• Bulletin of the Korean Mathematical Society
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• 제61권1호
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• pp.117-133
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• 2024

Let 𝓟 = {X_i : i ∈ I} be a partition of a set X. We say that a transformation f : X → X preserves 𝓟 if for every X_i ∈ 𝓟, there exists X_j ∈ 𝓟 such that X_if ⊆ X_j. Consider the semigroup 𝓑(X, 𝓟) of all transformations f of X such that f preserves 𝓟 and the character (map) χ^(f): I → I defined by i_χ^(f) = j whenever X_if ⊆ X_j is bijective. We describe Green's relations on 𝓑(X, 𝓟), and prove that 𝒟 = 𝒥 on 𝓑(X, 𝓟) if 𝓟 is finite. We give a necessary and sufficient condition for 𝒟 = 𝒥 on 𝓑(X, 𝓟). We characterize unit-regular elements in 𝓑(X, 𝓟), and determine when 𝓑(X, 𝓟) is a unit-regular semigroup. We alternatively prove that 𝓑(X, 𝓟) is a regular semigroup. We end the paper with a conjecture.

• Carbon letters
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• 제10권2호
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• pp.123-130
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• 2009

Multi-elements doped $TiO_2$ was prepared as a new photocatalyst in order to decrease the band gap of $TiO_2$ by sol-gel process which can provide the large active sites of $TiO_2$. Multi-elements were doped by using a single precursor, tetraethylammonium tetrafluoroborate (TEATFB). By the benefit of large specific surface area of $TiO_2$ prepared by sol-gel process, catalysts showed initial fast removal of dye. The photoactivity showed that the doped catalysts significantly promote the light reactivity than undoped $TiO_2$. The commendable photoactivity of prepared catalysts is predominantly attributable to the doping of anions which may reduce the band gap.

• Kyungpook Mathematical Journal
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• 제51권2호
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• pp.139-143
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• 2011

In this paper we consider mappings ${\sigma}$ which map the binary operation symbol f to the term ${\sigma}$(f) which do not necessarily preserve the arities. We call these mappings generalized hypersubstitutions. Any generalized hypersubstitution ${\sigma}$ can be extended to a mapping $\hat{\sigma}$ on the set of all terms of type ${\tau}$ = (2). We de ne a binary operation on the set $Hyp_G$(2) of all generalized hypersubstitutions of type ${\tau}$ = (2) by using this extension The set $Hyp_G$(2) together with the identity generalized hypersubstitution ${\sigma}_{id}$ which maps f to the term f($x_1,x_2$) forms a monoid. We determine all regular elements of this monoid.

• Honam Mathematical Journal
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• 제41권2호
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• pp.421-433
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• 2019

Let n denote an integer greater than 2 and let c denote a nonzero complex number. In this paper, we introduce a family of elements of the rational Cherednik algebra $H^{sl_n}(c)$ of type $sl_n$, which are analogous to the Dunkl-Cherednik elements of the rational Cherednik algebra $H^{gl_n}(c)$ of type $gl_n$. We also introduce the raising and lowering element of $H^{sl_n}(c)$ which are useful in the representation theory of the algebra $H^{sl_n}(c)$, and provide simple results related to these elements.

• Journal of Applied and Pure Mathematics
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• 제5권1_2호
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• pp.1-8
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• 2023

This study is on a Boolean B or Boolean lattice L in abstract algebra with closed binary operation *, complement and distributive properties. Both Binary operations and logic properties dominate this set. A lattice sheds light on binary operations and other algebraic structures. In particular, the construction of the elements of this L set from idempotent elements, our definition of k-order idempotent has led to the expanded definition of the definition of the lattice theory. In addition, a lattice offers clever solutions to vital problems in life with the concept of logic. The restriction on a lattice is clearly also limit such applications. The flexibility of logical theories adds even more vitality to practices. This is the main theme of the study. Therefore, the properties of the set elements resulting from the binary operation force the logic theory. According to the new definition given, some properties, lemmas and theorems of the lattice theory are examined. Examples of different situations are given.

