• Korean Journal of Mathematics
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• v.17 no.4
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• pp.361-374
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• 2009

We characterize a fuzzy partial order relation using its level set, find sufficient conditions for the image of a fuzzy partial order relation to be a fuzzy partial order relation, and find sufficient conditions for the inverse image of a fuzzy partial order relation to be a fuzzy partial order relation. Also we define a fuzzy lattice as fuzzy relations, characterize a fuzzy lattice using its level set, show that a fuzzy totally ordered set is a distributive fuzzy lattice, and show that the direct product of two fuzzy lattices is a fuzzy lattice.

• Honam Mathematical Journal
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• v.24 no.1
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• pp.67-73
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• 2002

In this paper we discuss on the existence of general solution of Partial Differential Equations $\frac{{\partial}w}{{\partial}\bar{z}}=F(z,\;w,\;\frac{{\partial}w}{{\partial}z})+G(z,\;w,\;\bar{w})$ in the Sololev Space $W_{1,p}(D)$, that is generalization of a first order Non-linear Elliptic System of Partial Differential Equations $\frac{{\partial}w}{{\partial}\bar{z}}=F(z,\;w,\;\frac{{\partial}w}{{\partial}z}).$

• Bulletin of the Korean Mathematical Society
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• v.53 no.2
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• pp.495-506
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• 2016

In this note we consider the monoid $\mathcal{PODI}_n$ of all monotone partial permutations on $\{1,{\ldots},n\}$ and its submonoids $\mathcal{DP}_n$, $\mathcal{POI}_n$ and $\mathcal{ODP}_n$ of all partial isometries, of all order-preserving partial permutations and of all order-preserving partial isometries, respectively. We prove that both the monoids $\mathcal{POI}_n$ and $\mathcal{ODP}_n$ are quotients of bilateral semidirect products of two of their remarkable submonoids, namely of extensive and of co-extensive transformations. Moreover, we show that $\mathcal{PODI}_n$ is a quotient of a semidirect product of $\mathcal{POI}_n$ and the group $\mathcal{C}_2$ of order two and, analogously, $\mathcal{DP}_n$ is a quotient of a semidirect product of $\mathcal{ODP}_n$ and $\mathcal{C}_2$.

• Journal of the Chungcheong Mathematical Society
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• v.33 no.1
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• pp.65-76
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• 2020

The notion of m-step competition graph was introduced by Cho et al. in 2000 as an interesting variation of competition graph. In this paper, we study the m-step competition graphs of d-partial orders, which generalizes the results obtained by Park et al. in 2011 and Choi et al. in 2018.

• Korean Journal of Mathematics
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• v.24 no.2
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• pp.169-179
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• 2016

In this article, we introduce the concept of ordered dualistic partial metric spaces and establish an order relation on quasi dualistic partial metric spaces. Later on, using this order relation, we prove xed point theorems for single and multivalued mappings. We support our results with some illustrative examples.

• Communications for Statistical Applications and Methods
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• v.22 no.6
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• pp.665-674
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• 2015

Lack of a general matrix formula hampers implementation of the semi-partial correlation, also known as part correlation, to the higher-order coefficient. This is because the higher-order semi-partial correlation calculation using a recursive formula requires an enormous number of recursive calculations to obtain the correlation coefficients. To resolve this difficulty, we derive a general matrix formula of the semi-partial correlation for fast computation. The semi-partial correlations are then implemented on an R package ppcor along with the partial correlation. Owing to the general matrix formulas, users can readily calculate the coefficients of both partial and semi-partial correlations without computational burden. The package ppcor further provides users with the level of the statistical significance with its test statistic.

• Journal of the Korean Mathematical Society
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• v.44 no.4
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• pp.767-777
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• 2007

By proving a summation formula, we enumerate the expansions for the mock theta functions of order 2 in terms of partial mock theta functions of order 2, 3 and 6. We show a relation between Ramanujan's ${\mu}(q)$-function and his sixth order mock theta functions. In addition, we also give the continued fraction representation for ${\mu}(q)$ and 2nd order mock theta functions and $Pad\acute{e}$ approximants.

• Bulletin of the Korean Mathematical Society
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• v.51 no.4
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• pp.1055-1062
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• 2014

Let $O_n$ and $PO_n$ denote the order-preserving transformation and the partial order-preserving transformation semigroups on the set $X_n=\{1,{\ldots},n\}$, respectively. Then the strictly partial order-preserving transformation semigroup $SPO_n$ on the set $X_n$, under its natural order, is defined by $SPO_n=PO_n{\setminus}O_n$. In this paper we find necessary and sufficient conditions for any subset of SPO(n, r) to be a (minimal) generating set of SPO(n, r) for $2{\leq}r{\leq}n-1$.

• Communications of the Korean Mathematical Society
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• v.35 no.2
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• pp.347-358
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• 2020

In this paper, we simplify the natural partial ordering ≼ on the semigroup 𝒪([n]) under composition of all order-preserving maps on [n] = {1, …, n}, and describe its maximal elements. Also, we show that the poset (𝒪([n]), ≼) is weakly graded and determine when (𝒪([n]), ≼) has a structure of (i + 1)-avoidance.

• The Journal of Korean Academy of Prosthodontics
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• v.14 no.1
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• pp.66-71
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• 1976

The purpose of this investigation was to evaluate the mouth preparation and design of removable partial dentures. A total of 187cases for the prefabricated partial denture frameworks in both maxillary and mandibular semi-dentulous situations (66 cases and 203 cases) was selected from this study. The evaluations of mouth preparation and design observed here involved the classification of edentulous spaces, status of abutment splinting with location, design of direct retainer and structure of maxillary major connector according to the incidence of both dental arches, ages, sexes and segment of semidentulousness. The analyzed results were as follows: 1) The order of frequency rate in removable partial denture construction was Class II (50.27%), Class I (36. 90%), Class III (10.69%), and Class IV (2.14 %). 2) The distribution on design of maxillary removable partial denture prosthesis was 33.22% and 64.11% in mandibular removable partial denture prosthesis. 3) The age distribution of removable partial denture prosthesis was prominent after40 years (41.71%). 4) The design pattern of maxillary major connectors was in order of anteroposterior bar, single palatal bar, palatal strap, U-shape connector. 5) The design pattern of direct retainer was in order of Aker's clasp, I-bar clasp, backaction clasp, cuspid universal clasp. 6) The abutment for partial denture clasp splinted between premolar and premolar and its frequency rate revealed 53.44%. 7) It seemed that the location and design of the indirect retainer showed accepatble limit.