• 대한수학회지
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• 제53권6호
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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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• 제28권1호
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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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• 제28권3호
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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.

• 대한수학회지
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• 제57권5호
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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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• 제28권4호
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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.

• 대한수학회보
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• 제60권2호
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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.

• 대한수학회지
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• 제61권5호
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• pp.975-995
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• 2024

In this paper, we utilize Nevanlinna theory to study the existence and forms of solutions for quadratic trinomial complex partial differential-difference equations of the form aF² + 2ωFG + bG² = exp(g), where ab ≠ 0, ω ∈ ℂ with ω² ≠ 0, ab and g is a polynomial in ℂⁿ. In order to achieve a comprehensive and thorough analysis, we study the characteristics of solutions in two specific cases: one when ω² ≠ 0, ab and the other when ω = 0. Because polynomials in several complex variables may exhibit periodic behavior, a property that differs from polynomials in single complex variables, our study of finding solutions of equations in ℂⁿ is significant. The main results of the paper improved several known results in ℂⁿ for n ≥ 2. Additionally, the corollaries generalize results of Xu et al. [Rocky Mountain J. Math. 52(6) (2022), 2169-2187] for trinomial equations with arbitrary coefficients in ℂⁿ. Finally, we provide examples that endorse the validity of the conclusions drawn from the main results and their related remarks.

• Advances in Computational Design
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• 제4권1호
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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.

• 대한수학회지
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• 제13권1호
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• pp.19-25
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• 1976

• Kyungpook Mathematical Journal
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• 제22권1호
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• pp.53-54
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• 1982