• Korean Journal of Childcare and Education
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• 제12권5호
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• pp.47-69
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• 2016

The purpose of this study was to examine teaching competency for character education of early childhood teachers and their demands to improve their capacities. 152 kindergarten and child care teachers responded to 30 survey questionnaires, which included 3 sub-factors(commutative, practical, instrumental) of teaching competency for character education of the teachers, as well as 16 detailed components, designed to check their current competency for character education and to investigate the priority elements that they desired to improve. The data were analyzed based on the Borich request formula, the locus for focus model, and the independent sample t-test across the teacher groups. The results were as follows: Firstly, the most highly demanded teaching competency by the teachers was using tools interactively for character education. And the teachers, among the sub-elements, requested (a) recording and evaluating character education systematically, (b) using local or national resources, (c) planning member's participation, and (d) performing character education related activities systematically. Secondly, more new teachers demanded instrumental competency and answered the need of parents' participation among the sub-elements, more than the more experienced teachers, respectively. The study discussed the implications of promoting early childhood teachers' teaching competency for character education.

• Korean Journal of Computational Design and Engineering
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• 제12권4호
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• pp.255-262
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• 2007

In the finite element analysis of forming process, objects are described with a finite number of elements and nodes and the approximated solutions can be obtained by the variational principle. One of the shortcomings of a finite element analysis is that the structure of mesh has become inefficient and unusable because discretization error increases as deformation proceeds due to severe distortion of elements. If the state of current mesh satisfies a certain remeshing criterion, analysis is stopped instantly and resumed with a reconstructed mesh. In the study, a new remeshing algorithm using tetrahedral elements has been developed, which is adapted to the desired mesh density. In order to reduce the discretization error, desired mesh sizes in each lesion of the workpiece are calculated using the Zinkiewicz and Zhu's a-posteriori error estimation scheme. The pre-constructed mesh is constructed based on the modified point insertion technique which is adapted to the density function. The object domain is divided into uniformly-sized sub-domains and the numbers of nodes in each sub-domain are redistributed, respectively. After finishing the redistribution process of nodes, a tetrahedral mesh is reconstructed with the redistributed nodes, which is adapted to the density map and resulting in good mesh quality. A goodness and adaptability of the constructed mesh is verified with a testing measure. The proposed remeshing technique is applied to the finite element analyses of forging processes.

• Journal of Korean Library and Information Science Society
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• 제42권4호
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• pp.281-309
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• 2011

This research designed and proposed metadata elements for the long-term preservation of digital research outcomes collected and managed in electronic file form. Metadata structure of both domestic and foreign agencies that manage research outcomes and CERIF and PREMIS-preserved preservation metadata were referred to design the metadata elements. The metadata design was divided into research information, bibliographic information and archival information. Research information is divided into project, name and institution, and composed of eight top-level elements and 29 sub-level elements. Bibliographic information is composed of 13 top-level elements as the source of research reports. Archival information is composed of 18 top-level elements and 62 sub-level elements as the elements for context, structure, contents and management process of the electronic records.

• Nuclear Engineering and Technology
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• 제56권3호
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• pp.1013-1021
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• 2024

A series of experiments were performed to produce a fuel source for a molten salt reactor (MSR) through pyroprocessing technology. A simulated LiCl-KCl-UCl₃-NdCl₃ salt system was prepared, and the U element was fully recovered using a liquid cadmium cathode (LCC) by applying a constant current. As a result, the salt was purified with an UCl₃ concentration lower than 100 ppm. Subsequently, the U/RE ingot was prepared by melting U and RE metals in Y₂O₃ crucible at 1473 K as a surrogate for RE-rich ingot product from pyroprocessing. The produced ingot was sliced and used as a working electrode in LiCl-KCl-LaCl₃ salt. Only RE elements were then anodically dissolved by applying potential at - 1.7 V versus Ag/AgCl reference electrode. The RE-removed ingot product was used to produce UCl₃ via the reaction with NH4Cl in a sealed reactor.

• Journal of the Optical Society of Korea
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• 제19권1호
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• pp.84-87
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• 2015

For large optical elements which are tested by many sub-apertures, it takes too much time for a sub-aperture stitching algorithm to get the stitching result. To solve this problem, we propose a fast sub-aperture stitching algorithm to quickly compensate for piston, tilt, and defocus errors. Moreover, the new algorithm is easy to understand and program. We use partial derivatives of measurement data to separately solve piston, tilt, and defocus errors. First, we show that the new algorithm has a lower time complexity than the currently used algorithm. Although simulation results indicate that the accuracy of the new algorithm is lower than the current algorithm in all 20 simulations, our experimental results validate the algorithm and show it is sufficiently accurate for general use.