• Journal of applied mathematics & informatics
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• v.41 no.6
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• pp.1237-1256
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• 2023

The tree products of groups with amalgamation subgroups are generalizations of the free products of groups with amalgamation subgroup. The aim of this paper is to construct a tree called the standard tree where the tree products of groups with amalgamation subgroups act without inversions and then find the quotient of this action. Furthermore, we show that if the amalgamation subgroups are finite and the factor groups act on disjoint trees then there exists a tree called the fiber tree where the tree products of groups with amalgamation subgroups act without inversions and find the quotients of this action. If each factor is a tree products with amalgamation subgroups, we get a new fiber tree and the corresponding factors.

• Communications of the Korean Mathematical Society
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• v.12 no.3
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• pp.521-530
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• 1997

We first prove a criterion for the conjugacy separability of free products with amalgamation where the amalgamated subgroup is not necessarily cyclic. Applying this result, we show that free products of finite number of polycyclic-by-finite groups with central amalgamation are conjugacy separable. We also show that polygonal products of polycyclic-by-finite groups, amalgamating central cyclic subgroups with trivial intersections, are conjugacy separable.

• Bulletin of the Korean Mathematical Society
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• v.48 no.1
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• pp.67-77
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• 2011

Let M be a compact orientable closed 3-manifold, and F a non-separating incompressible closed surface in M. Let M' = M - ${\eta}(F)$, where ${\eta}(F)$ is an open regular neighborhood of F in M. In the paper, we give a lower bound of genus of self-amalgamation of minimal Heegaard splitting $V'\;{\cup}_{S'}\;W'$ of M' under some conditions on the distance of the Heegaard splitting.

• Communications of the Korean Mathematical Society
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• v.36 no.1
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• pp.1-10
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• 2021

Let R and S be two commutative rings, J be an ideal of S and f : R → S be a ring homomorphism. The amalgamation of R and S along J with respect to f, denoted by R ⋈f J, is the special subring of R × S defined by R ⋈f J = {(a, f(a) + j) | a ∈ R, j ∈ J}. In this paper, we study some basic properties of a special kind of R ⋈f J-modules, called the amalgamation of M and N along J with respect to ��, and defined by M ⋈�� JN := {(m, ��(m) + n) | m ∈ M and n ∈ JN}, where �� : M → N is an R-module homomorphism. The new results generalize some known results on the amalgamation of rings and the duplication of a module along an ideal.

• YAKHAK HOEJI
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• v.55 no.4
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• pp.284-288
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• 2011

The test method for biologics of lot release system is based on 'Test procedure and specification for biological products,' generally, thimerosal content is measured by chemical analysis using O.D. In this study, the comparative analysis was carried out using the gold amalgamation method for thimerosal content was compared to the existing methods, which are described above. The gold amalgamation method, which uses atomic absorption spectrophotometry, was meets all the method validation acceptance criteria. It is considered to be proper as the assay and identification test for thimerosal. In this study, the comparative analysis was performed three times. As a result, gold amalgamation method is more convenient and easy to perform as this assay doesn't have pre-treatment procedure. Also this assay showed good precision and reproducibility compared to the conventional method. Therefore, it is appropriate to alternate the assay method of thimerosal from the conventional chemical analysis to gold amalgamation method to improve the credibility of lot release system and the quality control of biologics, by standardizing test method.

• Journal of the Korean Mathematical Society
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• v.36 no.4
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• pp.773-785
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• 1999

Shifts of finite type are represented by nonnegative integral square matrics, and conjugacy between two shifts of finite type is determined by strong shift equivalence between the representing nonnegative intergral square matrices. But determining strong shift equivalence is usually a very difficult problem. we develop splittings and amalgamations of nonnegative integral matrices, which are analogues of those of directed graphs, and show that two nonnegative integral square matrices are strong shift equivalent if and only if one is obtained from a higher matrix of the other matrix by a series of amalgamations.

• Journal of the Korean institute of surface engineering
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• v.38 no.5
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• pp.198-201
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• 2005

Nickel amalgam was Prepared by the electro-deposition with mercury cathode in a modified Watts bath. Homogeneous nickel amalgam was obtained. The fluidity of the amalgam decreased gradually with increased nickel quantity and become solid finally. Nickel powders of sub-micron size were obtained by a distillation of mercury from the amalgam. The characterization of the nickel amalgam was studied by SEM and x-ray diffractometry.

• Bulletin of the Korean Mathematical Society
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• v.58 no.4
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• pp.1021-1029
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• 2021

This paper establishes necessary and sufficient conditions for a bi-amalgamation to inherit the S-Noetherian property. The new results compare to previous works carried on various settings of duplications and amalgamations, and capitalize on recent results on bi-amalgamations. Our results allow us to construct new and original examples of rings satisfying the S-Noetherian property.

• Feed Journal
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• v.4 no.2 s.30
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• pp.61-64
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• 2006

• Journal of the Korean Mathematical Society
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• v.26 no.1
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• pp.83-95
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• 1989