pipeline system in the inverse transient analysis can be neglected in the proposed method.

• Kyungpook Mathematical Journal
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• v.53 no.1
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• pp.13-23
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• 2013

In this present work, the authors obtain Fekete-Szeg$\ddot{o}$ inequality for certain normalized analytic function $f(z)$ defined on the open unit disk for which $$\frac{{\lambda}{\beta}z^3(L(a,c)f(z))^{{\prime}{\prime}{\prime}}+(2{\lambda}{\beta}+{\lambda}-{\beta})z^2(L(a,c)f(z))^{{\prime}{\prime}}+z(L(a,c)f(z))^{{\prime}}}{{\lambda}{\beta}z^2(L(a,c)f(z))^{{\prime}{\prime}}+({\lambda}-{\beta})z(L(a,c)f(z))^{\prime}+(1-{\lambda}+{\beta})(L(a,c)f(z))}\;(0{\leq}{\beta}{\leq}{\lambda}{\leq}1)$$ lies in a region starlike with respect to 1 and is symmetric with respect to the real axis. Also certain applications of the main result for a class of functions defined by Hadamard product (or convolution) are given. As a special case of this result, Fekete-Szeg$\ddot{o}$ inequality for a class of functions defined through fractional derivatives are obtained.

• 유체기계공업학회:학술대회논문집
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• 2003.12a
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• pp.397-403
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• 2003

In an attempt to solve multiobjective optimization problems, weighted sum method is most widely used for the advantage that a designer can consider the relative significance of each object functions by weight values but it can be highly sensitive to weight vector and occasionally yield a deviated optimum from the relative weighting values designer designated because the multiobjective function has the form of simple sum of the product of the weighting values and the object functions in traditional approach. To search the design solution well agree to the designer's weighting values, we proposed new multiobjective function which is the functional of each normalized objective functions and considered to find the design solution comparing the distance between the characteristic line and the ideal optimum. In this study, proposed multiobjective function was applied to design high efficiency and low noise axial flow fan and the result shows this approach will be effective for the case that the qualify of the design can be highly affected by the designer's subjectiveness represented as weighting values in multiobjective design optimization process.

• Bulletin of the Korean Mathematical Society
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• v.55 no.3
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• pp.957-965
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• 2018

We study the class $C{\mathcal{V}} ({\Omega})$ of analytic functions f in the unit disk ${\mathbb{D}}=\{z{\in}{\mathbb{C}}$ : ${\mid}z{\mid}$ < 1} of the form $f(z)=z+{\sum}_{n=2}^{\infty}a_nz^n$ satisfying $$1+\frac{zf^{{\prime}{\prime}}(z)}{f^{\prime}(z)}{\in}{\Omega},\;z{\in}{\mathbb{D}}$$, where ${\Omega}$ is a convex and proper subdomain of $\mathbb{C}$ with $1{\in}{\Omega}$. Let ${\phi}_{\Omega}$ be the unique conformal mapping of $\mathbb{D}$ onto ${\Omega}$ with ${\phi}_{\Omega}(0)=1$ and ${\phi}^{\prime}_{\Omega}(0)$ > 0 and $$k_{\Omega}(z)={\displaystyle\smashmargin{2}{\int\nolimits_{0}}^z}{\exp}\({\displaystyle\smashmargin{2}{\int\nolimits_{0}}^t}{\zeta}^{-1}({\phi}_{\Omega}({\zeta})-1)d{\zeta}\)dt$$. Let $z_0,z_1{\in}{\mathbb{D}}$ with $z_0{\neq}z_1$. As the first result in this paper we show that the region of variability $\{{\log}\;f^{\prime}(z_1)-{\log}\;f^{\prime}(z_0)\;:\;f{\in}C{\mathcal{V}}({\Omega})\}$ coincides wth the set $\{{\log}\;k^{\prime}_{\Omega}(z_1z)-{\log}\;k^{\prime}_{\Omega}(z_0z)\;:\;{\mid}z{\mid}{\leq}1\}$. The second result deals with the case when ${\Omega}$ is the right half plane ${\mathbb{H}}=\{{\omega}{\in}{\mathbb{C}}$ : Re ${\omega}$ > 0}. In this case $CV({\Omega})$ is identical with the usual normalized class of convex univalent functions on $\mathbb{D}$. And we derive the sharp upper bound for ${\mid}{\log}\;f^{\prime}(z_1)-{\log}\;f^{\prime}(z_0){\mid}$, $f{\in}C{\mathcal{V}}(\mathbb{H})$. The third result concerns how far two functions in $C{\mathcal{V}}({\Omega})$ are from each other. Furthermore we determine all extremal functions explicitly.

