• Journal of the Korean Mathematical Society
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• v.48 no.5
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• pp.1017-1041
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• 2011

The parabolic Bergman space is the set of $L^p(\lambda)$-solution of the parabolic operator $L^{(\alpha)}$. In this paper, we study representin sequences on parabolic Bergman spaces. We establish a discrete version of the reproducing formula on parabolic Bergman spaces by using fractional derivatives of the fundamental solution of the parabolic operator.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.21 no.4
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• pp.677-682
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• 2012

For the product with small diameter, long column, and parabolic shape, the forging formability of the high-carbon steel wire rod was investigated in this study. By using the three-dimensional finite element method, the formability of wire was reviewed by forming analysis for the desired parabolic shape of local part. Analysis results due to forging direction, forging velocity, friction coefficient and constraint location were also investigated. On the basis of these results, it is noted that the forging direction has the big influence when the product with long column is forged. As the forging velocity increases, buckling tends to be limited and formability of parabolic shape is improved. By constraining the lower parabolic shape part to suppress plastic strain, the effect depending on friction coefficient is not almost appeared. And good parabolic shape is obtained at the region of the forging velocity of more than 0.5 m/s.

• Journal of the Korean Mathematical Society
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• v.58 no.4
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• pp.1001-1017
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• 2021

In this paper, we first apply parabolic inequalities and a maximum principle to give a new proof for symmetry and monotonicity of solutions to fractional elliptic equations with gradient term by the method of moving planes. Under the condition of suitable initial value, by maximum principles for the fractional parabolic equations, we obtain symmetry and monotonicity of positive solutions for each finite time to nonlinear fractional parabolic equations in a bounded domain and the whole space. More generally, if bounded domain is a ball, then we show that the solution is radially symmetric and monotone decreasing about the origin for each finite time. We firmly believe that parabolic inequalities and a maximum principle introduced here can be conveniently applied to study a variety of nonlocal elliptic and parabolic problems with more general operators and more general nonlinearities.

• Journal of applied mathematics & informatics
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• v.31 no.1_2
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• pp.87-97
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• 2013

The purpose of this paper is to employ a new useful technique to solve the initial-Neumann boundary value problems for parabolic, hyperbolic and parabolic-hyperbolic equations and obtain a solution in form of infinite series. The results obtained indicate that this approach is indeed practical and efficient.

• Bulletin of the Korean Mathematical Society
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• v.60 no.2
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• pp.281-291
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• 2023

A normalized analytic function f is parabolic starlike if w(z) := zf' (z)/f(z) maps the unit disk into the parabolic region {w : Re w > |w - 1|}. Sharp estimates on the third Hermitian-Toeplitz determinant are obtained for parabolic starlike functions. In addition, upper bounds on the third Hankel determinants are also determined.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.2 no.2
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• pp.97-109
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• 1998

A comparison of the two dimensional heat loss, computed using the analytical method and the finite difference method in two models(i.e. one is a parabolic fin whose parabolic curves meet at the fin center line and the other is a transformed parabolic fin whose tip cuts vertically), is made assuming the analytical method is correct. For these methods, the root temperature and surrounding convection coefficients of these fins are assumed as constants. The results show that the relative errors of the heat loss between the two methods for the parabolic fin whose tip cuts vertically are smaller than those for the one whose tip does not cut. In case of Bi=0.01, the values of the heat loss obtained using a finite difference method are close to those values obtained using the analytical method for both models. The values of the heat loss from both models calculated by using the analytical method are almost the same for given range of non-dimensional fin length in case of Bi = 0.01 and 0.1.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2008.10a
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• pp.510-513
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• 2008

As number of cyber traders are growing, the uses of technical analyzing indicators in trading increase as well. Parabolic SAR, which indicates changes of trend in the market, is one of the most used indicators by cyber traders. Especially when a market shows a specific trend, it is very useful. However, this indicator often gives late signals and shows less trustful ones in a stable market. This paper proposes a method that give more conservative signals by a composition of Parabolic SAR and Moving Average. The experiment will compare the earning rates of using only Parabolic SAR strategy and of using a composition strategy of Parabolic SAR and Moving Average.

• Communications of the Korean Mathematical Society
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• v.12 no.4
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• pp.921-933
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• 1997

An Ambrosetti-Prodi type multiplicity result for periodic-Dirichlet problem to semilinear parabolic equation is treated.

• Journal of the Korean Mathematical Society
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• v.35 no.4
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• pp.881-890
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• 1998

Sufficient conditions for forced oscillations of the solutions of impulsive nonlinear parabolic differential-difference equations are obtained.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.18 no.4
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• pp.360-371
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• 2006

In order to calculate waves propagating into the shallow water region, a generalized parabolic approximate model is presented. The model is derived from the modified mild slope equation and includes all the existing parabolic models presented in the paper. Numerical results are presented in comparison to laboratory data of Berkhoff et al.(1982). The existing parabolic model shows almost same accuracy against the modified parabolic model and both results of models stand in closer agreement to the laboratory data. Therefore the existing parabolic model based on mild slope equation is a useful tool to compute shallow water waves which turns out to be more fast and stable in computational aspect.