• Korean Journal of Mathematics
• /
• 제28권1호
• /
• pp.105-121
• /
• 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
• /
• 제28권3호
• /
• pp.489-507
• /
• 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.

• Korean Journal of Mathematics
• /
• 제28권4호
• /
• pp.819-845
• /
• 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.

• 대한수학회지
• /
• 제13권1호
• /
• pp.19-25
• /
• 1976

• Kyungpook Mathematical Journal
• /
• 제14권2호
• /
• pp.185-194
• /
• 1974

• Steel and Composite Structures
• /
• 제47권5호
• /
• pp.569-585
• /
• 2023

This paper proposes an efficient approach for the structural topology optimization of bi-directional functionally graded structures by incorporating popular radial basis functions (RBFs) into an implicit level set (ILS) method. Compared to traditional element density-based methods, a level set (LS) description of material boundaries produces a smoother boundary description of the design. The paper develops RBF implicit modeling with multiquadric (MQ) splines, thin-plate spline (TPS), exponential spline (ES), and Gaussians (GS) to define the ILS function with high accuracy and smoothness. The optimization problem is formulated by considering RBF-based nodal densities as design variables and minimizing the compliance objective function. A LS-RBF optimization method is proposed to transform a Hamilton-Jacobi partial differential equation (PDE) into a system of coupled non-linear ordinary differential equations (ODEs) over the entire design domain using a collocation formulation of the method of lines design variables. The paper presents detailed mathematical expressions for BiDFG beams topology optimization with two different material models: continuum functionally graded (CFG) and mechanical functionally graded (MFG). Several numerical examples are presented to verify the method's efficiency, reliability, and success in accuracy, convergence speed, and insensitivity to initial designs in the topology optimization of two-dimensional (2D) structures. Overall, the paper presents a novel and efficient approach to topology optimization that can handle bi-directional functionally graded structures with complex geometries.