• Korean Journal of Mathematics
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• 제27권1호
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• pp.17-51
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• 2019

In the paper we establish some new results depending on the comparative growth properties of composite entire and meromorphic functions using relative $_pL^*$-order, relative $_pL^*$-lower order and differential monomials, differential polynomials generated by one of the factors.

• 대한수학회지
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• 제52권4호
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• pp.685-697
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• 2015

For a field K, a square-free monomial ideal I of K[$x_1$, . . ., $x_n$] is called an f-ideal, if both its facet complex and Stanley-Reisner complex have the same f-vector. Furthermore, for an f-ideal I, if all monomials in the minimal generating set G(I) have the same degree d, then I is called an $(n, d)^{th}$ f-ideal. In this paper, we prove the existence of $(n, d)^{th}$ f-ideal for $d{\geq}2$ and $n{\geq}d+2$, and we also give some algorithms to construct $(n, d)^{th}$ f-ideals.

• 대한수학회지
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• 제51권2호
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• pp.427-442
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• 2014

A previous work gave a combinatorial description of the crystal B(${\infty}$), in terms of certain simple Young tableaux referred to as the marginally large tableaux, for finite dimensional simple Lie algebras. Using this result, we present an explicit description of the crystal B(${\lambda}$), in terms of the marginally large tableaux, for the $G_2$ Lie algebra type. We also provide a new description of B(${\lambda}$), in terms of Nakajima monomials, that is in natural correspondence with our tableau description.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제7권2호
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• pp.1-11
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• 2003

We suggest a method of $C^2$ surface extension with the aid of well-controlled functions. The extended surface is $C^2$ continuous along the old boundary. The function of the extension surface is obtained by replacing the monomials in the quadratic Taylor polynomial of the given surface-representing function by other functions subject to some boundary conditions. We present several sets of control functions. In order to illustrate our suggestion, it is shown that surfaces with a circular boundary and a square boundary can be extended using several base functions.

• 대한수학회보
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• 제46권1호
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• pp.183-198
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• 2009

In this paper, we derive a characterization of orthonormal balanced multiwavelets of order p in terms of the continuous moments of the multiscaling function $\phi$. As a result, the continuous moments satisfy the discrete polynomial preserving properties of order p (or degree p - 1) for orthonormal balanced multiwavelets. We derive polynomial reproduction formula of degree p - 1 in terms of continuous moments for orthonormal balanced multiwavelets of order p. Balancing of order p implies that the series of scaling functions with the discrete-time monomials as expansion coefficients is a polynomial of degree p - 1. We derive an algorithm for computing the polynomial of degree p - 1.

• Structural Engineering and Mechanics
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• 제84권6호
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• pp.723-731
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• 2022

Functionally graded materials (FGMs) have been spotlighted as an advanced composite material, accordingly the intensive studies have focused on FGMs to examine their mechanical behaviors. Among them is thermal buckling which has been a challenging subject, because its behavior is connected directly to the safety of structural system. In this context, this paper presents the numerical analysis of thermal buckling of metal-ceramic functionally graded (FG) plates. For an accurate and effective buckling analysis, a new numerical method is developed by making use of (1,1,0) hierarchical model and 2-D natural element method (NEM). Based on 3-D elasticity theory, the displacement field is expressed by a product of 1-D assumed thickness monomials and 2-D in-plane functions which are approximated by NEM. The numerical method is compared with the reference solutions through the benchmark test, from which its numerical accuracy has been verified. Using the developed numerical method, the critical buckling temperatures of metal-ceramic FG plates are parametrically investigated with respect to the major design parameters.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제27권1호
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• pp.1-22
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• 2023

In this paper we settle some polynomial identity which provides a family of explicit Waring decompositions of any monomial Xa00 Xa11··· Xann over a field k. This gives an upper bound for the Waring rank of a given monomial and naturally leads to an explicit Waring decomposition of any homogeneous form and, eventually, of any polynomial via (de)homogenization. Note that such decomposition is very useful in many applications dealing with polynomial computations, symmetric tensor problems and so on. We discuss some computational aspect of our result as comparing with other known methods and also present a computer implementation for potential use in the end.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제31권1호
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• pp.57-81
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• 2024

We introduce a new degree reduction method for homogeneous symmetric polynomials on binary variables that generalizes the conventional degree reduction methods on monomials introduced by Freedman and Ishikawa. We also design an degree reduction algorithm for general polynomials on binary variables, simulated on the graph coloring problem for random graphs, and compared the results with the conventional methods. The simulated results show that our new method produces reduced quadratic polynomials that contains less variables than the reduced quadratic polynomials produced by the conventional methods.

• Journal of Electrical Engineering and Technology
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• 제8권2호
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• pp.271-281
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• 2013

In order to improve the performance of analysis, it is important to consider the nonlinearity in power system. The Carleman embedding technique (linearization procedure) provides an effective approach in reduction of nonlinear systems. In the approach, a group of differential equations in which the state variables are formed by the original state variables and the vector monomials one can build with products of positive integer powers of them, is constructed. In traditional Carleman linearization technique, the tensor matrix is truncated to form a square matrix, and then regular linear system theory is used to solve the truncated system directly. However, it is found that part of nonlinear information is neglected when truncating the Carleman model. This paper proposes a new approach to solve the problem, by combining the Poincar$\acute{e}$ transformation with the Carleman linearization. Case studies are presented to verify the proposed method. Modal analysis shows that, with traditional Carleman linearization, the calculated contribution factors are not symmetrical, while such problems are avoided in the improved approach.