• Journal of the Korean Mathematical Society
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• v.53 no.6
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• pp.1391-1409
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• 2016

In this paper, we investigate a family of holomorphic functions in several complex variables concerning the total derivative (or called radial derivative), and obtain some well-known normality criteria such as the Miranda's theorem, the Marty's theorem and results on the Hayman's conjectures in several complex variables. A high-dimension version of the famous Zalcman's lemma for normal families is also given.

• Korean Journal of Mathematics
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• v.28 no.1
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• pp.105-121
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• 2020

The principal objective of this paper is to introduce the ideas of relative 𝜑-type, relative 𝜑-weak type of entire functions of several complex variables and study some growth properties concerning them.

• Korean Journal of Mathematics
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• v.28 no.3
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• pp.489-507
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• 2020

In this paper we discussed some growth properties of entire functions of several complex variables on the basis of (p, q)-𝜑 relative Gol'dberg type and (p, q)-𝜑 relative Gol'dberg weal type where p, q are positive integers and 𝜑(R) : [0, +∞) → (0, +∞) is a non-decreasing unbounded function.

• Journal of the Korean Mathematical Society
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• v.57 no.5
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• pp.1287-1298
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• 2020

Inspired by a classical approximation result of Bagemihl and Seidel on the disc, we provide generalized results on some proper domains in ℂⁿ about approximation of a continuous function by a holomorphic function in the Mergelyan's style.

• Korean Journal of Mathematics
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• v.28 no.4
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• pp.819-845
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• 2020

In this paper, we established sum and product theorems connected to (p, q)-𝜑 relative Gol'dberg type and (p, q)-𝜑 relative Gol'dberg weak type of entire functions of several complex variables with respect to another one under somewhat different conditions.

• Bulletin of the Korean Mathematical Society
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• v.60 no.2
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• pp.425-441
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• 2023

This paper is concerned with the value distribution for meromorphic solutions f of a class of nonlinear partial differential-difference equation of first order with small coefficients. We show that such solutions f are uniquely determined by the poles of f and the zeros of f - c, f - d (counting multiplicities) for two distinct small functions c, d.

• Advances in Computational Design
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• v.4 no.1
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• pp.15-32
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• 2019

One of the efficient and useful tools to achieve the optimal design of structures is employing the sensitivity analysis in the finite element model. In the numerical optimization process, often the semi-analytical method is used for estimation of derivatives of the objective function with respect to design variables. Numerical methods for calculation of sensitivities are susceptible to the step size in design parameters perturbation and this is one of the great disadvantages of these methods. This article uses complex variables method to calculate the sensitivity analysis and combine it with discrete sensitivity analysis. Finally, it provides a new method to obtain the sensitivity analysis for linear structures. The use of complex variables method for sensitivity analysis has several advantages compared to other numerical methods. Implementing the finite element to calculate first derivatives of sensitivity using this method has no complexity and only requires the change in finite element meshing in the imaginary axis. This means that the real value of coordinates does not change. Second, this method has the lower dependency on the step size. In this research, the process of sensitivity analysis calculation using a finite element model based on complex variables is explained for linear problems, and some examples that have known analytical solution are solved. Results obtained by using the presented method in comparison with exact solution and also finite difference method indicate the excellent efficiency of the proposed method, and it can predict the sustainable and accurate results with the several different step sizes, despite low dependence on step size.

• Journal of the Korean Mathematical Society
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• v.13 no.1
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• pp.19-25
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• 1976

• Kyungpook Mathematical Journal
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• v.22 no.1
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• pp.53-54
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• 1982

• Kyungpook Mathematical Journal
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• v.21 no.2
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• pp.251-262
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• 1981