• Korean Journal of Mathematics
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• v.24 no.3
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• pp.409-445
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• 2016

The class $\mathcal{W}^{\delta}_{\beta}({\alpha},{\gamma})$ defined in the domain ${\mid}z{\mid}$ < 1 satisfying $Re\;e^{i{\phi}}\((1-{\alpha}+2{\gamma})(f/z)^{\delta}+\({\alpha}-3{\gamma}+{\gamma}\[1-1/{\delta})(zf^{\prime}/f)+1/{\delta}\(1+zf^{\prime\prime}/f^{\prime}\)\]\)(f/z)^{\delta}(zf^{\prime}/f)-{\beta}\)$ > 0, with the conditions ${\alpha}{\geq}0$, ${\beta}$ < 1, ${\gamma}{\geq}0$, ${\delta}$ > 0 and ${\phi}{\in}{\mathbb{R}}$ generalizes a particular case of the largest subclass of univalent functions, namely the class of $Bazilevi{\check{c}}$ functions. Moreover, for 0 < ${\delta}{\leq}{\frac{1}{(1-{\zeta})}}$, $0{\leq}{\zeta}$ < 1, the class $C_{\delta}({\zeta})$ be the subclass of normalized analytic functions such that $Re(1/{\delta}(1+zf^{\prime\prime}/f^{\prime})+1-1/{\delta})(zf^{\prime}/f))$ > ${\zeta}$, ${\mid}z{\mid}$<1. In the present work, the sucient conditions on ${\lambda}(t)$ are investigated, so that the non-linear integral transform $V^{\delta}_{\lambda}(f)(z)=\({\large{\int}_{0}^{1}}{\lambda}(t)(f(tz)/t)^{\delta}dt\)^{1/{\delta}}$, ${\mid}z{\mid}$ < 1, carries the fuctions from $\mathcal{W}^{\delta}_{\beta}({\alpha},{\gamma})$ into $C_{\delta}({\zeta})$. Several interesting applications are provided for special choices of ${\lambda}(t)$. These results are useful in the attempt to generalize the two most important extremal problems in this direction using duality techniques and provide scope for further research.

• Structural Engineering and Mechanics
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• v.53 no.4
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• pp.703-723
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• 2015

In this paper optimization of volume fraction distribution in a thick hollow cylinder with finite length made of two-dimensional functionally graded material (2D-FGM) and subjected to steady state thermal and mechanical loadings is considered. The finite element method with graded material properties within each element (graded finite elements) is used to model the structure. Volume fractions of constituent materials on a finite number of design points are taken as design variables and the volume fractions at any arbitrary point in the cylinder are obtained via cubic spline interpolation functions. The objective function selected as having the normalized effective stress equal to one at all points that leads to a uniform stress distribution in the structure. Genetic Algorithm jointed with interior penalty-function method for implementing constraints is effectively employed to find the global solution of the optimization problem. Obtained results indicates that by using the uniform distribution of normalized effective stress as objective function, considerably more efficient usage of materials can be achieved compared with the power law volume fraction distribution. Also considering uniform distribution of safety factor as design criteria instead of minimizing peak effective stress affects remarkably the optimum volume fractions.

• Nuclear Engineering and Technology
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• v.33 no.3
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• pp.270-282
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• 2001

A simple measure of uncertainty importance based on normalized metric distance to quantify the entire change of cumulative distribution functions (CDFs) has been developed for use in probability safety assessments (PSAs). The metric distance measure developed in this study reflects the relative impact of distributional changes of inputs on the change of an output distribution, white most of the existing uncertainty importance measures reflect the magnitude of relative contribution of input uncertainties to the output uncertainty. Normalization is made to make the metric distance measure a dimensionless quantity. The present measure has been evaluated analytically for various analytical distributions to examine its characteristics. To illustrate the applicability and strength of the present measure, two examples are provided. The first example is an application of the present measure to a typical problem of a system fault tree analysis and the second one is for a hypothetical non-linear model. Comparisons of the present result with those obtained by existing uncertainty importance measures show that the metric distance measure is a useful tool to express the measure of uncertainty importance in terms of the relative impact of distributional changes of inputs on the change of an output distribution.