• Journal of the Korean Mathematical Society
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• v.44 no.6
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• pp.1329-1338
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• 2007

In this paper, we study the location of zeros and Borel direction for the solutions of linear homogeneous differential equations $$f^{(n)}+A_{n-1}(z)f^{(n-1)}+{\cdots}+A_1(z)f#+A_0(z)f=0$$ with entire coefficients. Results are obtained concerning the rays near which the exponent of convergence of zeros of the solutions attains its Borel direction. This paper extends previous results due to S. J. Wu and other authors.

• Korean Journal of Mathematics
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• v.13 no.1
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• pp.113-122
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• 2005

We consider the iterative schemes for the large sparse linear system to solve partial differential equations. Using spectral radius of iteration matrices, the optimal relaxation parameters and good parameters can be obtained. With those parameters we compare the effectiveness of the SOR and SSOR algorithms. Applying Crank-Nicolson approximation, we observe the error distribution according to domain decomposition. The number of processors due to domain decomposition affects time and error. Numerical experiments show that effectiveness of SOR and SSOR can be reversed as time size varies, which is not the usual case. Finally, these phenomena suggest conjectures about equilibrium time grid for SOR and SSOR.

• Bulletin of the Korean Mathematical Society
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• v.50 no.5
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• pp.1415-1432
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• 2013

We consider the value distribution of a class of the functions analytic in the exterior of a disc and their applications to complex oscillation theory of differential equations with periodic coefficients in the complex plane.

• Bulletin of the Korean Mathematical Society
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• v.53 no.5
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• pp.1411-1425
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• 2016

We provide a partial differential equation for European options on a stock whose price process follows a general geometric Riemannian Brownian motion. The existence and the uniqueness of solutions to the partial differential equation are investigated, and then an expression of the value for European options is obtained using the fundamental solution technique. Proper Riemannian metrics on the real number field can make the distribution of return rates of the stock induced by our model have the character of leptokurtosis and fat-tail; in addition, they can also explain option pricing bias and implied volatility smile (skew).

• The Pure and Applied Mathematics
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• v.3 no.1
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• pp.47-52
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• 1996

We consider the third order linear homogeneous differential equation L$_3$(y) = y(equation omitted) ＋ P($\chi$)y' ＋ Q($\chi$)y = 0 (E) P($\chi$) $\geq$ 0, Q($\chi$) ＞ 0 and P($\chi$)/Q($\chi$) is nondecreasing on [${\alpha}$, $\infty$) for some real number ${\alpha}$. (1) In this paper we discuss the distribution of zeros of solutions and a condition of oscillatory for equation (E).(omitted)

• Proceedings of the KIEE Conference
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• 1995.07c
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• pp.1229-1231
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• 1995

XLPE cable, which has excellent electrical and thermal performance, has been widely used for HV transmission & distribution lines. The most important thing to produce the cable products having good performance is to set the optimal operating conditions of cable machinery. Because it is very difficult to measure the temperature of cable under curing process practically, it is necessary to evaluate the cable temperature by using the method to simulate real conditions numerically. In this work, We investigate the basic theory on transient heat transfer between curing tube and cable for making a numerical simulation program using computer. In this program, a differential equation is approximated by a infinite differential method and a few assumptions are used to simplify the model and minimize the calculation time of program.

• Structural Engineering and Mechanics
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• v.50 no.3
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• pp.403-417
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• 2014

The present paper addresses a general formulation for the thermo elastic analysis of a functionally graded cylindrical shell subjected to external loads. The shear deformation theory and energy method is employed for this purpose. This method presents the final relations by using a set of second order differential equations in terms of integral of material properties along the thickness direction. The proposed formulation can be considered for every distribution of material properties, whether functional or non functional. The obtained formulation can be used for manufactured materials or structures with numerical distribution of material properties which are obtained by using the experiments. The governing differential equation is applied for two well-known functionalities and some previous results are corrected with present true results.

• Advances in concrete construction
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• v.9 no.1
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• pp.103-113
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• 2020

This paper deal with the critical fluid velocity response of nanocomposite pipe conveying fluid based on numerical method. The pressure of fluid is obtained based on perturbation method. The motion equations are derived based on classical shell theory, energy method and Hamilton's principle. The shell is reinforced by nanoparticles and the distribution of them are functionally graded (FG). The mixture rule is applied for obtaining the equivalent material properties of the structure. Differential quadrature method (DQM) is utilized for solution of the motion equations in order to obtain the critical fluid velocity. The effects of different parameters such asCNT nanoparticles volume percent, boundary conditions, thickness to radius ratios, length to radius ratios and internal fluid are presented on the critical fluid velocity response structure. The results show that with increasing the CNT nanoparticles, the critical fluid velocity is increased. In addition, FGX distribution of nanoparticles is the best choice for reinforcement.

• Proceedings of the KSRS Conference
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• 2007.10a
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• pp.302-305
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• 2007

During the CareBeijing campaign in September 2006, Imaging Differential Optical Absorption Spectroscopy (IDOAS) measurements were made over the city of Beijing, China using a spatial resolution of 146 pixels horizontally and 61 pixels vertically, each with a field of view of $0.133^{\circ}$ and $0.072^{\circ}$ in the horizontal and vertical directions, respectively. Using Fraunhofer reference spectra (FRS) for the evaluation of data for two consecutive days, the diurnal variation of $NO_2$ distributions was determined from data measured every single hour from 08:00 until 16:00 on September 9 and 10. Both days presented a fairly clear sky with high visibility. The setup allowed detailed images of the low surface $NO_2$ distribution over Beijing. Images with less than a 30-min temporal resolution showed variation of plume dispersal in both horizontal and vertical directions. An in-situ measurement was also conducted. Results from both instruments are interpreted by considering local emission sources and wind conditions.

• Structural Engineering and Mechanics
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• v.70 no.1
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• pp.97-112
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• 2019

Using the classical, first order and third order shear deformation plates theories the motion equations of an undrained porous FG circular plate which is located on visco-Pasternak elastic foundation have been derived and used for free vibration analysis thereof. Strains are related to displacements by Sanders relationship. Fluid has saturated the pores whose distribution varies through the thickness according to three physically probable given functions. The equations are discretized and numerically solved by the generalized differential quadrature method. The effect of porosity, pores distribution, fluid compressibility, viscoelastic foundation and aspect ratio of the plate on its vibration has been considered.