• 대한수학회지
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• 제40권2호
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• pp.225-239
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• 2003

(G, <) is an ordered group if'<'is a total order relation on G in which f < g implies that xfy < xgy for all f, g, x, y $\in$ G. We say that (G, <) is centrally ordered if (G, <) is ordered and ［G,D］ $\subseteq$ C for every convex jump C $\prec$ D in G. Equivalently, if $f^{-1}g f{\leq} g^2$ for all f, g $\in$ G with g > 1. Every order on a torsion-free locally nilpotent group is central. We prove that if every order on every two-generator subgroup of a locally soluble orderable group G is central, then G is locally nilpotent. We also provide an example of a non-nilpotent two-generator metabelian orderable group in which all orders are central.

• 한국수학사학회지
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• 제31권3호
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• pp.151-166
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• 2018

The rule of the game of Chomp is simple and the existence of a winning strategy can easily be proved. However, the existence tells us nothing about what strategies are winning in reality. Like in Chess or Baduk, many researchers studied the winning moves using computer programs, but no general patterns for the winning actions have not been found. In the paper, we aim to construct practical winning strategies based on backward induction. To do this we develop how to analyze Chomp and prove and find the winning strategies of the simple games of Chomp.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제14권3호
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• pp.181-187
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• 2014

Dealing with uncertainty is always a challenging problem. Intuitionistic fuzzy sets was presented to manage situations in which experts have some membership and non-membership value to assess an alternative. Hesitant fuzzy sets was used to handle such situations in which experts hesitate between several possible membership values to assess an alternative. In this paper, the concept of intuitionistic hesitant fuzzy set is introduced to provide computational basis to manage the situations in which experts assess an alternative in possible membership values and non-membership values. Distance measure is defined between any two intuitionistic hesitant fuzzy elements. Fuzzy technique for order preference by similarity to ideal solution is developed for intuitionistic hesitant fuzzy set to solve multi-criteria decision making problem in group decision environment. An example is given to illustrate this technique.

• Nonlinear Functional Analysis and Applications
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• 제26권1호
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• pp.137-155
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• 2021

In this paper, first, we prove some common fixed point theorems for the generalized contraction condition under newly defined modified simulation function which generalize and include many results in the literature. Second, we give two numerical examples with graphical representations for verifying the proposed results. Third, we discuss and study a set of common fixed point theorems for two pairs (finite families) of self-mappings. Finally, we give some applications of our results in discrete and functional fractional economic systems.

• Communications for Statistical Applications and Methods
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• 제30권6호
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• pp.605-629
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• 2023

This paper proposes some diagnostics procedures for the skew-t linear regression model with censored response. The skew-t distribution is an attractive family of asymmetrical heavy-tailed densities that includes the normal, skew-normal and student's-t distributions as special cases. Inspired by the power and wide applicability of the EM-type algorithm, local and global influence analysis, based on the conditional expectation of the complete-data log-likelihood function are developed, following Zhu and Lee's approach. For the local influence analysis, four specific perturbation schemes are discussed. Two real data sets, from education and economics, which are right and left censoring, respectively, are analyzed in order to illustrate the usefulness of the proposed methodology.

• 대한수학회지
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• 제58권6호
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• pp.1327-1345
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• 2021

In this paper, we are concerned with a Liouville-type result of the nonlinear integral equation of Chern-Simons-Higgs type $$u(x)=\vec{\;l\;}+C_{\ast}{{\displaystyle\smashmargin{2}{\int\nolimits_{\mathbb{R}^n}}}\;{\frac{(1-{\mid}u(y){\mid}^2){\mid}u(y){\mid}^2u(y)-\frac{1}{2}(1-{\mid}u(y){\mid}^2)^2u(y)}{{\mid}x-y{\mid}^{n-{\alpha}}}}dy.$$ Here u : ℝⁿ → ℝ^k is a bounded, uniformly continuous function with k ⩾ 1 and 0 < α < n, $\vec{\;l\;}{\in}\mathbb{R}^k$ is a constant vector, and C_* is a real constant. We prove that ${\mid}\vec{\;l\;}{\mid}{\in}\{0,\frac{\sqrt{3}}{3},1\}$ if u is the finite energy solution. Further, if u is also a differentiable solution, then we give a Liouville type theorem, that is either $u{\rightarrow}\vec{\;l\;}$ with ${\mid}\vec{\;l\;}{\mid}=\frac{\sqrt{3}}{3}$, when |x| → ∞, or $u{\equiv}\vec{\;l\;}$, where ${\mid}\vec{\;l\;}{\mid}{\in}\{0,1\}$.

• 융합경영연구
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• 제10권5호
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• pp.1-6
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• 2022

Purpose: To overcome the question that depends too much on expert's subjective judgment in traditional risk identification, this paper structure the multilevel generalized fuzzy comprehensive evaluation mathematics model of the risk identification of project, to research the risk identification of the project. Research design, data and methodology: This paper constructs the multilevel generalized fuzzy comprehensive evaluation mathematics model. Through iterative algorithm of AHP analysis, make sure the important degree of the sub project in risk analysis, then combine expert's subjective judgment with objective quantitative analysis, and distinguish the risk through identification models. Meanwhile, the concrete method of multilevel generalized fuzzy comprehensive evaluation is probed. Using the index weights to analyse project risks is discussed in detail. Results: The improved fuzzy comprehensive evaluation algorithm is proposed in the paper, at first the method of fuzzy sets core is used to optimize the fuzzy relation matrix. It improves the capability of the algorithm. Then, the method of entropy weight is used to establish weight vectors. This makes the computation process fair and open. And thereby, the uncertainty of the evaluation result brought by the subjectivity can be avoided effectively and the evaluation result becomes more objective and more reasonable. Conclusions: In this paper, we use an improved fuzzy comprehensive evaluation method to evaluate a railroad engineering project risk. It can give a more reliable result for a reference of decision making.

• Communications for Statistical Applications and Methods
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• 제22권6호
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• pp.557-573
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• 2015

In this paper we develop a Bayesian inference for a multiplicative double seasonal autoregressive (DSAR) model by implementing a fast, easy and accurate Gibbs sampling algorithm. We apply the Gibbs sampling to approximate empirically the marginal posterior distributions after showing that the conditional posterior distribution of the model parameters and the variance are multivariate normal and inverse gamma, respectively. The proposed Bayesian methodology is illustrated using simulated examples and real-world time series data.

• Communications for Statistical Applications and Methods
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• 제15권6호
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• pp.799-813
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• 2008

This paper deals with the properties of the fuzzy least squares estimators for fuzzy linear regression model. Especially fuzzy triangular input-output model including error term is proposed. The error term is considered as a fuzzy random variable. The asymptotic unbiasedness and the consistency of the estimators are proved using a suitable metric.

• 대한수학회보
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• 제53권1호
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• pp.153-161
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• 2016

It is shown that the algebra $\mathfrak{H}^{\infty}$ of bounded Dirichlet series is not a coherent ring, and has infinite Bass stable rank. As corollaries of the latter result, it is derived that $\mathfrak{H}^{\infty}$ has infinite topological stable rank and infinite Krull dimension.