• 한국수학교육학회지시리즈B:순수및응용수학
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• 제13권4호
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• pp.281-294
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• 2006

Many partial differential equations defined on a rectangular domain can be solved numerically by using a domain decomposition method. The most commonly used decompositions are the domain being decomposed in stripwise and rectangular way. Theories for non-overlapping domain decomposition(in which two adjacent subdomains share an interface) were often focused on the stripwise decomposition and claimed that extensions could be made to the rectangular decomposition without further discussions. In this paper we focus on the comparisons of the two ways of decompositions. We consider the unconditionally stable scheme, the MIP algorithm, for solving parabolic partial differential equations. The SOR iterative method is used in the MIP algorithm. Even though the theories are the same but the performances are different. We found out that the stripwise decomposition has better performance.

• East Asian mathematical journal
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• 제36권1호
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• pp.61-71
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• 2020

Up to the present day, the best solution we can get to the truncated moment problem (TMP) is probably the Flat Extension Theorem. It says that if the corresponding moment matrix of a moment sequence admits a rank-preserving positive extension, then the sequence has a representing measure. However, constructing a flat extension for most higher-order moment sequences cannot be executed easily because it requires to allow many parameters. Recently, the author has considered various decompositions of a moment matrix to find a solution to TMP instead of an extension. Using a new approach with the Hadamard product, the author would like to introduce more techniques related to moment matrix decompositions.

• 충청수학회지
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• 제28권4호
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• pp.603-614
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• 2015

For a map $p:X{\rightarrow}A$, we define and study a concept of $G^{\prime}_p$-space for a map, which is a generalized one of a G'-space. Any G'-space is a $G^{\prime}_p$-space, but the converse does not hold. In fact, $CP^2$ is a $G^{\prime}_{\delta}$-space, but not a G'-space. It is shown that X is a $G^{\prime}_p$-space if and only if $G^n(X,p,A)=H^n(X)$ for all n. We also obtain some results about $G^{\prime}_p$-spaces and homology decompositions for spaces. As a corollary, we can obtain a dual result of Haslam's result about G-spaces and Postnikov systems.

• 충청수학회지
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• 제30권1호
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• pp.129-139
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• 2017

For a map $p:X{\rightarrow}A$, there are concepts of co-$H^p$-spaces, co-$T^p$-spaces, which are generalized ones of co-H-spaces [17,18]. For a principal cofibration $i_r:X{\rightarrow}C_r$ induced by $r:X^{\prime}{\rightarrow}X$ from $\imath:X^{\prime}{\rightarrow}cX^{\prime}$, we obtain some sufficient conditions to having extensions co-$H^{\bar{p}}$-structures and co-$T^{\bar{p}}$-structures on $C_r$ of co-$H^p$-spaces and co-$T^p$-structures on X respectively. We can also obtain some results about co-$H^p$-spaces and co-$T^p$-spaces in homology decompositions for spaces, which are generalizations of Golasinski and Klein's result about co-H-spaces.

• Environmental Sciences Bulletin of The Korean Environmental Sciences Society
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• 제10권S_4호
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• pp.165-172
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• 2001

We investigated the optimal experimental conditions and reaction kinetics for the decompositions of PCE, TCE, naphthalene, and chloroform using conventional Fenton oxidation process. Additionally, the influence of pH on the decompositions of PCE was also evaluated. The results indicated that the optimal pH value was around 3. The dosage of Fenton's reagent and the molar ratio of hydrogen peroxide to ferrous ion for an approximately complete decomposition was found to depend on the properties of the organic compound. Due to their unsaturated structures, the results show that PCE, TCE, and naphthalene could be all effectively decomposed by Fenton's reagent oxidation. Their unsaturated structures could be mostly destoyed within first 1-2 minutes at a low dosage with an certain molar ratio of hydrogen peroxide to ferrous ion. However the saturated compound such as chloroform was more difficult to decompose even with a relatively high dosage of Fenton's reagent.

• Elastomers and Composites
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• 제51권2호
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• pp.122-127
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• 2016

Thermal decomposition kinetics for two different types of polyurethane elastomers prepared with 2,2'-dichloro-4,4'-methylenedianiline (MOCA) and 3,5-dimethyl-thiotoluenediamine (Ethacure-300), based on PTMG/TDI isocyanate prepolymer, were studied using non-isothermal thermogravimetric analysis (TGA). Thermograms were obtained and analyzed using Friedman (FR) and Kissinger-Akahira-Sunose (KAS) methods for activation energy, $E_a$. The results obtained showed that decomposition reaction of both samples was observed similarly to occur through three different stages, i.e., initial stage with vaporization of low molecular weight materials, second stage of urethane linkage decompositions, and later stage of polyol segment decompositions. However, activation energy values at each stage for the sample cured with Ethacure-300 was much lower than those for the sample with MOCA, exhibiting relatively lower thermal stability for the sample with Ethacure-300 than that with MOCA.

• East Asian mathematical journal
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• 제26권5호
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• pp.655-670
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• 2010

The complete multipartite graph $K_{n(m)}$ with n $ {\geq}$ 4 partite sets of size m is shown to have a decomposition into 4-cycles in such a way that vertices of each cycle belong to distinct partite sets of $K_{n(m)}$, if 4 divides the number of edges. Such cycles are called gregarious, and were introduced by Billington and Hoffman ([2]) and redefined in [3]. We independently came up with the result of [3] by using a difference set method, and improved the result so that the composition is circulant, in the sense that it is invariant under the cyclic permutation of partite sets. The composition is then used to construct gregarious 4-cycle decompositions when one partite set of the graph has different cardinality than that of others. Some results on joins of decomposable complete multipartite graphs are also presented.

• 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.

• 한국지능시스템학회논문지
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• 제10권2호
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• pp.103-106
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• 2000

We introduce the concepts of TL-finite state machines TL-transformation semigroups and coverings and several decompositions of transformation semigroups and investigate some their algebraic structures.

• 한국경영과학회:학술대회논문집
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• 한국경영과학회 2008년도 추계학술대회 및 정기총회
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• pp.121-121
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• 2008